Probabilistic Modeling of Action Potential Generation by Neurons

The function of many cells and organs in the body is absolutely dependent on their ability to generate an electrical signal termed an action potential. The action potential represents a temporal sequence of changes in the electrical potential across a local domain of a cell’s plasma membrane, and results from a carefully coordinated sequence of changes in membrane conductance for sodium and potassium ions. We present a model of the dynamical behavior of the gated sodium ion channel, which is determines the event of an action potential. Our model is based on the electrical properties of parallel RC circuits, but improves on most current models because it incorporates timeand membrane-potential dependent probabilities that the gated sodium ion channel is in one of three states: closed, open, or inactive. More importantly, our model accounts for the so-called membrane threshold, which is the membrane potential at which the sequence of changes in conductance commences.