A multi-scale continuum model of skeletal muscle mechanics predicting force enhancement based on actin–titin interaction

Abstract

Contractions on the descending limb of the total (active + passive) muscle force-length relationship (i. e. when muscle stiffness is negative) are expected to lead to vast half-sarco-mere-length inhomogeneities. This is however not observed in experiments-vast half-sarcomere-length inhomogeneities can be absent in myofibrils contracting in this range, and initial inhomogeneities can even decrease. Here we show that the absence of half-sar-comere-length inhomogeneities can be predicted when considering interactions of the semi-active protein titin with the actin filaments. Including a model of actin-titin interactions within a multi-scale continuum-mechanical model, we demonstrate that stability, accurate forces and nearly homogeneous half-sarcomere lengths can be obtained on the descending limb of the static total force-length relation. This could be a key to durable functioning of the muscle because large local stretches, that might harm, for example, the transverse-tubule system, are avoided. Author summary Muscle force generation is a complex process depending on muscle length, activation, and other time-dependent properties. Contractions on the descending limb of the force-length relation (i. e. when the maximum isometric force decreases with increasing muscle length) are interesting, since this behaviour is expected to result in non-physiological length inhomogeneities of the muscle microstructure. Previously, different mechanisms have been suggested that could have a stabilising effect on the muscle microstructure. However, superposition of several phenomena makes it difficult to separate the influence of a single mechanism in an experimental setup. Within a model, individual phenomena can be knocked out to quantify the influence of a single process. Here we show, using a PLOS Computational Biology | https://doi.org/10.1371/journal.pcbi. physiologically motivated model of the whole muscle, that variable mechanical properties of the large protein titin (controlled by calcium as a second messenger) can guarantee stability of the muscle microstructure during contractions on the descending limb of the force-length relation.

Force enhancement and stability of finite element muscle models

“…Because there is no serial elasticity, the active stresses are obtained in a straightforward manner by subtracting the passive stresses from the total isometric stresses. Reproduced from [7] with permission.…”

“…Using the finite element model of [7], which includes force enhancement based on actin-titin interaction, active stretches have been performed starting from different muscle lengths (indicated by the initial fibre stretch λ init f ). The resulting stress-stretch curves are summarised in Fig.…”

“…In [7], the force enhancement model of [8] has been integrated into the multiscale continuum-mechanical model of [9,10]. The model in [8] describes actin-titin interaction at the microscopic half-sarcomere level.…”

In Vivo Multiscale and Spatially-Dependent Biomechanics Reveals Differential Strain Transfer Hierarchy in Skeletal Muscle

“…Computational research has thoroughly investigated how continuum mechanics, molecular mechanics, or a combination of both can explain the multiscale force transfer and downstream chemical pathway activation in soft tissues (e.g. skeletal muscle 6–8 , cardiovascular system 9,10 and articular cartilage 11,12 ). Experimental paradigms have used isolated single cell mechanics, tissue equivalents, or in situ studies to probe multiscale strain transfer and mechanotransduction mechanisms in the ECM, cell, and nucleus 13,14 .…”

An Investigation of Fatigue in Stationary Biking with Application to Iliotibial Band Syndrome Development

“…While these models have predictive strength, they are limited in their generalizability to other activities and to the wider population (Noakes 2000). Lower level hierarchical models and neural networks are also investigated to predict muscle dynamics, but would require higher computational cost that could limit extension to real-time applications (Cecchini et al 2014;Heidlauf et al 2016). Through this investigation, the model development approach has been reevaluated.…”