Fluid flow in the sarcomere

Haemolymph viscosity in hawkmoths and its implications for hovering flight

Viscosity determines the resistance of haemolymph flow through the insect body. For flying insects, viscosity is a major physiological parameter limiting flight performance by controlling the flow rate of fuel to the flight muscles, circulating nutrients and rapidly removing metabolic waste products. The more viscous the haemolymph, the greater the metabolic energy needed to pump it through confined spaces. By employing magnetic rotational spectroscopy with nickel nanorods, we showed that viscosity of haemolymph in resting hawkmoths (Sphingidae) depends on wing size non-monotonically. Viscosity increases for small hawkmoths with high wingbeat frequencies, reaches a maximum for middle-sized hawkmoths with moderate wingbeat frequencies, and decreases in large hawkmoths with slower wingbeat frequencies but greater lift. Accordingly, hawkmoths with small and large wings have viscosities approaching that of water, whereas hawkmoths with mid-sized wings have more than twofold greater viscosity. The metabolic demands of flight correlate with significant changes in circulatory strategies via modulation of haemolymph viscosity. Thus, the evolution of hovering flight would require fine-tuned viscosity adjustments to balance the need for the haemolymph to carry more fuel to the flight muscles while decreasing the viscous dissipation associated with its circulation.

A mechanism for sarcomere breathing: volume change and advective flow within the myofilament lattice

During muscle contraction, myosin motors anchored to thick filaments bind to and slide actin thin filaments. These motors rely on energy derived from ATP, supplied, in part, by diffusion from the sarcoplasm to the interior of the lattice of actin and myosin filaments. The radial spacing of filaments in this lattice may change or remain constant during contraction. If the lattice is isovolumetric, it must expand when the muscle shortens. If, however, the spacing is constant or has a different pattern of axial and radial motion, then the lattice changes volume during contraction, driving fluid motion and assisting in the transport of molecules between the contractile lattice and the surrounding intracellular space. We first create an advective-diffusive-reaction flow model and show that the flow into and out of the sarcomere lattice would be significant in the absence of lattice expansion. Advective transport coupled to diffusion has the potential to substantially enhance metabolite exchange within the crowded sarcomere. Using time-resolved x-ray diffraction of contracting muscle, we next show that the contractile lattice is neither isovolumetric nor constant in spacing. Instead, lattice spacing is time varying, depends on activation, and can manifest as an effective time-varying Poisson ratio. The resulting fluid flow in the sarcomere lattice of synchronous insect flight muscles is even greater than expected for constant lattice spacing conditions. Lattice spacing depends on a variety of factors that produce radial force, including cross-bridges, titin-like molecules, and other structural proteins. Volume change and advective transport varies with the phase of muscle stimulation during periodic contraction but remains significant at all conditions. Although varying in magnitude, advective transport will occur in all cases in which the sarcomere is not isovolumetric. Akin to "breathing," advective-diffusive transport in sarcomeres is sufficient to promote metabolite exchange and may play a role in the regulation of contraction itself.

Why exercise builds muscles: titin mechanosensing controls skeletal muscle growth under load

Muscles sense internally generated and externally applied forces, responding to these in a coordinated hierarchical manner at different timescales. 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 of titin (TK) located at the M-band is a known candidate for mechanical signaling. Here, we develop a 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, for the model to be stable and give coherent predictions, in particular for the lag after the onset of an exercise regime, we have to account for the associated kinetics of phosphate (carried by ATP) and for the nonlinear dependence of protein synthesis rates on muscle fiber 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 after an extended reduction in tension.