Department of Medical Pharmacology and Physiology, University of Missouri, Columbia, Missouri 65212
Submitted 26 January 2004 ; accepted in final form 7 April 2004
![]() |
ABSTRACT |
---|
![]() ![]() ![]() ![]() ![]() ![]() |
---|
muscle mechanics; force-velocity relationship; cross-bridge cycle
|
Another factor in this cross-bridge schematic is the fact that transition rates vary as a function of load on the muscle, becoming faster as muscle load is reduced. For instance, the rate constant of force decline after rapid increase in solution Pi (kPi) varied linearly as a function of load (18). Thus the rate-limiting steps may be different as the load on the myofilaments changes. For instance, unloaded muscle shortening is likely limited by cross-bridge detachment rates, because cross bridges that remain bound ultimately become an internal load as filaments slide past each other. Thus the speed of shortening of an unloaded muscle is thought to reach its limit when compressive resistance forces equal positive forces (19). At the other intercept of the force-velocity curve, isometric force is ultimately determined by the number of force-generating cross bridges, which is limited by the balance between the rates of force-generating transitions and detachment of positively strained cross bridges. It is unknown which chemomechanical transitions are most important in determining force and shortening speeds and thus power output at intermediate loads where muscles perform work. Because elevations in Pi concentration ([Pi]; from 0 to 15 mM) increase the rate of force development (2, 16, 37, 38) but have no effect on unloaded shortening velocity in skinned fast-twitch skeletal muscle fibers (4, 26, 42), experiments in the presence of increased [Pi] should indicate at which loads shortening velocities are most influenced by Pi transitional states, i.e., those that are associated with weak to strong-binding to force-producing states (steps 35, Fig. 1). Thus we investigated the effects of elevated [Pi] on loaded shortening and power output in permeabilized single cardiac myocytes to gain mechanistic insights into the cross-bridge steps that are most important in determining power output in cardiac myocytes, with particular interest in loads where power output is optimal because these are the loads that in vivo myocytes are thought to encounter during the ejection phase of the cardiac cycle.
![]() |
METHODS |
---|
![]() ![]() ![]() ![]() ![]() ![]() |
---|
Solutions. The relaxing solution in which the ventricles were disrupted, skinned, and resuspended contained (in mM) 2 EGTA, 5 MgCl2, 4 ATP, imidazole 10, and 100 KCl at pH 7.0. Compositions of relaxing and activating solutions used in mechanical measurements were as follows (in mM): 7 EGTA, 1 free Mg2+, 20 imidazole, 4 MgATP, 14.5 creatine phosphate, pH 7.0, Ca2+ concentrations of 109 M (relaxing solution) and 104.5 M (maximal activating solution), and sufficient KCl to adjust ionic strength to 180 mM. Activating solutions used in phosphate experiments were identical to those described above except for inclusion of 2.5, 5, and 10 mM KH2PO4 before adjustment to ionic strength of 180 mM. The final concentrations of each metal, ligand, and metal-ligand complex at 13°C were determined with a computer program (8). Immediately before activations, muscle preparations were immersed for 60 s in a solution of reduced Ca2+-EGTA buffering capacity, identical to normal relaxing solution except that EGTA was reduced to 0.5 mM. This protocol resulted in more rapid steady-state force development and helped preserve the striation pattern during activation.
Experimental apparatus. The experimental apparatus for physiological measurements of myocyte preparations was similar to one previously described in detail (28) and modified specifically for cardiac myocyte preparations (24). Briefly, myocyte preparations were attached between a force transducer and a torque motor by gently placing the ends of the myocyte into stainless steel troughs (25 gauge). The ends of the myocyte were secured by overlaying a 0.5-mm-long piece of 3-0 monofilament nylon suture (Ethicon) onto each end of the myocyte and then tying the suture into the troughs with two loops of 10-0 monofilament suture (Ethicon). The attachment procedure was performed under a stereomicroscope (approximately x100 magnification) with finely shaped forceps.
Before mechanical measurements the experimental apparatus was mounted on the stage of an inverted microscope (model IX-70, Olympus Instrument), which rested on a pneumatic antivibration table with a cutoff frequency of 1 Hz. Force measurements were made with a capacitance-gauge transducer (model 403, sensitivity of 20 mV/mg plus a x10 amplifier and resonant frequency of 600 Hz; Aurora Scientific, Aurora, ON, Canada). Length changes during mechanical measurements were introduced at one end of the preparation with a direct current (DC) torque motor (model 308; Aurora Scientific) driven by voltage commands from a personal computer via a 12-bit digital-to-analog converter (AT-MIO-16E-1; National Instruments, Austin, TX). Force and length signals were digitized at 1 kHz with a 12-bit analog-to-digital converter, and each was displayed and stored on a personal computer with custom software based on LabView for Windows (National Instruments).
Images of the myocyte preparations were recorded digitally on a personal computer while myocytes were relaxed and during activation with a Hamamatsu charge-coupled device camera (model 2400) and video snapshot software (Fig. 2). Videomicroscopy was completed with a x40 objective (Olympus UWD 40) and x25 intermediate lenses. During and after each experiment, the images were reviewed to obtain sarcomere length measurements from the myocyte while relaxed and activated; myocyte length and width for cross-sectional area calculations were also obtained from these images. The sarcomere length of these preparations was set to yield passive forces near zero. The dimensions of the skinned cardiac myocyte preparations are reported in Table 1.
|
|
Isotonic shortening velocities were measured in activating solutions containing varied amounts of additional Pi (0, 2.5, 5, and 10 mM). Each cell underwent a series of loaded contractions in each of the Pi solutions, whose order was chosen at random. In this way, each cell served as its own control and pairwise statistical analysis could be performed. Isometric force was measured in activating solution with no additional Pi before and after measurements of isotonic shortening velocities to detect rundown of the preparation. Myocytes were discarded if a 20% or greater decrease in isometric tension occurred.
The kinetics of force redevelopment were obtained by following a procedure previously described for skinned cardiac myocyte preparations (21). While in Ca2+-activating solution, the myocyte preparation was rapidly shortened by 15% of the myocyte's initial length (Lo) to produce zero force. The myocyte preparation was then allowed to shorten for
20 ms; after 20 ms the preparation was rapidly restretched to
105% of Lo for 2 ms and then returned to Lo. The slack-restretch maneuver caused dissociation of cross bridges, and subsequent force redevelopment was due to reattachment of cross bridges and transition to force-generating states. Force redevelopment measurements were carried out before the series of loaded contractions at each [Pi].
Vo was measured during maximal Ca2+ activations by the slack test method (7, 33). Once steady-state force was reached, the myocyte preparation was rapidly (<2 ms) slackened to a predetermined value between 5% and 20% of its initial length. The time between the imposition of the slack step and the onset of force redevelopment was measured from the intersection of two lines fitted by eye through the zero-force baseline and the initial phase of force redevelopment (Fig. 3). The length of release was plotted against the duration of unloaded shortening, and Vo was determined from the slope of a line fitted to the data by linear regression analysis.
|
![]() | (1) |
Hyperbolic force-velocity curves were fit to the relative force-velocity data using the Hill equation (17):
![]() | (2) |
![]() | (3) |
Force redevelopment traces were fit by a single-exponential function:
![]() |
Statistics. One-way repeated-measures ANOVA was used to determine significant effects on force, absolute and normalized power output, and ktr from varied [Pi]. The Student-Newman-Keuls test was used post hoc to assess the differences among means. A paired t-test was used to compare Vo values before and after addition of 5 mM Pi. P < 0.05 was chosen as indicating significance. Values are expressed as means ± SD unless otherwise indicated.
![]() |
RESULTS |
---|
![]() ![]() ![]() ![]() ![]() ![]() |
---|
Previous studies reported that maximal velocity of shortening (i.e., unloaded) is minimally affected by addition of up to 15 mM added Pi in fast-twitch skeletal muscle fibers (4, 26, 42). We addressed whether Pi alters Vo in cardiac myocyte preparations with slack tests before and after the addition of 5 mM Pi. Figure 3 shows force traces after rapid slack steps in a cardiac myocyte preparation during maximal Ca2+ activation in the presence and absence of 5 mM added Pi. Consistent with skeletal muscle reports, Vo was unchanged in response to added Pi in cardiac myocyte preparations (control 1.83 ± 0.75, 5 mM added Pi 1.75 ± 0.58 muscle lengths/s). This finding suggests that cross-bridge interaction transitions that limit maximal shortening velocity (i.e., detachment of compressively strained cross bridges) are minimally affected by addition of Pi.
A main focus of this study was to examine the effects of added Pi on rates of loaded shortening and power output of cardiac myofibrils. Because previous studies using skinned fiber preparations imply that added Pi speeds force-generating transitions (2, 27) but has no effect on detachment rates of compressively strained cross bridges (see above), the addition of Pi would be expected to increase normalized power only at loads at which loaded shortening is limited by force-generating transition rates. We measured skinned myocyte shortening velocities over a range of loads and plotted averaged force-velocity and power-load curves in response to added Pi (Fig. 2). For these curves, force was normalized for the Pi-induced decrease in isometric force, which allowed direct observation of how Pi alters shortening velocity and power at given relative loads. Addition of Pi sped loaded shortening and increased normalized power output over load ranges above 10% isometric force. Peak normalized power output increased 16% with 2.5 mM added Pi and was further elevated by the addition of 5 and 10 mM to a plateau of
35% greater than that at 0 mM Pi (Fig. 2C). These results together with the Vo results imply that force-generating transition rates (which are Pi dependent) as opposed to detachment rates (of compressively strained cross bridges) determine power output over most load ranges in cardiac myocytes. Interestingly, though, the increase in loaded shortening with added Pi was not great enough to offset the Pi-induced fall in force to maintain absolute power output (Fig. 2D). Peak absolute power output (85 ± 12 pW with no additional Pi) decreased 16% (71 ± 14 pW) with 2.5 mM Pi added, 16% (71 ± 12 pW) with 5 mM Pi, and 52% (41 ± 13 pW) with 10 mM Pi. Thus added Pi increases power output at a given relative load, but not at a specific absolute load, because of its marked effect of depressing force generation capacity.
We also addressed the effects of added Pi on the rate of myocyte force development after a mechanical perturbation to assess the potential role of this process in determining loaded shortening and power output. The rate constant of force redevelopment (ktr) increased in the presence of rising [Pi] (Fig. 4): ktr increased from 6.1 ± 1.4 s1 in controls to 8.5 ± 1.3 s1 in the presence of 2.5 mM Pi, representing a 40% increase from control. Addition of 5 mM and 10 mM Pi further increased ktr 94% (11.8 ± 3.1 s1) and 379% (28.1 ± 7.8 s1) above control, respectively. Interestingly, the residual force (i.e., the force just before force redevelopment) was consistently higher as added Pi increased. Residual forces were 20 ± 3%, 30 ± 3%, 37 ± 4%, and 47 ± 11% of isometric force at 0, 2.5, 5, and 10 mM added Pi, respectively. The exact reason for this is unclear, but it may involve faster transition(s) to force-generating cross bridges as a function of [Pi]. Because of this potentially confounding influence of residual force, we also examined the rate of force redevelopment after a 10% slack step. The rates of force development were 4.77 ± 1.81 s1 with no added Pi and 8.57 ± 2.30 s1 with 5 mM Pi (P = 0.003, n = 6); this result is quantitatively similar to that observed with the slack-restretch maneuver. Overall, these results are quantitatively different from the Pi-induced increase in normalized power output, suggesting that cross-bridge steps that determine power output differ from the transitions that limit force redevelopment in cardiac muscle.
|
![]() |
DISCUSSION |
---|
![]() ![]() ![]() ![]() ![]() ![]() |
---|
The effects of Pi on contractile properties have been examined extensively in both skinned skeletal and cardiac muscle preparations. Interestingly, the contractile properties of cardiac muscle preparations appear to be more sensitive to added Pi than those of skeletal muscle preparations. For instance, Nosek et al. (29) reported that 10 mM added Pi decreased cardiac muscle force 60% compared with a 40% force decline in skeletal muscle preparations in the same study. We also observed that force declined
65% in the cardiac myocyte preparation in response to 10 mM added Pi. Although data from skeletal muscle fiber preparations demonstrate a wide range of force decline in response to added Pi (
3055%), more recent data from myofibrils from fast-twitch skeletal muscle have demonstrated greater effects of Pi (e.g., 70% decline in force) with 10 mM Pi (36). The exact reasons for the differences in Pi responsiveness between fibers and myofibril preparations are unclear but may involve the procedures used to reduce contaminating Pi as described by Pate et al. (30) and used in the myofibril experiments (36, 37). Also, there is likely an inverse relationship between preparation diameter and force decline in response to added [Pi] because of greater accumulation of Pi from myofibrillar ATPases (and thus higher baseline [Pi]) in thicker preparations (20, 32). Regarding other contractile properties, added Pi has been reported to increase kPi (the rate constant of force decline after rapid increases in solution Pi) to a greater extent in cardiac myocyte preparations than in fast-twitch skeletal muscle fibers (2, 41). Additionally, the increase in ktr with added [Pi] (from 0 to 10 mM) was upward of threefold in our skinned cardiac myocyte preparations vs. a 50% increase in fast-twitch skinned skeletal muscle fibers (38). Together these results suggest that contractile properties appear to be more sensitive to elevations in [Pi] in cardiac muscle than skeletal muscle at least over a range of 010 mM added Pi. This may have implications in the response of these two striated types of myofibrils to metabolite (i.e., Pi) buildup associated with ischemia. For cardiac muscle, [Pi] is thought to rise to as high as 30 mM during ischemia (1); such a rise in [Pi] would likely result in a marked fall in force-generating cross bridges, but the faster rates of force development and loaded shortening would tend to compensate to possibly help sustain adequate stroke volume and cardiac output.
A primary purpose of this study was to assess which step(s) in the cross-bridge cycle may be most important in determining myocyte shortening and power output at various loads. In looking at a force-velocity curve (Fig. 5), shortening velocity at low loads is thought to be limited by detachment of compressively strained cross bridges, which appears to be limited by ADP release from actomyosin (31, 44) and/or by mechanical detachment of highly compressed cross bridges (5). Conversely, loaded shortening and power at high loads are thought to be determined by force-generating steps in the cross-bridge cycle, which are thought to be coupled to Pi release (16) and/or an isomerization that is in rapid equilibrium with Pi release from the actomyosin complex (27, 41). The question then arises as to what load the cross-bridge step(s) that limits power shifts from force-generating transitions to detachment rates.
|
Our results are also consistent with similar studies on skeletal muscle fiber preparations that sought insight into which chemomechanical transitions might determine power output at various loads. For example, a study by Ford et al. (13) examined power output over a range of loads in rabbit skinned fast-twitch skeletal muscle fibers and discovered that osmotic compression of fibers resulted in reduced velocity and power at low loads but had little effect at intermediate and high loads. Because osmotic compression reduced Vo, this implies that cross-bridge detachment limits power output at low loads. Consistent with this idea, lowering ATP concentrations or substituting ATP with CTP also reduced Vo and decreased power output only at low loads in rat skinned slow-twitch skeletal muscle fibers (39). A recent study also found that increased [Pi] sped loaded shortening in fast-twitch skeletal muscle fibers at loads greater than 15% isometric force (11). Together these studies suggest that power output in striated myofibrils is rate limited at low loads by the same chemomechanical transitions that limit unloaded shortening speeds and at intermediate and high loads by chemomechanical transitions that are associated with force generation.
Interestingly, the addition of Pi also increased the rates of force development but to a much greater extent than increases in peak normalized power. The exact reasons for the differing Pi dependencies of force development and power are unclear. One possibility is that force development is limited by the cooperative activation of near-neighbor regulatory units on the thin filament by strongly binding cross bridges (10, 12, 34) and addition of Pi increases the number of strongly binding non-force-generating cross bridges (actin-myosin ADP Pi). This is consistent with the finding that Pi addition, like addition of strongly binding N-ethylmaleimide (NEM)-modified cross bridges (35), eliminated the slow phase of unloaded shortening after slack steps in skinned fast-twitch skeletal muscle fibers during submaximal Ca2+ activations (26). Loaded shortening, on the other hand, is not likely limited by the number of strongly bound non-force-generating cross-bridges (actin-myosin ADP Pi), at least during maximal Ca2+ activations (25). Rather, shortening velocity and power output (over most loads) appear to be determined by Pi release steps in the cross-bridge cycle, which are modulated to a different extent than thin filament activation rates by addition of Pi.
In summary, this study implies that myocyte power output is determined by Pi-sensitive force-generating transitions in the cross-bridge cycle as opposed to detachment of compressively strained cross bridges. However, even though Pi speeds loaded shortening at given relative loads, the increase in velocity does not appear to be great enough to compensate for the Pi-induced decrease in force; this yields an overall decrease in absolute power-generating capacity, providing a myofibrillar mechanism for depressed myocardial work capacity and function during ischemia.
|
![]() |
ACKNOWLEDGMENTS |
---|
![]() |
FOOTNOTES |
---|
The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
![]() |
REFERENCES |
---|
![]() ![]() ![]() ![]() ![]() ![]() |
---|
2. Araujo A and Walker JW. Phosphate release and force generation in cardiac myocytes investigated with caged phosphate and caged calcium. Biophys J 70: 23162326, 1996.[Abstract]
3. Cooke R. Actomyosin interaction in striated muscle. Physiol Rev 77: 671697, 1997.
4. Cooke R and Pate E. The effects of ADP and phosphate on the contraction of muscle fibers. Biophys J 48: 789798, 1985.[Abstract]
5. Cooke R, White H, and Pate E. A model of the release of myosin heads from actin in rapidly contracting muscle fibers. Biophys J 66: 778788, 1994.[Abstract]
6. Dantzig JA, Hibberd MG, Trentham DR, and Goldman YE. Cross-bridge kinetics in the presence of MgADP investigated by photolysis of caged ATP in rabbit psoas muscle fibers. J Physiol 432: 639680, 1991.[Abstract]
7. Edman KAP. The velocity of unloaded shortening and its relation to sarcomere length and isometric force in vertebrate muscle fibers. J Physiol 291: 143159, 1979.[Abstract]
8. Fabiato A. Computer programs for calculating total from specified free or free from specified total ionic concentrations in aqueous solutions containing multiple metals and ligands. Methods Enzymol 157: 378417, 1988.[ISI][Medline]
9. Ferenczi MA and Spencer CI. The elementary steps of the actomyosin ATPase in muscle fibres studied by caged-ATP. Adv Exp Med Biol 368: 181188, 1988.
10. Fitzsimons DP, Patel JR, Campbell KS, and Moss RL. Cooperative mechanisms in the activation dependence of the rate of force development in rabbit skinned skeletal muscle fibers. J Gen Physiol 117: 133148, 2001.
11. Fitzsimons DP, Patel JR, Campbell KS, and Moss RL. Effect of phosphate on loaded shortening in skeletal muscle fibers (Abstract). Biophys J 84: 246a, 2003.
12. Fitzsimons DP, Patel JR, and Moss RL. Cross-bridge interaction kinetics in rat myocardium are accelerated by strong binding of myosin to the thin filament. J Physiol 530: 263272, 2001.
13. Ford LE, Nakagawa K, Desper J, and Seow CY. Effect of osmotic compression on force-velocity properties of glycerinated rabbit skeletal muscle cells. J Gen Physiol 97: 7388, 1991.[Abstract]
14. Goldman YE, Hibberd MG, and Trentham DR. Relaxation of rabbit psoas muscle fibres from rigor by photochemical generation of adenosine-5'-triphosphate. J Physiol 354: 577604, 1984.[Abstract]
15. Gordon AM, Homsher E, and Regnier M. Regulation of contraction in striated muscle. Physiol Rev 80: 853924, 2000.
16. Hibberd MG, Dantzig JA, Trentham DR, and Goldman YE. Phosphate release and force generation in skeletal muscle fibers. Science 228: 13171319, 1985.[ISI][Medline]
17. Hill AV. The heat of shortening and the dynamic constants of muscle. Proc R Soc Lond B 126: 136195, 1938.
18. Homsher E, Lacktis J, and Regnier M. Strain-dependent modulation of phosphate transients in rabbit skeletal muscle fibers. Biophys J 72: 17801791, 1997.[Abstract]
19. Huxley AF. Muscle structure and theories of contraction. Prog Biophys Biophys Chem 7: 255318, 1957.
20. Kentish JC. The effects of inorganic phosphate and creatine phosphate on force production in skinned muscles from rat ventricle. J Physiol 370: 585604, 1986.[Abstract]
21. Korte FS, McDonald KS, Harris SP, and Moss RL. Loaded shortening, power output, and rate of force redevelopment are increased with knockout of cardiac myosin binding protein-C. Circ Res 93: 752758, 2003.
22. Lu Z, Swartz DR, Metzger JM, Moss RL, and Walker JW. Regulation of force development studied by photolysis of caged ADP in rabbit skinned psoas fibers. Biophys J 81: 334344, 2001.
23. Ma YZ and Taylor EW. Kinetic mechanism of myofibril ATPase. Biophys J 66: 15421553, 1994.[Abstract]
24. McDonald KS. Ca2+ dependence of loaded shortening in rat skinned cardiac myocytes and skeletal muscle fibers. J Physiol 525: 169181, 2000.
25. McDonald KS and Moss RL. Strongly binding myosin cross-bridges regulate loaded shortening and power output in cardiac myocytes. Circ Res 87: 768773, 2000.
26. Metzger JM. Effect of phosphate and ADP on shortening velocity during maximal and submaximal calcium activation of the thin filament in skeletal muscle fibers. Biophys J 70: 409417, 1996.[Abstract]
27. Millar NC and Homsher E. The effect of phosphate and calcium on force generation in glycerinated rabbit skeletal muscle fibers. J Biol Chem 265: 2023420240, 1990.
28. Moss RL. Sarcomere length-tension relations of frog skinned muscle fibres during calcium activation at short lengths. J Physiol 292: 177202, 1979.[Abstract]
29. Nosek TM, Leal-Cardoso JH, McLaughlin M, and Godt RE. Inhibitory influence of phosphate and arsenate on contraction of skinned skeletal and cardiac muscle. Am J Physiol Cell Physiol 259: C933C939, 1990.
30. Pate E, Franks-Skiba K, and Cooke R. Depletion of phosphate in active muscle fibres probes actomyosin states within the powerstroke. Biophys J 80: 369380, 1998.
31. Siemankowski RF, Wiseman MO, and White HD. ADP dissociation from acto-S1 is sufficiently slow to limit unloaded shortening velocity in muscle. J Biol Chem 260: 658662, 1985.
32. Stienen GJM, Roosemalen MCM, Wilson MGA, and Elzinga G. Depression of force by phosphate in skinned muscle fibers of the frog. Am J Physiol Cell Physiol 259: C349C357, 1990.
33. Strang KT, Sweitzer NK, Greaser ML, and Moss RL. -Adrenergic receptor stimulation increases unloaded shortening velocity of skinned single ventricular myocytes from rats. Circ Res 74: 542549, 1994.[Abstract]
34. Swartz DR and Moss RL. Influence of a strong-binding myosin analogue on calcium-sensitive mechanical properties of skinned skeletal muscle fibers. J Biol Chem 267: 2049720506, 1992.
35. Swartz DR and Moss RL. Strong binding of myosin increases shortening velocity of rabbit skinned skeletal muscle fibers at low levels of calcium. J Physiol 533: 357365, 2001.
36. Tesi C, Colomo F, Piroddi N, and Poggesi C. Characterization of the cross-bridge force generating step using inorganic phosphate and BDM in myofibrils from rabbit skeletal muscle. J Physiol 541: 187199, 2002.
37. Tesi C, Colomo S, Nencini S, Piroddi N, and Poggesi C. The effect of inorganic phosphate on force generation in single myofibrils from rabbit skeletal muscle. Biophys J 78: 30813092, 2000.
38. Wahr PA, Cantor HC, and Metzger JM. Nucleotide-dependent contractile properties of Ca2+-activated fast and slow skeletal muscle fibers. Biophys J 72: 822834, 1997.[Abstract]
39. Wahr PA and Metzger JM. Peak power output is maintained in rabbit psoas and rat soleus single muscle fibers when CTP replaces ATP. J Appl Physiol 85: 7683, 1998.
40. Wahr PA and Metzger JM. Role of Ca2+ and cross-bridges in skeletal muscle thin filament activation probed by Ca2+ sensitizers. Biophys J 76: 21662176, 1999.
41. Walker JW, Lu Z, and Moss RL. Effects of Ca2+ on the kinetics of phosphate release in skeletal muscle. J Biol Chem 267: 18, 1992.
42. Widrick JJ. Effect of Pi on unloaded shortening velocity of slow and fast mammalian muscle fibers. Am J Physiol Cell Physiol 282: C647C653, 2002.
43. Woledge RC, Curtin NA, and Homsher E. Energetic Aspects of Muscle Contraction. London: Academic, 1985, p. 4771.
44. Zhang X, Jiang W, and White HD. Kinetic mechanism of the interaction between myosin subfragment-1 (S1) nucleoside diphosphates, and actin (Abstract). Biophys J 61: 440a, 1992.