Simulation of potassium accumulation in clefts of Purkinje fibers: effect on membrane electrical activity.

Purkinje fiber action potentials and concomitant intercellular cleft [K] variations were reconstructed by using modified McAllister, Noble & Tsien (1975) equations including the pump current, ip, and the pacemaker current, if. Three different mean cleft widths were chosen: 40, 200 and 1000 nm. Assuming a cylindrical arrangement of the cells in the bundle, the cleft [K] gradient across the bundle was calculated by using the radial cylindrical diffusion equation. The effects of varying several parameters (cleft width, tortuosity, ip and if) were studied in conditions corresponding to two different values of [K] in the bulk solution, namely 2.7 and 5.4 mM. The shortening influence on the action potential of the systolic increase in cleft [K] was detectable only in the case of the smallest cleft width. Reduction in electrogenic pump activity led to alterations of the electrical activity which depended on the cleft width. The evolution of the intercellular [K] during each action potential and the following diastolic period was normally biphasic; a small reaccumulation during the late part of the diastole was induced by the K component of the if current. Experimentally determined intercellular [K] variations described in the literature exhibit a monophasic evolution. Such a monophasic evolution could be reproduced after reduction of both if and the transient outward K current and suppression of the negative slope of the ik1-Em relationship. In this case the amplitude of the cyclic change in intercellular [K] was approximately equal to 0.2 mM (for a 200 nm cleft width), a value much lower than that experimentally recorded. Possible reasons for this discrepancy are discussed. A simplified three compartment model for K diffusion was also used. Results obtained with the two models demonstrated that the simplified model can be used as a reasonable approximation of the more complex radial diffusion model, with a reduction in computation time reaching 80% or more.