A continuum-mechanical skeletal muscle model including actin-titin interaction predicts stable contractions on the descending limb of the force-length relation

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-sarcomere—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-sarcomere—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 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.