Simulation of Ca²⁺ Release from the Sarcoplasmic Reticulum with Three-Dimensional Sarcomere Model in Cardiac Muscle

Abstract

A simulation of some basic features of Ca²⁺ release from the sarcoplasmic reticulum (SR) in cardiac muscle was made with a model based on the mechanism of Ca²⁺-induced Ca²⁺-release. The half-sarcomere modeled as a circular cylinder was divided into 20 annular elements in the radial, 50 slices in the axial, and 125 slices in the azimuthal direction. The cylindrical surface of the sarcomere was covered by a layer of the SR. The rate of Ca²⁺ release from the terminal sac (TS) is proportional to the product of the open probability of the Ca²⁺ release channel and the difference of [Ca²⁺] between the TS and an element facing the TS. Ca²⁺ moves from element to element by simple diffusion and is taken up by the tubular SR via Ca²⁺-ATPase. Ca²⁺ influx (I_ca) to trigger the TS Ca²⁺ release was introduced to either a single element facing the TS (local I_ca) or to 20 elements aligned at the level of the Z-line (uniform I_ca). The simulation showed that with both types of I_ca, TS Ca²⁺ release is smoothly graded over a wide range of I_ca with the TS moderately loaded with Ca²⁺. The gain determined by dividing the total amount of TS Ca²⁺ release by I_ca was greater with local than with uniform I_ca. Mechanical alternans was simulated with both the local and uniform I_ca with an appropriate rate of Ca²⁺ replenishment to the TS. A Ca²⁺ wave was simulated with a model consisting of 8 longitudinally consecutive sarcomeres with TS heavily loaded with Ca²⁺. Thus the present model accounted for graded TS Ca²⁺ release, mechanical alternans, and Ca²⁺ wave in cardiac muscle at the same time.