The authors derive an explicit solution of an important special case of a kinetic model of adsorption processes proposed by \textit{J. Gani} [Math. Biosci. 1, 545-554 (1967)]. These processes describe a number of different situations, all involving the reversible adsorption of monovalent particles to sites on cell surfaces. Applications to somatic gene therapy for hereditary diseases and the kinetics of cell-mediated cytotoxicity are discussed. The authors promise further work on the biological relevance and quality of the estimates obtained.