The neuron as a population of ion channels: the emergence of a stochastic and history dependent mode

Abstract

AbstractExperiments show that synaptically isolated cortical neurons, stimulated with periodic extra-cellular current pulses for long durations, respond in a complex irregular and history dependent manner - over a large range of timescales (from seconds to days). With the aim of finding a biophysical explanation to these results, we developed a general novel scheme to analytically solve conductance based Hodgkin-Huxley like models under pulse stimulation, and derived closed-form expressions for the transient behavior, firing rates and firing patterns of the neuron. Using this approach we were able to reproduce most experimental results using only slow sodium inactivation - with the important exceptions of the irregular behavior and the large range of timescales. By ruling out chaotic behavior, we proved that both of these features could not occur in deterministic conductance based models - even when using an arbitrary large number of gating variables (accounting for potassium activation, changes in ion concentrations, etc.). Additionally, we showed channel noise is highly likely to play a very significant role in the neuronal dynamics, and to be the cause of the observed irregularity. Finally, we came to the conclusion that, even when taking into account ion channel stochasticity, current conductance based models cannot reproduce the experimentally observed very slow changes in the neuronal response, necessitating the introduction of long term processes such as ion channel regularization.