Abstract
Strong interactions between cross-bridges (XB) and regulatory units (RU) lead to a steep response of cardiac muscle to an increase in intracellular calcium. We developed a model to quantitatively assess the influence of different types of interactions within the sarcomere on the properties of cardiac muscle. In the model, the ensembles consisting of cross-bridge groups connected by elastic tropomyosin are introduced, and their dynamics is described by a set of partial differential equations. Through large scans in the free energy landscape, we demonstrate the different influence of RU-RU, XB-XB, and XB-RU interactions on the cooperativity coefficient of calcium binding, developed maximal force, and calcium sensitivity. The model solution was fitted to reproduce experimental data on force development during isometric contraction, shortening in physiological contraction, and ATP consumption by acto-myosin. On the basis of the fits, we quantified the free energy change introduced through RU-RU and XB-XB interactions and showed that RU-RU interaction leads to ~ 5 times larger change in the free energy profile of the reaction than XB-XB interaction. Due to the deterministic description of muscle contraction and its thermodynamic consistency, we envision that the developed model can be used to study heart muscle biophysics on tissue and organ levels.
Highlights
Strong interactions between cross-bridges (XB) and regulatory units (RU) lead to a steep response of cardiac muscle to an increase in intracellular calcium
Due to interactions between cross-bridges (XB) and regulatory units (RU) in cardiac muscle, the heart can relax at resting state calcium levels and develop tension when the intracellular calcium concentration increases during a twitch[1]
We describe only changes that were introduced in this work, allowing us to reproduce the high cooperativity of calcium binding in cardiac muscle
Summary
Strong interactions between cross-bridges (XB) and regulatory units (RU) lead to a steep response of cardiac muscle to an increase in intracellular calcium. Our earlier works[10,11,12] and this study are addressing this gap and assessing the contribution of cooperative interaction mechanisms, when dynamics of physiological contractions and energy consumption by the muscle are taken into account. We assumed that all cross-bridges in the group are connected by tropomyosin and, by considering tropomyosin as an elastic string, we could estimate the influence of neighboring cross-bridges on the free energy of a cross-bridge group This description allowed us to reproduce experimental data for isometric contraction and the linear relationship between ATP consumption and SSA at different contraction modes. We developed a mathematical model of cardiac muscle on the basis of the theoretical framework considering ensembles of cross-bridges[12], fitted the measurements from different types of experiments, and assessed the resulting free energy profile of the reactions. We describe only changes that were introduced in this work, allowing us to reproduce the high cooperativity of calcium binding in cardiac muscle
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