Signals recorded from neurons with extracellular planar sensors have a wide range of waveforms and amplitudes. This variety is a result of different physical conditions affecting the ion currents through a cellular membrane. The transmembrane currents are often considered by macroscopic membrane models as essentially a homogeneous process. However, this assumption is doubtful, since ions move through ion channels, which are scattered within the membrane. Accounting for this fact, the present work proposes a theoretical model of heterogeneous membrane conductivity. The model is based on the hypothesis that both potential and charge are distributed inhomogeneously on the membrane surface, concentrated near channel pores, as the direct consequence of the inhomogeneous transmembrane current. A system of continuity equations having non-stationary and quasi-stationary forms expresses this fact mathematically. The present work performs mathematical analysis of the proposed equations, following by the synthesis of the equivalent electric element of a heterogeneous membrane current. This element is further used to construct a model of the cell-surface electric junction in a form of the equivalent electrical circuit. After that a study of how the heterogeneous membrane conductivity affects parameters of the extracellular electrical signal is performed. As the result it was found that variation of the passive characteristics of the cell-surface junction, conductivity of the cleft and the cleft height, could lead to different shapes of the extracellular signals.
Biophysical characterization of membrane phase transition profiles for the discrimination of Outer Membrane Vesicles (OMVs) from Escherichia coli grown at different temperatures
On 1/f^alpha power laws originating from linear neuronal cable theory: power spectral densities of the soma potential, transmembrane current and single-neuron contribution to the EEG
Mapping the energy and diffusion landscapes of membrane proteins at the cell surface using high-density single-molecule imaging and Bayesian inference: application to the multi-scale dynamics of glycine receptors in the neuronal membrane
Max Planck Institute for Human Cognitive and Brain Sciences（马克斯·普朗克人类认知与脑科学研究所）；University Medical Center Freiburg, Faculty of Medicine, University of Freiburg（弗赖堡大学医学院弗赖堡大学医学中心）；Inria-Saclay, Equipe Idefix, UMA, ENSTA Paris, Institut Polytechnique de Paris（巴黎理工学院ENSTA巴黎萨克雷Inria，Idefix团队，UMA）
