Before revision:  Multiple regimes that characterize qualitatively different physics due to the differential prevalence of rebinding effects and their relation to systems-level properties are predictedand studied . Calculations suggest that when ligand rebinding contributes significantly to the dose response, a purely allovalent model can influence the binding curves nonlinearly but other mechanistic ingredients are required to achieve high degrees of biochemical cooperativity. It is our hope that these calculations motivate experiments that can further unravel the many functional consequences of multi-site phosphorylation .
After revision:  Multiple regimes that characterize qualitatively different physics due to the differential prevalence of rebinding effects and their relation to systems-level properties are predictedand studied . 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 .