The effect of slow allosteric transitions in a coupled biochemical oscillator model

The effect of slowed allosteric transitions in a coupled biochemical oscillator model showing complex dynamic behavior is investigated. When the allosteric transitions are sufficiently fast one can obtain a low-dimensional asymptotic approximation for the dynamics of the species that evolve on a slow time-scale. Such low-dimensional models are common in studies of biological control systems and little attention has, so far, been given to the dynamic effect of the large number of species usually eliminated from more biochemically detailed models. Here we investigate the dynamic effect of explicit inclusion of allosteric transitions having finite time-scales of equilibration. It is found that slowed allosteric transitions suppress complex dynamic modes such a bursting, quasi-periodicity and chaos. The effect arises as the enzyme of consideration becomes trapped in an active state where it is unable to respond to changes in effector concentration on the time-scale necessary to support the modes of complex dynamics. Slow allosteric transitions may be favourable in biological systems in which complex oscillations are not desirable but which, at the same time, may benefit from the presence of positive feedbacks. Our findings suggest that slow allosteric transitions and finite internal rates in general may contribute significantly to the dynamics of biological control mechanisms.