The interaction between membrane kinetics and membrane geometry in the transmission of action potentials in non-uniform excitable fibres: a finite element approach

Abstract

By solving the partial differential equations for an axonal segment using a finite element method, the interaction between membrane kinetics and axonal inhomogeneities, measured by their influence on propagated action potentials and stochastic spike trains, is investigated for Morris–Lecar and Hodgkin–Huxley membrane models. To facilitate comparisons of both kinetic models, parameter values are matched to give approximately the same speed for propagated action potentials. In all cases examined, the Morris–Lecar membrane model is more sensitive to geometric inhomogeneities than the comparable Hodgkin–Huxley membrane model. This difference in sensitivity can, in part, be attributed to significant differences in the membrane current supplied by each kinetic model ahead of the action potential. Also, the Morris–Lecar membrane model did not generate reflected action potentials whereas these were observed over a narrow range of geometric parameters for the comparable Hodgkin–Huxley membrane model. Simulations using stochastic spike train input showed that the presence of a sharp flare could significantly modify the statistical characteristics of the spike train output. The behaviour of action potentials governed by Morris–Lecar kinetics were more sensitive to changes in axonal geometry than those generated by comparable Hodgkin–Huxley kinetics. As a consequence of the fine balance between membrane kinetics and axon geometry, local changes in membrane properties, such as those caused by synaptic activity, can be expected to have a strong influence on the behaviour of stochastic spike trains at regions of changing axonal geometry.