Insights From Computational Modeling Into the Contribution of Mechano-Calcium Feedback on the Cardiac End-Systolic Force-Length Relationship

Figures

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  FIGURE 1. Schematic of the THR excitation-contraction model. The connections indicate the coupling between the Tran et al. (2017) cross-bridge model, the Hinch et al. (2004) Ca2+ model, and the Rogers and McCulloch (1994) action potential model. Ca-Trop represents Ca2+ bound to troponin-C, which is modulated by active force, and therefore mediates the mechano-calcium feedback pathway.

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  FIGURE 2. Comparison of THR model simulations with experimental quick-release data. Experimental quick-release shortening of ferret papillary muscle by Kurihara and Komukai (1995) (left) at 30°C and equivalent simulations from the THR model (right). Each of the four panels for the experimental (A1–D1) and model (A2–D2) outputs represent different timings of the quick release. Within each panel are traces of outputs from isometric (black lines) and quick-release protocols (gray lines). From top to bottom, the traces represent muscle length, intracellular Ca2+ concentration, total force development, and difference of Ca2+ between the two protocols. (A1–D1 were reproduced with permission from John Wiley and Sons).

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  FIGURE 3. Simulation of isometric and work-loop end-systolic force-length relations (ESFLR). (A) The isometric ESFLR (gray) was simulated from six isometric contractions at sarcomere lengths ranging from 1.95 to 2.3 μm (Lo). Sarcomere lengths were normalized to Lo. The work-loop ESFLR was simulated from five work-loop contractions commencing at an initial sarcomere length of Lo. Each work-loop contraction is matched by an isometric contraction of equivalent force. Note that the work-loop contraction at the highest afterload is identical to the Lo-isometric contraction. (B) Experimental data depicting the isometric ESFLR and work-loop ESLFR from left ventricular rat trabeculae. Reproduced from data reported in Tran et al. (2016).

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  FIGURE 4. Simulated Ca2+ transients arising from isometric and work-loop contractions. Isometric contractions (gray) as functions of initial sarcomere length and work-loop contractions (black) as functions of afterload. The arrow indicates the direction of decreasing sarcomere length for the isometric simulations, and decreasing afterload for the work-loop simulations. Inset: Ca2+ transients of the Lo-isometric contraction (gray) and the work-loop contraction (black) at the lowest afterload.

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  FIGURE 5. Simulations highlighting the mechano-calcium feedback mechanism. Simulated intracellular Ca2+ transient (A), total force production (B), and Ca-troponin flux (C) for an Lo-isometric contraction, and a pair of isometric (SL = 0.91 Lo) and work-loop (normalized afterload at 0.45) contractions at the same peak force. Inset: close-up of the Ca-troponin flux at the start of the twitch. The dotted vertical lines indicate the times at the start of force production (t1) and at the start of the isotonic phase in the work-loop contraction (t2).

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  FIGURE 6. Simulations of work-loops driven by Ca2+ transients generated from isometric contractions. The isometric and work-loop ESFLR are replotted from Figure 4. Driving work-loops with Ca2+ transients generated from force-equivalent isometric contractions leads to a left-ward shift of the work-loop end-systolic force-length relation (ESFLR; dashed line) but it does not superimpose on the isometric ESFLR.