  The utilization of multiple phosphorylation sites in regulating a biological
response is ubiquitous in cell signaling. If each site contributes an
additional, equivalent binding site, then one consequence of an increase in the
number of phosphorylations may be to increase the probability that, upon
disassociation, a ligand immediately rebinds to its receptor. How such effects
may influence cell signaling systems has been less studied. Here, a
self-consistent integral equation formalism for ligand rebinding, in
conjunction with Monte Carlo simulations, is employed to further investigate
the effects of multiple, equivalent binding sites on shaping biological
responses. Multiple regimes that characterize qualitatively different physics
due to the differential prevalence of rebinding effects are predicted.
Calculations suggest that when ligand rebinding contributes significantly to
the dose response, a purely allovalent model can influence the binding curves
nonlinearly. The model also predicts that ligand rebinding in itself appears
insufficient to generative a highly cooperative biological response.
