Statistical properties predicted by the ball and chain model of channel inactivation

It has been proposed that part of a voltage gated channel is a tethered ball and that inactivation occurs when this wandering ball binds to a site in the channel. In order to be able to quantitatively test this model by comparison to experiments we developed analytical solutions and numerical simulations of the distribution of times it takes the ball to reach the binding site when the motion of the ball is random and when it is also influenced by a directed force. If the motion of the ball is one-dimensional, at long times this distribution is a single exponential with a rate constant that is inversely proportional to the square of the length of the chain and does not depend on the starting position of the ball. This dependence on the chain length is not significantly altered if there are short range electrical forces between the ball and its binding site. These predictions suggest that to confirm the validity of this model additional experiments should be done to more precisely determine the form of this distribution and its dependence on the length of the chain.