Capacity of a Simple Intercellular Signal Transduction Channel

We model biochemical signal transduction, based on a ligand-receptor binding mechanism, as a discrete-time finite-state Markov channel, which we call the binding in discrete time channel. We show how to obtain the capacity of this channel, for the case of binary output, binary channel state, and arbitrary finite input alphabets. We show that the capacity-achieving input distribution is identically and independently distributed. Furthermore, we show that feedback does not increase the capacity of this channel. We show how the capacity of the discrete-time channel approaches the capacity of Kabanov's Poisson channel, in the limit of short time steps and rapid ligand release.