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

Abstract

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

“…The model used to represent the cross-bridge kinetics and force generation is based on the model of Tewari et al [15] which is extended here to account for the calcium activation and force generation at body temperature. The kinetics of myofilament activation are based on the model of Rice et al [26] which assumes that filament overlap between thick and thin filament increases binding affinity of Ca 2+ for Troponin C (TrpC) and hence increases the transition rate between non-permissible ( N ) to permissible cross bridges ( P ) (see Figure 1B).…”

“…Specifically, we have developed a multi-scale model of cardiovascular dynamics that integrates myocardial energetics and cross-bridge kinetics with whole-organ and whole-body models of the heart and the circulation. The model is based on previously developed and independently validated models of myocardial energy metabolism [2, 3, 14], cardiac muscle dynamics [15], and whole-organ heart mechanics and pumping [16]. Integrating these components together using a recently developed model of the cardiac cross-bridge kinetics/dynamics that accounts for the influence of [MgATP], [MgADP] and [P i ] on state transitions [15], we are able to computationally predict how metabolic state influences cardiac function and whole-body cardiovascular state.…”

“…The model is based on previously developed and independently validated models of myocardial energy metabolism [2, 3, 14], cardiac muscle dynamics [15], and whole-organ heart mechanics and pumping [16]. Integrating these components together using a recently developed model of the cardiac cross-bridge kinetics/dynamics that accounts for the influence of [MgATP], [MgADP] and [P i ] on state transitions [15], we are able to computationally predict how metabolic state influences cardiac function and whole-body cardiovascular state. These simulations allow us to computationally isolate the metabolic component of heart failure, representing other components (such as calcium handling processes, cardiac geometry, passive mechanical properties) as normal.…”

“…To build this integrated model, data on calcium concentration and tension time courses in rat cardiac muscle are used to extend the model presented in [15] to account for calcium-dependent activation of myofilaments. This updated cross-bridge model, is combined with a model of oxidative ATP synthesis to capture the effect of altered energetic state, as seen in decompensated hypertrophy [3], on whole-organ (and whole-body) function.…”

Mechanistic Systems Modeling to Improve Understanding and Prediction of Cardiotoxicity Caused by Targeted Cancer Therapeutics

“…Once these are tuned to reflect apoptotic signaling in cardiac myocytes, the models can be integrated with the experimental gene expression data to generate novel predictions. Similarly, models describing mitochondrial function, including the production of reactive oxygen species (Aon and Cortassa, 2012;Bazil et al, 2016;Wacquier et al, 2016), and the coupling of electrical excitation, and contractile function (Rice et al, 2008;Tewari et al, 2016), are also likely to be relevant. Finally, once a number of QSP models, describing additional processes, have been added, further secondary analyses can be performed.…”