ATP binding and cross‐bridge detachment steps during full Ca2+ activation: comparison of myofibril and muscle fibre mechanics by sinusoidal analysis
Authors: Iorga Bogdan , Wang Li , Stehle Robert , Pfitzer Gabriele , Kawai Masataka 
Published: May 2012

Key points
Sinusoidal length change was employed to study the single myofibril mechanics during full Ca2+ activation for the first time, and the tension time course results were compared with those of single muscle fibres.
With myofibrils, the rate constants of exponential processes (tension transients) B and C were very close to each other at 8 mm phosphate, indicating that they could not be analysed independently. Thus, the sum and the product of the two rate constants were fitted to a cross‐bridge model.
The results demonstrate that the association constant of MgATP to cross‐bridge is K1= 2.91 mm−1, and the rate constants of the cross‐bridge detachment step are k2= 288 s−1 and k−2= 10 s−1. These values compare to those for fibres: K1= 2.35 mm−1, k2= 243 s−1, and k−2= 6 s−1, which are respectively not significantly different from myofibril values.
With inspection of video records, we did not observe any local shortening, wave propagation, or sarcomere inhomogeneity along myofibrils during isometric contraction or while applying sinusoidal length oscillations, indicating the integrity of the analysis method and the data acquired.
Abstract  Single myofibrils 50–60 μm in length and 2–3 μm in diameter were isolated from rabbit psoas muscle fibres, and cross‐bridge kinetics were studied by small perturbations of the length (∼0.2%) over a range of 15 frequencies (1–250 Hz). The experiments were performed at 15°C in the presence of 0.05–10 mm MgATP, 8 mm phosphate (Pi), 200 mm ionic strength with KAc (acetate), pCa 4.35–4.65, and pH 7.0. Two exponential processes, B and C, were resolved in tension transients. Their apparent rate constants (2πb and 2πc) increased as the [MgATP] was raised from 0.05 mm to 1 mm, and then reached saturation at [MgATP] ≥ 1. Given that these rate constants were similar (c/b∼1.7) at [Pi]≥ 4 mm, they were combined to achieve an accurate estimate of the kinetic constants: their sum and product were analysed as functions of [MgATP]. These analyses yielded K1= 2.91 ± 0.31 mm−1, k2= 288 ± 36 s−1, and k−2= 10 ± 21 s−1 (±95% confidence limit, n= 13 preparations), based on the cross‐bridge model: AM+ATP ↔ (step 1) AM.ATP ↔ (step 2) A+M.ATP, where K1 is the ATP association constant (step 1), k2 is the rate constant of the cross‐bridge detachment (step 2), and k−2 is the rate constant of its reversal step. These kinetic constants are respectively comparable to those observed in single fibres from rabbit psoas (K1= 2.35 ± 0.31 mm−1, k2= 243 ± 22 s−1, and k−2= 6 ± 14 s−1; n= 8 preparations) when analysed by the same methods and under the same experimental conditions. These values are respectively not significantly different from those obtained in myofibrils, indicating that the same kinetic constants can be deduced from myofibril and muscle fibre studies, in terms of ATP binding and cross‐bridge detachments steps. The fact that K1 in myofibrils is 1.2 times that in fibres (P≈ 0.05) may be explained by a small concentration gradient of ATP, ADP and/or Pi in single fibres.