Kinetic cooperativity in the concerted model for allosteric enzymes

The cooperativity of enzyme-substrate interactions is investigated in the concerted allosteric model of Monod, Wyman and Changeux. The general case of K-V systems is considered, in which the two protomer conformational states R and T postulated in the theory differ in catalytic and binding properties. An expression for the Hill coefficient nH defined with respect to the asymptotic velocity V infinity to is analyzed in conditions which exclude substrate inhibition. Kinetic cooperativity is always positive (nH greater than 1) in the case of a dimer enzyme, and in the case of an inactive T state. Slight kinetic negative cooperativity (nH less than 1) occurs under restrictive conditions for larger numbers of protomers when the substrate binds significantly to the less active state of the enzyme, but the phenomenon remains negligible for trimers and tetramers. These conclusions differ from those obtained [A. Goldbeter, J. Mol.Biol.90 (1974) 185] with the Hill coefficient based on the absolute maximum velocity, which may exceed the experimental value V infinity to in K-V systems. The results extend those of Paulus and DeRiel [J. Mol. Biol. 97 (1975) 667] and support the view that in most cases, negative cooperativity is not compatible with a mechanism based on a concerted and conservative allosteric transition. The Hill coefficients for binding and catalysis are compared in K-V systems.