Abstract
The aim of this work is to incorporate cooperativity into Huxley-type cross-bridge model in thermodynamically consistent way. While the Huxley-type models assume that cross-bridges act independently from each other, we take into account that each cross-bridge is influenced by its neighbors and cooperativity is induced by tropomyosin movement. For that, we introduce ensembles of cross-bridge groups connected by elastic tropomyosin. By taking into account that the mechanical displacement of tropomyosin induces free energy change of the cross-bridge group ensemble, we develop the formalism for thermodynamically consistent description of the cooperativity in muscle contraction. An example model was composed to test the approach. The model parameters were found by optimization from the linear relation between oxygen consumption and stress-strain area as well as experimentally measured stress dynamics of rat trabecula. We have found a good agreement between the optimized model solution and experimental data. Simulations also showed that it is possible to study cooperativity with the approach developed in this work.
Highlights
In the heart, the mechanical work is tightly linked to energy conversion processes to ensure that the main function of the heart—pumping blood—is always possible
When compared with the three-state model (Fig 1), the five-state model has three force-producing states instead of one. This allows to describe the movement of myosin head by shifting free-energy minima between two force-producing states and detachment of calcium from troponin-C while the cross-bridge is in force-producing state
The aim of these simulations is to demonstrate that the model can be used in practice to reproduce different dynamic aspects of heart muscle contraction
Summary
The mechanical work is tightly linked to energy conversion processes to ensure that the main function of the heart—pumping blood—is always possible. As a manifestation of a tight link between mechanics and energetics in the heart, it has been shown that oxygen consumption (VO2) of the heart is linearly related to pressure-volume area (PVA) [1]. As a analog of PVA-VO2 relationship on tissue level, stress-strain area (SSA)-VO2 linear relationship has been demonstrated [2] and can be used for estimation of regional VO2 in the heart [3]. We have shown that it is possible to reproduce PVA-VO2 relationship by the finite element model of the left ventricle [4] if the active properties of myocardium are described by the model that reproduces SSA-VO2 relationship [5].
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