Analyzing and Simulating the Force Development of Active Muscle Fibers During Lengthening

  • Millard, Matthew (University of Stuttgart)
  • Tomalka, André (University of Stuttgart)
  • Siebert, Tobias (University of Stuttgart)
  • Rode, Christian (University of Rostock)

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Locomotion, athletic movements, and some injuries cause active muscles to be lengthened. When active muscle is lengthened, it can develop larger forces than are otherwise possible. To simulate these events, muscle models should accurately develop the same enhanced forces in response to active lengthening as biological muscle. Tomalka et al. [1] recently made a surprising observation: skinned active muscle fibers produce a linear increase in force during constant velocity stretches across the active force-length relation fL(lN) (where lN is the normalized fiber length). Even more intriguing, when the active fiber was stretched from 0.70-1.15 lo (where lo is the optimal fiber length), 0.85-1.30 lo, and 1.0-1.45 lo the resulting force profiles are all linear and nearly parallel. Conventional thinking would suggest that the force profile should contain a bell-shaped artefact from fL(lN) as the cross-bridge force contribution increases and decreases as lN crosses lo. Instead, no hint of fL(lN) is visible in Tomalka et al.'s measurements. Titin [2] is the only other known structure that could influence the force profile in Tomalka et al.'s experiments [1]. In an active muscle, parts of titin are thought to bind to actin, reducing the length of titin available to stretch and increasing its stiffness [2]. Assuming that crossbridge forces are proportional to fL(lN) during Tomalka et al.'s experiments [1], we estimate titin's force contribution, and then simulate these experiments using the VEXAT model [3] to evaluate a possible mechanism. Our estimation of titin's force contribution suggests that titin's active force-length relation is stiffer when lengthening begins at longer fiber lengths. One mechanism that might explain these data is if the point Q on titin that attaches to actin is not constant but varies with fiber length. When we fit the point-of-attachment Q of the VEXAT's titin model [3], the resulting force profiles do resemble Tomalka et al.'s experimental data [1], and so, our proposed mechanism remains a viable candidate. REFERENCES [1] Tomalka A, Rode C, Schumacher J, Siebert T. Proc R Soc Lond B Biol Sci, 284, 20162497, 2017. [2] Linke WA. J Biomech, 152, 111553, 2023. [3] Millard M, Franklin DW, Herzog W. eLife, 12, RP88344, 2024.