Modeling of mammalian myelinated nerve with stochastic sodium ionic channels

This paper presents the excitation properties of mammalian myelinated nerve fibers with the nodes of Ranvier represented with stochastic sodium channels. The hybrid multi-compartment cable model developed here consisted of twenty one nodes: five central “stochastic nodes” including sodium ionic channels obeying a Markov process, and otherwise conventional deterministic nodes. The strength duration relationship and the threshold current versus the electrode-to-fiber distance were investigated to see whether the neural excitability differs from that of the conventional model possessing twenty one deterministic nodes. The stochastic nodes created variability in the fiber response, including changes in the latency of action potential generation and failures to fire on some trials. The influence of the stochastic nodes on threshold was dependent on the duration of the stimulus. At short durations the threshold of the stochastic model was greater than that of the deterministic model, while at longer durations the threshold of the stochastic model was less than that of the deterministic model. The differences between the stochastic and deterministic models were only weakly dependent on the electrode-to-fiber distance. The hybrid-cable model is computationally efficient and demonstrates the role of the stochastic properties of ionic channels in neural excitation