Recent studies have demonstrated a role for the elastic protein titin in active muscle, but the mechanisms by which titin plays this role remain to be elucidated. In active muscle, Ca 2þ -binding has been shown to increase titin stiffness, but the observed increase is too small to explain the increased stiffness of parallel elastic elements upon muscle activation. We propose a 'winding filament' mechanism for titin's role in active muscle. First, we hypothesize that Ca 2þ -dependent binding of titin's N2A region to thin filaments increases titin stiffness by preventing low-force straightening of proximal immunoglobulin domains that occurs during passive stretch. This mechanism explains the difference in length dependence of force between skeletal myofibrils and cardiac myocytes. Second, we hypothesize that cross-bridges serve not only as motors that pull thin filaments towards the M-line, but also as rotors that wind titin on the thin filaments, storing elastic potential energy in PEVK during force development and active stretch. Energy stored during force development can be recovered during active shortening. The winding filament hypothesis accounts for force enhancement during stretch and force depression during shortening, and provides testable predictions that will encourage new directions for research on mechanisms of muscle contraction.
Movement planning is thought to be primarily determined by motor costs such as inaccuracy and effort. Solving for the optimal plan that minimizes these costs typically leads to specifying a time-varying feedback controller which both generates the movement and can optimally correct for errors that arise within a movement. However, the quality of the sensory feedback during a movement can depend substantially on the generated movement. We show that by incorporating such state-dependent sensory feedback, the optimal solution incorporates active sensing and is no longer a pure feedback process but includes a significant feedforward component. To examine whether people take into account such state-dependency in sensory feedback we asked people to make movements in which we controlled the reliability of sensory feedback. We made the visibility of the hand state-dependent, such that the visibility was proportional to the component of hand velocity in a particular direction. Subjects gradually adapted to such a sensory perturbation by making curved hand movements. In particular, they appeared to control the late visibility of the movement matching predictions of the optimal controller with state-dependent sensory noise. Our results show that trajectory planning is not only sensitive to motor costs but takes sensory costs into account and argues for optimal control of movement in which feedforward commands can play a significant role.
SUMMARYMusculoskeletal models are often created by making detailed anatomical measurements of muscle properties. These measurements can then be used to determine the parameters of canonical models of muscle action. We describe here a complementary approach for developing and validating muscle models, using in situ measurements of muscle actions. We characterized the actions of two rat hindlimb muscles: the gracilis posticus (GRp) and the posterior head of biceps femoris (BFp; excluding the anterior head with vertebral origin). The GRp is a relatively simple muscle, with a circumscribed origin and insertion. The BFp is more complex, with an insertion distributed along the tibia. We measured the six-dimensional isometric forces and moments at the ankle evoked from stimulating each muscle at a range of limb configurations. The variation of forces and moments across the workspace provides a succinct characterization of muscle action. We then used this data to create a simple muscle model with a single point insertion and origin. The model parameters were optimized to best explain the observed force-moment data. This model explained the relatively simple muscle, GRp, very well (R 2 >0.85). Surprisingly, this simple model was also able to explain the action of the BFp, despite its greater complexity (R 2 >0.84). We then compared the actions observed here with those predicted using recently published anatomical measurements. Although the forces and moments predicted for the GRp were very similar to those observed here, the predictions for the BFp differed. These results show the potential utility of the approach described here for the development and refinement of musculoskeletal models based on in situ measurements of muscle actions.
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