Brownian Dynamics Theory for Predicting Internal and External Blockages of Tetraethylammonium in the KcsA Potassium Channel

Date

2008-11-12

Authors

Hoyles, Matthew
Krishnamurthy, Vikram
Siksik, May
Chung, Shin-Ho

Journal Title

Journal ISSN

Volume Title

Publisher

Biophysical Society

Abstract

The theory of Brownian dynamics is used to model permeation and the blocking of KcsA potassium channels by tetraethylammonium (TEA). A novel Brownian dynamics simulation algorithm is implemented that comprises two free energy profiles; one profile is seen by the potassium ions and the other by the TEA molecules whose shape is approximated by a sphere. Our simulations reveal that internally applied TEA blocks the passage of K(+) ions by physically occluding the pore. A TEA molecule in the external reservoir encounters an attractive energy-well created by four tyrosine residues at position 82, in addition to all other attractive and repulsive forces impinging on it. Using Brownian dynamics, we investigate how deep the energy-well needs to be to reproduce the experimentally determined inhibitory constant k(i) for the TEA blockade of KcsA or the mutant Shaker T449Y. The one-dimensional free energy profile obtained from molecular dynamics is first converted into a one-dimensional potential energy profile, and is then transformed into a three-dimensional free energy profile in Brownian dynamics by adding the short-range potential from the channel walls. When converted, the free energy profile calculated from molecular dynamics gives a well-depth of approximately 10 kT. We systematically alter the depths of the profiles, and then use Brownian dynamics simulations to numerically determine the current versus TEA-concentration curves. We show that the sequence of binding and unbinding events of the TEA molecule to the binding pocket can be modeled by a first-order Markov process. The Brownian dynamics simulations also reveal that the probability of a TEA molecule binding to the binding pocket in KcsA potassium channels increases exponentially with TEA concentration and depends also on the applied potential and the K(+) concentration in the simulation assembly.

Description

Keywords

algorithms, computational biology, kinetics, potassium, potassium channels, protein subunits, tetraethylammonium, thermodynamics, models, chemical

Citation

Source

Biophysical Journal

Type

Journal article

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