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1. Effects of shortening velocity on the stiffness to force ratio during isometric force redevelopment suggest mechanisms of residual force depression

   https://doi.org/10.1038/s41598-023-28236-5  

   Jeong, Siwoo; Nishikawa, Kiisa (January 2023, Scientific Reports)

   Abstract Although the phenomenon of residual force depression has been known for decades, the mechanisms remain elusive. In the present study, we investigated mechanisms of residual force depression by measuring the stiffness to force ratio during force redevelopment after shortening at different velocities. The results showed that the slope of the relationship between muscle stiffness and force decreased with decreasing shortening velocity, and the y-intercept increased with decreasing shortening velocity. The differing slopes and y-intercepts indicate that the stiffness to force ratio during isometric force redevelopment depends on the active shortening velocity at a given muscle length and activation level. The greater stiffness to force ratio after active shortening can potentially be explained by weakly-bound cross bridges in the new overlap zone. However, weakly-bound cross bridges are insufficient to explain the reduced slope at the slowest shortening velocity because the reduced velocity should increase the proportion of weakly- to strongly-bound cross bridges, thereby increasing the slope. In addition, if actin distortion caused by active shortening recovers during the force redevelopment period, then the resulting slope should be similar to the non-linear slope of force redevelopment over time. Alternatively, we suggest that a tunable elastic element, such as titin, could potentially explain the results. 

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2. Non-cross Bridge Viscoelastic Elements Contribute to Muscle Force and Work During Stretch-Shortening Cycles: Evidence From Whole Muscles and Permeabilized Fibers

   https://doi.org/10.3389/fphys.2021.648019  

   Hessel, Anthony L.; Monroy, Jenna A.; Nishikawa, Kiisa C. (March 2021, Frontiers in Physiology)

   null (Ed.)

   The sliding filament–swinging cross bridge theory of skeletal muscle contraction provides a reasonable description of muscle properties during isometric contractions at or near maximum isometric force. However, it fails to predict muscle force during dynamic length changes, implying that the model is not complete. Mounting evidence suggests that, along with cross bridges, a Ca 2+ -sensitive viscoelastic element, likely the titin protein, contributes to muscle force and work. The purpose of this study was to develop a multi-level approach deploying stretch-shortening cycles (SSCs) to test the hypothesis that, along with cross bridges, Ca 2+ -sensitive viscoelastic elements in sarcomeres contribute to force and work. Using whole soleus muscles from wild type and mdm mice, which carry a small deletion in the N2A region of titin, we measured the activation- and phase-dependence of enhanced force and work during SSCs with and without doublet stimuli. In wild type muscles, a doublet stimulus led to an increase in peak force and work per cycle, with the largest effects occurring for stimulation during the lengthening phase of SSCs. In contrast, mdm muscles showed neither doublet potentiation features, nor phase-dependence of activation. To further distinguish the contributions of cross bridge and non-cross bridge elements, we performed SSCs on permeabilized psoas fiber bundles activated to different levels using either [Ca 2+ ] or [Ca 2+ ] plus the myosin inhibitor 2,3-butanedione monoxime (BDM). Across activation levels ranging from 15 to 100% of maximum isometric force, peak force, and work per cycle were enhanced for fibers in [Ca 2+ ] plus BDM compared to [Ca 2+ ] alone at a corresponding activation level, suggesting a contribution from Ca 2+ -sensitive, non-cross bridge, viscoelastic elements. Taken together, our results suggest that a tunable viscoelastic element such as titin contributes to: (1) persistence of force at low [Ca 2+ ] in doublet potentiation; (2) phase- and length-dependence of doublet potentiation observed in wild type muscles and the absence of these effects in mdm muscles; and (3) increased peak force and work per cycle in SSCs. We conclude that non-cross bridge viscoelastic elements, likely titin, contribute substantially to muscle force and work, as well as the phase-dependence of these quantities, during dynamic length changes. 

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3. Biophysical model for predicting muscle short-range stiffness during movement

   https://doi.org/10.1101/2025.10.31.685881  

   van_der_Zee, Tim J; Simha, Surabhi N; Milburn, Gregory N; Campbell, Kenneth S; Ting, Lena H; De_Groote, Friedl (November 2025, bioRxiv)

   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. 

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4. Linking in vivo muscle dynamics to force–length and force–velocity properties reveals that guinea fowl lateral gastrocnemius operates at shorter than optimal lengths

   https://doi.org/10.1242/jeb.246879  

   Janneke_Schwaner, M; Mayfield, Dean L; Azizi, Emanuel; Daley, Monica A (August 2024, Journal of Experimental Biology)

   ABSTRACT The isometric force–length (F–L) and isotonic force–velocity (F–V) relationships characterize the contractile properties of skeletal muscle under controlled conditions, yet it remains unclear how these properties relate to in vivo muscle function. Here, we map the in situ F–L and F–V characteristics of guinea fowl (Numida meleagris) lateral gastrocnemius (LG) to the in vivo operating range during walking and running. We test the hypothesis that muscle fascicles operate on the F–L plateau, near the optimal length for force (L0) and near velocities that maximize power output (Vopt) during walking and running. We found that in vivo LG velocities are consistent with optimizing power during work production, and economy of force at higher loads. However, LG does not operate near L0 at higher loads. LG length was near L0 at the time of electromyography (EMG) onset but shortened rapidly such that force development during stance occurred on the ascending limb of the F–L curve, around 0.8L0. Shortening across L0 in late swing might optimize potential for rapid force development near the swing–stance transition, providing resistance to unexpected perturbations that require rapid force development. We also found evidence of in vivo passive force rise in late swing, without EMG activity, at lengths where in situ passive force is zero, suggesting that dynamic viscoelastic effects contribute to in vivo force development. Comparison of in vivo operating ranges with F–L and F–V properties suggests the need for new approaches to characterize muscle properties in controlled conditions that more closely resemble in vivo dynamics. 

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5. One size does not fit all: diversity of length–force properties of obliquely striated muscles

   https://doi.org/10.1242/jeb.244949  

   Thompson, Joseph T.; Taylor-Burt, Kari R.; Kier, William M. (April 2023, Journal of Experimental Biology)

   ABSTRACT Obliquely striated muscles occur in 17+ phyla, likely evolving repeatedly, yet the implications of oblique striation for muscle function are unknown. Contrary to the belief that oblique striation allows high force output over extraordinary length ranges (i.e. superelongation), recent work suggests diversity in operating length ranges and length–force relationships. We hypothesize oblique striation evolved to increase length–force relationship flexibility. We predict that superelongation is not a general characteristic of obliquely striated muscles and instead that length–force relationships vary with operating length range. To test these predictions, we measured length–force relationships of five obliquely striated muscles from inshore longfin squid, Doryteuthis pealeii: tentacle, funnel retractor and head retractor longitudinal fibers, and arm and fin transverse fibers. Consistent with superelongation, the tentacle length–force relationship had a long descending limb, whereas all others exhibited limited descending limbs. The ascending limb at 0.6P0 was significantly broader (P<0.001) for the tentacle length–force relationship (0.43±0.04L0; where L0 is the preparation length that produced peak isometric stress, P0) than for the arm (0.29±0.03L0), head retractor (0.24±0.06L0), fin (0.20±0.04L0) and funnel retractor (0.27±0.03L0). The fin's narrow ascending limb differed significantly from those of the arm (P=0.004) and funnel retractor (P=0.012). We further characterized the tentacle preparation's maximum isometric stress (315±78 kPa), maximum unloaded shortening velocity (2.97±0.55L0 s−1) and ultrastructural traits (compared with the arm), which may explain its broader length–force relationship. Comparison of obliquely striated muscles across taxa revealed length–force relationship diversity, with only two species exhibiting superelongation. 

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