Non-Monotonic Dependence Of Reaction Rate On Rate Constants: Role Of Time-Averaging

The rate of a reaction may not always show a monotonic dependence on some specific rate constant. In the context of stochastic single-substrate enzyme kinetics, such a behavior has recently [PNAS 111 (2014) 4391] been demonstrated; specifically, rate is noted to increase with increasing dissociation rate constant of the enzyme-substrate complex, contrary to standard expectation. In this work, we identify this counter-intuitive trait in several solvable and deterministic situations too. However, these anomalies are also analytically shown to disappear after a time-averaging. Numerical results of the deterministic enzyme kinetics scheme reveal similar features. The age-old intuitive chemistry thus retains its significance as an average.