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

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, AW. 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 approximately 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 approximately 0.013). However, the activation time constant (r = 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 approximately 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+ approximately 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 approximately 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 AW) 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 AW.