Computer model for action potential propagation through branch point in myelinated nerves

A mathematical model is developed for simulation of action potential propagation through a single branch point of a myelinated nerve fiber with a parent branch bifurcating into two identical daughter branches. This model is based on a previously published multi-layer compartmental model for single unbranched myelinated nerve fibers. Essential modifications were made to couple both daughter branches to the parent branch. There are two major features in this model. First, the model could incorporate detailed geometrical parameters for the myelin sheath and the axon, accomplished by dividing both structures into many segments. Second, each segment has two layers, the myelin sheath and the axonal membrane, allowing voltages of intra-axonal space and periaxonal space to be calculated separately. In this model, K ion concentration in the periaxonal space is dynamically linked to the activity of axonal fast K channels underneath the myelin in the paranodal region. Our model demonstrates that the branch point acts like a low-pass filter, blocking high-frequency transmission from the parent to the daughter branches. Theoretical analysis showed that the cutoff frequency for transmission through the branch point is determined by temperature, local K ion accumulation, width of the periaxonal space, and internodal lengths at the vicinity of the branch point. Our result is consistent with empirical findings of irregular spacing of nodes of Ranvier at axon abors, suggesting that branch points of myelinated axons play important roles in signal integration in an axonal tree.