Information capacity and its approximations under metabolic cost in a simple homogeneous population of neurons

We calculate and analyze the information capacity-achieving conditions and their approximations in a simple neuronal system. The input-output properties of individual neurons are described by an empirical stimulus-response relationship and the metabolic cost of neuronal activity is taken into account. The exact (numerical) results are compared with a popular "low-noise" approximation method which employs the concepts of parameter estimation theory. We show, that the approximate method gives reliable results only in the case of significantly low response variability. By employing specialized numerical procedures we demonstrate, that optimal information transfer can be near-achieved by a number of different input distributions. It implies that the precise structure of the capacity-achieving input is of lesser importance than the value of capacity. Finally, we illustrate on an example that an innocuously looking stimulus-response relationship may lead to a problematic interpretation of the obtained Fisher information values.