a New Sedimentation-enumeration Method

J. gen. Virol. (I972), I6, I35-I52
I35
Printed in Great Britain
The Kinetics of Haemagglutination by Semliki Forest Virus:
a N e w Sedimentation-enumeration Method
By K. R. C A M E R O N * AND C. J. B R A D I S H
Microbiological Research Establishment,
Porton Down, Salisbury, Wiltshire, England
(Accepted 4 April ~972)
SUMMARY
A novel method is described for the quantitative study of haemagglutination in
terms of the continuous and direct sizing and counting of aggregates of red blood
cells (RBC) as they settle in free suspension. This sedimentation-enumeration
(SE) method was used to estimate the concentration of haemagglutinating particles
in terms of the number of new RBC-RBC bonds formed. In haemagglutination
by Semliki Forest virus (SFV), the formation of RBC-RBC bonds is interpreted
in terms of two competitive and near first-order reactions: the rate of inactivation
of SFV haemagglutinin at low values of pH, and the rate of adsorption of residual
SFV haemagglutinin by RBC. The SE method provides an estimation of the
concentration of virus in terms of haemagglutinating activity which is independent
of container wall effects and of the concentration of RBC. Results were compared
with parallel estimates of the concentrations of infective and physical particles.
At the optimum pH 6"3 for haemagglutination, and at a concentration of
io 7 RBC/ml., about 7 particles of haemagglutinin were required for the formation
of one RBC-RBC bond.
At low concentrations of SFV haemagglutinin, the distribution of single RBC
and of aggregates of RBC was consistent with a statistical-mechanical theory of
aggregation which provides a basis for the interpretation of the mechanism of
haemagglutination. The distributions observed in this study were not consistent
with the 'dimers-only' hypothesis of Levine, Puck & Sagik (~953) which was
used by Cheng (I96 0 in an early study of haemagglutination by SFV.
INTRODUCTION
Haemagglutination by myxoviruses has been quantitated by the pattern test (Salk, I944;
W.H.O., I953), by photometric methods (Hirst & Pickels, r942; Levine, Puck & Sagik, 1953 ;
Drescher, Hennessy & Davenport, I962) and by modifications of these methods in the
Autoanalyzer (Grunmeier, Gray & Ferrari, 1965; Morris, Jenkins & Horswood, I965) and
the Fragiligraph apparatus (Kohn & Danon, 1965). Data obtained by such methods refer
to unspecified distributions of aggregates and cannot be related to the concentration of
virus particles unless other data are available. The sedimentation-enumeration (SE) method
described here was developed to allow the direct recognition and counting of settling free
goose red blood cells and aggregates of various sizes; the results may then be related to
mechanisms of haemagglutination without complication by container wall effects. The
* Present Address: Department of Virology,The Medical School,BirminghamBI5 2TJ.
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I36
K. R. C A M E R O N
AND
C. J. B R A D I S H
population distributions observed have been related to the kinetics of the haemagglutination
reaction and provide a quantitative estimate of the initial concentration of Semliki Forest
virus, used here as a representative Group A arbovirus.
METHODS
Red blood cells (RBC). Pooled bloods from selected geese were stored at 4 ° in Alsever's
solution and washed in o'85% saline immediately before use. Cell counts were made
using an Improved Neubauer haemocytometer.
Virus. The stock Semliki Forest virus (SFV) was a suspension of infected mouse brains
at the 13th passage of the Original strain (VR67) of the American Type Culture Collection.
Haemagglutinin was prepared by treatment of this suspension with fluorocarbon (trifluorotrichloroethane as Arklone P from I.C.I. Ltd) (Porterfield & Rowe, ~96o). Studies
by gel filtration on columns of Sephadex G-2oo or Sepharose-4B (Pharmacia, Ltd) and by
equilibrium density gradient centrifugation in caesium chloride showed that the SFV
haemagglutinin was homogeneous and similar to the infective particle in size and density
(I-24 g./ml.). Virus to be purified (v t3. C2) was from stirred suspensions of primary chickembryo cells (Zwartouw & Algar, t968). The virus was concentrated in a density gradient
of Io % to 50 % (w/w) sucrose in a continuous flow zonal ultracentrifuge and, after concentration on to a 50 % (w/w) sucrose pad, was purified further and separated from sucrose
by gel filtration through Sepharose-4B (J. D. Oram, D. H. J. Titmuss & K. H. Grinstead,
personal communication). Purified SFV was stored in the dark at 4 ° since it is sensitive to
inactivation by daylight (Appleyard, I967).
Borate buffer solution (BB-BSA) (Clarke & Casals, I958). This contained 0-2% (w/v)
bovine serum albumin, BSA (Fraction V, Armour Pharmaceuticals Co.), and was used
at pH 9"o as diluent for haemagglutinins.
Phosphate buffered saline (PBS) (Begum, I963) was used as diluent for goose RBC before
mixing with an equal volume of BB-BSA to give the required reaction pH.
Alsever's solution. This was prepared according to Bukantz, Rein & Kent 0946).
Parker's 'I99' Medium (Morgan, Morton & Parker, I95o). This synthetic medium
(Glaxo Ltd, Middlesex) was used in assays of virus infectivity.
Assay ofhaemagglutinin in the pattern test. Perspex dimple trays of W.H.O. design were
used since these gave more reproducible results than the disposable trays of the microtitre
method (Sever et al. ~964). Preliminary studies showed that SFV haemagglutinin
agglutinated goose RBC in the BB-BSA and PBS system at pH 6qo to 6.6o with an optimum
at pH 6"35 _+o'o5. This is discussed later and in detail by Cameron (I969). When the borate
component was replaced by McIlvaine's citrate, Sorensen's phosphate (o.o66 M), tris
(o'2 M) or verona1 (o.I M) buffer solutions (Hale, I965) only the first gave an optimum
haemagglutinating activity greater (I o %) than that for the borate system (Courtney, Maney
& Smith, I967). The borate system was nevertheless used for greater convenience in pH
adjustment. Other results showed that haemagglutinating activity at pH 6"3 was unaffected
by a range of concentrations of borate, citrate, phosphate and chloride ions. Protein as
0.2 % (w/v) BSA was included in the haemagglutinin diluent at pH 9"o to stabilize activity
during storage and ensure clear haemagglutination patterns in comparative tests.
Assay of virus infectivity. Infectivity assays were made by plaque counting in agar suspensions of primary chick-embryo cells (Bradish & Allner, 1966; Bradish, Allner & Maber, 197 I).
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Kinetics o f haemagghaination by S F V
137
Table I. Size distribution of aggregates of goose RBC formed in free suspension by
Semliki ForeSt virus ( v I 3 . c2) at p H 6- 3
c
Number of RBC in aggregate (n)
~
2
3
4
5
6
7
8
C~ = Number of aggregates of given size
B/R
*Score
in
pattern
test
8
8o
i6o
32o
2,56o
IO,24o
2o,48o
0'9
I"9
2.2
2'5
3'4
4-o
4"3
68
57
75
98
144
156
153
40
4o
40
51
41
32
33
23
16
i9
I7
I8
I4
9
2t
t6
14
I9
11
4
2
5
I3
4
3
3
3
i
8
i2
8
6
2
i
o
3
2
3
1
o
o
o
2
6
6
3
2
o
o
o
o
o
o
o
o
o
i
1
3
i
o
o
o
0"494
o'538
o'478
o-418
o'3o3
o.225
o-185
4
4
4
4
3
o
o
40,960
4'6
138
22
Io
3
I
o
o
o
o
o
o'I89
I
Haemagglutinin
dilution, D
log D •
C o n t r o l without
haemagglutinin
9
~
I0
~
Bonds
per
red cell,
o
(B)
140
24
11
I
o
o
o
o
o
o
o" 171 =
o
0
* Scores for a s a m p l e of h a e m a g g l u t i n i n initially containing 31oo H . A . U . / m l . Total (4), intermediate (I to 3)
a n d n o (o) agglutination. A score o f grade 2 c o r r e s p o n d s with 5 o % agglutination a n d t H . A . U . / m l .
Spray counting and electron microscopy. The c o n c e n t r a t i o n s o f virus particles in suspensions
o f purified S F V with polystyrene latex were estimated b y a modification o f the m e t h o d o f
N i x o n & F i s h e r (1958). T h e virus was negatively stained with a m m o n i u m m o l y b d a t e at
1 % (w/v) overall a n d e x a m i n e d with a Philips E M 3oo electron microscope.
The sedimentation-enumeration method ( C a m e r o n , I969). T o identify a n d c o u n t directly
the freely settling r e d cell aggregates, an o'5 ml. sample o f the r e a c t i o n mixture was held
in a Spectrosil s p e c t r o p h o t o m e t e r cuvette o f internal d i m e n s i o n s 43 × IO ram. a n d p a t h length 2 mm. T h e cuvette was held vertically in a firmly m o u n t e d , b r a s s - P e r s p e x h o l d e r
a n d screened f r o m external h e a t sources to minimize disturbances due to t h e r m a l convection. The o p t i c a l unit a n d focusing a d j u s t m e n t s o f a light m i c r o s c o p e were a d a p t e d
for h o r i z o n t a l viewing a n d accurate t h r e e - d i m e n s i o n a l adjustment. D i s t u r b a n c e s due to
surface-wall effects were m i n i m i z e d b y restricting o b s e r v a t i o n to aggregates settling at the
centre o f the cuvette. A l l observations were m a d e at r o o m t e m p e r a t u r e (23°).
T h e m i c r o s c o p e used for counting settling aggregates o f r e d b l o o d cells was fitted with
a g r a d u a t e d eyepiece graticule a n d the aggregates o r single cells were c o u n t e d as their
leading edges crossed a h o r i z o n t a l reference line o f effective length I ram. To ensure
stabilization o f initial disturbances due to mechanical swirling, all observations were
m a d e at a level o f 15 mm. below the meniscus in the cuvette a n d after an e q u i l i b r a t i o n
p e r i o d o f 15 min.
RESULTS
Presentation of results
T h e results p r e s e n t e d in T a b l e I show representative values o f the ratio o f R B C - R B C
b o n d s to red cells, B]R, as calculated directly f r o m the observed counts o f aggregates o f
various sizes (see e q u a t i o n 5 o f A p p e n d i x I). T h e i n d i c a t e d size distributions o f aggregates
are characteristic o f the o p t i m u m r e a c t i o n o f S F V haemagglutinins with io 7 R B C / m l . at
p H 6. 3. The c o r r e s p o n d i n g scores in parallel p a t t e r n tests are also shown in T a b l e I for
comparison.
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I38
K. R. C A M E R O N
A N D C. J. B R A D I S H
0.6
0.5
0
e~
e~
,,
B
0-4
o
:\o
¢.
"= 0-3
A
0.2
Ii
A
Control, no haemagglutinin
i
III
o.1
0
log DL
I
I
t
I
1"0
2"0
3.0
4"0
log D -= log (overall dilution of haemagglutinin)
Fig. I. Characteristic relationship between bonds/red cell (B[R)and dilution of SFV haemagglutinin
in three separate assays of haemagglutinating activity by the method of sedimentation-enumeration.
The same reactants (see methods) were used in three separate experiments on consecutive days;
©, 9"4x Io 6 RBC/ml.; 0 , 8-8x io 6 RBC/ml.; A, ~o.ox Io 6 RBC/ml.
A; base-line region showing spontaneous agglutination (B]R)o in the absence of haemagglutinin.
B; central linear region of reaction with haemagglutinin as limiting reactant.
C; upper plateau region of reaction with RBC as limiting reactant.
DL; limiting dilution at which SFV specific haemagglutinating activity is first detectable.
log DL = Haemagglutination Index, HI.
The characteristic ratio of RBC-RBC bonds to red-ceils, B[R, is presented (Fig. I) as
a plot against the logarithm of the overall haemagglutinin dilution, D. This shows three
reproducible and distinct regions:
(A) A base-line region, defining the spontaneous agglutination of red cells in the
absence of haemagglutinin, (B[R)o.
(B) A central linear region of constant slope defined by interactions at critical intermediate concentrations of haemagglutinin and independent of the concentration of red
cells. This provides a unique estimate of initial haemagglutinating activity in terms of the
limiting dilution, DL, at which haemagglutinating activity is first detectable. It is convenient to define log DL as the haemagglutination index (HI).
(C) An upper plateau defined by the red cell concentration, and in which the haemagglutinin is in excess.
Precision and reproducibility of SE method
The following tests were made to confirm the reproducibility of the reaction-characteristic
shown in Fig. I and the internal consistency of the interpretation presented in Appendix I.
(i) Reproducibility. Replicate tests on three consecutive days confirmed a common
reaction-characteristic of B[R as a function of log D (Fig. I).
(ii) The function Zn. C,.F~ calculated (Fig. z) from each distribution of aggregates was
proportional to the time of counting and independent of the haemagglutinin concentration
or the different distributions of aggregates (Appendix I, equation 5).
(iii) For a given reaction mixture the characteristic ratio B[R was constant regardless
of the reaction time (Fig. 3): this was confirmed repeatedly.
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Kinetics of haemagglutination by SFV
250
I39
i/
'
'
I
I
2O
40
60
6,...,
o ,~ 200
.~',=
at
.~
15o
Nil ~
a.
~, lOO
. .,...
0
0
5
Counting time, sec.
10
Settling time, rain.
15
Fig. z. Reproducibility of assay of haemagglutination by sedimentation-enumerationin terms of
proportionality with time of number of red cells in any state (Zn. C~ .Fn; Appendix I) settling past
observation line. The characteristic is independent of the presence or dilution (D) of haemagglutinin;
m, no haemagglutinin; A, log D = 3"6; A, log D = 3"3; ©, log D = 2'4; O, log D = I'8.
0.6
I
I
i
o 0"5
e>
M 0-4
m~
~0.3
,o
0.2
m
~
m
•
Ill
I
0
5
i
tO
Settling time, rain.
I
15
Fig. 3. Reproducibility of assay of haemagglutination by sedimentation-enumerationin terms of
independence of extent of agglutination (B/R) of time of reaction or settling. Reaction mixtures as
for Fig. 2,
A l t h o u g h c o u n t i n g for 20 sec. gave consistent results a n d showed that h a e m a g g l u t i n a t i o n e q u i l i b r i u m was attained within [5 min., a s t a n d a r d total c o u n t i n g time of 6o sec. was
a d o p t e d to m a i n t a i n sampling errors below + Io %. This observation for 6o sec. was made
as 3 periods of 2o sec. each at intervals of 5 min.
(iv) The direct estimate of R B C c o n c e n t r a t i o n o b t a i n e d f r o m the observation of
aggregates (equation 5 of A p p e n d i x I) was c o m p a r e d with the alternative estimate o b t a i n e d
b y use of a h a e m o c y t o m e t e r chamber. The estimate by s e d i m e n t a t i o n - e n u m e r a t i o n (SE)
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I4O
K . R. C A M E R O N
I
AND
C. J. B R A D I S H
I
I
0.6
e~
,¢
"~ 0.5
o
..o
= 0"4
.q
0-3
0.2
Control, no haemagglutinin
rll 0-1
0
0-5
I
1-0
I
2.0
I
3.0
I
4-0
log D~-log (overall dilution of haemagglutinin)
Fig. 4. Influence of concentration of R B C and concentration of SFV haemagglutinin on extent of
agglutination (B]R) observed by sedimentation-enumeration. • - - • , 2"5 × Io 7 RBC/ml. ; O - - O,
1-7×iO7 RBC/ml.; A - - A ,
8.o×Io6RBC/ml.; ~--A,
3 ' 2 × I O ~ RBC/ml.; I - - L
I'3XlO 6
RBC]ml.
was 75 -+ 4 % (~6 observations) of that by haemocytometer and probably reflects uncertainty
in the definition of short counting times or of haemocytometer chamber volume. However,
this does not influence the characteristic-ratio B/R which is time-independent.
Effect of red cell concentration on the extent of agglut&ation
For the sedimentation-enumeration (SE) method, the maximum red cell concentration
is limited to about 2"5 x lO7 RBC/ml. by difficulty in identifying and counting all RBC
aggregates when more than about ten are in the field of view at one time. The effect of a
range of RBC concentrations (I.3 x ~o6 to 2"5 x ~o7 RBC/ml.) on a range of dilutions of
haemagglutinin reacting at p H 6"3 is shown in Fig. 4. The central, linear region in the
characteristic indicates that if RBC are in excess then the ratio B[R is independent of RBC
concentration. Also, with increasing haemagglutinin concentration, the extent of agglutination rises to a maximum and then maintains a distinct plateau at a B]R ratio determined
by the concentration of available RBC.
An optimal RBC concentration of about ~oT/ml. was selected for later experiments since
this gave a convenient width to the central linear portion of the relationship between B/R
and log D. At this concentration aggregates composed of more than ten RBC were rare
(~ % at high haemagglutinin concentrations).
Effect of pH on haemagglutination
In view of the different mechanisms involved it was possible that the p H of the reaction
mixture was critical in the pattern test for haemagglutination at the container wall surface
but not in the SE method for initial attachment of haemagglutinin or for formation of the
earliest small aggregates in free suspension. The optimal ranges o f p H for the haemagglutina-
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Kinetics of haemagglutination by SFV
4'0
I
I
I
I
I4I
I
0
0
e-
o
.~ = 3'0
~.~_
~
1"0
¢4)
bl) bO
-E
0
6.
I
I
I
I
I
6'2
6"3
6-4
6-5
6"6
6'7
pH of reaction mixture
Fig. 5. Comparison of influence of pH on observation of haemagglutination in the pattern test
( 0 - O) and by sedimentation-enumeration ( © - ©). In order to express the results of both
tests on a common basis, the limiting dilution of SFV haemagglutinin for first detectable agglutination is presented. For the sedimentation-enumeration method this dilution (Dz, Fig. I) defines the
Haemagglutination Index (HI = log Dz).
The BB-BSA medium was used throughout, as defined in Methods.
100 --H 7.6
>
~
80
.?.
.~ ':
60
~~
~ 4o
=
pH 6"3
20
pH 6-0
10
20
30
40
50
60
Reaction time, rain.
Fig. 6. Influence of pH of reaction mixture on inactivation of SFV haemagglutinin. A standard
SFV haemagglutinin was held in the BB-BSA medium at different pH values for various times at
23 ° and then rapidly adjusted to pH 8'o with BB-BSA prior to assay of residual haemagglutinating
activity by the pattern test.
tion of goose RBC by SFV were therefore determined in parallel by the pattern and SE
methods. The results are expressed (Fig. 5) as the logarithm of the limiting dilution
(log D~ = haemagglutination index, HI) at which virus-specific haemagglutinating activity
was first detected. The optimum and the range of p H for the formation of aggregates are
identical for reactions in free suspension in the SE method and for the formation of more
massive settled aggregates in the pattern test.
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I42
K. R. C A M E R O N
I00
i
-
80
= ~
"-.-~
60
~E
40
i
!
I
A N D C. J. B R A D I S H
I
I
i
I
1
1
x 107 RBC/ml.
k
~
0
I
0
~
I
10
1~0 ~
I
I
20
I
~
30
-
I
I
40
I
I
i
-
50
60
Reaction time, rain.
Fig. 7. Influence of RBC concentration in reaction mixture on adsorption of SFV haemagglutinin.
A standard SFV haemagglutinin was adsorbed by RBC in the BB-BSA medium at pH 6"3 for
various times at 23 °. The RBC were then removed by centrifugation and the residual haemagglutinating activity of the supernatant fluid sample assayed by the pattern test.
Rate of inactivation of haemagglutinating activity by pH
Reaction mixtures of SFV haemagglutinin without RBC, at pH 6.o, 6"3, 6"4, 6-6 and
7"6 were sampled at defined times at room temperature (23°). Samples were adjusted
immediately to pH 8.o with BB-BSA medium to limit further p H inactivation, and the
residual haemagglutinating activities estimated by the pattern test. The percentage of initial
haemagglutinating activity detected at various reaction times (Fig. 6) showed that there
was complete and rapid inactivation at pH 6-o. At the assay-optimum of p H 6"3 about
5o % of the initial haemagglutinating activity was inactivated within a reaction time of
15 to 3o min.
Rate of adsorption of haemaggtutinin by RBC
It has been shown above that the haemagglutinin-RBC reaction mixture must be at
pH 6"3 for maximal adsorption or bond formation to be observed as haemagglutination.
Since it has also been shown that the haemagglutinin was significantly inactivated at
pH 6"3, it is clear that the final expression of haemagglutination depends upon the competition between inactivation and aggregation.
To test this further, reaction mixtures at pH 6"3 of haemagglutinin with different RBC
concentrations (2" 5 × IO6 to 3"8 × 107 RBC/ml.) were sampled at defined times at 23 °.
After the removal of free RBC and aggregates by centrifugation at 2ooo rev./min, for
5 rain., the cell-free supernatant fluids were assayed by the pattern test for residual haemagglutinating activity. The percentage of initial activity detected at different adsorption times
showed (Fig. 7) that the greater the concentration of RBC, the greater the rate and extent
of adsorption of haemagglutinin. This was confirmed by further experiments in which a
constant concentration of RBC adsorbed a constant proportion of haemagglutinin regardless of the initial haemagglutinin concentration. Such results (Fig. 8) illustrate that the
'percentage law' which describes neutralization of virus infectivity (Andrewes & Elford,
I933; Bradish, Farley & Ferrier, I962) may also be applied to adsorption of haemagglutinin.
When the results for the pH inactivation of haemagglutinin and for its adsorption to
RBC at p H 6"3 are presented together, it appears that at the RBC concentration of about
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Kinetics o f haemagglutination by S F V
lO0 ~1
._>
~
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
80
~
60
E
~
¢} O
40
=
20
=
1
I43
0
-\.
I
20
30
40
Reaction time, min.
10
0
50
60
Fig. 8. Expression of adsorption of SFV haemagglutinin to RBC as percentage law showing
constancy of fraction adsorbed regardless of haemagglutinin concentration. The various dilutions
of a standard SFV haemagglutinin were adsorbed by lo 7 RBC/ml. at 23° and pH 6"3 in the
BB-BSA medium. The RBC were removed by centrifugation at specified times and the residual
haemagglutinating activity of the supernatant fluid samples assayed by the pattern test. The overall
dilutions of haemagglutinin were, 01~, 0-~-o-,~An_o_
,1 ~81¢, I ~ .
100
/
I
,1
/%,
~
,
..........-o
,," /
,>"
\N %\\
0
6.0
6.l
L
6-2
6.3
6.4
6.5
pH of reaction mixture
6.6
6-7
Fig. 9. Comparison of pH stability (O - - O) of haemagglutinin, efficiency of adsorption (- - -)
of haemagglutinin to RBC, and overall expression of haemagglutination (0 - - O) after reactions
for 15 min. at 23 °. A standard preparation of haemagglutinin was tested for pH stability (as for
Fig. 6), for adsorption to RBC at Io~[ml. (as for Fig. 7) and for overall haemagglutination in the
complete pattern test.
IO 7 R B C / m l . , a d s o r p t i o n occurs m o r e rapidly than p H inactivation at reaction times up
to a b o u t 15 min. Thus, the a d s o r p t i o n a n d p H inactivation o f h a e m a g g l u t i n i n at near
o p t i m a l p H values are c o m p e t i t i v e reactions which c o n t r o l the extent o f final h a e m a g g l u t i n a tion. Fig. 9 shows as a f u n c t i o n o f p H the efficiency o f detection o f h a e m a g g l u t i n a t i n g
activity due to a c o n s t a n t initial c o n c e n t r a t i o n o f virus as haemagglutinin.
IO
FIR
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I6
I44
K. R. C A M E R O N
AND
C. J. B R A D I S H
Table 2. Correlation of estimates of concentration of Semiliki Forest virus
by different methods
Number of physical
particles/ml, by
electron
microscopy
Ho = Io × IO9
50 ×
96×
I9 ×
20 x
Number of initial
infective units/ml,
by plaque
counting*
I "o ×
4"2 × I01°
I 0 ~i
IO × I011
IO TM
i o 12
0'73 × IO TM
0.62 × IO 12
Physical
particles per
infective unit
Physical
particles per
RBC-RBC bond
9"8
h,~ : 2"6
I I'9
9"4
26
32
I0"3
83
37
50
H°
h-'~-= 3"8 × IO9
IO9
I 0 TM
Minimum number of
haemagglutinating
units/ml, by
sedimentationenumerationS"
4 ' 9 × IO1°
I ' 2 × I o 11
o"52 × I o 12
0,40 × Io 12
* Before preparation of haemagglutinin the virus sample was assayed for infectivity by plaque counting
in agar suspensions of primary chick-embryo cells.
t Assay of haemagglutinating activity (equation 2 ) b y sedimentation-enumeration under optimum
conditions of pH 6"3 and 2o7 RBC/ml.
Virus concentration and haemagglutination
Since the extent o f agglutination o f R B C in excess by a given preparation o f SFV haemagglutinin has been shown to be independent o f R B C concentration, it follows that appropriate observations m a y be used to estimate the particle concentration o f virus as haemagglutinin. Thus the outcome o f the reactions discussed above and shown typically in Fig.
and 9, m a y be expressed through the relationship:
Concentration o f haemagglutinating particles (HolD) at dilution used
x fraction o f haemagglutinating particles which escape p H inactivation ( I - ~)
= n u m b e r of specific bonds per red cell { ( B / R ) - (B[R)o}
x concentration of red cells (R)
x m a x i m u m n u m b e r of haemagglutinating particles[bond (h,~).
On transposition of terms this yields,
Ho = D. hm. R. {(B/R) - (B/R)o}
(0
(~ -~)
It is shown in Appendix II that ~, the fraction of haemagglutinating particles inactivated
by pH, m a y be defined in terms o f the rate constant (k) for p H inactivation and the rate
constant (K) for adsorption of haemagglutinin by RBC.
Thus,
k
K.R+k
The rate constants k and K are independent of R B C concentration but are otherwise
characteristic of the reaction conditions o f pH, medium and temperature. F o r a concentration o f I.o9 x 2o v RBC[ml. at p H 6"3 we find (Appendix II),
k = 4"o + o'55 × Io-4[sec.
K = 5"4-+ o'63 × xo -11 ml./cell sec.
= o'4;
k[K = o'76 × I o 7 cells/ml.
On inserting these values into equation 0 ) , the estimate of haemagglutinin particle concentration reduces to
Ho
hm
D. R+T:
"
~ o
(2)
.
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Kinetics of haemagglutination by S F V
0-12
010
~
uE
~= Ill
I
0.08
0"06
I45
oO//C
0.04
0.02
0
I
0
0.2
I
I
0.4
0.6
10
I
I
I
0.8
TM
D(R+ k )
Fig. Io. Estimation of h,,, the number of virus particles adsorbed/RBC for formation of one
RBC-RBC bond. It has been shown, see text and equation 2, that
Ho/h,,~= D.(R+k[K).{(B[R)--(B[R)o}
expresses the extent of bond formation (B[R)-(B[R)o as a function of the haemagglutinin concentration (HolD) and the extent of pH inactivation (equation 7) which occurs before adsorption.
Thus the slope of the above characteristic is Ho[h,~,where an estimate of the initial haemagglutinin
concentration as physical particles is available through electron microscopy as Ho = I'o2 × IO1°
particles/m1. Thus the mean slope of 1.42 x lo ~ bonds/ml, indicates a central value for h,~ of about
7 particles/bond.
This is the f o r m for which experimental values are tabulated in Table 2 and c o m p a r e d
with estimates of infectivity (p.f.u.[ml.) and particle concentration for different virus
preparations. These estimates were calculated for values of b = (B/R)- (B[R)o below o.2o
since these f o r m the lower part o f the central linear region B (Fig. I) where the sensitivity
of the m e t h o d is optimal and h~ is a small and constant integer.
The small integer h .... the n u m b e r of haemagglutinating particles/bond, m a y be determined by presenting b = (B[R)- (B]R)o for low concentrations of haemagglutinin against
I/D(R+(k/K)). The mean slope (Fig. Io) is equal to the ratio Ho]hm.
Comparisons with estimates o f virus concentrations (Ho) by counting in the electron
microscope indicate that for the o p t i m u m reaction each R B C - R B C b o n d requires f r o m
3 to IO (Table 2, Fig. Io) virus particles to be adsorbed after escaping p H inactivation.
These estimates for hm depend u p o n the status o f each virus preparation and the extent
to which physical particles retain the potential for haemagglutination. Haemagglutinating
activity and b o n d formation are not simply correlated with either physical or initially
infective particles.
The size distribution of aggregates
A n interpretation of the observed distribution o f aggregates formed by haemagglutination
m a y be obtained t h r o u g h the statistical-mechanical theory proposed by Goldberg (I 952, 1953)
for the antigen-antibody interaction. This theory m a y be applied to the haemagglutination
I0-2
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I46
K. R. C A M E R O N
A N D C. J. B R A D I S H
C
4.0
I
f
I
I
1
2
3
4
I
I
I
]
I
5
6
7
8
9
~5 3.0
~0 2.0
1.0
"~
hi)
0
--~
( n - I)
Fig. ~1. Estimation of extent of haemagglutination as bonds per red cell (B/R) from distribution
of sizes of aggregates formed at different concentrations of haemagglutinin. The Goldberg distribution (see text and equation 3) indicates that the frequency An of aggregates of n red cells is
given by log A,, = ( n - I).log (B/R)+log A1. The results above for observation by sedimentationenumeration of a standard reaction mixture of IO7 RBC]mI., pH 6"3, 23 °, in BB-BSA medium,
conform well to this equation and show by their slopes, log (B/R), the values discussed further
in Table 3.
Table 3. Comparison of estimates of the extent of agglutination p = B/R derived from
enumeration of bonds (Appendix I) and distribution of aggregate sizes (equation 3)
Reaction
mixture
A
B
C
D
E
F r o m enumeration of bonds :
B
NAn
R - [ Zn.A~
From distribution of aggregate sizes (equation 3) :
B
log A n - log A1
log~=
n-1
B
o'19
0.26
0"32
0"41
0"49
-- o'I74-35 ~
o.32+22 ~°
0'384- 12 ~
0'494- I3 ~
0.59_+ I2 ~o
R
logA1 = 3"3---9
3-I±6~o
3"1 4-3
3'0---4
2"94-4
The reaction mixtures are those giving the distributions of aggregate sizes shown in Fig. 11 ; details are as
given in the legend.
reaction in the simplified form presented by Bradish & Crawford ([96o), since RBC are
in excess to haemagglutinin as the limiting reactant.
The fractional concentrations of RBC which appear free or as dimers, trimers, tetramers
and n-mers may be defined as F1, Fz, F3, F4 and F,~, so that,
I = FI+F2+Fa+F4+ ... +F~,
and the number of RBC-RBC bonds/red cell,
B
R
=
I
F1F~
[
2
F3
3
F4
4""
Fn
n"
For a given RBC concentration, this ratio is proportional to the concentration of haemagglutinin in the reaction mixture if the number of particles of haemagglutinin/RBC-RBC
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Kinetics of haemagglutination by S F V
0-5
I
I
I
~47
I
0-10 0.25 1-0x 101° particles/ml.
0-4
O
,.Q
o
e~
III
I
0.3
0.2
0.1
0
4"0
5.0
1"0
2"0
3"0
log D~-log (overall dilution of haemagglutinin)
Fig. 12. Relationship between extent of agglutination and concentration of SFV haemagglutinin
in direct observation (0) by sedimentation-enumeration and as anticipated by text equations 2
and 3 for limiting virus concentrations of 0'[, 0"25 artd I .o x ]o 1° particles/ml. The lower values
observed indicate the falling efficiency of haemagglutination as an increasing number of virus
particles are wastefully adsorbed and sterically hindered in reactions at higher concentrations of
haemagglutinin.
bond is constant. If the effective valency of the RBC in haemagglutination is taken to
be z, the Goldberg distribution then reduces to
Fn = n.p ~'-1 - ( I - p ) ~ ;
B
p = ~,
and the fractional concentration of n-fold aggregates of RBC then becomes,
log A,~ = ( n - ~ ) . l o g p + l o g A1.
(3)
When actual values for log A~ are presented (Fig. ~0 against corresponding values for
( n - I ) , the resulting lines show slopes which correspond closely with the theoretical expectation of log p, or log (B/R), obtained from other experiments (Table ~). The intercepton
the ordinate is at log A1. The scatter in the points of the lines at ( n - I) values above six
is due to the much smaller number of aggregates counted at these sizes and to the uncertainty in the identification of size for aggregates of more than about 6 red cells. Thus,
the distribution of aggregates following haemagglutination is consistent with this simple
theory and provides a further distinct estimate of the extent of agglutination p = B/R
(equation 3 and Table 3) to be compared with that by equation 5 of Appendix I. The
general agreement between these estimates by distinct methods justifies this simple analysis
of haemagglutination in the present system.
Adsorption of haemagglutinin by RBC
The analysis given above for the formation of bonds as the primary reaction is related
to the concentration of particles of haemagglutinin by the assumption that, under conditions of limiting dilution, every RBC-RBC bond is formed by one particle of adsorbed
haemagglutinin but not that every particle is adsorbed or can give rise to a bond (h~ > I).
The present results indicate that, for optimal conditions of reaction, of every to initial
particles 4 are inactivated by pH and about 6 are adsorbed by RBC. However, of these 6,
4 or 5 are adsorbed at ineffective or sterically hindered sites and only I or 2 then form
detectable RBC-RBC bonds. The presence of wastefully adsorbed haemagglutinin has been
demonstrated by the formation of further bonds when fresh RBC are added.
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I48
K. R. C A M E R O N
A N D C. J. B R A D I S H
In reactions of I0 v RBC/ml. with more concentrated virus preparations (b > o'25,
Table 2) the RBC are increasingly saturated with haemagglutinin so that up to 25 %
escape agglutination and only I to 3 % of virus particles are associated with the formation
of RBC-RBC bonds. This is illustrated by the saturation regions in Fig. I and 4 and in
more detail in Fig. I2. Each experimental point lies on a theoretical curve determined by
the concentration of particles of haemagglutinin available after pH inactivation. These
experimental results are acceptable for quantitation of concentration of haemagglutinin
only under conditions (b ~< o.2o) for which steric hindrance is negligible and wasteful
adsorption is minimal and may be estimated (Fig. IO) with some confidence.
The much simpler estimation of relative activities or concentrations of haemagglutinin
is not restricted by these absolute considerations and may be obtained directly and quantitatively from the reproducible characteristics of the type shown in Fig. I.
DISCUSSION
Unlike the pattern method of haemagglutination, the sedimentation-enumeration (SE)
method allows the distributions of single and aggregated RBC to be characterized in detail
and in free suspension without influence by shape or charge of container walls. One of the
most fundamental observations of the SE method is that a definite population distribution
of aggregates is formed in haemagglutination reaction mixtures. This differs from the
implications of work by Levine et aL (I953), Cheng (I961) and Nozima et aL (I964) who
interpreted their results in terms of the 'dimers-only' hypothesis by which the distribution
of aggregates in a mixture of RBC and haemagglutinin (haemagglutinin: RBC = c. o. 15)
is assumed to be composed entirely of single RBC and dimers in which two RBC are bound
by haemagglutinin. Other studies (Cameron, I969) have shown that the simple 'step-curve'
anticipated as a consequence of this 'dimers-only' hypothesis cannot be observed photometrically for haemagglutination reaction mixtures but is produced by synthetic and nonagglutinating mixtures of, for example, sheep and goose RBC of distinct sedimentation
rates.
The observation that a high proportion (about 25 °/o) of RBC remain unagglutinated
even at high concentrations of haemagglutinin may be explained in terms of the saturation
of some cells by adsorbed haemagglutinin. These ' saturated' cells cannot combine to form
aggregates and thus constitute the 'free-cell' phenomenon of McKerns & Denstedt 0950);
this effect is most pronounced under reaction conditions of high relative concentrations of
haemagglutinin.
It has been shown repeatedly that there is a small but significant extent of agglutination
which occurs spontaneously in RBC suspensions in the absence of haemagglutinin. Although
this spontaneous agglutination has been noted by Smith & Courtney (I965) as responsible
for a background effect, the phenomenon has not been emphasized in other studies of
haemagglutination.
This study has established the importance of the pH of the reaction mixture in determining the level of haemagglutinating activity subsequently observed. There is direct
competition between pH inactivation and adsorption of haemagglutinin to RBC and any
quantitation of the overall reaction must take account of the two rate constants. Although
this important feature of haemagglutination by representative arboviruses has been recognized (Chanock & Sabin, I954), its impact on quantitation and interpretation has been
disregarded.
Any method for the estimation of haemagglutinating activity estimates some quantity
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Kinetics o f haemagglutination by S F V
I49
related to the concentration of RBC-RBC bonds rather than that of potential haemagglutinating particles. Such estimates therefore cannot include the numbers of particles not
available for the formation of bonds due to pH inactivation, aggregation of particles and
adsorption to the walls of the reaction vessel. Not every potentially haemagglutinating
particle is necessarily involved in the formation of RBC-RBC bonds since some may be
wastefully adsorbed to the RBC in unfavourable sites and others sterically hindered. Thus,
the experimental estimate of 3 to Io particles/bond is an overall estimate of the initial
number of particles required for a bond to be formed in reaction mixtures containing
about Io 7 RBC]ml., but not of the number of particles actually involved in each bond.
The consideration of the kinetics of adsorption provides a relationship between the concentration of particles of haemagglutinin and the number of bonds formed between RBC,
and is complementary to the Goldberg treatment of the formation and distribution of
aggregates of various sizes. Thus, the sedimentation-enumeration method and its associated
interpretation allow a direct evaluation of the initial concentration of particles of haemagglutinin in terms of the concentrations of RBC and bonds, together with the appropriate
rate constants for pH inactivation and adsorption to RBC.
It must be emphasized that for SFV, at least, optimum haemagglutination at pH 6"3
is a dynamic interaction taking place under conditions contrary to those for preservation
of infectivity (above pH 7"3). Thus haemagglutinating activity is not an intrinsic or colligative property of the infective particle (Table 2).
This work formed part of a thesis (K.R.C.) submitted for Ph.D. degree of the University
of Edinburgh (I969).
The authors are indebted to Mr S. Peto and Mr B. J. Maidment for statistical and
computational advice and support, and to Mr K. Allner and Mr D. H. J. Titmus for much
help in experiment and preparation of this paper.
APPENDIX I
Theoretical basis of sedimentation enumeration (SE) method
If haemagglutination occurs in a reaction mixture at equilibrium containing haemagglutinin and RBC, then each unit volume contains A 1 single cells, A2 dimers and An n-fold
aggregates. The available R red cells are then distributed so that;
R = AI+2A2+3A3+...+n.A~.
Each n-fold aggregate has a minimum of ( n - I ) effective RBC-RBC bonds due to the
presence of haemagglutinin, so that the minimum concentration of bonds/ml., and by
inference of haemagglutinating particles/ml., is defined by;
or
B = A2 + 2A3 + ... + ( n - I) A~
B = R - ( A I + A 2 + A 3 + ... +An).
Thus, the distribution of RBC and aggregates defines the average number B[R of bonds/red
cell;
B
ZA~
i
(4)
R
Zn. A~'
where An is the actual concentration of aggregates containing n RBC each.
However, A, is not observed directly but in terms of the number, C,, of n-fold aggregates
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I50
K. R. C A M E R O N A N D C. J. B R A D I S H
0"5 /--
,
I
I
f
f
Slope K.R+lc
2-303
•
•y,
-~
~ 0"4
~
~
,
~
0
~- ~ 0.3
k
.
0
0
300
600
900
Reaction time, sec., t
Fig. 13. Evaluation of the first order rate constants for pH inactivation of haemagglutinin (©)
and for adsorption of haemagglutinin (O) to red cells. Reactions at a3 ° at pH 6"3 generally as
indicated in legends to Fig. 6 and 7. The slopes of the lines indicate the rate constants for pH inactivation (0, k) and for adsorption (O, K) as discussed in Appendix I[. Red cell concentration,
I'O9 x ioT]ml.
settling past the reference base-line of length I in the observation time t. The relationship
between C. and A, may be determined in terms of the sedimentation velocity, s., and the
depth of focus, f~, for n-fold aggregates. We may then write;
cn
A~ - sn-fn,
l.-----~t"
Substituting these expressions for each An into equation 4 leads to the form
B
p = ~ = i
Y~Cn.Vn .
~n. Cn.E~'
sl .fl
(5)
E, =Sn.¢;,"
The values of s~, fr, and Fn, determined in preliminary calibration experiments, are method
constants for the optical arrangement (see methods) and goose RBC used in this study.
A Ferranti Meteor Mercury Computer was programmed in Autocode to evaluate B[R
and related quantities from the distribution Cn observed for each haemagglutination
reaction mixture.
The extent of bond formation due to self aggregation of RBC in the absence of haemagglutinin is termed (B/R)o and requires to be subtracted from the overall extent of bond
formation to show that due specifically to added haemagglutinin;
These features are illustrated in Table I and have been discussed elsewhere (Cameron, 2969).
A P P E N D I X 12
The competition between pH inactivation of haemagglutinin and adsorption
of haemagglutinin by RBC
Consider a reaction mixture containing 1to particles of haemagglutinin/ml, and R red
blood cells/ml. The haemagglutinin is being inactivated by pH while it is also being ad-
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Kinetics of haemagglutination by SFV
I5I
sorbed by red cells (see equation 8 below) so that a terminal state is established in which
the fraction of haemagglutinin inactivated by pH before adsorption is given by (Cameron,
I969);
k
- K. g + ~ '
(7)
where K is the first order rate constant for adsorption of haemagglutinin and k is the first
order rate constant for inactivation at the specified pH.
The rate constants may be evaluated from the first order equations;
Ht = Ho. exp ( - K. R. t); H~ = Ho. exp ( - kt),
(8)
which define, respectively, the time course of adsorption and pH inactivation in appropriate separate experimental systems. In each case Ht is the concentration of free and still
active haemagglutinin detected after time t sec.
When the results (Fig. I3) for representative experiments at constant red cell concentration are presented as log depression of haemagglutinating activity, log (HJHo), as a
function of time up to I5 rain., acceptable lines of proportionality are obtained for which
the slopes indicate the values of the required rate constants. The mean values (_+ I o % )
obtained for the rate constants are quoted in the text and characterize the haemagglutination
reaction under the present conditions.
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