Brownian Dynamics Study of Ion Transport in the Vestibule of Membrane Channels

Abstract

Brownian dynamics simulations have been carried out to study the transport of ions in a vestibular geometry, which offers a more realistic shape for membrane channels than cylindrical tubes. Specifically, we consider a torus-shaped channel, for which the analytical solution of Poisson's equation is possible. The system is composed of the toroidal channel, with length and radius of the constricted region of 80 A and 4 A, respectively, and two reservoirs containing 50 sodium ions and 50 chloride ions. The positions of each of these ions executing Brownian motion under the influence of a stochastic force and a systematic electric force are determined at discrete time steps of 50 fs for up to 2.5 ns. All of the systematic forces acting on an ion due to the other ions, an external electric field, fixed charges in the channel protein, and the image charges induced at the water-protein boundary are explicitly included in the calculations. We find that the repulsive dielectric force arising from the induced surface charges plays a dominant role in channel dynamics. It expels an ion from the vestibule when it is deliberately put in it. Even in the presence of an applied electric potential of 100 mV, an ion cannot overcome this repulsive force and permeate the channel. Only when dipoles of a favorable orientation are placed along the sides of the transmembrane segment can an ion traverse the channel under the influence of a membrane potential. When the strength of the dipoles is further increased, an ion becomes detained in a potential well, and the driving force provided by the applied field is not sufficient to drive the ion out of the well. The trajectory of an ion navigating across the channel mostly remains close to the central axis of the pore lumen. Finally, we discuss the implications of these findings for the transport of ions across the membrane.

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

“…[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.…”

Experimental and Theoretical Methods of Study of Ionic Channels

“…Однако, учитывая область применения БД и возможность моделирования относительно продолжительной эволюции системы (10 −6 ÷ 10 −3 c [5]), характерный временной шаг, выбираемый при данных экспериментах [145][146][147], позволяет рассматривать броуновские блуждания в пространстве скоростей и координат как марковский процесс без учета функции памяти [148,149].…”