A simple mathematical model of cooperativity in receptor mosaics based on the "symmetry rule"

The phenomenon of receptor–receptor interactions was hypothesized about 20 years ago. It has been demonstrated by now that receptor–receptor interactions between G-protein coupled receptors (GPCRs) occur at plasma membrane level and result in the reciprocal modulation of their binding characteristics (i.e., cooperativity). One of the most important feature of this phenomenon is the concept of cluster of receptors, or receptor mosaic (RM). However, no proper mathematical approach has still been available to characterize RMs as far as their receptor composition, receptor topography and order of receptor activation inside the RM. This paper tries to fill the gap. A simple mathematical approach to the cooperativity in RMs formed by dimers of identical receptors and/or by iso-receptors is proposed. To this aim the so-called “symmetry rule” has been considered. This approach allows to describe by means of a simple energy function the effects of receptor composition (number of dimers), spatial organisation (respective location of the dimers) and order of activation (order according to which the single receptors are ligated) on the integrative cooperativity (index) of the RMs.