Reliable biological communication with realistic constraints.

Communication in biological systems must deal with noise and metabolic or temporal constraints. We include these constraints into information theory to obtain the distributions of signal usage corresponding to a maximal rate of information transfer given any noise structure and any constraints. Generalized versions of the Boltzmann, Gaussian, or Poisson distributions are obtained for linear, quadratic and temporal constraints, respectively. These distributions are shown to imply that biological transformations must dedicate a larger output range to the more probable inputs and less to the outputs with higher noise and higher participation in the constraint. To show the general theory of reliable communication at work, we apply these results to biochemical and neuronal signaling. Noncooperative enzyme kinetics is shown to be suited for transfer of a high signal quality when the input distribution has a maximum at low concentrations while cooperative kinetics for near-Gaussian input statistics. Neuronal codes based on spike rates, spike times or bursts have to balance signal quality and cost-efficiency and at the network level imply sparseness and uncorrelation within the limits of noise, cost, and processing operations.