Molecular Forces Involved in Force Generation During Skeletal Muscle Contraction

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 muscle generates work on the forcing apparatus. This quantity is called ‘oscillatory work’ (Pringle, 1967; Kawai and Brandt, 1980) and it includes information on the step that generates force (Kawai and Halvorson, 1991; Zhao and Kawai, 1994). Our focus in this paper is on how the characteristic frequency of oscillatory work changes with the phosphate concentration and temperature. In muscle fibres, inorganic phosphate (P_i) is known to perturb the force-generating step and its neighbouring reaction steps (Rüegg et al. 1971; Kawai and Halvorson, 1991; Fortune et al. 1991; Dantzig et al. 1992; Walker et al. 1992). From the temperature-dependence of the equilibrium constant, the entropy, enthalpy and heat capacity changes are obtained. These thermodynamic parameters can then be used to estimate the changes in hydrophobic and polar surface areas using empirically derived relationships (Murphy et al. 1992).

Chemicals and solutions were prepared as reported in Zhao and Kawai (1994). The relaxing solution contained (in mmol l⁻¹): 6 EGTA, 2 MgATP, 5 free ATP, 8 potassium phosphate, 48 potassium propionate, 62 sodium propionate and 10 3-[N-Morpholino]propane-sulfonic acid (MOPS). The activating solutions used for the P_i study contained (in mmol l⁻¹): 6 CaEGTA, 5.3 MgATP, 4.7 free ATP, 15 creatine phosphate, 0–24 potassium phosphate (K_1.5H_1.5PO₄), 57–0 potassium propionate (compensated for the change in [potassium phosphate]), 25 sodium propionate, 10 MOPS and 160 units ml−1 of creatine kinase (CK). pCa (=—log[Ca2+]) of this solution was 4.82, pMg was 3.68 and [MgATP] was 5.0 mmol l−1. The rigor solution contained (in mmol l−1): 8 potassium phosphate, 76 sodium propionate, 103 potassium propionate and 10 MOPS. In all solutions used for experiments, ionic strength was adjusted to 200 mmol l−1 with sodium/potassium propionate and pH was adjusted to 7.00±0.01. The CK level was doubled for experiments at 25 °C and quadrupled for experiments at 30 °C. Chemically skinned psoas muscle fibres were prepared from rabbits as reported in Zhao and Kawai (1994). Preparations consisting of 2–3 fibres were isolated and used for experiments. The ends of the fibres were double-knotted, and each end was placed in a hook made of J-shaped tungsten wire with a gap of about 100 μm. One tungsten wire was connected to the length driver, and the other wire to the tension transducer assembly, as described in Zhao and Kawai (1994). The sarcomere length was adjusted to 2.5 μm. At the end of each experiment, rigor was induced from control activation, and the complex modulus of the rigor state was measured. A preliminary account of the present results was reported at a recent Biophysical Society Meeting (Zhao et al. 1996).

Since sinusoidal analysis is a less commonly employed technique than time-course analysis to study cross-bridge kinetics, an elaboration may be beneficial. The following experiments illustrate this analysis method. A preparation consisting of two fibres was initially relaxed in the relaxing solution. The preparation was then activated with the control activating solution that contained (in mmol l⁻¹): 6 CaEGTA, 5.8 MgATP, 1.36 ATP, 15 creatine phosphate, 8 potassium phosphate, 11 sodium propionate, 73 potassium propionate, 10 MOPS and 160 units ml⁻¹CK (pCa 4.66, pMg 3.30, pH 7.0). This was followed by two washes with the rigor solution. These experiments were carried out at 20 °C, 200 mmol l⁻¹ionic strength and with pH adjusted to 7.00. In each condition, sinusoidal analysis was carried out, and results are plotted in Fig. 1. Fig. 1A shows the elastic modulus and Fig. 1B shows the viscous modulus, both of which are plotted against frequency on a logarithmic scale. As seen in Fig. 1, the relaxed fibres do not have much elasticity or viscosity, indicating that cross-bridges are detached or weakly attached. The rigor fibres have a high elasticity and low viscosity, indicating that cross-bridges are strongly attached. In contrast, active fibres demonstrate complex spectra in both elastic and viscous moduli, indicating that cross-bridges are undergoing state changes. Under this condition, two positive peaks (at approximately 0.7 Hz and 100 Hz) and one negative peak (at approximately 14 Hz) are noticeable in the viscous modulus plot (Fig. 1B). These are labelled as the characteristic frequencies a (≈0.7 Hz), b (≈14 Hz) and c (≈100 Hz). When multiplied by 2π, they represent the apparent (=measured) rate constants. Their reciprocals are the time constants and are indicated below Fig. 1B. As seen in Fig. 1B, the three peaks are absent during relaxation or rigor, indicating that these peaks are characteristic of actively cycling cross-bridges.

Of the three frequencies, 2πb is the most interesting because work is produced at this frequency. By following the [P_i]-dependence of 2πb, which increases and saturates as the P_i concentration is gradually raised from 0 to 24 mmol l−1 (Fig. 2), we are able to deduce the following cross-bridge scheme (Kawai and Halvorson, 1991; Zhao and Kawai, 1994):

To deduce thermodynamic parameters, we then studied the effect of temperature on k₄, k₋₄ and K₅. As shown in Fig. 3, k₄ is strikingly temperature-sensitive, whereas k₋₄ and K₅ are weakly temperature-sensitive. The equilibrium constant of the force generation step K₄ is equal to k₄/k₋₄ and is included in Fig. 3. As expected, K₄ increases significantly with temperature. From this observation, we conclude that the force-generating reaction is an endothermic reaction and absorbs heat. These results explain the large increase in isometric tension with temperature both during the steady state (Ford et al. 1977; Bressler, 1981; Ranatunga and Wylie, 1983; Zhao and Kawai, 1994) and after a sudden increase in temperature (Goldman et al. 1987; Bershitsky and Tsaturyan, 1989; Davis and Harrington, 1993). The data of Fig. 4 are fitted to the modified van’t Hoff equation (see Appendix):

The K₄ data from Fig. 3 are replotted on a magnified scale in Fig. 4. The number of total data points was 43. The data with all 43 points were fitted to equation 2 using a standard linear least-squares fitting program (note that equation 2 is linear with respect to three unknowns ΔH°_r, ΔS°_r and ΔC_p). The resulting best-fit curve is plotted in Fig. 4 and the best-fit values of ΔH°_r, ΔS°_r and ΔC_p along with their 95 % confidence ranges as determined from the fit are given in Table 1. For the calculation of 95 % confidence ranges, the facts that 43 data points were used and that there are three unknown parameters in equation 2 were considered. As seen in Fig. 4, the data fit equation 2 well and the three parameters can be determined accurately (Table 1). It should be noted here that ΔH°_r takes on a high positive value (124 kJ mol−), implying that the force-generating transition is an endothermic reaction. It is also

When hydrophobic residues interact, the water molecules surrounding these residues lose structure, resulting in a large entropy increase (Frank and Evans, 1945; Sturtevant, 1977). Thus, high positive values of ΔH°_r and ΔS°_r imply that the force-generating transition is an entropy-driven, hydrophobic interaction. It should also be noted that ΔC_p has a high negative value (—6.4 kJ K⁻¹ mol⁻¹) and is comparable to that observed for the folding of a 126-residue globular protein (Privalov and Gill, 1988). The negative value of ΔC_p is also indicative of hydrophobic interactions and implies that ‘structured’ water is removed (Frank and Evans, 1945).

It has been known for some time that the thermodynamics of the hydrophobic effect scale with the size of the hydrophobic molecule, in particular with the hydrophobic accessible surface area (Hermann, 1972; Gill and Wadsö, 1976; Chothia, 1976). More recently, it was learned that the energetics of hydrogen bonding in proteins can also be scaled with accessible surface area (Murphy and Freire, 1992; Spolar et al. 1992). These observations have led to empirical approaches to calculate the thermodynamics of protein unfolding transitions on the basis of changes in polar and apolar accessible surface areas (denoted ΔA_p and ΔA_ap, respectively). In this method, both ΔH° and ΔC_p are assumed to be linear combinations of contributions from ΔA_p and ΔA_ap. The linear coefficients are determined experimentally from model compounds and protein unfolding data. Using this method, ΔH° and ΔC_p of protein unfolding can be accurately predicted from the protein structure (Murphy and Freire, 1992; Murphy, 1995).

This approach has recently been successfully applied to predicting the thermodynamics of protein–protein interactions including the binding of angiotensin II to a monoclonal antibody (Murphy et al. 1993), the dimerization of interleukin-8 (Burrows et al. 1994) and the binding of pepstatin to endothiapepsin (Gómez and Freire, 1995). The same method has also been used in a reverse sense to estimate ΔA_p and ΔA_ap from experimentally determined thermodynamic parameters (Murphy et al. 1995). In this case, the thermodynamics of binding of two different antibodies to cytochrome c was studied. It was shown that the estimated surface areas were in good agreement with estimates obtained from epitope mapping. In this report, we apply the same principle to estimate the structural changes associated with the force generation step (K₄). Because these interactions involve the same forces (hydrophobic and polar interactions) that are responsible for protein stability, this approach should provide reasonable estimates of accessible surface areas.

The estimated changes in surface area provide insight into the structural effects that accompany force generation. The crystallographic structure of actin (Kabsch et al. 1990) indicates that globular actin is approximately disk-shaped with a diameter of 5.5 nm and a thickness of 3.5 nm, giving rise to a total surface area of approximately 110 nm². Thus, our calculated change in total ASA (80 nm²) is large when compared with the total actin surface area, although only approximately 40 nm² (=80/2) is applicable to actin, because two surfaces are involved in a macromolecular interaction. Evidently, a significant portion of this ASA must be located in the interface between the actin and myosin molecules. A recent computer-aided analysis (Rayment et al. 1993a) revealed that at least five hydrophobic amino acid residues on actin (Ala144, Ile341, Ile345, Leu349, Phe352) and at least eight hydrophobic amino acid residues on myosin (Pro529, Met530, Ile535, Met541, Phe542, Pro543, Tyr626, Gln647) are involved in the stereospecific and hydrophobic interaction when actin and myosin are brought into close proximity so that their contours fit to the three-dimensional reconstruction of the cryo-electron microscope images of F-actin decorated with subfragment-1 (Milligan et al. 1990). However, the combined ASA of these residues is approximately 16 nm², only 31 % of the ΔA_ap estimated here from the thermodynamic analysis. This would suggest either the presence of additional amino acid residues interacting in the actomyosin interface or the presence of a conformational change within the myosin head and/or in the actin molecule. Since 37 % of the actin surface area could not be used for the interaction with myosin, an additional conformational change within the myosin head and/or actin seems likely.

One possibility is a closure of the myosin ‘cleft’ upon force generation. This cleft exists between the upper 50 kDa domain and the lower 50 kDa domain in the heavy chain of the myosin head (Rayment et al. 1993b), and it must be closed for actin and myosin to interact (Rayment et al. 1993a). The closure of this cleft is believed to swing the C-terminal α-helical region of the myosin head, thus propelling the thick filament to cause force generation and filament sliding (Fisher et al. 1995). Our results are consistent with the hypothesis that cleft closure takes place simultaneously with force generation. It is not difficult to imagine that stereospecific interaction between amino acid residues would take place when the upper 50 kDa domain and the lower 50 kDa domain interact through cleft closure. These interactions would account for the large ASA indicated by the thermodynamic data.

In conclusion, our analysis indicates that force is generated simultaneously with the burial of a considerable surface area of actin and myosin, especially of the hydrophobic surface, implying that hydrophobic interactions are the primary cause of force generation. Our analysis also indicates that the surface area associated with polar amino acid residues is involved to a lesser extent. Our analysis further implies that the actomyosin interface is not adequate to account for our data and an additional conformational change, such as the cleft closure of the myosin head, must accompany force generation. Although our analysis provides only an approximate sketch of the structural changes involved in force generation, it should be useful in further modelling of the molecular events that occur during actomyosin interaction and in elucidating the mechanism of force generation by cross-bridges.

This work was supported by The Roy J. Carver Charitable Trust (K.P.M.) and grants from the National Science Foundation IBN93-18120 (M.K.) and the American Heart Association, Iowa Affiliate IA-94-GS-45 (M.K.).