Comparison of the cardiac force-time integral with energetics using a cardiac muscle model

Cross-Bridge Group Ensembles Describing Cooperativity in Thermodynamically Consistent Way

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.

Myocardial twitch duration and the dependence of oxygen consumption on pressure-volume area: experiments and modelling

We tested the proposition that linear length dependence of twitch duration underlies the well-characterised linear dependence of oxygen consumption (V(O(2)) ) on pressure–volume area (PVA) in the heart. By way of experimental simplification, we reduced the problem from three dimensions to one by substituting cardiac trabeculae for the classically investigated whole-heart. This allowed adoption of stress–length area (SLA) as a surrogate for PVA, and heat as a proxy for V(O(2)) . Heat and stress (force per cross-sectional area), at a range of muscle lengths and at both 1 mM and 2 mM [Ca(2+)](o), were recorded from continuously superfused rat right-ventricular trabeculae undergoing fixed-end contractions. The heat–SLA relations of trabeculae (reported here, for the first time) are linear. Twitch duration increases monotonically (but not strictly linearly) with muscle length. We probed the cellular mechanisms of this phenomenon by determining: (i) the length dependence of the duration of the Ca(2+) transient, (ii) the length dependence of the rate of force redevelopment following a length impulse (an index of Ca(2+) binding to troponin-C), (iii) the effect on the simulated time course of the twitch of progressive deletion of length and Ca(2+)-dependent mechanisms of crossbridge cooperativity, using a detailed mathematical model of the crossbridge cycle, and (iv) the conditions required to achieve these multiple length dependencies, using a greatly simplified model of twitch mechano-energetics. From the results of these four independent investigations, we infer that the linearity of the heat–SLA relation (and, by analogy, the V(O(2))–PVA relation) is remarkably robust in the face of departures from linearity of length-dependent twitch duration.