Kinetic Analysis of Adsorption Processes

We derive the explicit solution to a kinetic model proposed by J. Gani (Math. Biosci., 1 (1967), pp. 545–554) for the reversible attachment of antibodies to viruses. This model generally applies to the reversible adsorption of monovalent particles to binding sites on cell surfaces. Assuming that all binding sites are equivalent, that adsorbed particles do not interact, and that initially no particles are bound, we derive an explicit expression for the number of cells with i bound particles as a function of time. Two special cases are considered in detail; (i) irreversible adsorption, and (ii) adsorption when the number of particles greatly exceeds the number of binding sites. Applications to problems arising in somatic gene therapy and cell-mediated cytotoxicity are discussed.