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The possible role of steric forces in cellular cohesion
J. theor. Biol. (1976) 63, 405-419
The Possible Role of Steric Forces in Cellular Cohesion R. G. GREIG and M. N. JONES Department of Biochemistry, University of Manchester, Manchester M13 9PL, Great Britain (Received 20 October 1975, and in revised form 15 January 1976) The possible involvement of steric repulsion which may originate between the surface glycoproteins of interacting cells, has been considered with particular reference to cellular cohesion. By employing recently available analytical expressions, the magnitude of the steric energy has been estimated and compared with the electrostatic and electrodynamic interaction energies. In an attempt to illustrate the characteristics of the repulsive steric force relative to the electrostatic force, the surfaces of three mammalian cell lines were defined in terms of surface carbohydrate and zeta potential. It has been shown that the steric force is very large relative to the force arising from the overlap of the electrical double layers and is critically dependent on the amount and density of glycoprotein on the cell surface. In this respect the true cell surface area is an important parameter. The introduction of the steric force does not however unambiguously explain the relative cohesiveness of the cells examined.
1. Introduction The morphogenesis and integrity of tissues depends in part on the way in which cells interact with one another. Despite the extensive work which has been published on the interactions between cells covering both biochemical and biophysical aspects (e.g. Curtis, 1967; Weiss, 1967; Trinkaus, 1969) there is as yet no unified theory of cellular cohesion. The mechanisms of cohesion proposed range from short-range biochemical interactions of the enzyme-substrate type and specific aggregating factors to the more general theories of the relatively long-range physical interactions between charged cellular bodies. Roseman (1970) illustrated the possible role of enzymesubstrate interactions with specific reference to surface glycosyltransferases in cellular cohesion and there have also been several reports of the identification and isolation of specific cell aggregating factors [Hausman & Moscona (1973); McClay & Moscona (1974); Kudo, Tasaki, Hanaoka & Hayaski (1974); Balsam0 & Lilien (1975)J and of specific inhibitors of cell aggregation
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[Merrell (1975)]. The physical study of the problem has been dominated by attempts to explain cellular cohesion in terms of the classical theory of the interaction between lyophobic colloidal particles. The work of Pethica (,1961), Curtis (1967) and Weiss & Harlos (1972) exemplify this approach. It is very questionable whether the surfaces of most cells should be regarded as lyophobic since there is a substantial body of information which indicates that they possess a variety of complex carbohydrates in the form of glycoproteins and glycolipids, which must impart lyophilic character to them. The importance of this “glycocalyx” has been recently emphasized by Maroudas (1975a,b). Qualitatively the existence of polysaccharides attached to the surfaces of cells could give rise to steric repulsive forces as a consequence of the mutual excluded volumes of polymer chains on interacting cells. Analytical theories of steric repulsion are available [Hesselink, Vrij & Overbeek (1971); Evans & Napper (1973); Smitham, Evans & Napper (1975)] and it is now possible to take the first steps towards a quantitative assessment of the significance of steric forces in cellular systems. To do this it is necessary to know the amount of polysaccharide associated with the cell surface and ideally its composition. At present there is little quantitative data on membrane bound polysaccharides ; Kessel & Bosmann (1970, 1974) have reported some values which show that there are differences of two orders of magnitude between different cell lines. Qualitative and comparative studies of membrane bound polysaccharide have also been reported (Leblond-Larouche, Morais, Nigam & Karasaki, 1975; Shin, Ebner, Hudson & Carraway, 1975). We have investigated the polysaccharide levels and physically characterized the surfaces of three cell lines which differ markedly in their cohesiveness. A mouse lymphoma cell (P388 F-36) of low cohesiveness which grows in suspension (Fisher & Sartorelli, 1964) a Chinese hamster fibroblast (CH23) which grows as a monolayer (Tijo & Puck, 1958) and a hybrid cell (PCMl) produced by cell fusion of the two cell lines by u.v.-inactivated Sendai virus (Ayad & Delinassios, 1974). The hybrid cell grows as a monolayer but unlike the CH23 cells does not exhibit any degree of contact inhibition. The chemical and physical characterization of these cell surfaces has enabled us to discuss the possible significance of the steric forces between the cells and we have attempted to use theoretical calculations to explain their relative cohesiveness. It should be stressed however, that there are considerable difficulties in applying sophisticated analytical physical theories to cells, tirstly because cellular surfaces differ markedly from the idealized models to which the theories strictly apply and secondiy the values of all the parameters required for the calculations are not in general precisely known. Although in this
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paper we have attempted to use realistic estimates of the various parameters our main concern is with the relative orders of magnitude of the components of the total interaction energies between cells. In particular we show that the steric forces are very large relative to the forces arising from the overlap of the electrical double layers for these cell lines and cannot be neglected, although their inclusion does not unambiguously explain the relative cohesiveness. 2. Experimental (A)
CELL
Procedures
CULTURES
The three cell lines were routinely cultured in Eagles minimum essential medium supplemented with 10% heat inactivated new born calf serum, 2.0 mM glutamine, 100 units penicillin/cm3, 100 pg streptomycin/cm3 and l-32 mM sodium bicarbonate and gassed with 95 % air and 5 % carbon dioxide. For subculturing purposes CH23 and PCMl cells were released from the monolayer state with 0.05 y/g Difco trypsin (1 lO/BAEE units/cm3), gently dispersed by pipetting and reseeded into fresh medium. (B) ASSAY
PROCEDURES
Sialic acid was liberated from the cells by digestion with neuraminidase (50 units per 10’ cells) at pH 5.5 for 60 min. at 37°C. The supernatant was deproteinized with trichloroacetic acid (final concentration 5%) and the precipitate removed by centrifugatiol;. The resulting fluid was concentrated, and sialic acid assayed by the method of Warren (1959). Suitable control incubations of cells without enzyme and enzyme without cells were also included. Cell surface carbohydrate was liberated from the monolayer cells by digestion with trypsin (Sigma Chemical Co. Ltd., Type III) at a concentration of 55 BAEE units/cm3, pH 7.6, for 15 min. at 37’C. The conditions for P388 digestion involved incubation with a trypsin concentration of 1 BAEE unit/cm3, pH 7.6, for 60 min. at 37X, as high concentrations of trypsin caused rapid lysis of the P388 cells. Longer incubation times did not change the total amounts of carbohydrate released. The supernatant from the trypsin treated cells was deproteinized with trichloroacetic acid (final concentration 5 s’,) and the precipitate removed by centrifugation. The resulting solution was concentrated under reduced pressure and the total carbohydrate was assayed by the anthrone method (Herbert, Phipps & Strange, 1971). Suitable control incubations of cells without enzyme and enzyme without cells were also included. Total cellular carbohydrate was determined in a similar manner on cells homogenized by sonication.
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MICROELECTROPAORESIS
The electrophoretic mobilities of the cells were measured at 25°C in a flat cell equipped with platinum electrodes. The apparatus used has been described by Bangham, Flemens, Heard & Seaman (1958) and was obtained from Rank Bros., Bottisham, Cambridge. The performance and alignment of the apparatus was checked using human red blood cells at pH 7.0, I = O-0172. Preparation of the cells was as follows. The monolayer cells CH23 and PCMl were released from the culture vessel by trypsination (Difco Trypsin, 110 BAEE units/cm3), washed twice with a phosphate buffer pH 7.5 ionic strength O-0172 containing 10.8 % sucrose. The cell suspension was placed in the electrophoretic cell and the mobility measurements completed within 15 min. during which time the cells remained viable as judged by the trypan blue exclusion test. The preparation of the P388 cells was identical, although no trypsin treatment was necessary it was established that trypsinization under the conditions which released the fibroblastic cells from the culture vessel walls did not change their mobilities. Zeta potentials ([) were calculated from the measured mobilities (u) using the Smoluchowski equation (Henry, 1931)
where v is the viscosity of the medium the permittivity of free space. (D)
CELL
of relative permittivity
E, and E, is
VOLUMES
Cell volumes were determined on suspensions of cells in isotonic sodium chloride using a model B Coulter Counter in conjunction with a model J Particle Size Analyzer, 3. Results Table 1 summarizes the results obtained on the three cell lines. The second and third lines give the measured zeta potentials and the surface charge densities (0) calculated from the equation: 1 uq = 0 ; + (
(2)
ai >
deduced by Hunter (1960). In equation (‘2) ai is the average radius of the counterions (taken as 0.25 nm) and K is the Debye-Hiickel function defined
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COHESIOS
TABLE
1
Surface characteristics of mammalian cells Cells
P388
Zeta potential (c)t mV Z = 0.0172 -17 Surface charge density (a) C mm2 4.37 x lo- 3 Zeta potential ([) mV Z = 0.152 -6 Surface carbohydratet yg per lOa cells 5 Number of membrane bound glucose equivalent residues per cell 1.7 :: 108 Total cellular carbohydrate pg per lo* cells 26 Surface sialic acid pmol per 10B cells OGO61 Apparent cell radius (nm) 5000
CH23
PCMl
-22 5.50 x 10-Z -8 50
-20 5.04 ‘I 10-Z -7 105
16 x lOa 237 0.021 8000
35 x 108 345 0.031 7000
t The standard deviations of the measured zeta potentials calculated from the distribution of mobilities was 1.4 mV for the P388 cells and 1.9 mV for the CH23 and PCMl cells. $ Anthrone sensitive material expressed as pg glucose equivalents. by the equation: k.2 =
2N103e2 ( q,~,kT >
I
(3)
where N, e, k, T and Z are Avogardo’s number, the electronic charge, the Boltzmann constant, the absolute temperature and the ionic strength respectively. Line four gives the zeta potentials calculated for physiological ionic strength from equations (1) and (2) assuming constancy of surface charge density (Hunter, 1960). While the zeta potentials of the three cell lines are very similar the surface and total carbohydrate levels are much greater for the fibroblastic cells. We attempted to remove as much surface carbohydrate as possible from the cells but unfortunately the conditions which gave maximum removal from the fibroblasts were too severe for the P388 cells and a lower trypsin concentration had to be used for a longer time. There is the possibility that removal of surface carbohydrate from the P388 cells was not as complete as for the fibroblastic cells, however the sialic acid liberation by neuraminidase was carried out under identical conditions for the three cell lines and here also the fibroblastic cells gave larger sialic levels. 4. Discussion
The total potential energy of interaction (V,> between cells can, to a first approximation, be written as the sum of three terms, a repulsive electrostatic term (V,) due to overlap of electrical double layers, an attractive dispersion
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force interaction (V,) and a term arising from the interaction between membrane bound macromolecules or polymers which protrude into the intercellular environment, the so-called steric interaction term (C’,,). Except in the particular casewhen the medium behaves as a O-solvent for the membrane bound macromolecules the steric interaction is repulsive. Thus we may write v, = v,+ VsR=Va. (4) Becauseof the very large radius of curvature of cells relative to the range of these forces it is reasonable to represent the interaction between spherical cells by a flat parallel model. For fibroblastic cells this approximation is even more justified. According to the DLVO theory for charged parallel plates with a doublelayer potential tie separated by a distance 2d in a symmetrical electrolyte of valency z and concentration n ions wp3, the electrostatic and dispersion energiesare given by the following equations (Verwey & Overbeek, 1948):
6411kTy'
V, = -I,--
-.- exp (- 2~d)
(5)
where y = tanh (~e$,,/4li7’)
(6)
where A is the London-Hamaker constant. Equation (5) is valid provided zeJ/J4kT 3 1; a condition which holds for the relatively low values of I,!I~ pertaining to cells, although lc/o > { to a first approximation tie can be set to the zeta potential since, as will be shown below, V,, % V, whatever value is used for tie within reasonable limits. Smitham et af. (1975) have recently developed analytical expressions for V,, which are applicable to steric interactions between monodisperse polymeric molecules. For a flat plate model in which the polymeric chains are allowed to interpenetrate and can also be compressed V,, is given by the equation?
v is the number of polymeric chains per unit area of contour length L, each chain having i segmentsof volume V,. 1 is the polymer-solvent interaction and VI is the volume of a solvent molecule. t Equation (8) is obtained by combination of equations (1) and (8) of Smitham et rrl, (1975). In thelatter paper equation (8) is incorrect. Thecorrect form is R = (r’?f (l/d - l/L) where the plate separation is 2d (privatecommunications).
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Equation (8) is based on a constant segment density step function, it should be noted however that if a more sophisticated model is used based on a Gaussian segment density distribution values of I’,, are obtained which are very similar to those calculated from equation (8). An equation for V,, based on a statistical model of a confined polymer chain has been derived by Dolan & Edwards (1974). At short distances (< 7 nm) Dolan and Edwards equation also gives numerical results which are of the same order of magnitude as those given by equation (8). Inspection of equation (8) reveals that if d < L, vSR becomes independent of the contour length of the polymeric. chains and furthermore it depends only on the total amount of polymeric material adsorbed per unit area of the plates since the product vi is constant under these conditions. In the context of the interactions between membrane bound macromolecules, such as glycoproteins, this means that if we know the amount of carbohydrate per unit area of the cell surface for the purpose of calculating the magnitude of I/,, for small intercellular separations of the order of a few hundred angstrom units, the molecular weight and the number of chains per unit area are not required. The product vi is simply the number of chain segments per unit area. Thus if we take the hexose unit of a polysaccharide as a chain segment (Flory, 19530) then from the surface area of a cell, the total mass of membrane bound carbohydrate and the molecular weight of a hexose unit (- 180) iv can be calculated. In the calculations below the volume of the hexose unit (V,) was estimated from molecular models as 1-8 x IO-” m3 and the volume of a water molecular (V,) as 3.0 x 10dz9 m3. The polymer-solvent interaction parameter x, can only take values between 0 and 0.5. A value of 0.45 was calculated from solution studies on dextran in water @ink, 1971). Figure I shows potential energy curves for P388 cells at physiological ionic strength calculated in several different ways. Firstly, curves 1 and 2 were calculated on the basis of the DLVO theory, i.e. (I&+ V,) using a surface potential of -6 mV and London-Hamaker constants of 8 x 10e2’ J and 2 x lo-” J respectively. These values of A are of the order of those reported for cells by other workers (Curtis, 1967; Wilkins, Ottewill & Bangham, 1962; Parsegian & Gingell, 1973). Neither of these potential energy curves have a secondary minimum. These calculations predict that the P388 cells should spontaneously aggregate in the primary potential minimum, a result which conflicts with the known behaviour of the cells. The extrapolation of the measured zeta potential from low ionic strength (O-0172) to physiological ionic strength on the assumption of constancy of surface charge by use of equation (2) and also the assumption that the zeta potential is approximately equal to the surface potential are questionable. At physiological ionic strength the
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- -3.0 -40 I
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10
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FIG. 1. Potential energies of interaction of mouse lymphoma cells (p388-F36) as a function of distance of separation at physiological ionic strength. Curve 1 (VR + va), A = 8 x 10mzl J, vvo= -6 mV; curve 2 (V, + V,), A = 2 x lo-*I J, w0 = -6 mV; curve 3 (V, + V, + VSR), A = 8 x 1O-2’ J, v0 = -6 mV; curve 4 ( Vn -k V, + V,,), A = 2 x 10Ya’ J, vu0= -6 mV; curve 5 (VR + V,), A = 2 x 10ezl J, v/o = -17 mV. Left-hand axis curves 1 and 2. Right-hand axis curves 3, 4 and 5.
surface potential will be larger than -6 mV, it would however be most unlikely to exceed the value of - 17 mV we measured at low ionic strength. Taking the extreme value of - 17 mV and a London-Hamaker constant of 2 x lo-” J gives the potential energy curve 5, which has a large potential energy barrier sufficient to prevent aggregation in the primary minimum but also a secondary minimum (not perceptible on the figure) located at 2d = 5.2 nm; assuming a contact area of one-thousandth of the surface area of the cell (Weiss, 1961) this secondary minimum has a depth of 53 times the thermal energy of two interacting cells and aggregation could now occur in the secondary minimum. To prevent aggregation in a secondary minimum, the numerical value of the surface potential would have to considerably increase above - 17 mV, Thus for -30 mV the depth of the secondary minimum is still 38 times the thermal energy and occurs at 2d = 6.5 nm. If we introduce the steric repulsion term calculated on the assumption that the cells are smooth spheres, then for both values of A there are large
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potential barriers (curves 3 and 4), consistent with stable dispersions of cells. The magnitude of the steric interaction energy relative to the electrical double layer repulsive energy at physiological ionic strength is illustrated in Fig. 2 for several values of surface potential. These calculations show that V,, is always greater than V, and only at very small separations do V,, and V, approach the same order of magnitude. The inset in Fig. 2 shows how
1600’ 5 1400.
4 3
I200-
2 jl_/, ‘0
2
IOOO-
.,@ _. .
8GG-
3
600.
3 2dinm)
0
I
2
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910
2dhm)
FIG. 2. Ratio of steric repulsion energy to electrical double layer repulsion for mouse lymphoma cells (P388-F36) as a function of distance of separation at physiological ionic strength. The numbers adjacent to the curves denote the surface potentials in mV. The inset shows the details of VSR/VR at short distances for a surface potential of -17 mV.
V&/V, changes at small separations for a surface potentiai of - 17 mV. At larger separations the interactions between the cells will be entirely dominated by I$, provided that d is much less than the contour length, L, of the glycoprotein chains. It is noteworthy that the use of only the surface carbohydrate levels in the calculation of vi will underestimate I’,, because the contribution from the protein backbones of the membrane bound glycoproteins is ignored. Furthermore our figures for the surface carbohydrate level for these cells could be a low estimate (see results). Turning now to the fibroblastic cells CH23 and PCMI, we find that both these cells have high surface carbohydrate levels. The total potential energy
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for these cells, including the steric term, are shown in Fig. 3. As for the P388 cells these calculations were based on the assumption that the measured carbohydrate is uniformly spread over a surface area of 4nR” where R is the effective cell radius. In both cases kSR + V, and V, so that the curves arc essentially plots of V,, versus 2d. The curves were calculated for values of A of 2 x lo-” J and surface potentials of -8 mV (CH23) and - 7 mV (PCMl) but changing A to S x lO-‘r J and increasing the surface potentials to the measured values at low ionic strength has a negligible effect on the
1-l 2d(nm) FIG. 3. Potential energies of interaction (V, + V, + V,,) as a function of distance of separation. Curve 1, Chinese hamster cells (CH23) A = 2 x lo-“’ J, w. = -8 mV; curve 2, hybrid cells (PCMl) A = 2 x 10ezl J, vyo= -7 mV. Left-hand axis curve 1.
calculated potential energies. The calculations predict that the steric repulsion should stabilize the cells against aggregation which is contrary to their known behaviour. It follows that the introduction of a steric term into the total potential energy of interaction between these cells will explain the stability of dispersions of P388 cells assuming they are smooth spheres but fails to account for the aggregation of the fibroblastic cells. Given the existence of a cellular glycocalyx steric repulsion cannot be disregarded, however the calculations depend directly on the number of polymeric chain segments per unit area of cell surface and require a figure for the true surface area of the cell. Scanning electron micrographs of cells show that they do not have smooth surfaces
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but are ruffled and often covered with microvilli (Revel, 1974; Shay, Porter & Prescott, 1974; Collard & Temmink, 1975; Knutton, Sumner & Pasternak, 1975). The true surface area of the cells will be much larger than that calculated on our assumption that they are smooth and spherical and as a consequence the chain segment surface density will be lower and the steric repulsion weaker. The smooth sphere model will however be rather more justified for the P388 cells which are approximately spherical than for the fibroblastic cells. It follows that proper account should be taken of the surface morphology of the cells in the calculations. While this presents a difficult problem we can allow for the effects of shape and surface roughness by the introduction of a “shape-roughness factor”-SRF defined by the equation S,=SRFxS,
(9)
where S, is the true surface area of the cell and S, is the surface area of a smooth sphere of volume equal to that of the cell. Although this is essentially an empirical approach it is useful to explore what values of SRF are required to account for the known behaviour of the cells. To do this we have calculated families of potential energy curves for the CH23 and PCMl cells at physiological ionic strength as a function of shape-roughness factor and determined the heights of the potential barriers (V,,,). From these we calculate the maximum potential energy of interaction relative to the thermal energy of two interacting cells, i.e. cV,,,/2kT where c is a cell-cell contact area taken here as one-thousandth of S,. For cohesion to occur cV,,,/2kT would have to fall below approximately 15 as is assumed for the classical DLVO theory (Verwey & Overbeek, 1948). Figures 4 and 5 show the results of these calculations for two values of the London-Hamaker constant. For the CH23 cells the cVm,,/2kT would fall below 15 for shape-roughness factors of 18 and 25 for London-Hamaker constants of 8 x lO-‘l J and 2 x 10s2’ J respectively. For the PCMl cells Fig. 5 shows that for aggregation to occur shaperoughness factors of 45 and 65 for London-Hamaker constants of 8 x lO-‘l J and 2x IO- 21 J respectively would be required. These cells do not exhibit the same degree of contact inhibition as the CH23 cells and at confluence “sphere-up” become detached from their substratum and remain dispersed but partially aggregated in the medium. This behaviour is consistent with a rather lower cohesiveness as compared to the CH23 cells which may in part be a consequence of the larger amount of surface carbohydrate and hence increased steric repulsion. In the dispersed state when the cells are more spherical a large SRF due primarily to surface roughness may not be achievable.
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r
350 300 2x>250 I. 5 B P Q
200. 200 ISOI50 100. 100 50. 50
SRF FIG. 4. Potential energy maximum relative to the thermal energy (cV,,,/ZkT) as a function of the shape-roughness factor (SRF) for Chinese hamster fibroblasts (CH23). The numbers against the points denote the distance of separation between the cells (nm) at the maximum in the potential energy curves. Curve 1, A = 2 x 10m21 J, v/o = -8 mV; curve 2, A = 8 x 10ezl J, v,, = -8 mV.
It is not easy to assessat the present time whether these values of SRF are realistic. The shape contribution to the shape-roughnessfactor for fibroblastic cells can be estimated from simple geometrical considerations. Thus the ratio of the surface area of a smooth disc of thickness 8 to that of a smooth sphere of the same volume, V, which gives the shape contribution to SRF is given by the equation
From equation (10) it follows that to give a SRF = 18 the cell would have to be flattened to a disc of approximately 0.3 pm thickness assuming the roughness of the surface remained constant on flattening. It follows that a substantial fraction of the values calculated to explain the behaviour of the CH23 cells could be accounted for on the basis of the shape contribution alone but the situation is not so satisfactory in the case of the PCMI cells. Collard & Temmink (197.5) and also Knutton et al. (1975) have made
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SRF
FIG. 5. Potential energy maximum relative to the thermal energy (cV,,,/ZRT) as a function of the shape-roughness factor @RF) for hybrid cells (PCMl). The numbers against the points denote the distance of separation between the cells (nm) at the maximum in the potential energy curves. Curve 1, A = 2 x 1O-21 J. v0 y= -7 mV; curve 2. A = 8 x 10e21 J, v/o = -7 mV.
estimates of the surface areas of cells from the number and dimensions of the microvilli. From these data values of SRF in the region of 1.5 to 3.4 can be estimated but it must be realized that these figures are obtained for resolutions which are a long way from the molecular level required for the calculation of the surface density of carbohydrate and must be regarded as lower limits. These studies do however show that the surface of spherical cells are not necessarily smooth and hence even for the P388 cells we should perhaps include a shape-roughness factor greater than unity. The value of SRF required for aggregation of the P388 cells would be 5 for A = 2 x 10s21 J and 3.8 for A = 8 x lO-‘l J. Since these cells do not aggregate we may conclude either that they have rather smooth surfaces or that their dispersions are stable for reasons which the current theoretical approaches do not adequately explain. Finally it must be pointed out that we have based our calculations on the assumption that the charge on the cells is located at the surface of the plasma membrane and coincides with the plane containing the lipid bilayer head groups. The electrical double layer is thus developed through the glycocalyx. This is one of two possible extreme approximations the other being the
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location of the ifi,,-plane to coincide with the outer edge of the glycocalyx. If the latter was the case then the double layer repulsion would be much stronger at larger separations and the behaviour of the cells would be governed by the magnitudes of I’, and V,, and steric repulsion would only be of importance when aggregation occurred in the primary minimum. Clearly the true situation most probably lies between these two extremes but it is not clear at present how the intermediate situation can be theoretically treated. In so far as the charges on the extracellular surface of the lipid bilayer are co-planar our approach is reasonable but the charges on the surface carbohydrate are unlikely to be co-planar and it is very questionable whether they should be regarded as constituting a double layer at all. The charges are distributed in three dimensions and each charged group will have around it its own ionic atmosphere so there will probably be a substantial amount of ionic shielding. One approach to this difficulty would be to offset the $,-plane at some point from the lipid bilayer surface. Depending on the value chosen for the offset it would be possible to produce a range of potential energy curves with a variety of features, however since this necessitates invoking another parameter for which we have no precise value such calculations should perhaps await a more detailed structural knowledge of the cell surface. We thank Dr S. R. Ayad for supplying the cell lines and assistance with the tissue culture techniqueand the ScienceResearchCouncil for a studentshipto R.G.G. REFERENCES AYAD, S. R. & DELINASSIOS, J. G. (1974). Biochem. Genet. BALSAMO, J. & LILIEN, J. (1975). Biochem. 14, 167. BANGHAM, A. D., FLEMANS, R., HEARD, D. H. & SEAMAN,
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182, 642. COLLARD, J. G. & TEMMINK, J. H. M. (1975). J. Cell Sci. 19, 21. COLLINS, M. (1966). .I. Exptl. Zool. 163, 39. CURTIS, A. S. G. (1967). The Cell Surface. London: Logos-Academic DOLAN. A. K. & EDWARDS. S. F. (1974). Proc. R. Sot. A337.509. EvANs,‘R. & NAPPER, D. G. (1973‘). Kojloid-Z.u.Z. PoIymer i51, 329. FISHER, G. A. & SARTORELLI, A. C. (1964). Meth. Med. Res. 10, 247. FLORY, P. J. (1953a). Princigles of Polymer Chemistry, Ch. 10, p. 421.
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New York: Cornell University Press. FLORY, P. 3. (1953b). Principles ofPo!ymer Chemistr~~, Ch. 13, p. 556. New York: Cornell University Press. Goon, R. J. (1972). J. theor. Biol. 37, 413. HAUSMAN, R. E. & MOSCONA, A. A. (1973). Proc. naatn. Acad. Sri. U.S.A. 70, 3111. HENRY, D. C. (1931). Proc. R. Sot. A133, 106. HERBERT, D., PHIPPS, P. J. & STRANGE, R. E. (1971). In Methods in Microbiology (J. R. Norris &P. D. W. Ribbons,eds), Vol. 5B, p. 265. London and NewYork: Academic Press. HESSELINK, F. Th., VRIJ, A. & OVERBEEK, J. Th. G. (1971). J. Phys. Chem. 75, 2094. HUNTER, R. J. (1960). Arch. Biochem. Biophys. 88, 308.
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KESXL, D. & BOSMANN, H. B. (1970). Cancer Res. 30, 2695. KESSEL, 1). & BOSIIANN, H. B. (1974). Cuncer Rex 34, 603. KNUTTON, S., SUMNER, C. B. & PASTERNAK, c‘. A, (1975). J. Cell Biol. 66, 568. KUDO, I(., TASAKI, I., HANAOKA, Y. & HAYASKI, H. (1974). Br. J. Cancer 30, 549. LEBLOND-LAROUCHE, L., MORAIS, R., NIGAM, V. N. & KARAS~KI. S. (197%. Arch. Siochcn1. Biophys. 167, 1. MAROUDAS. N. G. (19750). J. theor. Biol. 49, 417. MAROUDAS. N. G. (197563. Nature. Lond. 254. 695. MERRELL, k.. GOT~LIEB, b. I. & GLASEK, L. (1975). J. hiol. C’hcwz. 250, 5655 MCCLAY, D. R. & MOSCONA, A. A. (1974). Exptl Cell Res. 87. 438. PARSEGJAN, V. A. & GINGELI., D. (1973). In Recer:t Adw~ce.s itz Adhesiot~ (L. I I. Lee, ed.j, pp. 153-190. New York: Gordon & Breach. I’~.niI(.A, B. A. (1961). E.vprf Cell Res., Suppl. 8, 123. Rt MEL, J. P. (1974). Symposid of the .Socict,v of’ E.~:perimer~t~l Bioko,q),, No. 17, p. 437. London : Cambridge University Press. ROSFMAN, S. (1970). Chem. Phys. Lipids 5, 270. %A)., J. W., PORTER, K. R. & PRESCOTT, D. M. (1974). P.,I)(‘. nutn. .ACf/d. .Tc,i. I~‘.S..4. 71. 3059. SHIN, B. c’., EBNER. K. E., HUDSON, B. G. R: CARRA~A~, K. I.. (1975). Cancer Res. 35. 1135. STEINBERG, M. S. (1970). J. Exptl Zool. 173, 395. SMITHAM, J. B., EVANS, R. & NAPPER, D. II. (1975). J. Chern. Sot. (Furaday I) 71. 285. TIJO, J. G. & PUCK, T. T. (1958). J. Exp. Med. 108,259. Ff’RINKAus, J. 1’. (1969). Cells into Organs. Engfewood Cfii& N.J.: Prentice-Hall. VIRWEY, E. J. W. & OVERBEEK, J. Th. G. (1948). Theory of the S/ability I$ L?aophohir Culloiak. Amsterdam: North-Holland. VINK, H. (1971). Eur. Pofymer J. 7, 1411. WARREN, L. (1959). J. biol. Chem. 234. 1971. WEISS, L. (1961). Exptl Cell Res. Suppl. 8, 141. WFJSS, L. (1967). The Cell Periphery, Metastasis and Other Contact Phenotrrerm. Amsterdam : North-Holland. WEISS, L. & HARLOS, J. P. (1972). Progress in Swjke Science I, 355. \VII GAINS. D. J.. OTTTWILI., R. H. SC BANGHAM, D. A. (1962). J. theor. Biol. 2, 176.
T.“.
27
The Possible Role of Steric Forces in Cellular Cohesion R. G. GREIG and M. N. JONES Department of Biochemistry, University of Manchester, Manchester M13 9PL, Great Britain (Received 20 October 1975, and in revised form 15 January 1976) The possible involvement of steric repulsion which may originate between the surface glycoproteins of interacting cells, has been considered with particular reference to cellular cohesion. By employing recently available analytical expressions, the magnitude of the steric energy has been estimated and compared with the electrostatic and electrodynamic interaction energies. In an attempt to illustrate the characteristics of the repulsive steric force relative to the electrostatic force, the surfaces of three mammalian cell lines were defined in terms of surface carbohydrate and zeta potential. It has been shown that the steric force is very large relative to the force arising from the overlap of the electrical double layers and is critically dependent on the amount and density of glycoprotein on the cell surface. In this respect the true cell surface area is an important parameter. The introduction of the steric force does not however unambiguously explain the relative cohesiveness of the cells examined.
1. Introduction The morphogenesis and integrity of tissues depends in part on the way in which cells interact with one another. Despite the extensive work which has been published on the interactions between cells covering both biochemical and biophysical aspects (e.g. Curtis, 1967; Weiss, 1967; Trinkaus, 1969) there is as yet no unified theory of cellular cohesion. The mechanisms of cohesion proposed range from short-range biochemical interactions of the enzyme-substrate type and specific aggregating factors to the more general theories of the relatively long-range physical interactions between charged cellular bodies. Roseman (1970) illustrated the possible role of enzymesubstrate interactions with specific reference to surface glycosyltransferases in cellular cohesion and there have also been several reports of the identification and isolation of specific cell aggregating factors [Hausman & Moscona (1973); McClay & Moscona (1974); Kudo, Tasaki, Hanaoka & Hayaski (1974); Balsam0 & Lilien (1975)J and of specific inhibitors of cell aggregation
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[Merrell (1975)]. The physical study of the problem has been dominated by attempts to explain cellular cohesion in terms of the classical theory of the interaction between lyophobic colloidal particles. The work of Pethica (,1961), Curtis (1967) and Weiss & Harlos (1972) exemplify this approach. It is very questionable whether the surfaces of most cells should be regarded as lyophobic since there is a substantial body of information which indicates that they possess a variety of complex carbohydrates in the form of glycoproteins and glycolipids, which must impart lyophilic character to them. The importance of this “glycocalyx” has been recently emphasized by Maroudas (1975a,b). Qualitatively the existence of polysaccharides attached to the surfaces of cells could give rise to steric repulsive forces as a consequence of the mutual excluded volumes of polymer chains on interacting cells. Analytical theories of steric repulsion are available [Hesselink, Vrij & Overbeek (1971); Evans & Napper (1973); Smitham, Evans & Napper (1975)] and it is now possible to take the first steps towards a quantitative assessment of the significance of steric forces in cellular systems. To do this it is necessary to know the amount of polysaccharide associated with the cell surface and ideally its composition. At present there is little quantitative data on membrane bound polysaccharides ; Kessel & Bosmann (1970, 1974) have reported some values which show that there are differences of two orders of magnitude between different cell lines. Qualitative and comparative studies of membrane bound polysaccharide have also been reported (Leblond-Larouche, Morais, Nigam & Karasaki, 1975; Shin, Ebner, Hudson & Carraway, 1975). We have investigated the polysaccharide levels and physically characterized the surfaces of three cell lines which differ markedly in their cohesiveness. A mouse lymphoma cell (P388 F-36) of low cohesiveness which grows in suspension (Fisher & Sartorelli, 1964) a Chinese hamster fibroblast (CH23) which grows as a monolayer (Tijo & Puck, 1958) and a hybrid cell (PCMl) produced by cell fusion of the two cell lines by u.v.-inactivated Sendai virus (Ayad & Delinassios, 1974). The hybrid cell grows as a monolayer but unlike the CH23 cells does not exhibit any degree of contact inhibition. The chemical and physical characterization of these cell surfaces has enabled us to discuss the possible significance of the steric forces between the cells and we have attempted to use theoretical calculations to explain their relative cohesiveness. It should be stressed however, that there are considerable difficulties in applying sophisticated analytical physical theories to cells, tirstly because cellular surfaces differ markedly from the idealized models to which the theories strictly apply and secondiy the values of all the parameters required for the calculations are not in general precisely known. Although in this
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paper we have attempted to use realistic estimates of the various parameters our main concern is with the relative orders of magnitude of the components of the total interaction energies between cells. In particular we show that the steric forces are very large relative to the forces arising from the overlap of the electrical double layers for these cell lines and cannot be neglected, although their inclusion does not unambiguously explain the relative cohesiveness. 2. Experimental (A)
CELL
Procedures
CULTURES
The three cell lines were routinely cultured in Eagles minimum essential medium supplemented with 10% heat inactivated new born calf serum, 2.0 mM glutamine, 100 units penicillin/cm3, 100 pg streptomycin/cm3 and l-32 mM sodium bicarbonate and gassed with 95 % air and 5 % carbon dioxide. For subculturing purposes CH23 and PCMl cells were released from the monolayer state with 0.05 y/g Difco trypsin (1 lO/BAEE units/cm3), gently dispersed by pipetting and reseeded into fresh medium. (B) ASSAY
PROCEDURES
Sialic acid was liberated from the cells by digestion with neuraminidase (50 units per 10’ cells) at pH 5.5 for 60 min. at 37°C. The supernatant was deproteinized with trichloroacetic acid (final concentration 5%) and the precipitate removed by centrifugatiol;. The resulting fluid was concentrated, and sialic acid assayed by the method of Warren (1959). Suitable control incubations of cells without enzyme and enzyme without cells were also included. Cell surface carbohydrate was liberated from the monolayer cells by digestion with trypsin (Sigma Chemical Co. Ltd., Type III) at a concentration of 55 BAEE units/cm3, pH 7.6, for 15 min. at 37’C. The conditions for P388 digestion involved incubation with a trypsin concentration of 1 BAEE unit/cm3, pH 7.6, for 60 min. at 37X, as high concentrations of trypsin caused rapid lysis of the P388 cells. Longer incubation times did not change the total amounts of carbohydrate released. The supernatant from the trypsin treated cells was deproteinized with trichloroacetic acid (final concentration 5 s’,) and the precipitate removed by centrifugation. The resulting solution was concentrated under reduced pressure and the total carbohydrate was assayed by the anthrone method (Herbert, Phipps & Strange, 1971). Suitable control incubations of cells without enzyme and enzyme without cells were also included. Total cellular carbohydrate was determined in a similar manner on cells homogenized by sonication.
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MICROELECTROPAORESIS
The electrophoretic mobilities of the cells were measured at 25°C in a flat cell equipped with platinum electrodes. The apparatus used has been described by Bangham, Flemens, Heard & Seaman (1958) and was obtained from Rank Bros., Bottisham, Cambridge. The performance and alignment of the apparatus was checked using human red blood cells at pH 7.0, I = O-0172. Preparation of the cells was as follows. The monolayer cells CH23 and PCMl were released from the culture vessel by trypsination (Difco Trypsin, 110 BAEE units/cm3), washed twice with a phosphate buffer pH 7.5 ionic strength O-0172 containing 10.8 % sucrose. The cell suspension was placed in the electrophoretic cell and the mobility measurements completed within 15 min. during which time the cells remained viable as judged by the trypan blue exclusion test. The preparation of the P388 cells was identical, although no trypsin treatment was necessary it was established that trypsinization under the conditions which released the fibroblastic cells from the culture vessel walls did not change their mobilities. Zeta potentials ([) were calculated from the measured mobilities (u) using the Smoluchowski equation (Henry, 1931)
where v is the viscosity of the medium the permittivity of free space. (D)
CELL
of relative permittivity
E, and E, is
VOLUMES
Cell volumes were determined on suspensions of cells in isotonic sodium chloride using a model B Coulter Counter in conjunction with a model J Particle Size Analyzer, 3. Results Table 1 summarizes the results obtained on the three cell lines. The second and third lines give the measured zeta potentials and the surface charge densities (0) calculated from the equation: 1 uq = 0 ; + (
(2)
ai >
deduced by Hunter (1960). In equation (‘2) ai is the average radius of the counterions (taken as 0.25 nm) and K is the Debye-Hiickel function defined
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TABLE
1
Surface characteristics of mammalian cells Cells
P388
Zeta potential (c)t mV Z = 0.0172 -17 Surface charge density (a) C mm2 4.37 x lo- 3 Zeta potential ([) mV Z = 0.152 -6 Surface carbohydratet yg per lOa cells 5 Number of membrane bound glucose equivalent residues per cell 1.7 :: 108 Total cellular carbohydrate pg per lo* cells 26 Surface sialic acid pmol per 10B cells OGO61 Apparent cell radius (nm) 5000
CH23
PCMl
-22 5.50 x 10-Z -8 50
-20 5.04 ‘I 10-Z -7 105
16 x lOa 237 0.021 8000
35 x 108 345 0.031 7000
t The standard deviations of the measured zeta potentials calculated from the distribution of mobilities was 1.4 mV for the P388 cells and 1.9 mV for the CH23 and PCMl cells. $ Anthrone sensitive material expressed as pg glucose equivalents. by the equation: k.2 =
2N103e2 ( q,~,kT >
I
(3)
where N, e, k, T and Z are Avogardo’s number, the electronic charge, the Boltzmann constant, the absolute temperature and the ionic strength respectively. Line four gives the zeta potentials calculated for physiological ionic strength from equations (1) and (2) assuming constancy of surface charge density (Hunter, 1960). While the zeta potentials of the three cell lines are very similar the surface and total carbohydrate levels are much greater for the fibroblastic cells. We attempted to remove as much surface carbohydrate as possible from the cells but unfortunately the conditions which gave maximum removal from the fibroblasts were too severe for the P388 cells and a lower trypsin concentration had to be used for a longer time. There is the possibility that removal of surface carbohydrate from the P388 cells was not as complete as for the fibroblastic cells, however the sialic acid liberation by neuraminidase was carried out under identical conditions for the three cell lines and here also the fibroblastic cells gave larger sialic levels. 4. Discussion
The total potential energy of interaction (V,> between cells can, to a first approximation, be written as the sum of three terms, a repulsive electrostatic term (V,) due to overlap of electrical double layers, an attractive dispersion
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force interaction (V,) and a term arising from the interaction between membrane bound macromolecules or polymers which protrude into the intercellular environment, the so-called steric interaction term (C’,,). Except in the particular casewhen the medium behaves as a O-solvent for the membrane bound macromolecules the steric interaction is repulsive. Thus we may write v, = v,+ VsR=Va. (4) Becauseof the very large radius of curvature of cells relative to the range of these forces it is reasonable to represent the interaction between spherical cells by a flat parallel model. For fibroblastic cells this approximation is even more justified. According to the DLVO theory for charged parallel plates with a doublelayer potential tie separated by a distance 2d in a symmetrical electrolyte of valency z and concentration n ions wp3, the electrostatic and dispersion energiesare given by the following equations (Verwey & Overbeek, 1948):
6411kTy'
V, = -I,--
-.- exp (- 2~d)
(5)
where y = tanh (~e$,,/4li7’)
(6)
where A is the London-Hamaker constant. Equation (5) is valid provided zeJ/J4kT 3 1; a condition which holds for the relatively low values of I,!I~ pertaining to cells, although lc/o > { to a first approximation tie can be set to the zeta potential since, as will be shown below, V,, % V, whatever value is used for tie within reasonable limits. Smitham et af. (1975) have recently developed analytical expressions for V,, which are applicable to steric interactions between monodisperse polymeric molecules. For a flat plate model in which the polymeric chains are allowed to interpenetrate and can also be compressed V,, is given by the equation?
v is the number of polymeric chains per unit area of contour length L, each chain having i segmentsof volume V,. 1 is the polymer-solvent interaction and VI is the volume of a solvent molecule. t Equation (8) is obtained by combination of equations (1) and (8) of Smitham et rrl, (1975). In thelatter paper equation (8) is incorrect. Thecorrect form is R = (r’?f (l/d - l/L) where the plate separation is 2d (privatecommunications).
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Equation (8) is based on a constant segment density step function, it should be noted however that if a more sophisticated model is used based on a Gaussian segment density distribution values of I’,, are obtained which are very similar to those calculated from equation (8). An equation for V,, based on a statistical model of a confined polymer chain has been derived by Dolan & Edwards (1974). At short distances (< 7 nm) Dolan and Edwards equation also gives numerical results which are of the same order of magnitude as those given by equation (8). Inspection of equation (8) reveals that if d < L, vSR becomes independent of the contour length of the polymeric. chains and furthermore it depends only on the total amount of polymeric material adsorbed per unit area of the plates since the product vi is constant under these conditions. In the context of the interactions between membrane bound macromolecules, such as glycoproteins, this means that if we know the amount of carbohydrate per unit area of the cell surface for the purpose of calculating the magnitude of I/,, for small intercellular separations of the order of a few hundred angstrom units, the molecular weight and the number of chains per unit area are not required. The product vi is simply the number of chain segments per unit area. Thus if we take the hexose unit of a polysaccharide as a chain segment (Flory, 19530) then from the surface area of a cell, the total mass of membrane bound carbohydrate and the molecular weight of a hexose unit (- 180) iv can be calculated. In the calculations below the volume of the hexose unit (V,) was estimated from molecular models as 1-8 x IO-” m3 and the volume of a water molecular (V,) as 3.0 x 10dz9 m3. The polymer-solvent interaction parameter x, can only take values between 0 and 0.5. A value of 0.45 was calculated from solution studies on dextran in water @ink, 1971). Figure I shows potential energy curves for P388 cells at physiological ionic strength calculated in several different ways. Firstly, curves 1 and 2 were calculated on the basis of the DLVO theory, i.e. (I&+ V,) using a surface potential of -6 mV and London-Hamaker constants of 8 x 10e2’ J and 2 x lo-” J respectively. These values of A are of the order of those reported for cells by other workers (Curtis, 1967; Wilkins, Ottewill & Bangham, 1962; Parsegian & Gingell, 1973). Neither of these potential energy curves have a secondary minimum. These calculations predict that the P388 cells should spontaneously aggregate in the primary potential minimum, a result which conflicts with the known behaviour of the cells. The extrapolation of the measured zeta potential from low ionic strength (O-0172) to physiological ionic strength on the assumption of constancy of surface charge by use of equation (2) and also the assumption that the zeta potential is approximately equal to the surface potential are questionable. At physiological ionic strength the
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- -3.0 -40 I
2
3
4
5
6
7
8
9
10
2db-d
FIG. 1. Potential energies of interaction of mouse lymphoma cells (p388-F36) as a function of distance of separation at physiological ionic strength. Curve 1 (VR + va), A = 8 x 10mzl J, vvo= -6 mV; curve 2 (V, + V,), A = 2 x lo-*I J, w0 = -6 mV; curve 3 (V, + V, + VSR), A = 8 x 1O-2’ J, v0 = -6 mV; curve 4 ( Vn -k V, + V,,), A = 2 x 10Ya’ J, vu0= -6 mV; curve 5 (VR + V,), A = 2 x 10ezl J, v/o = -17 mV. Left-hand axis curves 1 and 2. Right-hand axis curves 3, 4 and 5.
surface potential will be larger than -6 mV, it would however be most unlikely to exceed the value of - 17 mV we measured at low ionic strength. Taking the extreme value of - 17 mV and a London-Hamaker constant of 2 x lo-” J gives the potential energy curve 5, which has a large potential energy barrier sufficient to prevent aggregation in the primary minimum but also a secondary minimum (not perceptible on the figure) located at 2d = 5.2 nm; assuming a contact area of one-thousandth of the surface area of the cell (Weiss, 1961) this secondary minimum has a depth of 53 times the thermal energy of two interacting cells and aggregation could now occur in the secondary minimum. To prevent aggregation in a secondary minimum, the numerical value of the surface potential would have to considerably increase above - 17 mV, Thus for -30 mV the depth of the secondary minimum is still 38 times the thermal energy and occurs at 2d = 6.5 nm. If we introduce the steric repulsion term calculated on the assumption that the cells are smooth spheres, then for both values of A there are large
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41.3
COHESION
potential barriers (curves 3 and 4), consistent with stable dispersions of cells. The magnitude of the steric interaction energy relative to the electrical double layer repulsive energy at physiological ionic strength is illustrated in Fig. 2 for several values of surface potential. These calculations show that V,, is always greater than V, and only at very small separations do V,, and V, approach the same order of magnitude. The inset in Fig. 2 shows how
1600’ 5 1400.
4 3
I200-
2 jl_/, ‘0
2
IOOO-
.,@ _. .
8GG-
3
600.
3 2dinm)
0
I
2
3
4
5
6
7
8
910
2dhm)
FIG. 2. Ratio of steric repulsion energy to electrical double layer repulsion for mouse lymphoma cells (P388-F36) as a function of distance of separation at physiological ionic strength. The numbers adjacent to the curves denote the surface potentials in mV. The inset shows the details of VSR/VR at short distances for a surface potential of -17 mV.
V&/V, changes at small separations for a surface potentiai of - 17 mV. At larger separations the interactions between the cells will be entirely dominated by I$, provided that d is much less than the contour length, L, of the glycoprotein chains. It is noteworthy that the use of only the surface carbohydrate levels in the calculation of vi will underestimate I’,, because the contribution from the protein backbones of the membrane bound glycoproteins is ignored. Furthermore our figures for the surface carbohydrate level for these cells could be a low estimate (see results). Turning now to the fibroblastic cells CH23 and PCMI, we find that both these cells have high surface carbohydrate levels. The total potential energy
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for these cells, including the steric term, are shown in Fig. 3. As for the P388 cells these calculations were based on the assumption that the measured carbohydrate is uniformly spread over a surface area of 4nR” where R is the effective cell radius. In both cases kSR + V, and V, so that the curves arc essentially plots of V,, versus 2d. The curves were calculated for values of A of 2 x lo-” J and surface potentials of -8 mV (CH23) and - 7 mV (PCMl) but changing A to S x lO-‘r J and increasing the surface potentials to the measured values at low ionic strength has a negligible effect on the
1-l 2d(nm) FIG. 3. Potential energies of interaction (V, + V, + V,,) as a function of distance of separation. Curve 1, Chinese hamster cells (CH23) A = 2 x lo-“’ J, w. = -8 mV; curve 2, hybrid cells (PCMl) A = 2 x 10ezl J, vyo= -7 mV. Left-hand axis curve 1.
calculated potential energies. The calculations predict that the steric repulsion should stabilize the cells against aggregation which is contrary to their known behaviour. It follows that the introduction of a steric term into the total potential energy of interaction between these cells will explain the stability of dispersions of P388 cells assuming they are smooth spheres but fails to account for the aggregation of the fibroblastic cells. Given the existence of a cellular glycocalyx steric repulsion cannot be disregarded, however the calculations depend directly on the number of polymeric chain segments per unit area of cell surface and require a figure for the true surface area of the cell. Scanning electron micrographs of cells show that they do not have smooth surfaces
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but are ruffled and often covered with microvilli (Revel, 1974; Shay, Porter & Prescott, 1974; Collard & Temmink, 1975; Knutton, Sumner & Pasternak, 1975). The true surface area of the cells will be much larger than that calculated on our assumption that they are smooth and spherical and as a consequence the chain segment surface density will be lower and the steric repulsion weaker. The smooth sphere model will however be rather more justified for the P388 cells which are approximately spherical than for the fibroblastic cells. It follows that proper account should be taken of the surface morphology of the cells in the calculations. While this presents a difficult problem we can allow for the effects of shape and surface roughness by the introduction of a “shape-roughness factor”-SRF defined by the equation S,=SRFxS,
(9)
where S, is the true surface area of the cell and S, is the surface area of a smooth sphere of volume equal to that of the cell. Although this is essentially an empirical approach it is useful to explore what values of SRF are required to account for the known behaviour of the cells. To do this we have calculated families of potential energy curves for the CH23 and PCMl cells at physiological ionic strength as a function of shape-roughness factor and determined the heights of the potential barriers (V,,,). From these we calculate the maximum potential energy of interaction relative to the thermal energy of two interacting cells, i.e. cV,,,/2kT where c is a cell-cell contact area taken here as one-thousandth of S,. For cohesion to occur cV,,,/2kT would have to fall below approximately 15 as is assumed for the classical DLVO theory (Verwey & Overbeek, 1948). Figures 4 and 5 show the results of these calculations for two values of the London-Hamaker constant. For the CH23 cells the cVm,,/2kT would fall below 15 for shape-roughness factors of 18 and 25 for London-Hamaker constants of 8 x lO-‘l J and 2 x 10s2’ J respectively. For the PCMl cells Fig. 5 shows that for aggregation to occur shaperoughness factors of 45 and 65 for London-Hamaker constants of 8 x lO-‘l J and 2x IO- 21 J respectively would be required. These cells do not exhibit the same degree of contact inhibition as the CH23 cells and at confluence “sphere-up” become detached from their substratum and remain dispersed but partially aggregated in the medium. This behaviour is consistent with a rather lower cohesiveness as compared to the CH23 cells which may in part be a consequence of the larger amount of surface carbohydrate and hence increased steric repulsion. In the dispersed state when the cells are more spherical a large SRF due primarily to surface roughness may not be achievable.
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r
350 300 2x>250 I. 5 B P Q
200. 200 ISOI50 100. 100 50. 50
SRF FIG. 4. Potential energy maximum relative to the thermal energy (cV,,,/ZkT) as a function of the shape-roughness factor (SRF) for Chinese hamster fibroblasts (CH23). The numbers against the points denote the distance of separation between the cells (nm) at the maximum in the potential energy curves. Curve 1, A = 2 x 10m21 J, v/o = -8 mV; curve 2, A = 8 x 10ezl J, v,, = -8 mV.
It is not easy to assessat the present time whether these values of SRF are realistic. The shape contribution to the shape-roughnessfactor for fibroblastic cells can be estimated from simple geometrical considerations. Thus the ratio of the surface area of a smooth disc of thickness 8 to that of a smooth sphere of the same volume, V, which gives the shape contribution to SRF is given by the equation
From equation (10) it follows that to give a SRF = 18 the cell would have to be flattened to a disc of approximately 0.3 pm thickness assuming the roughness of the surface remained constant on flattening. It follows that a substantial fraction of the values calculated to explain the behaviour of the CH23 cells could be accounted for on the basis of the shape contribution alone but the situation is not so satisfactory in the case of the PCMI cells. Collard & Temmink (197.5) and also Knutton et al. (1975) have made
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SRF
FIG. 5. Potential energy maximum relative to the thermal energy (cV,,,/ZRT) as a function of the shape-roughness factor @RF) for hybrid cells (PCMl). The numbers against the points denote the distance of separation between the cells (nm) at the maximum in the potential energy curves. Curve 1, A = 2 x 1O-21 J. v0 y= -7 mV; curve 2. A = 8 x 10e21 J, v/o = -7 mV.
estimates of the surface areas of cells from the number and dimensions of the microvilli. From these data values of SRF in the region of 1.5 to 3.4 can be estimated but it must be realized that these figures are obtained for resolutions which are a long way from the molecular level required for the calculation of the surface density of carbohydrate and must be regarded as lower limits. These studies do however show that the surface of spherical cells are not necessarily smooth and hence even for the P388 cells we should perhaps include a shape-roughness factor greater than unity. The value of SRF required for aggregation of the P388 cells would be 5 for A = 2 x 10s21 J and 3.8 for A = 8 x lO-‘l J. Since these cells do not aggregate we may conclude either that they have rather smooth surfaces or that their dispersions are stable for reasons which the current theoretical approaches do not adequately explain. Finally it must be pointed out that we have based our calculations on the assumption that the charge on the cells is located at the surface of the plasma membrane and coincides with the plane containing the lipid bilayer head groups. The electrical double layer is thus developed through the glycocalyx. This is one of two possible extreme approximations the other being the
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location of the ifi,,-plane to coincide with the outer edge of the glycocalyx. If the latter was the case then the double layer repulsion would be much stronger at larger separations and the behaviour of the cells would be governed by the magnitudes of I’, and V,, and steric repulsion would only be of importance when aggregation occurred in the primary minimum. Clearly the true situation most probably lies between these two extremes but it is not clear at present how the intermediate situation can be theoretically treated. In so far as the charges on the extracellular surface of the lipid bilayer are co-planar our approach is reasonable but the charges on the surface carbohydrate are unlikely to be co-planar and it is very questionable whether they should be regarded as constituting a double layer at all. The charges are distributed in three dimensions and each charged group will have around it its own ionic atmosphere so there will probably be a substantial amount of ionic shielding. One approach to this difficulty would be to offset the $,-plane at some point from the lipid bilayer surface. Depending on the value chosen for the offset it would be possible to produce a range of potential energy curves with a variety of features, however since this necessitates invoking another parameter for which we have no precise value such calculations should perhaps await a more detailed structural knowledge of the cell surface. We thank Dr S. R. Ayad for supplying the cell lines and assistance with the tissue culture techniqueand the ScienceResearchCouncil for a studentshipto R.G.G. REFERENCES AYAD, S. R. & DELINASSIOS, J. G. (1974). Biochem. Genet. BALSAMO, J. & LILIEN, J. (1975). Biochem. 14, 167. BANGHAM, A. D., FLEMANS, R., HEARD, D. H. & SEAMAN,
12,
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G. V. F. (1958). Nature, Land.
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