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Cross-bridge movement and stiffness during the rise of tension in skeletal muscle – a theoretical analysis

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Abstract

Predictions for the time courses of cross-bridge attachment, N(t), stiffness, S(t), and force, T(t), during the tetanus rise were analysed for a special class of cross-bridge models where cross-bridges initially attach in a non-stereospecific weak-binding state, A w. This state is in rapid equilibrium (equilibrium constant K) with detached states and the force generating transition (rate constant F +) is delayed. One model (model IA) which assumed step-function rise of activation at onset of tetanus, gave a poor fit to the experimental data (judged by root mean square error, RMSe ≈ 0.038) but the experimentally observed lead of N(t) over T(t) was reproduced qualitatively. An activation mechanism where K increased towards its maximum value according to an exponential function (Model IB) improved the fit considerably (RMSe ≈ 0.013). However, the activation time constant (τ = 30 ms) derived in the fit was too high to reflect Ca2+ binding to troponin. In a further developed model (model II) both Ca2+-binding to troponin and cross-bridge attachment were assumed to be required for full activation. This more complex model gave a good fit to the experimental data (RMSe ≈ 0.013) with a realistic time constant for Ca2+ binding to troponin (9 ms). In both model IB and model II the best fit was obtained with F + ∼ 40 s−1 . An extended version of model IB, with distributed cross-bridge attachment and a series elastic element, gave a fit of similar quality (RMSe ≈ 0.009) as obtained with model IB and model II and with a similar value of F+. The results support the view that weakly bound cross-bridges (state A w) may account for the lead of cross-bridge movement over force during tension rise. It is also shown that, if the stiffness of the myofilaments is non-linear (stiffness increasing with tension) the experimentally observed lead of S(t) over T(t) may, to a significant degree, be attributed to cross-bridges in the state A w.

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  1. Department of Pharmacology, University of Lund, S-223 62 Lund

    A. Månsson

  2. Department of Chemistry and Biomedical Sciences, University of Kalmar, S-391 82, Kalmar, Sweden

    A. Månsson

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Månsson, A. Cross-bridge movement and stiffness during the rise of tension in skeletal muscle – a theoretical analysis. J Muscle Res Cell Motil 21, 383–403 (2000). https://doi.org/10.1023/A:1005682712789

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