  Muscles sense internally generated and externally applied forces, responding
to these in a coordinated hierarchical manner at different time scales. The
center of the basic unit of the muscle, the sarcomeric M-band, is perfectly
placed to sense the different types of load to which the muscle is subjected.
In particular, the kinase domain (TK) of titin located at the M-band is a known
candidate for mechanical signaling. Here, we develop the quantitative
mathematical model that describes the kinetics of TK-based mechanosensitive
signaling, and predicts trophic changes in response to exercise and
rehabilitation regimes. First, we build the kinetic model for TK conformational
changes under force: opening, phosphorylation, signaling and autoinhibition. We
find that TK opens as a metastable mechanosensitive switch, which naturally
produces a much greater signal after high-load resistance exercise than an
equally energetically costly endurance effort. Next, in order for the model to
be stable, give coherent predictions, in particular the lag following the onset
of an exercise regime, we have to account for the associated kinetics of
phosphate (carried by ATP), and for the non-linear dependence of protein
synthesis rates on muscle fibre size. We suggest that the latter effect may
occur via the steric inhibition of ribosome diffusion through the sieve-like
myofilament lattice. The full model yields a steady-state solution
(homeostasis) for muscle cross-sectional area and tension, and a quantitatively
plausible hypertrophic response to training as well as atrophy following an
extended reduction in tension.
