A spatially detailed myofilament model as a basis for large-scale biological simulations

Abstract

The availability of increased computing power will make possible new classes of biological models that include detailed representations of proteins and protein complexes with spatial interactions. We develop such a model of the interaction of actin and myosin within one pair of thick and thin filaments in the cardiac sarcomere. The model includes explicit representations of actin, myosin, and regulatory proteins. Although this is not an atomic-scale model, as would be the case for molecular dynamics simulations, the model seeks to represent spatial interactions between protein complexes that are thought to produce characteristic cardiac muscle responses at larger scales. While the model simulates the microscopic scale, when model results are extrapolated to larger structures, the model recapitulates complex, nonlinear behavior such as the steep calcium sensitivity of developed force in muscle structures. By bridging spatial scales, the model provides a plausible and quantitative explanation for several unexplained phenomena observed at the tissue level in cardiac muscles. Model execution entails Monte-Carlo-based simulations of Markov representations of calcium regulation and actin-myosin interactions. While most of the results presented here are preliminary, we suggest that this model will be suitable to serve as a basis for larger-scale simulations of multiple fibers assembled into larger sarcomere structures.

Approximation for Cooperative Interactions of a Spatially-Detailed Cardiac Sarcomere Model

“…On the other hand, the probability distribution in this study (Fig. 6) is continuous thus making clear contrast to other spatial MC models, which show discrete “pockets” in probability distributions 2,10. This difference was originated by our assumption of homogeneous binding probability along the thin filament which ignores the discrete distribution of myosin binding site and differences in their interval (pitch) from that of MHs.…”

Approximate Model of Cooperative Activation and Crossbridge Cycling in Cardiac Muscle Using Ordinary Differential Equations

“…Moreover, the model F-Ca relations show slight deviations from true Hill functions such that the low Ca region is somewhat more cooperative than the high Ca region as seen in many experimental studies (64-66). The spatially explicit approach is carried over to a second study using Monte Carlo approaches that include more detail such as crossbridges and the thick-and thin-filament structure of the sarcomere (51). This study also shows that end-to-end interaction of RUs produces steep F-Ca relations that resemble those measured experimentally.…”

“…This representation conflicts with most common notions of crossbridge cycling in which strain affects the transitions rates on an individual crossbridge basis only. However, tracking such interactions requires partial differential equations (e.g., (24)(25)(26)) or Monte Carlo approaches (e.g., (49)(50)(51)). In fact, common notions suggest individual strain strongly affects the transition rates, so that mean-field approaches may prove difficult to apply.…”

Dissociation of force decline from calcium decline by preload in isolated rabbit myocardium

“…One of our previous studies [17] investigated possible mechanisms of delayed relaxation in which we hypothesized that relaxation may be slower because of either prolonged Ca 2+ binding to troponin-C and/or crossbridge cooperativity to override the inhibitory effects of tropomyosin with decreasing calcium. The data of these experiments have been used in many different modeling studies [15,23,28,30], but the use of small rodents, room temperature, and absence of calcium transient data have not allowed to unambiguously determine the quantitative effects of governing factors of cardiac relaxation under physiological conditions resembling the ones prevailing in vivo. Force is dependent on many factors including muscle length, myofilament calcium sensitivity, calcium concentration, and frequency.…”