| Since the introduction of the Hodgkin-Huxley equations, used to describe the excitation of neurons, the Nernst equilibria for individual ion channels have assumed to be constant in time. Recent biological recordings call into question the validity of this assumption. Very little theoretical work has been done to address the issue of accounting for these non-static Nernst equilibria using the Hodgkin-Huxley formalism. This body of work incorporates non-static Nernst equilibria into the generalized Hodgkin-Huxley formalism by considering the first-order effects of the Nernst equation. It is further demonstrated that these effects are likely dominate in neurons with diameters much smaller than that of the squid giant axon and permeate important information processing regions of the brain such as the hippocampus. Particular results of interest include single-cell bursting due to the interplay of spatially separated neurons, pattern formation via spiral waves within a soliton-like regime, and quantifiable shifts in the multifractality of hippocampal neurons under the administration of various drugs at varying dosages. This work provides a new perspective on the variability of Nernst equilibria and demonstrates its utility in areas such as pharmacology and information processing. |
