A Data-driven Surrogate Model for Work Computation of a Periodically Forced Half-Sarcomere

Abstract

Muscle force generation follows from molecular scale interactions that drive macroscopic behaviors and macroscopic processes that influence those at the molecular scale. A particuarly challenging issue is that models at the molecular level of organization are often quite difficult to apply to larger spatial scales. This is particularly true of moleuclar models driven by Monte-Carlo simulations. This challenge of multiscale dynamics requires methods to extract reduced order behaviors from detailed high-dimensional simulations. In this work we present a novel deterministic simulation method yielding accurate predictions of force-length behaviors of contracting muscle sarcomeres undergoing periodic length changes (work loops). The model maintains interpretability by tracking macroscopic state variables throughout the simulation while using data-driven representations of dynamics. Parameters of the data-driven dynamics are learned from trajectories from Monte-Carlo simulations of a half-sarcomere. Our method significantly reduces computational cost by tracking the state of the sarcomere in a course grained set of variables while maintaining accurate prediction of macroscopic level observables and time series for course grained variables. This allows for rapid sampling of the models output and builds towards the ability to scale to multiple-sarcomere simulations. Author SummaryWe develop a data-driven surrogate model for the dynamics of the half-sarcomere. This model achieves the same behavior with respect to force traces as more sophisticated Monte Carlo models at a substantially lower computational cost. The model is built by finding a course grained description of the full state space of the Monte Carlo simulation and learning dynamical models on the course grained space. Data-driven representations of the dynamics in the course grained space are trained using data from the full model. Data-driven models for forcing are also learned, and the result fed back into the dynamics. In doing so, the model seeks to replicate the effects of filament compliance on macro scale dynamics without explicitly tracking micro scale features. We withhold some input parameter regimes and demonstrate accurate reconstruction of course grained state and force traces using the data-driven model and given only knowledge of the initial condition and input. This work allows for faster computation of the forcing behavior of the half-sarcomere, as well as consistent representations of the course grained state variables. It is therefore promising as a step towards multi-sarcomere or even tissue scale models of skeletal muscle.