Abstract
Using a combination of branching processes and kinetic equations a solution is provided to the problem of describing the size of aggregates formed on cell surfaces when multivalent ligands bind and cross-link multivalent receptors. A criterion is given for the onset of gelation in infinite 2-dimensional systems, which may be relevant to the phenomenon of ligand-induced receptor patching.
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DeLisi, C., Perelson, A. S.: The kinetics of aggregation phenomena. I. Minimal models for patch formation on lymphocyte membranes. J. Theoret. Biology 62, 159–210 (1976)
Dembo, M., Goldstein, B.: Theory of equilibrium binding of symmetric bivalent haptens to cell surface antibody: Application to histamine release from basophils. J. Immunol. 121, 345–353 (1978)
Gandolfi, A., Giovenco, M. A., Strom, R.: Reversible binding of multivalent antigen in the control of B lymphocyte activation. J. Theoret. Biology 74, 513–521 (1978)
Good, I. J.: Cascade theory and the molecular weight averages of the sol fraction. Proc. R. Soc. London A:272, 54–59 (1963)
Good, I. J.: The generalization of Lagrange's expansion and the enumeration of trees. Proc. Camb. Phil. Soc. 61, 499–517 (1965)
Gordon, M.: Good's theory of cascade processes applied to the statistics of polymer distributions. Proc. R. Soc. London A:268, 240–259 (1962)
Gordon, M., Malcolm, G. N.: Configurational statistics of copolymer systems. Proc. R. Soc. London A:295, 29–54 (1966)
Macken, C. A., Perelson, A. S.: An application of branching processes to the study of multivalent ligand-receptor interactions on cell surfaces. J. Math. Biology, in press (1982)
Perelson, A. S.: Receptor clustering on a cell surface. III. Theory of receptor cross-linking by multivalent ligands: Description by ligand states. Math. Biosciences 53, 1–39 (1981)
Perelson, A. S., DeLisi, C.: Receptor clustering on a cell surface. I. Theory of receptor cross-linking by ligands bearing two chemically identical functional groups. Math. Biosciences 48, 71–110 (1980)
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Macken, C.A., Perelson, A.S. Aggregation of cell surface receptors by multivalent ligands. J. Math. Biology 14, 365–370 (1982). https://doi.org/10.1007/BF00275399
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DOI: https://doi.org/10.1007/BF00275399