Modeling CICR in rat ventricular myocytes: voltage clamp studies

Abstract

BackgroundThe 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).MethodsThe 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.ResultsOur 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.ConclusionsWe 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.

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

“…A fixed-step Merson-modified Runge-Kutta 4th-order numerical integration scheme [3] was used to solve this set of 1st-order differential equations (ODE) describing the dynamic model. The free C a 2 + concentration in the dyad is governed by the time courses of the C a 2 + fluxes through C a 2 + transport systems, as well as by the time course of C a 2 + binding to C a 2 + buffers present in the junction [4]. Description of the spatio-temporal dynamics of calcium transients in the dyad triggered by C a 2 + stimulus (basis of CICR) requires calculation of the partial differential equations (PDE) of the whole reaction-diffusion system.…”

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

“…cGMP also enhances I PMCA , C a 2+ activated K + channel ( I KCa ) and suppresses I C a , L , I c y t , s e r c a via PKG (not explicitly modeled, but lumped into a cGMP term). ‡ The rat ventricular cell model used in this study is however limited to C a 2+ related channel, exchanger and pumps ( I C a , L , I NaCa , I PMCA and I c y t , s e r c a ), while lacking exclusive N a + or K + related channels and transporters (as shown in Figure 2, Krishna et al [15]). The part of the model describing cAMP-mediated pathway used in our study is highlighted (blue).…”

“…CDI is a critical negative feedback mechanism which causes decreased C a 2+ entry via I C a , L when the SR load is high with an accompanying large myoplasmic C a 2+ transient, and it results in increased C a 2+ entry via I C a , L when [ C a 2+ ] myo is small due to a low SR load. We utilize a 2-state model, as shown in Figure 3A of our previous study Krishna et al [15], to simulate CDI.…”

“…Although CDF and CDI of I C a , L coexist, CDI responds much faster (within the same beat) than CDF (over several beats). Our model incorporates CDF by allowing the rate constants in the 6-state Markovian model of the I C a , L channel ($k_{24}^{\text{italicdhpr}}$, $k_{25}^{\text{italicdhpr}}$ and $k_{12}^{\text{italicdhpr}}$ in Figure 3A, Krishna et al [15]) to be a function of the available active CaMKII and CaN.…”

“…Thus, the functional consequence of phosphorylation of RyR by CaMKII remains controversial. Since the bulk of the published literature on this topic points toward an activating effect of CaMKII on RyR, this concept is adopted in our model by making the rate constants in our 4-state Markovian model of the RyR channel ($k_{12}^{\text{italicryr}}$, $k_{41}^{\text{italicryr}}$, $k_{43}^{\text{italicryr}}$ and $k_{32}^{\text{italicryr}}$ in Figure 3B, Krishna et al [15]) functions of the available active CaMKII. Although CaN is reported to regulate ryanodine receptor C a 2+ release channels in rat heart [50], we have refrained from modeling its influence on the RyR channel because CaN is known to be constitutively active in the dyad [2] exhibiting only minor frequency-dependent modulation in its level, hence making its rate-dependent regulatory role insignificant.…”