The elucidation of the mechanisms of force generation is an important milestone in understanding the molecular basis of muscle contraction. To identify intermediate states of hydrolysis and elementary reactions among various states, two methods have been employed: solution studies of extracted contractile proteins (Taylor, 1979; Eisenberg and Greene, 1980; Geeves et al. 1984) and studies of tension transients in muscle fibres (Pringle, 1967; Huxley and Simmons, 1971; Ford et al. 1977; Kawai and Brandt, 1980). These methods are complementary, and each method has strengths and weaknesses. While solution studies can give detailed information on various intermediate states of the cross-bridge cycle, the outcome of energy transduction (force) cannot be detected using this method. In muscle fibre studies, force can be measured but it is difficult to detect the elementary steps of contraction because multiple states are involved. Our method applies a high-resolution technique called ‘sinusoidal analysis’ to skinned muscle fibres (Pringle, 1967; Kawai and Brandt, 1980; Kawai and Halvorson, 1991) which takes advantage of both methods. The sinusoidal analysis method enables us to deduce details of the cross-bridge scheme and its rate and equilibrium constants (Kawai and Zhao, 1993; Zhao and Kawai, 1993, 1994). The use of skinned fibres enables us to apply chemical perturbations, so that hypotheses can be more rigorously tested than in intact preparations. By studying the temperature-dependence of the equilibrium constants, we obtain information on the molecular forces involved in the actin and myosin interaction which results in force generation. In sinusoidal analysis, the length of single muscle fibres is perturbed with sine waves of varying frequencies and a low amplitude (±1.6 nm per half-sarcomere). From the tension time course, the elastic modulus and viscous modulus of the fibres are obtained. The elastic modulus is the in-phase component of the tension change and the viscous modulus is the quadrature (90 ° out of phase) component of the tension change, both with respect to the length change. Both quantities are standardized by using the length and the cross-sectional area of the fibres. The sinusoidal analysis method is in essence a mechanical equivalent of spectroscopy: when the viscous modulus is plotted against frequency (Fig. 1B), the modulus represents the amount of work absorbed by the preparation. We can characterize the property of a preparation by looking at a shift of the peak just as in spectroscopic analysis. What is interesting in muscle is that there is a frequency at which the viscous modulus becomes negative (see Fig. 1B); thereby, the 2565 The Journal of Experimental Biology 199, 2565–2571 (1996) Printed in Great Britain © The Company of Biologists Limited 1996 JEB0413 Recent advances in protein chemistry and the kinetic analysis of tension transients in skeletal muscle fibres have enabled us to elucidate the molecular forces involved in force generation by cross-bridges. On the basis of the temperature effect, we conclude that the elementary step that generates force is an endothermic reaction (the enthalpy change ∆H°=124 kJ mol -1 at 15 °C), which accompanies a large entropy increase (∆S°= 430 J K -1 mol -1 ) and a reduction in the heat capacity (∆C p =-6.4 kJ K -1 mol -1 ). Thus, it can be concluded that the force-generating step is an entropy-driven reaction. The above results suggest that hydrophobic interactions are the primary cause of force generation, and that polar interactions (hydrogen bonding and charge interactions) are involved to a lesser degree. On the basis of the thermodynamic data, we estimate that during force generation approximately 50 nm 2 of surface area is involved for hydrophobic interactions and another 30 nm 2 for polar interactions. These data suggest that both the actomyosin interaction and the cleft closure of the myosin head are essential for force generation. Key words: cross-bridge, temperature effects, enthalpy change, entropy change, hydrophobic interaction, polar interaction, accessible surface area, skeletal muscle. Summary Introduction MOLECULAR FORCES INVOLVED IN FORCE GENERATION DURING SKELETAL MUSCLE CONTRACTION KENNETH P. MURPHY 1 , YAN ZHAO 2 AND MASATAKA KAWAI 2, * 1 Department of Biochemistry and 2 Department of Anatomy, The University of Iowa, College of Medicine, Iowa City, IA 52242, USA Accepted 3 September 1996 *Author for correspondence (e-mail: masataka-kawai@uiowa.edu).