Optimal observability of sustained stochastic competitive inhibition oscillations at organellar volumes

When molecules are present in small numbers, such as is frequently the case in cells, the usual assumptions leading to differential rate equations are invalid and it is necessary to use a stochastic description which takes into account the randomness of reactive encounters in solution. We display a very simple biochemical model, ordinary competitive inhibition with substrate inflow, which is only capable of damped oscillations in the deterministic mass-action rate equation limit, but which displays sustained oscillations in stochastic simulations. We define an observability parameter, which is essentially just the ratio of the amplitude of the oscillations to the mean value of the concentration. A maximum in the observability is seen as the volume is varied, a phenomenon we name system-size observability resonance by analogy with other types of stochastic resonance. For the parameters of this study, the maximum in the observability occurs at volumes similar to those of bacterial cells or of eukaryotic organelles.