The Channel Capacity of Channelrhodopsin and Other Intensity-Driven Signal Transduction Receptors

Biological systems transduce signals from their surroundings through a myriad of pathways. In this paper, we describe signal transduction as a communication system: the signal transduction receptor acts as the receiver in this system, and can be modeled as a finite-state Markov chain with transition rates governed by the input signal. Using this general model, we give the mutual information under independent, identically distributed (IID) inputs in discrete time, and obtain the mutual information in the continuous-time limit. We show that the mutual information has a concise closed-form expression with clear physical significance. We also give a sufficient condition under which the Shannon capacity is achieved with IID inputs. We illustrate our results with three examples: 1) the light-gated Channelrhodopsin-2 (ChR2) receptor; 2) the ligand-gated nicotinic acetylcholine receptor; and 3) the ligand-gated calmodulin receptor. In particular, we show that the IID capacity of the ChR2 receptor is equal to its Shannon capacity. We finally discuss how the results change if only certain properties of each state can be observed, such as whether an ion channel is open or closed.