Energetics of contraction.

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Energetics of Contraction C. J. Barclay*1 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.

Introduction Skeletal muscles generate the force and mechanical work required for a great range of functions including locomotion, respiration, and maintenance of posture. The fundamental process in muscle contraction is the generation of force and work by myosin cross-bridges. These molecules convert chemical energy, which they obtain by hydrolyzing adenosine triphosphate (ATP), into mechanical energy; that is, crossbridges, during their transient interactions with attachment sites on an actin filament, act as biological energy transducers. Cross-bridge cycling is supported by the processes of excitation and activation, which translate neural signals into the release of calcium ions (Ca2+ ) into the myoplasm [i.e., the portion of the muscle fiber that contains the contractile apparatus and excludes the sarcoplasmic reticulum (SR)] which permits cross-bridges to cycle. Both excitation and activation involve rapid movements of ions across membranes: excitation involves influx of sodium ions (Na+ ) across the sarcolemma into the myoplasm and efflux of potassium ions (K+ ) and activation involves the release of Ca2+ from the SR into the myoplasm. For continued or repeated contraction, these processes must be reversed and this is achieved by ATPpowered ion pumps. Muscle cells only contain enough ATP to power brief amounts of activity so to enable the prolonged muscular activity there are multiple biochemical mechanisms for regenerating ATP on both short and long time scales. The field of muscle energetics is concerned with all these processes and includes measurement of rates of ATP splitting by the various processes in different types of muscles and during different types of activity. It also encompasses identification and determination of the rates and capacities

Volume 5, April 2015

of ATP regenerating processes. Not all the energy obtained by splitting of ATP is converted into work and the remainder is converted into heat. Production of heat by muscles is important for some animals to help maintain body temperature above the ambient temperature or to warm critical parts of the body to optimize specific functions (32, 43). The study of energetics also includes quantification of the fractions of ATP energy that is converted into useful work and into heat from which it is possible to determine the efficiency of contraction. This review is composed of three sections. The first describes the main biochemical reactions involved in muscle contraction and the relationship between these reactions and the energy liberated from contracting muscles as heat and mechanical work. Central to this section are the “energy balance” experiments which sought the biochemical underpinnings of the mechanical and thermal energy produced during contraction. The second section describes muscle energy use during different types of activity—isometric contractions, steady shortening and lengthening and more complex patterns similar to those that occur during animal locomotion. The final section is a consideration of the factors that limit the efficiency of muscle contraction. Efficiency quantifies how much of the energy made available to perform work when ATP is hydrolyzed that is actually converted into useful work. This section includes detailed considerations of the amount * Correspondence

to c.barclay@griffith.edu.au of Allied Health Sciences/Griffith Health Institute, Griffith University, Gold Coast, Queensland, Australia Published online, April 2015 (comprehensivephysiology.com) DOI: 10.1002/cphy.c140038 Copyright © American Physiological Society. 1 School

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Skeletal Muscle Energetics

Table 1

Definitions of Symbols and Abbreviations

Symbol

Meaning

CK

Creatine kinase

ε

Enthalpy efficiency, initial enthalpy efficiency

η

Thermodynamic efficiency

ΔGATP

Free energy change of ATP hydrolysis

0 ΔGATP

Standard free energy change ATP hydrolysis

ΔHPCr

Molar enthalpy change of PCr hydrolysis

f, fS

Force output, shortening force

f0

Maximum isometric force

Comprehensive Physiology

filaments, pumping of Ca2+ from the myoplasm against their concentration gradient into the SR and the pumping of Na+ and K+ ions against their concentration gradients across the sarcolemma. The energy for these processes is provided by ATP hydrolysis. In the following section, an overview is given of the biochemical reactions underpinning muscle contraction and their thermodynamic characteristics. There are a number of detailed reviews of these reactions, the conditions under which they occur and their detailed stoichiometry (63, 155, 255) and of the thermodynamic aspects of muscle contraction (56,151,194,248,250). The purpose of the following section is to provide sufficient background information to assist the subsequent descriptions of muscle energetics.

h,ḣ ḣ

Enthalpy output, rate of enthalpy output Rate of enthalpy output in isometric contraction

ḣ F ḣ

ATP is the energy source for contraction

Rate of force-dependent enthalpy output

Ka

Association constant

K′

Apparent equilibrium constant

l0

Length at which isometric force output is maximum

Δl

Change in muscle length

nATP

ATP yield of substrate oxidation

natt

Fraction of cross-bridges attached

Pv

Parvalbumin

q, q̇

Heat output, rate of heat output

q̇ 0

Rate of heat output in isometric contraction

Q10

Relative change in rate for a 10◦ C temperature increase

ATP was suspected of playing a role in muscle energetics from the 1930s (for a review, see Ref. 192, pp. 16-19) but convincing experimental evidence that it was the source of energy for contraction was not easily produced. In 1959, Davies et al. (70) reviewed 30 years of efforts to identify the source of energy for contraction and that review illustrates just how difficult the pursuit was, with progress slowed by erroneous theories, difficulties identifying energetically important compounds and understanding the relationships among reactions and insufficiently sensitive assays. A much-simplified summary of the situation at the start of the 1960s is that chemical analyses of muscles rapidly frozen during contraction consistently found little or no change in concentration of ATP ([ATP]). However, it was observed that the concentration of phosphocreatine ([PCr]) decreased during contraction. It is now known that these two observations are accounted for as follows.

0

A

Rate of activation-dependent enthalpy output

SEE

Series elastic element

SR

Sarcoplasmic reticulum

T2 force

Force attained in rapid phase of force recovery after length step

Δt

Change in muscle temperature

Tn, TnCa

Troponin-C, troponin-C with Ca2+ bound

v, vmax

Shortening velocity, maximum shortening velocity

w, ẇ

Mechanical work output, power output

ξ

Extent of reaction

of energy that can potentially be used for performing work when ATP is split, the capacity of the fundamental work generating unit—the myosin cross-bridge—to perform work and concludes with a comparison of the maximum efficiencies of various muscles to the limits set by ATP energy provision and cross-bridge work capacity. A list of the main abbreviations used is given in Table 1.

Reactions Underlying Contraction In quantitative terms, three processes dominate the energy expenditure of contracting muscle: the cycling of myosin cross-bridges that generate force against neighboring actin

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Reaction 1, ATP hydrolysis

ATP → ADP + Pi

Reaction 2, creatine kinase (CK) reaction PCr + ADP → ATP + Cr The CK reaction rapidly phosphorylates adenosine diphosphate (ADP) formed in Reaction 1 so the net reaction associated with contraction is the breakdown of PCr. Reaction 3, net initial reaction

PCr → Cr + Pi

It was only when the role of the CK reaction in buffering ATP use was appreciated and a means was found to inhibit that reaction pharmacologically, with fluorodinitrobenzene (FDNB), that it became possible to perform the experiment to demonstrate that breakdown of ATP was indeed the primary source of energy for contraction (39, 40). With CK inhibited, ATP concentration decreased and was balanced by increases in the concentrations of ADP and adenosine monophosphate. Reaction 4, adenylate kinase (AK) reaction 2ADP → ATP + AMP


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In skeletal muscle with the CK reaction operating and during nonfatiguing activity, the AK reaction does not contribute significantly to ATP supply so that ATP turnover is reflected, via the 1:1 stoichiometry of Reaction 2, in the breakdown of PCr. Biochemical or energetic changes that occur more or less simultaneously with contraction (i.e., Reactions 1-3) are known as initial reactions. Hence PCr breakdown is the net initial biochemical change. The processes associated with the reversal of the initial reactions are known as recovery reactions.

Reversal of PCr breakdown Although the CK reaction could be considered to be the first recovery reaction (140), it occurs so rapidly that it is categorized as an initial reaction. Therefore, the net initial reaction is PCr breakdown and the recovery reactions are those leading to reversal of PCr breakdown. In the presence of O2 , creatine (Cr) is phosphorylated at the mitochondria at the expense of ATP. Reaction 5, reversal of CK reaction Cr + ATP → PCr + ADP ATP is then regenerated in the mitochondria by oxidative breakdown of metabolic substrates (e.g., glucose, as shown below). Reaction 6, Oxidative phosphorylation C6 H12 O6 + xADP + xPi + 6O2 → xATP + 6CO2 + 6H2 O In Reaction 6, x represents the ATP yield from oxidation of one glucose molecule. A useful index of oxidative ATP generation is the ratio of substrate or oxygen (O2 ) consumed to the amount of ATP formed, which is typically expressed as the P:O2 ratio. The classical stoichiometry of Reaction 6 is that one glucose molecule requires 6 O2 molecules for complete oxidation and produces 38 ATP molecules (i.e., x = 38). In that case the P:O2 ratio is 38/6 = 6.3. Recent estimates of the ATP yield of mitochondrial oxidative phosphorylation give lower values, consistent with P:O2 ratios of ∼5 (211). A comparison between that value and those estimated from muscle energetics is provided later in this review. Once recovery is complete (i.e., when all the PCr used in the contraction is regenerated), the overall net reaction is simply oxidation of metabolic substrates. Reaction 7, Substrate oxidation Substrate + yO2 → yCO2 + yH2 O In Reaction 7, y represents the moles of O2 required for oxidation of one mole of the substrate, which depends on the


substrate. PCr breakdown can also be reversed by glycolytic reactions, via production of ATP and lactic acid (La). Reaction 8

Glucose + 2Pi + 2ADP → 2ATP + 2La

That reaction is followed by rephosphorylation of PCr giving a net recovery reaction Reaction 9

Glucose + 2Pi + 2Cr → 2PCr + 2La

These last two reactions do occur under anaerobic conditions but in the presence of O2 they make at most a small contribution to regeneration of ATP (57, 167).

Thermodynamics and limits to deriving work from ATP Thermodynamics is central to understanding muscle energetics because it provides the basis for understanding the origins of the energy produced by contracting muscles as heat and work and offers a way to determine the upper limit to the efficiency of a contracting muscle. It is worth clarifying the terms used to describe energy output from muscles. Energy output is typically expressed as the change in enthalpy content of the muscle (ΔH). In thermodynamic terms, the definitions of energy output and enthalpy output differ. Energy output (ΔE) is the sum of the heat produced, work done against the atmosphere (i.e., pressure-volume work) and any other form of work output (e.g., work done by a muscle to lift a load). The definition of enthalpy output (ΔH) excludes pressure-volume work. However, in biological tissues the chemical reactions take place in solution and thus take place at essentially constant pressure and volume so no pressure-volume work is performed (248). In muscle, therefore, the magnitudes of ΔE and ΔH are the same and the terms energy change or output and enthalpy change or output are synonymous. Thermodynamic aspects of muscle contraction have been reviewed in detail previously (56, 224, 248). The following paragraphs are intended to provide just sufficient information to understand the energy balance experiments. The hydrolysis of ATP is accompanied by liberation of enthalpy as heat (q) and, if the muscle is able to shorten, mechanical work (w). The other reactions that occur in muscle are also associated with enthalpy changes and if several reactions are coupled together (i.e., the products of one are the reactants of another), then the overall enthalpy change is the sum of the enthalpy changes of the individual reactions. In this review, the symbol ΔH will be used to denote molar enthalpy changes (i.e., the enthalpy produced per mole of reaction) and h will be used to represent experimentally observed enthalpy changes for contracting muscle. Consider, for example, ATP hydrolysis and its regeneration at the expense of PCr. ATP → ADP + Pi is associated with an output of enthalpy (indicated by −ve sign to represent energy lost from the system), ΔH = −48 kJ mol−1 . ΔH for the CK reaction,

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the basis of the equilibrium constant and the concentrations of the reactants and products. In the third section of this review, the value of ΔG for ATP hydrolysis (ΔGATP ) is considered in detail because it sets the upper limits for work generation by and efficiency of myosin cross-bridges.

–50

Hobs (kJ/mol)

pMg = 3 –40

–30

–20 5.5

0 12 25 37

Energy Balance Experiments

C C C C

6

6.5

7 pH

7.5

8

8.5

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.

In the 1970s and 1980s, muscle energetics research was dominated by “energy balance” experiments (for reviews, see 63, 122, 125, 155, 156, 255). The foundation of that work was the idea that the energy liberated from muscles as heat and work should be explicable in terms of the extents of the underlying reactions and their thermodynamic characteristics. That is, q+w=

∑

𝜉 i ΔHi

i

PCr + ADP → ATP + Cr, is +14 kJ mol−1 and this arises from the enthalpy changes for its constituent parts: (i) the reversal of ATP splitting, Pi + ADP → ATP, for which ΔH is of equal magnitude and opposite sign to that for ATP splitting, ΔH = +48 kJ mol−1 , and (ii) phosphocreatine splitting, PCr → Cr + Pi, for which ΔHPCr is −34 kJ mol−1 (Fig. 1) (258). Remembering that this last reaction is the net initial reaction, ΔHPCr is the conversion factor to determine the amount of ATP hydrolyzed (ξATP ) from the measured enthalpy output: ξATP (μmol g−1 ) = h mJ g−1 /34 mJ μmol−1 . Note that ΔHPCr is pH dependent (Fig. 1) so the conversion factor needs to be adjusted as appropriate for the likely cellular conditions. One aspect of the importance of enthalpy output from muscle contraction is that enthalpy obeys the first Law of Thermodynamics so that the enthalpy change that accompanies contraction must be accountable in terms of the identity and extent of the reactions that occur in the muscle during contraction. Experiments designed to check the ledger of the enthalpy change expected on the basis of the known reactions and the enthalpy produced during contraction are known as “energy balance” experiments and are described in the following section. Muscles use the energy provided by ATP splitting to produce work in various forms. The amount of energy that can potentially converted into work from a reaction is not equal to ΔH because part of ΔH is accounted for by an entropy component (quantified as TΔS, where T is the absolute temperature and ΔS the change in entropy) that is associated changes in “orderliness” that accompany biochemical reactions at the molecular level. The important point is that the entropy component of ΔH cannot be converted into work; muscles operate at constant temperature which means that they cannot act as heat engines and convert heat into work. The remainder, ΔH − TΔS, is the upper limit to work that can be done and is called the free energy change, ΔG. ΔG for a reaction cannot be measured directly but can be calculated on

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where ξi and ΔHi are the extent of the ith reaction and its molar enthalpy change, respectively. These experiments are necessarily performed using isolated muscle preparations which allow for precise measurement of the quantities on both sides of the equation. The energy balance experiments were important because they identified all the energetically important (and not so important) reactions associated with contraction, quantified their thermodynamic properties and measured the extent to which each reaction occurs under different cellular conditions. Our current detailed knowledge of the biochemistry of ATP hydrolysis and the reactions involved in maintaining ATP supply arises from these experiments. There are a number of comprehensive reviews focused on the energy balance experiments (63, 122, 125, 155, 156, 255) and the following section provides an overview of the main conclusions from the energy balance studies. If the identity in the above equation can be established or the conditions under which such equivalence holds, then it would be possible to use the readily measurable enthalpy output as an index of the less readily determined extent of biochemical breakdown. To determine appropriate values for the left-hand side of the above equation, the enthalpy output must be measured, which involves measuring the work performed and heat produced. Work is straightforward to measure as it is calculated from the force output (f) and change in muscle length (Δl); in its simplest form, w = f × Δl. Muscle heat production is determined from measurements of the change in muscle temperature (Δt) during contraction and the heat capacity of the muscle: again in its simplest form, q = Δt × heat capacity. Changes in muscle temperature, which are typically ∼10−3◦ C in magnitude, have mostly been measured using specialized thermopiles (1, pp. 248-265, Ref. 116, pp. 171-188, Ref. 257). The heat measurement technique, in contrast to biochemical analysis, is nondestructive so multiple measurements or complete time course information can be obtained from a single preparation.


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Determining values for the right-hand side of the equation is less straightforward. First, all reactions or chemical changes that might be accompanied by thermal changes must be identified. These include not only the biochemical reactions associated with ATP turnover but also hydrogen ion (H+ ) buffering reactions, association and/or dissociation of other ions to various molecules, heats of dilution and so on. Second, molar ΔH values for all these reactions must be determined in vitro but under conditions matching as closely as possible those in the myoplasm. Third, measurements must be made of the often small changes in concentrations of products and reactants of the reactions that occur in response to contraction. These measurements are logistically challenging for several reasons. (i) When using traditional chemical analysis methods, analysis is performed on extracts from frozen muscle; that is, the method is destructive. Therefore, each muscle provides data concerning the chemical change at a single time point. To investigate time courses of energy balance thus requires analyses on many muscles to build a comprehensive picture (64, 127, 131). (ii) Muscles must be frozen very rapidly at a precisely known time after the start of stimulation. This was achieved using systems with automated timing of either fast immersion of muscles into a pool of rapid freezing agent, such as Freon or isopentane (41, 193), which freezes an average frog sartorius muscle in 100 to 200 ms (193), or flattening of muscles between metal hammers cooled in liquid nitrogen (153), which freezes in ∼80 ms (87, 131). (iii) The calculation of the extent of chemical breakdown for each muscle must be made with respect to a baseline value measured in a different muscle, normally the contralateral muscle. The uncertainty in the difference in concentrations is greater than that in either of the composite values. This is further exacerbated by the need to combine the mean values from multiple muscles of changes in concentration to determine a best estimate of the extent of breakdown of particular reactants (60). The impact of the uncertainty inherent in these types of determinations is particularly problematic because many of the chemical changes that occur are small. Both variables in the final comparison between q + w and chemical change involve uncertainties and these need to be considered when determining how well matched are the measured and expected enthalpy outputs (44). The majority of energy balance experiments used muscles from frogs studied at 0◦ C. Frog muscle is a robust preparation. The low temperature means that the initial reactions occur slowly enough to make it practical to get a good spread of extents of reaction and enthalpy production and also delays the onset of recovery reactions so that these will not reduce the extent of initial reactions (64). Another simplifying feature of that preparation is that the extent of glycolytic ATP generation is small, even under anaerobic conditions (64), so that the only reactions that occur to a significant extent are PCr breakdown and, under some conditions (e.g., CK inhibition), ATP breakdown. One complicating factor is that muscles from two species of frog have been used: Rana temporaria (European common frog) and Rana (or Lithobates) pipiens (Northern


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leopard frog). The muscles from these frogs have slightly different energetic properties which may confound some comparisons between similar energy balance experiments performed with muscles from different frog species. Energy balance experiments can be separated into two general categories. The majority of energy balance experiments investigated the enthalpy output associated with the initial chemical change. In that type of experiment, the observed energy output was compared to the energy output expected from the extent of the initial biochemical reactions that occurred during a tetanus. In the second type of energy balance, the chemical change that occurred during a contraction was compared to the amount of oxygen required to reverse the chemical change.

Energy balance for initial reactions In frog muscle at 0◦ C, it was consistently found that the amount of enthalpy produced was greater than that expected from the extent of PCr breakdown. At 0◦ C in frog muscle with an intracellular pH of 7, the expected enthalpy from PCr breakdown is usually taken to be 34 kJ mol−1 (258) (although 35 kJ mol−1 may be more accurate, see Fig. 1). In contrast, for sartorius muscle from R. temporaria, the ratio of enthalpy produced to amount of PCr consumed after 5 s of isometric contraction was between 40 and 70 kJ mol−1 (64, 87, 131, 249); that is, heat from some source other than PCr breakdown accounted for between 10% and 50% of the total heat produced in the first 5 s of contraction. Part of the enthalpy produced during contraction could be explained as arising from PCr breakdown but a substantial fraction was unexplained. The “unexplained enthalpy” was thoroughly characterized in the course of many experiments and the results have been discussed at length in a number of reviews (63, 122, 125, 126, 155, 156, 206, 255), so only a summary of the results is provided here. Unexplained enthalpy has the following characteristics: (i) produced predominantly during the first 2 to 3 s of a tetanus (64,127); (ii) not eliminated by inhibiting cross-bridge cycling by stretching muscles before stimulation to reduce filament overlap (65); (iii) reduced in the second of two tetani when the second starts 20 s after the end of stimulation (absorbing heat) and will be pumped back into the SR (producing heat); this would account for the continued PCr breakdown during recovery. Pumping Ca2+ into the SR produces less heat than is absorbed by dissociation from PA: dissociation of Ca2+ absorbs 32 kJ mol−1 and, because 2 Ca2+ are pumped into the SR for each ATP, and thus PCr, used, the return of Ca2+ to the SR produces 34/2 = 17 kJ mol−1 which gives a net thermal change of −32 + 17 = −15 kJ mol−1 . Over a complete cycle of Ca2+ binding to and dissociation from Pv and the return of the Ca2+ into the SR there is a net heat output of 17 kJ mol−1 , which is produced during the postcontraction recovery phase and would contribute to recovery heat production.

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Heat from Ca2+ -binding reactions explains part of “unexplained” enthalpy It should be noted that these estimates of heat produced by Ca2+ -binding reactions depend in particular on the assumed intracellular resting [Ca2+ ]. This is difficult to measure (102) and thus is somewhat uncertain. They also depend on the concentration of parvalbumin, which can vary twofold among different fibers in the same muscle (133). It is also possible that resting [Ca2+ ] and/or [Pv] differs among species of frog or with the condition of frogs. All these factors have the potential to underlie the marked variability in amounts of unexplained heat reported in different studies. The estimates in Table 3 indicate that for frog muscle the combined heat from Ca2+ binding to Tn and Pv is ∼26 mJ g−1 . The total unexplained enthalpy in R. temporaria is at least 30 mJ g−1 so the thermal changes expected to accompany these Ca2+ -binding reactions could explain a large fraction, but probably not all, of the unexplained heat. For R. pipiens, the magnitudes of the unexplained enthalpy and the estimated heat from Ca2+ binding do match so for muscles from that species of frog it is possible that an energy balance is achieved if heat from both PCr breakdown and Ca2+ binding is taken into account.

Does any of the initial enthalpy output remain unexplained? As convincing as the Ca2+ -binding hypothesis for unexplained heat may appear, there remains experimental evidence that is inconsistent with the idea that all the unexplained heat is due to Ca2+ binding reactions. (i) If unexplained enthalpy output is all due to Ca2+ -binding reactions and independent of the contractile process, then it would not be affected by decreasing the amount of filament overlap by stretching muscles to long sarcomere


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lengths prior to contraction. Interpretation of this type of experiment requires that Ca2+ release be unaffected by increasing muscle length to reduce filament overlap and this appears reasonable (for a review, see Ref. 22). Three such studies have been performed, with contrasting results. Kean et al. (148), using muscles from R. pipiens, found that the amount of unexplained heat was independent of muscle length but Homsher et al. (129), also using muscles from R. pipiens, and Curtin and Woledge (65), using muscles from R. temopraria, and found that when filament overlap was eliminated, about half the unexplained heat was also eliminated. That result suggests that there remains an additional unknown process or processes related to actin-myosin interaction that also contributes to the unexplained enthalpy output. (ii) Unexplained enthalpy accounts for 30% to 40% of the initial enthalpy output from rat soleus muscles (99, 200) but these muscles do not contain parvalbumin (110). In both these experiments, initial enthalpy output was measured (e.g., Fig. 3A) but different methods were used to measure the extent of chemical breakdown. Gower and Kretzschmar (99) used traditional biochemical analysis whereas Phillips et al. (200) used nuclear magnetic resonance (NMR), which enabled the time course of changes in PCr concentration to be measured through stimulation and recovery on each muscle (Fig. 3B). As with frog muscle, the heat expected from the measured PCr breakdown was less than the measured enthalpy output (Fig. 4) and there appeared to be additional PCr use during the recovery period (Fig. 3B) (200), consistent with the idea that whatever produces the unexplained heat during contraction is reversed at the expense of PCr breakdown during recovery. However, the time at which the extra PCr splitting occurred in the rat muscle (∼100 s after the contraction) is quite different to the situation for frog muscle in which the additional PCr splitting occurred within 30 s of a short tetanus. It seems likely that Ca2+ -binding accounts for a substantial fraction of the unexplained enthalpy in frog muscle but in both frog muscle (at least for R. temporaria) and rat slowtwitch muscle there almost certainly remains an unidentified source of enthalpy and postcontraction PCr breakdown. To date there have only been the two energy balance studies using mammalian muscle and this is an area of muscle energetics that needs to be explored further.

Enthalpy output and PCr breakdown during shortening When shortening, muscles produce enthalpy and break down high-energy phosphate at rates that are greater than during isometric contraction. In frog muscle shortening at a velocity of 50% of the maximum shortening velocity (vmax ), with shortening starting after 2 s of isometric contraction, the rates


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of enthalpy output and PCr breakdown are greater than during isometric contraction and the enthalpy output is consistent with the amount of PCr used (132). Similarly, in the period immediately after the shortening, when the rates of enthalpy output and PCr breakdown have decreased, the observed and explained enthalpy outputs are the same. Therefore there is an energy balance during and after moderate velocities shortening when the shortening starts after the heat production due to Ca2+ binding to Pv is complete. However, this is not so when shortening at velocities close to vmax . In that case, there is a temporal dissociation between enthalpy output and PCr breakdown: enthalpy is produced at a high rate during rapid shortening but the rate of PCr breakdown is relatively low (124,207) and, conversely, in the period immediately following the shortening the rate of enthalpy output is relatively low and the rate of PCr breakdown relatively high (124, 207). When considered across the duration of shortening (350 ms) and the 650 ms after shortening, the observed and expected amounts of enthalpy match (259). The conclusion drawn from those observations was that during high velocity shortening heat is produced by a reaction other than ATP or PCr breakdown and after the shortening that reaction is reversed at the expense of ATP (122). Irving and Woledge (144) proposed that during rapid shortening cross-bridges complete only part of their cycle, which does not include ATP splitting, and that the enthalpy output reflects the difference in enthalpy between the two states. After shortening, the cross-bridges are able to complete the cycle and hydrolyze ATP. Another proposal (122) is that during rapid shortening cross-bridges with ADP bound detach and remain detached with ADP bound until shortening has ended; it is proposed that detachment along that path is associated with enthalpy production. Once shortening has ended, those cross-bridges reattach and the ATP hydrolysis cycle can be completed but with little enthalpy production.

High rate of PCr breakdown at the start of a contraction The observed rate of enthalpy output from frog, tortoise and dogfish muscles is transiently high early in a tetanic contraction (e.g., Fig. 2). Part of this most likely arises from the previously “unexplained” Ca2+ binding reactions. However, part of the high rate falls in the “explained” category in that it is mirrored by a transient high rate of PCr breakdown (64, 127, 131). In particular, the cross-bridge component of PCr breakdown shows an early high rate; that is, the rate of cross-bridge cycling is initially high and then decreases with a time constant of 1 to 2 s (244). The rate of decline is too slow and the amount of energy produced is too great to be due to shortening of the contractile component against series elastic elements (SEEs) (244). West et al. (244) suggested, on the basis of model simulations, that the most likely cause of the decline in rate of cross-bridge cycling during the first few seconds of contraction in intact muscle was accumulation of Pi.

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(A)

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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.

Summary of energy balance experiments The experimentally observed energy imbalances (i.e., when rate of enthalpy output is not consistent with rate of PCr breakdown) early in contraction and during rapid shortening have a common foundation in that in each case the

970

imbalance is likely to have arisen because the times over which measurements were made included only part of a complete thermodynamic cycle. At early times in contraction, Ca2+ has bound to Tn and Pv but has not dissociated and thus those reactions have produced heat but the absorption of heat


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250

Heat (mJ (g dry wt)–1)

200

150

100

50

0 0

100

200

300

400

Time (s)

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.

that would occur upon dissociation has not been included in the measurement. In rapid shortening, cross-bridges are likely to have undergone only part of their normal ATP splitting cycle and only when the cycles have been completed following the shortening is the energy balance re-established. The energy balance experiments were important for several reasons. They provided precise quantification of the time courses of both enthalpy output and high energy phosphate breakdown, identified which biochemical reactions occur under given conditions, extended understanding of the roles Ca2+ binding proteins play in contraction and highlighted the possibility that more complex cross-bridge cycle schemes are required to explain the full range of muscle behavior. Paradoxically, it can be considered lucky that an energy balance was not established in the first experiments for it was that which stimulated so many additional experiments. The energy balance story cannot be considered complete given that it appears that there may still be unexplained enthalpy production, for example from slow-twitch rat muscles, but a strong framework has been laid down for progressing from identifying energetic imbalances to uncovering the bases of those imbalances.

Energetics of Contraction In this section the rates of ATP turnover in different types of contraction are described. The rates have been derived


from reported rates of muscle enthalpy output and chemical energy usage made using intact fiber preparations and of ATP turnover in skinned muscle fiber preparations. A brief critique of the various indices of ATP turnover is provided below. This is followed by consideration of energy turnover during isometric contraction, including descriptions of the effects of fiber type, temperature, muscle length and the partitioning of ATP use between cross-bridge cycling and ion pumping. Then descriptions are provided of energy turnover during steady shortening and lengthening. Information about energy turnover during isometric, shortening and lengthening contractions is derived from experiments in which the contraction protocols used were designed to provide unambiguous information about the energy turnover related to the contractile process while avoiding confounding influences such as varying level of activation, transient high rates of energy expenditure in the early stages of contraction, heat from Ca2+ -binding reactions and effects of the SSEs (elastic structures mechanically connected in series with the force-generating cross-bridges) on work and heat outputs. That is, those protocols were designed to clarify our understanding of fundamental aspects of contraction rather than to simulate in vivo muscle activity. In the last 20 years, as methods have been developed for measuring excitation patterns and changes in muscle length during locomotion (90,220), there has been increasing use in vitro of contraction protocols designed to more closely match those that occur during in vivo muscle activity (10,21,68,109,146).

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Energy turnover in these cyclic contraction protocols are considered in the last part of this section.

Methods for measuring ATP turnover The description of the energy balance experiments illustrated the three classical methods of measuring energy turnover in muscle: measurements of enthalpy output, oxygen consumption, and biochemical breakdown in extracts of muscles frozen during contraction. Measurement of enthalpy output is based on the first Law of Thermodynamics. The first law is the principle of energy conservation and, as applied to muscle, indicates that the enthalpy change associated with the initial reactions must all appear as either heat or work. Work output is calculated from measurements of muscle length change and force output, both of which can be measured accurately and with high temporal precision. Heat output from a contracting muscle can also be measured accurately using thermopiles and with good temporal resolution. Decent records can be made from short contractions of preparations as small as single frog fibers (19, 38, 61, 174). Heat signals are distorted in time for some tens of milliseconds after a change in rate of muscle heat production due to the time required for diffusion of heat through the muscle to the thermopile surface and then through the insulating layers of the thermopile (e.g., varnish or thin sheets of melinex, kapton, or mica) to the thermocouples. Mathematical correction for these effects can be made using deconvolution techniques (88, 89). The method also allows heat from both PCr breakdown and PCr regeneration to be measured and can in this way quantify both energy demand and supply. The method is nondestructive so many measurements can be made on a single preparation. The main limitation of enthalpy measurements is the nonspecificity of heat production. As seen in the energy balance section, the identities and time courses of reactions giving rise to thermal changes need to be known to use the method with confidence; in particular, measurements of enthalpy output should be made only after a sufficient duration of contraction to avoid contamination of heat records with heat from Ca2+ -Pv binding (i.e., 2-3 s of contraction in frog muscle at 0◦ C). The method has been used mainly with isolated muscle preparations, for which it is easiest to ensure that all the heat produced by the muscle is measured, but heat measurements have also been made from human muscle in vivo (76, 97). Biochemical analysis of muscle extracts provides a direct insight into the extent and nature of the biochemical changes associated with contraction (40). However, such experiments are logistically challenging because a pair of muscles (one unstimulated control, one stimulated) are required to produce one measurement of chemical change at one time point so many muscles are required to reconstruct the time course of chemical breakdown during a contraction (64, 127). The experiments can be analytically challenging in that the extents of chemical changes can be small and can be quite variable among muscles. The extent of chemical breakdown can also

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be assessed using NMR which is nondestructive and can be used to study muscle both in vitro (71, 72, 158, 159, 187, 200) and in vivo (105, 251). NMR has poor sensitivity which is overcome by averaging repeated signals from relatively large tissue volumes, resulting in an effective time resolution that is poor compared to that of enthalpy measurements. ATP use can also be assessed by measuring the amount of O2 consumed to completely reverse the initial chemical change (27,57,119,162,184,198,227). There is necessarily a delay, of physiological origin, between ATP use and the corresponding O2 uptake because the mitochondrial response to changes in rate of ATP turnover is relatively slow. For example, after a 0.5 s tetanus at 20◦ C, the rate of oxygen consumption by frog muscle is maximal 1 minute after the contraction and remains above resting levels for at least another 10 min (184,215). The time course is quicker for mammalian muscle but oxidative recovery metabolism takes 3 min after a 6 s tetanus of rat soleus muscle at 20◦ C (200). There are several indirect indices of mitochondrial activity, including measurements of mitochondrial NADH fluorescence (45,46,239) and intracellular PO2 (236). Skinned muscle fiber techniques allow direct measurement of ATP use by cross-bridges. Two methods have been used to measure ATP turnover. In one, ADP formation is linked by pyruvate kinase and lactate dehydrogenase to oxidation of NADH, the progress of which can be monitored using spectrophotometry (231). This method has been used to measure steady-state ATP breakdown during prolonged activation. In some studies (33, 94, 210), the fibers and the ATP regenerating/monitoring system were contained in a small volume bath but more recent studies have restricted the volume in which the reactions occur, and thus improved the sensitivity of the method, by immersing the activated fiber in oil (111, 228, 230, 244). A more recent method to monitor ATP turnover in skinned fibers uses a fluorescent Pi probe (79). That method has very high time resolution but is effective for a restricted time because the probe becomes irreversibly saturated. The method is typically combined with rapid activation using either caged ATP or caged Ca2+ ; these approaches not only initiate contraction rapidly but also prevent Pi formation prior to activation and avoid consuming the probe before activation.

Muscle preparations for studying ATP turnover Precise measurements of energy turnover in contracting muscle have been made using two types of muscle preparation: intact preparations and skinned or permeabilized fiber preparations. Intact preparations consist of one or many muscle fibers with an intact sarcolemma (i.e., the cell membrane). The membrane exhibits a normal resting potential, the fibers can be stimulated electrically, either directly or via the nerve (253) and the intracellular milieu is maintained by cellular regulatory processes. ATP turnover can be monitored indirectly using measurements of enthalpy output, by arresting


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metabolic activity by rapidly freezing the muscles and subsequently measuring the concentrations of metabolically relevant compounds (as in the energy balance experiments) and by measuring oxygen consumption (119, 164, 185) or its analogs (45, 239). From an energetics perspective, intact preparations have the advantages that the excitation-contraction coupling processes produce rapid development and relaxation of force and that ATP breakdown and regeneration occur as they do in vivo. Intact preparations have the disadvantages that ATP turnover can be studied only indirectly or at particular instants in time and measurements necessarily incorporate ATP turnover by activation processes (i.e., pumping of Ca2+ and Na+ out of the myoplasmic space). Another important consideration is that an isolated preparation obtains O2 only by diffusion from its outer surface. If the radius of a preparation is too large it is possible that diffusive O2 supply will be inadequate to meet the metabolic demands through the full cross-section of the muscle, leaving an anoxic area in the center (218, 219). This is handled in two ways: preparations are kept as thin as possible and/or the experimental temperature is minimized. The former reduces the diffusion distance and the latter favors O2 supply because the temperature dependence of metabolic rate is greater than that of O2 diffusivity (182). There are several published accounts of mathematical analysis of O2 diffusion into muscle (15, Chapter 6 of Ref. 116) and of practical ways to determine likely adequacy of oxygenation (15, Appendix to Ref. 20). Skinned or permeabilized fiber preparations consist of short fiber segments with a sarcolemma that is deliberately disrupted either by exposure to detergent or by mechanically peeling the sarcolemma off the fiber (7). This allows the experimenter to control the composition of the intracellular solution. The advantage of such preparations is that the time course of ATP turnover by cross-bridges can be assessed directly and nondestructively. Disadvantages of the skinned fiber preparation include the need to provide an artificial ATP regenerating system, the potential for ATP hydrolysis products to accumulate and the difficulty maintaining preparation viability and generating stable contractions at higher temperatures (107, 191, 244), although the latter has been improved by a method in which fibers are activated at low temperatures and then transferred to a higher temperature bath once a stable contraction has developed (173, 245).


temperatures ≤20◦ C (119, 167, 180, 183, 200). In an isomeṫ The first ric contraction no work is performed so that ḣ = q. phase is the initial heat production, arising largely from the net breakdown of PCr (in 1:1 proportion to ATP hydrolysis) and is independent of O2 supply (167). The subsequent heat production, the recovery heat, arises mainly from the oxidative regeneration of PCr by mitochondria. The oxidative origin of the recovery heat is readily demonstrated by comparing the magnitude of recovery heat production in the presence and absence of O2 : in the absence of O2 , recovery heat is production is much reduced (167, 242). In Table 4, rates of ATP turnover measured during isometric contraction of intact fiber preparations are collated. Values are shown for a variety of species and across a range Table 4

Rate of ATP Turnover in Isometric Contraction of Intact Muscle Preparations Rate of ATP turnovera

Temp Species/muscle Frog sartorius

Tortoise

◦C

mJ g−1

μmol g−1 s−1

s−1

Reference

0

15

0.44

1.5

(118)

20

85

2.5

8.3

(42)

0.01

0.03

(254)

0

0.35

Dogfish white

12

26

0.76

2.6

(244)

Rat soleusb

17

10.9

0.21

0.7

(99)

20

13.6

0.38

1.2

(200)

27

18.6

0.52

1.67

(85)

27

25

0.69

2.2

(241)

27

136

3.8

13.5

(240)

27

138

3.8

13.5

(241)

20

23

0.64

2.3

(24)

20

41

1.14

4.1

(57)

20

32

0.89

3.2

(168)

27

54

1.55

5.5

(238)

30

49

1.36

4.8

(24)

20

118

3.3

11.6

(24)

20

98

2.8

9.8

(57)

20

170

4.8

16.9

(168)

Energy turnover in isometric contraction

27

142

4.1

14.4

(238)

Figure 3A shows an example of the heat produced by a rat soleus muscle in response to 6 s of stimulation. At the start of contraction, the rate of heat output increased quickly to a steady value that was sustained throughout the period of stimulation. When stimulation ended and the muscle relaxed, there was a short-lived period when the rate of heat output was very low before the onset of a sustained production of heat lasting 2 to 3 min. These two phases of heat production—the rapid, steady heat output during contraction and the prolonged, transient, postcontraction heat output—are temporally distinct at

30

195

5.5

19.2

(24)


Rat EDL

Mouse soleus

Mouse EDL

a ATP

turnover calculated from reported steady rates of enthalpy output during isometric contraction assuming: ΔHPCr = 35 kJ mol−1 (258); rates expressed relative to mass refer to blotted, whole muscle mass. Rates expressed s−1 are ATP turnover per cross-bridge calculated by subtracting presumed activation component (see Table 5) and assuming cross-bridge concentrations of 0.21 μmol g−1 for frog and tortoise muscle (23), 0.194 μmol g−1 for dogfish muscle (197), and 0.183 μmol g−1 for mammalian muscles (24). b Data for rat soleus at 17◦ C from heat produced and PCr used in response to 10 s tetanus. Heat output was ∼30% more than expected on basis of PCr breakdown.

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(A) Intact preparations

(B)

Skinned fibers 0.7

6

4

R

3 2 Slow twitch 1 0

R

20

25

0.5

2A

2 0

0.3

1/2A 2B 2X 2A 1

0.2

1

30

6 Rabbit psoas Pi probe 4

0.4

0.1

R

R

2A/2B

ATPase

Fast twitch

5

ATP turnover (μmol g–1 s–1)

ATP turnover (μmol g–1 s–1)

2A

0.6

0.0

5

10 15 20 Temperature

2

1

Rat Human Rabbit

1

10

15

Temperature (°C)

20

Temperature (°C)

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.

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Force Soleus

50 kPa

EDL

0.5 s

Heat

EDL

50 mJ g–1

of temperatures. For nonmammalian muscles, the rates given are those after completion of any transient high rate of ATP splitting or heat output at the start of contraction. Isometric ATP turnover varies among species. For example at 0◦ C, the rate of ATP splitting in frog sartorius is 0.44 μmol g−1 s−1 whereas that for tortoise is only 0.01 μmol g−1 s−1 . The highest rate in Table 4 is that for mouse EDL muscle at 30◦ C which, at 5.5 μmol g−1 s−1 , is ∼25 times faster than that for frog muscle at 0◦ C. The rates of ATP turnover for mammalian muscles and the effects of temperature and fiber type are illustrated in Figure 5A. The most notable aspect of the data is the large difference in rate of ATP turnover between fast- and slowtwitch muscles: the rate of energy turnover in fast-twitch muscles is much greater than that from slow-twitch muscles (11, 17, 18, 33, 37, 106, 210, 238, 241). Muscles from rodents are particularly useful for characterizing fiber type differences because muscles are often of quite uniform fiber type (6). Studies with mouse and rat muscles have shown threefold to fivefold differences in the rates of isometric energy turnover between fast and slow muscles (18,24,57,85,168,240). There are also fourfold to fivefold differences in rates of ATP splitting between individual skinned Type 1 and Type 2 fibers from the rat (Fig. 5B) (33, 210). In Figure 6 a direct comparison is shown of the time courses of heat output from mouse EDL and soleus muscles. The EDL muscle is mechanically fast (i.e., force develops and relaxes rapidly and vmax is high) and is composed predominantly of fast-twitch Type 2a and 2x fibers (161) whereas soleus is mechanically slow (i.e., relatively low rates of force development and relaxation and

Soleus 0.5 s

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.


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low vmax ) (18,34,50) and is a mixture of slow Type 1 and fast Type 2x fibers (93). In the example shown, the rate of initial heat output from, and thus the rate of ATP splitting in, EDL is five times greater than that from soleus. A second important aspect of the data shown in Figure 5 is that the rate of isometric energy turnover increases with temperature (Fig. 5A). The temperature sensitivity (Q10 ; increase in rate for a 10◦ C increase in temperature) of ḣ 0 is 4.5 between 0 and 10◦ C for frog muscle (36, 209) and is 1.6 and 2.1 for mouse EDL and soleus muscle, respectively, between 20 and 30◦ C (24). The third notable point from the isometric energy turnover data is that values from rat muscles are 70% to 80% as great as those for the same muscles of the mouse. Rat muscles also contract and relax more slowly and have a lower vmax than the homologous mouse muscles (51). These observations are all consistent with slower rates of cross-bridge turnover during isometric contraction in muscles from the larger species. The observation that heat is produced and PCr broken down throughout an isometric tetanus is important because it indicates that there is a constant turnover of ATP. This is observed during normal isometric contraction and also when cross-bridge cycling is inhibited (19, 129, 169). This indicates that ATP is used continuously during contraction for cross-bridge cycling and for ion pumping. In most schemes of cross-bridge kinetics, binding of ATP to an attached crossbridge is required for detachment to occur so ongoing, crossbridge-dependent ATP splitting during an isometric contraction implies that cross-bridges must be undergoing repeated cycles of attachment, generating force and detaching even in the absence of filament sliding. When the filaments do slide, cross-bridges cycle more rapidly, consistent with the idea that during shortening the rate of cycling is modulated by the strain experienced by cross-bridges so that when a cross-bridge reaches the end of its power stroke any further strain applied to the attached cross-bridge by the action of other cross-bridges attached along the same thin filament will promote detachment. However, during isometric contraction, the rate of ATP splitting by cross-bridges must reflect the actin-activated myosin ATPase activity, independent of any influence of cross-bridge strain. Energy use for ion pumping also continues throughout a contraction. As mentioned previously, the SR Ca2+ pump is the main contributor to cross-bridge-independent energy turnover so Ca2+ pumping occurs throughout a contraction. The rate of Ca2+ pumping depends on the intracellular free Ca2+ concentration so from the time that Ca2+ enters the myoplasm upon excitation until the time at which resting Ca2+ levels are attained, the Ca2+ pump can be expected to be working at rates exceeding that required to maintain the resting Ca2+ level. The time course of recovery heat output also differs between fast- and slow-twitch rodent muscles. Experiments with these muscles are usually conducted at ≤30◦ C. At these temperatures, although recovery heat production probably



starts within the time course of even a short contraction (242), the majority of the recovery heat is produced after the contraction (Fig. 3A). In the immediate postcontraction period, the rate of recovery heat output increases and does so more quickly in fast-twitch muscle than slow (17,21,167,239,242). The rate of onset of recovery heat must reflect the time required to build up the signal (e.g., the phosphorylation potential) that stimulates mitochondrial oxidation. That this, at least in part, is limited by the creatine kinase reaction is apparent because the mitochondrial response is faster when myoplasmic creatine kinase is inhibited (103, 150).

Partitioning ATP turnover between cross-bridge cycling and ion pumping The rate of ATP turnover or enthalpy output during contraction can be divided into two components (129, 223): a forcedependent component (ḣ F ), which arises from cross-bridge cycling, and an activation component (ḣ A ), which is independent of force generation and arises from ATP-powered ion pumps. The two components can be distinguished by comparing energy turnover of a contracting muscle with that of the muscle after cross-bridge cycling, but not ion pumping, has been inhibited. Cross-bridge cycling can be inhibited by eliminating overlap between the thick and thin filaments by stretching muscles to long lengths before stimulation (Fig. 7) (129, 208, 223) or pharmacologically using the specific crossbridge cycling inhibitors N-benzyl-p-toluenesulfonamide for fast-twitch muscle (20, 47, 104) or blebbistatin (169, 170) for fast or slow muscles. When cross-bridge cycling is eliminated, isometric heat output is reduced but not eliminated (Fig. 7). In the absence of cross-bridge cycling, the rate of energy turnover is 30% to 40% of that measured with cross-bridge cycling at maximum filament overlap; that is 30% to 40% of isometric energy turnover is independent of cross-bridge cycling and is attributed to ion pumping and 60% to 70% is attributable to generation of force by crossbridges. Energy turnover for Ca2+ pumping was the subject of a recent review (22) and a summary of relative ḣ A values (i.e., ḣ A ∕ḣ 0 ) is provided in Table 5. ḣ A when expressed as a fraction of ḣ 0 is similar in twitch and tetanic contractions (129) and increases slightly with temperature in amphibian muscle (22) but probably not in mammalian muscle (20, 22).

Rate of cross-bridge cycling Cross-bridge cycling accounts for a slightly larger fraction of isometric energy use in frog muscle than in mammalian muscle. In frog muscle, ḣ F is ∼70% of the steady isometric heat production and in mammalian muscle ḣ F is ∼60% of energy turnover. Knowing ḣ F , it is possible to calculate the rate of ATP breakdown per cross-bridge; the values are given in Table 4 (column labeled with units of “s−1 ”). For frog muscle at 0◦ C, the rate is 1.5 s−1 , which means an individual cross-bridge takes 1/1.5 = 0.67 s to complete an ATP-splitting

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Partitioning activation costs between Na+ pumping and Ca2+ pumping Force a

b

c

d

Heat

3.5

Initial twitch heat (mcal/g)

3.0 2.5 2.0 1.5 1.0 0.5 0

Increasing muscle length 0

20

40

60

80

100

120

Twitch tension (g)

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.

cycle during an isometric contraction. At the other extreme, the rate for mouse EDL at 30◦ C is ∼20 s−1 or an ATP-splitting cycle time of 50 ms. Note that if one ATP is split for each cross-bridge cycle, then the duration of the ATP splitting cycle is the sum of the times for which a cross-bridge is attached and detached. The fraction of the ATP cycle time for which a cross-bridge is attached (i.e., the attachment duty cycle) is the same as the fraction of cross-bridges attached at any instant (nAtt ). nAtt is not known with great precision with various lines of evidence indicating that during isometric contraction of frog muscle nAtt is between 20% and 40% (see Section 3.4 of Ref. 23). If we take a middle value of 30%, then during an isometric contraction of frog muscle at 0◦ C a cross-bridge would be attached for 0.3 × 0.67 s = 0.2 s in each ATP splitting cycle and detached for 0.47 s. If the same fraction of cross-bridges was attached in mouse EDL muscle at 30◦ C then an average cross-bridge would be attached for 15 ms and detached for 35 ms in each cycle.

976

The two quantitatively important processes that underpin ḣ A are the SR Ca2+ pump and the sarcolemmal Na+ -K+ pump. The magnitude of ḣ A reflects the ATP used by both pumps. There has been no experimental partitioning of ḣ A between these processes. However, estimates based on the amount of Na+ that enters a muscle cell in response to an action potential indicate that the Na+ -K pump probably accounts for l0 and then activated, the maximum force produced was reduced in proportion to the reduction in filament overlap. This is consistent with the expected decrease in the number of cross-bridges that can attach to the actin filament as overlap between the thick and thin filaments is reduced (98). The rate of ATP splitting also decreased at long sarcomere lengths and decreased to the same extent as force. Thus, at lengths above l0 both force production and ATP splitting by cross-bridges are reduced in proportion to the reduction in number of cross-bridges that can cycle (111, 228). In intact muscle, ATP is used not only by cross-bridges but also by activation-related processes. Energy turnover for activation processes is independent of sarcomere length above L0 (129) so, as shown earlier (Fig. 7), there is still ATP splitting when force is completely eliminated and the relative decline in total ATP splitting as filament overlap is reduced to zero is less than the decline in force (9, 77, 129, 223). Force output is also less than f0 when muscles contract at lengths below l0 . However, the rate of ATP splitting at short


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Shortening contractions Energy turnover during shortening

0.8 0.6 0.4 Force

0.2

ATPase rate 0.0 1.0

1.5

2.0

2.5

3.0

3.5

4.0

Sarcomere length (μm)

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., ∼50% vmax ), the enthalpy change during lengthening is negative (Fig. 12) that is, energy is absorbed by the muscle (53,117,175). This occurs because part (at least 50%) of the energy put into the muscle as work did not simply appear as heat but instead was stored in the muscle during the stretch. Qualitatively similar results are seen for muscles of amphibians and mammals (53). There are a number of ways in which energy might be stored: stretching of SEEs, stretching of titin, stretching of compliant thick and thin filaments and change in cross-bridge energy. Although all of these might contribute, it is not possible, using reasonable assumptions as to the energy storage capacity of each mechanism, to quantitatively account for the amount of


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200

Force Stiffness Strain

150

100

50

–1600

–800 0 800 Half-sarcomere velocity (nm h–1 s–1)

1600

Figure 13 Variations in force, fraction of cross-bridges attached and cross-bridge strain with velocity for frog muscle at 0◦ C. Fraction of crossbridges 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 ( v) 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.

energy stored. The storage of energy only persists for the duration of lengthening and appears as heat once the lengthening ends (175). It has recently been established using x-ray diffraction (35) and from analysis of muscle stiffness (23) that during lengthening the number of attached cross-bridges is about double that during isometric contraction (Fig. 13). This observation gave rise to the idea that during isometric contraction only one of each cross-bridge pair is attached to actin but that when lengthening starts, the second cross-bridge of each pair also attaches (35), accounting for the doubling of stiffness and force output during lengthening.

performed at frequencies similar to those that occur in vivo. Measurements of energy turnover using these cyclic contraction protocols have been made using skeletal muscles from fish (67-69), mice (10, 12, 21, 121, 169), rats (109), insects (8, 147), and frogs (109) and using both sinusoidal length changes and more complex patterns of length change designed to more closely approximate the patterns of muscle length changes that occur during terrestrial activity (21, 121). An example of records of energy output from a mouse muscle performing a protocol using sinusoidal length changes is shown in Figure 14. Clear steps in work output and enthalpy output coincide with the times that the muscle contracted. The timing of the stimulation was adjusted so that the muscle was relaxed during the lengthening phase of each cycle and thus not much work had to be done on the muscle to stretch it out; that maximized the net work output in each cycle which is the difference between the work done by the muscle during shortening and the work done on the muscle during lengthening. A consistent finding with cyclic contraction protocols is that the rate of ATP turnover does not vary as greatly across the possible range of cycle frequencies that a muscle can perform (the upper limit to the frequency that can be used is determined by the time required for force relaxation) as it does across the full range of shortening velocities. For example, the maximum value of ḣ across a range of cycle frequencies that encompassed that at which ẇ was maximal was only ∼50% greater than ḣ 0 (Fig. 14B). Maximum enthalpy efficiency values determined from cyclic contraction protocols are at least as high as those measured during isovelocity protocols (68) which is surprising as when using a sinusoidal protocol shortening velocity must be at the optimum for efficiency only briefly in each cycle. The unexpectedly high efficiency is not due to enhanced force or reduced energy cost arising from the brief period of lengthening that occurs at the start of contraction (68) or to reduced activation costs in brief contractions (169). The most likely explanation is that efficiency is increased because a substantial fraction of the work performed in each cycle occurs during relaxation and it is known that efficiency is higher when work is performed during relaxation than during full activation (179).

Cyclic contractions

Efficiency of Contraction

Since the mid-1980s interest has developed in studying the energetics of skeletal muscle during activity mimicking that which occurs during locomotion. Initially, this work focused on the mechanical performance of insect flight muscles using repeated cycles of sinusoidal length changes with a brief period of stimulation in each cycle (146). Those protocols produce contractions that differ greatly from those used previously to probe the behavior of the muscles during steady activity. The contractions are brief, peak forces are submaximal and force output and velocity of length changes alter throughout the cycle. Typically, a series of contractions are

The degree to which a muscle converts chemical free energy into mechanical work is quantified by the efficiency. In general terms, efficiency is the ratio of the work produced to the amount of energy used from which work could have been obtained. At the level of the initial processes, the energy available for conversion into work is ΔG from ATP hydrolysis. For a given amount of ATP breakdown (𝜉 ATP ) the total free energy change is 𝜉 ATP × ΔGATP .


𝜂=

w ξATP ΔGATP

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(A) 100 95 150 100 50 0 50 Energy output (J kg–1)

(B) 50

Total

Rate of energy output (W kg–1)

Force (mN mm–2)

Length (% I0)

Soleus 105

40

30 Total 20 Heat 10

Power

Work 25 Heat

0 0

Stimulation

0 0

0.5 1.0 Time (s)

1 2 3 Contraction frequency (Hz)

4

1.5

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.

Precise definitions of 𝜂 depend of which ATP-consuming processes are included in the denominator. The following conventions will be used here. (i) 𝜂 will be used for efficiency expressed in relation to ΔG, called thermodynamic efficiency, and 𝜀 for efficiency expressed relative to ΔH (i.e., enthalpy efficiency). (ii) If the denominator of Equation includes ATP breakdown by all initial processes (i.e., cross-bridge cycling and ion pumping), this is indicated by a subscript I. For instance, initial thermodynamic efficiency is 𝜂 I . (iii) If only ATP use by cross-bridge cycling is included in the denominator, the subscript CB is used so that cross-bridge thermodynamic efficiency is 𝜂 CB . Thermodynamic efficiency can also be expressed in relation to the free energy made available from substrate oxidation (ΔGS ). For a given extent of substrate oxidation (𝜉 S ) 𝜂 Net =

w 𝜉 S ΔGS

This is called 𝜂 Net because substrate breakdown that is accounted for by resting or basal metabolism is excluded from 𝜉 S (224). If resting metabolism is included, then the efficiency is called overall thermodynamic efficiency (𝜂 O ). It is clear from these definitions that the ultimate limiting factor to muscle efficiency is the amount of free energy that can be obtained from each molecule of ATP split. In

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the following section, the information required to calculate ΔGATP is reviewed and values are calculated for different muscle types.

How much free energy is provided by ATP hydrolysis? The free energy change accompanying ATP hydrolysis cannot be measured directly; instead, it must be calculated on the basis of a standard free energy (ΔG0ATP ) and the concentrations of ATP, ADP, and Pi: ( ΔGATP = ΔG0ATP + RT ln

[ADP][Pi] [ATP]

)

ΔGATP is the molar free energy change (i.e., expressed per mole of ATP), R is the gas constant (8.315 J mol−1 K−1 ), and T is the absolute temperature. ΔG0ATP is the standard free energy change for the reaction when the reactants (in this case, ATP) and products are at concentrations of 1 M and at a specified temperature, pH and magnesium ion (Mg2+ ) concentration. The term in brackets in the above equation is the apparent equilibrium constant (K ′ ) for ATP hydrolysis. Apparent equilibrium constants are expressed in terms of the total concentration of all the ionic species of each compound. For example, ATP exists in four ionic states under muscle


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conditions [ATP4− , ATP3− , (MgATP)2− , and (MgATP)− ] and to calculate K ′ the sum of the concentrations of all those species is used. K ′ values, and therefore ΔGATP values, are only applicable under specified values of pH and [Mg2+ ]. In contrast, calculation of the reference, or chemical, equilibrium constant explicitly includes terms for concentrations of all ionic species involved, including H+ and Mg2+ (95, 194).

comparison, the range of reported intracellular free [Mg2+ ] values is 0.3 to 3 mmol/L (28, 72, 246, 247). For most determinations shown in Table 9, [Mg2+ ] was 1 mmol L−1 , which is in the middle of the range of likely physiological values. In contrast to the influence of [Mg2+ ], pH (over the range of 6-7) and temperature (over the range 25-37◦ C) have relatively little effect on ΔG0ATP (2, 3).

Standard free energy change for ATP hydrolysis

Calculating ADP concentration

ΔG0ATP

To calculate ΔGATP when [ATP] is not 1 M, the concentrations of ATP, ADP, and Pi must be specified. [ATP] and [Pi] can be readily measured from chemical analysis of muscle extracts or NMR spectra, but determining the concentration of ADP is less straightforward. Chemical analysis of muscle extracts indicate that [ADP] is ∼1 mmol/L (154) but the majority of that ADP is normally bound, mostly to actin, rather than free (86, 235). In fact, free [ADP] is too low to be accurately measured so, instead, the concentration is calculated from the creatine kinase reaction for which the value of the apparent ′ ) is equilibrium constant (KCK

can be determined experimentally from either equilibrium constants, taking account of the involvement of H+ and Mg2+ , or the free energies of formation (2, 151). The equilibrium constant approach cannot be used to determine ΔG0ATP directly because the equilibrium constant is so large that [ATP] is too low to measure (143, 252). To circumvent this problem, ΔG0ATP is determined by coupling ATP splitting to another reaction, such as the glutaminase reaction (31,199), for which equilibrium constants can be determined. Reported values of ΔG0ATP from different studies and under conditions comparable to those in muscle cells (e.g., temperature, 25-37◦ C; ionic strength (I), 0.2-0.25 M; pH, 7; [Mg2+ ], 1 mmol/L) are shown in Table 9, arranged in chronological order. Given the number and complexity of the reactions involved in determining ΔG0ATP , it is notable how similar the reported values are, ranging from −29 kJ mol−1 (31, 216) to −37 kJ mol−1 (143), with more recent values converging on −32 kJ mol−1 . The negative value indicates that, under standard conditions, ATP hydrolysis is a reaction that will occur spontaneously. The factor having the most influence on ΔG0ATP under near-physiological conditions is [Mg2+ ] (2, 3). At pH 6 or 7, increasing [Mg2+ ] makes ΔG0ATP less negative: for instance, at pH 7, 25◦ C and in the absence of Mg2+ , ΔG0ATP is −36 kJ mol−1 whereas with 1 mM Mg2+ it is −32.5 kJ mol−1 and with 10 mmol L−1 Mg2+ it is −30.8 kJ mol−1 (2, 3). For

Table 9

Reported Values for Standard Free Energy of ATP Hydrolysis

(ΔG0 ) T

I

[Mg2+ ]

◦C

M

mmol/L

ΔG0 pH

kJ mol−1

Reference

30

n/s

∼0

7

−31.8

(212)

37

0.2

25

7

−29.3

(31)

25

0.2

35

7

−37.5

(199)

25

0.2

1

7

−28.5

(216)

37

0.2

1

7

−28.4

(216)

38

0.25

1

7

−31.8

(165)

38

0.25

1

7.2

−32.3

(235)

25

0.25

1

7

−32.5

(2)

37

0.25

1

7

−33.0

(143)

n/s: not stated.


′ = KCK

[ATP][Cr] [ADP][PCr]

By rearranging, the expression for calculating [ADP] is found. [ADP] =

[ATP][Cr] ′ [PCr] KCK

′ under the Therefore to calculate [ADP], the value of KCK ′ conditions in muscle cells must be known. Determining KCK is not trivial and must take account of all the equilibria of Mg2+ and H+ with ATP, ADP, and PCr, as well as the effects of temperature and ionic strength (95, 143, 165, 233, 234). ′ is inversely related to temperature: Teague & Dobson KCK (233) showed that there was a linear relationship between ′ ) and 1/absolute temperature (Fig. 15). If pH is log10 (KCK 7, ionic strength is 0.25 M and [Mg2+ ] is 1 mmol/L, then ′ ) = 0.2428 + 623/T. Using this relationship, K ′ is log10 (KCK CK ′ also increases ∼179 at 37◦ C, 215 at 25◦ C and 305 at 5◦ C. KCK with increasing [Mg2+ ] and [H+ ] (95).

Calculating ΔGATP ′ can be determined, then [ADP] can be calculated and, If KCK lastly, ΔGATP can be calculated. In Table 10, the informa′ , [ADP] and ΔG tion required to calculate KCK ATP is shown, along with the values of those variables, for a number of muscles under resting conditions. The list is not intended to be exhaustive but rather to illustrate representative values for a range of muscles. In all cases, it was assumed that ΔG0ATP was −32 kJ mol−1 , [Mg2+ ] was 1 mM and intracellular pH was ′ values were calculated for the temperature at which 7. KCK

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log (K′) 2.55 K′ 316 2.50 282 2.45

5°C

251 2.40 15°C 224 2.35 200 2.30

25°C

178 2.25 38°C 0.0032

0.0033

0.0034

0.0035

0.0036

1/Temperature (K–1)

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.

the concentrations of ATP, PCr, and their metabolites were measured. A notable aspect of the values in Table 10 is how uniform the calculated ΔGATP values are for muscles from different species and across temperatures from 0 to 38◦ C. Most values Table 10

are close to −60 kJ mol−1 . The only exceptions are two mammalian fast-twitch muscles [mouse EDL (160) and cat flexor brevis (187)] for which ΔGATP is close to −70 kJ mol−1 . In both those studies, comparable data were obtained from slow-twitch muscles from the same species and the calculations show that ΔGATP is of greater magnitude in fast-twitch muscles than slow-twitch muscles. In contrast to that idea, ΔGATP for rat biceps femoris, another fast-twitch muscle (6), is −60 kJ mol−1 (235). However, it is possible that this is an underestimate due to overestimation of [Pi]. Pi concentration determined from chemical analysis, as used for the rat muscle, are typically higher than those determined from analysis of NMR, as used for the cat and mouse data (187), most likely as a result of additional PCr hydrolysis occurring during the freezing process (87, 187). If [Pi] in the rat muscle was the same as that in fast-twitch mouse muscle, which was determined by NMR, then ΔGATP would be −65 kJ mol−1 in the rat muscle. The comparison of data from fast- and slow-twitch mammalian muscles (Table 10) emphasizes how sensitive calculated ΔGATP values are to the concentrations of Cr and Pi, because they are present in relatively low concentrations in most muscles. The two values of ΔGATP with the greatest magnitude arise in one case due to a low [Cr] and in the other a low [Pi]. However, even if the uncertainties in these values are taken into account, the magnitude of ΔGATP is greater in fast muscles than in slow (187). The data in Table 10 show no systematic difference in ΔGATP among muscles from amphibians, reptiles and mammals (excluding the fast-twitch muscles discussed above). The average (±s.e.) value of ΔGATP for all but the

Intracellular Composition and Calculated [ADP] and ΔGATP for Different Muscles

Muscle

Temp

ATP

PCr

Pi

Cr

◦C

mmol/L

mmol/L

mmol/L

mmol/L

ADP ′ KCK

μmol/L

ΔGATP kJ

mol−1

zJ

Reference

Frog sartoriusa

0

5.3

40

4

6.6

335

2.6

−62

−103

′′

4

3.4

23

4.5

8

310

3.8

−60

−99

(73)

4

35

9.3

12

234

5.9

−59

−98

(156)

20

′′

(156)

sartoriusb

0

5.5

33.8

4.2

6.5

335

2

−61

−102

(131)

Tortoise ilio fibularisc

0

3.6

25.3

4

7.5

335

3.2

−60

−99

(237)

Cat biceps brachii

30

8.9

34.9

3.1

0.2

199

0.4

−73

−121

(187)

Cat soleus

30

5.0

16.6

10.1

7.8

199

11.9

−59

−98

(187)

Rat biceps femoris

38

8

27

8

12.8

176

21.5

−60

−99

(235)

Mouse fast

25

8

32

0.8

7

220

8

−68

−110

(160)

Mouse slow

25

5

16

6

7

220

11

−61

−100

(160)

Frog

Human soleus

37

8.2

33

4.5

9

179

7

−63

−101

(149)

Human FDId

37

6.3

28

3.4

14

179

18

−62

−103

(4)

a Rana temporaria b Rana pipiens c Pi not reported, assumed value similar to frog muscle. d FDI, first dorsal interosseus. Shaded cells, calculated values.

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fast-twitch mammalian muscles is −60.5 (±0.4) kJ mol−1 . When expressed per molecule of ATP, this value is ∼100 zJ (z, SI prefix for 10−21 ).

A note on concentrations Physiologically relevant concentrations of compounds in muscle cells are those expressed relative to the volume that the compounds can access. Thus, concentrations must take account of extracellular volume in multi-fibered preparations (15%-25% of whole muscle volume, 48, 96, 187, 221) and the fraction of muscle fiber volume occupied by myofibrils, mitochondria and SR [12%-20% of fiber volume, depending on muscle (181, 190)]. The question of relevance to cellular energetics is what difference does the way the concentrations are expressed have on values of ΔGATP ? The differences in ΔGATP between concentrations expressed relative to muscle volume and fiber water or myoplasmic water volumes are small, about 1.5% and 1%, respectively.

Effect of compartmentalization of ATP and ADP on ΔGATP The preceding calculations of ΔGATP were based on the assumption that ATP, PCr, and their breakdown products are able to move freely within the relevant cellular compartment. Note that this is not the same as “well-mixed” because there must of necessity be concentration gradients within the cell between locations at which ATP is consumed and regenerated (188). In many models devised to explain the mechanism of linking of ATP supply and demand, transfer of phosphate groups from sites of ATP generation to sites of use, or phosphotransfer, is driven by concentration gradients that develop as ATP and PCr are used. It should be noted that the creatine kinase reaction is likely to ensure that most of the phosphotransfer occurs via PCr/Cr rather than ATP/ADP and that this characteristic will set up spatial differences in [ATP] and [ADP] even in the absence of any physical barrier (e.g., semipermeable membrane or low diffusivity of ATP and ADP) (188). However, the idea that ATP and ADP either cannot or do not diffuse freely with muscle cells, but rather are confined to regions close to sites of ATP use and regeneration, is fundamental to some phosphotransfer models (75, 145). In the more complex models of this type, phosphotransfer is thought to occur by phosphate groups being passed along spatially directed creatine kinase networks that run between the pools of ATP at sites of ATP use and regeneration (75). Regardless of the causes of spatial variations in the concentrations of ATP or ADP or their theoretical implications, the question for the current discussion is whether ΔGATP would be affected if ATP and ADP are confined to some subcellular space? The answer depends on whether it is only ATP and ADP that have restricted movement. If not only ATP and ADP but also Pi were retained within subcellular compartments, then the magnitude of ΔGATP would be reduced but


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the effect is not large: if all three compounds were confined to a volume only one-tenth as great as the whole cell, then the magnitude of ΔGATP would be 10% smaller than if the compounds were distributed throughout the myoplasm. However, proponents of the compartmentalization model have suggested that Pi diffuses freely within the cell (100) while ATP and ADP remain in restricted regions; in that case ΔGATP would be unaffected because the ratio of [ADP] to [ATP] would be the same regardless of the volume in which they are constrained. In summary, ΔGATP in muscle is ∼100 zJ per ATP molecule. On the basis that one cross-bridge cycle is performed for each ATP used, ΔGATP sets the upper limit for the amount of work that can be performed per cross-bridge cycle. In the next section, the mechanical characteristics of cross-bridges are analyzed to establish the maximum work that a cross-bridge could possibly perform in one attachment cycle.

Cross-bridge work output Upper limit to cross-bridge work output The maximum possible work that a cross-bridge could perform in a single ATP-splitting cycle can be estimated from the T2 curves derived from rapid transient experiments (Fig. 16A) [for a review, see (136)]. Huxley and Simmons (138) described the relationship between the force developed during the quick recovery after an abrupt change in the length of a contracting fiber—the T2 force—and the amplitude of the applied length change (Fig. 16B). This stage of the force recovery is rapid, too fast to involve ATP-splitting cycles, and so is thought to be due to re-equilibration among attached states of cross-bridges that were attached when the length step was applied (81). In that case, the relationship between T2 force and length step amplitude gives the average forceextension relationship of attached cross-bridges and the integral of the curve, between the limits of attachment, is the maximum work that could be achieved in one cross-bridge cycle (wmax ) (138). It is envisaged that during a single attachment a cross-bridge traverses at least part of the length-tension curve shown in Figure 16B, moving along the curve from right to left. The measured T2 relationship cannot be used directly to estimate wmax because only part of the length change applied to the fiber to initiate the T2 process is transmitted to the crossbridges; the remainder of the length change is taken up by the compliant contractile filaments. To determine wmax from the T2 curve, the abscissa values must be adjusted to reflect only the length change experienced by the cross-bridges (for a detailed description, see Ref. 23). In Figure 16B, T2 data, with corrected length step amplitudes, are shown for muscle fibers from rat, frog and dogfish; these are the only muscles for which all the data required to estimate wmax is available. For rat, data from three different fiber types have been pooled because the T2 data were independent of fiber type (83). T2 curves are similar across species and across

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(A)

T2 force (f/f0) 1.4

(B)

ΔL (nm h–1)

0

1.2

–2

Rat

–4

1.0

Frog

–6 Dogfish

0.8

Force (T T0–1)

1.0

0.6

0.8 0.4

0.6 0.4

T2 0.2

0.2 T1

0.0 0.0

0.4

0.8

1.2

Time after start of length step (ms)

–12

–10

–8

–6

–4

–2

0

2

4

ΔL (nm h–1)

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.

fiber types within a species. Further, T2 curves, with force expressed relative to isometric force, are also independent of temperature (82). These observations are consistent with the idea that the T2 curve reflects a fundamental aspect of crossbridge mechanics that is common to mammalian, amphibian and fish skeletal muscle. The maximum work a cross-bridge can perform is the area under the T2 curve between the limits of attachment (138). The upper limit for cross-bridge attachment is taken to be the maximum distance between a cross-bridge and the nearest actin binding site (139). If actin binding sites are 5.5 nm apart, then this distance is 2.75 nm so the maximum attachment distance would be +2.75 nm. The minimum is the amplitude of displacement for which the T2 force reaches 0 (i.e., the x-intercept of the T2 curve), which is ∼11 nm (Fig. 16B). The absolute value of wmax would be: 2.75

wMax = TCB

∫−11

T2 dL

Here T2 refers to the normalized T2 curve (i.e., with force normalized by the isometric force), as in Figure 16, and TCB is the average force per attached cross-bridge during isometric contraction. The area under the normalized T2 curves for rat

988

and frog fibers is ∼10 TCB zJ (with TCB in pN) and that for dogfish is ∼9.5 TCB zJ. Estimates of TCB are between 4.5 and 5.5 pN in skeletal muscle from frog, dogfish, rabbit and mouse muscle (24, 197). If we take an intermediate value of 5 pN for TCB and a value of 10 nm TCB for the T2 integral, then wmax is 10 nm TCB × 5 pN/TCB = 50 zJ. That is, this analysis indicates that the maximum work a cross-bridge could do in a single attachment is ∼50 zJ. In the previous section, it was shown that the free energy available from the splitting of one ATP molecule is ∼100 zJ. Assuming each cross-bridge cycle is associated with the splitting of one ATP molecule, then the work output in one cycle must be ≤100 zJ; the estimated wmax , 50 zJ, is consistent with this fundamental thermodynamic constraint.

Upper limit to cross-bridge efficiency wmax sets an upper limit to the efficiency of cross-bridge work generation. Efficiency is the ratio of work generated to the energy used to generate that work (for a review, see Ref. 224). At the cross-bridge level, efficiency is the work performed in one ATP-splitting cycle relative to ΔG from splitting one ATP; that is, the cross-bridge thermodynamic efficiency, ηCB (224). Thus, the maximum ηCB , given the mechanical properties of


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the cross-bridge evident in the T2 curve, is wmax /ΔGATP . If ΔGATP is 100 zJ ATP−1 , as in resting muscle, and wmax is 50 zJ then maximum ηCB = 50/100 = 0.5. Therefore, in a scheme in which one mechanical cycle is associated with the splitting of one ATP molecule, it is likely that cross-bridge efficiency is no greater than 50%.

Upper limit to net muscle efficiency The upper limit for ηCB can be used to estimate the upper limit for the net efficiency of muscle (ηNet ). For this efficiency definition, the energy cost term is increased to take account of additional energetic costs associated with (i) activation, which encompasses ATP use by the SR Ca2+ pump and the sarcolemmal Na+ -K+ pump, and (ii) mitochondrial oxidative phosphorylation. Activation accounts for 25% to 35% of energy turnover for most muscles during an isometric contraction (Table 5). When a muscle is shortening with maximal efficiency, the rate of enthalpy output is typically twofold to threefold greater than isometric rate (23). If it is assumed that the rate of activation heat production is unaltered by shortening (169), then, using values from the middle of the ranges given above, activation heat accounts for ∼30%/2.5 = 12% of the enthalpy output. Therefore, the maximum possible value of initial muscle (as opposed to cross-bridge) thermodynamic efficiency, nI,Max = 𝜂 CB ∕1.12 = 45%. The initial thermodynamic efficiency is defined in terms of ΔG from ATP breakdown. Across a full cycle of contraction and recovery, in which all the PCr breakdown is reversed by oxidative processes, efficiency is defined in terms of ΔG of metabolic substrate oxidation. If we consider a single crossbridge cycle, this is ΔG associated with oxidative breakdown of the substrate to produce one ATP, which is ΔG per substrate molecule (ΔGS ) divided by the ATP yield per substrate molecule (nATP ). Then the maximum possible value of the overall thermodynamic efficiency is 𝜂 Net, Max =

𝜂 I,Max ΔGS ∕nATP

If the metabolic substrate is glucose, ΔGS = 2870 kJ mol−1 or 4614 zJ per molecule. The traditional view was that nATP is 38 ATP (ΔGS /nATP = 4614/38 ≈ 120 zJ ATP−1 ) but more recent estimates suggest that as few as 30 ATP are produced by complete oxidation of one glucose molecule (211), which gives ΔGS /nATP = 4614/30 ≈ 150 zJ ATP−1 . If the former applies to muscle, then nNet,Max = 45/120 = 37.5% and if the ATP yield is the lower value, nNet,Max = 45/150 = 30%. To summarize, using the T2 curve as the force-extension relationship for a cross-bridge, the maximum possible work that could be performed during a single attachment cycle is 50 zJ. If the energy for that cycle is ΔG derived from hydrolysis of one ATP (i.e., 100 zJ), then the maximum possible cross-bridge efficiency is 50% and that corresponds to an net


efficiency of ∼30% to 35%, depending on the ATP yield of oxidative phosphorylation. These are upper limits, derived just from consideration of the potential for cross-bridges to perform work and the assumption that one mechanical cycle is powered by energy from one ATP. No consideration has been made of the effects of shortening velocity, energy expended to develop force or energy costs of relaxation which are features that affect in vivo muscle efficiencies.

Maximum cross-bridge work output during steady shortening How do the estimated upper limits for cross-bridge work output and efficiency compare to actual muscle work output and efficiency? The answers would be straightforward to obtain if thermodynamic efficiency could be measured, but it cannot because it involves ΔG, which cannot be measured. Instead, experimentally determined enthalpy efficiencies are typically defined with respect to the rate of enthalpy output. 𝜀=

ẇ ẇ = ẇ + q̇ ḣ

This is traditionally called mechanical efficiency, following Hill (113). But this term has been criticized on several grounds (257), including the implication that the quantity in the denominator is the maximum energy from which work could be produced. This is incorrect as it is only the free energy component of ḣ that has potential to be used for work. In Table 11 values of maximum initial enthalpy efficiency (εI,Max ) for a variety of skeletal muscles are shown. These values were determined by measuring ẇ and ḣ during steady shortening at the velocity at which efficiency was maximal. Values of εMax range from 0.26 for the fast-twitch mouse EDL muscle (24) to 0.77 for tortoise ilio fibularis muscle (254), the highest value recorded for any muscle. ηCB can be estimated from εMax , as described in detail previously (13, 23, 224), by taking account of the fraction of enthalpy output unrelated to cross-bridge cycling (ḣ A ; rate of activation heat output, expressed as fraction of ḣ 0 ) and the ratio of ΔHPCr and ΔGATP . 𝜂 CB = 𝜀 ⋅

ΔHPCr ḣ ⋅ ̇h − ḣ A ΔGATP

ḣ is the rate of enthalpy output when shortening with maximal efficiency, expressed in multiples of the ḣ 0 . Equation gives ηCB = 0.19 for the mouse muscle and 0.46 for the tortoise muscle, with values for the other muscles in between; that is, the highest known ηCB , that for tortoise muscle, is about half the magnitude of ΔGATP . It is evident from the definition of ηCB that if ηCB and ΔGATP (per molecule) are known, wCB , the actual work performed per cross-bridge per ATP splitting cycle, can be estimated. wCB = ηCB ⋅ ΔGATP

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Table 11


Enthalpy and Thermodynamic Efficiencies and Cross-Bridge Work Output

Species

εMax

g

ḣ A ∕ḣ 0

Frog sartorius

0.49 (23)

3.1 (23)

0.27 (19, 129)

wCB

wCB /wmax

ηCB,Max

zJ

%

0.30

30.3

61

Dogfish white

0.33 (66)

2.5 (66)

0.34 (178)

0.22

21.6

43

Tortoise ilio fibularisa

0.77 (254)

5.3 (254)

0.27

0.46

45.8

92

Mouse soleus

0.48 (24)

2.5 (24)

0.35 (11, 238)

0.33

32.4

65

Mouse EDL

0.26 (24)

1.9 (24)

0.35 (20, 238)

0.19

18.5

37

a Activation

heat component for tortoise assumed same as for frog. Numbers in parentheses, references from which data were obtained. εmax , maximum initial enthalpy efficiency. g, rate of enthalpy output when shortening at the velocity at which efficiency is maximal, expressed relative to rate of enthalpy output in an isometric contraction; fA , fraction of isometric enthalpy output attributable to activation processes; ηcb,max , maximum cross-bridge thermodynamic efficiency; wCB , maximum measured work output per crossbridge ATP-splitting cycle; wMax , theoretical maximum cross-bridge work output per attachment cycle (50 zJ; derived from T2 curve).

wCB values, estimated in this way, are given in Table 11. Of particular interest is the comparison between wCB and wmax (estimated above to be ∼50 zJ). For most of the muscles considered, actual cross-bridge work output is between 30% and 60% of wmax , equating to cross-bridge work output per cycle of between 20 and 30 zJ for most muscles. Mechanistically, this observation indicates that individual cross-bridges in those muscles must traverse only part of the cross-bridge force-extension relationship in each attachment cycle. The one exception is the tortoise muscle for which actual work output is >90% of the estimated maximum that cross-bridges can achieve. This high efficiency is most likely related to the slow cross-bridge cycling that characterizes tortoise muscle, underpinning the idea that a muscle can either be slow and efficient or fast but less efficient (69, 254). The estimates of the theoretical maximum ηNet can be compared to the highest reported ηNet , which is 35% for tortoise muscle (254). This is higher than the maximum ηNet estimated assuming nATP is 30. If ηNet = 35% then ΔGS /nATP = 45/0.35 = 129 zJ and this is consistent with an ATP yield of 36 per substrate molecule oxidized. ATP yields have also been estimated using enthalpy data from mouse EDL and soleus muscles (21). That analysis indicated an ATP yield of 39 for EDL and 36 for soleus. These data from functioning muscles are not consistent with the biochemical analyses that indicate the yield is as low as 30 (211).

Summary This analysis of muscle efficiency defined upper limits for efficiency on the basis of ΔGATP and cross-bridge mechanical characteristics. It was evident that ΔGATP exceeds the single cycle capacity of cross-bridges to perform work by a factor of 2. The work per cross-bridge cycle in tortoise muscle approached close to the suggested limit, which reinforces the idea that efficiency is fundamentally constrained by cross-bridge properties that can be quantified on the basis of

990

purely mechanical experiments. For most muscles, the work performed per cycle is well below the maximum, reflecting a trade-off between fast, powerful contractions and efficiency.

Conclusion Since Helmholtz first measured the heat produced by contracting isolated muscle and recognized its likely relationship to chemical changes occurring in the muscle over 160 years ago (see Introduction to Ref. 116) a substantial literature on muscle energetics has been produced. We now have an extensive knowledge of muscle energetics, including a good understanding of the thermodynamic and biochemical underpinnings of muscle contraction. It is clear that the mechanical and biochemical aspects of the cross-bridge cycle are closely (54), but perhaps not always tightly (171, 256), coupled and a more detailed mapping of steps within the attachment phase of the cross-bridge cycle to the associated energy changes is developing, providing insights into the thermodynamic bases of cross-bridge energy transduction (23, 256). In compiling a review such as this, it is necessary to be selective to produce a coherent account of the main aspects of skeletal muscle energetics. Consequently, many areas have not been discussed but this is not to negate the importance of those areas. For example, control of mitochondrial respiration was mentioned only briefly, resting metabolism (55,222) was not covered and neither were changes in energetics with fatigue (11, 17, 19), advanced age (52) or pathological states. Another area only briefly mentioned in this review was efforts at understanding the energetics of muscles in vivo. There remain many avenues to explore. For example, there are still uncertainties concerning the basis of enthalpy output, especially in mammalian muscle so there is scope for further energy balance experiments on mammalian muscles. There is also plenty of opportunity to expand the range of muscles and species of animals about which we have detailed knowledge.


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Most of our knowledge of muscle energetics is built on study of a small number of muscles from just a few species of small animals. Another area that warrants further investigation is the energetics of lengthening, both in relation to biochemical changes (only studied in detail using frog muscle) and energy absorption (where does the energy go during lengthening?). In relation to in vivo muscle function, we are on the cusp of a more comprehensive understanding of the bases of energetics of moving animals, including humans, through integration of information about energetics of animal movement with that from muscle energetics. Exploring these and other avenues will ensure that the story of muscle energetics will continue to evolve.

Acknowledgements The author would like to acknowledge those who inspired his interest in muscle energetics and whose thoroughness and attention to detail have set the standards for those who follow. The author is especially grateful to his past and present colleagues Denis Loiselle, Nancy Curtin, Roger Woledge, Colin Gibbs, and Igor Wendt. The influences of Earl Homsher, Martin Kushmerick, and Jack Rall have been derived largely from their published work but have been no less important.

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995

Models of muscle contraction and energetics.

Influence of temperature on mechanics and energetics of muscle contraction.

Ventricular energetics.

Energetics of paraplegic walking.

Cardiac energetics.

Energetics of enzyme catalysis.

Energetics of rhodopsin and isorhodopsin.

Energetics of thrombin-fibrinogen interaction.

Energetics of active transport processes.

Stem cell energetics.

Energetics of membrane protein folding.

Myonemal contraction of Spirostomum. III. The thermal dependence of contraction, relaxation and excitation-contraction coupling.

CKD and Muscle Mitochondrial Energetics.

Species differences in cardiac energetics.

Energetics of active fluctuations in living cells.

Revelation of Interfacial Energetics in Organic Multiheterojunctions.

Applications and implications of ecological energetics.

Energetics of running: a new perspective.

Energetics (and kinematics) of short shuttle runs.

Energetics of repacking a protein interior.

The energetics of middle-distance running.

Excitation-contraction coupling and the mechanism of muscle contraction.

Energetics of defects on graphene through fluorination.

Role of physiological energetics in ecotoxicology.