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. 2006 Feb 23;573(Pt 1):5–15. doi: 10.1113/jphysiol.2006.104992

ATP splitting by half the cross-bridges can explain the twitch energetics of mouse papillary muscle

C Widén 1, C J Barclay 1
PMCID: PMC1779702  PMID: 16497711

Abstract

The aim of this study was to quantify the fraction of cross-bridges that cycle during a cardiac twitch. Measurements of the energetics of contracting left ventricular mouse papillary muscle were made in vitro (27°C) using the myothermic technique. Enthalpy output was partitioned into force-dependent and force-independent components using 2,3-butanedione monoxime (BDM) to selectively inhibit cross-bridge cycling. For isometric contractions and a contraction frequency of 2 Hz the net enthalpy output was 5.7 ± 0.8 mJ g−1 twitch−1 and initial enthalpy output was 2.3 ± 0.3 mJ g−1 twitch−1 (n = 11). Assuming that low concentrations of BDM did not affect Ca2+ cycling, force-independent enthalpy output was 18.6 ± 1.9% (n = 7) of the initial enthalpy output. Enthalpy output decreased with increased contraction frequency but was independent of shortening velocity. On the basis of these values, it was calculated that the twitch energetics were consistent with ATP splitting by half the cross-bridges and the pumping of one Ca2+ into the sarcoplasmic reticulum for every three cross-bridge cycles. The simplest interpretation is that half the cross-bridges completed one ATP-splitting cycle in each twitch. The lack of influence of shortening velocity on energy cost supports the idea that the amount of energy to be used is determined early in a twitch and is not greatly influenced by events that occur during the contraction.

The basic contractile event in striated muscle is the twitch, which is the response of a muscle or fibre to a single neural or electrical stimulus. Given its fundamental nature, it is of interest to characterize the molecular events that underlie the twitch. Under both physiological and typical laboratory conditions peak twitch force is less than the maximum force that a muscle or fibre can produce. Support for this idea comes from the observations that skeletal muscle twitch force is less than tetanic force and that cardiac twitch force can be increased substantially by inotropic agents and changes in experimental conditions (e.g. cooling) that increase intracellular [Ca2+] (for a review, see Endoh, 2004). Because twitch force is submaximal, it is unlikely that the force output reflects the simultaneous action of all the available myosin cross-bridges.

The purpose of this study was to quantify the fraction of cross-bridges that cycle during a cardiac twitch. This has not been determined before. Under most conditions, each force-generating interaction between a myosin cross-bridge and an adjacent actin filament is associated with the hydrolysis of one ATP molecule. Therefore, one way of counting the number of cross-bridge cycles that occur during a contraction is to measure the number of ATP molecules used; that is, to measure the energy cost of the contraction. In the current study, the fraction of cycling cross-bridges was estimated from measurements of the energy cost of contraction using isolated papillary muscles taken from the left ventricle of the mouse heart. Energy cost was determined using the myothermic technique, which has the chemical and temporal resolution to accurately monitor the biochemical changes occurring within a brief twitch (Woledge, 1998). In addition, with this technique it is possible to separate energy used by the cross-bridges from energy used by other cellular ATPases (i.e. those associated with pumping ions across membranes) (Gibbs et al. 1988; Alpert et al. 1989). Mouse cardiac muscle was used because the advent of heart-focused genetic manipulations (e.g. Headrick et al. 1998; Bluhm et al. 2000) has made it important to develop experimental techniques and protocols that can be used to probe the basic physiology of cardiac muscle in this species. For example, although in a number of studies the intracellular free Ca2+ and Ca2+ content of the sarcoplasmic reticulum (SR) of mouse cardiac muscle have been measured (Gao et al. 1998; Georgakopoulos & Kass, 2001; Stull et al. 2002), in no cases has the amount of Ca2+ released been quantified.

This study is the first in which the energetics of contracting, isolated mouse cardiac muscle have been measured. It is important to ensure that diffusive O2 supply is adequate to meet the needs of isolated muscles so we combined the metabolic data obtained in the current study with a theoretical model of diffusive O2 supply (Barclay, 2005) to confirm that the muscles used were small enough to maintain a favourable balance between O2 supply and consumption. The results of the study indicate that the energy used in a cardiac twitch can be accounted for by the cycling of about half the cross-bridges and the uptake into the SR of about one Ca2+ for every three cross-bridge cycles.

Methods

Papillary muscle preparation

The preparation and apparatus have been described in detail previously (Mellors et al. 2001; Widén & Barclay, 2005) and only a brief description is provided here. Male Swiss mice, 6–12 weeks old, were rendered unconscious by inhalation of an 80% CO2–20% O2 gas mixture (Kohler et al. 1999) and killed by cervical dislocation. The Griffith University Animal Ethics Committee approved all animal handling procedures. Papillary muscles (length, 3.4 ± 0.1 mm; mass, 1.7 ± 0.1 mg; mean ± s.e.m., n = 24) were dissected from the left ventricle with the heart immersed in oxygenated (95% O2–5% CO2) Krebs-Henseleit solution of the following composition (mm): 118 NaCl, 4.75 KCl, 1.18 KH2PO4, 1.18 MgSO4, 24.8 NaHCO3, 2.5 CaCl2, 10 glucose, 30 2,3-butanedione monoxime (BDM). BDM was included in the solution only during dissection to avoid contracture upon freeing the muscle from its in situ length constraints; it does not alter the energetic properties once washed out (Kiriazis & Gibbs, 1995). Platinum clips were attached to the tendon at one end of the muscle and to a piece of ventricular wall at the other.

Experimental apparatus

In the experimental chamber, muscles were mounted between a semiconductor force transducer (AE801, SensorOne, CA, USA) and a servo-controlled motor (322B, Aurora Scientific Inc., Ontario, Canada) via fine stainless steel wires that provided a low compliance linkage between the preparation and the recording equipment. The muscle lay along the active thermocouples of a thin-film, antimony–bismuth thermopile (Mulieri et al. 1977; Barclay et al. 1995), which was used to measure changes in muscle temperature, from which muscle heat production was calculated. The recording region of the thermopile was 6 mm long, contained 24 thermocouples and produced 1.25 mV °C−1. Supramaximal, rectangular stimulus pulses (amplitude, 6 V; duration, 2 ms) were delivered to the muscles via fine platinum wires (diameter, 25 μm; Goodfellow, UK) connected to the platinum clips.

Recordings

The temperature of the chamber was maintained at 27°C by circulating water from a thermostatically controlled reservoir (F-10-HC, Julabo Labortechnik, Germany). The thermopile output was filtered (low-pass filter, cut-off frequency 100 Hz) and amplified using a series arrangement of two low-noise amplifiers (15C-3A, Ancom Instruments, Cheltenham, UK; SR560, Stanford Research, CA, USA). The outputs of the force transducer and thermopile were sampled at 220 Hz, digitized, displayed on a monitor and stored on disk. Data sampling and control of muscle length via the motor were performed using a multifunction circuit board (DAS-1802AO, Keithley Instruments, Cleveland, OH, USA). The amount of heat produced by passage of the stimulus current through the muscle was measured using an artificial muscle (agar gel made with Krebs solution and with the same dimensions as a muscle). The stimulus heat was ∼0.1 μJ pulse−1, which was ∼2% of the net heat produced by the muscle in response to a stimulus pulse. For all recordings, stimulus heat was subtracted from the calculated heat output.

Measuring enthalpy output

The heat and the work liberated from a contracting muscle arise from enthalpy changes associated with the biochemical reactions that underlie contraction. Enthalpy output associated with contractile activity can be separated into a component resulting from the breakdown of high-energy phosphates, called initial enthalpy output, and a component resulting from the oxidative resynthesis of high-energy phosphates, called recovery enthalpy output. Initial enthalpy output can be separated from recovery metabolism because of the difference in the time courses with which they are produced during the transition from rest to steady activity. Initial enthalpy is produced simultaneously with contractile activity and thus its production commences in synchrony with the activity (Fig. 1A and B). In contrast, recovery enthalpy output increases exponentially from its resting value towards its steady-state value with a time constant, in the mouse papillary muscle at 27°C, of about 12 s (see legend to Fig. 3). In this study, the total, suprabasal enthalpy output produced (called the net enthalpy output) during and after a short set of contractions (lasting 20 s) was measured (Fig. 1C and D) and then the initial enthalpy output was determined from the enthalpy produced during the first few contraction cycles, before the rate of recovery enthalpy production became significant (Fig. 1B). Initial enthalpy output was used to partition energy use into force-dependent and force-independent components (Alpert et al. 1989) and recordings of net enthalpy output were used to calculate the time course of recovery heat output and also to verify the number of cross-bridge cycles occurring in each twitch.

Figure 1. Example of the time course of force production and enthalpy output.

Figure 1

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An example of force production and enthalpy output of a mouse papillary muscle. The muscle performed 20 isometric contractions at a frequency of 1 Hz. A, force output for the first three twitches. B, cumulative enthalpy production during the first three twitches. Because the muscle was not shortening, there was no work production so enthalpy output was equal to the heat output. The continuous line indicates the measured heat output and the dashed line indicates the estimated time course of recovery heat production (from eqn (2)). The quantities indicated by the arrows labelled IH1, IH2 and IH3 represent the cumulative initial heat production up to the end of each of the first three contraction cycles. C, the time course of force output for the whole contraction series. D, the cumulative enthalpy output during and after the 20 contractions. The vertical dashed line indicates the time at which contractions ended. The rate of heat production remained above the resting heat rate for ∼60 s, indicating the ongoing recovery metabolism. Muscle mass 1.72 mg; length 3.4 mm.

Figure 3. Simulations of time course of PO2 at muscle centre during contraction series.

Figure 3

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Simulations of the PO2 profile through muscle were made using eqn (5). The diffusivity of O2 through muscle was taken to be 2.43 × 10−5 ml cm−1 min−1 atm−1 at 27°C (adjusted from value at 22.8°C using a Q10 of 1.06; Mahler et al. 1985). Prior to the start of the contraction series, metabolic rate was assumed to be constant and equal to the resting metabolic rate (4 mW g−1; Widén & Barclay, 2005). It was further assumed that during the series of contractions the rate of O2 consumption increased exponentially towards a steady value of 7 mJ g−1 twitch−1 with a time constant equal to that for the decline in rate of heat output when contractile activity ended (i.e. 12.2 ± 0.8 s, n = 11). Metabolic rates were converted to rates of O2 consumption using an energetic equivalent of ∼19 mJ μl−1, which was calculated on the basis that the primary substrate for mitochondrial oxidation was glucose for which the molar enthalpy is 2820 kJ mol−1. Note, however, that the calculated PO2 values are only ∼2.5% smaller if it were assumed that fat oxidation, yielding 17.3 mJ μl−1, fuelled the contractions. The PO2 in the solution surrounding the muscle was 0.84 atm. Muscle radius was taken to be 0.38 mm. Simulations were made for 20 s of contractile activity (as used in this study) and for contraction frequencies of 1, 2, 3 and 4 Hz.

The relative contributions of initial and recovery processes to enthalpy output at the start of a contraction protocol were estimated as follows. An exponential increase in the rate of recovery heat production (Inline graphic) can be described by:

graphic file with name tjp0573-0005-m1.jpg (1)

where Inline graphic is the steady-state recovery heat rate. The cumulative recovery enthalpy production associated with contractile activity (QR) is given by the integral of eqn (1) and assuming that Inline graphic:

graphic file with name tjp0573-0005-m2.jpg (2)

Inline graphic was estimated on the basis that the amount of recovery heat required to completely reverse the initial heat (i.e. R/I ratio) was 1.2 × the amount of initial heat (see below) and that in an energetic steady state this amount of recovery heat would be produced within each contraction cycle (i.e. in 0.5 s when contracting at 2 Hz). The value of the R/I ratio was calculated from the ratio of the initial mechanical efficiency (ɛI) to the net mechanical efficiency (ɛNet) (for the derivation of this equation, see Barclay & Weber, 2004):

graphic file with name tjp0573-0005-m3.jpg

ɛI was the ratio of the work done in the first three contractions to the enthalpy output in the same three contractions and ɛNet was the ratio of the work performed in all contractions in the series to the net enthalpy output (as defined above). The R/I for mouse papillary muscles contracting at 2 Hz was 1.20 ± 0.09 (mean ± s.e.m, 30 observations on 9 preparations) and was independent of muscle mass.

The initial enthalpy output was ∼2.3 mJ g−1 twitch−1 at a contraction frequency of 2 Hz so Inline graphic. Substituting this value into eqn (2), the amounts of recovery heat produced between the start of recording and the ends of the first, second and third contraction cycles were 0.028, 0.11 and 0.25 mJ g−1, respectively, which was 1.2, 2.4 and 3.6% of the total heat produced by the end of those cycles (Fig. 1B). In some records, the heat produced in the first one or two cycles was not well resolved so initial heat production was determined from the total heat produced over the first three cycles.

Partitioning initial metabolism into force-dependent and force-independent components

Initial enthalpy output was partitioned, using an isometric contraction protocol (2 Hz), into a force-dependent component (i.e. enthalpy output associated with cross-bridge activity) and a force-independent, or activation, component (i.e. enthalpy output associated primarily with ion pumping) by selectively inhibiting cross-bridge cycling with BDM and/or exposure to hyperosmotic solution (Alpert et al. 1989; Widén & Barclay, 2005). The relationship between initial enthalpy output and the force–time integral (FTI) was determined by making incremental reductions in FTI by step-wise increases in BDM concentration from 2 to 10 mm. The magnitude of force-independent enthalpy output was determined by extrapolating the enthalpy output–FTI relationship to zero FTI (Fig. 2).

Figure 2. Example of determining force-independent enthalpy output.

Figure 2

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Force-independent enthalpy output was determined from the relationship between initial enthalpy output and force–time integral (FTI). FTI was varied by bathing muscles in Krebs solution containing increasing concentrations of BDM. Initial enthalpy output is expressed as a percentage of that measured in the absence of BDM. The lowest force–time integral was obtained using a combination of 5 mm BDM and 150 mm sucrose. A line was fitted through the data using the method of least squares; its equation is: Relative initial heat = 0.82 × FTI + 13.6 (r2 = 0.97). The value of the y-intercept was used to quantify the force-independent fraction of initial enthalpy output.

Experimental protocols

Once in the experimental chamber, muscle length was adjusted to give a passive force of 5 mN mm−2; this length was designated L0. It has previously been shown that this passive force corresponds to a sarcomere length of ∼2.1 μm in these muscles (Widén & Barclay, 2005). Muscles were then allowed to equilibrate for 60 min. When first dissected, the resting metabolism of isolated papillary muscles is high and central anoxia can develop (Widén & Barclay, 2005). To minimize the possibility of this occurring, muscles were not stimulated during the equilibration. After 60 min, the muscles were stimulated at 0.2 Hz for 10 min. For 5 min prior to making heat measurements, muscles were not stimulated to allow metabolic rate to decrease to its resting value. This provided the thermal baseline for heat measurements.

To investigate the effects of contraction frequency on number of cross-bridge cycles in a twitch, an isometric contraction protocol was used; the protocol consisted of 20 s of contractions at frequencies of 1, 2, 3 and 4 contractions s−1. To investigate the effects of shortening on number of cross-bridge cycles, a protocol that incorporated a cyclic strain pattern in each twitch was used (Mellors & Barclay, 2001). The strain pattern was designed to mimic strains experienced by papillary muscles in vivo (Semafuko & Bowie, 1975). The protocol consisted of a 60 ms isometric phase after delivery of the stimulus pulse, isovelocity shortening with an amplitude equal to 0.15 L0, followed by isovelocity lengthening back to L0. The velocity of the shortening phase ranged between 1 and 5 mm s−1 (∼0.4–1.7 L0 s−1). These velocities were calculated by dividing the strain amplitude by the reported duration of the ejection phase in isolated, working mouse hearts (Larsen et al. 1999). To accommodate the subphysiological temperature used in this study, it was assumed that the Q10 for shortening velocity (i.e. change in velocity for a 10°C temperature change) was 2. This particular strain pattern was used because it was found in preliminary experiments to maximize work output at 2 Hz.

Calculation of number of cross-bridge cycles

The number of cross-bridge cycles that occurred in a twitch was estimated from the amount of ATP used and assuming that each cross-bridge cycle was associated with the hydrolysis of one ATP molecule. It was further assumed that under the conditions used in this study ATP splitting was fully buffered by the creatine kinase reaction so that the enthalpy output arises from the net breakdown of PCr. The number of ATP molecules hydrolysed (NATP; ATP g−1 twitch−1) was calculated as follows:

graphic file with name tjp0573-0005-m4.jpg (3)

ΔHI is the initial heat per twitch (mJ g−1), f is the force-independent enthalpy output expressed as a fraction of the initial enthalpy output, ΔHPCr is the molar enthalpy change for PCr hydrolysis and NA is Avogadro's constant. ΔHPCr was calculated from the R/I ratio (1.2), as described by Woledge and colleagues (p. 219, Woledge et al. 1985; Woledge & Reilly, 1988), and was 34 kJ mol−1. To compare this value to the number of cross-bridges present in mouse cardiac muscle, we scaled NATP to a volume of muscle containing a precisely known number of cross-bridges, the unit sarcomere cylinder. This is a region bounded transversely by four neighbouring thick filaments and longitudinally by successive Z-lines and encloses four thin filaments (Squire et al. 1990). About 150 cross-bridges can interact with each thin filament (see Appendix) so this volume contains a total of 600 cross-bridges. Then the number of ATP molecules used can be related to the number of cross-bridge cycles that occurred in this volume per twitch (NCB) as follows:

graphic file with name tjp0573-0005-m5.jpg (4)

where Vs is the volume of a sarcomere cylinder, ρ is the density of muscle (1.06 g cm−3) and VM is the fraction of muscle volume occupied by myofibrils. The volume of a sarcomere unit cell was calculated assuming that sarcomere length was 2.1 μm (Widén & Barclay, 2005) and that the spacing between the thick filaments was 41 nm (Yagi et al. 2004), giving a sarcomere cell volume of 3.5 × 10−15 cm3. VM takes account of the volume density of myofibrils in myocytes (0.52 in mouse myocytes; Barth et al. 1992) and the fraction of muscle volume that is occupied by myocytes (0.79 in rat myocardium; Dobson & Cieslar, 1997); therefore, VM is 0.52 × 0.79 = 0.41 × muscle volume.

Analysis of diffusive O2 supply

The adequacy of diffusive O2 supply to papillary muscles was assessed by numerical solution of the equation describing diffusion of O2 into muscles of cylindrical geometry (p. 229, Hill, 1965) as described in detail previously (Barclay, 2005):

graphic file with name tjp0573-0005-m6.jpg (5)

where t is time, PO2 is the partial pressure of O2, r is the radial distance from the muscle's centre, A(t) is the time-dependent rate of O2 consumption, and K is the diffusivity of O2 through muscle. The value of PO2 at the muscle centre was calculated for 20 s of contractile activity (as used in this study) and for contraction frequencies of 1, 2, 3 and 4 Hz (Fig. 3). PO2 at the muscle surface, measured using an O2-sensitive microelectrode (OX500, Unisense, Aarhus, Denmark), was 0.84 atm (85 kPa). At rest, PO2 at the muscle centre was calculated to be ∼0.7 atm. Central PO2 decreased upon stimulation (Fig. 3). However, even in the worst case (contraction frequency 4 Hz), at the end of the contraction protocol central PO2 (minimum value ∼4 kPa) would have remained greater than the values at which mitochondrial respiration becomes compromised (∼1.3 kPa Schenkman, 2001).

Data normalization and statistical analysis

At the end of experiments, the platinum clips were cut off the preparation, the muscle was lightly blotted and its mass determined using an electronic balance (Cahn 25, Cahn Instruments, Cerritos, CA, USA). The average cross-sectional area was calculated by dividing mass by length, and assuming muscle density was 1.06 g cm−3. Active force was normalized by cross-sectional area. All data are presented as the mean ± s.e.m. The statistical significance of variations in initial and net enthalpy use with contraction frequency and shortening velocity was assessed using one-way analysis of variance (ANOVA); for the contraction frequency data, a repeated measures one-way ANOVA was used. The significance of variations in force, measured at different times during the contraction series, with contraction frequency were assessed using a 2-way ANOVA. Where appropriate, post hoc analyses were performed using Dunnett's test for comparisons with a control group (Hancock & Klockars, 1996). Decisions concerning statistical significance were made at the 95% level of confidence.

Results

Energy cost of a twitch and effects of contraction frequency

The energy cost of papillary muscle contraction was first assessed using a series of isometric contractions at frequencies between 1 and 4 Hz. At a frequency of 1 Hz, the initial enthalpy output, averaged over the first three contractions (Fig. 1B), was 3.3 ± 0.6 mJ g−1 twitch−1 and the net enthalpy output, from all the twitches, was 6.8 ± 1.1 mJ g−1 twitch−1 (n = 11). Both the initial and net enthalpy outputs declined significantly with increasing contraction frequency (Fig. 4). At a frequency of 4 Hz the mean initial enthalpy output was 1.2 ± 0.2 mJ g−1 twitch−1 and the mean net enthalpy output was 3.9 ± 0.6 mJ g−1 twitch−1 (n = 11). Isometric force output also decreased significantly with contraction frequency. This analysis was performed using the average forces in each of the four 5 s intervals in the contraction protocol. The effect of contraction frequency was independent of the time interval over which force was averaged (Fig. 5).

Figure 4. Enthalpy output per twitch in isometric and shortening contractions.

Figure 4

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The initial (grey bars) and net (black bars) enthalpy output per twitch was measured in both isometric and shortening contractions. A, the heat output of the papillary muscles was measured at four different frequencies (1–4 Hz) using glucose as substrate. The enthalpy output decreased as twitch rate increased. * Statistically significant difference between enthalpy outputs of higher frequencies compared to 1 Hz value. B, enthalpy output of a muscle shortening using a realistic contraction protocol. Heat and work was expressed as a function of shortening velocity normalized to muscle length at a realistic range of velocities.

Figure 5. Contraction frequency dependence of isometric force output.

Figure 5

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Isometric force output is shown as a function of contraction frequency. For each muscle, the average force output was calculated over 5 s intervals and normalized by the average force over the corresponding interval at 1 Hz. At all frequencies the full protocol was of 20 s duration. The symbols represent the mean values of data from 11 muscles. The data for different 5 s intervals are distinguished as indicated by the key in the figure. Only at 4 Hz did the mean values for all groups differ significantly from those at 1 Hz (indicated by *).

Effects of shortening on twitch energy cost

The effects of shortening velocity on energy cost were investigated using a contraction frequency of 2 Hz with a period of shortening in each contraction at one of a range of velocities. The shortening velocities used ranged from 0 (isometric) to 1.7 L0 s−1 and enthalpy data were sorted into velocity bins, with bin width determined using Sturge's rule (no. bins = 1 + 3.322 × log(no. data points)). Shortening velocity had no significant effect on either initial or net enthalpy output (Fig. 4). The net enthalpy output, averaged across all velocities, was 5.6 ± 0.4 mJ g−1 twitch−1 and the corresponding initial enthalpy output was 2.1 ± 0.2 mJ g−1 twitch−1 (n = 9).

Partitioning energy cost between force-dependent and force-independent components

Initial enthalpy output, measured over the first three contraction cycles, was partitioned into force-dependent and force-independent components by selectively inhibiting force output using BDM (Fig. 2). Force-independent enthalpy output accounted for 18.6 ± 1.9% (n = 7) of the initial enthalpy output.

Number of cross-bridge cycles per twitch

Using eqns (3) and (4), the number of ATP molecules split was calculated and compared to the number of cross-bridges in the same volume of muscle. At 2 Hz and contracting isometrically, it was calculated that 290 ATP molecules were used in the unit sarcomere. There are 600 cross-bridges in that volume and if one cross-bridge cycle involves the splitting of one ATP, then the amount of ATP used is consistent with 48% of the cross-bridges completing one ATP-splitting cycle in each twitch. These values can also be expressed in micromoles per gram of muscle mass (i.e. taking into account non-myofibrillar intracellular volume and extracellular volume). In that case, the amount of ATP split is:

graphic file with name tjp0573-0005-m7.jpg

The cross-bridge concentration, worked out similarly, is 110 nmol g−1.

The initial enthalpy measurements encompassed just the first three twitches so it is possible that these calculations are not representative of energetics during more prolonged activity. To see whether energy use averaged over 20 s can be accounted for by a similar number of ATP-splitting cycles per twitch, the calculations were repeated using the net enthalpy output produced in response to the complete 20 s protocol (i.e. 40 twitches when contraction frequency was 2 Hz). In that case, the denominator in eqn (3) was the molar enthalpy output associated with substrate oxidation, expressed per mole of ATP formed. The enthalpy of glucose (the exogenous substrate provided in this study) oxidation is 2820 kJ mol−1 (Crabtree & Nicholson, 1988). If this generates 38 ATP (i.e. P/O2 ratio of 6.3) then glucose oxidation produces 2820/38 = 74 kJ per mole of ATP. Substituting 5.6 mJ g−1 twitch−1 for ΔHI and 74 kJ mol−1 for ΔHPCr in eqn (3) gives the number of ATP molecules used per twitch per unit sarcomere cell as 336, which is equal to 56% of the number of cross-bridges. If the energy came from oxidation of endogenous fat (which gives 76 kJ per mole of ATP) rather than glucose, then the number of ATP molecules used per twitch per unit sarcomere cell would be 328, which is equal to 55% of the number of cross-bridges.

Amount of Ca2+ released from the SR in each twitch

The approach taken to calculating NCB can also be applied to calculate the amount of Ca2+ cycled through the SR of a mouse cardiac cell in each twitch. This was done by modifying eqn (3) to take account of Ca2+ pump energetics and combining the result with eqn (4):

graphic file with name tjp0573-0005-m8.jpg (6)

where k is the fraction of the force-independent enthalpy output associated with Ca2+ pumping (assumed to be the same as in rabbit myocytes, 0.77; Delbridge et al. 1996) and the factor of 2 reflects the stoichiometry of the SR Ca2+ pump (2 Ca2+ pumped for each ATP hydrolysed). It should be noted that in mouse cardiac cells > 90% of Ca2+ cycling is via the SR Ca2+ pump (Georgakopoulos & Kass, 2001). Substituting appropriate values, again for the case of a muscle contracting at 2 Hz, gives a value of 98 Ca2+ released per twitch in the sarcomere cylinder volume, which, taking account of the non-myofibrillar volume of muscle, is equivalent to 18 nmol g−1 twitch−1. The SR Ca2+ content in mouse myocytes contracting steadily at 0.5 Hz at 22°C has been estimated to be 43 nmol (g muscle mass)−1 (Terracciano et al. 1998). Thus, the amount estimated to be released in the current study is probably about half the SR Ca2+ content, consistent with other estimates (e.g. Delbridge et al. 1996).

Discussion

Number of ATP-splitting cross-bridge cycles in each twitch

The main finding of this study was that in a twitch of mouse cardiac muscle the number of ATP-splitting cross-bridge cycles is about half the total number of cross-bridges in the muscle. The simplest interpretation of this observation is that half the cross-bridges completed one ATP-splitting cycle in each twitch. That only a fraction of cross-bridges complete one ATP-splitting cycle has been suggested previously for rabbit papillary muscle (Mast & Elzinga, 1990; see Discussion following Gibbs & Barclay, 1995) and could be inferred from estimates of cross-bridge cycling rate for rat papillary muscle (e.g. Hoh et al. 1988) but the current study is the first to attempt to quantify the fraction. It is possible that fewer than half the cross-bridges completed more than one cycle, in which case it might be expected that the number of cross-bridge cycles could be modulated by events, such as shortening, occurring during the twitch. However, the lack of influence of shortening velocity on energy cost is consistent with the idea that the amount of energy to be used is determined early in a twitch (Gibbs & Barclay, 1995) and is not greatly influenced by events that occur during the contraction. Two factors that strongly influence twitch force and that are established at the start of a contraction are pre-load and the amount of Ca2+ entering the cell, each of which, via different mechanisms (e.g. Yagi et al. 2004), influences the number of cross-bridges that can bind. Contraction frequency also influences the status of muscles at the start of the twitch by, for instance, determining how much Ca2+ is available for release from the SR (e.g. Stull et al. 2002). The enthalpy output observed at 4 Hz was ∼60% of the value for 2 Hz, so the number of cross-bridge ATP-splitting cycles would have been reduced similarly. Consistent with this, the mean force output at 4 Hz was reduced by the same fraction as the enthalpy output relative to that at 2 Hz.

The observation that, across a realistic range of shortening velocities, energy cost was independent of shortening velocity, is equivalent to stating that in a beating heart at constant pre-load, varying stroke work does not alter energy cost. In terms of Suga's time-varying elastance model (for reviews, see Suga, 1990, 2003; Gibbs, 1995), the current papillary muscle protocol was equivalent to varying work output by altering stroke volume (i.e. shortening) while maintaining a constant pressure–volume area (PVA); rate of O2 consumption depends on PVA rather than upon stroke work (e.g. Kameyama et al. 1998; Suga, 2003; How et al. 2005). Equating energy cost to number of cross-bridge cycles provides a mechanistic insight into this observation: the number of cross-bridge cycles is not much altered by what the muscle does during the twitch. Thus, sliding of the contractile filaments, at least when the sliding starts once force has begun to develop (as in the current study), does not promote additional or accelerated cross-bridge cycling, as occurs in skeletal muscle. Rather, the number of cross-bridge cycles that will occur is set early in a twitch, presumably by the pre-load and by the amount of Ca2+ released.

Partitioning of energy between force-dependent and force-independent components

The calculation of the number of ATP molecules split depends on the partitioning of energy between cross-bridge and non-cross-bridge processes. In this study, it was assumed that BDM inhibited cross-bridge cycling without affecting Ca2+ cycling (Alpert et al. 1989; Higashiyama et al. 1994). Alpert et al. (1989) described a comprehensive set of experiments, using rabbit papillary muscles, that were designed to establish whether BDM selectively inhibited cross-bridge cycling and those experiments supported the notion that this was correct. In contrast, the effects of BDM on the relationship between rate of O2 consumption and PVA for blood-perfused dog hearts have been interpreted as indicating that BDM acted primarily by reducing Ca2+ release (Takasago et al. 1997). If that also applied to the papillary muscles used in this study, then the force–time integral (FTI) and enthalpy output would decline in proportion so that the enthalpy–FTI relation would pass through the origin; this was not so (Fig. 2). It remains possible that the linear relationship between enthalpy output and FTI reflects a partial inhibitory effect on Ca2+ cycling as well as a direct effect on cross-bridge cycling; in that case, our estimate of force-independent enthalpy output represents a lower limit.

Schramm et al. (1994) also used BDM (1–10 mm) to measure force-independent enthalpy output of guinea pig trabeculae at 37°C. They found that force-independent enthalpy output was 23% of the total energy cost. Gibbs and colleagues (Gibbs et al. 1988; Kiriazis & Gibbs, 2001) used a different technique for measuring force-independent enthalpy output: force output was reduced by rapidly shortening muscles during the latent period between the delivery of the stimulus and the start of the mechanical response. Using this technique, force-independent enthalpy output was calculated to account for 25–30% of energy cost in papillary muscles from the rabbit (Gibbs et al. 1988) and rat (Kiriazis & Gibbs, 2001). The cause of the discrepancy in values from the latency release method and the BDM method is unclear, although it has been suggested that in the former residual cross-bridge cycling may occur, increasing estimates of force-independent enthalpy output (Alpert et al. 1989). Further insight into the force-independent enthalpy output can be gained from the estimated amount of Ca2+ released from the SR in each twitch.

Relation between Ca2+ released and cross-bridge cycles

It was calculated that there are 290 ATP-splitting cross-bridge cycles in the sarcomere unit volume in each twitch and 98 Ca2+ released into the same volume. Therefore about three cross-bridge cycles were completed for each Ca2+ released. Most Ca2+ released into muscle cells is bound: peak free Ca2+ concentration (∼0.5–1 nmol g−1; Gao et al. 1998; Stull et al. 2002) is < 5% of the total Ca2+ released into the cell in each twitch (e.g. 18 nmol g−1; see Results). The concentration of troponin-C–tropomyosin regulatory units (each of which binds 1 Ca2+ in cardiac muscle) is 25% of the cross-bridge concentration (for a review, see Gordon et al. 2000), which would be 0.25 × 110 = 28 nmol g−1. If it were assumed that all the 18 nmol g−1 Ca2+ released in a twitch was bound to troponin-C, then for mouse muscle contracting at 2 Hz and 27°C about two-thirds of the regulatory units would have been occupied by Ca2+.

The dependence of the number of Ca2+ released per twitch on the assumed magnitude of the force-independent enthalpy output is shown in Fig. 6. The greater the fraction of enthalpy output that is independent of force generation, the greater the number of Ca2+ ions released. If it were assumed that under physiological conditions, the maximum amount of Ca2+ that was released into the cell was just sufficient to saturate the troponin-C Ca2+ binding sites, then this would correspond to 28 nmol Ca2+ g−1 twitch−1 or 150 Ca2+ per sarcomere cylinder. From Fig. 6 it can be seen that this would be consistent with a relative force-independent enthalpy output of ∼25%. This would then be the maximum relative force-independent enthalpy output, which supports the idea that estimates that were substantially higher than this value may have been in error. Also shown in Fig. 6 is the variation in number of ATP molecules split with magnitude of force-independent enthalpy output. This number decreases as force-independent enthalpy output increases but, over the likely range of force-independent enthalpy output, it is always greater than the number of Ca2+ ions released.

Figure 6. Dependence of Ca2+ released and ATP used on magnitude of force-independent enthalpy output.

Figure 6

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The number of Ca2+ released into a sarcomere cylinder or the number of ATP molecules hydrolysed in the sarcomere cylinder volume per twitch is shown as a function of the magnitude of the force-independent enthalpy output (expressed relative to the total initial enthalpy output). The horizontal dashed line corresponds to the number of troponin-C Ca2+ binding sites in a sarcomere cylinder in cardiac muscle (i.e. 150 or one-quarter of the number of cross-bridges; Gordon et al. 2000). The vertical dotted line is the relative force-independent enthalpy output measured in the current study.

Conclusion

In conclusion, this study has demonstrated that the energetics of isolated preparations of mouse cardiac muscle can be satisfactorily determined using the myothermic technique. By combining a number of approaches used in previous studies, we have calculated that the energy required for a twitch under the conditions used in this study can be accounted for by ATP-splitting cycles by half the available cross-bridges and cycling of about one Ca2+ for every three cross-bridge cycles.

Acknowledgments

C.W. was the recipient of a scholarship from the Heart Foundation Research Centre, Griffith University.

Appendix

The length of the myosin filament in a half-sarcomere that overlaps with actin is ∼700 nm. Along the myosin filament, there are three myosin molecules (i.e. 6 cross-bridges) every 14.3 nm (Cooke, 1986), giving a total of 294 cross-bridges per myosin filament. From the geometrical arrangement of the filaments, each myosin filament can interact with six neighbouring actin filaments so, in round figures, 300/6 = 50 cross-bridges from one myosin filament can interact with each actin filament. Each actin filament can receive cross-bridges from three myosin filaments and thus can interact with approximately 3 × 50 = 150 cross-bridges.

References

  1. Alpert NR, Blanchard EM, Mulieri LA. Tension-independent heat in rabbit papillary muscle. J Physiol. 1989;414:433–453. doi: 10.1113/jphysiol.1989.sp017697. [DOI] [PMC free article] [PubMed] [Google Scholar]
  2. Barclay CJ. Modelling diffusive O2 supply to isolated preparations of mammalian skeletal and cardiac muscle. J Muscle Res Cell Motil. 2005;26:225–235. doi: 10.1007/s10974-005-9013-x. [DOI] [PubMed] [Google Scholar]
  3. Barclay CJ, Arnold PD, Gibbs CL. Fatigue and heat production in repeated contractions of mouse skeletal muscle. J Physiol. 1995;488:741–752. doi: 10.1113/jphysiol.1995.sp021005. [DOI] [PMC free article] [PubMed] [Google Scholar]
  4. Barclay CJ, Weber CL. Slow skeletal muscles of the mouse have greater initial efficiency than fast muscles but the same net efficiency. J Physiol. 2004;559:519–533. doi: 10.1113/jphysiol.2004.069096. [DOI] [PMC free article] [PubMed] [Google Scholar]
  5. Barth E, Stammler G, Speiser B, Schaper J. Ultrastructural quantitation of mitochondria and myofilaments in cardiac muscle from 10 different animal species including man. J Mol Cell Cardiol. 1992;24:669–681. doi: 10.1016/0022-2828(92)93381-s. [DOI] [PubMed] [Google Scholar]
  6. Bluhm WF, Kranias EG, Dillmann WH, Meyer M. Phospholamban: a major determinant of the cardiac force-frequency relationship. Am J Physiol Heart Circ Physiol. 2000;278:H249–H255. doi: 10.1152/ajpheart.2000.278.1.H249. [DOI] [PubMed] [Google Scholar]
  7. Cooke R. The mechanism of muscle contraction. CRC Crit Rev Biochem. 1986;21:53–118. doi: 10.3109/10409238609113609. [DOI] [PubMed] [Google Scholar]
  8. Crabtree B, Nicholson BA. Thermodynamics and metabolism. In: Jones MN, editor. Biochemical Thermodynamics. Amsterdam: Elsevier Scientific; 1988. pp. 359–373. [Google Scholar]
  9. Delbridge LM, Bassani JW, Bers DM. Steady-state twitch Ca2+ fluxes and cytosolic Ca2+ buffering in rabbit ventricular myocytes. Am J Physiol. 1996;270:C192–C199. doi: 10.1152/ajpcell.1996.270.1.C192. [DOI] [PubMed] [Google Scholar]
  10. Dobson GP, Cieslar JH. Intracellular, interstitial and plasma spaces in the rat myocardium in vivo. J Mol Cell Cardiol. 1997;29:3357–3363. doi: 10.1006/jmcc.1997.0560. [DOI] [PubMed] [Google Scholar]
  11. Endoh M. Force-frequency relationship in intact mammalian ventricular myocardium: physiological and pathophysiological relevance. Eur J Pharmacol. 2004;500:73–86. doi: 10.1016/j.ejphar.2004.07.013. [DOI] [PubMed] [Google Scholar]
  12. Gao WD, Perez NG, Marban E. Calcium cycling and contractile activation in intact mouse cardiac muscle. J Physiol. 1998;507:175–184. doi: 10.1111/j.1469-7793.1998.175bu.x. [DOI] [PMC free article] [PubMed] [Google Scholar]
  13. Georgakopoulos D, Kass D. Minimal force-frequency modulation of inotropy and relaxation of in situ murine heart. J Physiol. 2001;534:535–545. doi: 10.1111/j.1469-7793.2001.00535.x. [DOI] [PMC free article] [PubMed] [Google Scholar]
  14. Gibbs CL. Mechanical determinants of myocardial oxygen consumption. Clin Exp Pharmacol Physiol. 1995;22:1–9. doi: 10.1111/j.1440-1681.1995.tb01910.x. [DOI] [PubMed] [Google Scholar]
  15. Gibbs CL, Barclay CJ. Cardiac efficiency. Cardiovasc Res. 1995;30:627–634. [PubMed] [Google Scholar]
  16. Gibbs CL, Loiselle DS, Wendt IR. Activation heat in rabbit cardiac muscle. J Physiol. 1988;395:115–130. doi: 10.1113/jphysiol.1988.sp016911. [DOI] [PMC free article] [PubMed] [Google Scholar]
  17. Gordon AM, Homsher E, Regnier M. Regulation of contraction in striated muscle. Physiol Rev. 2000;80:853–924. doi: 10.1152/physrev.2000.80.2.853. [DOI] [PubMed] [Google Scholar]
  18. Hancock GR, Klockars AJ. The quest for α: developments in multiple comparison procedures in the quarter century since Games (1971) Rev Educ Res. 1996;66:296–306. [Google Scholar]
  19. Headrick JP, Gauthier NS, Berr SS, Morrison RR, Matherne GP. Transgenic A1 adenosine receptor overexpression markedly improves myocardial energy state during ischemia-reperfusion. J Mol Cell Cardiol. 1998;30:1059–1064. doi: 10.1006/jmcc.1998.0672. [DOI] [PubMed] [Google Scholar]
  20. Higashiyama A, Watkins MW, Chen Z, LeWinter MM. Preload does not influence nonmechanical O2 consumption in isolated rabbit heart. Am J Physiol. 1994;266:H1047–H1054. doi: 10.1152/ajpheart.1994.266.3.H1047. [DOI] [PubMed] [Google Scholar]
  21. Hill AV. Trails and Trials in Physiology. London: Arnold; 1965. [Google Scholar]
  22. Hoh JF, Rossmanith GH, Kwan LJ, Hamilton AM. Adrenaline increases the rate of cycling of crossbridges in rat cardiac muscle as measured by pseudo-random binary noise-modulated perturbation analysis. Circ Res. 1988;62:452–461. doi: 10.1161/01.res.62.3.452. [DOI] [PubMed] [Google Scholar]
  23. How OJ, Aasum E, Kunnathu S, Severson DL, Myhre ES, Larsen TS. Influence of substrate supply on cardiac efficiency, as measured by pressure-volume analysis in ex vivo mouse hearts. Am J Physiol Heart Circ Physiol. 2005;288:H2979–H2985. doi: 10.1152/ajpheart.00084.2005. [DOI] [PubMed] [Google Scholar]
  24. Kameyama T, Chen Z, Bell SP, Fabian J, LeWinter MM. Mechanoenergetic studies in isolated mouse hearts. Am J Physiol. 1998;274:H366–H374. doi: 10.1152/ajpheart.1998.274.1.H366. [DOI] [PubMed] [Google Scholar]
  25. Kiriazis H, Gibbs CL. Papillary muscles split in the presence of 2,3-butanedione monoxime have normal energetic and mechanical properties. Am J Physiol. 1995;269:H1685–H1694. doi: 10.1152/ajpheart.1995.269.5.H1685. [DOI] [PubMed] [Google Scholar]
  26. Kiriazis H, Gibbs CL. Effects of ageing on the activation metabolism of rat papillary muscles. Clin Exp Pharmacol Physiol. 2001;28:176–183. doi: 10.1046/j.1440-1681.2001.03416.x. [DOI] [PubMed] [Google Scholar]
  27. Kohler I, Meier R, Busato A, Neiger-Aeschbacher G, Schatzmann U. Is carbon dioxide (CO2) a useful short acting anaesthetic for small laboratory animals? Lab Anim. 1999;33:155–161. doi: 10.1258/002367799780578390. [DOI] [PubMed] [Google Scholar]
  28. Larsen TS, Belke DD, Sas R, Giles WR, Severson DL, Lopaschuk GD, et al. The isolated working mouse heart: methodological considerations. Pflugers Arch. 1999;437:979–985. doi: 10.1007/s004240050870. [DOI] [PubMed] [Google Scholar]
  29. Mahler M, Louy C, Homsher E, Peskoff A. Reappraisal of diffusion, solubility, and consumption of oxygen in frog skeletal muscle, with applications to muscle energy balance. J Gen Physiol. 1985;86:105–134. doi: 10.1085/jgp.86.1.105. [DOI] [PMC free article] [PubMed] [Google Scholar]
  30. Mast F, Elzinga G. Heat released during relaxation equals force-length area in isometric contractions of rabbit papillary muscle. Circ Res. 1990;67:893–901. doi: 10.1161/01.res.67.4.893. [DOI] [PubMed] [Google Scholar]
  31. Mellors LJ, Barclay CJ. The energetics of rat papillary muscles undergoing realistic strain patterns. J Exp Biol. 2001;204:3765–3777. doi: 10.1242/jeb.204.21.3765. [DOI] [PubMed] [Google Scholar]
  32. Mellors LJ, Gibbs CL, Barclay CJ. Comparison of the efficiency of rat papillary muscles during afterloaded isotonic contractions and contractions with sinusoidal length changes. J Exp Biol. 2001;204:1765–1774. doi: 10.1242/jeb.204.10.1765. [DOI] [PubMed] [Google Scholar]
  33. Mulieri LA, Luhr G, Trefry J, Alpert NR. Metal-film thermopiles for use with rabbit right ventricular papillary muscles. Am J Physiol. 1977;233:C146–C156. doi: 10.1152/ajpcell.1977.233.5.C146. [DOI] [PubMed] [Google Scholar]
  34. Schenkman KA. Cardiac performance as a function of intracellular oxygen tension in buffer-perfused hearts. Am J Physiol Heart Circ Physiol. 2001;281:H2463–H2472. doi: 10.1152/ajpheart.2001.281.6.H2463. [DOI] [PubMed] [Google Scholar]
  35. Schramm M, Klieber HG, Daut J. The energy expenditure of actomyosin-ATPase, Ca2+-ATPase and Na+,K+-ATPase in guinea-pig cardiac ventricular muscle. J Physiol. 1994;481:647–662. doi: 10.1113/jphysiol.1994.sp020471. [DOI] [PMC free article] [PubMed] [Google Scholar]
  36. Semafuko WE, Bowie WC. Papillary muscle dynamics: in situ function and responses of the papillary muscle. Am J Physiol. 1975;228:1800–1807. doi: 10.1152/ajplegacy.1975.228.6.1800. [DOI] [PubMed] [Google Scholar]
  37. Squire JM, Luther PK, Morris EP. Organisation and properties of the striated muscle sarcomere. In: Squire JM, editor. Molecular Mechanisms in Muscular Contraction. London: Macmillan; 1990. pp. 1–48. [Google Scholar]
  38. Stull LB, Leppo MK, Marban E, Janssen PM. Physiological determinants of contractile force generation and calcium handling in mouse myocardium. J Mol Cell Cardiol. 2002;34:1367–1376. doi: 10.1006/jmcc.2002.2065. [DOI] [PubMed] [Google Scholar]
  39. Suga H. Ventricular energetics. Physiol Rev. 1990;70:247–277. doi: 10.1152/physrev.1990.70.2.247. [DOI] [PubMed] [Google Scholar]
  40. Suga H. Cardiac energetics: from Emax to pressure-volume area. Clin Exp Pharmacol Physiol. 2003;30:580–585. doi: 10.1046/j.1440-1681.2003.03879.x. [DOI] [PubMed] [Google Scholar]
  41. Takasago T, Goto Y, Kawaguchi O, Hata K, Saeki A, Taylor TW, et al. 2,3-Butanedione monoxime suppresses excitation-contraction coupling in the canine blood-perfused left ventricle. Jpn J Physiol. 1997;47:205–215. doi: 10.2170/jjphysiol.47.205. [DOI] [PubMed] [Google Scholar]
  42. Terracciano CM, Souza AI, Philipson KD, MacLeod KT. Na+-Ca2+ exchange and sarcoplasmic reticular Ca2+ regulation in ventricular myocytes from transgenic mice overexpressing the Na+-Ca2+ exchanger. J Physiol. 1998;512:651–667. doi: 10.1111/j.1469-7793.1998.651bd.x. [DOI] [PMC free article] [PubMed] [Google Scholar]
  43. Widén C, Barclay CJ. Resting metabolism of mouse papillary muscle. Pflugers Arch. 2005;450:209–216. doi: 10.1007/s00424-005-1408-4. [DOI] [PubMed] [Google Scholar]
  44. Woledge RC. Techniques for muscle energetics. In: Sugi H, editor. Current Methods in Muscle Physiology. New York: Oxford University Press; 1998. pp. 343–370. [Google Scholar]
  45. Woledge RC, Curtin NA, Homsher E. Energetic Aspects of Muscle Contraction. London: Academic Press; 1985. [PubMed] [Google Scholar]
  46. Woledge RC, Reilly PJ. Molar enthalpy change for hydrolysis of phosphorylcreatine under conditions in muscle cells. Biophys J. 1988;54:97–104. doi: 10.1016/S0006-3495(88)82934-5. [DOI] [PMC free article] [PubMed] [Google Scholar]
  47. Yagi N, Okuyama H, Toyota H, Araki J, Shimizu J, Iribe G, et al. Sarcomere-length dependence of lattice volume and radial mass transfer of myosin cross-bridges in rat papillary muscle. Pflugers Arch. 2004;448:153–160. doi: 10.1007/s00424-004-1243-z. [DOI] [PubMed] [Google Scholar]

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