Clusters of calcium release channels harness the Ising phase transition to confine their elementary intracellular signals.

Intracellular Ca signals represent a universal mechanism of cell function. Messages carried by Ca are local, rapid, and powerful enough to be delivered over the thermal noise. A higher signal-to-noise ratio is achieved by a cooperative action of Ca release channels such as IP3 receptors or ryanodine receptors arranged in clusters (release units) containing a few to several hundred release channels. The channels synchronize their openings via Ca-induced Ca release, generating high-amplitude local Ca signals known as puffs in neurons and sparks in muscle cells. Despite the positive feedback nature of the activation, Ca signals are strictly confined in time and space by an unexplained termination mechanism. Here we show that the collective transition of release channels from an open to a closed state is identical to the phase transition associated with the reversal of magnetic field in an Ising ferromagnet. Our simple quantitative criterion closely predicts the Ca store depletion level required for spark termination for each cluster size. We further formulate exact requirements that a cluster of release channels should satisfy in any cell type for our mapping to the Ising model and the associated formula to remain valid. Thus, we describe deterministically the behavior of a system on a coarser scale (release unit) that is random on a finer scale (release channels), bridging the gap between scales. Our results provide exact mapping of a nanoscale biological signaling model to an interacting particle system in statistical physics, making the extensive mathematical apparatus available to quantitative biology

Mechanisms of Calcium Leak from Cardiac Sarcoplasmic Reticulum Revealed by Statistical Mechanics

Heart muscle contraction is normally activated by a synchronized Ca release from sarcoplasmic reticulum (SR), a major intracellular Ca store. However, under abnormal conditions Ca leaks from the SR, decreasing heart contraction amplitude and increasing risk of life-threatening arrhythmia. The mechanisms and regimes of SR operation generating the abnormal Ca leak remain unclear. Here we employed both numerical and analytical modeling to get mechanistic insights into the emergent Ca leak phenomenon. Our numerical simulations using a detailed realistic model of Ca release unit (CRU) reveal sharp transitions resulting in Ca leak. The emergence of leak is closely mapped mathematically to the Ising model from statistical mechanics. The system steady-state behavior is determined by two aggregate parameters: the analogues of magnetic field ($h$) and the inverse temperature ($\beta$) in the Ising model, for which we have explicit formulas in terms of SR Ca and release channel opening/closing rates. The classification of leak regimes takes the shape of a phase $\beta$-$h$ diagram, with the regime boundaries occurring at $h$=0 and a critical value of $\beta$ ($\beta*$) which we estimate using a classical Ising model and mean field theory. Our theory predicts that a synchronized Ca leak will occur when $h$>0 and $\beta>\beta*$ and a disordered leak occurs when $\beta<\beta*$ and $h$ is not too negative. The disorder leak is distinguished from synchronized leak (in long-lasting sparks) by larger Peierls contour lengths, an output parameter reflecting degree of disorder. Thus, in addition to our detailed numerical model approach we also offer an instantaneous computational tool using analytical formulas of the Ising model for respective RyR parameters and SR Ca load that describe and classify phase transitions and leak emergence.Comment: 20 pages, 6 figures, supplemental materia

Effects of muscarinic receptor stimulation on Ca2+ transient, cAMP production and pacemaker frequency of rabbit sinoatrial node cells

We investigated the contribution of the intracellular calcium (Cai2+) transient to acetylcholine (ACh)-mediated reduction of pacemaker frequency and cAMP content in rabbit sinoatrial nodal (SAN) cells. Action potentials (whole cell perforated patch clamp) and Cai2+ transients (Indo-1 fluorescence) were recorded from single isolated rabbit SAN cells, whereas intracellular cAMP content was measured in SAN cell suspensions using a cAMP assay (LANCE®). Our data show that the Cai2+ transient, like the hyperpolarization-activated “funny current” (If) and the ACh-sensitive potassium current (IK,ACh), is an important determinant of ACh-mediated pacemaker slowing. When If and IK,ACh were both inhibited, by cesium (2 mM) and tertiapin (100 nM), respectively, 1 μM ACh was still able to reduce pacemaker frequency by 72%. In these If and IK,ACh-inhibited SAN cells, good correlations were found between the ACh-mediated change in interbeat interval and the ACh-mediated change in Cai2+ transient decay (r2 = 0.98) and slow diastolic Cai2+ rise (r2 = 0.73). Inhibition of the Cai2+ transient by ryanodine (3 μM) or BAPTA-AM (5 μM) facilitated ACh-mediated pacemaker slowing. Furthermore, ACh depressed the Cai2+ transient and reduced the sarcoplasmic reticulum (SR) Ca2+ content, all in a concentration-dependent fashion. At 1 μM ACh, the spontaneous activity and Cai2+ transient were abolished, but completely recovered when cAMP production was stimulated by forskolin (10 μM) and IK,ACh was inhibited by tertiapin (100 nM). Also, inhibition of the Cai2+ transient by ryanodine (3 μM) or BAPTA-AM (25 μM) exaggerated the ACh-mediated inhibition of cAMP content, indicating that Cai2+ affects cAMP production in SAN cells. In conclusion, muscarinic receptor stimulation inhibits the Cai2+ transient via a cAMP-dependent signaling pathway. Inhibition of the Cai2+ transient contributes to pacemaker slowing and inhibits Cai2+-stimulated cAMP production. Thus, we provide functional evidence for the contribution of the Cai2+ transient to ACh-induced inhibition of pacemaker activity and cAMP content in rabbit SAN cells

Crosstalk between Mitochondrial and Sarcoplasmic Reticulum Ca2+ Cycling Modulates Cardiac Pacemaker Cell Automaticity

Mitochondria dynamically buffer cytosolic Ca(2+) in cardiac ventricular cells and this affects the Ca(2+) load of the sarcoplasmic reticulum (SR). In sinoatrial-node cells (SANC) the SR generates periodic local, subsarcolemmal Ca(2+) releases (LCRs) that depend upon the SR load and are involved in SANC automaticity: LCRs activate an inward Na(+)-Ca(2+) exchange current to accelerate the diastolic depolarization, prompting the ensemble of surface membrane ion channels to generate the next action potential (AP).To determine if mitochondrial Ca(2+) (Ca(2+) (m)), cytosolic Ca(2+) (Ca(2+) (c))-SR-Ca(2+) crosstalk occurs in single rabbit SANC, and how this may relate to SANC normal automaticity.Inhibition of mitochondrial Ca(2+) influx into (Ru360) or Ca(2+) efflux from (CGP-37157) decreased [Ca(2+)](m) to 80 ± 8% control or increased [Ca(2+)](m) to 119 ± 7% control, respectively. Concurrent with inhibition of mitochondrial Ca(2+) influx or efflux, the SR Ca(2+) load, and LCR size, duration, amplitude and period (imaged via confocal linescan) significantly increased or decreased, respectively. Changes in total ensemble LCR Ca(2+) signal were highly correlated with the change in the SR Ca(2+) load (r(2) = 0.97). Changes in the spontaneous AP cycle length (Ru360, 111 ± 1% control; CGP-37157, 89 ± 2% control) in response to changes in [Ca(2+)](m) were predicted by concurrent changes in LCR period (r(2) = 0.84).A change in SANC Ca(2+) (m) flux translates into a change in the AP firing rate by effecting changes in Ca(2+) (c) and SR Ca(2+) loading, which affects the characteristics of spontaneous SR Ca(2+) release

Simulation and Mechanistic Investigation of the Arrhythmogenic Role of the Late Sodium Current in Human Heart Failure

Heart failure constitutes a major public health problem worldwide. The electrophysiological remodeling of failing hearts sets the stage for malignant arrhythmias, in which the role of the late Na+ current (INaL) is relevant and is currently under investigation. In this study we examined the role of INaL in the electrophysiological phenotype of ventricular myocytes, and its proarrhythmic effects in the failing heart. A model for cellular heart failure was proposed using a modified version of Grandi et al. model for human ventricular action potential that incorporates the formulation of INaL. A sensitivity analysis of the model was performed and simulations of the pathological electrical activity of the cell were conducted. The proposed model for the human INaL and the electrophysiological remodeling of myocytes from failing hearts accurately reproduce experimental observations. The sensitivity analysis of the modulation of electrophysiological parameters of myocytes from failing hearts due to ion channels remodeling, revealed a role for INaL in the prolongation of action potential duration (APD), triangulation of the shape of the AP, and changes in Ca2+ transient. A mechanistic investigation of intracellular Na+ accumulation and APD shortening with increasing frequency of stimulation of failing myocytes revealed a role for the Na+/K+ pump, the Na+/Ca2+ exchanger and INaL. The results of the simulations also showed that in failing myocytes, the enhancement of INaL increased the reverse rate-dependent APD prolongation and the probability of initiating early afterdepolarizations. The electrophysiological remodeling of failing hearts and especially the enhancement of the INaL prolong APD and alter Ca2+ transient facilitating the development of early afterdepolarizations. An enhanced INaL appears to be an important contributor to the electrophysiological phenotype and to the dysregulation of [Ca2+]i homeostasis of failing myocytes

Diastolic dysfunction and arrhythmias caused by overexpression of CaMKIIδC can be reversed by inhibition of late Na+ current

Transgenic (TG) Ca2+/calmodulin-dependent protein kinase II (CaMKII) δC mice develop systolic heart failure (HF). CaMKII regulates intracellular Ca2+ handling proteins as well as sarcolemmal Na+ channels. We hypothesized that CaMKII also contributes to diastolic dysfunction and arrhythmias via augmentation of the late Na+ current (late INa) in early HF (8-week-old TG mice). Echocardiography revealed severe diastolic dysfunction in addition to decreased systolic ejection fraction. Premature arrhythmogenic contractions (PACs) in isolated isometrically twitching papillary muscles only occurred in TG preparations (5 vs. 0, P < 0.05) which could be completely terminated when treated with the late INa inhibitor ranolazine (Ran, 5 μmol/L). Force–frequency relationships revealed significantly reduced twitch force amplitudes in TG papillary muscles. Most importantly, diastolic tension increased with raising frequencies to a greater extent in TG papillary muscles compared to WT specimen (at 10 Hz: 3.7 ± 0.4 vs. 2.5 ± 0.3 mN/mm2; P < 0.05). Addition of Ran improved diastolic dysfunction to 2.1 ± 0.2 mN/mm2 (at 10 Hz; P < 0.05) without negative inotropic effects. Mechanistically, the late INa was markedly elevated in myocytes isolated from TG mice and could be completely reversed by Ran. In conclusion, our results show for the first time that TG CaMKIIδC overexpression induces diastolic dysfunction and arrhythmogenic triggers possibly via an enhanced late INa. Inhibition of elevated late INa had beneficial effects on arrhythmias as well as diastolic function in papillary muscles from CaMKIIδC TG mice. Thus, late INa inhibition appears to be a promising option for diastolic dysfunction and arrhythmias in HF where CaMKII is found to be increased

Graphical Approach to Model Reduction for Nonlinear Biochemical Networks

Model reduction is a central challenge to the development and analysis of multiscale physiology models. Advances in model reduction are needed not only for computational feasibility but also for obtaining conceptual insights from complex systems. Here, we introduce an intuitive graphical approach to model reduction based on phase plane analysis. Timescale separation is identified by the degree of hysteresis observed in phase-loops, which guides a “concentration-clamp” procedure for estimating explicit algebraic relationships between species equilibrating on fast timescales. The primary advantages of this approach over Jacobian-based timescale decomposition are that: 1) it incorporates nonlinear system dynamics, and 2) it can be easily visualized, even directly from experimental data. We tested this graphical model reduction approach using a 25-variable model of cardiac β1-adrenergic signaling, obtaining 6- and 4-variable reduced models that retain good predictive capabilities even in response to new perturbations. These 6 signaling species appear to be optimal “kinetic biomarkers” of the overall β1-adrenergic pathway. The 6-variable reduced model is well suited for integration into multiscale models of heart function, and more generally, this graphical model reduction approach is readily applicable to a variety of other complex biological systems

Local Control of Excitation-Contraction Coupling in Human Embryonic Stem Cell-Derived Cardiomyocytes

We investigated the mechanisms of excitation-contraction (EC) coupling in human embryonic stem cell-derived cardiomyocytes (hESC-CMs) and fetal ventricular myocytes (hFVMs) using patch-clamp electrophysiology and confocal microscopy. We tested the hypothesis that Ca2+ influx via voltage-gated L-type Ca2+ channels activates Ca2+ release from the sarcoplasmic reticulum (SR) via a local control mechanism in hESC-CMs and hFVMs. Field-stimulated, whole-cell [Ca2+]i transients in hESC-CMs required Ca2+ entry through L-type Ca2+ channels, as evidenced by the elimination of such transients by either removal of extracellular Ca2+ or treatment with diltiazem, an L-type channel inhibitor. Ca2+ release from the SR also contributes to the [Ca2+]i transient in these cells, as evidenced by studies with drugs interfering with either SR Ca2+ release (i.e. ryanodine and caffeine) or reuptake (i.e. thapsigargin and cyclopiazonic acid). As in adult ventricular myocytes, membrane depolarization evoked large L-type Ca2+ currents (ICa) and corresponding whole-cell [Ca2+]i transients in hESC-CMs and hFVMs, and the amplitude of both ICa and the [Ca2+]i transients were finely graded by the magnitude of the depolarization. hESC-CMs exhibit a decreasing EC coupling gain with depolarization to more positive test potentials, “tail” [Ca2+]i transients upon repolarization from extremely positive test potentials, and co-localized ryanodine and sarcolemmal L-type Ca2+ channels, all findings that are consistent with the local control hypothesis. Finally, we recorded Ca2+ sparks in hESC-CMs and hFVMs. Collectively, these data support a model in which tight, local control of SR Ca2+ release by the ICa during EC coupling develops early in human cardiomyocytes