A thermodynamic model of the cardiac sarcoplasmic/endoplasmic Ca(2+) (SERCA) pump

Models of excitation-contraction coupling in cardiac ventricular myocytes

Excitation-contraction coupling describes the processes relating to electrical excitation through force generation and contraction in the heart. It occurs at multiple levels from the whole heart, to single myocytes and down to the sarcomere. A central process that links electrical excitation to contraction is calcium mobilization. Computational models that are well grounded in experimental data have been an effective tool to understand the complex dynamics of the processes involved in excitation-contraction coupling. Presented here is a summary of some computational models that have added to the understanding of the cellular and subcellular mechanisms that control ventricular myocyte calcium dynamics. Models of cardiac ventricular myocytes that have given insight into termination of calcium release and interval-force relations are discussed in this manuscript. Computational modeling of calcium sparks, the elementary events in cardiac excitation-contraction coupling, has given insight into mechanism governing their dynamics and termination as well as their role in excitation-contraction coupling and is described herein.

NHE inhibition does not improve Na(+) or Ca(2+) overload during reperfusion: using modeling to illuminate the mechanisms underlying a therapeutic failure

Reperfusion injury results from pathologies of cardiac myocyte physiology that develop when previously ischemic myocardium experiences a restoration of normal perfusion. Events in the development of reperfusion injury begin with the restoration of a proton gradient upon reperfusion, which then allows the sodium-proton exchanger (NHE) to increase flux, removing protons from the intracellular space while importing sodium. The resulting sodium overload drives increased reverse-mode sodium-calcium exchanger (NCX) activity, creating a secondary calcium overload that has pathologic consequences. One of the attempts to reduce reperfusion-related damage, NHE inhibition, has shown little clinical benefit, and only when NHE inhibitors are given prior to reperfusion. In an effort to further understand why NHE inhibitors have been largely unsuccessful, we employed a new mathematical cardiomyocyte model that we developed for the study of ischemia and reperfusion. Using this model, we simulated 20 minutes of ischemia and 10 minutes of reperfusion, while also simulating NHE inhibition by reducing NHE flux in our model by varying amounts and at different time points. In our simulations, when NHE inhibition is applied at the onset of reperfusion, increasing the degree of inhibition increases the peak sodium and calcium concentrations, as well as reducing intracellular pH recovery. When inhibition was instituted at earlier time points, some modest improvements were seen, largely due to reduced sodium concentrations prior to reperfusion. Analysis of all sodium flux pathways suggests that the sodium-potassium pump (NaK) plays the largest role in exacerbated sodium overload during reperfusion, and that reduced NaK flux is largely the result of impaired pH recovery. While NHE inhibition does indeed reduce sodium influx through that exchanger, the resulting prolongation of intracellular acidosis paradoxically increases sodium overload, largely mediated by impaired NaK function.

Myocardial ischemia, commonly observed when arteries supplying the heart become occluded, results when cardiac tissue receives inadequate blood perfusion. In order to minimize the amount of cardiac damage, ischemic tissue must be reperfused. However, reperfusion can result in deleterious effects that leave the heart muscle sicker than if the ischemia had been allowed to continue. Examples of these reperfusion injuries include lethal arrhythmias and an increased region of cell death. Some of the early events that result in reperfusion injury include changes in pH and an overload of sodium inside the cell. During reperfusion, the sodium-proton exchanger (NHE) removes protons from the cell in an effort to restore normal pH, in turn importing sodium ions. Many strategies have been attempted to prevent reperfusion injury, including inhibition of the NHE, with little clinical effect. Using a mathematical model that we developed to study ischemia and reperfusion in cardiac cells, we found that NHE inhibition produces more severe sodium overload, largely due to adverse consequences of the delayed pH recovery produced by NHE inhibition. These results suggest that NHE inhibition alone may not be a viable strategy, and that therapies which prolong intracellular acidosis may be problematic.

Dynamics of calcium sparks and calcium leak in the heart

We present what we believe to be a new mathematical model of Ca(2+) leak from the sarcoplasmic reticulum (SR) in the heart. To our knowledge, it is the first to incorporate a realistic number of Ca(2+)-release units, each containing a cluster of stochastically gating Ca(2+) channels (RyRs), whose biophysical properties (e.g., Ca(2+) sensitivity and allosteric interactions) are informed by the latest molecular investigations. This realistic model allows for the detailed characterization of RyR Ca(2+)-release properties, and shows how this balances reuptake by the SR Ca(2+) pump. Simulations reveal that SR Ca(2+) leak consists of brief but frequent single RyR openings (~3000 cell(-1) s(-1)) that are likely to be experimentally undetectable, and are, therefore, "invisible". We also observe that these single RyR openings can recruit additional RyRs to open, due to elevated local (Ca(2+)), and occasionally lead to the generation of Ca(2+) sparks (~130 cell(-1) s(-1)). Furthermore, this physiological formulation of "invisible" leak allows for the removal of the ad hoc, non-RyR mediated Ca(2+) leak terms present in prior models. Finally, our model shows how Ca(2+) sparks can be robustly triggered and terminated under both normal and pathological conditions. Together, these discoveries profoundly influence how we interpret and understand diverse experimental and clinical results from both normal and diseased hearts.

Stochastic simulation of cardiac ventricular myocyte calcium dynamics and waves

A three dimensional model of calcium dynamics in the rat ventricular myocyte was developed to study the mechanism of calcium homeostasis and pathological calcium dynamics during calcium overload. The model contains 20,000 calcium release units (CRUs) each containing 49 ryanodine receptors. The model simulates calcium sparks with a realistic spontaneous calcium spark rate. It suggests that in addition to the calcium spark-based leak, there is an invisible calcium leak caused by the stochastic opening of a small number of ryanodine receptors in each CRU without triggering a calcium spark. The model also explores the mechanism of calcium wave propagation between release sites under the conditions of calcium overload.

Integrative modeling of the cardiac ventricular myocyte

Cardiac electrophysiology is a discipline with a rich 50-year history of experimental research coupled with integrative modeling which has enabled us to achieve a quantitative understanding of the relationships between molecular function and the integrated behavior of the cardiac myocyte in health and disease. In this paper, we review the development of integrative computational models of the cardiac myocyte. We begin with a historical overview of key cardiac cell models that helped shape the field. We then narrow our focus to models of the cardiac ventricular myocyte and describe these models in the context of their subcellular functional systems including dynamic models of voltage-gated ion channels, mitochondrial energy production, ATP-dependent and electrogenic membrane transporters, intracellular Ca dynamics, mechanical contraction, and regulatory signal transduction pathways. We describe key advances and limitations of the models as well as point to new directions for future modeling research. WIREs Syst Biol Med 2011 3 392-413 DOI: 10.1002/wsbm.122

A metabolite-sensitive, thermodynamically constrained model of cardiac cross-bridge cycling: implications for force development during ischemia

We present a metabolically regulated model of cardiac active force generation with which we investigate the effects of ischemia on maximum force production. Our model, based on a model of cross-bridge kinetics that was developed by others, reproduces many of the observed effects of MgATP, MgADP, Pi, and H(+) on force development while retaining the force/length/Ca(2+) properties of the original model. We introduce three new parameters to account for the competitive binding of H(+) to the Ca(2+) binding site on troponin C and the binding of MgADP within the cross-bridge cycle. These parameters, along with the Pi and H(+) regulatory steps within the cross-bridge cycle, were constrained using data from the literature and validated using a range of metabolic and sinusoidal length perturbation protocols. The placement of the MgADP binding step between two strongly-bound and force-generating states leads to the emergence of an unexpected effect on the force-MgADP curve, where the trend of the relationship (positive or negative) depends on the concentrations of the other metabolites and [H(+)]. The model is used to investigate the sensitivity of maximum force production to changes in metabolite concentrations during the development of ischemia.

Cardiac cell modelling: observations from the heart of the cardiac physiome project

In this manuscript we review the state of cardiac cell modelling in the context of international initiatives such as the IUPS Physiome and Virtual Physiological Human Projects, which aim to integrate computational models across scales and physics. In particular we focus on the relationship between experimental data and model parameterisation across a range of model types and cellular physiological systems. Finally, in the context of parameter identification and model reuse within the Cardiac Physiome, we suggest some future priority areas for this field.

Energetic state is a strong regulator of sarcoplasmic reticulum Ca2+ loss in cardiac muscle: different efficiencies of different energy sources

AIMS

Increased diastolic sarcoplasmic reticulum (SR) Ca(2+) loss could depress contractility in heart failure. Since the failing myocardium has impaired energetics, we investigated whether Ca(2+) loss is linked to changes in energetic pathways.

METHODS AND RESULTS

Leakage from SR in mouse permeabilized preparations was assessed using exogenous ATP, ATP + phosphocreatine (activation of bound creatine kinase, CK), ATP + mitochondrial substrates (mitochondrial activation), or with all of these together (optimal energetic conditions) in Ca(2+)-free solution. In ventricular fibres caffeine-induced tension transients under optimal energetic conditions were used to estimate SR [Ca(2+)]. In cardiomyocytes, intra-SR Ca(2+) was monitored by use of the fluorescent marker Mag-fluo 4. In fibres, SR Ca(2+) content after 5 min incubation strongly depended on energy supply (100%-optimal energetic conditions; 27 +/- 5%-exogenous ATP only, 52 +/- 5%-endogenous CK activation; 88 +/- 8%-mitochondrial activation, P < 0.01 vs. CK system). The significant loss with only exogenous ATP was not inhibited by the ryanodine receptor blockers tetracaine or ruthenium red. However, the SR Ca(2+)-ATPase (SERCA) inhibitors cyclopiazonic acid or 2,5-di(tert-butyl)-1,4-benzohydroquinone significantly decreased Ca(2+) loss. At 100 nM external [Ca(2+)], the SR Ca(2+) loss was also energy dependent and was not significantly inhibited by tetracaine. In cardiomyocytes, the decline in SR [Ca(2+)] at zero external [Ca(2+)] was almost two times slower under optimal energetic conditions than in the presence of exogenous ATP only.

CONCLUSION

At low extra-reticular [Ca(2+)], the main leak pathway is an energy-sensitive backward Ca(2+) pump, and direct mitochondrial-SERCA ATP channelling is more effective in leak prevention than local ATP generation by bound CK.