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

Matthew Hoyles ^*, Vikram Krishnamurthy , May Siksik  and Shin-Ho Chung ^*

^* Research School of Biological Sciences, The Australian National University, Canberra, Australia; and Department of Electrical Engineering, The University of British Columbia, Vancouver, British Columbia, Canada

Correspondence: Address reprint requests to Shin-Ho Chung, E-mail: shin-ho.chung{at}anu.edu.au.

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 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.

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