A coarse-grained model of the myofibril: Overall dynamics and the evolution of sarcomere non-uniformities

A theoretical framework for predicting the macroscopic behavior of a muscle myofibril based on the collective behavior of sarcomeres is presented. The analysis is accomplished by rigorously transforming the nonlinear dynamics of an assemblage of sarcomeres into a partial differential equation for the probability distribution function of sarcomere lengths in the presence of stochastic temporal fluctuations and biological variability. This enables the study of biologically relevant specimens with reasonable computational effort. The model is validated by a comparison to quantitative experimental results. Further, it reproduces experimental observations that cannot be explained by standard single sarcomere models, and provides new insights into muscle function and muscle damage during cyclic loading. We show that the accumulation of overstretched sarcomeres, which is related to muscle damage, depends on a delicate interplay between the dynamics of a large number of sarcomeres and the load characteristics, such as its magnitude and frequency. Further, we show that biological variability rather than stochastic fluctuations are the main source for sarcomere non-uniformities.