Part IV. Brownian Dynamics Simulations

Using Brownian dynamics simulations, we follow the trajectories of interacting ions in the potassium channel. With a fast supercomputer, we simulate the motion of 26 potassium ions and 26 chloride ions interacting through the intermolecular potential. Here we apply a potential difference across the channel such that inside is positive with respect to outside. The motion of each ion during each discrete time step is determined by, first, the net electrical force acting on it; secondly, the frictional force and, finally, random force originating from incessant collisions of the ion with its surrounding water molecules.
We take a snap shot of the assembly once every 100 femto seconds. By determining the position of each and every particle in the assembly at each discrete time step, we deduce how many ions navigate across the channel under various conditions during a fixed time interval.

From these simulations, we show that, by placing appropriate strengths of dipoles in the channel wall, we can replicate many of the macroscopically observable properties of the potassium channel. Among these are the channel conductance, current-voltage relationships, and the conductance-concentration relationship.

We illustrate here where in the channel ions dwell predominantly. Three ions tend to reside near the selectivity filter and one near the entrance of the channel.
We now reverse the direction of the applied electric field so that potassium ions will drift from outside to inside, while leaving the strengths of all the dipoles unchanged. The magnitude of current flowing from outside to inside is about a half of that flowing from inside to outside. The channel, in other words, is outwardly rectifying. Ions do not traverse the channel in the absence of dipole on the channel wall. The driving force provided by the applied electric field is not sufficient to overcome the repulsive dielectric force. Only when dipoles of a favourable orientation are placed on the channel wall can an ion traverse the channel under the influence of the membrane potential.
The preferred positions of the ions in the channel are shifted when the direction of the applied electric field is reversed. Under this condition, two ions linger in the channel.
Finally, we can study the current flowing across the channel with asymmetrical ionic solutions in the two reservoirs. Combining the results obtained from electrostatic calculations and molecular dynamics and Brownian dynamics simulations, we attempt to relate the structural parameters of the potassium channel to experimental measurements.

Brownian Trajectory Movie brownian.mpg (1.4 M)

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Last modified: Fri Dec 11 14:48:11 "EST 1998