The dynamics of enzymatic switch cascades

Abstract

We examine the dynamics of the mitogen-activated protein kinase (MAPK) multi-step enzymatic switching cascade, a highly conserved architecture utilised in cellular signal transduction. In treating the equations of motion, we replace the usual deterministic differential equation formalism with stochastic equations to accurately model the 'effective collisions' picture of the biochemical reactions that constitute the network. Furthermore we measure the fidelity of the signaling process through the mutual information content between the output of a given switch and the original environmental input to the system. We find that the enzymatic switches act as low-pass filters, with each switch in the cascade able to average over high frequency stochastic fluctuations in the network and throughput cleaner signals to downstream switches. We find optimal regions of mutual information transfer with respect to reaction velocity and species number parameters, and observe the dynamical memory-gain and memory-loss as well as decay in mutual information in quadruple-linked switch systems.