The Diffusion-Limited Biochemical Signal-Relay Channel

Biochemical signal-transduction networks are the biological information-processing systems by which individual cells, from neurons to amoebae, perceive and respond to their chemical environments. We introduce a simplified model of a single biochemical relay and analyse its capacity as a communications channel. A diffusible ligand is released by a sending cell and received by binding to a transmembrane receptor protein on a receiving cell. This receptor-ligand interaction creates a nonlinear communications channel with non-Gaussian noise. We model this channel numerically and study its response to input signals of different frequencies in order to estimate its channel capacity. Stochastic effects introduced in both the diffusion process and the receptor-ligand interaction give the channel low-pass characteristics. We estimate the channel capacity using a water-filling formula adapted from the additive white-noise Gaussian channel.