Extracellular electrical signals in a neuron-surface junction: model of heterogeneous membrane conductivity

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

Роль потенциал-зависимых калиевых каналов в формировании клеточного отклика на электрическую стимуляцию клеток в культуре

Usage of electric fields for forming a certain cellular response finds application in various fields of biology and medicine. The efficiency of the methods based on the electric field action was discussed repeatedly. However, the process of developing stimulation protocols is being complicated by the absence of the specification of the precise mechanism of the electric stimulation action upon cells in the culture. Thus, the identification of signal transduction mechanism in cells under the electric field action is of current interest. The objective of this work is to investigate the role of potassium potential-dependent channels in forming the cellular response at long-term electrical stimulation. Studies were carried out using glioma cells C6. The pulsed electric field with the strength of 3-20 V/m, with 2 ms biphase pulses and with a frequency of 10 Hz was used for electric stimulation. 4-Aminopyridine was used for inhibitory analysis. It was shown that the change in the membrane potential under the electric field action takes place involving the potassium potential-dependent ion channels. It was revealed that the use of a potassium potential-dependent ion channels inhibitor partially levels the field effects. Thus, potassium potential-dependent channels play a significant role in the processes of signal transduction in cells at long-term electrical stimulation of the culture of cells.Применение электрических полей для формирования определенного клеточного отклика находит применение в различных областях биологии и медицины. Неоднократно обсуждалась эффективность методов, основанных на действии электрических полей. Однако отсутствие описания точного механизма действия электрической стимуляции на клетки в культуре осложняет процесс разработки протоколов стимуляции. Таким образом, установление механизма трансдукции сигнала в клетках при действии электрических полей является актуальным. Цель работы - изучение роли калиевых потенциал-зависимых каналов в формировании клеточного отклика в условиях долговременной электрической стимуляции. Исследования проводили на культуре клеток глиомы С6. Для проведения электрической стимуляции использовали импульсное электрическое поле с напряженностью 3-20 В/м с длительностью бифазных импульсов 2 мс и частотой 10 Гц. Для проведения ингибиторного анализа использовали 4-аминопиридин. Установлено, что изменение мембранного потенциала при действии электрического поля происходит при участии калиевых потенциал-зависимых ионных каналов. Выявлено, что применение ингибитора калиевых потен-циал-зависимых ионных каналов частично нивелирует эффекты действия поля. Таким образом, калиевые потенци-ал-зависимые каналы играют важную роль в процессах трансдукции сигнала в клетках при долговременной электрической стимуляции культуры клеток

Design of Deterministic Model of Signal Transduction between Neuronal Cells

Mathematical model describing signal transduction between neurons has been presented using the system of nonlinear ordinary differential equations. The Cauchy problem for the given system has been solved numerically and system parameters were adjusted to match the results of experimental measurements of extracellular postsynaptic potentials in rat hippocampus slices. While fitting model to the experimental data some values of synaptic parameters have been determined