Abstract
Cooperative regulation of biomolecular function is critical for the ability of all organisms to respond effectively to environmental changes. Such regulation is often manifested in a sigmoidal dependence of enzyme activity on ligand concentration. Various molecular mechanisms have been proposed to underlie such sigmoidal behavior, but they are usually assumed to occur independently of one another. We hypothesized that coexistence of allosteric mechanisms can lead to complex kinetic behavior and higher or lower cooperativity than expected. A mathematical framework that analyses sigmoidal behavior as a function of two cooccurring mechanisms, hysteresis and homotropic binding cooperativity, was developed. The model shows, for example, that i) the observed cooperativity, as measured by the Hill coefficient, can decrease with increasing binding cooperativity, and that ii) unusually high values of the Hill coefficient can be observed. Our mathematical analysis is shown to be relevant for a mutant of Escherichia coli glutathione reductase with an unusually high value of a Hill coefficient for a dimer of about 1.9, in which hysteresis and binding cooperativity coexist. More generally, our findings imply that the repertoire of allosteric regulation is richer than anticipated and suggest that ultrasensitive control in natural or designed systems may arise even in low-order oligomers.