Effects of MgATP on ATP utilization and force under normal and simulated ischaemic conditions in rat cardiac trabeculae

Analysis of metabolite and strain effects on cardiac cross-bridge dynamics using model linearisation techniques

Multi-scale models of cardiac energetics are becoming crucial in better understanding the prevalent chronic diseases operating at the intersection of metabolic and cardiovascular dysfunction. Computationally efficient models of cardiac cross-bridge kinetics that are sensitive to changes in metabolite concentrations are necessary to simulate the effects of disease-induced changes in cellular metabolic state on cardiac mechanics across disparate spatial scales. While these models do currently exist, deeper analysis of how the modelling of metabolite effects and the assignment of strain dependence within the cross-bridge cycle affect the properties of the model is required. In this study, model linearisation techniques were used to simulate and interrogate the complex modulus of an ODE-based model of cross-bridge kinetics. Active complex moduli were measured from permeabilised rat cardiac trabeculae under five different metabolite conditions with varying ATP and Pi concentrations. Sensitivity to metabolites was incorporated into an existing three-state cross-bridge model using either a direct dependence or a rapid equilibrium approach. Combining the two metabolite binding methods with all possible locations of strain dependence within the cross-bridge cycle produced 64 permutations of the cross-bridge model. Using linear model analysis, these models were systematically explored to determine the effects of metabolite binding and their interaction with strain dependence on the frequency response of cardiac muscle. The results showed that the experimentally observed effects of ATP and Pi concentrations on the cardiac complex modulus could be attributed to their regulation of cross-bridge detachment rates. Analysis of the cross-bridge models revealed a mechanistic basis for the biochemical schemes which place Pi release following cross-bridge formation and ATP binding prior to cross-bridge detachment. In addition, placing strain dependence on the reverse rate of the cross-bridge power stroke produced the model which most closely matched the experimental data. From these analyses, a well-justified metabolite-sensitive model of rat cardiac cross-bridge kinetics is presented which is suitable for parameterisation with other data sets and integration with multi-scale cardiac models.

Cell to whole organ global sensitivity analysis on a four-chamber heart electromechanics model using Gaussian processes emulators

Cardiac pump function arises from a series of highly orchestrated events across multiple scales. Computational electromechanics can encode these events in physics-constrained models. However, the large number of parameters in these models has made the systematic study of the link between cellular, tissue, and organ scale parameters to whole heart physiology challenging. A patient-specific anatomical heart model, or digital twin, was created. Cellular ionic dynamics and contraction were simulated with the Courtemanche-Land and the ToR-ORd-Land models for the atria and the ventricles, respectively. Whole heart contraction was coupled with the circulatory system, simulated with CircAdapt, while accounting for the effect of the pericardium on cardiac motion. The four-chamber electromechanics framework resulted in 117 parameters of interest. The model was broken into five hierarchical sub-models: tissue electrophysiology, ToR-ORd-Land model, Courtemanche-Land model, passive mechanics and CircAdapt. For each sub-model, we trained Gaussian processes emulators (GPEs) that were then used to perform a global sensitivity analysis (GSA) to retain parameters explaining 90% of the total sensitivity for subsequent analysis. We identified 45 out of 117 parameters that were important for whole heart function. We performed a GSA over these 45 parameters and identified the systemic and pulmonary peripheral resistance as being critical parameters for a wide range of volumetric and hemodynamic cardiac indexes across all four chambers. We have shown that GPEs provide a robust method for mapping between cellular properties and clinical measurements. This could be applied to identify parameters that can be calibrated in patient-specific models or digital twins, and to link cellular function to clinical indexes.

Reduced cardiac muscle power with low ATP simulating heart failure

For patients with heart failure, myocardial ATP level can be reduced to one-half of that observed in healthy controls. This marked reduction (from ≈8 mM in healthy controls to as low as 3-4 mM in heart failure) has been suggested to contribute to impaired myocardial contraction and to the decreased pump function characteristic of heart failure. However, in vitro measures of maximum myofilament force generation, maximum shortening velocity, and the actomyosin ATPase activity show effective KM values for MgATP ranging from ≈10 μM to 150 μM, well below the intracellular ATP level in heart failure. Thus, it is not clear that the fall of myocardial ATP observed in heart failure is sufficient to impair the function of the contractile proteins. Therefore, we tested the effect of low MgATP levels on myocardial contraction using demembranated cardiac muscle preparations that were exposed to MgATP levels typical of the range found in non-failing and failing hearts. Consistent with previous studies, we found that a 50% reduction in MgATP level (from 8 mM to 4 mM) did not reduce maximum force generation or maximum velocity of shortening. However, we found that a 50% reduction in MgATP level caused a 20%-25% reduction in maximal power generation (measured during muscle shortening against a load) and a 20% slowing of cross-bridge cycling kinetics. These results suggest that the decreased cellular ATP level occurring in heart failure contributes to the impaired pump function of the failing heart. Since the ATP-myosin ATPase dissociation constant is estimated to be submillimolar, these findings also suggest that MgATP concentration affects cross-bridge dynamics through a mechanism that is more complex than through the direct dependence of MgATP concentration on myosin ATPase activity. Finally, these studies suggest that therapies targeted to increase adenine nucleotide pool levels in cardiomyocytes might be beneficial for treating heart failure.

Exploring Impaired SERCA Pump-Caused Alternation Occurrence in Ischemia

Impaired sarcoplasmic reticulum (SR) calcium transport ATPase (SERCA) gives rise to Ca²⁺ alternans and changes of the Ca2+release amount. These changes in Ca²⁺ release amount can reveal the mechanism underlying how the interaction between Ca²⁺ release and Ca²⁺ uptake induces Ca²⁺ alternans. This study of alternans by calculating the values of Ca²⁺ release properties with impaired SERCA has not been explored before. Here, we induced Ca²⁺ alternans by using an impaired SERCA pump under ischemic conditions. The results showed that the recruitment and refractoriness of the Ca²⁺ release increased as Ca²⁺ alternans occurred. This indicates triggering Ca waves. As the propagation of Ca waves is linked to the occurrence of Ca²⁺ alternans, the “threshold” for Ca waves reflects the key factor in Ca²⁺ alternans development, and it is still controversial nowadays. We proposed the ratio between the diastolic network SR (NSR) Ca content (Ca_nsr) and the cytoplasmic Ca content (Ca_i) (Ca_nsr/Ca_i) as the “threshold” of Ca waves and Ca²⁺ alternans. Diastolic Ca_nsr, Ca_i, and their ratio were recorded at the onset of Ca²⁺ alternans. Compared with certain Ca_nsr and Ca_i, the “threshold” of the ratio can better explain the comprehensive effects of the Ca²⁺ release and the Ca²⁺ uptake on Ca²⁺ alternans onset. In addition, these ratios are related with the function of SERCA pumps, which vary with different ischemic conditions. Thus, values of these ratios could be used to differentiate Ca²⁺ alternans from different ischemic cases. This agrees with some experimental results. Therefore, the certain value of diastolic Ca_nsr/Ca_i can be the better “threshold” for Ca waves and Ca²⁺ alternans.

Insights on the impact of mitochondrial organisation on bioenergetics in high-resolution computational models of cardiac cell architecture

Recent electron microscopy data have revealed that cardiac mitochondria are not arranged in crystalline columns but are organised with several mitochondria aggregated into columns of varying sizes spanning the cell cross-section. This raises the question—how does the mitochondrial arrangement affect the metabolite distributions within cardiomyocytes and what is its impact on force dynamics? Here, we address this question by employing finite element modeling of cardiac bioenergetics on computational meshes derived from electron microscope images. Our results indicate that heterogeneous mitochondrial distributions can lead to significant spatial variation across the cell in concentrations of inorganic phosphate, creatine (Cr) and creatine phosphate (PCr). However, our model predicts that sufficient activity of the creatine kinase (CK) system, coupled with rapid diffusion of Cr and PCr, maintains near uniform ATP and ADP ratios across the cell cross sections. This homogenous distribution of ATP and ADP should also evenly distribute force production and twitch duration with contraction. These results suggest that the PCr shuttle and associated enzymatic reactions act to maintain uniform force dynamics in the cell despite the heterogeneous mitochondrial organization. However, our model also predicts that under hypoxia activity of mitochondrial CK enzymes and diffusion of high-energy phosphate compounds may be insufficient to sustain uniform ATP/ADP distribution and hence force generation.

Mammalian cardiomyocytes contain a high volume of mitochondria, which maintains the continuous and bulk supply of ATP to sustain normal heart function. Previously, cardiac mitochondria were understood to be distributed in a regular, crystalline pattern, which facilitated a steady supply of ATP at different workloads. Using electron microscopy images of cell cross sections, we recently found that they are not regularly distributed inside cardiomyocytes. We created new spatially accurate computational models of cardiac cell bioenergetics and tested whether this heterogeneous distribution of mitochondria causes non-uniform energy supply and contractile force production in the cardiomyocyte. We found that ATP and ADP concentrations remain uniform throughout the cell because of the activity of creatine kinase (CK) enzymes that convert ATP produced in the mitochondria into creatine phosphate. Creatine phosphate rapidly diffuses to the myofibril region where it can be converted back to ATP for the contraction cycle in a timely manner. This mechanism is called the phosphocreatine shuttle (PCr shuttle). The PCr shuttle ensures that different areas of the cell produce the same amount of force regardless of the mitochondrial distribution. However, our model also shows that when the cellular oxygen supply is limited—as can be the case in conditions such as heart failure—the PCr shuttle cannot maintain uniform ATP and ADP concentrations across the cell. This causes a non-uniform acto-myosin force distribution and non-uniform twitch duration across the cell cross section. Our study suggests that mechanisms other than the PCr shuttle may be necessary to maintain uniform supply of ATP in a hypoxic environment.

In Silico Investigation into Cellular Mechanisms of Cardiac Alternans in Myocardial Ischemia

Myocardial ischemia is associated with pathophysiological conditions such as hyperkalemia, acidosis, and hypoxia. These physiological disorders may lead to changes on the functions of ionic channels, which in turn form the basis for cardiac alternans. In this paper, we investigated the roles of hyperkalemia and calcium handling components played in the genesis of alternans in ischemia at the cellular level by using computational simulations. The results show that hyperkalemic reduced cell excitability and delayed recovery from inactivation of depolarization currents. The inactivation time constant τ_f of L-type calcium current (I_CaL) increased obviously in hyperkalemia. One cycle length was not enough for I_CaL to recover completely. Alternans developed as a result of I_CaL responding to stimulation every other beat. Sarcoplasmic reticulum calcium-ATPase (SERCA2a) function decreased in ischemia. This change resulted in intracellular Ca (Ca_i) alternans of small magnitude. A strong Na⁺-Ca²⁺ exchange current (I_NCX) increased the magnitude of Ca_i alternans, leading to APD alternans through excitation-contraction coupling. Some alternated repolarization currents contributed to this repolarization alternans.

Dynamics of cross-bridge cycling, ATP hydrolysis, force generation, and deformation in cardiac muscle

Despite extensive study over the past six decades the coupling of chemical reaction and mechanical processes in muscle dynamics is not well understood. We lack a theoretical description of how chemical processes (metabolite binding, ATP hydrolysis) influence and are influenced by mechanical processes (deformation and force generation). To address this need, a mathematical model of the muscle cross-bridge (XB) cycle based on Huxley's sliding filament theory is developed that explicitly accounts for the chemical transformation events and the influence of strain on state transitions. The model is identified based on elastic and viscous moduli data from mouse and rat myocardial strips over a range of perturbation frequencies, and MgATP and inorganic phosphate (Pi) concentrations. Simulations of the identified model reproduce the observed effects of MgATP and MgADP on the rate of force development. Furthermore, simulations reveal that the rate of force re-development measured in slack-restretch experiments is not directly proportional to the rate of XB cycling. For these experiments, the model predicts that the observed increase in the rate of force generation with increased Pi concentration is due to inhibition of cycle turnover by Pi. Finally, the model captures the observed phenomena of force yielding suggesting that it is a result of rapid detachment of stretched attached myosin heads.

Influence of metabolic dysfunction on cardiac mechanics in decompensated hypertrophy and heart failure

Alterations in energetic state of the myocardium are associated with decompensated heart failure in humans and in animal models. However, the functional consequences of the observed changes in energetic state on mechanical function are not known. The primary aim of the study was to quantify mechanical/energetic coupling in the heart and to determine if energetic dysfunction can contribute to mechanical failure. A secondary aim was to apply a quantitative systems pharmacology analysis to investigate the effects of drugs that target cross-bridge cycling kinetics in heart failure-associated energetic dysfunction. Herein, a model of metabolite- and calcium-dependent myocardial mechanics was developed from calcium concentration and tension time courses in rat cardiac muscle obtained at different lengths and stimulation frequencies. The muscle dynamics model accounting for the effect of metabolites was integrated into a model of the cardiac ventricles to simulate pressure-volume dynamics in the heart. This cardiac model was integrated into a simple model of the circulation to investigate the effects of metabolic state on whole-body function. Simulations predict that reductions in metabolite pools observed in canine models of heart failure can cause systolic dysfunction, blood volume expansion, venous congestion, and ventricular dilation. Simulations also predict that myosin-activating drugs may partially counteract the effects of energetic state on cross-bridge mechanics in heart failure while increasing myocardial oxygen consumption. Our model analysis demonstrates how metabolic changes observed in heart failure are alone sufficient to cause systolic dysfunction and whole-body heart failure symptoms.

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.

Modulation of ischaemic contracture in mouse hearts: a 'supraphysiological' response to adenosine

While inhibition of ischaemic contracture was one of the first documented cardioprotective actions of exogenously applied adenosine, it is not known whether this is a normal function of endogenous adenosine generated during ischaemic stress. Additionally, the relevance of delayed contracture to postischaemic outcome is unclear. We tested the ability of endogenous versus exogenous adenosine to modify contracture (and postischaemic outcomes) in C57/Bl6 mouse hearts. During ischaemia, untreated hearts developed peak contracture (PC) of 85 +/- 5 mmHg at 8.9 +/- 0.8 min, with time to reach 20 mmHg (time to onset of contracture; TOC) of 4.4 +/- 0.3 min. Adenosine (50 microm) delayed TOC to 6.7 +/- 0.6 min, as did pretreatment with 10 microm 2-chloroadenosine (7.2 +/- 0.5 min) or 50 nm of A(1) adenosine receptor (AR) agonist N(6)-cyclohexyladenosine (CHA) (6.7 +/- 0.3 min), but not A(2A)AR or A(3)AR agonists (20 nm 2-[4-(2-carboxyethyl) phenethylamino]-5' N-methylcarboxamidoadenosine (CGS21680) or 150 nm 2-chloro-N(6)-(3-iodobenzyl)-adenosine-5'-N-methyluronamide (Cl-IB-MECA), respectively). Adenosinergic contracture inhibition was eliminated by A(1)AR gene knockout (KO), mimicked by A(1)AR overexpression, and was associated with preservation of myocardial [ATP]. This adenosine-mediated inhibition of contracture was, however, only evident after prolonged (10 or 15 min) and not brief (3 min) pretreatment. Ischaemic contracture was also insensitive to endogenously generated adenosine, since A(1)AR KO, and non-selective and A(1)AR-selective antagonists (50 microm 8-sulphophenyltheophylline and 150 nm 8-cyclopentyl-1, 3-dipropylxanthine (DPCPX), respectively), all failed to alter intrinsic contracture development. Finally, delayed contracture with A(1)AR agonism/overexpression or ischaemic 2,3-butanedione monoxime (BDM; 5 microm to target Ca(2+) cross-bridge formation) was linked to enhanced postischaemic outcomes. In summary, adenosinergic inhibition of contracture is solely A(1)AR mediated; the response is 'supraphysiological', evident only with significant periods of pre-ischaemic AR agonism (or increased A(1)AR density); and ischaemic contracture appears insensitive to locally generated adenosine, potentially owing to the rapidity of contracture development versus the finite time necessary for expression of AR-mediated cardioprotection.

A quantitative analysis of cardiac myocyte relaxation: a simulation study

The determinants of relaxation in cardiac muscle are poorly understood, yet compromised relaxation accompanies various pathologies and impaired pump function. In this study, we develop a model of active contraction to elucidate the relative importance of the [Ca2+]i transient magnitude, the unbinding of Ca2+ from troponin C (TnC), and the length-dependence of tension and Ca2+ sensitivity on relaxation. Using the framework proposed by one of our researchers, we extensively reviewed experimental literature, to quantitatively characterize the binding of Ca2+ to TnC, the kinetics of tropomyosin, the availability of binding sites, and the kinetics of crossbridge binding after perturbations in sarcomere length. Model parameters were determined from multiple experimental results and modalities (skinned and intact preparations) and model results were validated against data from length step, caged Ca2+, isometric twitches, and the half-time to relaxation with increasing sarcomere length experiments. A factorial analysis found that the [Ca2+]i transient and the unbinding of Ca2+ from TnC were the primary determinants of relaxation, with a fivefold greater effect than that of length-dependent maximum tension and twice the effect of tension-dependent binding of Ca2+ to TnC and length-dependent Ca2+ sensitivity. The affects of the [Ca2+]i transient and the unbinding rate of Ca2+ from TnC were tightly coupled with the effect of increasing either factor, depending on the reference [Ca2+]i transient and unbinding rate.

The mechanism of the force enhancement by MgADP under simulated ischaemic conditions in rat cardiac myocytes

In this study, the effects of MgADP and/or MgATP on the Ca2+ -dependent and Ca2+ -independent contractile force restoration were determined in order to identify the origin of the tonic force increase (i.e. ischaemic contracture) which develops during advanced stages of ischaemia. Experiments were performed at 15 degrees C during simulated ischaemic conditions in Triton-skinned right ventricular myocytes from rats. In the presence of 5 mM MgATP the maximal Ca2+ -dependent force (P(o)) of 39 +/- 2 kN m(-2) (mean +/- S.E.M.) under control conditions (pH 7.0, 15 mM phosphocreatine (CP)) decreased to 8 +/- 1 % during simulated ischaemia (pH 6.2, 30 mM inorganic phosphate (P(i)), without CP). This change was accompanied by a major reduction in Ca2+ sensitivity (pCa(50) 4.10 vs. 5.62). Substitution of MgADP for MgATP restored isometric force production and its Ca2+ sensitivity (pCa(50) 4.74 at 4 mM MgADP and 1 mM MgATP). In addition, it shifted the MgATP threshold concentration of Ca2+ -independent force development to higher levels in a concentration-dependent manner. However, Ca2+ -independent force was facilitated less by MgADP than Ca2+ -dependent force. The MgADP-induced increase in force was accompanied by marked reductions in the velocity of unloaded shortening and the rate of tension redevelopment. These data and simulations using a model of cross-bridge kinetics suggest that the ischaemic force is not a consequence of a reduction in intracellular MgATP concentration, but identify MgADP as a key modulator of the cross-bridge cycle under simulated ischaemic conditions in cardiac muscle, with a much lower inhibition constant (0.012 +/- 0.003 mM) than in skeletal muscle. Therefore, MgADP has a high potential to stabilize the force-generating cross-bridge state and to facilitate the development of ischaemic contracture, possibly involving a Ca2+ activation process in the ischaemic myocardium.