  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 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.
