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2 Cellular and Molecular Biology Letters

2 2008

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On the role of ball and chain interactions in recovery from the inactivation of the shaker potassium channel

100%

Borys P. , Grzywna Z. J.

Cellular and Molecular Biology Letters

2008

tom 13

nr 4

526-534

We describe a new factor in the recovery from inactivation in the ball and chain model. We propose a model in which the tension from the chain may help pull the ball away from its binding site, reducing the duration of the inactivation period. A corresponding model was built and analysed.

On the possible methods for the mathematical description of the ball and chain model of ion channel inactivation

72%

Malysiak K. , Grzywna Z. J.

Cellular and Molecular Biology Letters

2008

tom 13

nr 4

535-552

Ion channels are large transmembrane proteins that are able to conduct small inorganic ions. They are characterized by high selectivity and the ability to gate, i.e. to modify their conductance in response to different stimuli. One of the types of gating follows the ball and chain model, according to which a part of the channel’s protein forms a ball connected with the intracellular side of the channel by a polypeptide chain. The ball is able to modify the conductance of the channel by properly binding to and plugging the channel pore. In this study, the polypeptide ball is treated as a Brownian particle, the movements of which are limited by the length of the chain. The probability density of the ball’s position is resolved by different diffusional operators — parabolic (including the case with drift), hyperbolic, and fractional. We show how those different approaches shed light on different aspects of the movement. We also comment on some features of the survival probabilities (which are ready to be compared with electrophysiological measurements) for issues based on the above operators.