Abstract
Markov models with discrete states, such as closed ⇄ closed ⇄ open have been widely used to model the kinetics of ion channels in the cell membrane. In these models the transition probabilities per unit time (the kinetic rate constants) are independent of the time scale on which they are measured. However, in many physical systems, a property, L, depends on the scale, ϵ, at which it is measured such that L( ϵ)∝ ϵ 1− D where D is the fractal dimension. Such systems are said to be ‘fractal’. Based on the assumption that the kinetic rates are given by k( t)∝ t 1− D we derive a fractal model of ion-channel kinetics. This fractal model has fewer adjustable parameters, is more consistent with the dynamics of protein conformations, and fits the single-channel recordings from the corneal endothelium better than the discrete-state Markov model.
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