M-Current Inhibition in Hippocampal Neurons Triggers Intrinsic and Synaptic Homeostatic Responses at Different Temporal Scales

Abstract

Robust electrical signal propagation in the form of action potentials (AP) is a hallmark of neuronal activity. While it is well established that changes to ionic gradients across the bilayer are responsible for AP propagation, the contributions of ionic diffusion and membrane morphological heterogeneity are not well understood. New experimental imaging methods have already suggested that spatial complexities of dendrites and the spatial dynamics of ionic species influence membrane voltage locally. However, it remains difficult to extract detailed voltage information at short time and length scales, which motivates a need for mathematical models that can incorporate these spatial complexities and predict and dissect voltage dynamics. Owing to the well-mixed assumption employed by popular models such as the Hodgkin-Huxley model, Morris-Lecar model, and cable theory the influence of morphology on voltage propagation cannot be studied. Therefore, building on these models, we construct a spatial model of AP propagation along dendrites which relaxes the well-mixed assumption. We explicitly model local ionic concentrations and their dynamics as influenced by reaction-diffusion and Hodgkin-Huxley type ion channel currents. The local transmembrane potential is determined by the local transmembrane ionic gradient via the Nernst potential. We compare membrane voltage dynamics from this new model to the traditional passive cable equation for dendrites of various sizes and configurations. Using our model, we find that a) membrane voltage propagation depends on the complex geometries of dendrites, b) the presence of internal organelles modulates membrane voltage propagation, and c) downstream signaling dynamics can affect AP propagation.