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Physical and biochemical energy balance during an isometric tetanus and steady state recovery in frog sartorius at 0 degree C.

Frog sartorius muscle stimulated isometrically for 3 s every 256 s to attain a steady state in which initial heat (QI), recovery heat (QR), rate of O2 consumption (JO2), and isometric force (PO) generated are constant for each cycle. For a 3-s tetanus given every 256 s, JO2 was 0.106 mumol/(min . g blotted weight), approximately 71% of the maximum rate observed, whereas lactate production was negligible under these conditions. QI, QT(= QI + QR), and QT/QI were 88.2, 181.5, 2.06 mJ/g blotted weight, respectively. The high-energy phosphate breakdown (delta approximately P) breakdown during the first 3-s tetanus was not different from that during a contraction in the steady state and averaged 1.1 mumol/g blotted weight. Less than half of the initial heat could be accounted for in terms of the extent of the known chemical reactions occurring during contraction. From the stoichiometry of the theoretical biochemical pathways, the amount of ATP synthesized in the steady state exceeds delta approximately P during contraction by more than twofold, corresponding to an apparent ADP:O ratio of 1.5. If it is assumed that carbohydrate oxidation is the only net chemical reaction in the steady state, the total heat production can be explained on the basis of the measured JO2. Under this assumption, heat production during recovery was less than that expected on the basis of the oxygen consumption and delta approximately P during contraction. These observations support the hypothesis that the unexplained enthalpy production and low apparent ADP:O ratio are causally related, i.e., that the reaction(s) producing the unexplained heat during contraction is reversed during the recovery period.


INTRODUCTION
Within the past decade, two lines of experimental investigation have raised serious questions concerning our understanding of muscle energetics and metabolism . (a) It is now widely accepted (for reviews see Curtin and Woledge, 1978 ;Homsher and Kean, 1978) that the enthalpy (heat and work) change produced by an isometrically contracting muscle exceeds that which can be expected on the basis of the known initial chemical reactions occurring during contraction and the molar enthalpy for these reactions. These observations suggest that reactions other than the known chemical breakdown (ATP and PCr) occur during contraction. (b) The extent of recovery metabolism after contraction was found to exceed that calculated from the initial O-P using standard biochemical stoichiometry (for review cf. Kushmerick, 1977) . This biochemical imbalance was found both under aerobic (Kushmerick and Paul, 19766) and anaerobic (Defuria and Kushmerick, 1977) conditions . Both observations may be related to the same underlying phenomena. The unknown reaction(s) liberating enthalpy during contraction could be reversed during the recovery period at the expense of additional D-P, thus accounting for the biochemical imbalance. On the other hand, DeFuria and Kushmerick (1977Kushmerick ( , 1978 have suggested that these observations may not be causally related. They propose that the greater extent of recovery metabolism may not be related to reversal of some unknown reaction occurring during contraction but rather to the inability of muscle mitochondria in situ to achieve the theoretical stoichiometry during recovery . In particular, they have demonstrated the possibility of substrate cycling, as for example the cycle involving phosphorylation and dephosporylation of fructose 6-phosphate, which could considerably reduce the net phosphorylation efficiency. In this work, an energy balance study during recovery was used to differentiate between these mechanisms . An energy balance study during recovery requires measurement of recovery metabolism, recovery heat production, and the net change in the high-energy phosphate level. At 0°C the first two types of measurement following single isometric tetani are technically difficult because of the small extent of reactions and the long time for recovery . Particularly long-term baseline stability of thermopiles required for recovery heat measurement can be a formidable problem (Wilkie, 1968). An alternative method for measurement of recovery heat production involves a protocol of repeated stimulation. This approach was first used by Bugnard (1934), who showed that a periodically stimulated muscle achieves a cyclic steady state in which the heat produced during each cycle is constant . In this steady state, both the initial heat and that produced between tetani for each cycle are constant . In effect, the recovery period is shortened to the duration between stimuli, which considerably reduces the effects of baseline change on the heat measured. Using this technique, Bugnard (1934) measured recovery heat production and his results on initial-to-recovery heat ratios agree well with more modern measurements made on recovery after single isometric tetani (Godfraind-DeBecker, 1972) .
The choice of a steady state protocol also allowed the testing of the possibility that the abrupt transitions from rest to contraction and back might be a factor underlying the observed biochemical imbalance. In all previous studies, comparisons of recovery metabolism to O-P breakdown were made after single isometric tetani . Furthermore, one would anticipate (cf. Newsholme and Start, 1973) that the effects of substrate cycling would be minimized under conditions of high metabolic flux concomitant with steady state stimulation.
In this study, biochemical and physical energy balances were measured during contraction and recovery in a muscle periodically stimulated to achieve a cyclic steady state. The following two alternative hypotheses were tested : (a) the discrepancy between recovery metabolism and initial high-energy phosphate breakdown observed after single contractions is minimized in the steady state; (b) the unexplained enthalpy production observed during contraction is reversed during recovery .

Muscle Preparation
All experiments for physical and biochemical energy balance comparisons were performed on sartorius muscles of frogs (Rana temporaria), which were from a single batch obtained in the spring of 1977 . Preliminary measurements of isometric force and oxygen consumption to determine steady state parameters were made in muscles from frogs of different batches. Muscles were dissected on the day before the measurements and were left to recover in Ringer solution at 4°C. The Ringer solution contained (millimoles per liter) 115.5 NaCl ; 2 KCI; 1 .8 CaC12 ; 2 Na phosphate (pH 7.0 at 0°C) . Rest lengths were measured from tendon to tendon in the standard position, i.e ., with the legs perpendicular to the midline of the body ; all experiments were performed under isometric conditions at this length . The muscles were equilibrated for at least 40 min at 0°C before stimulation, which was achieved with condensor shocks (18 V, 0.5,uF) of alternating polarity at 10 Hz .

Measurements ofMetabolism
OXYGEN CONSUMPTION 02 was measured polarographically; the details of the apparatus and measurement procedure have been described previously (Kushmerick and Paul, 1976a;Paul, 1976) . LACTATE ELIMINATION Samples of the bathing medium were taken at intervals and were assayed for lactate as described below. The muscles were then subjected to extraction and analysis as described below.

Heat Production Measurements
Heat production was measured using a thermoelectric device (Th 1803) constructed of sintered bismuth telluride alloys (Thermagotron; MCP Electronics Ltd., Wembley, England) in a configuration designed by Dr. D. R. Wilkie. 54 elements were set in a field^-5 X 29 mm . These devices and their calibration by the Peltier method have been described previously (Kretzschmar and Wilkie, 1975) . In addition to the Peltier method of calibration, resistive heating methods and a novel, null detection method based on balancing joule heating against Peltier cooling were used and found to agree within 3% . The Thermagotron used produced 7 mV K-1 (130 1AV K-' element-) and was characterized by a heat loss of 0.042 J s-1 K-1 (0.785 mJ s-1 K-1 element -1 ) and a heat capacity of 0.65 J K -1 .
Because of the relatively large heat capacity of these devices, thermopile lag could be appreciable . A delay with a time constant of^"200 ms was required before the measured rate agreed with a steady rate of heat applied to an agar gel-simulated muscle . No correction for this lag in the Thermagotron response was made because 340 THE JOURNAL OF GENERAL PHYSIOLOGY " VOLUME 81 -1983 the exact time course of heat production at this level of resolution was not required . Before stimulating each muscle, its heat capacity was determined by the Peltier method ; when the muscle was longer than 29 mm, the total capacity was calculated from the observations on the assumption that its heat capacity was proportional to its length . The heat records were corrected for heat loss algebraically as described by Wilkie (1968) . The correction for stimulus heat was calculated from the number of stimuli and the parameters of the capacitor discharge stimulator used . This correction was -3% of the total heat measured. Because the work done against the series elastic elements is dissipated as heat when the muscle relaxes and is included in the total heat measured, this experimental design did not necessitate a separate measurement of this work.

Measurements of the Chemical Reactions Occurring during Contraction
MUSCLE EXTRACTS Chemical measurements were made on extracts of muscles rapidly frozen on a hammer apparatus (Kretzschmar and Wilkie, 1969) . Right and left muscles were varied systematically in a protocol similar to that reported by Curtin and Woledge (1977) to avoid biasing the results. The frozen, flattened muscles were extracted for 4 d in 3 ml of a solution of EDTA (1 .25 mM, pH 7 .6) in methanol (50% vol/vol) at -30°C. Details of this extraction procedure have been reported (Kushmerick and Paul, 19766 ;Curtin and Woledge, 1977) . The muscle residue was then removed, rinsed with cold methanol (rinses were added to the extract), and freezedried . Muscles used for measurements of heat production and metabolism after determination of the blot weight were also frozen and similarly extracted for later analysis of total creatine . After further drying over P20s, the muscle residue was weighed . The ratio of the blotted weight of a muscle to this extracted dry weight, used for comparisons on a blotted-weight basis, was 5.14 ± 0.13 (SE of mean of 16 observations) . ANALYTICAL TECHNIQUES Total creatine (Ct) and free creatine (Cr) were measured by the technique of Ennor (1957) . Phosphorylcreatine (PCr) was calculated using a 10 .8% correction for creatinine formation . Inorganic phosphate (Pi) was determined by an enzymatic method based on that of Fawaz et al . (1966) . Lactate was determined by an enzymatic method based on that of Hohorst (1962) . All these techniques were adapted for use with an auto-analyzer (Technicon Instruments Corp., Tarrytown, NY) . ATP, ADP, AMP, and Pi were measured by isotachophoresis, using a Tachophor (LKB Instruments, Inc., Rockville, MD) . Application of this technique to the analysis of anions in muscle extracts is described by Woledge (1976, 1977) .
EXTENT OF REACTIONS The extent (~) of each relevant reaction was determined from the difference (A) in the level of metabolite between experimental and control members of a pair of sartorius muscles . This extent is based on the assumption that the content in the experimental muscle before treatment was identical to that of the control . Both the dry weight of the muscle residue and the total creatine content were used as estimates of muscle mass (see Results) in normalization of the data . HIGH-ENERGY PHOSPHATE BREAKDOWN This term refers to the extent of the reactions expected to occur during the tetanus : Creatine kinase reaction ADP + PCr-* ATP + Cr . (2) Because of the rapidity of the creatine kinase reaction and the absence of adenylate kinase or deaminase reactions (no significant change in AMP was detected ; see Results), the extents of reactions 1 and 2 are the same and can be estimated by three parameters, OPCr, OCr, and OPi. The effects of normalization on variance and the independence of these estimates of phosphagen breakdown are discussed in Results.
TENSION TIME INTEGRALS fPdt was calculated from the myograms algebraically using Simpson's rule . In the experiments measuring 02 consumption, only peak fPdt isometric force was measured . This value was converted to fPdt using the ratio Pmax = 3 .47 t 0.06, N = 12, obtained from the experiments in the series measuring chemical changes (3-s tetani) .
REJECTION OF DATA Chemical experiments on 32 muscle pairs (2 sets of 16 pairs) were technically successful . Values >2 SD away from the mean (including aberrant values) were rejected. Not more than one data point per group was deleted. Data are presented in terms of the mean and standard error of the mean .

Steady State Stimulation Pattern
The choice of a stimulation pattern to be used for steady state energy balance studies is limited by the following considerations : (a) stimulus duration should be of sufficient length to achieve a cl-emical breakdown of magnitude compatible with the resolution of the chemical measurement techniques, and (b) the intensity of stimulation should be sufficient to allow for considerable metabolic flux without exceeding the maximum oxidative capacity of the tissue . Preliminary experiments characterizing the effects of periodic stimulation on peak isometric force and 02 consumption of frog sartorius muscle at 0°C were undertaken . As seen in Fig. 1, .Jo2 attained a steady state, and peak force records were qualitatively similar to earlier reports (Aljure and Borrero, 1968), provided the stimulation intensity was such that the maximum oxidative capacity of the muscle was not exceeded. The rate of oxygen consumption (lo,) approaches a constant value with a time course similar to that of the isometric force. Using these experiments as a guide, a stimulation protocol of 3-s tetani at 256-s intervals was chosen to achieve a steady state compatible with requirements of an energy balance study.

Steady State Metabolic Rate OXYGEN CONSUMPTION
Measurements of metabolism for this steady state stimulation procedure on muscles from the batch of frogs used for the energy balance comparisons are given in Table I. The basal and maximumfoe for all muscles studied were 15.6 t 1 .6 (SEM, N = 15) and 148 ± 11 .3 (SEM, N = 9) nmol/(min " g blotted weight) . These values were consistent with the values obtained for the primary batch of muscles (Table I), which suggests these parameters were not as sensitive to batch differences as measurements of initial heat and phosphocreatine breakdown in single tetani reported by Gilbert et al. (1971) . Although basal and maximal values of 02 consumption showed typical variations, presumably because of differences between animals, suprabasal oxygen consumption (Afoz) was considerably more reproducible Experimental record of simultaneous measurement of oxygen consumption and isometric force vs . time . The upper thin trace is the output of the polarographic electrode. As the chamber is a closed system, the slope of the trace is a measurement of the rate of oxygen consumption . Measurements were made between partial fractions of oxygen of 0.42 and 0.27 atm, well above the diffusion limit for these preparations . The output of the electrode is biased such that a full scale deflection represents a 10% change in the initial oxygen content ; a rapid vertical rise indicates a change of this bias. The bold numbers above the polarograph traces indicate the rate of oxygen consumption in nanomoles per minute per gram calculated from the slope of the line. The lower heavier lines are the force transducer output during the periodic isometric tetani . Joe was linearly related to P,,D/I (Po , isometric force ; D, stimulus duration ; I, interval between stimuli), a measure of the average tension time integral, a parameter previously used (Kushmerick and Paul, 19766) . For five experiments the average slope was 0 .021 ± 0.008 ,umol/(min .g blotted weight) per mN/mm2 ; the intercept was 0.057 ± 0.01 I umol/(min " g blotted weight) with an average correlation coefficient of 0.92 ± 0 .02 . as judged by standard deviations (Table 1) . Furthermore, for a particular muscle, AJo2 , after an increase when stimulation duration was changed to 5 s, returned to within 2 .5% of the previous value at 3 s when the duration was decreased to this value. The suprabasal recovery 02 consumption associated with each cycle is 256/60 X Ojo2 = 0.392 t 0.006 gmol/g blotted weight .
LACTATE PRODUCTION The values of lactate elimination are also given in Table I. As there was negligible change in muscle lactate content (see below), these values can be interpreted as lactate production . These levels of lactate production are considerably lower than the small but statistically significant lactate production during aerobic recovery from a single tetanus that was reported by Kushmerick and Paul (1976a) .

Measurements ofMuscle Heat Production
The Thermagotron recording of-temperature for each of 10 cycles of a muscle stimulated for 3 s every 256 s are shown superimposed in Fig. 2. After four to five cycles, the records were superimposible and indicated that a steady state had been obtained . The time required to achieve this steady state was 21 .2 ± 2.9 min and agreed closely with the time of 20 .8 ± 1 .6 estimated from 02 consumption measurements. When corrected for heat loss, the temperature records indicate a rapid evolution of heat complete in^-4-6 s. For the first contraction, a slower evolution of heat begins -60 s later. For a contraction in the steady state, a second linear phase is observed which immediately follows the rapid phase and continues throughout the remainder of the cycle. This behavior is shown in Fig. 3. Though delayed in time because of the thermal characteristics of the Thermagotron, these results are consistent with two phases (initial and recovery heat) reported for previous measurements (Hill, 1965) using themopiles of greater temporal resolution . The magnitude of the initial heat production was taken as the total deflection complete by 6 s, and for a contraction in the steady state, the total deflection at 6 s was extrapolated from the linear second phase (Fig . 3). The initial heat production in the first 3-s contraction was 108.9 ± 2 .0 mJ/g (± SEM; N= 10) . For a 3-s contraction in the steady state the initial heat was 88.2 ± 2.5 mJ/g (± SEM ; N = 10) and the total heat evolved over a 256-s steady state cycle was 181 .5 ± 4.4 mJ/g (± SEM; N = 10) . This separation of an initial heat, Q, from the total heat, QT, results in a measured QT/0 ratio of 2.06 ± 0.03 (± SEM ; N = 10), which agrees with many reports of this ratio (cf. Woledge, 1971) . The two types of experiments performed are shown schematically in Fig . 4. In the first type, the experimental muscle, E, received a 3-s tetanus, while the control muscle, C, remained unstimulated. Both muscles were frozen simultaneously on the hammer apparatus at the last shock of the tetani, facilitating comparison with previous studies (Kushmerick and Paul, 1976b) . Chemical change refers to the difference in contents of the appropriate chemical species and rests on the assumption that the content of the experimental muscle FIGURE 2 . Thermagotron records of temperature of a muscle stimulated isometrically for 3 s every 256 s . 10 cycles are shown superimposed ; the number given to the right of each curve indicates the temporal order . The vertical bar indicates a Thermagotron output of 7 g,V, corresponding to a temperature change of 1 m°C . Time runs from right to left ; the horizontal bar corresponds to 0.5 min . The muscle had a blot weight of 50.5 mg and t o of 3 .2 cm . Traces essentially superimpose after the fifth cycle ; for contractions 5-10, Thermagotron outputs before stimulus were identical and peak values had a coefficient of variation of 1% . Peak isometric forces (not shown) in contractions 3-10 were identical .
before stimulation was the same as the control muscle . In the second type of experiment, both muscles were given 3-s tetani at 256-s intervals . Mechanical reproducibility could be achieved after as few as four stimulations (three cycles) and thermal and oxygen consumption measurements indicated a steady state was achieved after^-21 min . To assure a steady state, both muscles were stimulated at least eight times (29 .9 min) . On the subsequent cycle, the control muscle was not stimulated and both muscles were frozen simultaneously at the time of the last tetanic shock to the experimental muscle .
Chemical change under this steady state regimen is also measured as the  Schematic outline of the isometric myograms in the protocol used to measure the chemical changes during the reactions in each member of a sartorius pair. The upper drawing (lE and 1C) represents the conventional pattern for measuring change in a single contraction using an unstimulated muscle as the control . The lower drawing (2E and 2C) represents the pattern for measuring change in a contraction in the steady state; the control muscle in this case receives one stimulation less than the other muscle of the pair. Muscles are rapidly frozen on hammers cooled to liquid nitrogen temperature at the time indicated by the vertical arrow. difference in muscle contents, and this again assumes that the content of the experimental muscle before the last stimulus was the same as the control muscle . It is assumed that the rate of synthesis during the contraction is the same in the experimental and control muscles, though this is less critical because it represents only a small fraction (3 /256) of the total recovery metabolism . The metabolite content and tension-time integrals of muscles for the Metabolite content and tension-time integrals for initial and steady state isometric tetani . Parameters for sartorius muscles given the following treatments before freezing: 3-s isometric tetanus (3-s), paired muscle unstimulated (O) ; N of 3-s isometric tetani, where N indicates the number of stimulations, paired muscle given (N -1) 3-s tetani. X, aX, and n indicate the mean, standard error of the mean, and number of muscles, respectively . For direct comparison with the heat production and metabolism experiments, f Pdt for the chemical experiments were corrected to account for 21 t 1% of the total f Pdt that occurs during relaxation .
various types of experiments are given in Table II. The muscles appear to be quite uniform based on the total creatine content and mechanical responses . Differences in the tension-time integrals or total creatine content for the muscle groups used in the comparisons discussed below were not statistically significant . As anticipated, the phosphocreatine content was lower in the steady state than at rest, the values of PCr/Ct being 0.76 ± 0.01 and 0.85 ± 0.01 (± SEM, n = 15), respectively . The coefficients of variation for the values of the various chemical contents of a muscle in the steady state are generally less than or near the values found for the unstimulated muscles. The reproducibility of the chemical parameters in the steady state is at least as good as that of the resting state. This supports the assumption underlying the use of a muscle stimulated N -1 times as a control, against which the chemical changes during a steady state contraction are measured .
No statistically significant differences in ATP, ADP, or AMP content under any conditions were found (Table II). A small but significant increase in the lactate content of muscles in the steady state compared with that of muscles at rest was found. If this difference represents a lactate production that is assumed to continue in the steady state, the measured changes in bath content would underestimate the true aerobic glycolysis by a factor of 2 . As such, the rate of lactate production would still be some 50-fold less than ,Jo2 and negligible (<I%) in terms of the total rate of ATP synthesis.

Chemical Changes during Contraction
Estimates of chemical change are given in Table III. Changes in ATP, ADP, AMP, and lactate were small and not statistically significant for either measurement protocol, and thus were not used in the determination of A-P. In both series, no statistically significant difference between the total creative contents of the control and experimental members of the paired sartorius muscles was found, so that total creatine could be used as an estimator of muscle mass. Consistent with previous reports (Wilkie, 1968), the use of total creatine to normalize chemical change was found to significantly reduce the variance in the mean value of APCr compared with that found using the extracted dry weight. Using this normalization, however, reduces the number of independent estimators of initial chemical change as APCr/Ct = OCr/Ct. For this reason OCr/g dry weight is included in Table III. For comparison, all values are expressed in terms of grams of dry weight, as indicated in Table III. It should be noted that the best estimates of chemical change based on paired differences using the normalization procedures described are presented for comparative purposes in terms of micromoles per gram dry weight. These values are not necessarily equal to differences in the group mean values of metabolite content given in Table II.
Though the values for APi tended to be somewhat lower, there was general agreement among OP;, OPCr, and OCr as estimators of 0^"P. In one comparison, OPCr and OPi for the initial contraction, the difference in group means showed a marginal (P = 0.02) statistical significance when tested using an unpaired means t test . Using a nonparametric sign test (Colquhoun, 1971) for differences in APi and OPCr on the individual muscle pairs, however, did not indicate a significant difference. On the whole, these measurements indicate that the creatine kinase reaction was close to equilibrium . Thus measurements of OPCr, OPi,and OCr can each provide a measure of 0^-P. The variance weighted mean of these values was used (Kushmerick and Paul, 19766) to provide an unbiased estimator of D-P. It can be argued that since OPCr/Ct = OCr/Ct, ACr/g dry weight may not be a true independent estimate . Estimates based on all three parameters and only APCr/Ct and OP;/Ct are given in Table III. Both estimates are similar; however, only the latter will be used in subsequent calculations .
O-P during a contraction in the steady state was nearly identical to that Chemical change during initial and steady state isometric tetani . Chemical change is based on the difference in content of a pair of sartorius muscles from the same animal . Initial 3-s tetanus refers to the difference between one muscle (E) stimulated for 3-s and its pair (C) unstimulated . 3-s tetanus in the steady state refers to the difference between one muscle (E) stimulated N times for 3 s at 256-s intervals and its pair (C) stimulated N -l times for 3 s at 256-s intervals (see text and Fig . 4 for details) . Various normalization procedures as described in the text were used to obtain the best estimates of these chemical changes, which for comparative purposes are all expressed in terms of micromols per gram weight . X, ar, and n indicate the mean, standard error of the mean, and number of muscle pairs, respectively .
during the first tetani . This was true for the tension-time integrals as well . Thus, in terms of the chemical and mechanical changes during an isometric tetanus, the first contraction and contractions in the steady state are indistinguishable.
Comparisons ofHigh-Energy Phosphate Breakdown, Heat Production, and Oxygen Consumption To facilitate comparison with previous studies, each type of measurement has been presented to this point in the units commonly used in each type of study. Comparisons of the energy balance parameters standardized to muscle size based on blotted weight, weight of the muscle residue after extraction and drying, or total creatine yielded similar results. As no significant reduction of variance was associated with any particular estimate of muscle mass, comparisons will be presented in terms of the more familiar blotted weight of the muscle .
Comparison ofHigh-Energy Phosphate Breakdown during Contraction with Steady State ATP Synthesis Using the theoretical value of the stoichiometry of the standard biochemical pathways, the predicted ATP synthesis based on the extent of the steady state metabolism occurring between tetani is 6.5 X A02 = 2.58 ± 0.038 [ umol/g blotted weight . This is more than twofold greater than can be accounted for by A-P during contraction of 1 .14 ± 0.24 jLmol/g blotted weight . The apparent ADP :O ratio based on t,-P during contraction and steady state oxygen consumption is 1 .5, a value much lower than the theoretical value of * Substrate oxidation enthalpy of 460.2 kJ/mol 02 (mixed, see text) .

Energy Balance during Contraction
The calculated energy balance during contraction is presented in Table IV. The initial heat measured in these experiments includes heat produced during mechanical relaxation . For an exact comparison with the chemical breakdown measured during contraction, the measured initial heat must be corrected for the heat production associated with chemical reactions occurring during relaxation . The temporal resolution of the Thermagotron does not allow for accurate determination of this correction, which is on the order of 10% of the initial heat measured . A precise estimate of this heat production, however, has been determined by Curtin and Woledge (1974) as 11 .7 mJ/g. This figure was used to correct the initial heat measurements in determination of observed enthalpy used for energy balance comparison during contraction. The ex- plained enthalpy is determined by multiplying the measured value of O~P by 34 kJ/mol, the molar enthalpy, h_P, of the known reactions (cf. Curtin and Woledge, 1978) . The difference between the observed enthalpy and the explained enthalpy, i.e., the unexplained enthalpy, was considerable for both the initial 3-s isometric tetanus and a tetanus of similar duration in the steady state. The absolute values of the unexplained enthalpy were 58 .8 ± 6.1 and 37 .7 ± 10.2 mJ/g blotted weight, respectively (values that are not significantly different from each other, P > 0.05) . The process or processes underlying the unexplained enthalpy observed in single isometric tetani appear to be nearly fully apparent in the steady state.
Total Energy Balance The hypothesis that the process(es) underlying the unexplained enthalpy production during contraction is reversed during recovery can be tested by evaluating the total energy balance. If reversal occurred during recovery, then the total heat production would be equal to that expected from the oxidation of substrate. The explained total enthalpy production rate would be ,JQ = hoe -foe, where hoe is the "calorific value" of one mole of 02, which is dependent on the substrate used . These experiments were performed in the absence of exogenous substrate and glycogen would presumably be the substrate oxidized, for which ho e would be 477 kJ/mol 02 (Curtin and Woledge, 1978) . The literature values for the respiratory quotient for isolated muscle, 0.9-0 .95 (Hill, 1940b;Fenn, 1927), suggest, however, that up to 25% of the substrate oxidized may be fatty acid; the hoe for this case would be 460.2 kJ/mot 02 (Woledge, 1971) .
The explained enthalpy production based on the steady state rate Of 02 consumption would range from 0 .70 ± 0.01 to 0.73 ± 0.01 mW/g blotted weight, depending on the substrate. This value is in close agreement with the observed enthalpy of 0.71 ± 0.02 mW/g blotted weight . Thus, an energy balance for the overall reaction of substrate oxidation is achieved .
Energy Balance during Recovery THE JOURNAL OF GENERAL PHYSIOLOGY " VOLUME 81 " 1983 If resynthesis of the high-energy phosphate broken down during contraction at the expense of substrate oxidation is the only net reaction occurring during recovery, the explained enthalpy change would be : OH = explained enthalpy = hoe -A02 -h_P " A-P.
Using the values for 002 and A-P in Table IV, the explained enthalpy production during the steady state recovery would range from 141 .5 to 147.7 mJ/g blotted weight, depending on the substrates . The observed enthalpy during recovery was substantially less (93.3 mJ/g blotted weight), which suggests that the imbalance established during contraction is reversed during recovery (see Curtin and Woledge, 1978) . DISCUSSION The measurement of high-energy phosphate breakdown during a 3-s tetanus is in good agreement with those recently reported by Curtin and Woledge (1979) for 2-and 5-s tetani in Rana temporaria, as well as with the results of many previous experiments summarized in recent reviews (Curtin and Woledge, 1978 ;Homsher and Kean, 1978) . The literature values for the initial enthalpy production in a 3-s tetanus for R. temporaria extrapolated from the values tabulated in recent reviews (Homsher and Kean, 1978 ;Curtin and Woledge, 1978) range from 2.7 to 3.5 expressed in units of millijoules per micromole total creatine . The value observed in this study is 3.12 ± 0.065 . The maximum rate of oxygen consumption measured in these experiments, 0.15 mmol/min " g blotted weight, agrees with the value of 0.18 j umol/min " g blotted weight reported by Hill (1940a). Furthermore, the rates of oxygen consumption were in good agreement with myothermal measurements based on the known overall reactions. This agreement is of significance in validating the use of these very different techniques, particularly in view of the recent differences in ADP :O ratios reported for single isometric tetani at 20°C (Mahler, 1979) . Thus, the discrepancy between the high-energy phosphate breakdown during contraction, the expected ATP synthesis, and enthalpy production is unlikely to be an artifact of the measurement techniques.
Under these steady state conditions, in which the effects of metabolic transitions and substrate cycling should be minimized, high-energy phosphate breakdown during contraction accounted for less than half of that expected from measurements of 02 consumption results similar to those reported earlier for single isometric tetani (Kushmerick and Paul, 19766) . Therefore, the discrepancy between the predicted synthesis during recovery and high-energy phosphate breakdown during contraction does not appear to be associated with the transitions in metabolism concomitant with a single tetanus. This conclusion is further supported by the energy balance comparisons. The observed energy balance is most simply interpreted as reflecting the oxidation of substrate as the only net reaction occurring in the steady state. Myothermal data, however, cannot rule out the presence of thermally neutral reactions or a series of reactions in addition to substrate oxidation whose enthalpy production fortuitously equals zero, although this is unlikely . The design of these experiments provides support for the assumption that substrate oxidation is the only net reaction because the attainment of a steady state implies that one has a complete recovery at the end of each cycle, i.e., the concentration of all metabolic intermediates is the same at the beginning and end of each steady state cycle.
The assumption that the recovery was complete at the end of each cycle was tested by two techniques. The first was measurement of the reproducibility of the heat production during each cycle in the steady state, a test first used by Bugnard (1934) . The superimposition of the thermal records in the steady state (Fig. 2) strongly implies that the underlying metabolic reactions are reproduced over each cycle. For the metabolic reactions to show this periodicity, the initial concentrations of metabolites must be the same for each cycle, i.e., recovery is complete. Myothermal evidence for cyclical recovery in the steady state is strengthened by the constancy of the rate of 02 consumption achieved . The steady state of 02 consumption reflects periodic constancy of the underlying reactions and implies no net change of metabolite concentra-tion from cycle to cycle in the steady state. Thus, although it is indirect, the evidence for the constancy of metabolic intermediates at the beginning and end of each steady state cycle supports the assumption that substrate oxidation is the only net reaction. If no other net reactions occur, the process underlying the unexplained enthalpy production during contraction must be reversed during recovery . This idea is supported by comparison of the amount of unexplained enthalpy during contraction and during recovery (Table IV), the amounts are both equal and of opposite sign .
The evidence presented here supports the hypothesis that the process(es) underlying the unexplained enthalpy production during contraction is reversed at the expense of substrate oxidation during recovery . Thus, the initial unexplained enthalpy production and the low apparent ADP :O ratios are likely to be causally linked . If the theoretical ADP : O ratio of 3 .25 is actually achieved, reversal of the unknown processes occurring during a 3-s steady state isometric tetanus requires at maximum 1 .4 tLmol/g blotted weight ATP breakdown during recovery . Although there is no direct evidence that reversal is coupled to ATP hydrolysis, such a process would require 1 jmol ATP per 26 .9 mJ/g blotted weight unexplained initial enthalpy production .
The evidence presented supports the hypothesis that an unknown reaction occurs during contraction and is reversed at the expense of ATP hydrolysis after the contraction. The energy cost of this unknown process can be substantial . About 50% of the total metabolic cost of a 3-s isometric contraction is thus not related to the phosphagen breakdown, presumably because of the actomyosin ATPase that occurs during contraction, but is expended during recovery to reverse some unknown exothermic reaction associated with contraction .