As a response to ligand binding, transmembrane cell receptors often enhance their clustering, or oligomerization, during the signalling process. Here we present a statistical mechanical model which combines the aspects of both clustering and signalling. In this model, receptors float on the surface, while for two neighboring receptors, there is an interaction energy dependent on their conformational states. On the other hand, ligand binding of a receptor shifts the energy difference between the two conformational states. Due to thermal fluctuation, the effects of clustering and signalling are statistical average quantities. This model reduces to a floating Ising model with a random field. We calculate the signalling in a grand canonical ensemble mean-field approach, using Hubbard–Stratonovich transformation and replica method. Monte Carlo simulations are also performed. Essential biological features are obtained in our model.
