Abstract
Despite decades of research, we lack a mechanistic framework capable of predicting how movement-related signals are transformed into the diversity of muscle spindle afferent firing patterns observed experimentally, particularly in naturalistic behaviors. Here, a biophysical model demonstrates that well-known firing characteristics of muscle spindle Ia afferents – including dependence on movement history, and nonlinear scaling with muscle stretch velocity – emerge from first principles of muscle contractile mechanics. Further, mechanical interactions of the muscle spindle with muscle-tendon dynamics reveal how motor commands to the muscle (alpha drive) versus muscle spindle (gamma drive) can cause highly variable and complex activity during active muscle contraction and muscle stretch that defy simple explanation. Depending on the neuromechanical conditions, the muscle spindle model output appears to “encode” aspects of muscle force, yank, length, stiffness, velocity, and/or acceleration, providing an extendable, multiscale, biophysical framework for understanding and predicting proprioceptive sensory signals in health and disease.
Competing Interest Statement
The authors have declared no competing interest.
Footnotes
This is a major revision to the previous manuscript, which includes new writing, simulations, and analyses. We believe that the revised manuscript is greatly improved and provides a simple biophysical framework for understanding the transformation between mechanical events in the muscle into muscle spindle sensory signals in both passive and active conditions. While many details are still yet to be incorporated, we hope to revive a more complex understanding of muscle spindle function in the current literature. To that end, we have developed a new set of simulations using a model that includes both extrafusal muscle and tendon dynamics. This model enabled us to run simulations now in new figures 8 and 9 explicitly demonstrating the independent and combined effects of extrafusal and intrafusal fiber twitch on muscle spindle firing in isometric conditions where overall muscle-tendon length is constant. The original simulations for Figure 8 were also re-run using this more sophisticated model where alpha drive, gamma drive, and tendon elongation are included. We then added an additional figure in which the independent and combined effect of alpha and gamma drive were simulated in the context of an external stretch. Taken together, we believe that these simulations address the concerns of the reviewers that the model did not sufficiently simulate interactions between intrafusal and extrafusal fibers. These simulations also enabled us to clearly illustrate that neither extrafusal force nor length can independently - or together - account for muscle spindle firing patterns, Instead, our model illustrates that the intrafusal force and yank arise from a complex interaction between muscle, tendon, load, and intrafusal muscle mechanics.