A Single-Equation Approach to Classifying Neuronal Operational Modes

The neural coding is yet to be discovered. The neuronal operational modes that arise with fixed inputs but with varying degrees of stimulation help to elucidate their coding properties. In neurons receiving {\it in vivo} stimulation, we show that two operation modes can be described with simplified models: the coincidence detection mode and the integration mode. Our derivations include a simplified polynomial model with non-linear coefficients ($\beta_i$) that capture the subthreshold dynamics of these modes of operation. The resulting model can explain these transitions with the sign and size of the smallest nonlinear coefficient of the polynomial alone. Defining neuronal operational modes provides insight into the processing and transmission of information through electrical currents. Requisite operational modes for proper neuronal functioning may explain disorders involving dysfunction of electrophysiological behavior, such as channelopathies.