Kinetics of cell agglutination

Experimental Cell Research 101 (1976) 191-201

KINETICS A Quantitative

W. A. M. LINNEMANS,’ Biological

OF CELL

AGGLUTINATION

Assay of Concanavalin A Mediated Agglutination of Acanthamoeba castellanii F. SPIES, TH. M. DE RUYTER DE WILDT and P. F. ELBERS

Ultrastructure

Research

Unit, State University,

Utrecht,

The Netherlands

SUMMARY ConA-mediated cell agglutination is studied by measuring changes in light transmission of cell suspensions. The results of experiments are compared with those from a model of agglutination kinetics. The agglutination rate, k;, is proved to be dependent on initial cell concentration, amount of agitation and temperature. In all cases it has a maximum at a given ConA concentration which is not influenced by the other agglutination conditions. From the light transmission data we found an average of 2.6X lo9 receptor sites/cell and a mean aflinity constant for ConA of 0.5X lo8 M-l. The differences between model and experiment give information on cell specific parameters. Especially the contribution of the acanthapodia in the agglutination process is discussed. Reproducible results cannot be obtained unless temperature and amount of agitation are kept constant.

We are studying single cell differentiation in ferences in membrane biochemistry deAcanthamoeba castellanii with a special in- pendent on cell density changes accomterest in the role of the cell surface in this panying population growth [5]. The ConA-mediated agglutination of process [la]. The cell surface is the site of interaction of the cell with the surrounding these amoebae differs also according to the stage of population growth [6]. Agglutinamedium and with other cells. We have found that during the growth of tion is maximal in the middle of the logaritha cell population the ultrastructure of the mic multiplication (LM) phase. No aggluplasma membrane changes [4]. The sym- tination can be observed in the stationary metrical membrane of the trophozoite is phase under our assay conditions. So a altered into an asymmetrical one by the change of agglutination behaviour may be time of decrease of the population growth. indicative of the onset of differentiation. Several factors can be put forward to exThis is followed by the appearance of electron-dense patches on the membrane when plain these observations. In the first place it population growth is stopped and cysts are is known that, at least in some mammalian initiated. We furthermore observed dif- cells, agglutination is maximal during the M phase of the cell cycle [7,8,9]. During pop ulation growth of A. castellanii the distrii Address: Department of Molecular Cell Biology, Biological Ultrastructure Research Unit, State Unibution of cells in the different phases of the versity Utrecht, Padualaan 8, de Uithof, Utrecht, The cell cycle is changing [ 10, Ill, which could Netherlands. 13-761806

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be reflected in a changing agglutination be- where .\- is the averagt’ number of cells per clump and cell concentration in cellsidm’. At time haviour. Secondly, changes in cell mem- In,,=O.thei =initial 1. so E,, is given by: brane composition during population (3) growth [5] could influence the mobility of E,,=0.434dn,,A,K, receptor sites and concomitantly the ag- To know the value off. we combine eqs (2) and (3) to glutinability of the cells [ 12, 131.In the third (E”/E,)“=x (4) place, the components of the external surwhich is assumed that the cell volume is a constant. face (like glycoproteins, charged groups, in which we have confirmed in our experiments. Merhod. Essentially the method of Born 1191 or etc.) can change during population growth Marikovsky [20] is followed. Light transmission at resulting in differences in receptors, re- X=500 nm is recorded. The cell suspension in the ceptor site accessibility and/or receptor site cuvette is agitated with a magnetic stirring device. stirring speed is calibrated with the aid of a affinity [14, 15, 161. Cell surface mor- The stroboscope. The cuvette and the cell suspension are phology and overall cell shape are further- thermostated (tO.Y’C). The method is further carried out as described elsewhere [6]. From the recorded more important factors in lectin-mediated graphs, .Uis calculated according to eq. (4). cell agglutination [9, 171. In a previous article [18] we proposed a Determination of the agglutination theoretical model for the process of cell ag- rate, k; glutination. In this model the average num- In the foregoing article [ 181the equation ber of single cells per cell clump is related to k;=k,nQe(l-e) (5) some pertinent parameters. In combination with a sensitive and quantitative agglutina- is given [eq. (16)]. Here k, is the agglutination rate constant and 6 represents the fraction of occupied receptor tion assay [ 19, 20, 211, this model is used to sites. During the first stage of agglutination, when disanalyse the agglutination kinetics in A. aggregation of cell clumps still can be neglected, X is only proportional to t and k; [ 181, according to the casteflanii. An understanding of the para- equation meters that are responsible for differences ,I-=l+k;t (6) in agglutinability, can lead to more insight in the physiological processes, underlying k; is determined from measurements in a small time interval at the beginning of agglutination. k; is proporthe cell surface changes that are involved in tional to k, at constant n, and 13(l-0). the process of cell differentiation. An approximation of K,, the affinity constant, and m, the mean number MATERIAL AND METHODS of receptor sites At low concentrations of ConA, 0 is nearly zero and The agglutination assay Theory. For large scattering particles the light extinc-

tion of a suspension is: E=0.434dZ,njA,Kj

(I -0) goes to unity. In our model we proposed the following equation for ConA binding to the cell surface.

(1)

“no pbP,-

[21, 22, 231. Here, A is the cross sectional area of a particle, K the scattering efficiency, n the number of particles and d. the cuvette path length. The subscript j denotes the class to which the particles belong. In our work we consider the process of agglutination in a homogeneous population of cells and we assume that cells and cell clumps are spherical. According to Kaneko et al. [21], the extinction of such a system at time t is:

AV

E,=0.434 dhrA,K,(B)-“” Erp Cd Res 101 (1976)

(2)

l++

a

(7)

where PO is the applied ConA concentration and N,, Avogadro’s number. The free ConA concentration at equilibrium is given by P, = P, - p

8,

(8)

AV

A first value of k; is related to 0,. If after equilibration

Kinetics of ConA mediated agglutination

193

all cells are removed and another n, cells are added, a second value of k; is determined by 0,. The free ConA concentration becomesI’, when equilibrium is reached again. When this procedure is repeated p times, the following equation can be given

(9) From eq. (5) we get the following expression

can be solved according to

(I-a)“=l-na+-.

n(n - l)u2

Fig. 1. Abscissa:

. ., a -+1, which is true at high

2! and low ConA concentrations Thus 0 becomes tl=f+t(l-2k;/kln,). concentrations we get 1 a,e 1-

e, 9 ~&;),i

When k,n,,/(k&,*l -

4

I-@,

At low ConA

cell cont. in cells/ml; ordinate: extinction. Extinction as a function of the cell concentration.

between extinction and cell concentration is given in fig. 1. From these data and eq. (3) we calculated A,K,=5.2x 10m6cm*/cell for cells from the middle of the LM phase of population growth.

- 1

RESULTS

this equation may be rewritten in

(k;), 4 =, substitution of 0, and k,n, l-0,

Second order reaction kinetics in agglutination processes One of the basic assumptions in our model is that all steps in the agglutination are sec-

in eq. (9) gives

30

which after some rearrangement gives

1

(10) According to this eq. (10) a plot of (k;),-,-(k&, versus (k&, will give a straight line from which the product K,m can be calculated. From other measurements (described in the results) a second function of K, and m can be found so the values of K, and m are obtained.

Cells cnstellanii cells were grown in a medium described by Neff [24]. Cells from different stages of population growth were harvested by centrifugation at 600 g for 1 min, washed and resuspended in MEM [6]. This cell suspension was used for the agglutination assay.

Acanthahzoeba

Determination of the cell concentration The number of cells/dm3 in a suspension was determined by hemocytometer counting. The relationship

-r 0

100

200

300

LOO

dN/dt X 1O-5. -, Theoretical; -O--, measured values. The relationship between dN/dt and no2indicates that the overall agglutination reaction is of second order kinetics.

Fig.

2. Abscissa:

nix 10e8; ordinate:

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6

/

I I

01

I

+-+-+--+-

I

I

I

I

I

I

I

1

2

3

4

5

6

7

8

9

I

10

Fig. 3. Abscissa: time (min); ordinate: (Eo/Er)3. ConA-mediated cell agglutination with different ConA concentrations. n,, 1.8X 10’ cells/ml; T, 3O”C, agitation, 520 rpm. The ConA concentrations are: 0, 10 pg/ml; *, 50 and 1000 pg/ml; X , 100 @g/ml; +, 200 *g/ml; l ,200O pg/ml.

ond order processes [18]. This means a linear dependency of dN/dt from N* at a constant k, and 8. The assumed linear dependency indeed exists as is shown in fig. 2. Only results at low agitation are given, because with high amounts of agitation and low cell concentrations k, is no longer a constant. The influence of the ConA concentration In our model [ 181the agglutination rate, k;, and the maximal mean number of cells/cell clump, X,, are predicted to increase with increasing ConA concentration up to a maximum (when 19=0.5) and to decrease thereafter. In figs 3 and 4 curves of (E,#Q3 versus t are given. From such graphs we determined X, and k: for several ConA concentrations (fig. 5a, 6). Theoretical curves of the relationship between X, or k; and the Exp Cell Res 101 (1976)

Fig. 4. Abscissa: time (min); ordinate: (Eo/Et)3. As fig. 3 except agitation 370 ‘pm. 0, 10 pg/ml; f, 50 /.&ml; x, 100 pg/ml; A, 500 ~g/ml; 0, 1000 f&ml; *, 2 000 pglml; l ,4 000 pg/ml.

ConA concentration are also given in fig. 5. Both experimental and theoretical curves are symmetrical, with the exception that the experimental curve of X, versus ConA concentration is less symmetrical at lower stirring speeds. The inj7uence of agitation In figs 3 and 4 the influence of agitation on agglutination is also demonstrated. The cell suspensions are stirred at 370 and 520 rpm, respectively. The agglutination rate, ki at all concentrations depends on agitation but its maximum remains at the same ConA concentration, at about 250 pg ConA/ml (fig. 5a, b). &,, also depends on the amount of agitation. Its curve becomes more sym-

Kinetics b

of ConA mediated agglutination

195

1.4x 1015sites/cellXmol. Fromeq. (7) and the assumption that 19=0.5 at 250 pg ConA/ml (fig. 5) we get for P,=2.3 x lo+ M and forn,=1.8~ lo5 cells/ml:

K,m=

E=2.3x 10-6-0.15~10-‘5m, with K,m = 1.4~ 1015,this yields: m =2.6x lo9 sites/cell, and K,=0.5x lo6 M-l. The influence of the initial concentration, no

cell

The relation between n, and k; can be calculated from eqs (5) and (7). For this cal1 3 2 L 1 2 3 L culation we used the values: Fig. 2. Abscissa: (a, b) log ConA cont. @g/ml); ordiK,=0.5~ 106,m=2.6x l@,P,=2.3~ lo+ nate: (a) i; (b) k; in min-I. n,,, 1.8x IO5 cells/ml; T, 30°C. Agitation x , 370 rpm and +, 520 rpm. Theo- and k,=4.4x 10°5. retical lines: -, k,, 5.6x 10m5ml/cell min; ---, k,, The results are presented in fig. 7, to4.4~ IO-§ ml/cell min. X and k, as a function of the gether with the observed relation between ConA concentration: k, represents the agglutination rate constant given in mlxcell-lxmin-~, while k; is a no and k;. From these figures it can be seen measure for the agglutination rate (comparable with that the predicted and observed relationhalf time) given in min-r. ship between no and k; is in good agreement. Differences in intercept between the calmetrical, with respect to the concentration culated and experimental lines are due to for maximum effect, at higher agitation. differences in k,. Differences in K, and m The value of X, then is lower because of in- would have resulted in a change of slope of creased disintegration of the cell clumps. the lines. From these observations we conclude that the values of K, and m are rather Determination of the k, values good approximations. From data such as given in fig. 5a, b we determined the k, value of an agglutination rate constant. kl has a maximum at 250 @g a ConA/ml. We now made the assumption 2 that here 8=0.5. For 370 t-pm and 520 rpm, ki is respectively 2.5 mitt-’ and 2.0 mitt-‘. With no= 1.8x lo5 cells/ml the k, values, according to eq. (5) become 5.6~ 10e5ml/cell min and 4.4x 10M5ml/cell min, respectively. 1

_r-

1

Approximation

of K, and m

In fig. 6a, b plots are given according to eq. (10). In fig. 6a, (k;), is plotted against p. From these data the plots in fig. 66 are constructed. We found a mean value for

2

4

68

Fig. 6. Abscissa: (a) p; (b) (k&; ordinate: (a) k; (mm’); (b) (k&,-l-(k&. For explanation see text.

0,100; x, 50 w/ml. Exp Cell Res 101 (1976)

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0.5

50

1.0

10.0

k; (mm’); ordinate: n, in cells/ml. 0, 250 pg ConA/ml; T, 30°C; 370 rpm; 0, 100 p.g ConA/ml; T, 30°C; 370 rpm; A, 250 /.+ ConA/ml; T, 35"C;520 rpm. From eqs (5) and (7) we can get the expression

Fig. 7. Abscissa:

In

--k;=PO----,

Navk, written as

k;

k,n,-k,

1

K,

this equation can be

0!

I

1

I

0

I

r

o-o-

I

I

I

8

9

I

10

o-o-o-o

I 7-

0’

*/

-*-*

*-*

*’ 6-

/

*

0

(k;)*K, m - (k;) N,v k&l + K, P,,, no =

1

234567

/

(k;) K, mk, - N,, K, k: PO

at constant K,, m; P, and k,, this is a function of the U.?+bX which for high values of x approxtype ~=cx+d’

4

imates a straight line. Because of the large trajectory of both values, we plotted it at a log versus log scale.

The influence of temperature The effect of temperature on ConAmediated cell agglutination is presented in fig. 8a, b. As can be seen X, is maximal at about 35°C and it decreases at higher ternperatures. The agglutination rate, k; is zero at 15°C. It increases with temperature up to the maximal temperature of 45°C. The cells could withstand this temperature only for the time course of the experiment. At higher temperatures they quickly disintegrate. We have no doubt however, that the viability of these cells is low after treatment at 45°C. k; is directly proportional to kl, when n, and 8 are kept constant. This offers a posExpCellRes IO1 (1976)

ol

;

I

2

1 1 I

3

4

5

1 1 1 1 1

6

7

8

910

Fig. 8. Abscissa: time (min); ordinate: (EO/E,)3. ConA-mediated agglutination at different temperatures. 6, 15; +, 20; X, 25; +, 30; 0, 35; 0, 40; A, 45°C. Agitation: (a) 520; (b) 370 rpm.

sibility to construct an Arrhenius plot (logk; versus l@ in “K-l) of the agglutination reaction (fig. 9). A kink at about 30°C is observed, dependent on the amount Of agitation.

Kinetics of ConA mediated agglutination

Fig. 9. Abscissa: l/T in OK-‘; ordinate: logk;, Arrhenius plot of ConA-mediated cell agglutination. Agitation: x , 520; +, 450; 0, 370 rpm.

DISCUSSION

197

13(l-13) is of more importance [ 18,331. It is a function of the ConA concentration [ 18,301, and it is important that we observed a bellshaped curve, which represents the relationship between k; and the ConA concentration. The point of symmetry is at 250 pg ConA/ml and is not influenced by agitation conditions (fig. 5). This means in the first place, that binding of ConA to the cell surface is no rate-limiting step (at concentrations above 25 pg ConA/ml) at our mixing conditions, and in the second place that the factor 19(l-0) is dominating the agglutination rate. We have made the assumption that at the ConA concentration of the point of symmetry the receptor site occupation is half maximal, which means 13(1-e) is 0.25. Singer et al. [32]. Vlodavsky et al. [29] and Kaneko et al. [2 11found maximal agglutination in model and cell systems at values of 0( l-0) of about 0.20, which agrees well with our results. Experiments with radioac-

The model for ConA-mediated agglutination presented in a previous report [18] is based on: (1) the fact that ConA binding to the cell surface is a process of simple equilibrium kinetics [25-301; (2) the assumption that time needed for binding of ConA to the cell surface is small compared to the time needed for agglutination [3 11; (3) the assumption that theories for colloid flocculation can be applied to cell aggregation and agglutination phenomena. Here we have tested the parameters on which our model is based and which are important in the flocculation of hydrophobic colloids. The cell specific parameters like cell morphology, mobility of the receptor sites and the influence of cytoplasmic peripheral membrane components [32], will cause differences between theory and experiment, which, in turn, give us information about these parameters. The amount of occupied receptor sites is an important factor in agglutination [25, 27, 31, 32, 331. In agglutination kinetics, how- Fig. 10. Scanning electron micrograph of A. castelever, the probability or bridging factor lanii. X 2 000. Exp Cc// Res 101 (1976)

198

Linnemans

et al.

Table 1 6

Cell type

CM-‘)

Lymphocytes Lymphocytes Hamster cells Hamster fibroblasts Rat lymphocytes Rat lymphocytes Mouse lymphocytes Human erythrocytes Ascites hepatoma A. castellanii

12X’lOfi

3x 106 30-40x 10” 10x 106 3.3x 10” 5x 106 10x 106 3x 106 2x 106 0.5x 106

tive ConA are in progress to confirm our assumption. X, also depends on the bridging factor but at lower agitation the results differ more from the predictions of our model (fig. 5a). In fact we are dealing here not with spheres but with cells showing many acanthapodia. The deviations from theory are probably due to cell specific parameters, like extension and mobility of these acanthapodia. Kaneko et al. [21] first described this dependency of X, on the ConA concentration, which in our hands seems to be strongly influenced by the amount of agitation. The higher the amount of agitation the better the .& values fit into the model. This means that at high agitation levels the influence of the acanthapodia diminishes and the cells behave more like spheres. In the statement that there is no simple relationship between ConA binding and agglutination [ 12, 36,371, in fact only X, is considered, mostly at relative low agitation levels. We found that k; and X, at high agitation levels depend on ConA binding in a simple way. The combination of model and assay technique makes it possible to approximate the number of ConA receptor sites and the affinity constant K, of these sites for ConA. Cells from the mid LM phase of population growth have 2.6~ lo9 sites/cell. Due to the E.xp Cell

Res

101 (1976)

T”C

Ref.

35 0

P51 P51 WI 1251

28

Cited [291 Cited Cited Cited

in ref. [25] in ref. [25] in ref. [25] in ref. [25]

20 ::

:5(1; This paper

large number and the complexity of the acanthapodia (fig. 10) we were not able to estimate the real surface area of amoeba cells; therefore, we have no accurate data about the receptor site density. The mean affinity constant, K,, has a value of 0.5~ lo6 M-l. In table 1 the K, values of several other cell types are given. As can be seen the K, value we found for our amoebae is low compared with that of most mammalian cells. However, K, and m determined by our technique must be compared with K, and m from radioactivity measurements. This will shed more light on the relationship between ConA binding and cell agglutinability (in progress). With a radioactivity technique all receptor sites are determined, but in the aggregatometer only those, which are involved in bridge formation. Furthermore, from a Scatchard plot [25, 301 it can be deduced whether all the receptor sites have the same K, value or not, while in our approach we get a mean value for K,. Some cell types have both high and low affinity receptor sites on their surface in contrast to other cells with receptors showing uniform affinity. Our results with respect to the influence of n,, on the kinetics of cell agglutination are in agreement with those of others [17, 33,

Kinetics

38, 39, 401. We found a minimal cell concentration for agglutination to be observed with our technique, which is about lo41 cells/ml. The agglutination reaction can grossly be considered as: cell-ConA+cell 2 cell-ConA-cell In the rate constant kI, the collision incidenc(e and the collision efficiency are considered as is discussed in a foregoing report [18]. Cells and cell clumps bind together by ConA bridges. Bridge formation takes a finite time. This time is a function of the speed of receptor alignment [41, 421 and of the surface contact fraction of the two cells involved. It will be clear that the larger the number and the extension of the acanthapodia is, the larger this contact fraction will be. Furthermore the mobility of the acanthapodia will affect the chance that a bridge is formed. The factors, which influence k2 are also discussed in our foregoing article [18]. In addition we mention here the cell specific parameters which also determine the value of k,. The shear forces, due to agitation of the cell suspension, which tend to disintegrate the cell clumps, are counteracted by the strength of the bridge and by the forces of friction between the cells in the cell clump. These forces of friction are largely determined by the cell surface architecture h 321. We have assumed [ 181that growing of the cell clumps (i.e. the value of X) stops when the rate of agglutination equals the rate of disintegration of the cell clumps. The cell clumps are maximal (i.e. X=X,) when equilibrium is reached. In order to check this assumption we have agglutinated cells at low agitation conditions (370 rpm). After equilibration (fm = 14), we suddenly increased the stirring speed up to 675 rpm.

of ConA mediated agglutination

199

This resulted in a complete destruction of both cells and cell clumps. After a more gradual increase of the amount of agitation we found a decrease of&, &=2.8) without a destruction of the individual cells. We thereafter lowered the stirring speed again, which resulted in an enhancement of X, up to the initial level (,?,= 13.7). This observation proves that at least in the time interval we are working, we are allowed to consider cell clump formation as a reversible process. Both k, and k, are associated with their own activation energies, which are the sum of activation energies of a complex system of reactions. Changing the temperature will affect k, and k2 in a different way, which is clearly demonstrated in fig. 8a, b. Increase of T results in an increase of k, and of k,. But as disintegration forces mainly depend on r(Z)1’3(at a constant amount of agitation) the influence of T on k, can only be observed some time after initiation of agglutination. As a result of the increase of T the initial agglutination rate is steadily enhanced while, after equilibrium, X, goes through a maximum at 35°C. In fig. 9 an Arrhenius plot of the agglutination reaction is given. At high amount of agitation the line is straight, while at lower agitation level there is a kink at about 30°C. For this phenomenon several explanations are possible. First the collision efficiency depends on the speed of receptor alignment, which on its turn depends on the short range rapid lateral mobilities (RLM) of the receptor sites [41, 421. With a high amount of agitation receptor sites with the highest RLM only will succeed in sufficient receptor alignment. The receptor sites with lower RLM will get a chance, when agitation is less vigorous. Especially these latter receptor sites are affected by temperature changes. Secondly, the value of fl can be changed Exp Cd Res IO1 (1976)

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Linnemans

et al.

due to the temperature influence on K,,. It is not clear, however, how the amount of agitation can introduce a change in activation energy of the ConA binding process. In the third place, the contribution of the acanthapodia in the cell-to-cell binding process can be changed above 30°C. A. castellanii cells react to changes in their surrounding medium towards less favourable conditions by a fast rounding up of the cells and retraction of their acanthapodia. The normal culturing temperature of these amoebae is 28°C. Seemingly a slightly higher temperature has more influence on cell shape or functioning of the acanthapodia than a slightly lower one. Apparently the contribution of the acanthapodia at high agitation conditions can be neglected. This is in agreement with our observations on the relationship of X, and amount of agitation. It is unlikely that we are dealing with a transition point in the fluidity of the amoeba membrane. The high cholesterol/phospholipid ratio and the general lipid composition of the amoeba membrane will result in a transition trajectory around 0°C or lower [43, 44, 461. Many results on thermal inhibition of ConA-mediated agglutination can be explained by a simple dissociation of the ConA tetramer into two dimers at lower temperature, low pH and low ionic strength [17, 34, 37, 461. Our temperature experiments are carried out above 15°C and at pH 7.4, so the dissociation effect will be negligible. Several methods are described where the agglutination assay is performed under carefully controlled agitation conditions, or under conditions where agitation is omitted [17, 26, 34, 35, 38, 46,47, 48, 501. Moscona et al. found that for the purpose of evaluation of cell aggregation [49] and of ConAmediated agglutination [ 161,swirled suspensions are superior. We also think, that agExp Cell Res 101 (1976)

glutination kinetics best can be studied under standardized agitation conditions. The forces which act in the agglutination reactions are either supported or counteracted by the forces due to agitation. The influence of agitation is therefore not equal for all steps in the agglutination reaction. Thus the forces acting in the agglutination reactions can be evaluated by studying them under different, but controlled amounts of agitation. An assay of agglutination by measuring the interaction of light with a cell suspension is generally used in cell biology. Recently this technique is applied to lectinmediated cell-to-cell binding [20,2 1.3 I, 501. It is a fast and sensitive method in which continuous measurements are possible without compromising interferences with the cell suspension itself. There are, however, several differences in measuring procedures and conditions, which, in our opinion, can lead to confusing conclusions [50] and which make it difficult to compare the results obtained by different authors [2 1, 29, 3 1, 50, this paper]. We have presented an agglutination assay which is reproducible and which can be used for several cell systems with relatively high and low agglutination rates. The accompanying theory provides a framework, which can be used to study cell specific parameters involved in the agglutination reaction. We wish to thank Lya Kooiman and Jessica Eken for typing the manuscript, Rudi Horsten for drawing the figures, Arie Verkley, Herman van Rijn and Piet Ververgaert for their critical discussions. We furthermore acknowledge the skilful technical assistance of Henk Pluygers and George van Deijl.

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