Rate-dependent Ca2+ signalling underlying the force-frequency response in rat ventricular myocytes: a coupled electromechanical modeling study.

BACKGROUND: Rate-dependent effects on the Ca2+ sub-system in a rat ventricular myocyte are investigated. Here, we employ a deterministic mathematical model describing various Ca2+ signalling pathways under voltage clamp (VC) conditions, to better understand the important role of calmodulin (CaM) in modulating the key control variables Ca2+/calmodulin-dependent protein kinase-II (CaMKII), calcineurin (CaN), and cyclic adenosine monophosphate (cAMP) as they affect various intracellular targets. In particular, we study the frequency dependence of the peak force generated by the myofilaments, the force-frequency response (FFR). METHODS: Our cell model incorporates frequency-dependent CaM-mediated spatially heterogenous interaction of CaMKII and CaN with their principal targets (dihydropyridine (DHPR) and ryanodine (RyR) receptors and the SERCA pump). It also accounts for the rate-dependent effects of phospholamban (PLB) on the SERCA pump; the rate-dependent role of cAMP in up-regulation of the L-type Ca2+ channel (ICa,L); and the enhancement in SERCA pump activity via phosphorylation of PLB. RESULTS: Our model reproduces positive peak FFR observed in rat ventricular myocytes during voltage-clamp studies both in the presence/absence of cAMP mediated ß-adrenergic stimulation. This study provides quantitative insight into the rate-dependence of Ca2+-induced Ca2+-release (CICR) by investigating the frequency-dependence of the trigger current (ICa,L) and RyR-release. It also highlights the relative role of the sodium-calcium exchanger (NCX) and the SERCA pump at higher frequencies, as well as the rate-dependence of sarcoplasmic reticulum (SR) Ca2+ content. A rigorous Ca2+ balance imposed on our investigation of these Ca2+ signalling pathways clarifies their individual roles. Here, we present a coupled electromechanical study emphasizing the rate-dependence of isometric force developed and also investigate the temperature-dependence of FFR. CONCLUSIONS: Our model provides mechanistic biophysically based explanations for the rate-dependence of CICR, generating useful and testable hypotheses. Although rat ventricular myocytes exhibit a positive peak FFR in the presence/absence of beta-adrenergic stimulation, they show a characteristic increase in the positive slope in FFR due to the presence of Norepinephrine or Isoproterenol. Our study identifies cAMP-mediated stimulation, and rate-dependent CaMKII-mediated up-regulation of ICa,L as the key mechanisms underlying the aforementioned positive FFR.

Multiphysics model of a rat ventricular myocyte: a voltage-clamp study.

BACKGROUND: The objective of this study is to develop a comprehensive model of the electromechanical behavior of the rat ventricular myocyte to investigate the various factors influencing its contractile response. METHODS: Here, we couple a model of Ca2 + dynamics described in our previous work, with a well-known model of contractile mechanics developed by Rice, Wang, Bers and de Tombe to develop a composite multiphysics model of excitation-contraction coupling. This comprehensive cell model is studied under voltage clamp (VC) conditions, since it allows to focus our study on the elaborate Ca2 + signaling system that controls the contractile mechanism. RESULTS: We examine the role of various factors influencing cellular contractile response. In particular, direct factors such as the amount of activator Ca2 + available to trigger contraction and the type of mechanical load applied (resulting in isosarcometric, isometric or unloaded contraction) are investigated. We also study the impact of temperature (22 to 38°C) on myofilament contractile response. The critical role of myofilament Ca2 + sensitivity in modulating developed force is likewise studied, as is the indirect coupling of intracellular contractile mechanism with the plasma membrane via the Na + /Ca2 + exchanger (NCX). Finally, we demonstrate a key linear relationship between the rate of contraction and relaxation, which is shown here to be intrinsically coupled over the full range of physiological perturbations. CONCLUSIONS: Extensive testing of the composite model elucidates the importance of various direct and indirect modulatory influences on cellular twitch response with wide agreement with measured data on all accounts. Thus, the model provides mechanistic insights into whole-cell responses to a wide variety of testing approaches used in studies of cardiac myofilament contractility that have appeared in the literature over the past several decades.

Modeling CICR in rat ventricular myocytes: voltage clamp studies.

BACKGROUND: The past thirty-five years have seen an intense search for the molecular mechanisms underlying calcium-induced calcium-release (CICR) in cardiac myocytes, with voltage clamp (VC) studies being the leading tool employed. Several VC protocols including lowering of extracellular calcium to affect Ca²(+) loading of the sarcoplasmic reticulum (SR), and administration of blockers caffeine and thapsigargin have been utilized to probe the phenomena surrounding SR Ca²(+) release. Here, we develop a deterministic mathematical model of a rat ventricular myocyte under VC conditions, to better understand mechanisms underlying the response of an isolated cell to calcium perturbation. Motivation for the study was to pinpoint key control variables influencing CICR and examine the role of CICR in the context of a physiological control system regulating cytosolic Ca²(+) concentration ([Ca²(+)](myo)). METHODS: The cell model consists of an electrical-equivalent model for the cell membrane and a fluid-compartment model describing the flux of ionic species between the extracellular and several intracellular compartments (cell cytosol, SR and the dyadic coupling unit (DCU), in which resides the mechanistic basis of CICR). The DCU is described as a controller-actuator mechanism, internally stabilized by negative feedback control of the unit's two diametrically-opposed Ca²(+) channels (trigger-channel and release-channel). It releases Ca²(+) flux into the cyto-plasm and is in turn enclosed within a negative feedback loop involving the SERCA pump, regulating[Ca²(+)](myo). RESULTS: Our model reproduces measured VC data published by several laboratories, and generates graded Ca²(+) release at high Ca²(+) gain in a homeostatically-controlled environment where [Ca²(+)](myo) is precisely regulated. We elucidate the importance of the DCU elements in this process, particularly the role of the ryanodine receptor in controlling SR Ca²(+) release, its activation by trigger Ca²(+), and its refractory characteristics mediated by the luminal SR Ca²(+) sensor. Proper functioning of the DCU, sodium-calcium exchangers and SERCA pump are important in achieving negative feedback control and hence Ca²(+) homeostasis. CONCLUSIONS: We examine the role of the above Ca²(+) regulating mechanisms in handling various types of induced disturbances in Ca²(+) levels by quantifying cellular Ca²(+) balance. Our model provides biophysically-based explanations of phenomena associated with CICR generating useful and testable hypotheses.