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A generalized phenomenological model is presented for stereospecific recognition between biological receptors and their ligands. We ask what is the distribution of binding constants psi(K) between an arbitrary ligand and members of a large receptor repertoire, such as immunoglobulins or olfactory receptors. For binding surfaces with B potential subsite and S different types of subsite configurations, the number of successful elementary interactions obeys a binomial distribution. The discrete probability function psi(K) is then derived with assumptions on alpha, the free energy contribution per elementary interaction. The functional form of psi(K) may be universal, although the parameter values could vary for different ligand types. An estimate of the parameter values of psi(K) for iodovanillin, an analog of odorants and immunological haptens, is obtained by equilibrium dialysis experiments with nonimmune antibodies. Based on a simple relationship, predicted by the model, between the size of a receptor repertoire and its average maximal affinity toward an arbitrary ligand, the size of the olfactory receptor repertoire (Nolf) is calculated as 300-1000, in very good agreement with recent molecular biological studies. A very similar estimate, Nolf = 500, is independently derived by relating a theoretical distribution of maxima for psi(K) with published human olfactory threshold variations. The present model also has implications to the question of olfactory coding and to the analysis of specific anosmias, genetic deficits in perceiving particular odorants. More generally, the proposed model provides a better understanding of ligand specificity in biological receptors and could help in understanding their evolution.
Lancet et al. (Thu,) studied this question.