skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

Explore Research Products in the PAR
It may take a few hours for recently added research products to appear in PAR search results.


This content will become publicly available on November 3, 2026

Title: Biophysical model for predicting muscle short-range stiffness during movement
Abstract Musculoskeletal simulations can offer valuable insight into how the properties of our musculoskeletal system influence the biomechanics of our daily movements. One such property is muscle’s history-dependent initial resistance to stretch, also known as short-range stiffness, which is key to stabilizing movements in response to external perturbations. Short-range stiffness is poorly captured by existing musculoskeletal simulations since they employ phenomenological Hill-type muscle models that lack the mechanisms underlying short-range stiffness. While it has been previously shown that biophysical cross-bridge models can reproduce muscle short-range-stiffness, it is unclear which specific biophysical properties are necessary to capture history-dependent muscle force responses in behaviorally relevant conditions. Here, we tested the ability of various biophysical cross-bridge models to reproduce empirical short-range stiffness and its history-dependent changes across a broad range of behaviorally relevant length changes and activation levels, using an existing dataset on permeabilized rat soleus muscle fibers (N = 11). We found that a biophysical cross-bridge model with cooperative myofilament activation reproduced the effects of muscle activation (R2= 0.86), stretch amplitude (R2= 0.71) and isometric recovery time (R2= 0.79) on history-dependent changes in short-range stiffness after shortening. Similar results were obtained when the cross-bridge distribution of the biophysical model was approximated by a Gaussian (R2= 0.73 - 0.88), but at a 20 times lower computational cost. These effects could not be reproduced by either a biophysical cross-bridge model without cooperative myofilament activation or a Hill-type model (R2< 0.5). The reduced computational demand of the Gaussian-approximated models facilitates implementing biophysical cross-bridge models with cooperative myofilament activation in musculoskeletal simulations to improve the prediction of short-range stiffness during movements.  more » « less
Award ID(s):
2319710
PAR ID:
10657293
Author(s) / Creator(s):
; ; ; ; ;
Publisher / Repository:
bioRxiv
Date Published:
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. ; ; ; ; (, American Journal of Physiology-Heart and Circulatory Physiology)
    null (Ed.)
    Cardiac myosin binding protein-C (cMyBP-C) is a thick filament protein that influences sarcomere stiffness and modulates cardiac contraction-relaxation through its phosphorylation. Phosphorylation of cMyBP-C and ablation of cMyBP-C have been shown to increase the rate of MgADP release in the acto-myosin cross-bridge cycle in the intact sarcomere. The influence of cMyBP-C on Pi-dependent myosin kinetics has not yet been examined. We investigated the effect of cMyBP-C, and its phosphorylation, on myosin kinetics in demembranated papillary muscle strips bearing the β-cardiac myosin isoform from nontransgenic and homozygous transgenic mice lacking cMyBP-C. We used quick stretch and stochastic length-perturbation analysis to characterize rates of myosin detachment and force development over 0–12 mM Pi and at maximal (pCa 4.8) and near-half maximal (pCa 5.75) Ca 2+ activation. Protein kinase A (PKA) treatment was applied to half the strips to probe the effect of cMyBP-C phosphorylation on Pi sensitivity of myosin kinetics. Increasing Pi increased myosin cross-bridge detachment rate similarly for muscles with and without cMyBP-C, although these rates were higher in muscle without cMyBP-C. Treating myocardial strips with PKA accelerated detachment rate when cMyBP-C was present over all Pi, but not when cMyBP-C was absent. The rate of force development increased with Pi in all muscles. However, Pi sensitivity of the rate force development was reduced when cMyBP-C was present versus absent, suggesting that cMyBP-C inhibits Pi-dependent reversal of the power stroke or stabilizes cross-bridge attachment to enhance the probability of completing the power stroke. These results support a functional role for cMyBP-C in slowing myosin detachment rate, possibly through a direct interaction with myosin or by altering strain-dependent myosin detachment via cMyBP-C-dependent stiffness of the thick filament and myofilament lattice. PKA treatment reduces the role for cMyBP-C to slow myosin detachment and thus effectively accelerates β-myosin detachment in the intact myofilament lattice. NEW & NOTEWORTHY Length perturbation analysis was used to demonstrate that β-cardiac myosin characteristic rates of detachment and recruitment in the intact myofilament lattice are accelerated by Pi, phosphorylation of cMyBP-C, and the absence of cMyBP-C. The results suggest that cMyBP-C normally slows myosin detachment, including Pi-dependent detachment, and that this inhibition is released with phosphorylation or absence of cMyBP-C. 
    more » « less
  2. ; ; ; (, Journal of The Royal Society Interface)
    Hill-type muscle models are highly preferred as phenomenological models for musculoskeletal simulation studies despite their introduction almost a century ago. The use of simple Hill-type models in simulations, instead of more recent cross-bridge models, is well justified since computationally ‘light-weight’—although less accurate—Hill-type models have great value for large-scale simulations. However, this article aims to invite discussion on numerical instability issues of Hill-type muscle models in simulation studies, which can lead to computational failures and, therefore, cannot be simply dismissed as an inevitable but acceptable consequence of simplification. We will first revisit the basic premises and assumptions on the force–length and force–velocity relationships that Hill-type models are based upon, and their often overlooked but major theoretical limitations. We will then use several simple conceptual simulation studies to discuss how these numerical instability issues can manifest as practical computational problems. Lastly, we will review how such numerical instability issues are dealt with, mostly in an ad hoc fashion, in two main areas of application: musculoskeletal biomechanics and computer animation. 
    more » « less
  3. ; ; ; ; ; (, British Journal of Pharmacology)
    Background and PurposeHeart failure can reflect impaired contractile function at the myofilament level. In healthy hearts, myofilaments become more sensitive to Ca2+as cells are stretched. This represents a fundamental property of the myocardium that contributes to the Frank–Starling response, although the molecular mechanisms underlying the effect remain unclear. Mavacamten, which binds to myosin, is under investigation as a potential therapy for heart disease. We investigated how mavacamten affects the sarcomere‐length dependence of Ca2+‐sensitive isometric contraction to determine how mavacamten might modulate the Frank–Starling mechanism. Experimental ApproachMulticellular preparations from the left ventricular‐free wall of hearts from organ donors were chemically permeabilized and Ca2+activated in the presence or absence of 0.5‐μM mavacamten at 1.9 or 2.3‐μm sarcomere length (37°C). Isometric force and frequency‐dependent viscoelastic myocardial stiffness measurements were made. Key ResultsAt both sarcomere lengths, mavacamten reduced maximal force and Ca2+sensitivity of contraction. In the presence and absence of mavacamten, Ca2+sensitivity of force increased as sarcomere length increased. This suggests that the length‐dependent activation response was maintained in human myocardium, even though mavacamten reduced Ca2+sensitivity. There were subtle effects of mavacamten reducing force values under relaxed conditions (pCa 8.0), as well as slowing myosin cross‐bridge recruitment and speeding cross‐bridge detachment under maximally activated conditions (pCa 4.5). Conclusion and ImplicationsMavacamten did not eliminate sarcomere length‐dependent increases in the Ca2+sensitivity of contraction in myocardial strips from organ donors at physiological temperature. Drugs that modulate myofilament function may be useful therapies for cardiomyopathies. 
    more » « less
  4. ; ; ; ; ; ; ; ; ; (, The Journal of Physiology)
    AbstractPrecise regulation of sarcomeric contraction is essential for normal cardiac function. The heart must generate sufficient force to pump blood throughout the body, but either inadequate or excessive force can lead to dysregulation and disease. Myosin regulatory light chain (RLC) is a thick‐filament protein that binds to the neck of the myosin heavy chain. Post‐translational phosphorylation of RLC (RLC‐P) by myosin light chain kinase is known to influence acto‐myosin interactions, thereby increasing force production and Ca2+‐sensitivity of contraction. Here, we investigated the role of RLC‐P on cardiac structure and function as sarcomere length and [Ca2+] were altered. We found that at low, non‐activating levels of Ca2+, RLC‐P contributed to myosin head disorder, though there were no effects on isometric stress production and viscoelastic stiffness. With increases in sarcomere length and Ca2+‐activation, the structural changes due to RLC‐P become greater, which translates into greater force production, greater viscoelastic stiffness, slowed myosin detachment rates and altered nucleotide handling. Altogether, these data suggest that RLC‐P may alter thick‐filament structure by releasing ordered, off‐state myosin. These more disordered myosin heads are available to bind actin, which could result in greater force production as Ca2+levels increase. However, prolonged cross‐bridge attachment duration due to slower ADP release could delay relaxation long enough to enable cross‐bridge rebinding. Together, this work further elucidates the effects of RLC‐P in regulating muscle function, thereby promoting a better understanding of thick‐filament regulatory contributions to cardiac function in health and disease.image Key pointsMyosin regulatory light chain (RLC) is a thick‐filament protein in the cardiac sarcomere that can be phosphorylated (RLC‐P), and changes in RLC‐P are associated with cardiac dysfunction and disease.This study assesses how RLC‐P alters cardiac muscle structure and function at different sarcomere lengths and calcium concentrations.At low, non‐activating levels of Ca2+, RLC‐P contributed to myofilament disorder, though there were no effects on isometric stress production and viscoelastic stiffness.With increases in sarcomere length and Ca2+‐activation, the structural changes due to RLC‐P become greater, which translates into greater force production, greater viscoelastic stiffness, slower myosin detachment rate and altered cross‐bridge nucleotide handling rates.This work elucidates the role of RLC‐P in regulating muscle function and facilitates understanding of thick‐filament regulatory protein contributions to cardiac function in health and disease. 
    more » « less
  5. ; (, Journal of Experimental Biology)
    ABSTRACT Recent studies have demonstrated that muscle force is not determined solely by activation under dynamic conditions, and that length history has an important role in determining dynamic muscle force. Yet, the mechanisms for how muscle force is produced under dynamic conditions remain unclear. To explore this, we investigated the effects of muscle stiffness, activation and length perturbations on muscle force. First, submaximal isometric contraction was established for whole soleus muscles. Next, the muscles were actively shortened at three velocities. During active shortening, we measured muscle stiffness at optimal muscle length (L0) and the force response to time-varying activation and length perturbations. We found that muscle stiffness increased with activation but decreased as shortening velocity increased. The slope of the relationship between maximum force and activation amplitude differed significantly among shortening velocities. Also, the intercept and slope of the relationship between length perturbation amplitude and maximum force decreased with shortening velocity. As shortening velocities were related to muscle stiffness, the results suggest that length history determines muscle stiffness and the history-dependent muscle stiffness influences the contribution of activation and length perturbations to muscle force. A two-parameter viscoelastic model including a linear spring and a linear damper in parallel with measured stiffness predicted history-dependent muscle force with high accuracy. The results and simulations support the hypothesis that muscle force under dynamic conditions can be accurately predicted as the force response of a history-dependent viscoelastic material to length perturbations. 
    more » « less
  • Citation Formats
  • MLA
  • APA
  • Chicago
  • BibTeX
  • Save / Share this Record
  • Send to Email