Quantitative mapping of force-pCa curves to whole-heart contraction and relaxation

Abstract

The force-pCa (F-pCa) curve is used to characterize steady-state contractile properties of cardiac muscle cells in different physiological, pathological and pharmacological conditions. This provides a reduced preparation in which to isolate sarcomere mechanisms. However, it is unclear how changes in the F-pCa curve impact emergent whole-heart mechanics quantitatively. We study the link between sarcomere and whole-heart function using a multiscale mathematical model of rat biventricular mechanics that describes sarcomere, tissue, anatomy, preload and afterload properties quantitatively. We first map individual cell-level changes in sarcomere-regulating parameters to organ-level changes in the left ventricular function described by pressure-volume loop characteristics (e.g. end-diastolic and end-systolic volumes, ejection fraction and isovolumetric relaxation time). We next map changes in the sarcomere-regulating parameters to changes in the F-pCa curve. We demonstrate that a change in the F-pCa curve can be caused by multiple different changes in sarcomere properties. We demonstrate that changes in sarcomere properties cause non-linear and, importantly, non-monotonic changes in left ventricular function. As a result, a change in sarcomere properties yielding changes in the F-pCa curve that improve contractility does not guarantee an improvement in whole-heart function. Likewise, a desired change in whole-heart function (i.e. ejection fraction or relaxation time) is not caused by a unique shift in the F-pCa curve. Changes in the F-pCa curve alone cannot be used to predict the impact of a compound on whole-heart function. KEY POINTS: The force-pCa (F-pCa) curve is used to assess myofilament calcium sensitivity after pharmacological modulation and to infer pharmacological effects on whole-heart function. We demonstrate that there is a non-unique mapping from changes in F-pCa curves to changes in left ventricular (LV) function. The effect of changes in F-pCa on LV function depend on the state of the heart and could be different for different pathological conditions. Screening of compounds to impact whole-heart function by F-pCa should be combined with active tension and calcium transient measurements to predict better how changes in muscle function will impact whole-heart physiology.

Keywords: Hill coefficient; force-calcium; force-pCa; left ventricular myocyte; pCa50; pCa50 shift; sarcomere modulators; steady-state force.