Study of Ionic Currents across a Model Membrane Channel Using Brownian Dynamics

Abstract

Brownian dynamics simulations have been carried out to study ionic currents flowing across a model membrane channel under various conditions. The model channel we use has a cylindrical transmembrane segment that is joined to a catenary vestibule at each side. Two cylindrical reservoirs connected to the channel contain a fixed number of sodium and chloride ions. Under a driving force of 100 mV, the channel is virtually impermeable to sodium ions, owing to the repulsive dielectric force presented to ions by the vestibular wall. When two rings of dipoles, with their negative poles facing the pore lumen, are placed just above and below the constricted channel segment, sodium ions cross the channel. The conductance increases with increasing dipole strength and reaches its maximum rapidly; a further increase in dipole strength does not increase the channel conductance further. When only those ions that acquire a kinetic energy large enough to surmount a barrier are allowed to enter the narrow transmembrane segment, the channel conductance decreases monotonically with the barrier height. This barrier represents those interactions between an ion, water molecules, and the protein wall in the transmembrane segment that are not treated explicitly in the simulation. The conductance obtained from simulations closely matches that obtained from ACh channels when a step potential barrier of 2-3 kTr is placed at the channel neck. The current-voltage relationship obtained with symmetrical solutions is ohmic in the absence of a barrier. The current-voltage curve becomes nonlinear when the 3 kTr barrier is in place. With asymmetrical solutions, the relationship approximates the Goldman equation, with the reversal potential close to that predicted by the Nernst equation. The conductance first increases linearly with concentration and then begins to rise at a slower rate with higher ionic concentration. We discuss the implications of these findings for the transport of ions across the membrane and the structure of ion channels.

A model of the glycine receptor deduced from Brownian dynamics studies

“…The Langevin equation is solved with the algorithm of van Gunsteren and Berendsen (30), by using the techniques described elsewhere (3,31,32). Electrostatic forces are determined by solving Poisson's equation with the boundary sector method (33), employing lookup table techniques (29,35).…”

Brownian dynamics simulations of ions channels: A general treatment of electrostatic reaction fields for molecular pores of arbitrary geometry

“…To reduce these requirements, Chung and co-workers assumed an azimuthal symmetry of the dielectric boundary and store the reaction field Green's function in a fivedimensional table. 6,7,10,17 These difficulties are circumvented by expressing the ion charge distribution in the simulation region using a normalized basis set ͕b m (r)͖ with N basis functions,…”

“…[1][2][3][4][5][6][7][8][9][10] The approach consists in generating the chaotic trajectory of the ions as a function of time by numerically integrating stochastic equation of motions using some effective potential function to calculate the microscopic forces operating between them. [11][12][13] In such BD simulations, the potential function itself is a central element because it provides the underlying thermodynamic structure of the theory, i.e., it completely determines all the equilibrium properties of the system.…”

“…To avoid this problem, Chung and co-workers have used an interpolation method and a large look-up table to store a discretized representation of the Green's function of the system. 6,7,10,17 The reaction field energy of a given ion configuration can be reconstructed from the stored information. A similar method was used by Coalson and co-workers.…”

Dynamic Monte Carlo Simulation of Coupled Transport through a Narrow Multiply-Occupied Pore

“…Simulations of these effects would be interesting (using one of the electrostatic algorithms of Refs. [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][44][45][46][47] and can be the topic of future studies. However, the main conclusions of this study would not change.…”