Mathematical modeling suggests cooperative interactions between a disordered polyvalent ligand and a single receptor site

Background: The CDK inhibitor Sic1 must be phosphorylated on at least six sites in order to allow its recognition by the SCF ubiquitin ligase subunit Cdc4. However, because Cdc4 appears to have only a single phosphoepitope binding site, the apparent cooperative dependence on the number of phosphorylation sites in Sic1 cannot be accounted for by traditional thermodynamic models of cooperativity. Results: We develop a general kinetic model, which predicts an unexpected multiplicative increase in affinity as a function of ligand sites. This effect, termed allovalency, derives from a high local concentration of interaction sites moving independently of each other. Modeling of this interaction by a first exit time approach indicates that the probability of ligand rebinding increases exponentially with the number of sites. This type of interaction is relatively immune to loss of any one site and may be easily tuned to any given threshold by adjusting the properties of individual sites. Conclusions: The allovalency model suggests that a previously undescribed mechanism may underlie certain cooperative interactions. The widespread occurrence of flexible polyvalent ligands in biological systems suggests that this principle may be broadly applicable.