A model of graded calcium release and L-type Ca²⁺ channel inactivation in cardiac muscle

Abstract

myocytes; computer simulation; inactivation; calcium-induced calcium release; excitation-contraction coupling CALCIUM IS OF VITAL IMPORTANCE in cells as both a transmembrane electrical signaling ion and a second messenger (3-5, 7, 36, 50, 59). The diverse range of Ca 2ϩ -mediated effects is particularly evident in cardiac myocytes, where the initial transmembrane flux of ions through L-type Ca 2ϩ channels contributes to the action potential (6,25,40,46 (5,10,18,36,59,73). [Ca 2ϩ ] i cycling is a fundamental part of normal cellular function, so any malfunction or perturbation of the systems that handle Ca 2ϩ can result in heart failure or fibrillation (21,33,44,45,49,58,60,67,69,75).Recently, CICR has been observed at the subcellular level in the form of Ca 2ϩ "sparks," which are extremely large, extremely localized increases in [Ca 2ϩ ] (18,19,29,34,35). Spontaneously occurring sparks have been observed. They can trigger a subcellular Ca 2ϩ wave that can propagate throughout the cell (17,30,35). Ca 2ϩ sparks were initially thought to reflect the opening and closing of a single SR ryanodine receptor (RyR) (18). However, they have been subsequently shown to be the result of the opening of a single L-type Ca 2ϩ channel (38), which is sufficient to initiate CICR from a cluster of RyRs (36). The number and timing of sparks depend in a nonmonotonic manner on the amplitude of the membrane depolarization.One of the most important features of intracellular [Ca 2ϩ ] cycling is the graded release of Ca 2ϩ from the SR (9,11,14). Recently, Rice et al. (57) published a model of graded CICR based on a Monte-Carlo simulation with a bell-shaped profile for the both integrated and peak RyR Ca 2ϩ release fluxes. Our model generates graded release through biophysically distinct mechanisms. The Rice et al. model (57) postulates that graded release occurs through stochastic changes in the release channel. Subsequent variants (64) added additional deterministic elements of structure, but the main mechanism of graded release remained stochastic. In contrast, our model assumes a physiological variability in diadic junction morphology to generate graded release. The models are, therefore, inherently different at a qualitative level, and there will be testable differences in predicted behavior between these models.In this paper, we present a new model of cardiac Ca 2ϩ handling that incorporates a novel Markov model for L-type Ca 2ϩ channels and graded SR Ca 2ϩ release in response to voltage-clamp simulations. We hypothesize that the structural inhomogeneity of the local calcium release subsystems is responsible for graded release. To model this situation, we introduced eight calcium release subsystems with different characteristics. The model myocyte has a series of physically distinct subsystems that represent the area where the junctional SR comes in close proximity to the T-tubular membrane. Each subsystem is a relatively small subspace volume bounded by the sarcolemma, which contains between one and eight L-type Ca 2ϩ ch...

Evoked centripetal Ca2+ mobilization in cardiac Purkinje cells: insight from a model of three Ca2+ release regions

“…(Stuyvers et al 2005) with the assumption that the movement of Ca 2+ ions is unidirectional from the cytosol to the ER lumen (Jafri et al 1998;Bondarenko et al 2004). The flux through the Ca 2+ pumps was described by:…”

Developmental changes in time course of recovery from inactivation in L-type calcium currents of rabbit ventricular myocytes

“…Such Ca 2ϩ -dependent potentiation may facilitate the positive force frequency relationship in many cardiac cells and has been reported to involve Ca 2ϩ -dependent activation of calmodulin-dependent protein kinase II (34). Recent mathematical models of I Ca have reproduced the time course of recovery from inactivation by incorporation of a state model of four closed states, one open state, and three inactivated states (9). These closed states represent the inactivation either from voltage alone or from interactions between the channel and a "tethered" calmodulin-binding ancillary subunit bound to calcium or a combination of slower voltage inactivation and the fast Ca 2ϩ -dependent inactivation.…”

EGL-19 and EXP-2 Ion Channels Modelling within C. Elegans Pharyngeal Muscle Cell Allows Reproduction of CA2+ Driven Action Potentials, Both Single Events and Trains

“…http://dx.doi.org/10.1101/228650 doi: bioRxiv preprint first posted online Dec. 20, 2017; model, we reproduced in silico the voltage-clamp experiments equivalent to those presented in Fig.3A,B of the same work 24 . Our calculations resulted in the similar dependence of Ca 2+ peak current on the voltage, including the position of maximal magnitude of the current corresponding to 0 mV.…”

“…We reproduced the corresponding Markov model based on the state diagram, differential equations and parameters from the work of V.E. Bondarenko and colleagues 24 . It was implemented as a MOD-file (written in Neuron Model Description Language), which was compiled to become accessible within NEURON simulation environment.…”

“…Changing the parameters of L-type calcium channel, one by one, we have found that there is a simple modification that moves the I-V dependence 20 mV to the right so that it becomes similar to the real current-voltage relationship for EGL-19 (see Fig.3B.). The changes which thus convert the model of cardiac myocyte's L-type Ca 2+ channel into the model of EGL-19 L-type Ca 2+ channel are the following: formulae (32) and (33) for α and β from the work 24 should be modified according to this schema: …”