Dynamic Information Transfer in Stochastic Biochemical Networks

Abstract

We develop numerical and analytical approaches to calculate mutual information between complete paths of two molecular components embedded into a larger reaction network. In particular, we focus on a continuoustime Markov chain formalism, frequently used to describe intracellular processes involving lowly abundant molecular species. Previously, we have shown how the path mutual information can be calculated for such systems when two molecular components interact directly with one another with no intermediate molecular components being present. In this work, we generalize this approach to biochemical networks involving an arbitrary number of molecular components. We present an efficient Monte Carlo method as well as an analytical approximation to calculate the path mutual information and show how it can be decomposed into a pair of transfer entropies that capture the causal flow of information between two network components. We apply our methodology to study information transfer in a simple three-node feedforward network, as well as a more complex positive feedback system that switches stochastically between two metastable modes.Introduction. Information theory provides a powerful mathematical framework to study information transfer in complex dynamical systems. Originating from man-made communication systems [1], information theory has made its way into the biological sciences where it has helped to understand diverse biological processes, ranging from tissue patterning [2] to signal transduction [3].

Nonequilibrium Effects on Information Recoverability of the Noisy Channels

“…In fact, because the transcription factor profiles are time-varying, the input signals and the corresponding output signals compose the complete trajectories of the input and output processes on a considered time interval [0, t]. In [42,43], it was shown that the mutual information can be used to quantify the cumulative amount of information exchanged along these trajectories. In the present work, we introduced the joint time sequence Z to describe the trajectories of the input and output processes.…”