Theory of the adhesion of cells and the spontaneous sorting-out of mixed cell aggregates

Abstract

A theory is developed, to explain the spontaneous segregation of cells from mixed aggregates. It employs a calculation of the energy of adhesion, per cell doublet, by the DLVO theory in slab-slab geometry. The equilibrium separation, at the secondary minimum of the potential function, is found to be strongly dependent on the parameters ψ 0 (the surface potential) and A (the so-called Hamaker constant.) The energy ε II at the secondary minimum is computed as a function of ψ 0 and A. A combining rule is developed for the energy of interaction of unlike cells, and this rule is employed to calculate the thermodynamic energy of mixing of the unlike cells. This computation allows us to use the well-known theory of the solubility of non-electrolytes, to predict the equilibrium degree of unmixing, as a function of the parameters ψ 0, A and the cell-cell contact area A . The degree of unmixing turns out to be a sensitive function of all three parameters, when they are in the range that is characteristic of cells that form tissues. Since the observed range of zeta potential is very much wider than the range of attractive potential constants that is to be expected for cells, it is concluded that differences in surface potential probably constitute a more important cause of the spontaneous sorting-out effect, than differences in the attractive force constant. Several biological consequences of these results are given. For example, it is concluded that the projection of pseudopods is necessary for the transition from the secondary minimum, past the primary maximum, to form molecular contact such as is needed for phagocytosis or the strong adhesion of a blood cell to glass. It is also shown how an increase in surface potential of cells, on malignant transformation, can (by way of the spontaneous segregation effect) be a necessary precursor to metastasis.