The Cyton Model of the adaptive immune response, part I

Transcription

The Cyton Model of the adaptive immune
response, part I
Ken Duffy
Hamilton Institute, National University of Ireland Maynooth
I2M Network Summer School, 31st Aug. 2009
Talk objectives
1st talk: Introduce and motivate the Cyton Model of the
adaptive immune response.
2nd talk: Show how branching processes can be used to
develop an analysis of it.
Part I: introduce and motivate the Cyton Model
• The Cyton Model is a consequence of 10+ years of feedback
between experiment design and model refinement by members
of the Hodgkin Lab. (now at the Walter and Eliza Hall
Institute of Medical Research).
• This work provides a good example of the scientific method,
illustrating a case where theory and experiment design develop
in tandem.
• This work provides a good example of the scientific method,
illustrating a case where theory and experiment design develop
in tandem.
Cue streptococcal throat video.
Our initial interest is in studying lymphocyte population dynamics.
Humoral Immune Response
B-lymphocytes stimulated by CpG DNA1
200000
Population size
150000
100000
50000
0
0
50
100
150
200
Time (Hours)
Linear Scale
1
M. L. Turner, E. D. Hawkins and P. D. Hodgkin. Journal of Immunology,
181(1):374–382, 2008. (in vitro)
200000
100000
Population size
Population size
150000
100000
10000
50000
0
0
50
100
Time (Hours)
Linear Scale
1
150
200
0
50
100
150
Time (Hours)
Log Scale
181(1):374–382, 2008. (in vitro)
200
200000
100000
Population size
Population size
150000
100000
10000
50000
0
0
50
100
Time (Hours)
Linear Scale
150
200
0
50
100
150
Time (Hours)
Log Scale
No action; proliferation through cell division; death by apoptosis.
1
181(1):374–382, 2008. (in vitro)
200
Cell Mediated Immune Response
CD8+ T cells infected with lymphocytic choriomeningitis virus2
1.4x107
1.2x107
Population size
1x107
8x106
6x106
4x106
2x106
0
0
100
200
300
400
Time (Hours)
Linear Scale
2
D. Homann, L. Teyton and M. B. A. Oldstone. Nature Medicine,
7:913–919, 2001. (in vivo)
1.4x107
1x107
1.2x107
8x10
Population size
Population size
1x107
6
6x106
1x106
100000
4x106
10000
2x106
0
0
100
200
Time (Hours)
Linear Scale
2
300
400
0
100
200
Time (Hours)
Log Scale
7:913–919, 2001. (in vivo)
300
400
1.4x107
1x107
1.2x107
8x10
Population size
Population size
1x107
6
6x106
1x106
100000
4x106
10000
2x106
0
0
100
200
Time (Hours)
Linear Scale
300
400
0
100
200
300
Time (Hours)
Log Scale
No action; proliferation through cell division; death by apoptosis.
2
7:913–919, 2001. (in vivo)
400
Flow cytometry
Flow cytometry
Possibility of division linked behavior
CFSE3 : an important flow cytometry dye
3
A. B. Lyons and C. R. Parish. Journal of Immunological Methods,
1(1):131–137, 1994.
Multi-colour flow cytometry
CD40L+IL-4
CD40L+IL-4+IL-5
Syndecan-14 & CFSE5
4
Hasbold J, Corcoran LM, Tarlinton DM, Tangye SG, Hodgkin PD. Nature
Immunology, 5(1):55-63, 2004.
5
Courtesy of N. Taubenheim
Multi-colour flow cytometry
CD40L+IL-4
CD40L+IL-4+IL-5
B220 & CFSE5
5
Courtesy of N. Taubenheim
How do we explain this?
CFSE time-courses and the cohort method6
“A cellular calculus for signal integration by T cells”.
CD 4+ T cells. Anti-CD3 stimulation in presence of saturated IL-2.
6
A. V. Gett and P. D. Hodgkin, Nature Immunology, 1 (3) 239-244, 2000
Three parameter model
Average time to first division: µ.
Standard deviation time to first division: σ.
Average time for subsequent division: b.
• Final point substantiated by fluorescent-activated cell sorting.
• Cells in a particular division assumed to constitute a “cohort”
that entered first division at roughly the same time.
• Cells in a particular division assumed to constitute a “cohort”
that entered first division at roughly the same time.
• Scaling by 2div. no. corrects for expansion of this cohort due to
division (assuming no death).
Deductions from the three parameter model
• Adding anti-CD28 results in a decrease in µ, but doesn’t
affect σ or b.
affect σ or b.
• Adding IL-4 significantly reduced all three parameters.
affect σ or b.
• Adding IL-4 significantly reduced all three parameters.
• Adding IL-12 doesn’t affect parameters, but modulates initial
cell survival.
• Adding anti-CD28 and IL-4, results matched a the model with
a linear addition of the affects of each stimulus, suggesting
independent, additive regulation.
• Adding anti-CD28 and IL-4, results matched a the model with
a linear addition of the affects of each stimulus, suggesting
independent, additive regulation.
• Without a term for death, relative numbers are accurate, but
absolute numbers are over-estimates. Add an exponential
death rate for zeroth division cells, with the rate deduced from
death in an IL-2 only experiment.
Warning on death and the Poisson approximation
Ladislaus von Bortkewitsch (1898): Number of Prussian soldiers
killed each year as a result of being kicked by horses follows a
Poisson distribution.
7
D. Daley & D. Vere-Jones, §11.2 of An introduction to the theory of point
processes Vol. II, Springer, 2008
Poisson distribution. Exponential decay in numbers does not imply
exponentially distributed event times.
7
T1
7
T2
T3
T1
T2
T3
Superposition of n independent, finite intensity, point processes
with time dilation n results in weak convergence to a Poisson
process7 . That is: {Tn } is i.i.d. exponential in this limit.
7
Understanding the impact of IL-2 concentration8
CD4+ T-cells stimulated with anti-CD3 in the presence of IL-2
mAb (S4B6) and hIL-2 (resistant to inhibitory effects of S4B6).
8
E. K. Deenick, A. V. Gett and P. D. Hodgkin. Journal of Immunology,
170(10):4963–4972, 2003.
Effect of increased IL-2 could be explained by:
1. Decrease in time to first division.
2. A decrease in time to subsequent division.
3. A combination of the two.
4. Could also impact upon the proportion of cells entering
division.
8
170(10):4963–4972, 2003.
Effect of increased IL-2 could be explained by:
1. Decrease in time to first division.
2. A decrease in time to subsequent division.
3. A combination of the two.
4. Could also impact upon the proportion of cells entering
division.
3 parameter model suggests that IL-2 concentration does not alter
average time to first division, while exerting a profound affect on
the subsequent division rate.
8
170(10):4963–4972, 2003.
Time to first division - the colecimid method
Colecimid inhibits cells in metaphase of their cell cycle, so that they
are able to replicate their DNA but not undergo cell division. DNA
replication is only possible for cells entering their first division.
Six parameter model to predict cell numbers
8
At low IL-2 concentrations, large number of dead cells are observed
• Log-normal time to first division - 2 parameters.
8
170(10):4963–4972, 2003.
8
• Precursor frequency for zeroth division.
• Death rate (exponential) in zeroth division.
8
170(10):4963–4972, 2003.
8
• Constant time for subsequent division.
8
170(10):4963–4972, 2003.
8
• Constant time for subsequent division.
• Proportion of cells dying per subsequent division.
8
170(10):4963–4972, 2003.
Parameter constraint
IL-2 doesn’t affect zeroth generation death rate.
Impact of IL-2
IL-2 changes: p, d, b.
A 30-50% change in parameters results in a 10-fold increase in
final total numbers.
Dangers of deductions from under-parameterized models
• The three parameter model: adding anti-CD28 results in a
decrease in µ, but doesn’t affect σ or b.
9
E. Dennick, Ph.D. Thesis U. Sydney, 2004.
• Data from colcemid experiment: µ unchanged upon adding
anti-CD289 .
9
• Data from colcemid experiment: µ unchanged upon adding
anti-CD289 .
• The six parameter model: anti-CD28 increases precursor
frequency in zeroth division, and decreases proportion dying in
subsequent divisions.
9
How do we explain this?
Log-normal death times10
B cells in the presence of IL-4 (normal or quick preparation).
10
E. D. Hawkins, M. L. Turner, M. R. Dowling, C. van Gend and P. D.
Hodgkin, PNAS, 104(12), 5032–5037, 2007
IL-4’s impact on death times10
B cells stimulated +/- IL-4; log-normal death times with only
mean changed.
10
Hodgkin, PNAS, 104(12), 5032–5037, 2007
Colcemid method and first division times10
B cells stimulated with anti-CD40 & IL-4 in presence of colcemid;
log-normal first division times.
10
Hodgkin, PNAS, 104(12), 5032–5037, 2007
Dependence between death & division?10
B cells activated with α-CD40 & IL-4.
10
Hodgkin, PNAS, 104(12), 5032–5037, 2007
Dependence between death & division?10
B cells activated with α-CD40 & IL-4.
Suggests: independence of apoptosis & division machinery.
10
Hodgkin, PNAS, 104(12), 5032–5037, 2007
Cyton Model of immune regulation10
• Each founding cell has a time to die by apoptosis.
• Mitogenic stimuli activates cell-division; sets a time to divide.
• Considerable variation in population of both these times.
10
Hodgkin, PNAS, 104(12), 5032–5037, 2007
• Underlying processes apparently unaware of each other.
• Process to finish first determines outcome: cell dies or divides.
• These appear to operate independently in distinct cells.
10
Hodgkin, PNAS, 104(12), 5032–5037, 2007
• Subsequent generations behave in a similar fashion.
• Divide time and death time distributions differ between 0th
generation and subsequent generations.
10
Hodgkin, PNAS, 104(12), 5032–5037, 2007
• Subsequent generations behave in a similar fashion.
• Divide time and death time distributions differ between 0th
generation and subsequent generations.
• Maximum number of divisions an initial cell can undergo.
• Division destiny differs for each initial cell.
10
Hodgkin, PNAS, 104(12), 5032–5037, 2007
Acknowledgments
• Mark Dowling, Philip Hodgkin, John Markham, Marian
Turner, Nadine Taubenheim and Cameron Wellard (Walter
and Eliza Hall Institute).
• Dirk Homann (U. Colorado).
• Edwin Hawkins (Peter MacCallum Cancer Institute).
Acknowledgments
• Mark Dowling, Philip Hodgkin, John Markham, Marian
Turner, Nadine Taubenheim and Cameron Wellard (Walter
and Eliza Hall Institute).
• Dirk Homann (U. Colorado).
• Edwin Hawkins (Peter MacCallum Cancer Institute).
Tomorrow: using branching processes to analyse the Cyton Model.

The Cyton Model of the adaptive immune response, part I

Transcription

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