Signal processing in stochastic biochemical systems with information theory

Biochemical networks can respond to temporal characteristics of time-varying signals. To understand how reliably biochemical networks can transmit information we must consider how an input signal as a function of time-the input trajectory-can be mapped onto an output trajectory. Here we estimate the instantaneous mutual information between input and output trajectories using a Gaussian model. By calculating the mutual information for instantaneous measurements of biochemical systems for a Gaussian model, we quantify the influence of the macroscopic elasticity of a transcriptional regulatory network on its ability to process environmental signals. we study the maximum mutual information between the input (chemical) signal and the output (genetic) response attainable by the network in the context of an analytic model of particle number fluctuations.