Compartment calcium model of frog skeletal muscle during activation

Abstract

Skeletal muscle contraction is triggered by a rise in calcium (Ca(2+)) concentration in the myofibrillar space. The objective of this study was to develop a voltage dependent compartment model of Ca(2+) dynamics in frog skeletal muscle fibers. The compartment model corresponds to the myofibrillar space (MS) and a calcium store, the sarcoplasmic reticulum (SR). Ca(2+) is released from the SR to the MS based on the voltage and is able to bind to several proteins in the MS. We use a detailed model to account for voltage dependent Ca(2+) release and inactivation. With this model, we are able to match previous experimental data for Ca(2+) release and binding to proteins for an applied (fixed) voltage. We explore the sensitivity of parameters in the model and illustrate the importance of inactivation of the SR; during a long depolarization, the SR must be inactivated in order to achieve realistic Ca(2+) concentrations in the MS. A Hodgkin Huxley type model was also developed to describe voltage at the surface membrane using electrophysiological data from previous experiments. This voltage model was then used as the time dependent voltage to determine Ca(2+) release from the SR. With this fully coupled model, we were able to match previous experimental results for Ca(2+) concentrations for a given applied current. Additionally, we examined simulated Ca(2+) concentrations in the case of twitch and tetanus, corresponding to different applied currents. The developed model is robust and reproduces many aspects of voltage dependent calcium signaling in frog skeletal muscle fibers. This modeling framework provides a platform for future studies of excitation contraction coupling in skeletal muscle fibers.

Keywords: Calcium dynamics; Excitation contraction; Hodgkin Huxley equations; Sarcoplasmic reticulum.