Effect of Morphologic Features of Neurons on the Extracellular Electric Potential: A Simulation Study Using Cable Theory and Electro-Quasi-Static Equations.

Microelectrode arrays serve as an indispensable tool in electro-physiological research to study the electrical activity of neural cells, enabling measurements of single cell as well as network communication analysis. Recent experimental studies have reported that the neuronal geometry has an influence on electrical signaling and extracellular recordings. However, the corresponding mechanisms are not yet fully understood and require further investigation. Allowing systematic parameter studies, computational modeling provides the opportunity to examine the underlying effects that influence extracellular potentials. In this letter, we present an in silico single cell model to analyze the effect of geometrical variability on the extracellular electric potentials. We describe finite element models of a single neuron with varying geometric complexity in three-dimensional space. The electric potential generation of the neuron is modeled using Hodgkin-Huxley equations. The signal propagation is described with electro-quasi-static equations, and results are compared with corresponding cable equation descriptions. Our results show that both the geometric dimensions and the distribution of ion channels of a neuron are critical factors that significantly influence both the amplitude and shape of extracellular potentials.

The stability of solitons in biomembranes and nerves.

We examine the stability of a class of solitons, obtained from a generalization of the Boussinesq equation, which have been proposed to be relevant for pulse propagation in biomembranes and nerves. These solitons are found to be stable with respect to small-amplitude fluctuations. They emerge naturally from non-solitonic initial excitations and are robust in the presence of dissipation. Solitary waves pass through each other with only minor dissipation when their amplitude is small. Large-amplitude solitons fall apart into several pulses and small-amplitude noise upon collision when the maximum density of the membrane is limited by the density of the solid phase membrane.