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Energetics of Contraction

C. J. Barclay

10.1002/cphy.c140038

Source: Volume 5, Issue 2, April 2015

Published online: March 2015

Full Article on Wiley Online Library



ABSTRACT

Muscles convert energy from ATP into useful work, which can be used to move limbs and to transport ions across membranes. The energy not converted into work appears as heat. At the start of contraction heat is also produced when Ca2+ binds to troponin‐C and to parvalbumin. Muscles use ATP throughout an isometric contraction at a rate that depends on duration of stimulation, muscle type, temperature and muscle length. Between 30% and 40% of the ATP used during isometric contraction fuels the pumping Ca2+ and Na+ out of the myoplasm. When shortening, muscles produce less force than in an isometric contraction but use ATP at a higher rate and when lengthening force output is higher than the isometric force but rate of ATP splitting is lower. Efficiency quantifies the fraction of the energy provided by ATP that is converted into external work. Each ATP molecule provides 100 zJ of energy that can potentially be converted into work. The mechanics of the myosin cross‐bridge are such that at most 50 zJ of work can be done in one ATP consuming cycle; that is, the maximum efficiency of a cross‐bridge is ∼50%. Cross‐bridges in tortoise muscle approach this limit, producing over 90% of the possible work per cycle. Other muscles are less efficient but contract more rapidly and produce more power. © 2015 American Physiological Society. Compr Physiol 5:961‐995, 2015.

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Figure 1. Figure 1. The dependence of molar enthalpy change for PCr hydrolysis (ΔHPCr) on pH and temperature when [Mg2+] is 1 mmol L−1. Intracellular pH in resting muscle is typically between 7 and 7.2 which correspond to ΔHPCr values of 35 and 37 kJ mol−1, respectively. In that pH range temperature has little effect on ΔHPCr. Reprinted from Ref. (258) with permission from Elsevier.
Figure 2. Figure 2. Comparison of time courses of enthalpy output (•, heat + work) and the enthalpy output expected from the extent of PCr breakdown (O). The vertical separation of the lines and the shaded area represent the magnitude of unexplained enthalpy. Enthalpy production is normalized by muscle dry weight; in the study from which these records were taken (64), the ratio of wet weight to dry weight was 6.3, therefore 500 mJ (g dry)−1 ≈ 80 mJ (g wet)−1. Reprinted from Ref. (64) with permission from John Wiley Inc., ©1979 The Physiological Society.
Figure 3. Figure 3. (A) Time course of heat production from a rat soleus muscle during and after an isometric tetanus. The main figure shows the complete time course of heat production associated with a 6 s tetanus and includes the initial heat output (qi), produced during the contraction, and recovery heat output (qR), produced mainly during the 4 min following the contraction. The inset shows the time course of the initial heat production, the rate of which is constant (∼15 mW g−1), and the force output during stimulation. The rate of recovery heat production reached a maximum ∼30 s after the start of stimulation. (B) Magnitude of PCr breakdown, determined using NMR, during and after 9 s of isometric contraction. For the first 80 s after the end of stimulation the change in [PCr] follows an exponential time course as PCr is regenerated (inset to Fig. 3B). At ∼100 s after the end of stimulation further PCr splitting occurred. Note that PCr concentration was normalized by muscle wet weight and heat output was normalized by dry weight; the ratio of wet weight to dry wet was taken to be 5 in that study. Experiment details: temperature, 20°C; stimulus frequency/duration, 35 Hz/ 6 s or 9 s. Both figures from Ref. (200) with permission from John Wiley Inc., ©1993 The Physiological Society.
Figure 4. Figure 4. Comparison of the measured and predicted time courses of heat production from a rat soleus muscle during and after an isometric tetanus. The upper line is the measured heat output and the lower line the heat output predicted from the extent of PCr breakdown, measured using NMR, and assuming ΔHPCr = 36 kJ mol−1. Throughout the recording the measured heat is ∼40% greater than that expected on the basis of the measured biochemical change. This indicates that an unknown process is contributing to the initial heat output. Adapted from Ref. (200) with permission from John Wiley Inc., ©1993 The Physiological Society.
Figure 5. Figure 5. Isometric ATP turnover of mammalian muscle and dependencies on temperature and fiber type. (A) ATP turnover in intact preparations of rat and mouse muscle with ATP turnover expressed relative to whole muscle mass; rates include ATP use by cross‐bridge cycling and ion pumps. Open symbols, slow‐twitch muscles; closed symbols, fast‐twitch muscles. Symbols labeled “R” are from rat muscle; other data points for mouse muscle. Points connected by lines were from the same study of temperature dependence of isometric energy turnover (24). Numeric values are given in Table 4. (B) ATP turnover from skinned fibers from rat, rabbit, and human muscle. Labels adjacent to symbols indicate fiber type. Note the difference in the y‐scales in A and B. The inset shows data from rabbit fibers with a fluorescent Pi indicator to determine ATP turnover (107). The rates of ATP breakdown measured in that experiment were an order of magnitude greater than the data from the other skinned fiber experiments shown in the figure but are similar to those for intact fibers. Numeric values given in Table 7.
Figure 6. Figure 6. Records of the time courses of force production (top) and heat output (bottom) of fast‐twitch EDL (black lines) and slow‐twitch soleus (gray lines) muscles from the mouse during isometric contraction. The peak force outputs from the two muscles were similar but the rate of heat output from the fast‐twitch muscle (average, 170 ± 10.5 mW g−1) was five times that from the slow‐twitch muscle (31.8 ± 2.6 mW g−1). These rates correspond to ATP turnovers of 4.7 and 0.88 μmol g−1 s−1 for EDL and soleus, respectively, assuming ΔHPCr was 36 mJ μmol−1 (258). Experiment details: temperature, 20°C; stimulus frequency/duration, EDL, 70 Hz/1 s; Soleus, 40 Hz/1.5 s. Adapted from Ref. (168) with permission from the American Physiological Society.
Figure 7. Figure 7. Measurement of activation heat in frog semitendinosus muscle at 0°C. The upper panel shows records of twitch force and heat production at 4 different muscle lengths from l0 (a) and in progressive steps to 1.5 × l0 in d. The graph shows heat output plotted as a function of twitch force for multiple measurements at different lengths >l0 for one muscle. Note that force decreased as muscle length was increased. The intercept on the y‐axis is the activation heat. Adapted from Ref. (129) with permission from John Wiley Inc., ©1972 The Physiological Society.
Figure 8. Figure 8. The dependence of force output and rate of ATP hydrolysis on sarcomere length. Data from skinned fibers from rabbit psoas muscle at 10°C. The only ATP‐consuming process in the fibers was cross‐bridge cycling. Therefore, when filament overlap was reduced by increasing sarcomere length above 2.5 μm force output and rate of ATP splitting were reduced to the same extent and in proportion to the degree of reduction in overlap. At short sarcomere lengths (i.e., <2.5 μm), force output declined markedly but the decline in rate of ATP utilization was much smaller. Adapted from Ref. (111) with permission from John Wiley Inc., ©2001 The Physiological Society.
Figure 9. Figure 9. (A) Records of force (top), change in sarcomere length (middle), and heat output (bottom) from a frog (R. pipiens) sartorius muscle at 0°C during a contraction containing a period of shortening. Isovelocity shortening at 0.8 l0 s−1 started after 0.75 s isometric contraction (indicated by dashed line). The amplitude of shortening was ∼15% l0. During shortening, force output is lower than the isometric value and rate of heat output is higher (compare record labeled e (contraction with shortening) to record f (from an isometric contraction). The spikes on the heat records are artifacts arising from the stimulus pulses. Muscle length 11.9 mm, mass 77.8 mg. Reprinted from Ref. (123) with permission from John Wiley Inc., ©1983 The Physiological Society. (B) Shortening velocity dependence of power and enthalpy outputs. Power output (solid symbols) and rate of enthalpy output (open symbols) from frog muscle at 0°C. Figure drawn using data taken from Ref. (114) with permission from the Royal Society.
Figure 10. Figure 10. The shortening velocity dependence of enthalpy efficiency of frog muscle at 0°C. Enthalpy efficiency is ratio of work output to enthalpy output. In the example shown maximum efficiency was 0.43 and occurred at a shortening velocity of ∼20% vmax. The inset shows the same efficiency data plotted as a function of afterload. Figure adapted from Fig. 1 in Ref. (115) with permission of the Royal Society.
Figure 11. Figure 11. The shortening velocity dependencies of power output, enthalpy output, and efficiency during steady shortening of fast‐ and slow‐twitch mouse muscles. Data are shown for mouse EDL (•) and soleus (O) muscles at 30°C. (A) Peak power output of soleus was lower and occurred at a lower absolute shortening velocity than for EDL. Mean vmax: soleus, 5.2 l0 s−1; EDL, 8.9 l0 s−1. (B) Rate of enthalpy output was higher at all shortening velocities in EDL than soleus. At velocities >50% vmax, rate of enthalpy output declined with increasing velocity. (C) Enthalpy efficiency was calculated as w·/(w·+h·). Maximum efficiency of soleus (mean ± S.E, 0.46 ± 0.01, n = 5) was higher than that of EDL (0.30 ± 0.01, n = 5) but efficiency of EDL was close to its maximum value across a broad velocity range. Adapted from Ref. (24) with permission from John Wiley Inc., ©2010 The Physiological Society.
Figure 12. Figure 12. Records of force output and heat output from a frog single muscle fiber at 1°C during a contraction containing a period of constant velocity lengthening. Lengthening (indicated by upper trace) started after 0.5 s isometric contraction. During lengthening, the force output was ∼50% greater than the isometric force and the rate of heat output was greater than that during the isometric phase. While lengthening, the rate of enthalpy change (heat + work) was negative; that is, energy was being absorbed so not all of the work being done on the muscle (lower record) appeared as heat. Adapted from Ref. (175) with permission from John Wiley & Sons Inc., Copyright ©2014 The Physiological Society.
Figure 13. Figure 13. Variations in force, fraction of cross‐bridges attached and cross‐bridge strain with velocity for frog muscle at 0°C. Fraction of cross‐bridges attached and cross‐bridge strain calculated from fiber stiffness measurements corrected for filament compliance. For each variable, values are expressed as a percentage of the value during isometric contraction. For shortening velocities between 0 and ∼50% vmax and for most lengthening velocities, force output (•) reflects variation in only the number of attached cross‐bridges (□); that is, variation in the number of attached cross‐bridges determines muscle force output across most of the force‐velocity relationship (202). Only at high shortening velocities was there a decrease in average cross‐bridge strain (▵). The increase in force during lengthening corresponds to a proportional increase in the number of attached cross‐bridges, consistent with the idea that the second cross‐bridge of each pair attaches during lengthening (35). Reprinted from Ref. (23) with permission from Elsevier.
Figure 14. Figure 14. (A) Records of muscle length, force output, and energy output during a cyclic contraction protocol. Records from a fiber bundle from mouse soleus muscle at 31°C. The period of stimulation in each cycle is indicated by the vertical dotted lines. Note that more than half the work performed in each cycle (middle record, lower panel) is performed after the end of stimulation. It is proposed that performance of work during relaxation increases efficiency. (B) Variations in power output, heat output, and rate of enthalpy output (labeled “Total”) with cycle frequency. Rate of heat output did not vary with contraction frequency. Maximum enthalpy efficiency (power/rate of enthalpy output) was 0.52 at a frequency of 3 Hz. Reprinted from Ref. (10) with permission from the Company of Biologists.
Figure 15. Figure 15. Temperature dependence of the apparent equilibrium constant for creatine kinase (K'). There is a linear dependence of log10(K') on 1/temperature. Temperatures in °C are shown alongside each point and absolute values of K' are shown adjacent to the vertical axis. Adapted, with permission, from Ref. (233) with permission from The American Society for Biochemistry and Molecular Biology.
Figure 16. Figure 16. T2 curves can be used to estimate the maximum work a cross‐bridge can perform in one attachment cycle. (A) T2 force is the force reached after the rapid force recovery following application of a fast, small change in fiber length to a contracting muscle. The upper record shows the change in fiber length and the lower record the force response. The quick recovery of force to the T2 level is thought to be due to redevelopment of force by cross‐bridges attached to the thin filament when the step was applied. Adapted from Fig. 6B of Ref. (81) with permission from John Wiley Inc., ©1977 The Physiological Society. (B) T2 forces for muscle fibers from frog, dogfish and rat. T2 forces are expressed relative to maximum isometric force (P0). Forces are plotted against the amplitude of the fiber length change, after correction for filament compliance; that is, the x‐axis indicates the step amplitude transmitted to the attached cross‐bridges (ΔL). To calculate ΔL, filament compliance was taken to be 0.012 μm kPa−1 h−1 for frog fibers (23), 0.017 μm kPa−1 h−1 for dogfish fibers (197) and 0.015 μm kPa−1 h−1 for rat fibers (172). The solid curve is a third‐order polynomial fitted through all the data. The area under that curve between ΔL of +2.75 nm h−1 and −11 nm h−1 was taken to be the maximum work that a cross‐bridge could perform in one attachment cycle; that area is 9.95 T0 nm. Adapted, with permission, from Ref. (24) with permission from John Wiley Inc., ©2010 The Physiological Society.


Figure 1. The dependence of molar enthalpy change for PCr hydrolysis (ΔHPCr) on pH and temperature when [Mg2+] is 1 mmol L−1. Intracellular pH in resting muscle is typically between 7 and 7.2 which correspond to ΔHPCr values of 35 and 37 kJ mol−1, respectively. In that pH range temperature has little effect on ΔHPCr. Reprinted from Ref. (258) with permission from Elsevier.


Figure 2. Comparison of time courses of enthalpy output (•, heat + work) and the enthalpy output expected from the extent of PCr breakdown (O). The vertical separation of the lines and the shaded area represent the magnitude of unexplained enthalpy. Enthalpy production is normalized by muscle dry weight; in the study from which these records were taken (64), the ratio of wet weight to dry weight was 6.3, therefore 500 mJ (g dry)−1 ≈ 80 mJ (g wet)−1. Reprinted from Ref. (64) with permission from John Wiley Inc., ©1979 The Physiological Society.


Figure 3. (A) Time course of heat production from a rat soleus muscle during and after an isometric tetanus. The main figure shows the complete time course of heat production associated with a 6 s tetanus and includes the initial heat output (qi), produced during the contraction, and recovery heat output (qR), produced mainly during the 4 min following the contraction. The inset shows the time course of the initial heat production, the rate of which is constant (∼15 mW g−1), and the force output during stimulation. The rate of recovery heat production reached a maximum ∼30 s after the start of stimulation. (B) Magnitude of PCr breakdown, determined using NMR, during and after 9 s of isometric contraction. For the first 80 s after the end of stimulation the change in [PCr] follows an exponential time course as PCr is regenerated (inset to Fig. 3B). At ∼100 s after the end of stimulation further PCr splitting occurred. Note that PCr concentration was normalized by muscle wet weight and heat output was normalized by dry weight; the ratio of wet weight to dry wet was taken to be 5 in that study. Experiment details: temperature, 20°C; stimulus frequency/duration, 35 Hz/ 6 s or 9 s. Both figures from Ref. (200) with permission from John Wiley Inc., ©1993 The Physiological Society.


Figure 4. Comparison of the measured and predicted time courses of heat production from a rat soleus muscle during and after an isometric tetanus. The upper line is the measured heat output and the lower line the heat output predicted from the extent of PCr breakdown, measured using NMR, and assuming ΔHPCr = 36 kJ mol−1. Throughout the recording the measured heat is ∼40% greater than that expected on the basis of the measured biochemical change. This indicates that an unknown process is contributing to the initial heat output. Adapted from Ref. (200) with permission from John Wiley Inc., ©1993 The Physiological Society.


Figure 5. Isometric ATP turnover of mammalian muscle and dependencies on temperature and fiber type. (A) ATP turnover in intact preparations of rat and mouse muscle with ATP turnover expressed relative to whole muscle mass; rates include ATP use by cross‐bridge cycling and ion pumps. Open symbols, slow‐twitch muscles; closed symbols, fast‐twitch muscles. Symbols labeled “R” are from rat muscle; other data points for mouse muscle. Points connected by lines were from the same study of temperature dependence of isometric energy turnover (24). Numeric values are given in Table 4. (B) ATP turnover from skinned fibers from rat, rabbit, and human muscle. Labels adjacent to symbols indicate fiber type. Note the difference in the y‐scales in A and B. The inset shows data from rabbit fibers with a fluorescent Pi indicator to determine ATP turnover (107). The rates of ATP breakdown measured in that experiment were an order of magnitude greater than the data from the other skinned fiber experiments shown in the figure but are similar to those for intact fibers. Numeric values given in Table 7.


Figure 6. Records of the time courses of force production (top) and heat output (bottom) of fast‐twitch EDL (black lines) and slow‐twitch soleus (gray lines) muscles from the mouse during isometric contraction. The peak force outputs from the two muscles were similar but the rate of heat output from the fast‐twitch muscle (average, 170 ± 10.5 mW g−1) was five times that from the slow‐twitch muscle (31.8 ± 2.6 mW g−1). These rates correspond to ATP turnovers of 4.7 and 0.88 μmol g−1 s−1 for EDL and soleus, respectively, assuming ΔHPCr was 36 mJ μmol−1 (258). Experiment details: temperature, 20°C; stimulus frequency/duration, EDL, 70 Hz/1 s; Soleus, 40 Hz/1.5 s. Adapted from Ref. (168) with permission from the American Physiological Society.


Figure 7. Measurement of activation heat in frog semitendinosus muscle at 0°C. The upper panel shows records of twitch force and heat production at 4 different muscle lengths from l0 (a) and in progressive steps to 1.5 × l0 in d. The graph shows heat output plotted as a function of twitch force for multiple measurements at different lengths >l0 for one muscle. Note that force decreased as muscle length was increased. The intercept on the y‐axis is the activation heat. Adapted from Ref. (129) with permission from John Wiley Inc., ©1972 The Physiological Society.


Figure 8. The dependence of force output and rate of ATP hydrolysis on sarcomere length. Data from skinned fibers from rabbit psoas muscle at 10°C. The only ATP‐consuming process in the fibers was cross‐bridge cycling. Therefore, when filament overlap was reduced by increasing sarcomere length above 2.5 μm force output and rate of ATP splitting were reduced to the same extent and in proportion to the degree of reduction in overlap. At short sarcomere lengths (i.e., <2.5 μm), force output declined markedly but the decline in rate of ATP utilization was much smaller. Adapted from Ref. (111) with permission from John Wiley Inc., ©2001 The Physiological Society.


Figure 9. (A) Records of force (top), change in sarcomere length (middle), and heat output (bottom) from a frog (R. pipiens) sartorius muscle at 0°C during a contraction containing a period of shortening. Isovelocity shortening at 0.8 l0 s−1 started after 0.75 s isometric contraction (indicated by dashed line). The amplitude of shortening was ∼15% l0. During shortening, force output is lower than the isometric value and rate of heat output is higher (compare record labeled e (contraction with shortening) to record f (from an isometric contraction). The spikes on the heat records are artifacts arising from the stimulus pulses. Muscle length 11.9 mm, mass 77.8 mg. Reprinted from Ref. (123) with permission from John Wiley Inc., ©1983 The Physiological Society. (B) Shortening velocity dependence of power and enthalpy outputs. Power output (solid symbols) and rate of enthalpy output (open symbols) from frog muscle at 0°C. Figure drawn using data taken from Ref. (114) with permission from the Royal Society.


Figure 10. The shortening velocity dependence of enthalpy efficiency of frog muscle at 0°C. Enthalpy efficiency is ratio of work output to enthalpy output. In the example shown maximum efficiency was 0.43 and occurred at a shortening velocity of ∼20% vmax. The inset shows the same efficiency data plotted as a function of afterload. Figure adapted from Fig. 1 in Ref. (115) with permission of the Royal Society.


Figure 11. The shortening velocity dependencies of power output, enthalpy output, and efficiency during steady shortening of fast‐ and slow‐twitch mouse muscles. Data are shown for mouse EDL (•) and soleus (O) muscles at 30°C. (A) Peak power output of soleus was lower and occurred at a lower absolute shortening velocity than for EDL. Mean vmax: soleus, 5.2 l0 s−1; EDL, 8.9 l0 s−1. (B) Rate of enthalpy output was higher at all shortening velocities in EDL than soleus. At velocities >50% vmax, rate of enthalpy output declined with increasing velocity. (C) Enthalpy efficiency was calculated as w·/(w·+h·). Maximum efficiency of soleus (mean ± S.E, 0.46 ± 0.01, n = 5) was higher than that of EDL (0.30 ± 0.01, n = 5) but efficiency of EDL was close to its maximum value across a broad velocity range. Adapted from Ref. (24) with permission from John Wiley Inc., ©2010 The Physiological Society.


Figure 12. Records of force output and heat output from a frog single muscle fiber at 1°C during a contraction containing a period of constant velocity lengthening. Lengthening (indicated by upper trace) started after 0.5 s isometric contraction. During lengthening, the force output was ∼50% greater than the isometric force and the rate of heat output was greater than that during the isometric phase. While lengthening, the rate of enthalpy change (heat + work) was negative; that is, energy was being absorbed so not all of the work being done on the muscle (lower record) appeared as heat. Adapted from Ref. (175) with permission from John Wiley & Sons Inc., Copyright ©2014 The Physiological Society.


Figure 13. Variations in force, fraction of cross‐bridges attached and cross‐bridge strain with velocity for frog muscle at 0°C. Fraction of cross‐bridges attached and cross‐bridge strain calculated from fiber stiffness measurements corrected for filament compliance. For each variable, values are expressed as a percentage of the value during isometric contraction. For shortening velocities between 0 and ∼50% vmax and for most lengthening velocities, force output (•) reflects variation in only the number of attached cross‐bridges (□); that is, variation in the number of attached cross‐bridges determines muscle force output across most of the force‐velocity relationship (202). Only at high shortening velocities was there a decrease in average cross‐bridge strain (▵). The increase in force during lengthening corresponds to a proportional increase in the number of attached cross‐bridges, consistent with the idea that the second cross‐bridge of each pair attaches during lengthening (35). Reprinted from Ref. (23) with permission from Elsevier.


Figure 14. (A) Records of muscle length, force output, and energy output during a cyclic contraction protocol. Records from a fiber bundle from mouse soleus muscle at 31°C. The period of stimulation in each cycle is indicated by the vertical dotted lines. Note that more than half the work performed in each cycle (middle record, lower panel) is performed after the end of stimulation. It is proposed that performance of work during relaxation increases efficiency. (B) Variations in power output, heat output, and rate of enthalpy output (labeled “Total”) with cycle frequency. Rate of heat output did not vary with contraction frequency. Maximum enthalpy efficiency (power/rate of enthalpy output) was 0.52 at a frequency of 3 Hz. Reprinted from Ref. (10) with permission from the Company of Biologists.


Figure 15. Temperature dependence of the apparent equilibrium constant for creatine kinase (K'). There is a linear dependence of log10(K') on 1/temperature. Temperatures in °C are shown alongside each point and absolute values of K' are shown adjacent to the vertical axis. Adapted, with permission, from Ref. (233) with permission from The American Society for Biochemistry and Molecular Biology.


Figure 16. T2 curves can be used to estimate the maximum work a cross‐bridge can perform in one attachment cycle. (A) T2 force is the force reached after the rapid force recovery following application of a fast, small change in fiber length to a contracting muscle. The upper record shows the change in fiber length and the lower record the force response. The quick recovery of force to the T2 level is thought to be due to redevelopment of force by cross‐bridges attached to the thin filament when the step was applied. Adapted from Fig. 6B of Ref. (81) with permission from John Wiley Inc., ©1977 The Physiological Society. (B) T2 forces for muscle fibers from frog, dogfish and rat. T2 forces are expressed relative to maximum isometric force (P0). Forces are plotted against the amplitude of the fiber length change, after correction for filament compliance; that is, the x‐axis indicates the step amplitude transmitted to the attached cross‐bridges (ΔL). To calculate ΔL, filament compliance was taken to be 0.012 μm kPa−1 h−1 for frog fibers (23), 0.017 μm kPa−1 h−1 for dogfish fibers (197) and 0.015 μm kPa−1 h−1 for rat fibers (172). The solid curve is a third‐order polynomial fitted through all the data. The area under that curve between ΔL of +2.75 nm h−1 and −11 nm h−1 was taken to be the maximum work that a cross‐bridge could perform in one attachment cycle; that area is 9.95 T0 nm. Adapted, with permission, from Ref. (24) with permission from John Wiley Inc., ©2010 The Physiological Society.
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Article Title: Energetics of Contraction
 

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C. J. Barclay. Energetics of Contraction. Compr Physiol 2015, 5: 961-995. doi: 10.1002/cphy.c140038