Co-operative response of oligomeric protein receptors coupled to non-co-operative ligand binding

A model in which co-operative membrane response can be generated by a cluster of oligomeric receptors is described, It is assumed that when one oligomeric receptor in the cluster is fully saturated with ligand, response is maximal. Under these conditions it is found that non-co-operative ligand binding leads to co-operativity in response. It is found that low ligand occupancy results in maximal response, thus offering a functional role for spare receptors. Co-operativity is found to increase as the number of oligomeric receptors in the cluster increases. The Hill coefficient assumes values between 1.0 and N, the total number of oligomeric receptors in the cluster. At low ligand occupancy the Hill coefficient approaches r, the number of receptor sites on a single oligomeric receptor molecule. The biological significance of this model is discussed.