Model representation of the nonlinear step response in cardiac muscle

Abstract

Motivated by the need for an analytical tool that can be used routinely to analyze data collected from isolated, detergent-skinned cardiac muscle fibers, we developed a mathematical model for representing the force response to step changes in muscle length (i.e., quick stretch and release). Our proposed model is reasonably simple, consisting of only five parameters representing: (1) the rate constant by which length change–induced distortion of elastic elements is dissipated; (2) the stiffness of the muscle fiber; (3) the amplitude of length-mediated recruitment of stiffness elements; (4) the rate constant by which this length-mediated recruitment takes place; and (5) the magnitude of the nonlinear interaction term by which distortion of elastic elements affects the number of recruited stiffness elements. Fitting this model to a family of force recordings representing responses to eight amplitudes of step length change (±2.0% baseline muscle length in 0.5% increments) enabled four things: (1) reproduction of all the identifiable features seen in a family of force responses to both positive and negative length changes; (2) close fitting of all records from the whole family of these responses with very little residual error; (3) estimation of all five model parameters with a great degree of certainty; and (4) importantly, ready discrimination between cardiac muscle fibers with different contractile regulatory proteins but showing only subtly different contractile function. We recommend this mathematical model as an analytic tool for routine use in studies of cardiac muscle fiber contractile function. Such model-based analysis gives novel insight to the contractile behavior of cardiac muscle fibers, and it is useful for characterizing the mechanistic effects that alterations of cardiac contractile proteins have on cardiac contractile function.

A model of cardiac contraction based on novel measurements of tension development in human cardiomyocytes

“…Following shortening, we do not observe the biphasic force response seen after a rapid stretch. In contrast, the induced distortion causes force to decrease instantly, before recovering in a smooth, monotonically increasing manner, consistent with previous experiments [14]. In addition, we have data on constant velocity shortening, where cell length decreases by 7-11% over 100-300 ms. We combine these two data sets to select a set of model parameters k ws , k uw , φ, γ s , γ w which fits both types of experimental data well.…”

“…The data ( Figure 5A-C) shows the response of a myocyte to a quick stretch. Force increases instantly due to distortion of crossbridges, then rapidly decays and drops below the eventual steady-state tension at the increased length as distorted crossbridges detach, before recovering to a higher steady-state level of tension due to length-dependent effects [14]. Following shortening, we do not observe the biphasic force response seen after a rapid stretch.…”

“…Here γ wu , γ su are distortion-dependent unbinding rates of crossbridges in the W and S state, given by a distortion-decay model [14,55]. We use a relatively simple distortion-decay model, inspired by the work of Ford et al [14], Razumova et al [55], and Rice et al [56].…”

“…We use a relatively simple distortion-decay model, inspired by the work of Ford et al [14], Razumova et al [55], and Rice et al [56]. These models assume crossbridges are linearly elastic, and tension is generated by both distortion induced by the powerstroke, and distortion induced by imposed changes in cell length.…”

Impact of the Myosin Modulator Mavacamten on Force Generation and Cross‐Bridge Behavior in a Murine Model of Hypercontractility

“…The stretch activation protocol used here was described in detail in previous studies 33, 39, 42. Skinned myocardial preparations were activated with pCa that generated a range of submaximal forces (eg, ≈40%–45% of maximal force at pCa 6.1 and ≈52%–57% of maximal force at pCa 6.0).…”