Enzymatic reactions in small spatial volumes: comment on a model of Hess and Mikhailov

Recently Hess and Mikhailov pointed out that in small subcellular compartments diffusion is so fast that mixing is instantaneous on the time scale of many enzymatic reactions. This opens the possibility for synchronizing individual reaction events. To illustrate this fact they discuss as example an irreversible enzymatic reaction with allosteric product activation. Under appropriate conditions their model shows coherent spiking in the number of product molecules, caused by the strong correlation between reaction events. In this model only substrate binding is an indeterministic process, all other subsequent transitions between different enzyme states being deterministic, contrary to real processes. The purpose of the present paper was to investigate this interesting phenomenon by means of a more realistic modification of the original model, with only probabilistic transitions. In an attempt to obtain spiking, which was not observed under these conditions, the model was extended to make a clear distinction between allosteric high and low affinity substrate binding, in contrast to the original model using a product dependent mean binding probability. However no periodic signal was detectable in the indeterministic version of the Hess Mikhailov model or the extended version, either by means of direct visualization or on autocorrelation or Fourier analysis. Reasons why spiking is not observed in indeterministic enzyme models are discussed.