Cross-bridge mechanics estimated from skeletal muscles’ work-loop responses to impacts in legged locomotion

Figures

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  Figure 1. Decline of isometric muscle force (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varvec{F}}$$\end{document}F) at TD versus time after muscle extraction. Only trials with TD force of at least 95% of its isometric value (converged force before or after TD) were included. The solid line is a linear fit to all data points below 40 min extrapolated back to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$t=0$$\end{document}t=0. \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{\dag }$$\end{document}†The measured isometric force in cat m. soleus in response to induced ischaemia from Mortimer et al.17. In the shown trial, they stimulated the cat…

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  Figure 2. Energy dissipated and viscous damping coefficient of MTC and CE for all isometric and passive force states. (a–d) Data in each trial are calculated for one work-loop, i.e. one oscillation period that spans between TD and the instant when \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$a_{COM}$$\end{document}aCOM returns closest to zero for the second time. See Fig. 3 for an example of one work-loop in a specific trial. For (a–d), the dashed, black line is the mean value of all data points \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$>\,16\,\hbox {N}$$\end{document}>16N: \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$17\,\upmu \hbox…

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  Figure 3. The work-loops of CE (a) and MTC (b) in one passive exemplary trial. The solid, dark-grey loops are the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_{CE,0}$$\end{document}LCE,0 or \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_{MTC,0}$$\end{document}LMTC,0 responses, respectively, to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta F$$\end{document}ΔF. The solid, thin, black line is the respective linear 2-parameter (force (length)) fit to the data. The solid, black loops depict the respective 3-parameter fits to the data, using the parameters \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym}…

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  Figure 4. Contractile element stiffness (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{k}}_{{{{CE}}}}$$\end{document}kCE). Trial specific \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{CE}$$\end{document}kCE values were inferred from a 3-parameter fit (Eq. 1), with information from one oscillation period after TD (Supplementary Fig. S1). \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{CE}$$\end{document}kCE is also given as scaled to the dimension of one representative half-sarcomere (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs}…

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  Figure 5. Elements that, according to model1 and model2, contribute to the half-sarcomere stiffness \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{hs}$$\end{document}khs. In the elastic model1, the myofilament compliance (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_{fil}$$\end{document}Cfil) is in series with stiffnes \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{CB}$$\end{document}kCB the number of attached in-parallel myosin heads (cross-bridges, CB). The force generated by a single cross-bridge is assumed to be a constant, with an associated constant deflection (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym}…

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  Figure 6. Drawing of the experimental setup. (a) The frame before TD. GAS is fixed between the upper and lower clamp (solid dark-grey rectangles). Above the upper clamp is an insulator (solid, black rectangle) and the force transducer, respectively, which are both fixated to the frame backbone (squared C-shape). The solid, black insulators prevent muscle stimulation to interfere with the force transducer. The light-grey spots on the muscle belly are illustrating the steel markers that pattern the muscle belly, which we used to calculate the dynamic force change between MTC ends in response to the impact (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta F\,=\,\ddot{\overline{BM}}\cdot m\,=\,a_{COM}\cdot m$$\end{document}ΔF=BM¯¨·m=aCOM·m) after TD, with m being the GAS mass, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt}…