Report - School of Electrical Engineering and Computer Science

Transcription

2004 Annual Report
For: The McLeod Modeling and Simulation Network – M&SNet –
of the Society for Modeling and Simulation International
From: The UCSF BioSystems Group
•• http://biosystems.ucsf.edu ••
The activities of the Group over past 12 months are adequately conveyed by
the following, key symposium and meeting presentations made by
BioSystem Group members.
C. Anthony Hunt, Glen E.P. Ropella, Michael S. Roberts, and Li Yan, Biomimetic In Silico Devices. Computational
Methods in Systems Biology, Second International Workshop, CMSB 2004, Paris, France, Proceedings. Lecture Notes
in Bioinformatics, Springer (in press).
p. 2-9
Mark R. Grant, C. Anthony Hunt, Lan Xia , Jimmie E. Fata, Mina J. Bissell, Modeling Mammary Gland
Morphogenesis as a Reaction-Diffusion Process. Proceedings of the 26th Annual International Conference of the IEEE
EMBS, San Francisco, CA, USA • September 1-5, 2004.
p. 10-13
Jon Tang, C. Anthony Hunt, J. Mellein, and K. Ley, Simulating Leukocyte-Venule Interactions – A Novel AgentOriented Approach. ibid.
p. 14-17
Li Yan, C. Anthony Hunt, Glen E.P. Ropella and Michael S. Roberts, In Silico Representation of the Liver: Connecting
Function to Anatomy, Physiology and Heterogeneous Microenvironments. ibid.
p. 18-21
Yu Liu, C. Anthony Hunt, Representing Intestinal Drug Transport In Silico: An Agent-Oriented Approach. ibid. p. 22-25
Suman Ganguli and C. Anthony Hunt, The Necessity of a Theory of Biology for Tissue Engineering: MetabolismRepair Systems. ibid.
p. 26-29
Tai Ning Lam and C. Anthony Hunt, Applying Models of Targeted Drug Delivery to Gene Delivery.
ibid.
p. 30-33
Song Chen, Suman Ganguli, C. Anthony Hunt, An Agent-based Computational Approach for Representing Aspects of
In Vitro Multi-Cellular Tumor Spheroid Growth. ibid.
p. 34-37
Yuanyuan Xiao, C. Anthony Hunt1, Jean Yee Hwa Yang, and Mark R. Segal, A Novel Stepwise Normalization
Method for Two-Channel cDNA Microarrays. ibid.
p. 38-41
BioDEVS: System-Oriented, Multi-Agent, Modeling & Simulation Framework Sunwoo Park, Glen E. P. Ropella,
and C. Anthony Hunt Multiscale Computational Modeling for Biomedical Research, Workshop, 25 - 27 March
2004, University of California, San Diego, La Jolla, CA <http://nbcr.ucsd.edu/multiscale.htm> Poster
p. 42
C. Anthony Hunt and Glen E. P. Ropella, A Decentralization Method For Modeling The Multiple Levels of
Organization and Function Within Liver, BISTI 2003 Symposium, "Digital Biology: The Emerging Paradigm,"
November 6-7, 2003, Natcher Conference Center, National Institutes of Health, Bethesda, Maryland. Poster
p. 43
Presented at CMSB ’04 (www.biopathways.org/CMSB04/), May 26-26, Paris, France
In Press: Lecture Notes in Bioinformatics (LNBI)
Biomimetic In Silico Devices
C. Anthony Hunt1,3, Glen E.P. Ropella1, Michael S. Roberts2, and Li Yan3
1
Dept. of Biopharmaceutical Sciences, Biosystems Group,
University of California, San Francisco, CA 94143-0446, USA
hunt@itsa.ucsf.edu; gepr@tempusdictum.com
http://biosystems.ucsf.edu
2
Department of Medicine, University of Queensland, Princess Alexandra
Hospital, Woolloongabba, Q 4102 Australia
mroberts@soms.uq.edu.au
http://www.som.uq.edu.au/som/Research/therapeutics.shtml
3
Joint UCSF/UC Berkeley Bioengineering Graduate Program
lyan@socrates.berkeley.edu
http://socrates.berkeley.edu/~lyan/
Abstract. We introduce biomimetic in silico devices, and means for validation
along with methods for testing and refining them. The devices are constructed
from adaptable software components designed to map logically to biological
components at multiple levels of resolution. In this report we focus on the liver;
the goal is to validate components that mimic features of the lobule (the hepatic
primary functional unit) and dynamic aspects of liver behavior, structure, and
function. An assembly of lobule-mimetic devices represents an in silico liver.
We validate against outflow profiles for sucrose administered as a bolus to
isolated, perfused rat livers. Acceptable in silico profiles are experimentally
indistinguishable from those of the in situ referent. This new technology is
intended to provide powerful new tools for challenging our understanding of
how biological functional units function in vivo.
1
Introduction
Cells of the same type in the same tissue can experience different environments, and as
a consequence exhibit quite different gene expression patterns [1]. This is just one of
the problems faced when modeling biological systems at multiple levels of resolution.
Network detail learned from experiments on isolated cells in vitro may not map directly
to the tissue level. Reflecting on this reality, Noble rejects the reductionist bottom-up
and the traditional top-down modeling and simulation approaches [2]. He makes the
case for a “middle-out” strategy that focuses on the “functional level between genes and
higher level function” [3], and calls for new ideas and new approaches to help move the
field to the next level. The new class of biological analogue models presented here,
which we refer to as biomimetic in silico devices (hereafter, devices), is an answer to
that call. The devices are designed to generate biomimetic behaviors and are constructed
from software components that map logically to biological components at multiple
levels of resolution. The focus here is the liver. The data used for validation are
outflow profiles from experiments on isolated, perfused rat livers (hereafter, perfused
livers) given bolus doses of compounds of interest [4, 5]. Acceptable devices are
hepato-mimetic in that they generate in silico outflow profiles that are experimentally
indistinguishable from those of the in situ referent.
–1–
2
Device Design
2.1 Modeling Approach and Biological Data
Rather than the traditional inductive, analytic modeling approach, we used a
constructive approach based in part on ideas and concepts from several sources,
including compositional modeling [6]. We focus more on the aspects of structure and
behavior that give rise to the data. We deconstruct the system into biologically
recognizable components and processes that can be represented as software objects,
agents, messages, and events. Next, we reconstruct using those objects within a
software medium that handles probabilistic events, and can represent dynamic spatial
heterogeneity. The process produces in silico devices [6] capable of biomimetic
behaviors. Of course, these devices are also models. We use device to stress their
modular, constructive nature, to emphasize the essential properties discussed below, and
to distinguish them from traditional equational models.
The devices represent aspects of the anatomic structure and behavior of the
functional unit of the liver that influences administered compounds. We conduct in
silico experiments that follow protocols that mimic the original in situ experimental
protocols. Because a device is not based on equations, we do not directly fit it to data.
We use a Similarity Measure [7] to quantify the similarity between data generated by
the device and data generated by the biological referent. Having completed that level of
validation we run simulation experiments to address what-if questions and/or grow the
device so that it accounts for additional, different data (e.g., perfused liver outflow
profiles of additional compounds and/or hepatic imaging data).
2.2 Properties: Essential and Desired
We create a device from data with as few assumptions as possible, by first building
and validating a simple, biomimetic device, and then iteratively improving it. Devices
and their components must be reusable, revisable, and easily updatable when critical
new data becomes available, without having to re-engineer the whole device. Device
components, like their biological referents, need to be sufficiently flexible and
adaptable to be useful in a variety of research contexts. They should be able to
function at multiple levels of resolution, from molecule to organ. In addition, device
and components must logically map to their biological counterparts. Spatial
heterogeneity is a quintessential characteristic of organisms at each organizational
level. So, it is essential that device components be capable of representing that
heterogeneity at different levels of resolution as required by the problem. Finally,
hepatic processes, drug disposition, and pharmacokinetic processes are characterized
by probabilistic events. So, our biomimetic devices are exclusively event driven and
most events can be probabilistic. These properties are deemed essential in part
because they are expected to make this new technology easily accessible and useful to
a majority of biomedical researchers.
2.3 Histological and Physiological Considerations
Changes in the architecture of hepatic fluid flow are associated with several disease
states, and such alterations can influence a drug’s disposition. These considerations
–2–
suggest that a device must have a flexible means of representing that architecture at
whatever level of detail is needed. We use directed graphs, with objects placed at graph
nodes, to represent that architecture. Because the lobule is the primary structural and
functional unit of the rat liver [8], the device must have a component that maps directly
1
to the lobule. Hereafter refer to that component as a LOBULE .
Hepatocytes exhibit locationspecific properties within lobules,
including
location-dependent
expression of drug metabolizing
enzymes [1]. Such intralobular
heterogeneity requires that a
LOBULE be capable of easily exhibiting heterogeneity and zonation when such properties are
required. LOBULES must also be
capable of representing special- Fig. 1. A schematic of an idealized cross-section of a
ized cell types, including endo- hepatic lobule showing half an acinus and the direction of
thelial, Kuppfer, and stellate flow between the terminal portal vein tract (PV), and the
central hepatic vein (CV). SS: Sinusoidal Segment
cells, and their specialized
behaviors in appropriate relative
relationships, when needed, without forcing restructuring or redesign. The blood supply
for one lobule, illustrated schematically by the cross section in Fig. 1, feeds into several
dozen sinusoids that merge as they feed into the lobule’s central vein (CV). Known
hepatic features that are not needed to account for outflow profiles of the targeted data
sets do not have corresponding components within the LOBULES. Examples include a
separate hepatic arterial blood supply, the biliary system, and drug transport systems
(into cells and into bile).
2.4 Designing the In Silico Components
Computational Framework. Our devices are constructed within the Swarm
framework (www.swarm.org). The methods do not require any particular formalism.
But, the experimental framework is always formulated using Partially Ordered Sets;
they are a generic way to specify concurrent processes with as few strictures as
possible [9].
Directed Graphs. A trace of flow paths within one lobule sketches a network that we
represent by an interconnected, directed graph. Literature data [8] are used to constrain
the accessible graph structures used. We only consider the subset of graphs that has
more nodes connected to the portal vein tract (PV) (source) and fewer nodes connected
to the CV (exit). Teutsch et al. [8] subdivide the lobule interior into concentric zones.
For now, we impose a three-zone structure and require that each zone contain at least
one node and that a shortest path from PV to CV will pass through at least one node and
no more than one node per zone. The insert in Fig. 1 illustrates a portion of a graph that
connects in silico PV outlets to the CV. Graph structure is specified by the number of
nodes in each zone and the number of edges connecting those nodes. Edges are further
identified as forming either inter-zone or intra-zone connections. The CV receives
1
When referring to the in silico counterpart of a biological component or process, such as
“lobule,” “endothelial cell,” or “partition,” we use SMALL CAPS.
–3–
solute from the last node in each shortest path between PV and CV. Edges specify
“flow paths” having zero length and containing no objects. A solute object exiting a
parent node is randomly assigned to one of the available outgoing graph edges and
appears immediately as input for the downstream child node. Randomly assigned intrazone connections are allowed but are confined to Zones I and II. We randomly assign
nodes to each of the zones so that the number of nodes in each zone is approximately
proportional to the fraction of the total lobule volume found in that zone.
Sinusoidal Segments and the Fate of Solutes. Agents called sinusoidal segments (SSs)
(Fig. 2) are placed at each graph node. There is one PV entrance (effectively covering
the exterior of the LOBULE) and one CV exit for each LOBULE. A solute object is a
passive representation of a chemical as it moves through the in silico environment. The
PV creates solute objects, as dictated by the experimental dosage function, and
distributes them to the SSs in Zone I. A solute object moving through the LOBULE
represents molecules moving through the sinusoids of a lobule, and their behavior is
dictated by rules specifying the relationships between solute location, proximity to other
objects and agents, and the solute's physicochemical properties. Each solute has dose
parameters and a scale parameter (molecules per solute object). The relative tendency
of a solute object to move forward within a SS determines the effective flow pressure
and this is governed by a parameter called Turbo. If there is no flow pressure (Turbo =
0), then solute movement is specified by a simple random walk. Increasing Turbo
biases the random walk in the direction of the CV.
We have studied the behaviors of several sinusoidal segment designs and describe
here the extensible design currently in use. Simpler designs generate behaviors that fail
to meet our Similarity Measure criterion. Viewed from the center of perfusate flow out
in Fig. 2, a SS is modeled as a
tube with a rim surrounded by
other layers. The tube and rim
represent the sinusoidal space
and its immediate borders. The
tube contains a fine-grained
abstract
Core
space
that
represents blood flow. Grid A is
the Rim. Grid B is wrapped
around Grid A and represents the
endothelial layer. Another fine- Fig. 2. Schematic of a sinusoidal segment (SS). Three
grained space (Grid C) is types of SS are discussed in the text. One SS is placed at
wrapped around Grid B to each node of the directed graph within each LOBULE.
collectively represent the Space
of Disse, hepatocytes, and bile
canaliculi2.
If
needed,
hepatocytes and connected features such as bile canaliculi can be moved to a fourth grid
wrapped around Grid C. The properties of locations within each grid can be
homogeneous or heterogeneous depending on the specific requirements and the
experimental data. Objects can be assigned to one or more grid points. For example, a
subset of Grid B points can represent one or more Kupffer cells. Objects that move
2
Because we are building a normalized model there is no direct coupling between grid points
within the fine-grained space and real measures such as hepatocyte volume or its dimensions in
microns.
–4–
from a location on a particular grid are subject to one or more lists of rules that are
called into play at the next step. Within Grid B a parameter controls the size and
prevalence of FENESTRATIONS1 and currently 10% of Grid B in each SS is randomly
assigned to FENESTRAE; the remaining 90% represents cells. Similarly, within the grid
where some locations map to hepatocytes, there is a parameter that controls their
relative density.
Classes of Sinusoidal Segments and Dynamics Within. To further enable accounting
for sinusoidal heterogeneity, we defined two classes of SSs, SA and SB. Additional
classes can be specified and used when needed. Relative to SB the SA have a shorter path
length and a smaller surface-to-volume ratio, whereas the SB have a longer path length
and a larger surface-to-volume ratio. The circumference of each SS is specified by a
random draw from a bounded uniform distribution. To reflect the observed relative
range of real sinusoid path lengths, SS length is given by a random draw from a gamma
distribution having a mean and variance specified by the three gamma function
parameters, a, b, and g.
Solute objects can enter a SS at either the Core or the Rim. At each step thereafter
until it is METABOLIZED or collected it has several stochastic options, the aggregate
properties of which are arrived at through Monte Carlo simulation. In the Rim or Core
it can move within that space, jump from one space to the other, or exit the SS. From a
Rim location it can also jump to Grid B or back to the Core. Within Grid B it can move
within the space, jump back to Grid A or to Grid C. When it encounters an
ENDOTHELIAL CELL within Grid B it may (depending on its properties) PARTITION into
it. Once inside, it can move about, exit, bind or not. Within Grid C it can move within
the space or jump back to Grid B. When a HEPATOCYTE is encountered the SOLUTE can
(depending on its properties) PARTITION into it or move on. Once inside a HEPATOCYTE
it can move about, exit, bind (and possibly get METABOLIZED) or not. Currently all
objects within a HEPATOCYTE that bind can also METABOLIZE. The probability of a
solute object being METABOLIZED depends on the object’s properties.
Once
METABOLIZED the object is destroyed. The only other way to exit a SS is from the Core,
Rim or into bile (not implemented here). When the SOLUTE exits a SS and enters the
CV, its arrival is recorded (corresponding to being collected), and it is destroyed.
2.5 Similarity Measure
The in situ liver perfusion protocol is detailed in [4]. Briefly, a compound of interest is
injected into the entering perfusate of the isolated liver. The entire outflow is collected
at intervals and the fraction of the dose within is determined. The 14C-sucrose outflow
profile contains information only about features of the extracellular environments
whereas the data for a drug contains information on those features as well as on
intracellular environments in that same liver. When the results of in silico and in situ
experiments are similar, an expert can inspect the two data sets and offer an opinion on
the degree of their similarity. However, automated model generation and refinement
requires having one or more Similarity Measure (SM) to substitute for the expert’s
judgment. A SM is a function which takes two sets of experimental data and returns a
number as a measure of their similarity [7]. Classical regression approaches do not
apply because we are comparing the outputs of two or more experiments.
There are two main contributors to intraindividual variability: methodological and
biological. For replicate experiments in the same liver the coefficient of variation for
–5–
fraction of dose within specific outflow collection intervals typically ranges between 10
and 40%. A coefficient of variation can define a continuous interval bounding the
experimental data. Any new set of results that falls within those bounds and has
essentially the same shape is defined as being experimentally indistinguishable. The
same should hold even if the data comes from an in silico experiment, and that provides
the basis for selecting and evaluating SMs.
The objective of the SM is to help select among device designs, not simply to
specify a device and select among variations on that device. Hence, the successful SM
must target the various features of the outflow profile that correlate with the generative
structures and building blocks inside the device. However, for simplicity in these early
studies we have assumed that the coefficients of variation of repeat observations within
different regions of the curve are the same. In that way we can use a simple interval
SM, which is what we do. A set of in situ outflow profiles, T, is used as training data.
From this data, we calculate a distance, D, from a reference that will be the basis for a
match. We then take two outflow profiles and pick one to be the reference profile, Pr.
For each observation in Pr, create a lower, Pl, and an upper, Pu, bound by multiplying
that observation by (1 – D) and (1 + D), respectively. The two curves Pl and Pu are the
lower and upper bounds of a band around Pr. The two outflow profiles are deemed
similar if the second profile, P, stays within the band. The distance D used for sucrose
is one standard deviation of the array of relative differences between each repeat
observation and the mean observations at that time. To calculate D for the training set T
we choose experimental data on different subjects that were part of the same protocol
[4, 5].
3
In Silico Experimental Results
To begin development of a new device we select an outflow profile and begin the
process of finding the simplest design, given restrictions: one is that it be comprised of
the minimum components needed to generate an acceptably similar profile. An initial
unrefined parameterization is chosen based on available information. Components are
added according to that initial parameterization. If the behavior of the resulting device
is not satisfactory, any given piece of the device may be surplused and replaced,
modified, or reparameterized with minimal impact on the other components within the
device. This process continues until the device provides reasonable coverage of the
targeted solution space. Once an acceptable parameterization is found, the parameter
space is searched further [10] for additional solution sets. Bounds for the parameter
space can be specified to indicate solution set regions for which the device validates
(i.e., acceptable SM measures are obtained). Subsequently, for a second data set, a
repeat of the first experiment or a data set for a second drug, we make only minimal
adjustments and additions to the structure of the first device so that the resulting new
device generates acceptable outflow profiles for both data sets.
The typical in situ outflow profile is an account of on the order of 1015 drug
molecules percolating through several thousand lobules. The typical in silico dose for
one run with one LOBULE is on the order of 5,000 drug objects, where each drug object
can represent a number (≥ 1) of drug molecules. Thus, a resulting single outflow profile
will be very noisy and will be inadequate to represent the referent in situ profile.
Another independent run with that same device, parameter settings, and dose will
produce a similar but uniquely different outflow profile. Changing the random number
generator seed alters the specifics for all stochastic parameters (e.g., placement of SSs
–6–
on the digraph), thus providing a unique, individual version of the LOBULE, analogous to
the unique differences between two lobules in the same liver. A full in silico
experiment is one that produces an outflow profile that is sufficiently smooth to use the
SM, and typically combines the results from 20 or more independent runs using the
same LOBULE.
One can identify several similar parameterizations that will yield outflow profiles
that are experimentally indistinguishable from each other. That is because there is a
region of device-structure space (model space) that will yield acceptable behaviors
relative to a specific data set. Such
a region can be viewed as a
metaphor for the fact that all
lobules are similar but not identical.
We currently do not attempt to
fully map acceptable regions of
either model or parameter space.
Our goal is simply to locate a
region in each that meets our
objectives.
Figure 3 shows results from
one parameterization of a LOBULE
against a perfused liver sucrose Fig. 3. An outflow profile for a device parameterized to
outflow profile. The shaded region match a sucrose outflow profile. Nodes per Zone: 55,
is a band enclosing the mean 24 and 3 for Zones I, II and III, respectively; total
edges: 60; intra-zone connections: Zone I = 10, Zone II
fraction of dose collected for each
= 8, Zone III = 0; inter-zone connections: IÆII = 14,
collection interval. The width of
IÆIII = 4, IIÆIII = 14; SSs: 50% SA and SB; Number of
the band is ± 1 std about the mean.
runs = 100.
The filled circles are results
obtained using the specified device
parameter vector.
4
Higher and Lower Levels of Resolution
Different regions of a normal liver are indistinguishable. That is generally not the case
for a diseased liver, where some lobules can be damaged or otherwise changed. So, to
understand and account for such differences we need methods to shift levels of
resolution without loss of information. The following summarizes how we are enabling
resolution changes. To represent a whole diseased liver with heterogeneous properties
we can first connect in parallel four to five different sized lobes, where each is a
directed graph having multiple parallel, single node paths connecting portal and hepatic
veins nodes (Fig. 4), and agents representing secondary units are placed at those nodes.
A lobe is comprised of a large number of these units [8]. Each secondary unit can be
similarly represented by a directed subgraph with LOBULES placed at each of its nodes
(insert, Fig. 4). When subcellular networks within CELLS located in Grids B and C are
needed, they may also be treated as directed graphs with nodes representing factors and
with edges representing interactions and influences [11]. Having a mechanism for
realizing networks allows us to replace sub-networks (at any location) with rules-based
software modules.
–7–
5
Conclusion
We have tested and affirmed the hypothesis that
perfused liver outflow data obtained following
bolus administration of sucrose can, in
conjunction with other data, be used to specify
and parameterize a physiologically recognizable
hepato-mimetic device that can generate outflow
profiles that are experimentally indistinguishable
from the original in situ data. Each device is
constructed from software components that
exhibit several essential properties including
being designed to map logically to hepatic
components at multiple levels of resolution, from
subcellular to whole organ. This new technology
is intended to provide powerful tools for
optimizing the designs of real experiments. It
will also help us challenge our understanding of
how mammalian systems function in normal and
diseased states, and when stressed or confronted
with interventions.
Fig. 4. An illustration of the
hierarchical structure of an in silico
liver. A lobe is comprised of a network
of secondary units (SEC. UNIT) [8]; they,
in turn are comprised of a network of
lobules (Lb) as pictured in Fig. 2. PV:
Portal vein. CV: Central hepatic vein
References
1.
Roberts, M., Magnusson, B., Burczynski, F., Weiss, M.: Enterohepatic Circulation: Physiological, Pharmacokinetic and Clinical Implications. Clin. Pharmacokinet. 41(2002), 751-90
2. Noble D.: The Rise of Computational Biology. Nat. Rev. Mol. Cell. Bio. 3 (2002) 460-63
3. Noble, D.: The Future: Putting Humpty-Dumpty Together Again. Biochem. Soc.
Transact. 31 (2003) 156-8
4. Roberts, M.S., Anissimov, Y.G.: Modeling of Hepatic Elimination and Organ
Distribution Kinetics with the Extended Convection-Dispersion Model. J. Pharmacokin.
Biopharm. 27 (1999) 343-382
5. Hung, D.Y., Chang, P., Weiss, M., Roberts, M.S.:
Structure-Hepatic Disposition
Relationships for Cationic Drugs in Isolated Perfused Rat Livers: Transmembrane Exchange
and Cytoplasmic Binding Process. J. Pharmacol. Exper. Therap. 297 (2001) 780–89
6. Falkenhainer, B., Forbus, K.D.: Compositional Modeling: Finding the Right Model for the
Job. Art. Intel. 51 (1991), 95-143
7. Santini, S., Jain, R.: Similarity Measures, IEEE Tran. Pattern Analysis and Machine
Intelligence 21 (1999) 871-83
8. Teutsch, H.F., Schuerfeld, D., Groezinger, E.: Three-Dimensional Reconstruction of
Parenchymal Units in the Liver of the Rat. Hepatology 29 (1999) 494-505
9. Burns, A., Davies, G.: Concurrent Programming. Addison-Wesley, Reading, MA (1993) 1-2
10. Sanchez, S.M., Lucas, T.W.: Exploring the World of Agent-Based Simulations: Simple
Models, Complex Analyses. In: Yücesan, E., Chen, C.-H., Snowdon, J.L., Charnes, C.M.,
(eds.): Proceedings of the 2002 Winter Simulation Conference (2002) 116-26
10. Gumucio, J.J., Miller, D.L.: Zonal Hepatic Function: Solute-Hepatocyte Interactions
Within the Liver Acinus. Prog. Liver Diseases 7 (1982) 17-30
11. Tyson, J.J., Chen, K., Novak, B.: Network Dynamics and Cell Physiology. Nat. Revs.
Mol. Cell Biol. 2 (2001) 908-17
–8–
Proceedings of the 26th Annual International Conference of the IEEE EMBS
San Francisco, CA, USA • September 1-5, 2004
Modeling Mammary Gland Morphogenesis as a
Reaction-Diffusion Process
Mark R. Grant1, C. Anthony Hunt2, Lan Xia3 , Jimmie E. Fata4, Mina J. Bissell4
1
Joint UCSF/UCB Bioengineering Graduate Group, The University of California, Berkeley, 2Biosystems Group, Department of
Biopharmaceutical Sciences, The University of California, San Francisco, CA 94143, USA
3
Comparative Biochemistry Graduate Group, The University of California, Berkeley, 4Life Sciences Division, Lawrence Berkeley
National Laboratory, University of California, Berkeley
Abstract- Mammary ducts are formed through a process of
branching morphogenesis. We present results of experiments
using a simulation model of this process, and discuss their
implications for understanding mammary duct extension and
bifurcation. The model is a cellular automaton approximation of
a reaction-diffusion process in which matrix metalloproteinases
represent the activator, inhibitors of matrix metalloproteinases
represent the inhibitor, and growth factors serve as a substrate.
We compare results from the simulation model with those from
in-vivo experiments as part of an assessment of whether duct
extension and bifurcation during morphogenesis may be a
consequence of a reaction-diffusion mechanism mediated by
MMPs and TIMPs.
through a process involving extracellular matrix (ECM)
remodeling, duct elongation, and branching. The process is
facilitated by crosstalk between the proliferating epithelia
and the mammary stroma. It has been demonstrated that
mammary branching morphogenesis is influenced by
extracellular matrix composition, growth factors, ECMdegrading enzymes including matrix metalloproteinases
(MMPs), and tissue inhibitors of MMPs (TIMPs) [1] (Fig.
1). The matrix metalloproteinases catalyze the cleavage of
extracellular matrix components, which is required for duct
extension. Treatment of mice with broad-spectrum MMP
inhibitors inhibits branching and duct elongation [2]. Tissue
inhibitors of metalloproteinases serve to regulate the
activities of matrix metalloproteinases, inhibiting MMP
activity by noncovalent binding. It has been hypothesized
that it is the coordinated action of MMPs and TIMPs that
give rise to branched growth (Fig. 1B).
A number of approaches have been taken to model
morphogenesis in biological systems. In particular,
Keywords—Branching
morphogenesis,
simulation,
modeling, mammary gland, extracellular matrix, reactiondiffusion, matrix metalloproteinase, tissue inhibitor of
metalloproteinase.
I. INTRODUCTION
A
Branching morphogenesis occurs in the development of
a variety of organs, from the trachea in Drosophila to
nephrons in the kidney.
Patterns in branching
morphogenesis have been identified and include branch
elongation, tip bifurcation, lateral branching, and
anastomosis. Elongation and tip bifurcation both occur
during mammary branching morphogenesis. What are the
key factors and events? To help answer that question and
gain a deeper insight into how such processes can unfold
(and be influenced by interventions), we developed a
cellular automata (CA) model and used it for
experimentation. Here we focus on two classes of factors
(defined below): MMPs alter the environment of the
developing cells, and TIMPs specifically inhibit them. Our
hypothesis is that they can work synergistically as activators
and inhibitors in a reaction-diffusion process that can guide
and control simulated branching morphogenesis.
B
II. BIOLOGICAL DETAILS
The formation of mammary ducts in the mouse also
involves branching morphogenesis. It occurs in several
stages, beginning in early development with the formation
of the mammary bud at mid-gestation, followed by invasion
of the epithelium into the mammary fat pad during puberty.
During invasion, a branched ductal network is formed
0-7803-8439-3/04/$20.00©2004 IEEE
Fig. 1. A. Representation of branching morphogenesis in the developing
mouse mammary gland. Black lines represent ductal cells, with each duct
terminated by a terminal end bud, where duct bifurcation occurs.
Development of the mature gland involves duct elongation, tip bifurcation,
and lateral branching. B. Representation of inhibition of MMP action by
TIMP expression.
679
reaction-diffusion systems have been used extensively in
modeling pattern formation, including branching
morphogenesis [3]. A reaction-diffusion system of the
substrate-depletion type was used to model the influence of
fibroblast growth factor 1 (FGF1) on the growth of lung
epithelial cultures in tissue culture, where FGF1 served the
role of the substrate, and cells served as the activator [4]. It
has also been demonstrated that a reaction-diffusion system
of the activator-inhibitor type is able to give rise to
fundamental branching features such as bifurcation and
lateral branching [5].
In the case of mammary branching morphogenesis, it is
possible that MMPs and TIMPs may be acting as activators
and inhibitors, respectively, in a reaction-diffusion process.
It is known that MMPs exhibit autocatalytic activation. It is
also known that MMP and TIMP expression is often colocalized. And finally, TIMPs are capable of inhibiting
MMP activity in a 1:1 stoichiometric ratio. We have
implemented a computer simulation of a reaction-diffusion
process of branching morphogenesis adapted from the work
in [5].
We compare results obtained from in-vivo
experiments modulating MMP and TIMP activity with
output generated from the simulation in order to explore
whether MMPs and TIMPs may be functioning as activators
and inhibitors in a reaction-diffusion process.
behavior. The relationships between the variables are
represented visually in Fig. 2, and the rules that govern the
CA are summarized in Fig. 3.
A. Metalloproteinases
MMPs are proteases that degrade components of the
extracellular matrix, particularly collagen and laminin.
Most matrix metalloproteinases are secreted as proenzymes,
and through autocatalysis they become activated. It is
known that MMPs are selectively expressed around sites of
duct elongation, and it has been demonstrated that MMP
activity is required for normal mammary gland development
[2]. It is also known that growth factors can induce
expression of MMPs [6]. The ability of MMP to induce
TIMP expression has not been verified in the literature;
however, MMP and TIMP expression is often colocalized
in-vivo, suggesting such a mechanism may exist. These
behaviors are represented and controlled within the model
by rules 1, 2, 3, 4, 7, 9, and 11.
B. Tissue Inhibitors of Metalloproteinases
Tissue inhibitors of metalloproteinases (TIMPs) are the
primary regulators of MMP activity. The TIMPs have also
been implicated in mammary branching morphogenesis [7].
One function of TIMPs is to bind to MMPs and inhibit their
III. MODELING AND SIMULATION
1. If MMP > d ⋅ TIMP , then MMP = c ⋅ MMP ⋅ GF
The simulation is implemented as a 2D square grid
cellular automata with closed boundaries. Four variables
determine the state of each grid position in the cellular
automata: matrix metalloproteinases (MMP)1, tissue
inhibitor of metalloproteinases (TIMP), growth factor (GF),
and duct cells (CELL). The following is a description of
each variable and the CA update rules which govern their
2. If MMP > MMP
max
, then MMP = MMP
max
3. MMP = δ 1 ⋅ MMP − δ 2
4. If MMP < 0 , then MMP = 0
5. TIMP = δ 3 ⋅ TIMP − δ 4
6. If TIMP < 0 , then TIMP = 0
7. TIMP = γ ⋅ MMP + TIMP
8. TIMP = TIMP + η
9. If MMP > ε , then CELL = 1
10. If CELL = 1 , then GF = GF + α − β ⋅ GF , else
1
GF = GF + α − β ⋅ GF
0
11. MMP = MMP , TIMP = TIMP , GF = GF
( )
12. GF = GF + ρ N 0, 1
Fig. 3. The CA transition rules used in the simulation, adapted from [5].
Default parameterizations: α = 0.2, β0 = 0.2, β1 = 1.0, β2 = 1.0, δ1 = 0.9,
δ2 = 1.0, δ3 = 0.5, δ4 = 0.5, ρ = 0.01, γ = 0.5, ε = 120, c = 3.0, d = 2.0,
MMPmax = 250, grid height = 300, and grid width = 300. Initial GF in
every cell was set to 0.75, whereas initial MMP, initial CELL, and initial
TIMP in every cell were set to zero. The simulation is triggered using a
positive value of MMP placed in the corner of the simulation grid. The
distances used for the averaging of Moore neighborhoods in rule 12 were
RMMP = 2, RGF = 3, and RTIMP = 6.
Fig. 2. Diagram of the relationships between the variables in the model,
adapted from [5]. The dashed arrows are used to indicate whether
diffusion occurs. MMP: stands for the variable representing matrix
metalloproteinase levels; TIMP: stands for the variable representing tissue
inhibitor of metalloproteinase; ECM: stands for the variable representing
extracellular matrix; CELL: stands for the variable that indicates the
presence of a simulated duct cell; and R: A small random variation in the
value of GF.
1
To avoid confusion, the simulation variables which correspond to
biological features are italicized.
680
is introduced into the model to model in-vivo heterogeneity
in the mammary fat pad by rule 12.
A.
D. Cell Proliferation
Cell proliferation occurs as a consequence of MMP
activity. It is known that MMP digestion of ECM
components generates growth-promoting fragments;
furthermore, MMPs are able to degrade cell-ECM contacts,
which can induce an epithelial-to-mesenchymal transition
and promote growth. Additionally, degradation of the ECM
by MMP activity removes physical constraints on cell
growth. These effects are modeled by rule 1. It is also
known that growth factor is depleted from the extracellular
environment through receptor internalization by cells which
bind growth factors. This effect has been observed in-vitro
[4], and the process is represented within the model as the
differential consumption of growth factor by proliferating
cells. This process is controlled by rule 10.
B.
distance
180
160
140
120
100
80
0 0.5 1 1.5 2 3.5
simulation parameter η
C.
bifurcation
frequency
0.15
III. MODEL BEHAVIOR PERTURBATION AND COMPARISON
WITH EXPERIMENTAL OBSERVATIONS
0.1
0.05
In order to evaluate whether MMPs and TIMPs may be
functioning as activators and inhibitors in morphogenesis,
we compare results from published in-vivo experiments with
output generated from corresponding changes to the
simulation. Specifically we compare the effects of increased
TIMP expression and inhibition of MMP activity on
maximal duct length.
0
0 0.5 1 1.5 2 3.5 4
simulation parameter η
Fig. 4. Effect of increasing basal TIMP level, η, on simulation output. A.
Simulation output with default parameter values from Fig. 2, but with
η = 0 , η = 2.0 , η = 3.5 , and η = 4.0 , from left to right. B. Simulated
duct extension distance for different values of η , after 300 steps, measured
from the initiation point to the tip of the furthest simulated duct, in points.
C. The effect of η on the number of bifurcations per unit distance after
300 steps.
A. Effect of changes in basal TIMP level
Transgenic mice overexpressing human TIMP1 have
been generated [2]. The TIMP1 transgene was driven by a
β-actin promoter, resulting in constitutive expression. The
effect of the introduction of TIMP1 is modeled through
manipulation of the simulation parameter η . The results are
summarized in Fig. 4.
protease activity. The inhibitory activity of TIMPs is
modeled in rule 1. Regulation of TIMP expression is
modeled by rules 6 and 7. In order to imitate experiments in
which TIMP is expressed constitutively, rule 8 has been
included the model. The diffusion of TIMPs is governed by
rule 11.
B. Effect of changes in MMP autocatalysis parameter
C. Growth Factor
There are 28 known MMP genes in humans. Broadspectrum MMP inhibitors have been developed which are
used to mimic the effect of knocking out all MMP genes.
These inhibitors have been used to study the role of MMPs
in branching morphogenesis. The effect of these inhibitors
is imitated in the simulation by decreasing the value of the
simulation parameter c. The results from this analysis are
summarized in Fig. 5.
It has been demonstrated in 3D cultures as well as invivo that growth factors can influence mammary branching
morphogenesis [8]. In addition to growth factors such as
epidermal growth factor, hepatocyte growth factor, and
fibroblast growth factor, byproducts of extracellular matrix
decomposition can stimulate branching. Growth factors are
able to diffuse through the mammary fat pad, as indicated by
studies of the effects of growth factor implants on duct
growth in-vivo [8]. It is also known that growth factors can
induce MMP synthesis [4]. Rules 1, 10, and 11 model these
behaviors in the simulation. A small stochastic component
681
A.
attenuated by continuous treatment, resulting in a ductal
network that is approximately 50% of the size of untreated
mice. Reduction in MMP activity is mimicked in the
simulation by reducing the value of the parameter c. The
simulated ducts respond in a fashion similar to ducts invivo, as decreasing values of c result in a slower rate of
simulated duct extension (Fig. 4A, B). However, unlike the
results from increasing the value of η (Fig. 3C), there was
not an apparent reduction in simulated duct bifurcations per
unit distance (Fig. 4C). Again, it is not known whether a
corresponding effect is observed in-vivo as a consequence of
MMP inhibition although this could also be analyzed using
existing data from in-vivo experiments.
B.
distance
200
150
100
50
0
1.7
2
2.3
2.6
3
VI. CONCLUSION
simulation parameter c
The simulation model of mammary gland
morphogenesis described in this report generates qualitative
results that are similar to those observed in-vivo, in response
to modulation of TIMP and MMP activity. The inhibition of
simulated duct extension is consistent with the possibility that
MMPs and TIMPs are serving as activators and inhibitors in a
reaction-diffusion-like process. Additional quantitative data
from in-vivo experiments is needed to test this hypothesis
further. Comparison of simulation model behavior and
experimental results will be useful in this effort.
C.
bifurcation
frequency
0.15
0.1
0.05
0
1
2
3
4
5
simulation parameter c
REFERENCES
Fig. 5. Effect of reduction of MMP activation coefficient, c, on simulation
output. A. Branching pattern after 300 steps, with c = 3.0, c = 2.3, c = 2.0,
and c = 1.7, from left to right. B. Simulated duct extension distance for
different values of c, after 300 steps, measured from the initiation point to
the tip of the furthest simulated duct in points. C. The effect of c on the
number of bifurcations per unit distance after 300 steps.
[1] B. Wiseman and Z. Werb, "Stromal Effects on Mammary Gland
Development and Breast Cancer", Science, vol. 296, no. 5570, pp.
1046-1049, May 2002.
[2] B. Wiseman, M. D. Sternlicht, L. R. Lund, C. M. Alexander, J.
Mott, M. J. Bissell, P. Soloway, S. Itohara, Z. Werb, "Site-specific
inductive and inhibitory activities of MMP-2 and MMP-3
orchestrate mammary gland branching morphogenesis", J Cell
Biol, vol. 162, no. 6, pp. 1123-1133, Sep. 2003.
[3] A. Turing, "The chemical basis of morphogenesis", Phil. Trans R.
Soc., vol. B327, pp. 549-578, 1952.
[4] T. Miura and K. Shiota,, "Depletion of FGF acts as a lateral
inhibitory factor in lung branching morphogenesis in vitro", Math
Biosci, vol. 156, no. 1-2, pp. 191-206, Mar. 1999.
[5] M. Markus, D. Böhm, M. Schmick, "Simulation of vessel
morphogenesis using cellular automata" Math Biosci, vol. 156, no.
1-2, pp. 191-206, Mar. 1999.
[6] S. E. Moon, M. K. Dame, D. R. Remick, J. T. Elder, J. Varani,
“Induction of matrix metalloproteinase-1 (MMP-1) during
epidermal invasion of the stroma in human skin organ culture:
keratinocyte stimulation of fibroblast MMP-1 production”, Br. J.
Cancer, vol. 85, no. 10, pp. 1600-1605, Nov. 2001.
[7] J. E. Fata, K. J. Leco, R. A. Moorehead, D. C. Martin, R. Khokha,
“Timp-1 is important for epithelial proliferation and branching
morphogenesis during mouse mammary development”, Dev. Biol.,
vol. 211, no. 2, pp. 238-254, Jul. 1999.
[8] M. Simian, Y. Hirai, M. Navre, Z. Werb, A. Lochter, M. J. Bissell,
“The interplay of matrix metalloproteinases, morphogens and
growth factors is necessary for branching of mammary epithelial
cells”, Development, vol. 128, no. 16, pp. 3117-3131, Aug. 2001.
V. DISCUSSION
It has been shown that constitutive expression of TIMP1
in mice inhibited duct extension by approximately 25%
compared to w.t. controls [2]. The simulated ducts behave
in a similar fashion, with a significant reduction in simulated
duct extension in response to increasing the basal level of
the TIMP variable by increasing the parameter η (Fig.
3A,B). The parameter η also influences the number of
simulated duct bifurcations events per unit distance (Fig.
3C). The effect of TIMP1 expression on the frequency of
duct bifurcation events in-vivo has not been measured to our
knowledge but such an analysis would be interesting in light
of the simulation output.
The effect of broad-spectrum MMP inhibitors on
mammary duct development in mice is quite dramatic, more
so than the effect of TIMP-1 expression. The inhibitor
GM6001 is able to completely block duct elongation during
the initial 3 weeks of mamary gland development [2].
Although duct growth eventually occurs, the process is
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1 of 4
Simulating Leukocyte-Venule Interactions – A Novel Agent-Oriented Approach
1
J. Tang1, C. A. Hunt1,2, J. Mellein2, and K. Ley3
Joint UCSF/UCB Bioengineering Graduate Group and 2The Biosystems Group, Department of Biopharmaceutical Sciences, The
University of California, San Francisco, CA 94143, USA
3
Department of Biomedical Engineering, University of Virginia Health Sciences Center, Charlottesville, VA 22908
Abstract—Leukocyte recruitment into sites of inflammation
involves a complex cascade of molecular interactions between the
leukocyte and the endothelial cells of the inflamed venule. This
report proposes a novel agent-oriented approach for simulating
leukocyte-venule interactions during inflammation. We focus on
modeling and simulating the initial steps of rolling, activation,
and firm adhesion of neutrophils on TNF-α-treated mouse
cremaster muscle venules.
Keywords—Adhesion, Agent-Based Model, Endothelium,
Inflammation, Leukocyte, Rolling, Transmigration
I. INTRODUCTION
Leukocyte recruitment into sites of inflammation
involves a complex cascade of molecular interactions
between the leukocyte and endothelial cells of the inflamed
venule. Initial interactions are primarily mediated by the
selectin family of receptors and their respective carbohydrate ligands found on the membranes of both leukocytes
and endothelial cells. Selectin-ligand interactions are transient due to the fluid force the leukocyte experiences within
the venule. As selectin-ligand bonds are constantly formed
at the leading edge of the leukocyte, bonds at the trailing
edge are broken, which causes the leukocyte to undergo
rolling [1]. Each selectin molecule is believed to have a
characteristic rate of bond association and dissociation and
thus rolling velocities are different when mediated by
different selectin molecules.
As leukocytes roll along the venular surface, they can
detect chemokines presented on the membrane of activated
endothelial cells via chemokine receptors. Upon chemokine
detection, intracellular signaling events are triggered that
activate the leukocyte. The result is an increased affinity and
avidity (clustering) of the integrins, another class of receptors found on leukocytes. When in a high affinity state,
these integrins are capable of forming strong interactions
with endothelial cell adhesion molecules that are believed to
enable leukocytes to decrease their rolling velocity and
eventually firmly adhere to the vessel wall [2]. In
neutrophils, it has also been observed that engagement of
the selectins and integrins with their ligands can lead to
intracellular signaling events and activate the leukocyte [3].
Once firmly adhered to an endothelial cell, a leukocyte
undergoes diapedesis: they apparently crawl between
adjacent endothelial cells and into the target tissue.
Here, we propose a novel computational approach for
simulating the events and interactions described here. We use
an agent-oriented approach and represent this system as a
collection of autonomous (software) entities, or agents, making
decisions on how to interact with their local environment based
on a set of encoded rules. Our initial simulation experiments
are designed to represent neutrophil rolling, activation, and firm
adhesion on TNF-α-treated mouse cremaster muscle venules.
II. MODEL STRUCTURE
The proposed agent-based model contains Ligand, Cell,
Membrane, and Space superclasses. The Ligand superclass
represents biological molecules that can form bonds with
other macromolecules. The Membrane superclass represents
cellular membranes. The Cell superclass corresponds to
cells within the biological model. Lastly, the Space
superclasses provide environments within which the objects
can interact.
A. Ligand
The Ligand superclass can be broken down into
AdhesMolecule, Chemok, and ChemokReceptor subclasses.
AdhesMolecule objects represent the behaviors of adhesion
molecules such as the selectins, integrins, and cellular
adhesion molecules.
Each AdhesMolecule object has
parameters that are used to calculate a probability that it will
form an interaction with its coreceptor AdhesMolecule object.
Such parameters include the total number of molecules that
the AdhesMolecule object represents, as well as an affinity
and avidity value. AdhesMolecules also contain parameters
that are used to calculate probabilities that they will break their
interaction with their respective LIGAND1. The values for these
parameters are dynamic and may change during the course of
a simulation to reflect the events that occur in the biological
model during cell activation by chemokine detection or by
engagement of the selectins and integrins with their ligands.
Rules that determine how these parameters will be updated
are encoded within the AdhesMolecule objects.
Chemok objects represent chemokine signaling
molecules, and ChemokReceptors correspond to the
chemokine receptors that bind them. Knowledge of which
AdhesMolecules are affected upon formation of
ChemokReceptor-Chemok LIGAND interactions are encoded
within the ChemokReceptors.
1
The same word may be used to refer to a biological molecule, component,
or event and the in silico object or event that represents them. In the latter
case the word is written using small caps.
2 of 4
A precondition for any Ligand-Ligand interaction to
occur is that the two Ligands in question map to an observed
biological receptor-ligand pair. A complete set of such
receptor-ligand pair rules will be specified during
implementation.
B. Cell and Membrane
The two types of Cell classes within our model are the
ECell and the Leuk. They represent endothelial cells and
leukocytes, respectively.
The Membrane class can be subdivided into two
subclasses, ECellMem and LeukMem. The LeukMem, which
represents the leukocyte membrane, is implemented as a 2-D
linked list data structure. As shown in Fig. 1-A, the linked
list in the first dimension is circular, and all linked lists in
the second dimension are of the same length. Each unit in
the secondary linked lists corresponds to a section of the
leukocyte membrane. When a Leuk object is created, a
unique, corresponding LeukMem object will also be created,
which involves randomly choosing items from these
secondary linked lists. These chosen items represent
locations on the membrane where the Ligands on the Leuk
object are exposed to the environment. At each chosen
section in the LeukMem, there will be AdhesMolecule and
ChemokReceptor objects.
Each ECell object has an ECellMem to represent the
entire luminal surface of the referent membrane. We
simplify our model by assuming that this section is
rectangular in shape.
As shown in Fig 1-B, it is
implemented as a 2-D array. Similar to LeukMem objects,
unique ECellMem objects are created for every ECell. Units
within the array will be uniquely chosen to indicate where
the AdhesMolecule objects are exposed to the environment.
At each such location there will be an AdhesMolecule object
for each adhesion molecule found on endothelial cells in the
biological model. In addition, if the ECell has a Chemok
object to present to Leuk objects, it will be positioned at one
of these specified locations.
D. Space
The first Space subclass is the FreeStreamSpace, which
represents the central region of a venule where the free
blood stream is located. As shown in Fig. 2, it is
implemented as a 1-D array, where each unit corresponds to
a particular cross-section of the venule. Each unit will
contain information about that particular cross-section, such
as pointers to Leuk objects within that region, shear rate, and
cross-sectional diameter. In addition, each unit will have a
parameter that determines the probability that a Leuk object
within that unit will move out of the FreeStreamSpace.
The MembraneSpace represents the endothelial cell
membrane. As shown in Fig. 2, it is a 2-D grid that is
circular in one dimension, and contains ECell objects.
Fig. 1. Illustration our representation of the leukocyte membrane (A) and
the luminal endothelial cell membrane (B) in our model.
Fig 2. Illustration of the FreeStreamSpace and the MembraneSpace classes
in our model.
III. MODELING BEHAVIORS
A. AdhesMolecule-AdhesMolecule Interactions
From the total number, affinity, and avidity parameters
of both the Leuk object and ECell object, a probability that
an interaction will form can be calculated. Interaction
formation will be Monte Carlo determined.
The
disengagement of interactions between AdhesMolecules will
also be determined in a similar manner.
B. Rolling
Leuk-ECell interactions can only occur when the Leuk
object is on the MembraneSpace near ECell objects. Leuk
objects are placed on the MembraneSpace in an orientation
that allows the LeukMem to rotate around its axis of rotation
and ROLL on the MembraneSpace in the direction of flow.
Only a small rectangular region of the LeukMem will be
placed on the MembraneSpace. Leuk AdhesMolecule and
ECell AdhesMolecule interactions occur only at overlapping
regions of the LeukMem and ECellMem where both have
been labeled as locations where AdhesMolecules are
exposed to the environment.
A Leuk ROLLING event consists of a partial rotation of
LeukMem around its axis of rotation and in the direction of
flow such that a new column of the linked list is placed on
top of the MembraneSpace, while an old one is removed. If
there is an overlapping region of LeukMem and ECellMem
where both regions have been labeled as locations where
AdhesMolecules are exposed to the environment, then all
Leuk AdhesMolecules will attempt to form interactions with
their respective AdhesMolecule LIGANDS on the ECell. A
prerequisite for a ROLLING event to occur is that all
AdhesMolecule-AdhesMolecule interactions dissociate at the
rear column of the linked list that is removed from the
MembraneSpace.
3 of 4
If at any time, a Leuk object is on the MembraneSpace,
but a sufficient number of AdhesMolecule-AdhesMolecule
interactions are not present, then the Leuk will disengage
and move back into the FreeStreamSpace.
B. Activation and Firm Adhesion
A Leuk object can encounter a Chemok object with its
ChemokReceptors when ROLLING on the MembraneSpace.
The Chemok object will be removed and all relevant
AdhesMolecule objects at nearby regions on the LeukMem
will modify their parameters appropriately. When ROLLING,
engagement of AdhesMolecule objects with their LIGANDS
can also result in SIGNALS (messages) being sent to relevant
and nearby AdhesMolecule objects to modify their
parameters in an appropriate manner.
FIRM ADHESION will only occur when AdhesMoleculeAdhesMolecule interactions have been formed and will not
disengage when they are within the very last column of the
LeukMem that is on the MembraneSpace.
IV. MODEL SIMULATION
A. Rolling
Our initial simulation experiments explore the
parameter space for the ADHESION MOLECULES that participate
in the process of NEUTROPHIL ROLLING. These will include the
parameters representing the selectin, α4 integrin, and β2
(CD18) integrin adhesion molecules. We use data from
intravital microscopy experiments [4-5], which observed
neutrophil rolling on cremaster muscle venules in mice that
lacked different combinations of the selectin and integrin
adhesion molecules after treatment of TNF-α.
The first simulated experimental condition is based on
short term TNF-α treatment [4]: TNF-α is injected
intrascrotally 2 h before the beginning of the intravital
microscopic experiment. In the in vivo model, the treatment
has been shown to induce E-selectin expression and increase
the expression of P-selectin [4]. Mice lacking E-selectin
(E-/-), P-selectin (P-/-), L-selectin (L-/-), L- and E- selectin
(L/E-/-), E- and P- selectin (E/P-/-), and L- and P-selectin
(L/P-/-) were generated by bone marrow transplantation.
Experimental observations for these mice are summarized in
Table I. E, L, and P-selectin deficient mice were generated,
but no rolling was observed for these mice.
Under short term TNF-α treatment conditions, it has
been shown that the β2 integrins play a cooperative role
with E-selectin in mediating slow rolling of neutrophils at
velocities below 5 µm/s. To refine the parameter space for
these adhesion molecules, we use experimental data from
[5]. Neutrophil rolling was observed under the same short
term TNF-α treatment conditions, but in wild-type mice
(WT) and in mutant mice lacking E-selectin (CD62E-/-), β2
integrins (CD18-/-), or β2 integrins and E-selectin (CD18-/CD62E-/-). Observations are summarized in Table II.
The second experimental condition that will be
simulated uses longer-term treatment with TNF-α: it is
injected intrascrotally 6 h before the beginning of the
intravital microscopic experiment. Evidence has shown that
the roles of L-selectin and α4 integrin in rolling are different
in long term TNF-α treatment than in short term treatment
[4]. In E- and P-selectin deficient mice, L-selectin and α4
integrin-dependent rolling is induced after long term TNF-α
treatment. L-/-, L/E-/-, L/P-/-, E- and P-selectin deficient
(E/P-/-), and E-, L-, and P-selectin deficient (E/L/P-/-) mice
were generated by bone marrow transplantation. Table III
summarizes observations for this experiment.
Parameter vectors for the AdhesMolecules will be
identified such that ROLLING behaviors in our model are
calibrated to the rolling behaviors observed from these in
vivo experiments.
B. Activation And Firm Adhesion
The third experimental condition being simulated is
aimed at refining parameters so that the model adequately
represents the steps of activation and firm adhesion. For this
we use experimental data from [6], which tracked individual
TABLE I *
HEMODYNAMICS AND MICROVASCULATURE PARAMETERS
FOR BONE MARROW-TRANSPLANTED MICE AFTER SHORT
TERM TREATMENT WITH TNF-α (2 h)
Rolling Flux
Avg. Rolling
Mouse
Avg. Vessel
Wall Shear
Fraction (%)
Velocity
Diameter
Rate (s-1)
(µm/s)
(µm)
L
37.3 ± 1.4
680 ± 30
10.1 ± 1.7
5.0 ± 0.3
E-/40.3 ± 1.4
710 ± 30
48.1 ± 5.5
31.1 ± 0.9
P-/40.5 ± 1.7
610 ± 20
11.5 ± 2.2
14.8 ± 0.4
L/E-/41.6 ± 1.6
720 ± 20
11.3 ± 1.3
5.9 ± 0.3
L/P-/49.1 ± 2.1
730 ± 30
1.3 ± 0.2
3.5 ± 0.2
* Reproduced from [4].
TABLE II **
FOR MUTANT MICE AFTER SHORT TERM TREATMENT WITH
TNF-α (2 h)
Avg. Rolling
Mouse
Avg. Vessel
Wall Shear
Rate (s-1)
Velocity (µm/s)
Diameter (µm)
WT
47 ± 2
470 ± 30
6.9 ± 0.2
37 ± 1
600 ± 40
21.1 ± 0.5
CD62E-/CD18-/43 ± 2
460 ± 30
22.7 ± 0.8
CD18-/-, CD62E-/- 51 ± 2
580 ± 50
50.1 ± 1.4
** Reproduced from [5].
TABLE III *
FOR BONE MARROW-TRANSPLANTED MICE AFTER LONG
TERM TREATMENT WITH TNF-α (6 h)
Rolling Flux
Avg. Rolling
Mouse
Avg. Vessel
Wall Shear
Fraction (%)
Velocity
Diameter
Rate (s-1)
(µm/s)
(µm)
L-/36.8 ± 1.1
560 ± 20
1.2 ± 0.3
10.7 ± 1.2
39.5 ± 1.7
660 ± 30
5.0 ± 1.0
15.2 ± 0.9
L/E-/L/P-/42.6 ± 2.2
590 ± 30
0.9 ± 0.3
4.8 ± 0.4
E/P-/43.4 ± 2.0
480 ± 40
0.9 ± 0.2
15.7 ± 1.2
E/L/P-/45.1 ± 2.1
540 ± 30
0.4 ± 0.06
13.6 ± 1.2
4 of 4
neutrophils rolling along a TNF-α-treated mouse cremaster
muscle venular tree. Reported cumulative distance versus
time profiles are shown in Fig. 3. Values for average
velocity and average distance rolled before firm adhesion
were calculated for CD18-/-, E-/-, and WT mice. Reported
values are shown in Table IV.
V. DISCUSSION
We have made many assumptions about the biological
system that will need to be iteratively revisited during the
course of these studies. For example, our initial in silico
experiments use one ECell object that spans the entire
MembraneSpace and we assume that the distribution of
AdhesMolecules is uniform on the ECellMem.
The
distribution of adhesion molecules on the surface of the
endothelial cells has not been fully characterized, but it is
known that it is not uniform [7].
In addition, it has been shown that LFA-1 and Mac-1,
the two major β2 integrins involved in neutrophil rolling and
firm adhesion, have distinct and cooperative roles [8-9].
Our initial experiments use a simplified model that
represents all β2 integrins as a single agent. Our future
models will contain separate agents for each of the β2
integrins and their ligands.
Finally, the dynamics of leukocyte activation by
chemokine detection and by engagement of selectins and
integrins with their ligands is not understood. An issue of
debate is whether each chemokine detection event or
selectin and integrin-ligand engagement event sends global
or local activation signals to the integrins [10]. We are
testing the latter hypothesis.
VI. CONCLUSION
We present a novel, agent-oriented approach to modeling
and simulating leukocyte-venule interactions during
inflammation. The leukocyte adhesion cascade involves
overlapping and intertwined processes [3]. An advantage of
this new approach to modeling and simulation is that it is
straightforward to systematically represent non-linear
systems, which makes it well suited for studying leukocytevenule interactions.
We anticipate that our models will be able to
progressively integrate and organize the knowledge that has
amassed on this system, thereby helping us to understand
how such a system functions under normal, stressed, and
diseased conditions. Furthermore, we anticipate that these
new models can provide an in silico environment to help
inspire and test novel cellular engineering approaches for
creating therapeutics.
REFERENCES
Fig 3. Distance-time curves for typical rolling leukocytes. Typical
distance-time tracings for individual leukocytes from WT (open circles),
CD18-/- (dark circles), and E-/- (triangles) mice. Leukocyte outcome is
indicated by arrows: up (detach), down (attach). Reproduced from [6].
TABLE IV *
AVERAGE TIME ROLLED, DISTANCE ROLLED,
AND AVERAGE ROLLING VELOCITY
Mouse
Outcome
Time
Distance
Avg. Rolling
Genotype
Rolled (s)
Rolled (µm)
Velocity (µm/s)
WT
Adhere
86 ± 18
560 ± 20
10.7 ± 1.2
Detach
140 ± 29
660 ± 30
15.2 ± 0.9
WT
CD18-/Adhere
------CD18-/Detach
12 ± 2
270 ± 26
32 ± 7
E -/Adhere
40 ± 14
280 ± 49
14 ± 2
E-/Detach
41 ± 3
350 ± 110
11 ± 2
[1] A. Tözeren and K. Ley, “How do selectins mediate leukocyte
rolling in venules?,” Biophys J., vol. 63, no. 3, pp. 700-709, Sep.
1992.
[2] R. Alon and S. Fiegelson, “From rolling to arrest on blood
vessels: leukocyte tap dancing on endothelial integrin ligands
and chemokines at sub-second contacts,” Semin Immunol., vol.
14, no. 2, pp. 93-104, Apr. 2002.
[3] K. Ley, “Integration of inflammatory signals by rolling
neutrophils,” Immunol Rev., vol 186, pp. 8-18, Aug. 2002.
[4] U. Jung and K. Ley, “Mice lacking two or all three selectins
demonstrate overlapping and distinct functions for each selectin,” J
Immunol., vol. 162, no. 11, pp. 6755-6762, Jun. 1999.
[5] S. B. Forlow., et al., “Severe inflammatory defect and reduced
viability in CD18 and E-selectin double-mutant mice,” J Clin
Invest, vol. 106, no. 12, pp. 1457-1466. Dec. 2000.
[6] E. Kunkel, J. L. Dunne, and K. Ley, “Leukocyte Arrest During
Cytokine-Dependent Inflammation in vivo,” J Immunol, vol.
164, no. 6, pp. 3301-3308, Mar. 2000.
[7] E. R. Damiano, et al., “Variation in the velocity, deformation,
and adhesion energy density of leukocytes rolling within
venules,” Circ Res., vol. 79, no. 6, pp. 1122-1130, Dec. 1996.
[8] J. L. Dunne, et al., “Control of leukocyte rolling velocity in
TNF-α-induced inflammation by LFA-1 and Mac-1,” J Immunol,
vol. 99, no. 1, pp. 336-341, Jan. 2002.
[9] J. Dunne, et al., “Mac-1, but not LFA-1, uses Intercellular
Adhesion Molecule-1 to mediate slow rolling in TNF-α-induced
inflammation,” J Immunol, vol. 171, no. 11, pp. 6105-61111.
Dec. 2003.
[10] R. Alon, V. Grabovsky, and S. Feigelson, “Chemokine induction
of integrin adhesiveness on rolling and arrested leukocytes local
signaling
events
or
global
stepwise
activation?”
Microcirculation, vol. 10, no. 3-4, pp. 297-311. Jun. 2003.
1 of 4
In Silico Representation of the Liver -- Connecting Function to Anatomy,
Physiology and Heterogeneous Microenvironments
Li Yan1, C. Anthony Hunt1,2, Glen E.P. Ropella2, and Michael S. Roberts3
1
2
Joint UCSF/UC Berkeley Bioengineering Graduate Program
Dept. of Biopharmaceutical Sciences, Biosystems Group, University of California, San Francisco, CA, USA
3
Department of Medicine, University of Queensland, Princess Alexandra Hospital, Woolloongabba, Q 4102 Australia
Abstract—We have built a collection of flexible, hepatomimetic, in silico components. Some are agent-based. We
assemble them into devices that mimic aspects of anatomic
structures and the behaviors of hepatic lobules (the primary
functional unit of the liver) along with aspects of liver function.
We validate against outflow profiles for sucrose administered
as a bolus to isolated, perfused rat livers (IPRLs). Acceptable
in silico profiles are experimentally indistinguishable from
those of the in situ referent based on Similarity Measure values.
The behavior of these devices is expected to cover expanding
portions of the behavior space of real livers and their
components. These in silico livers will provide powerful tools
for understanding how the liver functions in normal and
diseased states, at multiple levels of organization.
Keywords— Drug metabolism, in silico, agent-based,
modeling and simulation, computational biology, hepatic.
I. INTRODUCTION
The liver is primarily responsible for the conversion of
xenobiotics and endogenous compounds into more watersoluble, excretable forms. Liver disease alters the hepatic
microcirculation and can impair the disposition kinetics of
many drugs. Liver disease also complicates pharmacological treatments of other diseases, as well as itself, and can
influence pharmacotherapeutic decisions. Modeling and
simulation helps scientists and medical decision makers predict the likely consequences of various options, and thereby
make better decisions. Multiple, different traditional models
have been developed and validated ([1] and references
therein). They include well-stirred compartments, the single
tube, convection-dispersion, and interconnected tube model.
Those models work well in accounting for the specific data
and system conditions to which they are applied. However,
they also have limitations, and among them are the following.
Because the models are data-centric, considerable knowledge
about hepatic structure and function are mostly ignored.
Model components do not map well to specific biological
components.
In addition, their boundary conditions and
parameterizations are restricted to one level of organization.
Therefore, it is hard to reuse a model developed for one set of
experimental conditions (or for one drug) under new circumstances (or for a different drug). Also, related models on the
same system are hard to plug together.
When we discover something important about the
transport and metabolism of a new set of drugs and wish to
make intelligent decisions based on the likely clinical
implications, we will need an already existing, validated
model into which we can seamlessly import the new data in
order to address the what-if questions of interest. No such
models exist. Clearly, new ideas and new approaches are
needed. From what direction should new modeling and
simulations methods approach the biology: from the bottomup or the top-down? Noble makes the case for a “middleout” approach that focuses on the “functional level between
genes and higher level function” [2]. We used such a
middle-out approach in developing the silico liver described
here. We use data drawn from multiple sources, including
time series data from perfused liver studies. We focus more
on aspects of the structures and behaviors that give rise to
the data. We test and affirmed the hypothesis that perfused
liver outflow data, in conjunction with other data, can be
used to specify and parameterize a novel, physiologically
recognizable hepato-mimetic device. Furthermore, that
device can generate outflow profiles that are experimentally
indistinguishable from the original in situ data.
II. MODEL DESIGN
A. Histological and Physiological Considerations
The in situ liver perfusion protocol is detailed in [3]. A
compound of interest is injected into the entering perfusate of
the isolated liver. For each drug outflow profile there is a
corresponding sucrose profile and it is the latter that we focus
on first [1, 4]. Such profile pairing allows us to use a two-step
feature extraction procedure for building hepato-mimetic
devices: first, from the sucrose data extract information to
represent the extracellular environment. That process leads to
unique parameterizations for 1) vascular and sinusoidal
graphs, 2) the arrangement and attributes of the sinusoids, and
3) the extracellular topography within sinusoids. We then
expand that representation with essential intracellular details
to account for the outflow data of different drugs.
The lobule is the primary structural and functional unit
of the rat liver. Hepatic intralobular heterogeneity is well
documented [5]. No two lobules are identical. Sinusoids
separate meshworks of one cell-thick plates made up of
hepatocytes that perform the major metabolic functions of
the liver. Hepatocytes exhibit location-specific properties
within lobules, including location-dependent expression of
drug metabolizing enzymes [6]. Sinusoids experience
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different flows and have different surface to volume ratios
within different zones. In addition to hepatocytes, lobules
contain several specialized cell types. Endothelial cells line
sinusoids that contain Kuppfer, stellate, and other cell types.
B. In Silico Components: Directed Graphs
A trace of flow within one lobule sketches a network
that can be represented by an interconnected, directed graph.
Such graphs are the core architectural feature of our lobulemimetic devices (hereafter, LOBULE1). Teutsch et al. [7]
subdivide the lobule interior into concentric zones. For
now, we impose a three-zone structure on the graph (I, II
and III in Fig. 1) and require that each zone contain at least
one node and that a shortest path from portal vein tract (PV)
to central vein (CV) will pass through at least one node and
no more than one node per zone. The insert in Fig. 1
illustrates a portion of a graph network that connects in
silico PV outlets through nodes in Zones I and II and then
through one Zone III node to the CV. Graph structure is
specified by the number of nodes in each Zone and the
number of edges connecting those nodes. Edges are further
identified as forming either inter-zone or intra-zone
connections. Edges specify “flow paths” that have zero
length and contain no objects. A solute object exiting a
parent node is randomly assigned to one of the available
outgoing graph edges and appears immediately as input for
the SS located downstream at the child node. Randomly
assigned intra-zone connections are allowed but are
confined to Zones I and II. Nodes are randomly assigned to
each zone so that the number of nodes in each zone is
approximately proportional to the fraction of the total lobule
volume found in that zone.
C. In Silico Components: Sinusoidal Segments
Agents called sinusoidal segments (SSs) (Fig. 2) are
placed at each graph node. There is one PV entrance
(effectively covering the exterior of the LOBULE) and one
Fig. 1. A schematic of an idealized cross-section of a hepatic lobule
showing half an acinus and the direction of flow between the terminal
portal vein tract (PV), and the central hepatic vein (CV). SS: Sinusoidal
Segment. The insert is an illustration of a LOBULE and corresponds to a
portion of an acinus and a small fraction of a lobule.
1
The same word may be used to refer to a biological molecule, component,
or event and the in silico object or event that represents them. In the latter
case the word is written using small caps.
Fig. 2. Schematic of a sinusoidal segment (SS). Two types of SS are
discussed in the text. One SS is placed at each node of the directed graph.
CV exit for each ISL. A solute object is a passive
representation of a chemical as it moves through the in silico
environment. The PV creates solute objects, as dictated by
the experimental dosage function, and distributes them to
the SSs in Zone I.
Movement of solutes from place to place within a lobule can
be modeled as message passing. A solute object moving
through the LOBULE represents molecules moving through
the sinusoids of the lobule, and their behavior is dictated by
rules specifying the relationships between SOLUTE location,
proximity to other objects and agents, and the solute's
physicochemical properties. Each S O L U T E has dose
parameters (mass, constituents, timing, and catheter effects
[1]) and a scale parameter (molecules per solute object).
The relative tendency of a SOLUTE to move forward within a
SS determines the effective flow pressure and this is
governed by a parameter called Turbo. If there is no flow
pressure (Turbo = 0), then solute movement is specified by a
simple random walk. Increasing Turbo biases the random
walk in the direction of the CV.
Viewed from the center of perfusate flow out in Fig. 2,
a SS is modeled as a tube with a rim surrounded by other
layers. The tube and rim are the sinusoidal space and its
immediate borders. The tube contains a fine-grained
abstract Core space that represents blood flow. Grid A is
the Rim. Grid B is wrapped around Grid A and represents
the endothelial layer. Another fine-grained space (Grid C)
is wrapped around Grid B to collectively represent the Space
of Disse, hepatocytes, and bile canaliculi. If needed,
hepatocytes and connected features such as bile canaliculi
can be moved to a fourth grid wrapped around Grid C. The
properties of locations within each grid can be homogeneous
or heterogeneous depending on the specific requirements
and the experimental data being considered.
Objects can be assigned to one or more grid points. For
example, a subset of Grid B points can represent one or
more Kupffer cells. Another subset can map to intracellular
gaps and fenestrae for particulate sieving into the Space of
Disse. KUPFFER CELL activity can be added to the list of Grid
B objects, as they are needed. Objects that move from a
location on a particular grid location are subject to one or
3 of 4
more lists of rules that are called into play at the next step.
Within Grid B a parameter controls the size and
prevalence of FENESTRATIONS and currently 10% of Grid B
in each SS is randomly assigned to FENESTRAE; the remaining
90% represents cells. Similarly, within the grid where some
locations map to hepatocytes, there is a parameter that
controls their relative density.
D. Classes of Sinusoidal Segments (SS)
To further enable accounting for sinusoidal heterogeneity, including differences in transit time and flow [8], topographic arrangement [9], and the different surface to volume
ratios within three zones [5], we defined different classes of
SINUSOID, direct SINUSOID (DirSin) and tortuous SINUSOID
(TortSin). Additional SS classes can be specified and used
when needed. Relative to TortSins, the DirSins have a shorter
path length and a smaller surface-to-volume ratio, whereas the
TortSins have a longer path length and a larger surface-tovolume ratio. The circumference of each SS is specified by a
random draw from a bounded uniform distribution. To reflect
the observed relative range of real sinusoid path lengths, SS
length is given by a random draw from a gamma distribution
having a mean and variance specified by the three gamma
function parameters, a, b, and g.
E. Dynamics of Solutes within Sinusoidal Segments
Solute objects can enter a SS at either the Core or the
Rim. At each step thereafter until it is metabolized or
collected it has several options, most are stochastic. In the
Rim or Core it can move within that space, jump from one
space to the other, or exit the SS. From a Rim location it
can also jump to Grid B or back to the Core. Within Grid B
it can move within the space, jump back to Grid A or to
Grid C. When it encounters an ENDOTHELIAL CELL within
Grid B it may (depending on its properties) partition into it.
Once inside, it can move about, exit, bind or not. Within
Grid C it can move within the space or jump back to Grid B.
When a HEPATOCYTE is encountered the solute can (depending on its properties) partition into it or move on. Once
inside a HEPATOCYTE it can move about, exit, bind (and
possibly get METABOLIZED) or not. Currently all objects
within a HEPATOCYTE that bind can also METABOLIZE . The
probability of a solute object being METABOLIZED depends on
the object’s properties. Once METABOLIZED the object is
destroyed. The only other way to exit a SS is from the Core,
Rim or into BILE (not implemented here). When the object
exits a SS and enters the CV, its arrival is recorded (corresponding to being collected), and it is destroyed.
III. SIMILARITY MEASURE
Replicate in situ experiments conducted on the same
liver provide similar but not identical solute outflow
profiles. The same is true for experiments on LOBULES.
There are two main contributors to intraindividual
variability: methodological and biological. For replicate
experiments in the same liver the coefficient of variation for
fractional solute outflow within specific collection intervals
typically ranges between 10 and 40%. A coefficient of
variation can define a continuous interval bracketing the
experimental data. A new set of results that falls within that
bracketed range and has essentially the same shape is
defined as being experimentally indistinguishable. The
same should hold even if the data comes from an in silico
experiment. There would be no way to determine whether a
data set came from an in situ or an in silico experiment.
This last observation provides the basis for designing and
evaluating a Similarity Measure (SM).
The objective of the SM is to help select among various
models of the liver, not simply to assume a model and select
among variations on that model. Hence, the successful SM
targets the various features of the outflow profile that
correlate with the generative structures and building blocks
inside the model. Neither an instantaneous, per observation,
comparison, nor a whole-curve comparison is ideal because
the different regions of repeated outflow profiles clearly
show different variances. For these reasons, a multiple
observation SM seems most warranted. However, for
simplicity in these early stage studies we have assumed that
the coefficients of variation of repeat observations within
different regions of the curve are the same. In that way we
can use a simple interval SM. A set of in situ outflow
profiles, which are generated from different subjects
following the same protocol, is used as training data.
Calculate the mean of each time point and use this set of
means as reference profile (Pr). For each observation in P r,
create a lower, P l, and an upper, P u, bound by multiplying
that observation by (1 – D) and (1 + D), respectively. The
two curves P l and P u are the lower and upper bounds of a
band around Pr. The two outflow profiles are deemed
similar if the second profile, P, stays within the band. The
distance D used for sucrose is one standard deviation of the
array of relative differences between each repeat observation
and the mean observations at that time.
IV. IN SILICO EXPERIMENTAL RESULTS
In a normal liver each lobule is functionally similar.
Consequently, a model representing the liver using one
average lobule or even a portion thereof may be adequate to
account for a specific drug outflow profile. For the first
outflow profile we find the simplest LOBULE design, given
restrictions: one that is comprised of the minimum
components needed to generate an acceptably similar
profile. An initial unrefined parameterization is chosen
based on available hepatic physical and anatomic
information. Components are added according to that initial
parameterization. If the behavior of the resulting LOBULE is
not satisfactory, any given piece of the LOBULE may be
4 of 4
discarded and replaced, or modified or reparameterized with
minimal impact on the other components within the device.
This process continues until the LOBULE generates outflow
profiles that are experimentally indistinguishable: after
averaging several runs, the result falls between P l and P u.
Once that parameterization is found, the parameter space is
searched further [10, 11] for additional, possibly betterperforming, solution sets2.
The typical in situ IPRL outflow profile is an account of
approximately 1015 drug molecules percolating through several thousand lobules. The typical in silico dose for one run
with one LOBULE is on the order of 5,000 drug objects,
where each drug object can represent a number (≥ 1) of drug
molecules. Thus, a single outflow profile will be very noisy
and will be inadequate to represent the referent in situ profile. In the latter part of such an outflow profile it is
increasingly possible to encounter a collection interval
during which no drug objects are collected. Another independent run using that same LOBULE , parameter settings,
and DOSE will produce a similar but uniquely different outflow profile. Changing the random number generator seed
alters the specifics for all stochastic parameters (e.g., placement of SSs on the digraph), thus providing a unique, individual version of the LOBULE , analogous to the unique
differences between two lobules in the same liver. One in
silico experiment combines the results from 20 or more
independent runs using the same LOBULE thereby producing
an outflow profile that is sufficiently smooth to use the SM.
It takes one or more experiments to represent an outflow
profile for an in silico liver. Note that an experimental
result comprising 20 runs of the LOBULE is analogous to
results one might obtain if one could conduct an in situ
perfusion experiment on only 4-to-5 liver lobules.
Fig. 3 shows results from one parameterization of a
LOBULE against an IPRL sucrose outflow profile. The
shaded region is a band enclosing the mean fraction of dose
collected for each collection interval. The width of the band
is ± 1 std about the mean. The filled circles are results
obtained using a LOBULE parameter vector that provides an
acceptable solution set according to the SM.
V. CONCLUSION AND DISCUSSION
We have tested and affirmed the hypothesis that IPRL
outflow data obtained following bolus administration of
sucrose can, in conjunction with other data, be used to
specify and parameterize a physiologically recognizable
hepato-mimetic device, an in silico liver. Furthermore, that
device can generate outflow profiles that are experimentally
indistinguishable from the original in situ data. This new
technology is intended to provide powerful tools for
optimizing the designs of real experiments and for
2
Solution set is the combination of the inputs and parameters that result in
the biomimetic behavior, plus the actual device that is biomimetic.
Fig. 3. An outflow profile for an HMD parameterized to match a
sucrose outflow profile. Nodes per Zone: 55, 24 and 3 for Zones I, II
and III, respectively; total edges: 60; intra-zone connections: Zone I =
10, Zone II = 8, Zone III = 0; inter-zone connections: IÆII = 14, IÆIII
= 4, IIÆIII = 14; SSs: 50% SA and SB; Number of runs = 100
challenging our understanding for how mammalian systems,
such as the liver, function in normal and diseased states,
when stressed, or when confronted with interventions.
These biomimetic devices are expected to evolve to become
suitable experiment platform to test hypothesis.
REFERENCES
[1]
Roberts MS, and Anissimov YG., “Modeling of Hepatic
Elimination and Organ Distribution Kinetics with the Extended
Convection-Dispersion Model, ”J Pharmacokin. Biopharm.,
vol. 27, no. 4, pp. 343-382, 1999.
[2] Noble D, “The Future: Putting Humpty-Dumpty Together Again,”
Biochem. Soc. Transact., vol.31, no.1, pp.156-158, 2003.
[3] Cheung K, Hickman PE, Potter JM, et al. “An Optimized Model for
Rat Liver Perfusion Studies,” J. Sur. Resh., vol.66, pp. 81–89, 1996.
[4] Hung, D.Y., Chang, P., Weiss, M., Roberts, M.S.: StructureHepatic Disposition Relationships for Cationic Drugs in Isolated
Perfused Rat Livers: Transmembrane Exchange and
Cytoplasmic Binding Process. J. Pharmacol. Exper. Therap.
vol.297, pp. 780–89 2001.
[5] Gumucio, J.J., and Miller, D.L., “Zonal Hepatic Function:
Solute-Hepatocyte Interactions Within the Liver Acinus,” Prog.
Liver Diseases, vol. 7, pp. 17-30, 1982.
[6] Roberts, M.S., Magnusson, B.M., Burczynski, F.J., and Weiss, M.,
“Enterohepatic Circulation: Physio-logical, Pharmacokinetic and
Clinical Implications,” Pharmacokinet, vol.41, pp. 751-790, 2002.
[7] Teutsch, H.F., Schuerfeld, D., and Groezinger, E., “ThreeDimensional Reconstruction of Parenchymal Units in the Liver
of the Rat,” Hepatology, vol. 29, pp. 494-505, 1999.
[8] Koo, A., Liang, I.Y., and Cheng, K.K., “The Terminal Hepatic
Microcirculation in the Rat,” Quart. J. Exp. Physiol. Cogn. Med.
, vol. 60, pp. 261-266, 1975.
[9] Miller, D.L., Zanolli, C.S., and Gumucio, J.J., “Quantitative
Morphology of the Sinusoids of the Hepatic Acinus,”
Gastroenterology, vol. 76, pp. 965-969, 1979.
[10] Sanchez, S.M., and Lucas, T.W., “Exploring the World of
Agent-Based Simulations: Simple Models, Complex Analyses,”
in Proceedings of the 2002 Winter Simulation Conference,
Yücesan, E., Chen, C.-H., Snowdon, J.L., and Charnes, C.M.,
Ed. 2002, pp. 116-126.
[11] Kleijnen, J.P.C., “Experimental Design for Sensitivity Analysis,
Optimization, and Validation of Simulation Models,” Series
Discussion Paper No. 1, Research Papers in Economics, Center
for Economic Research, Tilburg University, 2003.
Available: http://econpapers.hhs.se/paper/dgrkubcen/199752.htm
1 of 4
Representing Intestinal Drug Transport In Silico: An Agent-Oriented Approach
Yu Liu1, C. Anthony Hunt1, 2
1
UCSF/UCB Joint Graduate Group in Bioengineering, University of California, Berkeley, CA, USA
Biosystems Group, Department of Biopharmaceutical Sciences, University of California, San Francisco, CA, USA
2
Abstract—A prototype Epithelio-Mimetic Device (EMD)
was developed and tested. EMD components are designed to
map logically to biological components at multiple levels of
resolution. Those components are engineered to represent
actual components within an in vitro cellular system used to
study intestinal drug transport. Our goal is that the behaviors
of the EMD closely match observed behaviors of the in vitro
systems for a wide variety of drugs. Early stage system
verification is achieved. The general patterns of experimental
results from the EMD for a set of hypothetical drugs having a
variety of physicochemical properties reasonably match
observed patterns for a wide range of experimental conditions.
computational
Keywords—Agents,
transport, modeling, simulation
biology,
drug
I. INTRODUCTION
Emerging, advanced computational methods [1] are
expected to provide drug development and basic biomedical
researchers with improved abilities to make useful
predictions and to better understand how the small intestine,
and other barriers to drug absorption, function in the
presence and absence of various stresses, including disease,
at multiple levels of organization. The envisioned methods
will improve R&D efficiency. Here we present such a
method. It is based on a completely new technology that is
comprised in part of new tools for simulating complex
biological processes, and a completely new class of
biological analogue models that we refer to as biomimetic in
silico devices (BISDs). The in silico components of these
devices are designed specifically to be assembled into BIDS
that represent behaviors of in vitro cellular systems or the
intact intestine in vivo. Our approach consists of methods
for developing, testing, and refining BISDs, as well as
means for early stage system verification and evaluation.
Early stage system verification is intended to verify that the
BISD and its components perform as anticipated, to
characterize their available modes of operation and their
performances, and to become suitable objects for scientific
experimentation, analogous to in vitro systems that they
mimic. The devices are designed to generate behaviors and
are constructed from software components that are
specifically designed to map logically to biological
components at multiple levels of resolution. The objective
of this study has been to systematically collect evidence to
support the feasibility of a prototype device designed to
provide in silico experimental results for known and new
compounds that, in time, will be experimentally
indistinguishable from results from the current high
through-put in vitro cellular systems, such as the industry
standard, the Caco-2 cell line in use for studying intestinal
drug absorption and metabolism.
II. METHODOLOGY
A. The In Vitro Membrane System
The class of BISDs described here is intended to mimic
Caco-2 in vitro cell culture system that, in turn, is a
biological model taken to represent the mature epithelia
lining the villi of the small intestine (Fig. 1). Caco-2 cells
are typically grown to confluence (e.g., 21 days) on the
microporous membrane insert of the Transwell diffusion
cell system, and are then used in drug transport studies (Fig.
2a). The Transwell insert is taken to represent the apical
lumen compartment of the small intestine, and the cell
culture well (into which the insert fits) represents the
basolateral side of the intestine. The structure of our
prototype epithelio-mimetic device (EMD), diagrammed in
Fig. 2b and discussed more below, mimics the essential
features of the Transwell system.
Fig. 1. Small intestine villi structure. The mature epithelia lining the villi
are the active absorptive area. The enlargement shows the four processes
involved in drug intestinal absorption: 1a: Passive transcellular diffusion;
1b: Passive paracellular diffusion; 1c: Transporter mediated active
transcellular transport; and 1d: Transcytosis.
Fig 2. In vitro and in silico experimental devices for the study of intestinal
drug transport. (a). Caco-2 in vitro Transwell system. (b). Our prototype
epithelio-mimetic device (EMD).
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B. A Constructive Approach to Modeling
Our approach to modeling includes some new and
novel features. We use a constructive approach that focuses
more on the aspects of biological system structure and
behavior that give rise to data. We conceptually deconstruct
the system into biologically recognizable components and
processes that can be represented as software objects,
agents, messages, and events. Next, we reconstruct using
these objects within a software medium that handles
probabilistic events and message passing, and can represent
dynamic spatial heterogeneity. The process makes in silico
devices capable of biomimetic behaviors. We use device
(rather than model) to stress their modular, constructive
nature, to emphasize the essential and desired properties
described next, and to distinguish them from traditional
equation-based (TEB) models. BISDs are not intended as
substitutes or replacements for TEB models. They do not do
the same things. We expect that they will dramatically
expand the repertoire of modeling and simulation options
available to researchers.
C. Essential and Desired Properties
Reaching our goals requires stipulating in advance
several essential and desired properties that we believe EMDs
need to have. Key among them is the following: EMDs and
their components must be reusable, revisable, and easily
updateable without having to re-engineer the whole device.
Drug interactions with tissue and cell components are
characterized by probabilistic events. So, our EMDs are
exclusively event driven and most events can be probabilistic.
They need to be flexible and adaptable to be useful in a
variety of contexts for addressing a broad range of research
questions and capable of exhibiting a broad range of
behaviors. They should function at multiple levels of
resolution, from subcellular to organ. EMD components must
logically map to their biological counterparts. A goal is for
EMDs to have more in common with in vitro and some ex
vivo laboratory models, such as tissue cultures and perfused
tissues, than they do with TEB models. So, evolvability is
also essential. Spatial heterogeneity is a quintessential
characteristic of the intestine at each organizational level. So,
it is essential that device components be capable of
representing dynamic spatial heterogeneity at different levels
of resolution as required by the problem.
D. Epithelio-Mimetic Devices: Design and Function
Our methods depend upon Object-Oriented (software)
Design. Objects are instances of classes with both state and
behavior. Some objects can be agents. Agents are objects
that have the ability to add, remove, and modify events.
Philosophically, they are objects that have their own
motivation and agenda; they can initiate causal chains, as
opposed to just participating in a sequence of events
something else initiated. An EMD is an agent whose
purpose is to mimic aspects of the behavior in vitro
Transwell cell culture devices. Agents can contain spaces,
objects and other agents. When representing a biological
system one might use agents to represent a tissue, cells
within that tissue, and components within cells, such as
macromolecules or networks of molecules.
An EMD has a minimum of five parallel spaces, G1 –
G5, as illustrated in Fig. 2b. Components are not introduced
into a device unless it is required to solve the current
problem or account for current or past data. Each space is
currently represented as a N×N 2D grid. G1 represents the
apical lumen compartment and the fluid in the Transwell
cell culture insert. G2 represents the apical cell membrane
and junctions between cells (viewed from the apical side).
G4 represents basolateral membrane and junctions between
cells (viewed from the basolateral side). G3 represents
everything that is intracellular. G5 represents the basolateral
compartment and the fluid in the cell culture well. Solutes
and drug molecules are represented by mobile objects that
can move within and between spaces. Each mobile object is
identified by type and has its own identity. In this study
each object type represents a specific drug. Each MOLECULE1
type has its own list of properties (applied to each object of
that type). In this study the properties list includes three
physicochemical properties: MW, pKa, and P (partition
coefficient). The list can be reduced or extended to include
any number of properties.
The movement of an object is subject to the set of rules2
and those rules can be adjusted based on properties of
objects and space they are in. Within each space movement
is governed by a simulated diffusion algorithm. Between
different spaces, the movement is governed by probabilistic
transition rules.
E. Early Stage EMD Verification
Our goal is that when a drug object representing a
specific drug such as Alfentanil is placed in G1 its in silico
permeability in the EMD will be experimentally
indistinguishable from its permeability measured in vitro in
a particular experimental system. To accomplish this the
grid point properties and the within and between space
transition probabilities and rules need to be specified and
calibrated so that the behavior of the EMD reasonably
matches the accumulated literature evidence. That process
requires an iterative sequence of adjustments, experiments,
and comparisons.
Early stage system verification is
achieved when the general patterns of experimental results
from the newly constructed EMD for numerous in silico
drug objects reasonably match observed patterns for a wide
range of actual drugs that cover a wide range of the
physicochemical properties of interest.
F. Representing Permeation
When DRUG i is placed in G1 an apparent permeability
coefficient can be calculated from the appearance of DRUG in
G5 according to PEMD,i =(dQi /ds)/a•c0, where PEMD,i is the
1
The same word may be used to refer to a molecule or event in, or
component of, the referent system and the corresponding in silico object or
event. In the latter case the word is written using small caps.
2
The rules can be simple or complicate; they may include an equation or
depend on the outcome of running a separate model.
3 of 4
apparent permeability of DRUG i measured in silico, dQi/ds is
the incremental change in the number of drug objects in G5
following simulation (time) step ds, a is the area of G2/G4,
and c0 is the initial “concentration” of DRUG i in G1 at time
step 0. The various parameters and rules of the model,
including the transition probabilities, are adjusted over a
range of experimental conditions so that for several different
DRUGS PEMD ~ {the apparent permeability coefficients
measured in vitro} [2]. The in silico studies documented the
influence of three interrelated physicochemical properties
(lipophilicity, ionization, and molecular size [3]) on DRUG
permeability, as well as concentration gradient on the
permeation rate. We assume that small (≤ 200 Dalton)
water-soluble DRUGS having P (partition coefficient) values
less than 2 [4] pass through cell monolayers only by passive
paracellular diffusion through aqueous pores. We also
assume that transmembrane movement of the unionized
fraction (calculated by environmental pH and the DRUG’S
pKa) of drug increases with increasing logP (increasing
lipophilicity) values up to 2.5~3.5 and declines thereafter [5,
6]. MW is used as the simplified molecular size descriptor
and is related to the in silico DIFFUSION COEFFICIENT (DEMD,i):
DEMD,i ∝ 1/(MWi)n). In these studies we assume n = 1 in
lipoid membrane and 0.6 in aqueous fluid.
III. RESULTS
The following experiments and their results show the
general relative patterns for results of experiments
conducted using the prototype EMD and numerous DRUGS
over the full range of EMD operation and over the full range
of the three physicochemical properties of interest. The
passive paracellular and transcellular transport of the
prototype EMD were evaluated over a wide initial
concentration range for two hypothetical drugs, both weak
bases with pKa = 6.5. One (DRUG I) is hydrophilic (logP =
0.2) with MW = 150. The other (DRUG II) is a hydrophobic
drug (logP = 2) with MW = 500. The in silico pH of G1
and G3 was fixed at 7.4. EMD concentration-time profiles
were recorded and the initial rate of DRUG permeation was
calculated under sink condition (≤ 10% initial DRUG in G1 is
transported into G5). Results are presented in Fig. 3.
Higher initial concentrations resulted in larger rates of
permeation for both hydrophilic and hydrophobic DRUGS, as
expected. Transcellular transport had a higher permeation
rate than paracellular transport due to the smaller surface
area in paracellular pathway (< 1000 fold) [7].
The rate of intestinal absorption is known to be
positively correlated with partition coefficient [8]. Membrane
permeability as a function of lipophilicity can exhibit
different patterns: linear, hyperbolic, sigmoid and bilinear
[3]. A set of sigmoidal relationships result from the
additional influence of MW [3, 5]. The EMD was
initialized to generate experimental results that reflect those
Fig. 3. Rate of permeation across an in silico EPITHELIA from experiments
using the prototype EMD at 12 different initial numbers of DRUGS
(representing initial concentration).
characteristics. To examine the consequences, the passive
permeability of five sets of DRUGS (MW values of 100, 150,
300, 500, and 700) was calculated from EMD experimental
results with logP values ranging from very hydrophilic
(logP = – 2) to very hydrophobic (logP = 4). For DRUGS
with logP < 3.5, a set of sigmoidal curves is observed (Fig.
4). For larger DRUGS, the curves are shifted to lower
permeabilities. Four patterns are observed, consistent with
the cited literature. DRUGS with small logP values are too
hydrophilic to significantly cross cell membranes, so the
passive paracellular pathway dominates for the two sets
with MW ≤ 150. For more hydrophobic DRUGS paracellular
transport is negligible and transcellular permeability is
strongly dependent on lipophilicity. For those drugs with
2.5 ≤ logP ≤ 3.5, the expected permeability plateaus are
reached. For more hydrophobic DRUGS, permeability
decreases with increasing lipophilicity.
Each portion of the human gastrointestinal tract
typically has a different pH. In the major absorptive part of
small intestine duodenum, pH 6.0 - 6.5 favoring absorption
of weak base drugs. We obtained results from EMD
experiments for one weak base DRUG Alfentanil with
properties (Table I) specified.
We changed pH in
G1(corresponding to a large variation in the degree of
ionization for Alfentanil) and used Monte Carlo simulation
for 8 experiments per pH value. Results are shown in Fig.
5. The rescaled permeability obtained in our EMD is in the
range of 81.9 to 101.8 × 10-6 cm/sec when the G1 properties
correspond to pH 8.0 and the patterns observed are
consistent with expectations [9].
IV. DISCUSSION
These results verify that for the conditions tested, the
prototype EMD exhibits patterns of drug permeability
behavior that are similar to those reported for in vitro
4 of 4
xenobiotics out of epithelial cells back into the lumen where
they can be degraded by bacteria. CYP3A4, the dominant
isoform of cytochrome P450 in epithelial cells, plays an
important role in the first pass effect for many drugs. Our
EMD is designed to easily add (and remove) components
(agents, objects and spaces) that can map to transporters and
enzymes to enable such an upgraded EMD to account for an
increasing fraction of observed drug transport properties.
Subsequently, guided by appropriate data, additional
components can be designed and added to account for
localized heterogeneous system properties including
intracellular transport systems and gene up- and downregulation.
ACKNOWLEDGMENT
Fig. 4. Influence of logP and MW on DRUG permeability (logPapp) from
experiments using the prototype EMD.
TABLE I
PHYSICOCHEMICAL PROPORTIES OF DRUG ALFENTANIL
Basic drug
MW
logP a
pKa a
Papp(10-6cm/sec) b
Alfentanil
416
2.16
6.5
93.5
a
Data from [9]. There is slight difference from those obtained in Chemical
Abstract Database, where Alfentanil’s pKa is 7.59, and logP is 2.033.
b
In Ref [9], 1.2 mM Alfentanil transported across Caco-2 cell monolayers
at pH 8.0 at a low stirring rate of 100 rpm.
experiments. Additional experiments are underway to further
verify that the EMD can generate experimental results that are
experimentally indistinguishable from in vitro results for a
variety of compounds. These verification studies have
focused on passive transport through paracellular and
transcellular pathways, the routes for a majority of drugs.
However, in the intestine active transport and
biotransformation of many important drugs do occur. These
processes are part of the body’s robust defense system
against potentially harmful xenobiotics. P-glycoprotein,
present on apical epithelial membranes, actively transports
Fig 5. In silico pH-dependent transport of a DRUG Alfentanil within the
EMD. (a) Simulated permeability has a linear relationship with fraction of
un-ionized DRUG. (b) EMD permeability as a function of G1 pH.
We thank Cindy (Song) Chen for helpful software
engineering discussions and the other members of
Biosystems Group for their helpful discussions, assistance,
and support.
REFERENCES
[1] H. Kitano, “Systems biology: a brief overview.” Science vol.
295, pp. 1662-1664, 2002.
[2] P. Artursson and J. Karlsson, “Correlation between oral drug
absorption in humans and apparent drug permeability coefficients
in human intestinal epithelia (CACO-2) cells.” Biochem. &
Biophy. Res. Comm. vol. 175, no. 3, pp. 880-885, 1991.
[3] G. Camenisch, G. Folkers, H. Waterbeemd, “Reviews of
theoretical passive drug absorption models: historical
background,
recent
developments
and
limitations.”
Pharmaceutica Acta Helvetiae, vol. 71, pp. 309-327, 1996.
[4] H. Kalant, and W. H. E. Roschlau, Principles of Medical
Pharmacology, Oxford University Press, 1998.
[5] G. Camenisch, J. Alsenz, H. Waterbeemd, G. Folkers,
“Estimation of permeability by passive diffusion through Caco-2
cell monolayers using the drugs’ lipophilicity and molecular
weight.” Euro. J. Pharma Sci. vol. 6, pp. 313-319, 1998.
[6] P. Wils, A. Warnery, V. Phung-Ba, S. Legrain and D. Scherman,
“High lipophilicity decreases drug transport across intestinal
epithelia cells.” JPET, vol. 269, no. 2, pp. 654-658, 1994.
[7] P. Artursson, K. Palm, K. Luthman, “Caco-2 cells in
experimental and theoretical predictions of drug transport”. Adv.
Drug Deliv. Rev. vol. 46, pp. 27-43, 2001.
[8] Y. C. Martin, “A practitioner’s perspective of the role of
quantitative structure-activity analysis in medicinal chemistry.”
J. Med. Chem. vol. 24, no. 3, pp. 229-237, 1981.
[9] K. Palm, K. Luthman, J. Ros, J. Grasjo, P. Artursson, “Effect of
molecular charge on intestinal epithelial drug transport: pHdependent transport of cationic drugs.” JPET. vol. 291, no. 2, pp.
435-443, 1999.
1 of 4
The Necessity of a Theory of Biology for Tissue Engineering:
Metabolism-Repair Systems
Suman Ganguli and C. Anthony Hunt*
Biosystems Group, Department of Biopharmaceutical Sciences, and The Joint UCSF/UCB Bioengineering Graduate Group
The University of California, San Francisco, CA 94143, USA
Abstract—Since there is no widely accepted global theory of
biology, tissue engineering and bioengineering lack a theoretical
understanding of the systems being engineered. By default,
tissue engineering operates with a "reductionist" theoretical
approach, inherited from traditional engineering of non-living
materials. Long term, that approach is inadequate, since it
ignores essential aspects of biology. Metabolism-repair systems
are a theoretical framework which explicitly represents two
“functional” aspects of living organisms: self-repair and selfreplication. Since repair and replication are central to tissue
engineering, we advance metabolism-repair systems as a
potential theoretical framework for tissue engineering. We
present an overview of the framework, and indicate directions to
pursue for extending it to the context of tissue engineering. We
focus on biological networks, both metabolic and cellular, as one
such direction. The construction of these networks, in turn,
depends on biological protocols. Together these concepts may
help point the way to a global theory of biology appropriate for
tissue engineering.
Key Words—Theoretical biology, bioengineering, selfrepair and self-replication, metabolism-repair systems
*
I. INTRODUCTION
Traditional engineering is based on solid theories of how
and why things work as they do. Engineering within the
domain of biology presents challenges because there is no
widely accepted global theory of biology, even though there
are standing theories dealing with aspects of biology, such
as the Mendelian theory of particulate inheritance. Without
a global theoretical framework, bioengineering efforts move
forward principally by trial and error on a foundation that
biological systems can be treated as machines. However,
current efforts in cell and tissue bioengineering can help
motivate development of such a theory, and parallel efforts
to develop such a theory should prove synergistic to those
bioengineering efforts. Bioengineering will benefit by
fostering, working within, and contributing to theory.
In this paper, we attempt to initiate such a synergy by
exploring the applicability of a proposed global theoretical
framework for biology to tissue engineering. That theory is
the metabolism-repair systems formalism, initially
developed by the theoretical biologist Robert Rosen.
Rosen’s work contained a strong criticism of reliance on
the Newtonian “reductionist” approach to understanding
biological systems. The Newtonian approach assumes that any
system can be understood (and furthermore, fabricated) by
*
Correspondence: hunt@itsa.ucsf.edu and/or
sganguli@itsa.ucsf.edu
understanding the physical forces (chemical, mechanical, etc.)
acting upon the constituent materials of the system. In other
words, any biological system can be “reduced” to its
materials and the forces at work on them. Mathematically,
this approach translates to the classical formalisms of
dynamical systems, differential equations, and input-output
systems.1
Heuristically, the Newtonian reductionist approach
treats living organisms as being analogous to machines [2].
In particular, the problems of engineering living tissue are
approached as analogous to those of engineering machines.
Bioengineering in general, and tissue engineering in
particular, has proceeded thus far largely by trial and error
guided by a reductionist approach. This is natural, since
that approach is inherited from traditional engineering, i.e.,
engineering of non-organic, non-living matter.
The nascent field of “systems biology” is based on the
realization that the reductionist approach to biology is
limited, and that a systems-level, organizational approach
must be adopted [3, 4]. Along these lines, we argue that
there are organizational and functional aspects of living
tissues that tissue engineering must address in a theoretical
manner if it is to move to the next level and begin the
serious business of engineering living systems.
The metabolism-repair framework offers a route for
doing so. It augments the reductionist “materials-only”
approach by explicitly addressing two “functional” activities
essential to living organisms: self-repair and selfreplication2. Within the metabolism-repair framework,
these activities are represented by functions.
These
functional components are included within and regulated by
the theoretical representation of the organism itself. Thus,
living organisms are explicitly represented as self-repairing
and self-replicating.
We begin by introducing the metabolism-repair
framework. Our immediate goal is to begin to translate the
concepts of the metabolism-repair formalism to the context
of tissue engineering. The metabolism-repair formalism
focuses on and is developed within the context of single cell
organisms. The theory has not been extended to address the
1
For example, the traditional approach to mathematical modeling
of morphogenesis “ assumes that each biological form is the
solution to a difficult calculus problem” [1]. The same article
quotes a molecular biologist’s experience with this approach:
“ Physicists are very dogmatic in saying that everything in these
systems can be explained with physics. I cannot believe that.”
The point is then made that organisms are organized mainly by
their genes, and Drosophila is given as a prime example.
2
Here, the concept of replication is not limited to replication of the
cell but extends to replication of any somewhat modular system,
such as a mitochondria or an endocytotic vesicle.
2 of 4
three-dimensional, hierarchical topology essential to most
biological domains, including mammals. We indicate a
direction for incorporating hierarchical topologies into the
metabolism-repair framework, via the concepts of networks
and protocols.
II. BACKGROUND
We begin with a brief exposition of the metabolismrepair framework. We refer the reader to [5], [6], [7], and
[8] for further details.
Let A represent a set of inputs and B a set of outputs. In
the initial context of a single cell, A could represent the set
of environments in which a cell operates3, and B the set of
cellular metabolic configurations4 [6].
The metabolism of a cell is then represented by a
function
f: A → B
We let H(A, B) denote the set of all physically and
contextually realizable maps between A and B (i.e., those
maps satisfying the physicochemical constraints of the
materials). Then f is an element of the set H(A, B). We
suggest that, given a tissue engineering objective, there exists
a minimal subset of f about which the bioengineer should be
sufficiently knowledgeable so that s/he can make optimum
use of that information during engineering decision making.
At this point the framework represents simply the
classical “ materials-only” input-output relationship. The
metabolic activity of a living cell, however, must have the
means to sustain itself.
This need requires and is
implemented, in part, by repair activities. Those processes
are represented within the formalism by a repair function P.
Such a repair function reconstitutes a METABOLISM5 from the
members of the set outputs, B. Recall that a METABOLISM is
an element of H(A, B). Thus, repair is represented by a
function
P: B → H(A, B)
Using the notation introduced above, the repair function P is
an element of the set of maps H(B, H(A, B)). Here also, we
suggest that, given a tissue engineering objective, there
exists a minimal subset of P about which the bioengineer
should be sufficiently knowledgeable so that s/he can make
optimum use of that information during engineering
decision making.
The repair function P may be interpreted simply as a
representation of the processes employed by the cell to
sustain itself as components of its metabolic machinery
degrade and need repair. Similarly, however, the repair
processes themselves degrade. Rather than invoking an
additional entity to repair the repair function, which would
3
These will include “ raw materials” that are taken in from outside
the cell plus recycled materials.
4
These will include gene products and the cellular components
composed of those products.
5
The definition and use of this term is new. To distinguish it from
traditional usage we use small caps.
quite obviously lead to an infinite sequence of repairers,
Rosen introduced REPLICATION6 into the framework.
In biology, replication processes allow the cell to
replace its repair machinery with a new version. In the
metabolism-repair formalism, REPLICATION is a function
which takes as input an existing METABOLISM and outputs a
new repair map. Thus, REPLICATION is represented by a
function
R: H(A, B) → H(B, H(A, B))
Where does the replication function come from?
Rosen’s central result was to show that replication arises
from the system of metabolism and repair itself. By
examining these mappings in the context of Category
Theory [9], he showed that, under certain conditions, the
replication map R could be identified with an element of the
set B. Hence replication does not need to be engineered
from outside the system, and the system of metabolism,
repair and replication is closed. It is in this sense that the
metabolism-repair formalism represents a theory of selfreplicating and self-repairing systems.
Here yet again, we suggest that, given a tissue
engineering objective, there exists a minimal subset of R
about which the bioengineer should be sufficiently
knowledgeable so that s/he can make optimum use of that
information during engineering decision making.
III. METHODS
Rosen took a strong ontological stance regarding the
“ functional” components of REPLICATION and repair in the
metabolism-repair framework. He viewed them not as just
mathematical constructs, but as representing real and
essential aspects of living organisms. We can then ask: if,
indeed, biological counterparts for the mathematical
mappings do exist, then what are they and where are they?
We propose that the concept of networks may lead to
the biological locations of the functional repair and
replication components. At the level of the single cell,
repair and replication may reside within the metabolic
network. This is addressed in the treatments of metabolismrepair systems in [7] and [8], so we do not repeat those
observations here. We note, however, that recent analyses
of metabolic networks have indicated that, more than the
materials that make them up, it may be the structures of the
networks that are conserved by evolution [10]. This in itself
begins to hint at the importance of “ relational” (versus
strictly “ material” ) aspects of biology, which Rosen saw the
metabolism-repair framework as addressing [8].
We believe these ideas may be applied toward the task
of scaling up the concepts of metabolism-repair systems to
address multicellular tissues. Metabolic networks contain
an implied intracellular topological component behind
replication and repair in the single cell case. Similarly,
cellular networks may be an essential dynamic topological
component behind replication and repair in the multicellular
case. In order for multicellular tissues to have functional
repair and replication components, the local repair and
replication components of the constituent cells must be
6
As with METABOLISM, the definition and use of this term is new.
To distinguish it from traditional usage we use small caps.
3 of 4
integrated into global repair and replication components for
the organism as a whole. We conjecture that this integration
is determined by the cellular network’s dynamic topology.
Reference [5] contains a sketch of some ideas in this
direction, with a brief discussion of cellular metabolismrepair networks. These are mentioned as a direction of future
study, with great potential for insight into areas relevant to
tissue engineering, such as cellular differentiation. It is a
direction that, to our knowledge, has yet to be pursued.
A longer-term program is to extend the metabolismrepair framework to an even wider variety of biological
contexts. One avenue for doing so may be to focus on the
concept of functional units. The clearest example of a
biological functional unit is the single cell. Subcellular
organelles may also be identified as functional units. Most
relevant to tissue engineering, of course, are multicellular
functional units that make up organs, and ultimately organs
themselves. In this sense, tissue engineering is involved in
the reconstruction of multicellular functional units outside
of their original context in vivo. Hence, tissue engineering
could benefit from a theory of functional units. The
metabolism-repair framework may be the basis of such a
theory. The concept of a functional unit is an intuitive one,
but it lacks a precise definition. Since the capacities for
self-repair and self-replication seem like they are central to
functional units, it may be that metabolism-repair systems
are a formalism for describing functional units.
Finally, we discuss some potential connections between
the ideas discussed above and another recently developed
abstraction of biological systems: protocols. Csete and
Doyle, in describing aspects of engineering theories that can
be applied to complex biological systems [11], focus on the
importance of what they call protocols. They define
protocols as rules that arise repeatedly in systems as
interfaces between “ modules.” As examples of biological
protocols, they cite a list of diverse abstractions: gene
regulation, signal transduction pathways, cell-mediated
activation, and many others.
Any engineered system cannot ignore the relevant
protocols. Hence, bioengineering efforts must discover the
biological protocols essential to the systems being
engineered. This in itself is another important point for
consideration by the tissue engineering community.
With respect to the ideas of biological networks
mentioned above, however, Csete and Doyle note that the
protocols are central to understanding and engineering
biological systems in part because they facilitate evolution.
Protocols allow existing systems to be cobbled together,
thus allowing the evolutionary construction of novel
systems. Csete and Doyle call this process “ evolutionary
tinkering,” and argue that it is essential to the robustness and
modularity of biological systems.
From this, it is possible to see roles for protocols in
biological networks. It has been widely observed that
biological networks are robust and highly modular (scalefree). Indeed, it has been noted that these aspects of
biological networks can be attributed to the fact that they
arise from evolutionary tinkering [12]. Thus, protocols may
in fact be the mechanisms that allow the evolutionary
construction of biological networks.
Returning finally to the repair and replication, we have
conjectured that these functions may be located within
certain biological networks, whether metabolic or cellular.
This indicates that biological protocols play a central role in
constructing these functions. We may go further and
speculate that replication and repair are themselves
protocols of a sort, but that they are “ meta-protocols.” They
are the protocols essential to life, and all other protocols are
the ingredients that give rise to replication and repair, via
the construction of appropriate networks.
Our premise is that in order to make progress on
engineering living tissues, we need a theory of biology.
However, in order to make progress in building such a
theory, we conversely need ways to test ideas.
Computational modeling and simulation methods may be
the best available bridge between theory (of metabolismrepair systems, for example) and practice (of
bioengineering) [13]. The theoretical frameworks described
above are abstract and far removed from the biological
reality. For example, to test hypotheses about aspects of the
theory, we first need ideas that posit form and location of
the repair and replication maps. We can begin to make
progress in this direction by developing modeling and
simulation techniques where the model components map to
the biological system in a natural way, yet also encode
aspects of the theoretical framework.
We believe that the envisioned modeling and
simulation techniques will have more in common with in
vitro model systems than with traditional modeling and
simulation methods, in that they will need to be dynamic,
flexible, adaptable, and thus capable of capturing multiple
aspects of the biological system. They should also be
capable of automatic model revision and extension when the
simulation system is presented with new data. The
Functional Unit Representation Method (FURM) is a step in
that direction in that it encompasses many of the concepts
discussed above [14]. As its name indicates, FURM focuses
on modeling at the level of biological functional units, and
initial applications of FURM have represented biological
networks. In the future, FURM may serve as a method of
discovering and testing biological protocols in silico, and
eventually may incorporate prototypes of the repair and
replication maps of the metabolism-repair framework.
IV. CONCLUSION
Over 30 years ago, Robert Rosen recognized the
applicability of his work to fields such as tissue engineering:
“ We may envisage the construction of artificial engineering
systems manifesting organizational characteristics of
biological organisms. Such attempts have been pursued for
a long time, especially in the area of artificial intelligence,
the design of artificial biological organs, and so forth, but
never in a completely systematic manner” [8].
Tissue engineering has been pursuing such attempts at
an ever-accelerating pace. But without a theory of living
organisms in place, it will continue to do so in an
unsystematic manner. Rosen’s metabolism-repair systems,
by treating in a theoretical manner the essential biological
processes of self-repair and self-replication, may be a path
to a theory of biology useful for tissue engineering.
ACKNOWLEDGMENT
This work was supported in part by funding provided by the
4 of 4
PhRMA Foundation. We thank the members of the
Biosystems Group at UCSF and Glen Ropella of Tempus
Dictum, Inc. for helpful discussions.
REFERENCES
[1] A. Cho, “ Life’ s patterns: no need to spell it out?”
Science, vol. 303, pp. 782-3, 2004.
[2] G. Bock and J. Goode, eds. The Limits of Reductionism
in Biology: Novartis Foundation Symposium 213.
Chichester; New York: J. Wiley, 1998.
[3] T. Ideker, T. Galitski, and L. Hood, “ A new approach to
decoding life: systems biology,” Ann. Rev. Hum. Genet.,
vol. 2, pp. 343-372, 2001.
[4] O. Wolkenhauer, “ Systems biology: the reincarnation of
systems theory applied in biology?” Brief Bioinform.,
vol. 2, pp. 258-270, 2001.
[5] J.L. Casti, “ The theory of metabolism-repair systems,”
Appl. Math. Comput., vol. 28, pp. 113-154, 1988.
[6] J.L. Casti, “ Biologizing control theory: how to make a
control system come alive,” Complexity, vol. 7, no. 4,
pp. 10-12, 2002.
[7] J.C. Letelier, G. Marin, and J. Mpodozis, “ Autopoietic
and (M,R) systems,” Journal of Theoretical Biology,
vol. 222, pp. 261-272, 2003.
[8] R. Rosen, “ Some relational cell models: the
metabolism-repair systems,” in Foundations of
Mathematical Biology, vol. 2, R. Rosen, ed. New York:
Academic Press, 1972, ch. 4, pp. 217-253.
[9] F.W. Lawvere and S.H. Shanuel, Conceptual
Mathematics: A First Introduction to Categories,
Cambridge University Press, 1997.
[10] Y.I. Wolf, G. Karev, and E.V. Koonin, “ Scale-free
networks in biology: new insights into the fundamentals
of evolution?” Bioessays, vol. 24, no. 2, pp.105-109,
2002.
[11] M.E. Csete and J.C. Doyle, “ Reverse engineering of
biological complexity,” Science, vol. 295, pp. 16641669, 2002.
[12] U. Alon, “ Biological networks: the tinkerer as
engineer,” Science, vol. 301, pp. 1866-1867, 2003.
[13] D. Noble, “ The rise of computational biology,” Nat.
Rev. Mol. Cell Bio., vol. 2, pp. 460-463, 2002.
[14] G.E.P. Ropella and C.A. Hunt, “ Prerequisites for
effective experimentation in computational biology,”
http://citeseer.ist.psu.edu/575600.html.
1 of 4
Applying Models of Targeted Drug Delivery to Gene Delivery
Tai Ning Lam and C. Anthony Hunt*
Biosystems Group, Department of Biopharmaceutical Sciences
University of California, San Francisco, School of Pharmacy, CA 94143, USA
Abstract—Gene delivery requires targeted delivery
systems. Exploratory simulations using models of targeted
drug delivery helps one assess the worthiness of such
systems, and helps quantify the expected therapeutic benefits
of the systems. The drug targeting index (DTI), a ratio of
availabilities, is a measure of pharmacokinetic benefit of the
delivery device, based on a combination of a physiologicallybased pharmacokinetic model and a single pharmacodynamic
Emax model. Pharmacodynamic outcomes are quantified by
the degree of separation between the dose-response and dosetoxicity curves (SRT).
Simulations are undertaken to
investigate the potential linkage of DTI and SRT, a
pharmacodynamic outcome. A significant positive linear
relationship is found between the DTI and SRT. The
relationship can be translated into a minimum
pharmacokinetic requirement that can be used to guide
making decisions regarding whether or not further pursue the
development of a candidate gene-delivery device as a
therapeutic agent.
Key Words—Targeted drug delivery, gene delivery,
population pharmacokinetics, pharmacodynamic, modeling,
simulation, systems biology
I. INTRODUCTION
Gene delivery faces intrinsic difficulties: genes or
gene-interfering agents, in form of plasmid, singlestranded or double stranded RNA or DNA, or short
oligonucleotides, cannot readily access their target
response sites – the nuclei of a specific cell group. Giving
a huge dose of free RNA or DNA, and hoping that enough
will distribute into target tissues does not work. On one
hand, free RNA and DNA cannot freely permeate cellular
membranes. On the other hand, free RNA and DNA are
rapidly degraded in the circulation. They therefore must
be protected by some carrier, or be chemically modified to
make them resistant to degradation.
Hence, there is a
need for targeting. Gene delivery to a specific cell group
usually requires targeted delivery devices, such as cationic
liposomes or viral vectors. Engineering an efficient
delivery system is a must to ensure proper gene delivery,
and in turn, expected efficacy. Hence, it is prudent to use
models of targeted drug delivery to analyze any candidate
gene delivery system and thereby help inform the decision
making process involved in development as a therapeutic
agent. Failure to identify poor candidate delivery systems
will result in a lengthy yet unsuccessful development
program, not to mention the burden of the financial loss.
Better-informed assessment is critical early in the drug
development process.
*
Correspondence: hunt@itsa.ucsf.edu
This study applies a physiologically-based population
pharmacokinetic model of targeted drug delivery to gene
delivery. The model used [1], provides a pharmacokinetic
assessment of the targeting device, namely, the drug
targeting index, DTI, which is a ratio of availability of
drug in the target response compartment to its
corresponding availability at the sites that give rise to
toxicity. DTI is conveniently taken as the ratio of area
under the concentration-time curves (AUC) or the ratio of
drug exposures at the two sites. In the simplest sense, if
one assumes steady state delivery, the DTI equals the ratio
of the level of drug or transcriptionally active genes at the
response site(s) to the corresponding level at the sites of
toxicity. It will be shown in this report, that such
pharmacokinetic assessments can directly reflect
pharmacodynamic consequences and thus can be a good
estimate of expected performance in terms of increasing
the separation between of dose-response and dose-toxicity
curves. These simulation experiments are populationbased so as to provide some insight into expected intersubject variability. That variability can have a have a
decisive impact on how likely it is that the device under
study functions as intended.
II. METHODS
A. Simulations
The physiologically-based pharmacokinetic model is
a simplification of that described earlier [1]. Briefly, the
body is represented as two physiologic compartments.
For the sake of discussions of gene delivery, the response
site is taken as the specific groups of cell to which genes
need to be delivered in order to generate the desired
pharmacological response.
The site of toxicity is
conservatively taken as everywhere else in the body. DTI
is the ratio of active levels at these two sites. A set of
differential equations is solved using the steady state
assumption to give concentrations at the two sites in terms
of dose (D), blood flows (to response site, Qr, and to the
site of toxicity, Qt), extractions at each site (at Er and Et),
delivery to each site (to response site, Fr, and to the site of
toxicity, Ft) and fu is the uncompromised fraction (for a
drug, bound)—the fraction available to generate gene
products. The values of Cr and Ct are given by the
following equations.
2 of 4
Cr =
Ct =
[
( )
D × (1 − fuEr ) × (Qr + fuQt Et ) Qr + (1 − fuEt ) × Ft
[
F
r
fu × (Qr Er + Qt Et )
D × (1 − fuEt ) × (Qt +
)(
F
fuQr Er Qt
t
]
)+ (1− fuE ) × F ]
r
r
fu × (Qr Er + Qt Et )
As
a
first
approximation,
a
simplistic
pharmacodynamic model is used.
Briefly, the
pharmacological effects follow a single Emax model for the
uncompromised level of active species at the response
site. The uncompromised fraction (unbound fraction for a
drug) is used because Tachibana et al [2] observed that
only a small fraction of delivered plasmid can be
transported into the nucleus to become available for
transcription
or
interference.
Although
the
pharmacodynamic model oversimplifies the complicated
sub-cellular processes, it allows assessment of the overall
pharmacodynamic outcomes of the targeted delivery of
genes or a drug given a simple steady state concentration.
The parameters are apparent maximum effects (of
response, Pmax, and of toxicity, Tmax) and apparent
concentrations at which half-maximal effect is seen (of
response, CP,50, and of toxicity, CT,50). The following
equations are used.
× fuC t
× fuC r
P
T
Response = max
Toxicity = max
fuC r + C P ,50
fuC t + C T ,50
TABLE 1:
SUMMARY STATISTICS OF THE POPULATION N = 1000
Variable
Mean
Blood flow to response site (Qr )
Blood flow to toxic site (Qt)
Extraction at response site (Er)
Extraction at toxic site (Et)
Delivery to response site (Fr)
Delivery to toxic site (Ft)
Uncompromised fraction (fu)
Apparent maximum response (Pmax)
Apparent maximum toxicity (Tmax)
Apparent concentration for halfmaximal response (CP,50)
Apparent concentration for halfmaximal toxicity (CT,50)
Median Std Dev
5.05
4978
0.900
0.896
0.0990
0.901
0.100
100
100
5.05
4974
0.987
0.990
0.0972
0.903
0.0768
101
101
3.00
495
0.177
0.182
0.0199
0.0199
0.0923
20.4
19.6
9.89e-5
9.89e-5
1.97e-5
2.00e-3
1.99e-3
4.02e-4
study, it is approximated by summing, over all doses, the
difference between response and toxicity at each dose:
∑Dose[(Response - Toxicity)].
B. Derivation
A single Emax expression can represent multiple
subcellular processes, if a single Emax model can represent
each of them, in turn.
B
×B
A
×A
Suppose B = max
and C = max
B 50 + B
A50 + A
A
A50
B max ×
A
1+
A50
C=
A
A max ×
A50
B 50 +
A
1+
A50
A max ×
The simulations are run using a population of N =
1000 hypothetical subjects. The values of each subject’s
individual variable are sampled from either a normal or a
beta distribution having a specified mean and coefficient
of variation. The key summary statistics that give rise to
the individual parameters of the population are listed in
Table 1.
To quantify pharmacodynamic benefit, each subject
is simulated to receive 14 doses, from 0.001 to 20, so as to
follow the entire dose-response and dose-toxicity curves.
The total separation between the response and toxicity
curves (SRT) is a pharmacodynamic assessment of the
drug. Graphically, it is the area between the response and
toxicity curves, shown as the shaded area in Fig 1. In the
B max × A max
×A
(B 50 + Amax )
=
B 50 × A50
+A
(B 50 + Amax )
is a E max model in A.
The effect of exposure is estimated by the area under
the effect-time curve (AUE), integrated from time zero to
infinity. Effect is represented using the above as an Emax
model. Following a bolus dose, in which the
concentration falls exponentially, AUE is derived as
follows.
∞ Emax × C
AUE =
dt
0
K +C
∫
Fig. 1. Dose-response and dose-toxicity curves. The shaded area is
the total separation of response and toxicity (SRT), and is a measure
of pharmacodynamic benefit.
∞
Emax × C 0 e − λ t
=
∫0
=
Emax
K + C 0 e −λt
λ
C ⎞
⎛
ln ⎜ 1 + 0 ⎟
K ⎠
⎝
dt
3 of 4
III. RESULTS
Fig. 2 depicts the relationship between the drug
targeting index (DTI) and the separation between the
response and toxicity curves (SRT). The pharmacokinetic
assessment, i.e., the DTI, is linearly related to the
pharmacodynamic assessment, the SRT. The significance
of this relationship is that, given a favorable
pharmacokinetic profile (e.g., high Fr /Ft in particular)
and information supporting that the assumptions are
reasonable, one can assert that the targeted drug will
perform well in the population, pharmacodynamically,
without having to actually test it in the population. The
DTI, in turn, is a valuable assessment of worthiness of
developing the candidate, targeted drug delivery system,
as it provides estimates of the expected pharmacodynamic
outcomes, before a clinical trial is run. A candidate drug
having a too small a DTI can be confidently dropped from
development for the reason that it is not likely to be
clinically successful.
It is possible to estimate a minimum DTI requirement
to be qualified for further development, if one has a sense
of how much separation of response and toxicity is
desired in the average patient. Suppose, it is arbitrarily
chosen that a minimum separation of 25 units is desired if
one assumes there is little toxicity associated for such a
“low” dose, then it is a quarter of maximum
transcriptional capacity of a gene, which can be a
substantial amount. The results of simulations show that
at the optimal dose (at which the maximum separation is
achieved) one actually obtains only about 15% of the total
achievable separation of about 167 units; that translates
into a DTI of about 3.8. So, a candidate drug for which
DTI = 3.81, can be expected to give a response-toxicity
separation of 25 units, at the optimal dose in the average
patient. Conversely, if a candidate is observed or
estimated to have a DTI of 3.8, then a separation of 25
can be expected in the average patient. The relationship
between SRT and DTI is thus translated into a guide for
drug development decision making.
IV. DISCUSSION
It is of interest to contrast predictions made using the
above over-simplified model with one that is more
complicate. Rowland et al[3] proposed a subcompartment
analysis at the response site to account for flux between
subcompartments. The same concepts as above can be
used
to
represent
and
simulate
intracellular
pharmacokinetics and nuclear transport. Kamiya et al [4]
and Tachibana et al [2] also proposed simple zero-order
or first-order intracellular models for intracellular
trafficking of gene and gene expression. So, modeling the
subcellular processes with these models will be the next
step. These more sophisticated models would be expected
to give a more detailed description of the intracellular
1
DTI = 3.8 means that the targeted delivery device successfully
delivers approximately 4 fold higher levels to target cells,
relative to an intravenous dose of untargeted therapeutic.
500
400
300
200
100
0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Fig. 2. The relationship between total SRT (y-axis) and logarithm of
DTI (x-axis) is shown. The regression equation is y = 4.08+125*x.,
R2 = 0.85. The intercept is not statistically significant, and the slope
has a p<0.0001.
processes, and should allow one to generate estimates of
the most meaningful mechanistic rate constants that are
need for effective delivery devices. However, early in a
drug development program little is known about such
properties. The above over-simplified model is therefore
the logical alternative. It gives a simple assessment of the
value or performance of the device, without extensive,
costly experimentation or lengthy clinical trials, and
therein lies the real advantage of its use.
The subcellcular processes are believed to be quite
complicated.
Is
the
above
oversimplified
pharmacodynamic Emax model, relating effect to
intracellular cytoplasmic unbound levels adequate to aid
decision making? That question will need to be answered
for each individual case in light of available information.
If an Emax model is adequate to represent each step in the
process, then one global Emax model will be sufficient to
represent the entire cascade of events, with the apparent
Emax and C50 representing hybrids of the microscopic
submodel parameters. The argument being made is
consistent with the usual reported pharmacodynamic
models in which a series of events, for example, a signal
transduction cascade, is modeled by a single
pharmacodynamic process. Consequently, a single global
pharmacodynamic Emax model is used in this study to
represent all of the subcellular processes. However, the
parameters of such a model are empirical, not
mechanistic, and cannot be used to explain or describe the
subprocesses.
A limitation of the above approach is use of the
steady state assumption. The simulation predictions are
difficult to test experimentally. It is difficult to provide
steady state gene delivery to cells in vivo. However,
because the time scale for intracellular processes such as
gene trafficking and gene expression are slow relative to
distribution of drug or therapeutic agents into the cell, as
observed by Tachibana et al [2], one can remove the
steady-state assumption and, instead, approximate the
input of gene as a bolus: assume that the therapeutic
agent is given as a short infusion, until intracellular
4 of 4
concentration of the loaded delivery device reaches its
pharmacokinetic steady state, at which time the infusion
is stopped. Now, the pharmacodynamic processes, which
are slower, are effectively seeing the therapeutic input as
a bolus into the cell. Both observing and simulating the
effects, as a function of time, are complicated, thus
rendering the simple model less valuable. What can be
quantified, however, is an estimation of exposure to the
effect, or the area under the effect-time curve (AUE.) To
do so, it is assumed that the effect does not depend upon
past exposure. Given therapeutic input as a bolus and
having the effect represented by a single Emax model
means that AUE is a function of C0, the initial
concentration and λ, first-order rate constant for
elimination of the therapeutic at the effector site. There is
still a positive relationship between the DTI, a ratio of C0,
and pharmacodynamic outcomes, quantified by ratio of
AUEs. The exact relationship between the two, including
consideration of the time lag and the dependence upon
past exposure, will be the topic of further study.
Jiang et al reported successful gene delivery and
expression with naked DNA injected intravenously into
tail vein of the mouse without using a delivery device [5].
The limitation of this strategy is that the gene does not
need to be delivered to a specific group of cells, and
therefore non-specific uptake and expression of the gene
by liver cells is sufficient to confer some therapeutic
effects. The report also described a typical Emax-shaped
dose-response effect of plasmid DNA on IL-10
expression in liver cells. Koh et al compared the delivery
of naked IL-10 plasmid DNA versus to that delivered and
protected by a biodegradable polymer [6]. The authors
argued that the carrier protected the plasmid from being
degraded in the circulation and, as a consequence, a larger
effective amount of gene is delivered and is available for
transcription. The study showed 3 to 5-fold increase in
IL-10 expression by the delivery device, thereby
validating the concept that improving the availability of
gene for the effector increase the response. Finally, Liu et
al compared the transfection efficiency of naked DNA
versus that delivered by cationic lipids [7]. The studies
measured radiolabeled intracellular DNA, and found that
delivery by cationic lipids achieved several fold
differences between different tissues, thereby supporting
the argument above that a minimum fold difference in
concentration between target and other tissue is
achievable by such delivery devices.
One must not overlook the toxicity profile when
developing a gene delivery device as a therapeutic agent.
The common toxicity seen in clinical trials were immune
reactions against the carrier vehicle, usually viral vectors,
inflammation reactions at the tissue where the gene is
delivered, is believed to be caused by a number of factors,
including infection of viral vectors, and mutagenesis in
normal cells into which genes are delivered [8]. One can
anticipate that these toxicities are dose-dependent and that
a Emax model for toxicity can be adequate. In the presence
of observable dose-dependent toxicities, gene and gene
delivery devices must be carefully engineered and dosed
so that sufficient of effective genes are delivered to the
target cells, while toxicities are minimized.
In conclusion, the present study applies a simple
simulation model for targeted drug delivery to gene
delivery, and shows that a simple pharmacokinetic
assessment of the delivery device, the DTI, is directly
related to pharmacodynamic outcome over a range of
delivered doses, and so can be used to guide decision
making during development of therapeutics.
ACKNOWLEDGMENT
The Biosystems Group and the Pharmaceutical
Sciences Pharm. D. Pathway, School of Pharmacy,
University of California, San Francisco supported this
work. We thank the members of the Biosystems Group
for assistance, support, and helpful discussions.
REFERENCES
[1] Hunt CA, MacGregor RD, Siegel RA. Engineering
Targeted In Vivo Drug Delivery I. The Physiological and
[2]
[3]
[4]
[5]
[6]
[7]
[8]
Physicochemical Principles Governing Opportunities and
Limitations. Pharm Res 1986; 3(6):333-344.
Tachibana R, Ide N, Shinohara Y, Harashima H, Hunt CA,
Kiwada H.
An assessment of relative transcriptional
availability from nonviral vectors. Int J Pharm. 2004 Feb
11;270(1-2):315-21.
Rowland M, McLachlan A. Pharmacokinetic considerations of
regional administration and drug targeting: influence of site of
input in target tissue and flux of binding protein. J
Pharmacokinet Biopharm. 1996 Aug;24(4):369-87.
Kamiya H, Akita H, Harashima H. Pharmacokinetic and
pharmacodynamic considerations in gene therapy. Drug
Discov Today. 2003 Nov 1;8(21):990-6.
Jiang J, Yamato E, Miyazaki JI. Intravenous delivery of naked
plasmid DNA for in vivo cytokine expression. Biochem.
Biophys Res Comm. 2001 289: 1088-1092.
Koh JJ, Kol KS, Lee M, Han S, Park JS and Kim SW.
Degradable polymeric carrier for the delivery of IL-10 plasmid
DNA to prevent autoimmune insulitis in NOD mice. Gene
Therapy (2000) 7, 2099–2104
Liu F, Qi H, Huang L, Liu D. Factors controlling the
efficiency of cationic lipid-mediated transfection in vivo via
intravenous administration. Gene Therapy (1997) 4, 517–523.
Arguilar LK, Arguilar-Cordova E. Evoluation of a gene
delivery clinical trial. Journal of Neuro-oncology. 2003; 65:
307-315.
1 of 4
An Agent-based Computational Approach for Representing
Aspects of In Vitro Multi-cellular Tumor Spheroid Growth
Song Chen, Suman Ganguli, C. Anthony Hunt*
Biosystems Group, Department of Biopharmaceutical Sciences
The University of California, San Francisco, CA 94143, USA
Abstract—There have been many efforts to explain and
simulate tumor growth with mathematical and
computational models.
However, none have
systematically examined the behaviors of tumor
spheroids during growth. The interactions among
tumor cells during growth are also not well understood.
We have implemented an agent-based computational
approach to study the macro- and microbehaviors of
avascular tumor spheroids during growth.
Our
simulations of tumor spheroid growth begin with a
single tumor cell in optimal environmental conditions.
We observe an initial phase of rapid growth, during
which the shape of the collective approximates a
spheroid.
Subsequently a characteristic layered
structure develops, consisting of an outermost
proliferating cell layer, an intermediate quiescent cell
layer, and a central necrotic core. These behaviors of
our in silico spheroids map well to experimental in vitro
observations.
Keywords—Agent-Based, Computational, Multicellular,
Tumor Spheroid, in vitro, simulation
I. INTRODUCTION*
In vivo, early stage tumor growth is a complicated
process,
involving
interactions
among
multiple
subprocesses, such as proliferation, quiescence, necrosis,
apoptosis, and angiogenesis. Moreover, early stage tumor
growth in vivo is very difficult to observe, particularly in
the avascular phase. Multicellular tumor spheroids (MTS)
are an in vitro model system that has been developed to
imitate the early, avascular growth phase of in vivo tumors.
Computational models of this process that are able to
account for the observed behavior of the in vitro system
and allow in silico experimentation could prove valuable.
Both mathematical and computational models have
been formulated to simulate MTS growth. Drasdo [1] used
a Monte-Carlo approach to model the initial exponential
growth phase of avascular tumors. Dormann and Deutsch
[2] used a hybrid cellular automaton to simulate avascular
tumor growth. Kansal et. al. [3] developed a cellular
automaton model of brain tumor growth. Casciari et. al. [4]
and Ward and King [5] are examples of differential
*
Correspondence: hunt@itsa.ucsf.edu
equation models have also been developed to study these
processes. These models, however, are unable to represent
certain aspects of this system well.
For example,
differential equation models cannot easily represent either
the individual and spatial heterogeneity of tumor cells or
their adaptive behaviors. Cellular automaton models do not
provide for detailed representation of individual tumor cell
behavior and state, and lack the flexibility to represent the
adaptive behavior of individual tumor cells. In addition,
none of these approaches allows the detailed study of
nutrient and waste transport through a spheroid.
We believe an agent-based approach is sufficiently
flexible to model this system. Agents are software objects
that have the ability to add, remove, and modify objects and
events. Philosophically, they are objects that have their
own motivation and can initiate causal chains, as opposed
to simply participating in a sequence of events created
elsewhere. Agent-based models are discrete in most
dimensions, including time, state, and the rules used to
govern agent behaviors.
Agent-based models were
specifically developed to provide more natural descriptions
of complex adaptive systems in various contexts [6].
Detailed descriptions of in vitro multicellular tumor
spheroids are provided in [7,8] Briefly, in vitro tumor cells
consume oxygen and nutrients and release metabolic
byproducts. Under optimal environmental conditions—
sufficient oxygen and nutrients and low levels of
byproducts—tumor cells undergo mitosis, producing new
tumor cells. This cell proliferation leads to an initial
exponential growth phase and a multicellular spheroid. As
spheroid size radius increases, oxygen and nutrient
availability internally is reduced, and metabolic byproducts
accumulate within the spheroid. Such conditions are
thought to contribute to necrosis of cells near the center of
the spheroid. The byproducts of necrosis can be cytotoxic,
and their presence can further inhibit tumor cell
proliferation. Tumor cells near the surface of the spheroid,
on the other hand, can continue to proliferate because of the
favorable environmental conditions. Cells located between
this outer proliferating layer and the inner necrotic regions
become quiescent—environmental conditions are adequate
to their survival, but not for proliferation. This dynamic
results in the characteristic layered structures of tumor
spheroids illustrated in below Fig. 1.
2 of 4
Proliferating Cell Layer
Quiescence Cell Layer
Necrotic Core
Fig. 1. Tumor Spheroid Schematic Diagram
II. COMPUTATIONAL APPROACH AND METHODS
Swarm1 is a software library that was designed to
facilitate multi-agent simulation by managing many
programming tasks common to agent-based models, thus
freeing the user to focus on the specific requirements of the
simulation. Core Swarm libraries provide vital functions
such as object creation, memory allocation, scheduling of
activities, and list management. All agents and objects in
Swarm can be probed. Once attached the probe can send a
message, change a variable, or retrieve values.
We have implemented an agent-based model of
multicellular tumor spheroid growth using the Swarm
framework. Swarm enables and facilitates the simulation
of collections of concurrently interacting agents.
Our model contains 4 computational spaces (Fig. 2.):
TumorSpace, OxygenSpace, NutrientSpace, InhibitorSpace.
Each space is represented as a (toroidal) 2-D square lattice.
They overlap as shown below. All factors other than
oxygen that contribute to growth and division are lumped
together into a class called Nutrients. Similarly, all factors
that inhibit growth or that are harmful to tumor cells are
grouped into the class Inhibitor. Corresponding objects in
each class are designated OXYGEN, NUTRIENT, and INHIBITOR
to distinguish them from their biological referents2.
TumorSpace
OxygenSpace
NutrientSpace
InhibitorSpace
Fig. 2. Schematic representation of overlapping grid spaces
1
2
See http://www.swarm.org. for further information on Swarm.
The same word may be used to refer to molecules, cells, system
components, or events in the referent system and to the
corresponding objects, agents, or events within the in silico
system. In the latter case the word is written using small caps.
TumorSpace contains tumor cell agents. Each location can
by occupied by a single agent. OXYGEN, NUTRIENT, and
INHIBITOR are integer values at each location in their
respective spaces.
For simulation of oxygen transport in OxygenSpace, we
use Swarm’s built-in diffusion algorithm. Swarm provides
a discrete 2nd-order approximation of 2-D diffusion with
evaporation. For simulation of NUTRIENT and INHIBITOR
transport, we have implemented data structures and
algorithms to represent the transport of these quantities
along the edges between cells. We call this the EdgeFlow
function. The EdgeFlow algorithm is implemented similar
to diffusion, except that edges can be “open” or “closed,”
and transport occurs only along open edges. This allows us
to simulate the heterogeneous transport of these materials
through a spheroid in a detailed manner.
Tumor cell agents, designated TUMOR AGENTs, have the
following internal attributes that, collectively, control their
behavior:
• state: proliferating, quiescent, or dead
• rates of OXYGEN consumption, NUTRIENT
consumption and INHIBITOR production
• OXYGEN minimum and maximum requirements
• NUTRIENT minimum and maximum requirements
• INHIBITOR minimum and maximum requirements
The initial conditions are as follows: Initializing
OxygenSpace sets the value of OXYGEN at each location to
OC. Initializing NutrientSpace sets the value of NUTRIENT at
each location to NC. One TUMOR AGENT in the proliferating
state is placed at the center of TumorSpace. The simulation
is started. At each time step thereafter, OXYGEN and
NUTRIENT values are “replenished” outside the spheroid: for
each location in the TumorSpace that neither contains a
TUMOR AGENT nor is surrounded by TUMOR AGENTs, the
corresponding location in OxygenSpace and NutrientSpace
is reset to OC or NC.
A list of functional TUMOR AGENTs is maintained,
(proliferating or quiescent). At each time step, each TUMOR
AGENT in the list caries out the following activities.
Consume OXYGEN and NUTRIENT only from the
corresponding location in OxygenSpace and NutrientSpace,
and release an amount of INHIBITOR to InhibitorSpace,
following individual internal rate values. Use resulting
OXYGEN, NUTRIENT, and INHIBITOR amounts to determine new
TUMOR AGENT state for the next time step.
The determination of the TUMOR AGENT state is made as
follows: the TUMOR AGENT compares OXYGEN, NUTRIENT, and
INHIBITOR values against its internal minimum and
maximum requirements. If OXYGEN and NUTRIENT values are
greater than the maximum requirements and INHIBITOR value
is less than the minimum requirement (representing ideal
conditions for the tumor cell), the TUMOR AGENT is
proliferating. If any of these values are between the agent’s
minimum and maximum levels, the TUMOR AGENT may take
3 of 4
on the proliferating or quiescent state, with varying
probabilities. If either OXYGEN or NUTRIENT is less than the
agent’s minimum requirements, or INHIBITOR is greater than
the maximum requirement (representing adverse
conditions), the agent goes to the dead state with a certain
probability.
If the new state of the TUMOR AGENT is proliferating,
attempt to divide. First, examine the eight neighboring
locations in TumorSpace. If any neighboring location is
unoccupied, create a new TUMOR AGENT in the proliferating
state and place it in the unoccupied location. If no
neighboring locations are unoccupied, simply remain in the
proliferating state. For every TUMOR AGENT in the necrotic
state increment InhibitorSpace in the corresponding
location to represent accumulation of toxic necrotic
material.
During the initial stage of simulation, each TUMOR
AGENT represents a single tumor cell.
As the spheroid
increases in size and fills TumorSpace, a “zoom function”
is introduced. This allows a TUMOR AGENT to represent
multiple tumor cells without distorting the spheroid shape
and behaviors. The numbers of tumor cells a TUMOR AGENT
represents increases each time the zoomFunction is applied.
This allows the model to simulate larger spheroids, in
which the total number of tumor cells may reach 1010,
without representing each cell individually, which would be
computationally intractable.
III. RESULTS
Following initiation of a simulation (Fig. 3a), TUMOR
proliferate, taking advantage of the optimal
environmental conditions. This results in a spheroid of
proliferating TUMOR AGENTs (Fig. 3b). The size of spheroid
increases rapidly, which causes OXYGEN and NUTRIENT
availability in the interior to decrease and INHIBITOR levels to
increase. This results in decreasing gradients of OXYGEN
and NUTRIENT and increasing gradient of INHIBITOR, moving
from the outer edges towards the center. As a result, the
TUMOR AGENTs toward the center become quiescent, and
proliferating TUMOR AGENTs are limited to the outer regions
(Fig. 3c). Eventually, three layers are formed (Fig. 3d).
Conditions in the interior become increasingly adverse,
causing transition of TUMOR AGENTs from quiescent to
necrotic state and the formation of a “necrotic core.”
For initial results and validation of our model, we
demonstrate the effects of varying OXYGEN and NUTRIENT
supply on spheroid growth. OXYGEN and NUTRIENT supply
are determined by the parameters OC and NC (the values to
which OXYGEN and NUTRIENT are replenished outside the
spheroid). We use Proliferating Fraction as an outcome
variable to measure spheroid growth. Proliferating Fraction
is defined as the number of proliferating TUMOR AGENTs
divided by the total number of TUMOR AGENTs.
AGENTs
(a).
(b)
(c)
(d)
Fig.
(a)
(b)
(c)
(d)
3. Tumor growth over time
TUMOR AGENTs at initial simulation (scale 1:1)
TUMOR AGENTs proliferate and form a spheroid (scale 1:1)
quiescent layer forms (scale 1:1)
spheroid increases in size, forms layered structure (scale 1:5)
Three sets of values for these parameters were used in
experiments: baseline OXYGEN and NUTRIENT supply (PF1),
doubled OXYGEN and NUTRIENT supply (PF2), and halved
OXYGEN and NUTRIENT supply (PF3). For each set of values,
we averaged the results of five simulations. The results are
shown in Fig. 4.
Fig. 4. shows that the Proliferating Fraction declines
over time for each of the three set of parameter values.
There is a sharp initial decrease, followed by a stabilization.
The results also show that Proliferating Fraction varies with
OXYGEN and NUTRIENT supply; greater supply of OXYGEN and
NUTRIENT result in higher Proliferating Fractions.
We use total number of TUMOR AGENTs to represent
spheroid size. Spheroid size rapidly increases in the initial
stage of simulation. The rate of increase slows and
eventually reaches saturation.
Similar to proliferating
Fraction, doubling the OXYGEN and NUTRIENT supplies
increases total number of TUMOR AGENTs and reducing the
supplies to half decreases the total number of TUMOR
AGENTs.
4 of 4
mathematical and computational applications. Our work is
intended to demonstrate that agent-based modeling can be
used to represent certain essential aspects of spheroid
growth, and thus can serve as the basis for future in silico
models of this complex system.
Proliferating Fraction
1.2
PF1
PF2
PF3
1
0.8
0.6
0.4
ACKNOWLEDGMENTS
0.2
0
0
20
40
60
80
100
120
140
Time (Days)
We thank Glen E.P. Ropella, President, Tempus Dictum,
Inc, for his tireless technical advice, and Dr. Amy H. Lin
for early contribution to this work. We also thank the
members of Biosystems group, Department of
Biopharmaceutical Science, UCSF for support, and Ms.
Pearl Johnson for administrative assistance.
Fig. 4. Proliferating Fraction vs. Time for three
different sets of parameter values
REFERENCES
III. DISCUSSION
Our model is an initial step towards the goal of
providing a flexible model of multicellular tumor spheroids
which will allow for in silico experimentation. At this
stage our model dynamically simulates formation and
growth of multicellular tumor spheroids based on a small
set of simple rules. The observed development of a spatial
layered structure simulates in vitro observations, and results
concerning major growth indicators, such as those
presented above for Proliferating Fraction, are very close to
those of in vitro data and results of other computational
models [9]. Furthermore, a strength of the agent-based
approach is that it enables us to observe the microbehaviors
of individual agents and their interactions throughout the
entire growth process.
Our model at this stage captures a small subset of the
biological complexity involved in tumor spheroid growth.
However, our approach provides an easy and effective way
to add, modify and remove the various parts of the model:
agents, rules, etc. As such, it can serve as a foundation for
more detailed models of the various biological processes
involved.
IV. CONCLUSION
Substantial progress has been made in various
specialized areas of cancer research. The complexity of the
disease on both the single cell level as well as the
multicellular tumor level has led to the first attempts to
describe tumors as complex, dynamic, self-organizing
biosystems. To begin to understand the complexity of the
system, novel models and simulation methods must be
developed, incorporating concepts from many areas such as
cancer biology, computer programming techniques, and
[1] Drasdo D. “A Monte-Carlo approach to growing solid
nonvascular tumors.” In: G. Beysens and G Forgacs (eds),
Dynamical networks in physics and biology, pp 171-185. 1998
Springer, New York.
[2] Dormann S, Deutsch A. “Modeling of self-organized avascular
tumor growth with a hybrid cellular automaton.” In Silico Biol.
2002;2(3):393-406.
[3] Kansal AR, Torquato S, Harsh GR IV, Chiocca EA, Deisboeck
TS. “Simulated brain tumor growth dynamics using a three
dimensional cellular automaton.” J. Theor. Biol. (2000) 203,
367-382.
[4] Casciari JJ, Sotirchos SV, Sutherland RM. “Variations in tumor
cell growth rates and metabolism with oxygen concentration,
glucose concentration, and extracellular pH.” J Cell Physiol.
1992 May;151(2):386-94.
[5] Ward JP, King JR. “Mathematical modelling of avasculartumour growth.” IMA J Math Appl Med Biol. 1997
Mar;14(1):39-69.
[6] Bonabeau E. “Agent-based modeling: methods and techniques
for simulating human systems.” Proc Natl Acad Sci U S A.
2002 May 14;99 Suppl 3:7280-7.
[7] Hamilton G. “Multicellular spheroids as an in vitro tumor
model.” Cancer Lett. 1998 Sep 11;131(1):29-34.
[8] Sutherland RM. “Cell and environment interactions in tumor
microregions: the multicell spheroid model.” Science. 1988
Apr 8;240(4849):177-184.
[9] Kansal AR, Torquato S, Harsh GR IV, Chiocca EA, Deisboeck
TS. “Simulated brain tumor growth dynamics using a threedimensional cellular automaton.” J. Theor. Biol. 2000 Apr
21;203(4):367-82.
1 of 3
A Novel Stepwise Normalization Method for Two-Channel cDNA Microarrays
Yuanyuan Xiao1,3, C. Anthony Hunt1, Jean Yee Hwa Yang2,3, Mark R. Segal2
1
Department of Biopharmaceutical Sciences
2
Department of Biostatistics
University of California, San Francisco, CA, USA
3
These authors contributed equally
Abstract—Microarray experiments contain many sources
assumption is that the majority of genes are equally
of systematic errors. In order to extract biologically relevant
expressed between the two mRNA samples, symmetrical
information from microarray data, normalization needs to be
distribution of points around the horizontal M=0 line is
applied to remove such variations. Although a number of
expected. Yet frequently we observe linear or nonlinear
normalization models have been proposed, it has not been well
trend between M and A signaling the undesirable
researched on how to assess model adequacy with respect to
dependence
of M on A. An example of nonlinear
the observed data. To tackle this problem, we propose in this
dependence
between
M and A is illustrated in Fig. 1a).
paper a new stepwise within-slide normalization method,
The
spatial
heterogeneity
(S) originates from different
STEPNORM. It is a normalization framework that integrates
experimental conditions applied on spots from different
various models of different complexities to sequentially detect
areas on the slide. There are usually three major sources that
and correct systematic variations associated with spot
intensities, print-tips, plates and two-dimensional spatial
contribute to this spatial variation. First, spots on the same
effects. We demonstrate the utility of STEPNORM on a set of
slide are divided into different grids, and spots of different
well-studied cDNA microarray expriment.
grids are printed by different print-tips from the printing
robot; the inequality among M from different print-tips is
Keywords—cDNA microarray, normalization
well illustrated in Fig. 1a). Second, spots of different rows
of the slide are often of different well plate sources; one can
imagine that there may be effects associated with different
I. INTRODUCTION
well plates. Last, the physical condition of the slide itself
could also differ region from region. Fig. 1b) reveals such
Microarray
technology
enables
simultaneous
artifacts on a Swirl slide by color-coding the ranks of ratios.
monitoring of the expression of thousands of genes ([1]).
It shows that the unnormalized ratios are not uniform, and
Like other measuring technologies, microarray data contain
are higher (yellow) at the middle and lower (blue) around
inherent systematic measurement errors stemming from
the edges especially in the left-most column.
variations in labeling, hybridization, spotting or other
We proceed in the next section to introduce a new
nonbiological sources ([2]). Normalization procedures,
stepwise
normalization method and then showcase its usage
which adjust microarray data to remove such systematic
on
a
Swirl
slide in the Result section. The last section
variations, are therefore important for subsequent analysis
concludes
with
discussion and some observations.
of either differential expression or gene expression
profiling. In this paper, we describe a new systematic
stepwise normalization procedure on two-channel cDNA
arrays and illustrate its usage on a Swirl zebrafish slide. The
Swirl experiment is comprised of four replicate
hybridizations that contain 8,448 spots. It was carried out
using zebrafish as a model organism to study the effect of a
point mutation in the BMP2 gene that affects early
development in vertebrates.
Two-channel microarrays measure relative abundance
of expression of thousands of genes in two mRNA
populations. This relative abundance is usually expressed as
ratios, M = log2(R/G), where R and G are the fluorescent
intensity measurements of the red and green channels. The
most pronounced systematic variation embodied in the
ratios that does not contribute to differential expression
between the two mRNA populations is the imbalance of the
green and red dye incorporation. This imbalance is
manifested as the dependence of ratios on primarily two
factors, the fluorescent intensity (hereafter represented by
the symbol A) and the spatial heterogeneity (hereafter
represented by the symbol S).
The A bias can be best illustrated using a MA plot ([3]),
where M is plotted against A (A = log2{\sqrt{RG}}). As the
II. METHODOLOGY
Having illustrated the existence of non-biological
variations in microarray data, we review a number of
a)
b)
Fig. 1. Diagnostic plots for a swirl slide: (a) MA plot with lowess fits for
individual print-tip groups. (b) Spatial plot of log ratios. The plot is divided
into 16 grids representing the 16 different print-tips. Spots are color coded
according to the ranks of the ratios, higher ratios are colored yellow and
lower ratios are colored blue.
2 of 3
popular normalization methods before proposing a new
systematic approach to remove such variations.
Within-slide intensity bias There are currently three
most applied models for the removal of the A bias from
ratios. Suppose Normalized ratios are obtained as,
Mnorm = M + c. Models differ in determining the correction
factor c. Global median shift, the most simplistic method,
assumes that c is constant regardless of the intensities of the
spots (A), and it merely shifts the median of the ratios to be
zero. As a refinement to global normalization, robust linear
regression (rlm) recognizes the need of A-dependent
correction. It does so by fitting a linear regression model.
The correction factor c in this model is therefore a linear
function of A. This model is sufficient when the relationship
between M and A is approximately linear, but fails to correct
any nonlinear relationship between them. Nonlinear
methods developed by Yang et al. ([3]) applied the robust
scatter-plot smoother lowess to perform a local intensitydependent normalization; the correction factor c is therefore
a nonlinear function of A.
Within-slide spatial bias: Print-tip and Plate Models,
such as median shift, rlm and lowess, if fitted within each
print-tip (PT) or plate (PL), corrects the PT or PL bias.
Median shift adjusts ratios within each PL (or PT) to be zero
in an effort to correct for existing inequality between such
spatial attributes, and it is a robust version of the ANOVA
approach proposed by Sellers et al. ([4]). Models rlm and
lowess, the latter being the most widely practiced
normalization method corrects for the A and PT (or PL)
biases simultaneously.
Within-slide spatial bias: 2D Spatial Other than printtip and plate effects, there could be other spatial attributes
that contribute to the spatial heterogeneity (see Figure 1b)).
Sellers et al. ([4]) applied an ANOVA model to test the
effects due to array rows and columns. They treat the row
and column effects as categorical variables; hence the
spatial heterogeneity is modeled as discreet and nonuniform changes. As a result the model fits a large number
of parameters as the size of arrays commonly runs up to
about a hundred rows and columns. An alternative approach
proposed by Yang et al. ([3]) models the spatial
heterogeneity as a smooth trend by treating rows and
columns as continuous variables and fitting a twodimensional lowess curve . So doing requires much fewer
parameters than the ANOVA model. Yet another way to
model local spatial effects is proposed by Wilson et al. ([5]).
The spatial trend in this model is estimated by computing
for each spot, the median log ratio over its spatial
neighborhood. The size of the smoothing element in the
spatial median filter in their article is a 3 X 3 block of spots,
although other sizes are also possible. This model is able to
correct any local spatial trend, for example, a small streak of
artifacts, yet so doing costs a lot more degrees of freedom.
We have reviewed several models that could be applied
for the elimination of non-biological biases in microarray
data. These models differ in their assumptions and
complexities. As biases are slide- and experimentdependent, different slides may show different intensity and
spatial trends. Using one model to correct all biases in a
slide or using the same model for different slides exhibiting
different biases might not be adequate. A more rigorous
scheme that captures the particularities of each slide by
assessing quantitatively the adequacy of each model with
respect to the observed data is urgently called for. Precisely
for this reason, we are proposing a new normalization
framework that is stepwise and adaptive in nature. This new
method is hereafter called STEPNORM.
Fig. 2 illustrates the procedures of STEPNORM using
the example of the swirl experiment. It consists of four steps
and in each step one bias is targeted for correction. The
intensity A bias is usually the major source of variation and
is therefore subjected to examination first. After the
correction of the A bias, normalized log ratios are subjected
to further normalizations based on the existence of spatial
biases. As illustrated earlier, there are primarily three types
of spatial biases, print-tip (PT), plate (PL) and twodimensional effects (2D) and they will be tested
sequentially. PT is subjected to testing first because the
number of print-tips is usually smaller than plates and
therefore costs fewer degrees of freedom; furthermore,
various research ([4]) has shown the PT effect is usually
more dominant than other spatial biases.
In each step of our new method, there are a number of
competing models of different complexities. The solution to
the problem of evaluating several candidate models is to
select the model that provides an adequate description of the
data while using a minimum number of parameters. Take
the example of the first step -- removal of A bias, among the
candidate models, median shift is the simplest, estimating
only one parameter -- the median; and its effect is
correspondingly very limited and probably only suits for
data that do not show a significant amount of linear or
nonlinear trend between M and A. On the other end of the
spectrum is the nonlinear local regression model lowess. Its
local fitting nature accommodates corrections for nonlinearity, yet doing so requires fitting more parameters and
runs the risk of over-fitting. Therefore, the challenge is to
select the model that achieves the best balance between
goodness of fit and simplicity. One of the most popular
methods, taking both data fitting and model complexity into
account, is the Bayesian Information Criterion (BIC), which
is defined as,
BIC = -2log(\hat{L}) + Klog(N) ,
where \hat{L} is the maximum likelihood, K the number of
free parameters in the model and N the sample size. We
integrate BIC into STEPNORM as the model selection
criterion; the model with the lowest BIC value is considered
to the preferred model in each step. Importantly, each step
also includes testing a “null” model, which doesn't fit any
parameters and represents the scenario that the systematic
variation in this step is not statistically significant to warrant
any correction.
3 of 3
such nonlinear trends disappeared after the first step
correction. Indeed, MA plot with lowess fits within printtips in Fig. 2c) shows largely vertical shifts and no evident
curvature. Appropriately, Table 1 indicates that median shift
is a better model than the more complex ones, such as rlm
and lowess. The same phenomenon also applies to the PL
bias. As a conclusion, this slide shows both PT and PL
effects, which could be corrected by a simple median shift.
The last step in STEPNORM tests if there are remaining
systematic variations associated with spot locations on the
slide. Fig. 2g) highlights spots with the highest and lowest
15% pre-normalization ratios and reveals some spatial
effects especially in the first and last column on the slide,
where high (red spots) and low (green spots) ratios show
noticeable separations. Table 1 indicates that lowess is the
preferred model to remove such spatial bias. Normalized
ratios using the 2D-lowess model is plotted in Fig. 2h)
which shows an improved distribution of ratios on the slide.
IV. DISCUSSION
Fig.2 STEPNORM procedures for the Swirl experiment
III. RESULTS
We illustrate in this section the application of
STEPNORM on a Swirl slide.
For the correction of the A bias, we have observed that
almost all data have some sort of trend between M and A,
though to various degrees. To find the most appropriate
model for the swirl slide, we compare three models median
shift, rlm and lowess. From the inspection of the BIC values
in Table 1, it is apparent that lowess is the preferred model,
possessing the lowest BIC value of all models. The span
parameter we used in lowess is the default value in the loess
function in the statistical software R, span = 0.4. The
number of free parameters required in the fitting is
estimated to be 4.95 from the output of this function, which
could also be approximated as follows. This span parameter
defines that about 40% of points are used for a local fitting
in each moving window. Each fitting here is linear and
therefore requires two degrees of freedom. Totally, about
1/0.4X2 = 5 degrees of freedom are needed. The model rlm
is a special case of lowess when within each local area the
fitting is linear and the span size is set to 1. We have
observed good behaviors of lowess for most of the slides
that we have analyzed, the Swirl slide being a typical
example. The results in Table 1 illustrate that due to the
typical high spot density nature of microarray data, the
default span parameter in the loess function in R (span =
0.4) is adequate to capture the nonlinear dependence of M
on A, and it is also large enough to avoid the over-fitting
concern.
We proceed next to the removal of the PT bias. Fig. 1a)
reveals that before any normalization is carried out intensity
trends within print-tips show nonlinear tendencies. Yet,
Efficient normalization is crucial for microarray
research. It directly influences outcomes of downstream
data analyses that could give rise to important biological
implication and discoveries. In this paper we have
presented a new normalization procedure STEPNORM,
which integrates a number of published methodologies
under the same framework and assesses their effectiveness
via a quantitative criterion. Such a process is applied to each
individual slide in an experiment so that data (slide)
specificity could be achieved.
Unlike other normalization methods, STEPNORM
could avoid data under-fitting or over-fitting as it
TABLE I
STEPWISE NORMALIZATION (SWIRL DATA)
Bias
A
PT
PL
2D
Spatial
Models
K
-2logL (X104)
BIC
Null
median shift
rlm
lowess
Null
median shift
rlm
lowess
Null
median shift
rlm
lowess
0
1
2
4.95
-1.978
-1.985
-2.002
-2.016
-1.978
-1.984
-2.008
-2.011
4.95
4.95+16
4.95+32
4.95+79.64
-2.016
-2.117
-2.122
-2.128
-2.011
-2.098
-2.089
-2.051
20.95
20.95+22
20.95+44
20.95+112.
-2.116
-2.172
-2.178
-2.098
-2.098
-2.133
-2.119
-2.077
Nulls
rlm
lowess
med filter
ANOVA
42.95
42.95+4
42.95+13.6
42.95+
42.95+183
-2.172
-2.172
-2.185
-2.133
-2.130
-2.134
-2.105
-2.020
-2.224
4 of 3
implements both bias detection and removal in the same
context. Intensity-dependent bias in ratios are usually the
most common and dominant in microarray spot
measurements. Very frequently such bias exhibits as a
nonlinear trend between M and A, the curvature can be
estimated using a suitable robust scatterplot smoother, such
as the lowess procedure, which have shown good
performance for the adjustment of the A bias for most slides
we have analyzed using STEPNORM. However, we have
also observed that the A bias is usually a whole-slide
phenomenon and doesn't localize within spots related to a
specific print-tip or plate. Therefore the current common
practice that performs lowess within each print-tip (LPT) to
remove the A and S biases simultaneously appears to be
over-fitting for most datasets. For slides like the Swirl
experiment that have 16 print-tips, LPT estimates about 5 X
6 = 80 parameters when the span size is set at 0.4. On the
other hand, the procedure preferred by STEPNORM applies
lowess for the removal of whole-slide A bias and then
employs a simple median shift among ratios in different
print-tips to remove the inequality of ratios among printtips; So doing estimates only 5 + 16 = 21 parameters.
The BIC criterion is no doubt an important component in
the STEPNORM framework. It is chosen for model
selection in STEPNORM for two reasons. First, it is quick
to compute which makes it more appropriate than other
computation-heavy criteria, such as cross-validation (CV),
in the application of microarray datasets, which are usually
large in size. Second, we have also observed that the
a)
b)
e)
f)
g)
h)
Fig. 3 Graphical display of bias before (left column) and after (right
column) stepwise normalization. The first row shows MA plots before a)
and after b) the removal of the A bias. The second row shows MA plots
before c) and after d) the removal of PT bias, with lowess fits for individual
print-tips. The third row displays boxplots of M before e) and after d) the
removal of PL bias. The last column illustrates image plots of M before g)
and h) the removal of 2D-spatial effects highlighting only the top 15%
spots in both directions.
outcome of applying BIC is largely compatible with that of
applying CV (results not shown), which indicates the using
BIC gives appropriate and reliable results and it is suitable
in the application of microarray normalization.
ACKNOWLEDGMENT
J. Q. Author thanks ... .” Sponsor and financial support
acknowledgments are placed in the unnumbered footnote on
the first page.
c)
d)
REFERENCES
[1] J. DeRisi, L. Penland, P. O. Brown, M. L. Bittner, P. S. Meltzer,
M. Ray, Y. Chen, Y. A. Su, and J. M. Trent, “Use of cDNA
microarray to analyse gene expression patterns in human
cancer,” Nature Genetics, vol. 14, pp. 457-460, 1996.
[2] M. Schena, editor, Microarray Biochip. Eaton, 2000.
[3] Y. H. Yang, S. Dudoit, P. Luu, D. M. Lin, V. Peng, J. Ngai, and
T. P. Speed, “Normalization of cDNA microarray data: a robust
composite method addressing single and multiple slide
systematic variation,” Nucleic Acid Research, 30(4):e15, 2002.
[4] K. F. Sellers, J. Miecznikowski, and W. F. Eddy, “Removal of
systematic variation in genetic microarray data,” unpublished
[5] D. L. Wilson, M. J. Buckley, C. A. Helliwell, and I. W. Wilson,
“New normalization methods for cDNA microarray data,”
Bioinformatics, vol. 19, pp. 1325-1332, 2003.
BioDEVS: System-Oriented, Multi-Agent, Modeling & Simulation Framework
Sunwoo Park1†, Glen E. P. Ropella1§, and C. Anthony Hunt1,2
1
Biosystems Group, Department of Biopharmaceutical Sciences, and 2The Joint UCSF/UCB Bioengineering Program, The University of California, San Francisco, CA
†
spark4@itsa.ucsf.edu
1
What is DEVS?
• A framework for discrete event-oriented modeling and simulation
• It provides a sold mathematical formalism based on a set theory
• It supports construction of multi-level, hybrid system Biomimetic In Silico Devices
•
•
•
•
(hereafter, Biomimetic Devices or BDs) and networks of Biomimetic Devices
§
gepr@tempusdictum.com
hunt@itsa.ucsf.edu
What is BioDEVS?
It is a new work in-progress
An extension of DEVS
It supports both system-oriented and agent-based modeling and simulation
It provides a set of generic, spatial Devices
- N-dimensional homogeneous & heterogeneous spaces
- N-dimensional Cellular Automata with neighborhood search support
OVERVIEW – Formal Specification of
Biomimetic In Silico Devices
libraries
- 1D, 2D and 3D visualization & 4D animation
- Extendible to N-Dimensional visualization & animation
• It provides a reusable, configurable, and self-evolving BD repository system
8
3
A System-oriented Multi-Agent M&S Framework
BioDEVS:
Integrates system-oriented and multi-agent M&S into a common framework
Agents are software objects that have the ability to add, remove, and modify objects and
events
Philosophically, they are objects that have their own motivation and can initiate causal
chains, as opposed to just participating in a sequence of events something else initiated
Devices Classification:
atomic - describes temporal behaviors of a biological system
coupled - describes structural relationships and event propagation between
components, where each component can be an atomic or coupled BDs
The Atomic device represents the smallest,
unbreakable biological system in the model
X
S' = dext((s, e), x)
S
l(S)
Y
6
Modular Multi-Level Biomimetic Devices and Their
Networks
Both a multi-level BD and networks of BDs can be constructed based on concept of
closure-under-coupling*
Couplings between BDs can be established either loosely or tightly, or allowed to evolve
over time
Evaluation testing can be done at the individual or aggregate Device level
Network classification:
homogeneous network (e.g., N-dimensional cellular automata)
heterogeneous network (e.g., adaptive grid network )
* Closure-under-coupling is a system property that guarantees aggregation of systems based on their coupling
information is also considered as a single system in the same formalism. A coupling specifies one-directional event
propagation from an event producer to a set of event consumers.
Provides for Device synthesis and decomposition configuration
and reuse of Devices
M2
Ym = {(p, v)|p Œ Portsoutput, v Œ Yp},
Y
Goals:
N
a bag of input events
S' = dint(S)
ta(s)
DEVSa = <Xm, Ym, S, dext, dint, dcon, l, ta>
Xm = {(p, v)|p Œ Portsinput, v Œ Xp}, set of input values
Ym = {(p, v)|p Œ Portsoutput, v Œ Yp}, set of output values
S : set of states
Behavior Causality; an example:
dext = Q ¥ Xb Æ S, external transition function
dint = S Æ S, internal transition function
S
dcon = Q ¥ Xb Æ S, confluent transition function
ta(S)
b
l = S Æ Y , output function
ta(S)
dext((s, e), x) dint(S)
l(S)
ta = S Æ R•
0 , time advance function
where,
X
Q = {(s, e)|s Œ S, 0 < e < ta(s)}
dcon((s, e), x)
e: elapsed time since last state transition
DEVSa = <Xm, Ym, D, {Md}, {Id}, {Zi,d}>
Xm = {(p, v)|p Œ Portsinput, v Œ Xp},
ZN,M1
a bag of output events
D : A set of component references
Md : A set of DEVS models for each d in D
Zi,d : i-to-d output event translation function
Zi,d : X Æ Xd, i = N :
An external input translation
Zi,d : Y Æ Yd, d = N : An external output translation
Zi,d : Yi Æ Xd, i π N Ÿ d π N : An internal translation
M21
ZM1,M2
M1
Facilitates evolvability of Devices
ZM1,N
M21
ZM1,M3
M3
Support Collections of Generic
Biomimetic Device Patterns
ZM1,M3
Atomic
Where,
M1
M2
M3
M21
Ordinary
Differential
Equation
M23
Hybrid Systems Construction
7
Hybrid Systems Constructions Based on:
• Closure-under-coupling
PDE
KTG Bond Graph, Acausal
• Behavioral compatibility
• Formalism transformation
DAE Non-Causal Set
Can Have Hybrid BDs at the:
• System Level
• Formalism Level
• Trajectory level (or I/O)
System Dynamics
Stochastic
Coupled
Processing,
Queuing, &/or
Coordinating
Spike
Neuron
Organized
Integrator
Petri Net
Networks,
Collaborations
Processing
Networks
Discrete Time/
State Chart
Physical
Space
Spike
Neuron
Networks
Cellular
Automata
Reactive
Agent
Fuzzy Logic
Source:
Bernard P. Zeigler, Brief Introduction to Modeling and Simulation
Framework and Discrete Event System Specification (DEVS),
UCSF Seminar, September, 2003
Partial
Differential
Equation
Multi-Agent
System
N-Dimensional
Cell Space
Self-Organized
Criticality
Bond Graph, Causal
DAE Causal Set
Integration with High-Performance Computing
Infrastructure
Transfer Function
DAE Non-Causal Sequence
Scheduling-Hybrid-DAE
PDE: Partial Dif. Eq.
KTG: Knotted Trivalent Graph
DAE: Dif. Algebraic Equation
DESS: Differential Eq. System Specification
DTSS: Discrete Time System Specification
DEVS: Discrete Event System Specification
10
BioDEVS will support a collection of generic and extendible devices and
Device components. Here is an example of such a collection from
systems engineering:
N
Portsinput : All input ports of an atomic model
Portsoutput : All output ports of an atomic model
Xp : A bag of input events associated with a port, p
Yp : A bag of output events associated with a port, p
9
Repository Management System For
Biomimetic Devices
BioDEVS will include a Device Repository Management System to facilitate
Device reuse.
Describe construction of (hybrid) multi-level BDs and networks of BDs
Specify event flows between Biomimetic Devices
Abstract networks of Biomimetic Devices to a single aggregated BD
State Transition Causality
It consists of a set of I/O interfaces,
behavior functions, and states
5
Formal Specification of Coupled
Biomimetic Devices
Formal Specification of Atomic Biomimetic Devices
2
• It supports visualization & animation of various Biomimetic Devices and support
BioDEVS:
• Elucidates structural, temporal, and behavioral properties of Biomimetic In Silico Devices
(hereafter, Biomimetic Devices or BDs) based on a solid mathematical formalism
• Systematically and mathematically specifies Biomimetic Devices
• Allow constructing scalable and modular multi-level Devices and networks of BDs
• Can support hybrid multi-formalism constructions of Biomimetic Devices
4
BIOENGINEERING
UCSF & UCB joint graduate group in
Finite State Automata
State Charts
Petri Nets
Event Scheduling
Activity Scanning
Process Interaction
Cellular Interaction
Sources:
1. Hans Vangheluwe. DEVS as a common denominator for multi-formalism hybrid systems modeling.
IEEE International Symposium on Computer-Aided Control System Design, pg 129-34, 2000.
2. Bernard P. Zeigler, H. Praehofer, and T.G. Kim. Theory of Modeling and Simulation, 2nd. Ed.,
Academic Press, San Diego, 2000
DEVS
DTSS
DESS
DEV &
DESS
Realtime
DEVS
Symbolic
DEVS
BIO
DEVS
Neuro
DEVS
BioDEVS Layered Architecture
Provides a set of system
components for a fully automated
simulation environment
Supports various high
performance software/
hardware configurations
11
Application Layer
Modeling Layer
Simulation Layer
Network Infrastructure Layer
Partitioner
Deployer
Activator
Simulator
MPI/MPP*
Grid/Cluster
P2P/Internet**
*MPI/MPP: Message Passing Interface/Massive Parallel Processors
**P2P/Internet: Peer-to-Peer/Internet
A Decentralization Method for Modeling the Multiple Levels
of Organization and Function Within Liver
1
A portion of the behavior space of a biological system within an
organism.
Laboratory experiments cover only a tiny aspect of a system's
behavior. Mathematical models typically over focus on such
narrow, well-defined behavior, and they lack flexibility to adapt to
represent more of the behavior space. They over-simplify and by so
doing can ignore key features of a systems true complex nature.
They can also be too inflexible to represent that same aspect of
behavior when viewed from a different perspective.
1,2
Department of Biopharmaceutical Sciences, Joint Bioengineering Program, The University of California, San Francisco, CA
RM
G
Set Up
Experiment
Instantiate
It does not require any particular formalism. Rather the
experimental framework is formulated using
Partially Ordered Sets.
Within lobules there is spatial heterogeneity.
Sinusoids contain heterogeneous microenvironments:
PA
SR
DP
different surface to volume ratios.
Opinion,
Decision
Hepatcytes have location dependent phenotypes.
Satisfaction
Gene expression within hepatocytes is location
dependent.
Inductive
Modeling
r
e
iv
L
f
o
s
l
e
v
Le
6
5
Define a new class of articulated biological simulation models that can achieve a higher level of
biological realism because they are event-driven.
g
r
O
Data
Data
Data
Data
Articulated
Model
Modular Molecular Networks
Files &
Databases
Vascular Graph is one Component
of the Articulated Model
Illustration of a Vascular Graph Segment
– Maps to Lobule –
Zone I
Dosage
Function
Zone II
SS
B
Without Loss of Information
C
PV:
SS
Flow
Link
CV:
Flow Link:
Path by which
particles flow
SS
SS
SS
GML
File
Zone
I
P ri m
a r y U n it
Each ArtModel is a directed graph. Each
shortest path has either two or three nodes. Either a
SA or SB agent is placed at each node. We allow for
cross connections between any two adjacent nodes
within Zones I and II. The PV and CV are sources
and sinks for solutes.
P
n
I
lan
The properties of grid points can be
homogeneous or heterogeneous – as
illustrated here – depending on the specific
requirements and the available data.
This illustrates Adaptive Simulation (see right) at the molecular level.
The graph represents a portion of a larger, interconnected molecular network
that has three subnetworks, A, B & C. The edges represent quasi-stable paths
for information flow as messages and/or events. Having a mechanism for
realizing networks allows us to replace sub-networks (at any location) with
rules-based software modules. In this illustration each of the three subnetworks
is replaced by a rule-based agent.
Enable knowledge discovery by designing for an
extended life cycle (so that models will outlast a
given research agenda), and
SS
Data Mgmt.
Module
Lobule
Spec.
*FURM web site: http://biosystems.ucsf.edu/Researc/furm/index.html
enter
Core
Core
Yes
Bind?
SSpace
enter
Rim
8
Encapsulating Experimental Procedures –
and parametrization. Modify any given piece of the
model or reparameterization to improve preformance.
This process continues until acceptable coverage of the
targeted solution space is obtained. Next, the
parameter space is searched. Similarity Measures are
specified to identify solutions for which the model
validates.
We promote sound methodology by following these
guidelines:
Jump
Validation and Verification – A DatModel (data
model) is used to represent the biological system.
During validation a solution set is compared to the
DatModel using a Similarity Measure. Because FURM
uses multiple models, verification is defined as
comparing one model solution set to another and is a
generalization of validation.
Model Granularity – All functionality is captured
within FURM in a method or object. Functional
granularity defines how composable, adaptive, and
scalable the model will be. The articulated model that
is fine-grained at all levels. We use three concepts in
categorizing functional granularity: fine-grained
execution control, fine-grained spatial specificity, the
ability to package modules arbitrarily.
model only the most salient characteristics of the
referent;
enter
SoD
Exit?
Yes
enter
Yes
Hepatocyte
No
No
Jump
ESpace
Bind?
focus first on a coarse or abstract description of the
referent, etc.
To bound any wandering of the process, FURM
encapsulates experimental procedures. It establishes
the experimental context in which the to-be-implemented
models must perform. The experimental procedure
consist of measures to be taken on the models, the
execution paradigm used, and the reporting requirements
for measurements and model execution.
5
Adaptive Simulation – When fine-grained parts of a
model (e.g., transporter or signal transduction networks
in hepatocytes) minimally influence the particular system
property being studied (e.g., metabolism of a solute), we
can ignore them or replace them in the simulation (even
during a simulation) with alternative components (agents
in this example) that roughly approximate their behavior.
When attention shifts to behavior where those
components have significant influence we can return to
using the original parts.
Turbo Factor: Changes contribute most to peak height.
SA SS Length: Length of SA influences the position
of peak; the larger the value, the later the peak. At
the same time, the length of the SA also affects peak
height: the smaller the value, the higher the peak.
SA SS Circumference: Larger values increase the
peak height and move the tail toward target values.
SB SS Length: Smaller values increase the peak
height and similarity score and move the tail below
target values. Larger values move the tail above
target values.
Maximum of SB Length: Smaller values increase the
peak height and give larger similarity scores.
Yes
Start
Timer
First, a relative difference is computed on the multiple
nominal time series. Then, we pool the normalized data
and take the standard deviation.
Wait
No
Move
Core
No
{n i}i = ({di}i – mi)/mi
Yes
Exit
Hep?
Yes
No
Metabolize
Timer
Off?
cvariation = std({ni}i)
The envelope is then defined using:
No
upperi = mi·(1 + cvariation), loweri = mi·(1 – cvariation).
Yes
These bands form the similarity envelope around the
outflow profile. The similarity score is then calculated.
Destroy D
Jump
Done
ESpace
13
14
Results – A & B
structure and architecture of the experimental liver. For
that task 14C-sucrose is used because it neither binds
significantly to tissues not partitions into cells.
A
Two in silico models are implemented.
The Reference Model is the accepted, reference
mathematical model2. It too is a functional unit model,
but it is not articulated.
Articulated Model: Parameter vectors are based on
experimental data in combination with criteria for likely
solutions. Given input parameters and initial conditions
the model is run until some stopping criteria are met.
Output is logged over time. Model outflow profiles are
identified as being close, or not, to the corresponding in
vitro data using a Similarity Measure.
B
15
0
Time, sec.
-0.5
C
-1
Figures A & B show results from two different parametrization of the In Silico Liver
Articulated Model against the sucrose outflow profile form rat 1. The 3 dashed curves
represent the mean ± 1 std. The filled circles in Figs. A & B are results obtained using
two of the parameter vectors that provide acceptable solution sets for the specific model.
Smoothness of the outflow profile increases with the number of runs. Both ArtModel
profiles match the data fairly well according to the Similarity Measure.
-1.5
-2
-2.5
-4
The relationship between the parameter space and the Articulated Model
outflow profiles is nonlinear. There is strong covariance between each of
the parameters. The follow describes parameter sensitivity of the results
in Fig. C.
Neither an instantaneous nor a whole-curve comparison
is appropriate because the features of the in vitro
outflow profiles clearly show different variances.
For these studies, however, the band width is based on
the Global Standard Deviation (std) of each outflow
profile data set, and that is calculated as follows.
For both A & B the No. of nodes/Zone is 28, 16 and 8 for Zones I, II and III,
respectively.
0
10
20
30
40
50
60
70
Time, sec.
80
90
100
Observations – C
prefer models that track the perceived characteristics
of the referent system
Timer No
Off?
A multiple observation SM is warranted.
-3.5
Number of runs = 20.
ArtModel v[2003-07-30]
Yes
No
-3
SSs: 50% SA and SB.
SM = 1 when in silico results fall completely with the
specified band for a set of in vitro data.
SoD
Move
No Jump 2 Yes
Rim
The initial modeling task is to extract from solute outflow
profiles as much information as possible about vascular
Inter-zone connections: IÆII = 14, IÆIII = 4, IIÆIII) = 14.
Wait
No
We consider ratios and normalized values rather than
exact values and units. We use output fraction versus
time to compare solution sets.
Total edges: 60.
Start
Timer
Yes
Rim
exit
Core?
Yes
12
The Similarity Measure (SM) determines whether or not
two experimental data sets (one in vitro, the other in
silico) are experimentally indistinguishable, e.g., they
both fall within a band of appropriate width.
Exit
EC?
Rim or Core?
Move
The in vitro liver perfusion protocol and experimental data
is detailed in Roberts and Anissimov1.
Figure C shows results from one parametrization of the Articulated Model
against the sucrose outflow profile form a second rat, #2.
The 3 curves represent the mean ± 1 std. The filled circles in are results
obtained using a parameter vectors that provide an acceptable solution
set according to the Similarity Measure.
Iterative Modeling – Start with an unrefined model
3
Programming is used to develop systems where any
one usage is likely to exercise only a small portion of the
system. Developers focus on separable aspects of the
system. We extend these ideas into FURM and refer to
the result as Aspect-Oriented Modeling (AOM). AOM
assumes that there are many, possibly infinite, similarly
plausible models that can adequately describe the
referent system and account for the available data4. The
researcher iteratively explores and systematically shrinks
the space of potential models in search of a set of
models that make sense in a given context, e.g., they
exhibit sufficient biological realism.
No
Experimental Procedures
No. of nodes/Zone is 55, 24 and 3 for Zones I, II and III,
respectively.
Similarity Measure
No
Results – C
Messages and events characterize the medium
of information flow in biology at all levels.
Networks – coherent nodes communicating over
quasi-stable paths – can represent that flow. In
the In Silico Liver everything is a network
because everything happens via messages, from
object to object, over a medium that handles
events. Both the objects and the medium can be
dynamically created, atomic, or composite.
Objects can be identified as nodes in a graph
Computational Methods
Use discrete interactions
Yes
Move
Enter
Sinusoid
Sinusoidal Segment (SS) circumference
(min, max)
SS length (a. b, g)
Solute Scale
(molecules per solute "particle")
Solute Dose
(mass, constituents, timing)
Turbo (effective solute flow pressure)
Graph Structure (number of SSs,
connections between them)
Fenestrations (size and prevalence)
Hepatocyte Relative Density
Intra-Cellular binding agents (min, max)
Probability of binding (given coincidence of a solute
and binding agent)
Probability of being metabolized (given coincidence of
solute and enzyme)
Mean time solute bount to binding agent
Intra-zone connections: I = 10, II = 8, III = 0.
Follow four fundamental guidelines:
enter EC
Graphs and Networks Play Key Roles
in This New Class of Models
A
Use FURM to iteratively create, execute and analyze
model variants in the context of experimental procedur-es
and available data.
D in PV
Solute is injected into the entering perfusate of an isolated
rat liver. The measured time course of solute outflow
contains information about the liver architecture,
physiology, and subcellular biochemistry as encountered
by the solute – each unique solute "sees" the liver from a
unique perspective and "experiences" only specific
aspects of the hepatic environment.
To account for sinusoidal heterogeneity (transit times, flow,
topography, different surface to volume ratios within zones, etc.), we
defined two classes of in silico SSs, SA and SB. The SA have a shorter
path length and a smaller surface-to-volume ratio. The SB have a longer
path length and a larger surface-to-volume ratio.
g
n
i
n
Agent
C
Aspect Oriented Modeling – Aspect-Oriented
SS
Central
Vein
Portal
Vein
Fr: Teutsch, et al., Hepatology 29, 495, ‘99.
Zone III
Intrahepatocyte
Agents
Agent B
Define observables that will submit to a
Similarity Measure.
Zone III
CV
Hepatocyte
Hepatocyte Layer
Agents Represent Modules
Standardize interfaces to multiparadigm, multimode,
and trans-domain models
SS
PV
Space of Disse
Network Level Chemistry
Data Mgmt.
Module
Data
500 mm
Zone I
Data
Reference
Model
SS: Sinusoidal
Segment
Sinusoid Network
as Directed Graph
Grid C
7
Statistical
Observer
Module
Control
Data
Zone III
Endothelial Layer
Cell Biology
Control
Control
CV
CV
Agent A
Framework of the In Silico Liver
– Key Components –
Data
d
e
t
Grid B
We refer to this method as FURM: Functional Unit Representation Method*
Control
Acinus
Zone II
Cu
Grid A
Use multiple models to cover more of a systems behavior space. Implement a
method for building a multitier, in silico apparatus designed to support iterative
experimentation on multiple models.
CV
10
enter
ESpace
To account for disease
heterogeneity within the liver
we can substitute "diseased"
for normal objects (hepatocytes, SSs, lobules or secondary units) at what ever levels
of resolution are needed.
A
PV
Flow Chart of Solute (S) Options
Within the Articulated Model (ArtModel )
Model Parameters 11
Lobule
p
m
I
y
tl
Flow
Implement models that represent the hepatic lobule and that can be extended
to account for the hepatic disposition of solutes.
Parameter
Mgr.
PV
t
u
ol
Sinusoidal Segment (SS)
Use a middle-out model design strategy: begin with the primary functional units.
Control
L
CV
Secondary Unit
e
v
i
Zone II
Design models and components that they are articulated.
Data
n
e
r
r
n
e
lem
u
F
r
P
lan
PV
Blood
disconnected, that can represent dynamic spatial heterogeneity at different levels of resolution, and
that are replaceable, reusable and easily adaptable to represent other tissues and systems.
Data
Model
t
a
iz
e
d
o
M
&
In
t
c
n
ng
ni
5
n
o
i
Blood "Core"
Articulated Model (ArtModel) – Composed of components that are easily joined and
Control
,
n
io
an
OA
Model Development Goals and Guidelines
es
lR
different topographic arrangements, and
Cogitate
Experiment
Agent
n
io
different flows,
Discover,
Mine paths
Find Patterns
Analyzed Data,
Patterns
It works by decentralizing the modeling process without requiring
that all of the data be of a specific type.
The primary functional unit of the liver is the lobule.
Experiment
Paths thru
AR space: data
It serves as an example of the new class of generative biological simulation models
whose components are easily joined and disconnected and
are replaceable and reusable.
To link genotype to hepatic phenotype and make better
predictions, we need a better understanding of how and
why these levels function as they do in health and during
disease.
In Silico
Devices
Actualization A R
It builds on a middle-out model design strategy to enable and encourage development of different
(multiple) models.
Live
rL
ob
e
Representations
A solute object represents molecules
moving through the articulated model.
In silico, solute behavior is dictated by
rules specifying the relationships
between solute type, location, and
proximity to other objects and agents.
Those rules can be specified to take
into account the solute's physicochemical properties.
4
It decouples the various aspects of functional units.
Drug effects are influenced by functional heterogeneity
within levels, which in turn is influenced by the health of
the liver.
Generators,
Building blocks
The overall project goal is to have one in silico model that can account for the hepatic outflow profiles
of any combination of the six drugs and be able to shift to either of two disease states, and in those
states also successfully account for the out-flow profiles of the six drugs. To achieve this goal we have
design and qre building an In Silico Liver (ISL) that has the following properties:
The multiple levels of organization within the liver have
made informative modeling and simulation difficult.
Synthetic
Modeling
Engineering
Design, Specs,
Prototype
Represent
5. Outflow for sucrose, but not metabolized or transported solutes, is solely a function
of the extracellular (vascular cavity) space and its geometry.
LIVER
Project Goals and Objectives
4. Solute transit times are governed by stochastic interactions between solute and
agents inside the vascular structures in combination with perfusion pressure.
Department of Medicine, University of Queensland, AU
hunt@itsa.ucsf.edu
3
3. Liver function is an aggregate of lobular function, with the lobule being the primary
functional unit.
Fraction
M
L
3
2
3
The Biological and Medical
Problems
2
1. Physiologically accurate models are necessary to begin fully exploring the liver
behavior space.
Fraction
1
To understand how and why biosystems function as they do we
need to build (assemble, synthesize) simulation devices, and then
iteratively test and refine them.
Mental model
2
9
Five Primary Assumptions:
C. Anthony Hunt , Glen E. P. Ropella , Li Yan , and Michael S. Roberts
New modeling and simulation methods are needed that are
sufficiently flexible and adaptable to cover much larger portions
of the behavior space.
Language
Elements
1
Key Assumptions
2. Hepatic vascular structure and the arrangement of lobules within a lobe can be
represented by a directed graph.
Fraction
Scientific Problems, Issues, and Needs
110
Total edges: A = 42, B = 50.
Intra-zone connections: AI = BI = 10, AII = 8, BII = 13,
AIII = 0, BIII = 3.
Inter-zone connections: A & B(IÆII) = 14, A & B(IÆIII) = 3,
A & B(IIÆIII) = 7.
The percent of total SSs that were SA was increased by 5% for B relative to A.
Minimum of SB length: When the maximum length is small (e.g., 15),
smaller values (e.g., 5) increase the peak height, lower the tail, and give
larger similarity scores. When the maximum of SB length is larger (e.g.,
45), further changes do not significantly affect either peak height, tail
location, or similarity score.
Number of runs = 100.
ArtModel v[2003-05-27]
Observations – A & B
The discretization of solute amount causes the variance to increse toward the tail
end of the outflow profile where solute amount/interval goes to zero.
References
1. Roberts MS, and Anissimov YG., Modeling of Hepatic Elimination and Organ Distribution
Kinetics with the Extended Convection-Dispersion Model, J. Pharmacokin. Biopharm.
27(4):343-382, 1999.
2. Hung DY, Chang P, Weiss M, and Roberts MS. Structure-Hepatic Disposition
Relationships for Cationic Drugs in Isolated Perfused Rat Livers: Transmembrane
Exchange and Cytoplasmic Binding Process. J. Pharmacol. Exper. Therap.
297(2):780–89, 2001.
3. Czarnecki K and Eisenecker U. Generative Programming: Methods, Tools, and
Applications. Addison-Wesley, pp. 10, 251-254, 2000.
4. Davis PK. Dealing with complexity: Exploratory Analysis Enabled By Multiresolultion, Mu
ltiperspective Modeling, Proceedings of the 2000 Winter Simulation Conference, J. A.
Joines, R. R. Barton, K. Kang, and P. A. Fishwick, eds. (PWSC2000), 293-302, 2000.
5. Grinspun E, Krysl P, Schroder P. CHARMS: A Simple Framework for Adaptive
Simulation. ACM TOG, 2002 / Proceedings of SIGGRAPH 2002.
We mitigate this effect by combining results from M runs (20-30 (for these
experiments) to make one study. By so doing we are representing an
in silico rat liver as being comprised of M lobules.
Graph topology within the zone-based architecture is important. Pseudo-random
number generators are used to vary topology. Runs were scored and the highest
scoring graphs was selected as candidates to be optimized. The rest of the
parameter vector was fine-tuned to optimize the ArtModel .
The relationship between the parameter space and ArtModel outflow profiles is
nonlinear and, in some cases, redundant. For example, the relationship between
the ratio of SA to SB and the connection topology of the graph is complex. Such
nonlinearity requires searching on both parameter sub-spaces (e.g., possible graph
topologies) and on the whole parameter space. It also demonstrates that the SM
being used at present is inadequate.

Report - School of Electrical Engineering and Computer Science

Transcription

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The new RS-35M, June, 2010 - Stu Martin, k2qde@optonline.net

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