Periodic spiking by a pair of ionic channels

Abstract

Neuronal cells present periodic trains of localized voltage spikes involving a large amount of different ionic channels. A relevant question is whether this is a cooperative effect or it could also be an intrinsic property of individual channels. Here we use a Langevin formulation for the stochastic dynamics of a pair of Na and K ionic channels. These two channels are simple gated pore models where a minimum set of degrees of freedom follow standard statistical physics. The whole system is totally autonomous without any external energy input, except for the chemical energy of the different ionic concentrations across the membrane. As a result it is shown that a unique pair of different ionic channels can sustain membrane potential periodic spikes. The spikes are due to the interaction between the membrane potential, the ionic flows and the dynamics of the internal parts (gates) of each channel structures. The spike involves a series of dynamical steps being the more relevant one the leak of Na ions. Missing spike events are caused by the altered functioning of specific model parts. The time dependent spike structure is comparable with experimental data.

A General Model of Ion Passive Transmembrane Transport Based on Ionic Concentration

“…If the depolarizing direct current stimulus remains at an appropriate intensity, the channels may be excited repeatedly, forming periodic spiking (Ram-rez Piscina and Sancho, 2018), of which the numerical stimulation is shown in Figures 13, 14.…”

Fixed-density boundary conditions in overdamped Langevin simulations of diffusion in channels

“…Therefore it is specially appropriate in Langevin approaches for the study of molecular channels and the modeling of the interaction between gates and individual ions and the action of the membrane potential, as used in Refs. [7,18,19].…”

“…Following the shape of the gates used in Refs. [7,18,19] we add a Gaussian 7); symbols: simulation results. Observed differences in J values between theory and simulations were in all cases smaller than 10 −3 .…”

“…Previous attempts involved for instance the simulation of particles in the reservoirs [12,13], the consideration of random walks as discrete-time Brownian dynamics [14], the employing of velocity variables [15,16], or some shooting method to empirically finding simulation parameters [17]. Here we make explicit the derivation and procedure of a satisfactory method for these boundary conditions, without such shortcomings, recently implemented in ionic channel simulations [7,18,19]. For simplicity, we will illustrate the method by the simulation of very simple cases, consisting of noninteracting particles in one-dimensional static channels devoid of any biological complexity.…”