Tailoring inputs to achieve maximal neuronal firing

A major component of theoretical neuroscience is the study of how various neuronal models respond to synaptic inputs. Indeed, chemical synaptic transmission offers a specific mechanism for the encoding of information that an organism senses from the external environment, filtered by the internal state of the organism. The functions performed by particular neurons and neuronal networks are in part determined by the nature of the inputs that they receive and are in part a result of the responses they generate to these inputs, due to their intrinsic properties. Thus, understanding neuronal input-output transformations represents a centrally important scientific goal.Although the framework for incorporating synaptic inputs into computational models is well established, and the computational implications of such inputs have received significant attention, optimization problems involving synaptic inputs are not well represented in the literature. In this paper, we consider such a problem, namely what is the optimal way to tailor synaptic inputs, subject to certain constraints, to maximize the number of spikes that a neuron will fire?In fact, we consider two variations on this problem, one based on maximizing the total number of spikes fired and one focused on maximal firing within a prescribed time interval. There are several reasons that maximizing numbers of spikes may be a biologically relevant neuronal goal. Since neurons operate under conditions in which efficient resource use could be evolutionarily advantageous, it could be useful if, subject to some constraint on the amount of input that is available, the synaptic input time course could be tailored to achieve the largest possible number of spikes. Certainly, there are brain areas, including areas of visual cortex and somatosensory cortex, where it appears that intensity of firing encodes stimulus information, with neurons showing maximal firing under optimally preferred stimulus conditions [1-3]. Similarly, a suf