Abstract
sparks and waves play important roles in calcium release and calcium propagation during the excitation-contraction (EC) coupling process in cardiac myocytes. Although the classical Fick’s law is widely used to model sparks and waves in cardiac myocytes, it fails to reasonably explain the full-width at half maximum(FWHM) paradox. However, the anomalous subdiffusion model successfully reproduces sparks of experimental results. In this paper, in the light of anomalous subdiffusion of sparks, we develop a mathematical model of calcium wave in cardiac myocytes by using stochastic release of release units (CRUs). Our model successfully reproduces calcium waves with physiological parameters. The results reveal how concentration waves propagate from an initial firing of one CRU at a corner or in the middle of considered region, answer how large in magnitude of an anomalous spark can induce a wave. With physiological currents (2pA) through CRUs, it is shown that an initial firing of four adjacent CRUs can form a wave. Furthermore, the phenomenon of calcium waves collision is also investigated.
Highlights
Nomenclature x,y t b DCx, DCy1⁄2Ca2z 1⁄2Ca2z? 1⁄2CaF 1⁄2F T 1⁄2CaBn1⁄2BnT kFz, knz kF{, kn{lx, ly ICRU F Kpump Vpmuamxp m n spatial coordinates, mm time, ms fractional order of the spatial derivative
In this work, based on the anomalous subdiffusion model, we find the current which can trigger a normal Ca2z wave initiating from a single Ca2z spark at the corner of considered region
Our model present that a spontaneous Ca2z spark can form a Ca2z wave
Summary
Nomenclature x,y t b DCx , DCy1⁄2Ca2z 1⁄2Ca2z? 1⁄2CaF 1⁄2F T 1⁄2CaBn1⁄2BnT kFz, knz kF{, kn{lx, ly ICRU F Kpump Vpmuamxp m n spatial coordinates, mm time, ms fractional order of the spatial derivative. Nomenclature x,y t b DCx , DCy. 1⁄2Ca2z 1⁄2Ca2z? Lx, ly ICRU F Kpump Vpmuamxp m n spatial coordinates, mm time, ms fractional order of the spatial derivative. Ca2z diffusion coefficients along x-axis and y-axis, mm2:ms{1 free Ca2z concentration, mM resting Ca2z concentration, mM. Ca-bound fluo-3 concentration, mM total fluo-3 concentration, mM. Ca-bound endogenous buffer concentration, mM total endogenous buffer concentration, mM forward rate constants for dye and endogenous buffer reactions, mM{1:s{1 reverse rate constants for dye and endogenous buffer reactions, s{1 spatial separation of CRUs along x-axis and y-axis, mm current through the CRU, pA Faraday’s constant, C:mol{1. CRU Hill coefficient s molar flux of a clustered RyR channel, mM :s{1. Topen S open time of CRU, ms stochastic switching function equaling either 0 or 1 K
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