A theoretical framework is proposed for the analysis of adhesion between cells or of cells to surfaces when the adhesion is mediated by reversible bonds between specific molecules such as antigen and antibody, lectin and carbohydrate, or enzyme and substrate. From a knowledge of the reaction rates for reactants in solution and of their diffusion constants both in solution and on membranes, it is possible to estimate reaction rates for membrane-bound reactants. Two models are developed for predicting the rate of bond formation between cells and are compared with experiments. The force required to separate two cells is shown to be greater than the expected electrical forces between cells, and of the same order of magnitude as the forces required to pull gangliosides and perhaps some integral membrane proteins out of the cell membrane.

We develop a thermodynamic calculus for the modeling of cell adhesion. By means of this approach, we are able to compute the end results of competition between the formation of specific macromolecular bridges and nonspecific repulsion arising from electrostatic forces and osmotic (steric stabilization) forces. Using this calculus also allows us to derive in a straightforward manner the effects of cell deformability, the Young's modulus for stretching of bridges, diffusional mobility of receptors, heterogeneity of receptors, variation in receptor number, and the strength of receptor-receptor binding. The major insight that results from our analysis concerns the existence and characteristics of two phase transitions corresponding, respectively, to the onset of stable cell adhesion and to the onset of maximum cell-cell or cell-substrate contact. We are also able to make detailed predictions of the equilibrium contact area, equilibrium number of bridges, and the cell-cell or cell-substrate separation distance. We illustrate how our approach can be used to improve the analysis of experimental data, by means of two concrete examples.

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We have examined the length distribution of perfect dimer repeats, where perfect means uninterrupted by any other base, using data from GenBank on primates and rodents. Virtually no lengths greater than 30 repeats are found, except for rodent AG repeats, which extend to 35. Comparable numbers of long AC and AG repeats suggest that they have not been selected for special functions or DNA structures. We have compared the data with predictions of two models: (1) a Bernoulli Model in which bases are assumed equally likely and distributed at random and (2) an Unbiased Random Walk Model (URWM) in which repeats are permitted to change length by plus or minus one unit, with equal probabilities, and in which base substitutions are allowed to destroy long perfect repeats, producing two shorter perfect repeats. The source of repeats is assumed to be from single base substutions from neighboring sequences, i.e., those differing from the perfect repeat by a single base. Mutation rates either independent of repeat length or proportional to length were considered. An upper limit to the lengths L approximately 30 is assumed and isolated dimers are assumed unable to expand, so that there are absorbing barriers to the random walk at lengths 1 and L + 1, and a steady state of lengths is reached. With these assumptions and estimated values for the rates of length mutation and base substitution, reasonable agreement is found with the data for lengths > 5 repeats. Shorter repeats, of lengths