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¹ Imperial College London, Division of Biomedical Sciences, Biological Structure & Function Section, SAF-Building, London SW7 2AZ² National Institute for Medical Research, The Ridgeway, Mill Hill, London NW7 1AA³ King's College London, School of Biomedical Science, New Hunt's House, Guy's Campus, London SE1 1UL⁴ UCL Institute of Human Performance, Royal National Orthopaedic Hospital Trust, Brockley Hill, Stanmore HA7 4LP, UK

	Abstract

Top Abstract Introduction Methods Results Discussion Conclusion Supplementary Material References

 
Energy turnover was measured during isometric contractions of intact and Triton-permeabilized white fibres from dogfish (Scyliorhinus canicula) at 12°C. Heat + work from actomyosin in intact fibres was determined from the dependence of heat + work output on filament overlap. Inorganic phosphate (P_i) release by permeabilized fibres was recorded using the fluorescent protein MDCC-PBP, N-(2-[1-maleimidyl]ethyl)-7-diethylamino-coumarin-3 carboxamide phosphate binding protein. The steady-state ADP release rate was measured using a linked enzyme assay. The rates decreased five-fold during contraction in both intact and permeabilized fibres. In intact fibres the rate of heat + work output by actomyosin decreased from 134 ±S.E.M. 28 µW mg^-1 (n= 17) at 0.055 s to 42% of this value at 0.25 s, and to 20% at 3.5 s. The force remained constant between 0.25 and 3.5 s. Similarly in permeabilized fibres the P_i release rate decreased from 5.00 ± 0.39 mmol l^-1 s^-1 at 0.055 s to 39% of this value at 0.25 s and to 19% at 0.5 s. The steady-state ADP release rate at 15 s was 21% of the P_i rate at 0.055 s. Using a single set of rate constants, the time courses of force, heat + work and P_i release were described by an actomyosin model that took account of the transition from the initial state (rest or rigor) to the contracting state, shortening and the consequent work against series elasticity, and reaction heats. The model suggests that increasing P_i concentration slows the cycle in intact fibres, and that changes in ATP and ADP slow the cycle in permeabilized fibres.

(Received 9 September 2003; accepted after revision 14 October 2003; first published online 17 October 2003)
Corresponding author N. A. Curtin: Biological Structure & Function Section, Division of Biomedical Sciences, Sir Alexander Fleming Building, Imperial College London, South Kensington Campus, London SW7 2AZ.  Email: n.curtin{at}imperial.ac.uk

	Introduction

Top Abstract Introduction Methods Results Discussion Conclusion Supplementary Material References

 
The rate of energy output measured as heat and work decreases substantially during an isometric tetanic contraction of skeletal muscle (Abbott, 1951; Curtin & Woledge, 1979 and references therein). This energy output comes principally from the ATPase activity of the actomyosin system and that of the sarcoplasmic reticulum Ca²⁺ pump, and to a lesser extent from other energy-producing processes. Measurements of P_i release by permeabilized muscle fibres have shown that the rate of the P_i release step in the actomyosin cycle decreases considerably during the first few turnovers (He et al. 1998b and references therein). The ADP release has been measured much later in an isometric contraction, while force is maintained at the plateau level (Hilber et al. 2001); the rate is constant in this period, but much lower than that measured at the start of activation. What is the time course of this reduction in the rate of the actomyosin cycle during an isometric contraction? Does this reduction match the change in the rate of energy release as heat + work by intact fibres?

To answer these questions we have made parallel experiments using intact and permeabilized muscle fibres. White fibres from dogfish were used because both series of experiments could be made under similar conditions, including temperature (12°C). The fish were acclimated to 12°C, which is within the normal range for the natural habitat of the dogfish. Another reason for using dogfish muscle was that fibres of uniform type could be obtained easily from the white part of the myotomes, which are the muscle fibres used for burst swimming. In the intact fibres, energy turnover was measured as heat output during 3.5-s tetani. Energy released as work done against series elasticity was also taken into account. In the permeabilized fibres the P_i release was measured with high time resolution during the initial part of the contraction using the fluorescent phosphate binding protein MDCC-PBP (Brune et al. 1994). However, this technique cannot follow ATP turnover for long enough to observe the transition to the steady state, so we also used a linked enzyme assay which coupled ADP production to the oxidation of NADH (Stephenson et al. 1989; Hilber et al. 2001).

Previous energy balance studies have shown that in frog muscle ATP hydrolysis is insufficient to explain all of the heat and work released during isometric contraction (Gilbert et al. 1971; Curtin & Woledge, 1977, 1979, 1981; Homsher et al. 1979). The experiments reported here tested whether the ATP hydrolysis by actomyosin can account for the heat + work due to actomyosin interaction.

Preliminary results of this work have been presented (West et al. 2002; Curtin et al. 2003).

	Methods

Top Abstract Introduction Methods Results Discussion Conclusion Supplementary Material References

 
Dogfish (Scyliorhinus canicula, L) were obtained from the Marine Biological Association (Plymouth, UK). No more than six fish were held in cylindrical aquaria (1000 l) supplied with re-circulated artificial seawater at 12°C. The aquarium facility has a light: dark cycle of 12 hours light: 12 hours dark. Fish were fed twice each week with chopped mackerel and they were used for experiments within 12 weeks of arriving in the local aquarium. The fish ranged from 50 to 60 cm in total length and from 300 to 900 g in wet weight.

Dissection of muscle bundles

Fish were killed by a blow to the head followed by destruction of the brain and spinal cord in accordance with Schedule I of the UK Animals (Scientific Procedures) Act 1986. Slices of white muscle were dissected from both epaxial and hypaxial regions of the myotome of the tail musculature located immediately posterior to the visceral cavity. Slices were stored in ice-cold saline containing (mmol l^-1): NaCl, 292; KCl, 3.2; CaCl₂, 5.0; MgSO₄, 1.0; Na₂SO₄, 1.6; NaHCO₃, 5.9; urea, 483 and 1.5 mg l^-1 of tubocurarine. The saline contains urea because this metabolite is present in the body fluids of chondrichthyean fishes where it provides osmoconformation with seawater. Fibre bundles (4–14 fibres, median 9) were dissected with myoseptum at each end, which served as attachment points.

Intact fibres

Apparatus.  The bundle was positioned horizontally along the midline of the thermopile (described below) and connected, via platinum wire hooks that served as stimulating electrodes, between a force transducer and a motor (models 400A and 300B, respectively; Cambridge Technology Inc., Watertown, MA, USA). The supra-maximal stimulus strength was established using 0.2-ms pulses with 2-minute rest between stimulations. The fibre length was adjusted to that optimal for force (L₀) using 0.5-s tetani with 50-Hz stimulation frequency at 10-minute intervals. Contraction heat and peak force (P₀) development at L₀ were then recorded during 3.5 s of electrical stimulation (50 Hz).

Muscle heat production was evaluated from the temperature change measured with a purpose-built thermopile (see Woledge et al. 1985). The thermopile was 12 mm long and consisted of a series of antimony–bismuth thermocouples (4 thermocouples per mm) sealed between two layers of Kapton^® film (Goodfellow Cambridge Ltd, UK). The Seebeck coefficient for the thermopile at 12°C was 63.26 µV per °C temperature difference per couple. Generally, 8–12 thermocouples (equivalent to 40–60% of the average L₀) were used to record the temperature changes. The temperature during all experiments was 12°C, which is the temperature to which the fish were acclimated and is in the normal range for the natural habitat of dogfish.

Heat records.  Calculation of heat production from measurements of temperature change requires the time constant for heat loss and the heat capacity for each muscle preparation (Woledge et al. 1985). These parameters were obtained by the Peltier method (Kretzschmar & Wilkie, 1972, 1975) for each bundle and for each new experimental condition.

The stimulus pulses produced electrical artefacts on the heat records, which were removed by masking regularly spaced segments of the raw data.

Stimulus heat was measured in muscle bundles that had been made inexcitable with procaine (18 mmol l^-1 saline), and the following relation was fitted to the results:

(1)

where SH is stimulus heat in µJ per pulse, k (= 0.0005) is the constant determined by the fitting procedure, V is the stimulus volts, and t is the stimulus pulse duration in ms. Records of heat during contraction were corrected for stimulus heat using this relationship. The stimulus heat for the 17 preparations was on average 1.7 ± 0.3% of the total heat at the end of the stimulation period.

Fibre bundle size.   Cross-sectional area was estimated from fibre length at L₀ and dry weight as described for white fibres by Lou et al. (2002). Sarcomere length at L₀ (SL₀) was determined by diffraction of laser light by unstimulated fibres. Force was normalized to wet cross-sectional area, kN m^-2. See Table 1.

(2)

where W_t is the work done up to time t from the start of contraction, P is the force and dL is the change in fibre length. In experiments on intact fibres, dL was found using the compliance value for structures in series with the contractile material as measured by Curtin et al. (1998) in the same type of fibre preparation and under the same conditions as used here. The work was added to the heat production to give total energy turnover. Heat + work is reported normalized by wet weight.

Heat + work and rate of heat + work due to actomyosin interaction.  Evaluations of heat + work due to actomyosin interaction in intact fibres were based on the assumption that actin–myosin interaction is proportional to the degree of filament overlap at muscle lengths beyond L₀. Records were made of force and heat production from nine fibre bundles at L₀ and at a greater length. The degree of filament overlap was evaluated from the force records corrected for creep in the following way. At L > L₀ force continued to ‘creep’ upward gradually after the initial rise at the start of stimulation (Fig. 1). Creep occurs because, in fibres at L > L₀, sarcomeres at the fibre ends have more overlap than the central sarcomeres, and shorten as stimulation continues (Huxley & Peachey, 1961; Gordon et al. 1966a,b). The force record at L₀ was scaled, using least-squares fitting, to give the best fit to the initial 0.15 s (the period least affected by creep) of the record at reduced filament overlap (Fig. 1B). The scaling factor was taken as the estimate of the relative filament overlap.

View larger version (9K): [in this window] [in a new window]   Figure 1.  Correction for creep force produced at L > L0 Example illustrating the method for correcting force in isometric contractions at L > L0 for creep. A, force produced by the same fibre bundle at L0(continuous line) and at L > L0 (broken line). B, the broken line is the same as in A. The continuous line is force produced at L0 multiplied by the scaling factor 0.241. The scaling factor was found by Excel Solver using forces produced in the first 0.15 s of the contraction (heavy part of the continuous line).

(3)

where t is the time since first stimulus, and A, a, B and b are fitted parameters. The constant d is the time (0.032 s) during which F_t was less than zero.

View larger version (20K): [in this window] [in a new window]   Figure 2.  Steps in evaluating the time course and rate of heat + work production A, an example of the dependence of heat + work release on filament overlap. This example is for 1 s of contraction. Corresponding plots were made for heat + work measured at 10-ms intervals during contraction. A regression line is shown with 95% confidence intervals. See Table 2 for regression slopes and S.E.M. values. Relative heat + work is the heat + work released at time t during a tetanus at L > L0 normalized by that released at time t during a tetanus at L0 by the same preparation. Relative filament overlap was estimated from isometric force. B, dependence of the rate of heat + work at 1 s of contraction on filament overlap. C, summary of the slopes, Ft values, of regressions as in A for heat + work production at 10-ms intervals during 3.5-s contraction. Shown are data points and a least-squares fitted line; see text. D, summary of the slopes, RFt (±S.E.M.), of the regressions as in B of the rates of heat + work production at 10-ms intervals during 3.5-s contraction. E, the time courses of the total heat + work production and of the part due to actomyosin (AM heat + work). Mean values ±S.E.M. (n= 17). F, the time courses of the rate of total heat + work production (upper curve) and the rate of the part due to actomyosin (lower curve).

(4)

The standard error (SE_AM) for the average AM_t at each time point was found by combining the variance of F_t, reflecting the goodness of fit of the data to the regression line at each time (examples in Fig. 2A), and the variance of E_t (reflecting variation between different fibre preparations):

(5)

where V_E is the variance of E_t (mean square of the deviation from the mean), and V_F is the variance of F_t (square of the standard error of the slope of the regression line, see examples in Fig. 2A and Table 2), and the other terms are defined above.

View larger version (23K): [in this window] [in a new window]   Figure 6.  Force, work and energy rate during contraction of intact and permeabilized fibres A, the force during 3.5-s contraction of intact fibres; B, during 0.5-s contraction of MDCC-PBP permeabilized fibres. C and D, the work done during these nominally isometric contractions. Means of measurements at 1-ms intervals in experiments on intact fibres and 0.5-ms intervals on permeabilized fibres, ±S.E.M. at selected times. E and F, how the rate of energy turnover (upper trace) changed after force had reached 95% of its maximum value at 0.175 s for intact fibres, and 0.2 s for permeabilized fibres. Note that after the work rate (lower trace) has declined to zero, the rate of energy turnover continues to decrease. For clarity S.E.M. values are shown for selected times only.

(6)

where t is the time since the start of activation and G, g, H, h and I are fitted parameters, and the value of d was constant (= 0.032 s) as explained above. Equation (6) was differentiated to give the rate of heat + work output:

(7)

Using the constants found by fitting eqn (6), rates at relevant times were calculated. The relative rate (rate at L > L₀/rate at L₀) was calculated for each fibre bundle at each time. A graph of relative rate versus relative filament overlap was made for each time (10-ms intervals) during the tetanus (see example in Fig. 2B). The slope of each graph gives an estimate of the fraction of the rate that is due to actomyosin interaction, RF_t, at that time (Table 2B). The RF_t values are plotted versus time in Fig. 2D and show the time course for the fraction of heat + work rate due to actomyosin. The time course of the rate of heat + work due to actomyosin and its standard error shown in Fig. 2F were found from eqns (6) and (7) using the rate of heat + work and the fraction of the rate of heat + work due to actomyosin and its standard error.

Permeabilized fibres

Fibre permeabilization and fibre end fixation.  Fibres were chemically permeabilized by immersing bundles for 30 min in an ice-cold relaxing solution (see Table 3 for composition of solutions) containing 2% Triton X-100. The ionic strength of the relaxing solution and all other solutions used with permeabilized fibres was 200 mmol l^-1.

MDCC-PBP assay of P_i release.  Procedures are described by He et al. (1997, 1999, 2000). Briefly, the fibre was transferred between solutions in troughs (30 µl volume) built into a temperature-controlled (12°C) stage of a Zeiss ACM upright microscope. The fibre was mounted between a force transducer (AE 801; Memscap AS, Horten, Norway) and a fixed hook. While in relaxing solution, the sarcomere length was set using laser diffraction and fibre length was recorded. The fibre was then transferred through the usual sequence of solutions (Table 3): (a) 1% Triton X-100 in relaxing solution for 30 min; (b) Ca-free rigor solution containing in addition an inorganic phosphate mop [P_i-mop, 1 mmol l^-1 7-methylguanosine (MEG) and 0.5 unit ml^-1 of purine nucleoside phosphorylase (PNPase)]; (c) Ca-rigor solution for 5–10 min; and (d) loading solution for 10 min. The fibre was transferred to silicone oil (Dow Corning, 10 centistoke) for activation by a laser pulse that released 1.5 mmol l^-1 ATP. MDCC-PBP fluorescence, force and sarcomere length signals were sampled at 2 kHz (RC Electronics EGAA Computerscope, Goletta, CA, USA) for 0.4 s before and for 1 s after photolysis. The epifluorescence microscope and photomultiplier are described by He et al. (1997). The fluorescence signal was corrected for aci-nitro decay as described by He et al. (1998a). Sarcomere length was recorded during contraction of six of the 15 fibres as described by He et al. (1999). Fibres were activated only once. See Table 1 for fibre dimensions and normalized force values.

Calibration of the MDCC-PBP signal.  The concentration of P_i bound to MDCC-PBP, [PiPBP], was calculated as follows:

(8)

where 1.2 is the concentration (mmol l^-1) of active MDCC-PBP present in the fibres and Q is the ratio of fluorescence/maximum fluorescence. indicates the increase in fluorescence above background value, and the maximum is the final plateau value reached when all active MDCC-PBP has P_i bound to it.

Total P_i (Pi_Total, mmol l^-1), the sum of PiPBP and free P_i, was calculated from the fluorescence signal as

(9)

where Pi_Total and Q are defined above, D is the ratio, apparent K_d/1.2, and 1.2 is the concentration of active MDCC-PBP. The apparent K_d for MDCC-PBP for the conditions used here was 0.0158 mmol l^-1 (see Curtin et al. 2003). The free P_i was 14% of the total P_i at 0.5 s of contraction.

Work.  Work output was determined from time courses for force production and length change using eqn (2). For permeabilized fibres used in the MDCC-PBP experiments, the length change was obtained from observations of sarcomere length in six of the 15 fibres.

Time course of P_i release.  Each record of P_i release by a permeabilized single fibre was fitted to eqn (6). The values of G, g, h and I were positive and the value of H was negative. The value of d was a fitted parameter; the average value was 0.006 s. The time courses of the rates (mmol l^-1 s^-1) were found from the differentiated form, eqn (7).

Linked enzyme assay for ADP release

ADP release in permeabilized fibres was measured during steady maintenance of force, with a fluorescent assay that linked ADP production to NADH oxidation through the pyruvate kinase (PK) and lactate dehydrogenase (LDH) reactions. With minor modifications, the methods are as described by Hilber et al. (2001). Bundles were first dissected down to single intact fibres with a fragment of myoseptum at each end. Permeabilization and fixation solution were identical to those used in the MDCC-PBP experiments (Table 3). The fragments of myoseptum at the ends of the fibre were held while the 0.5% glutaraldehyde solution flowed directly on to the fibre ends. The aluminium T-clips were positioned on the fibres after fixing the fibre ends and removing the myosepta (rather than before these steps as was done in the MDCC-PBP experiments). This modified end-fixing procedure improved the success and repeatability of fibre performance during activation.

After recording the fibre length corresponding to 2.4-µm sarcomere length, the fibre was mounted between a force transducer and fixed hook and then transferred to solutions as follows: (a) loading for 60 min with PK and LDH (nominally 500 units ml^-1) in relaxing solution; (b) 5 min in preactivating solution; (c) transfer to silicone oil and record the initial baseline fluorescence (F_max); (d) transfer to activating solution and monitor isometric force until the force plateau was achieved; and (e) transfer to silicone oil and record the fluorescence decrease as NADH is oxidized. Fluorescence and force records were collected at 1 kHz (AT-MIO-16E-2 A/D card and LabVIEW 5.0; National Instruments, Austin, TX, USA). The fluorescence change was converted to ADP production (ADP, mmol l^-1) as follows:

(10)

where 5 is the initial concentration (mmol l^-1) of NADH and F_max is the corresponding fluorescence, F is the fluorescence recorded during the force plateau of contraction, and F_b is the baseline fluorescence recorded when all the NADH had been oxidized.

	Results

Top Abstract Introduction Methods Results Discussion Conclusion Supplementary Material References

 
Figure 3 shows representative records of force and signals from the three assays: heat + work production by intact fibre bundles (A), fluorescence increase due to P_i binding to MDCC-PBP in single permeabilized fibres (B), and fluorescence decrease due to oxidation of NADH linked to ADP production in single permeabilized fibres (C).

View larger version (15K): [in this window] [in a new window]   Figure 3.  Records of force and heat + work output, Pi release and ADP release Each panel shows the time course of force production (upper record, grey symbols) and: A, total energy released as heat + work (black symbols) by intact fibre bundles; B, increase in relative fluorescence resulting from Pi binding to MDCC-PBP in single permeabilized fibres; and C, fluorescence decrease associated with NADH oxidation (coupled to ADP production) in single permeabilized fibres.

Intact fibres: the amount and rate of heat + work.

The fraction of heat + work release due to actomyosin interaction, F_t, was determined as described in the Methods. Figure 2C shows how F_t varied during the contraction. The points show the values of F_t measured at 10-ms intervals, and the continuous line was fitted through the values as described in the Methods. F_t increased rapidly during the first 0.2 s of stimulation and then more gradually; the fitted line reached 0.62 at 3.5 s. The heat + work due to actomyosin interaction at each time (AM_t) was calculated as the product of F_t and total heat + work release. Average time courses for total heat + work and the part due to actomyosin interaction are shown in Fig. 2E. Both of these quantities increase rapidly at the start of stimulation and then more slowly. At 3.5 s, total heat + work was 210.0 ± 9.6 µJ mg^-1 wet wt, and the part due to actomyosin interaction was 129.8 ± 7.4 µJ mg^-1 wet wt.

The fraction of the heat + work rate due to actomyosin interaction, RF_t, was determined as described in the Methods. Figure 2D shows how it varied during the contraction, and Fig. 2F shows how the total rate and the rate due to actomyosin both decreased during the contraction. See also Table 4.

The average time course of total P_i release is presented in Fig. 4 along with the heat + work produced by actomyosin in the intact fibres. The amount of P_i release in 0.5 s of contraction was 1.150 ± 0.054 mmol l^-1. At this time the amount of heat + work release due to actomyosin in the intact fibres was 32.4 ± 2.8 µJ mg^-1. In Fig. 4 the P_i and heat + work axes are scaled so that the time courses can be compared. The scaling factor was 34 kJ heat + work per mol of P_i released, which is the enthalpy released per mol of ATP hydrolysis under conditions in intact fibres where it is coupled to the creatine kinase reaction (Woledge et al. 1985; Woledge & Reilly, 1988). The appropriateness of this scaling factor will be considered in the Discussion. The P_i release in the permeabilized fibres starts somewhat earlier than heat + work production by actomyosin in intact fibres, which presumably reflects the difference in mode of activation. Permeabilized fibres in rigor were activated by flash photolysis of NPE-caged ATP and in the presence of high [Ca²⁺], whereas intact fibres were activated by the normal process involving several steps including calcium release and binding to troponin.

View larger version (17K): [in this window] [in a new window]   Figure 4.  Heat + work due to actomyosin interaction in intact fibres and Pi release due to actomyosin interaction in permeabilized fibres Comparison of average (±S.E.M.) time courses of heat + work release due to actomyosin in intact muscle bundles (lower points, n= 17) and Pi release by permeabilized fibres (upper points, n= 15) during 0.5 s of contraction. The heat + work and Pi axes are scaled so that 34 kJ of heat + work is equivalent to 1 mol Pi release. S.E.M. values are shown by grey shading.

Time courses of actomyosin-related heat + work and P_i release for individual experiments were fitted by equations with two exponential terms and a single linear term [see Methods, eqn. (6)]. These equations were differentiated (eqn 7) to give the time course of the rate for each experiment.

Averages of these individual time courses are shown in Fig. 5 with the vertical axes scaled as in Fig. 4 (scale factor 34 kJ mol^-1). The rate for permeabilized fibres increases initially, reaching a value of 5.00 ± 0.39 mmol l^-1 s^-1 at 0.055 s. After this time the rate dropped continuously to a value of 0.93 ± 0.08 mmol l^-1 s^-1 at 0.500 s; by this time the MDCC-PBP was almost saturated with P_i.

View larger version (18K): [in this window] [in a new window]   Figure 5.  Comparison of rates of energy release and of chemical change due to actomyosin interaction in intact and permeabilized fibres A, comparison of the rate of energy turnover due to actomyosin in intact muscle bundles during 3.5 s of contraction (broken line, n= 17), by permeabilized fibres during 0.5 s of contraction (MDCC-PBP assay, continuous line, n= 15), and by permeabilized fibres during maintenance of force after it reached a steady level (ADP release, NADH oxidation assay, filled point, n= 4). The dotted line joins the last MDCC-PBP point to the rate inferred from the NADH oxidation assay. For clarity the S.E.M. values are shown for selected means only. See Table 4. The energy and chemical change axes are scaled so that 34 kJ of energy is equivalent to 1 mol of Pi or ADP release (see text). B, results for the initial 0.5 s of contraction.

The steady-state rate of ADP production later during contraction of permeabilized fibres was determined from the NADH oxidation assay. The fibres were activated by increasing the Ca²⁺ concentration; the rate of ADP release, 1.05 ± 0.12 mmol l^-1 s^-1, was measured after force had reached a steady level at an average time of 15 s. As can be seen in Fig. 5A, which shows the entire time period, the rates for permeabilized and intact fibres decline in a similar manner (see also Table 4).

Rates of work output by intact and permeabilized fibres

Although the contractions were nominally isometric, the fibres did some work stretching the elastic structures in series with the sarcomeres. The amount of work done was evaluated as described in the Methods and is shown in Fig. 6C (intact fibres) and D (permeabilized fibres). The peak rate of work output occurred at about 0.05 s in both intact and permeabilized fibres. The intact fibres did somewhat more work than the permeabilized fibres, reflecting the higher force and greater L in the intact fibres.

As shown in Fig. 6E and F, little work was done after force had reached 95% of its maximum value at 0.175 s in intact fibres and 0.200 s in permeabilized fibres. Figure 6E and F also shows how the rate of energy turnover by actomyosin compares with the work rate. In both intact and permeabilized fibres, the work rate was virtually zero after 0.250 s. It is clear for both intact and permeabilized fibres that the rate of energy turnover by actomyosin continued to decline after work production ceased. Between 0.250 and 0.500 s, the rate of energy turnover by actomyosin for intact fibres decreased by 20%, and this was followed by a further decrease of 40% over the next 3.0 s of contraction. Between 0.250 and 0.500 s, the rate of actomyosin energy turnover by permeabilized fibres decreased by 52% (see Table 4).

	Discussion

Top Abstract Introduction Methods Results Discussion Conclusion Supplementary Material References

 
It is well established that the rate of energy release as heat and work by intact fibres is highest at the beginning of an isometric contraction and declines thereafter as tetanic stimulation continues (Hill & Hartree, 1920; Abbott, 1951; Aubert, 1956; Curtin & Woledge, 1979; Elzinga et al. 1987). This slowing of energy turnover is also apparent from measurement of ATP hydrolysis (Woledge, 1971; Curtin & Woledge, 1979; Crow & Kushmerick, 1982a,b,c, 1983; Kushmerick & Crow, 1983; Woledge et al. 1985; Lou et al. 1997). A period of recovery after relaxation is required before the initial high rate of energy turnover can be produced in a subsequent contraction (Aubert, 1968; Curtin & Woledge, 1977; Peckham & Woledge, 1986). Our present results (Fig. 2E and F) on white fibres from dogfish muscle are in agreement with these earlier observations on amphibian and mammalian muscles.

Most of the energy turnover during tetanic contraction of intact fibres is due to two processes: the actomyosin ATPase of the myofibrils and the ATP-driven Ca²⁺ pump of the sarcoplasmic reticulum (SR). Both operate continuously during a tetanus and the change in rate of energy release could be due to a change in the rate of either or both of these processes. From earlier experiments in which the actomyosin ATPase has been varied by changing the filament overlap, it has been shown that the rate of the energy turnover due to Ca²⁺ pumping does decrease during a contraction (Smith, 1972; Homsher et al. 1972; Curtin & Woledge, 1981; Lou et al. 1997). However, whether this explains all or only part of the decline in the total rate has not been discussed previously. A re-examination of the results of these earlier experiments suggests that the rate of energy release due to actomyosin may also decrease during a contraction. The present experiments were explicitly designed to examine the rate of energy release due to actomyosin.

He et al. (1997) observed that the rate of P_i release in permeabilized fibres is highest early in isometric contraction and then falls considerably, and suggested that this change in rate could explain much of the slowing in heat + work production previously observed in intact muscle. A comparison of these results with steady-state rates measured in permeabilized fibres (Hilber et al. 2001) confirms that the rate decreases greatly by the time a steady state has been established. He et al. (1998b, 1999) considered whether the initial higher rate of ATP turnover could be explained by the shortening of the sarcomeres early in the contraction, and concluded that this could not wholly explain the effect.

Here we have examined the question of whether the rate of energy turnover by actomyosin changes during contraction of both intact and permeabilized fibres (Fig. 5). The rate of energy turnover by actomyosin in permeabilized fibres was inferred from P_i or ADP release. The experiments were done on intact and permeabilized fibres from the same source, in the same conditions, including temperature (12°C, which is physiological for dogfish), and the results agree. Both types of preparation show a falling rate of energy turnover that continues beyond the period of force development when work is being done into the period of force maintenance when work is not being done (Fig. 6E and F). In each case the final rate was about 1/5 of the initial rate (Fig. 5). In the permeabilized fibres it was necessary to use two different assays to observe the initial high rate and later much lower rate. However, with the intact fibre preparations the time course of this change in rate of energy turnover was measured continuously. The results with intact fibres agree well with both of the assays used in the permeabilized fibre experiments.

Comparisons of actomyosin function in intact and permeabilized fibres

Mechanics.  Although fibres from the same source were used and conditions were similar, there were differences in the mechanical performance of the two types of preparation.

First, the force rises more promptly, that is with less delay, in the permeabilized than in the intact fibres (Fig. 3, Table 1). This is to be expected from the different methods of activation. In the permeabilized fibres, sufficient Ca²⁺ for full activation is already present before the laser flash, which rapidly releases ATP from the caged compound. In contrast, in the intact fibres the electrical stimulus has to be followed by several processes before any force is produced: the propagation of the action potential over the surface of the fibres, inward spread of the action potential along the T-tubules, sarcoplasmic reticulum Ca²⁺ release, Ca²⁺ binding to troponin and the subsequent structural changes in the thin filament which cause myofibril activation leading to force generation.

Secondly, the force exerted by the intact fibres, expressed per unit cross-sectional area (CSA), was clearly greater than that exerted by the permeabilized fibres (Fig. 3, Table 1). (CSA was based on dry weight and length, and thus its value is not influenced by swelling that may have occurred upon permeabilization.) The difference in force per CSA cannot be due to damage to some of the myofibrils in the permeabilized fibres, since in that case the ATPase would also be reduced (see Fig. 5). The experiments reported by Elzinga et al. (1989) showed that less force was produced by the same frog single fibre after permeabilization than before. The ratio (force after/force before) was smaller for fibres of larger CSA. Dogfish fibres are generally larger than frog fibres, and consequently the mean CSA for our single fibres (0.0238 ± 0.0025 mm², n= 19, mean ±S.E.M. for all single fibres, Table 1) is towards the upper end of the range of fibre sizes that Elzinga et al. investigated (0.00326–0.0270 mm², calculated from their reported values, 0.707–5.65 µg dry weight mm^-1 length and assuming wet-to-dry weight ratio of 4.9, and density 1.06). The mean ratio of maximum force in permeabilized fibres to that of intact fibres in our experiment (0.68, Table 1) is in reasonable agreement with the value, 0.57, expected from fig. 4D of Elzinga et al. for fibres of this size. On the basis of their observation that larger fibres produce relatively less force, Elzinga et al. suggested that the greater accumulation of P_i from ATP hydrolysis may account for the difference in force produced before and after permeabilization. However, the difference of force between intact and permeabilized fibres that we observe cannot be due to P_i accumulation, because in our experiments nearly all the P_i produced in the permeabilized fibres is immediately tightly bound to MDCC-PBP.

Another possibility is that the difference in forces between intact and permeabilized fibres is related to the ionic-strength-dependent swelling of permeabilized fibres. Matsubara & Elliott (1972) and Maughan & Godt (1979) reported an increase of approximately 30% in CSA of relaxed fibres upon permeabilization. This swelling of the lattice decreases in a sarcomere-length-dependent manner when the fibre develops force, indicating the presence of a radial component of cross-bridge force in the permeabilized fibres (Matsubara et al. 1984; Brenner & Yu, 1991), which may account for the lower longitudinal force component observed in permeabilized fibres compared with intact fibres. This suggestion is supported by the observation that isometric force can be increased by osmotic compression of permeabilized fibres (Ford et al. 1991).

Energetics.  Do the measured values (heat + work, P_i release and ADP release) reported here give a consistent and coherent view of energy turnover by actomyosin during isometric contraction? Fig. 5 shows that the results from the intact and permeabilized fibres agree qualitatively in showing that the rates of both heat + work release and P_i release fall substantially during the first 0.5 s of isometric contraction. The heat + work rate continues to decline during the next 3 s. The rate of ADP release measured at 15 s is compatible with the rate of heat + work output at 3.5 s, suggesting that the actomyosin rate is relatively stable between 3.5 and 15 s.

A scaling factor of 34 kJ mol^-1 (Woledge & Reilly, 1988) was used in Fig. 5 and there is good agreement between results from the intact and permeabilized fibres. A better fit would not be achieved by using a different scaling factor. Since 34 kJ mol^-1 is the amount of energy released per complete actomyosin cycle in intact fibres, we interpret these results as showing that there is a decline in the rate at which complete actomyosin ATPase cycles occur between approximately 0.2 and 3.5 s.

All the results agree in showing that the rate of actomyosin turnover continues to decline after the time, about 0.2 s, when force reaches its steady-state level (Fig. 6). In other words, although the force is constant during this time, ATP is not being hydrolysed at a constant rate.

Comparison with energy balance studies

How do the results reported here compare with earlier energy balance studies on frog muscle? The quantity of heat + work produced by dogfish fibres is somewhat less than that produced by frog muscle: dogfish fibres used here at 12°C produced 65% as much heat + work as frog sartorius at 0°C (Curtin & Woledge, 1979) at 1 and 2 s of isometric contraction. Curtin & Woledge (1979) also measured the time course of production of heat + work and of ATP hydrolysis (by all ATPases) during isometric tetani. The results showed that the rate of ATP hydrolysis (and thus energy explained by this process) was about three times greater in the first 1 s of contraction than during the rest of the contraction (2–15 s of stimulation). In this respect, the explained energy in the energy balance experiments behaves like the actomyosin energy reported here and shown in Fig. 5. Thus it seems likely that a large fraction of the explained energy in the energy balance experiment was actomyosin energy, although the two may not be identical. The results reported here suggest that all of the energy produced by the actomyosin system in intact fibres can be explained by actomyosin ATPase, and there is no unexplained energy associated with complete actomyosin cycles.

Energetics: kinetic model

We have used a kinetic model of the actomyosin cycle to calculate the time courses of force, energy, P_i and ADP release for comparison with the experimental results presented here. The aim of the modelling was to gain insight into the mechanism(s) responsible for the slowing of the actomyosin cycle during contraction.

During the contraction a number of different factors affect the rate of the actomyosin cycle. (a) Activation: this is equivalent to increasing the rate constant of a step in the cycle (in the MDCC-PBP experiments this is step 6, and in the intact fibre experiments this is step 3; see Fig. 7 and below). (b) Work is done by the active contractile component (actomyosin) as it develops force and stretches the elasticity in series with it. This influences the rate of the cycle because strain alters one of the rate constants (see below). (c) The concentrations of ATP, ADP and P_i change to different extents in intact and permeabilized fibres and affect the rates of the various steps. Our model is designed to take all of these factors into account.

View larger version (7K): [in this window] [in a new window]   Figure 7.  Reaction scheme for the actomyosin cycle used to describe force, heat and Pi release during isometric contraction The reactions are numbered 1–6. See Table 5 for the rate constants. M, myosin and A, actin.

Description of the model.  In the model one ATP is hydrolysed in each actomyosin cycle. There are five states as shown in Fig. 7 and the rate constants for the transitions between states are listed in Table 5. States AMADPPi and AMADP produce equal force (A is actin, M is myosin). A satisfactory description of the entire data set (intact and permeabilized results) could not be achieved by a model with only one force-producing state.

For modelling the behaviour of the intact fibres, the rate constant k₃ was assumed to be zero before activation, and 90% of the myosin was in the MADPPi state, and the rest in the MATP state. At the start of stimulation there was a latent period after which k₃ increased exponentially. The duration of the latent period was set to 0.020 s as observed for force; the rate constant of increasing k₃ was fitted (Table 5). It was assumed that all ADP released in step 5 was immediately converted to ATP by the creatine kinase reaction. To calculate the energy output it is necessary to have the H value, molar enthalpy change, for each step of the cycle. Values for steps 1, 2 and 4 have been measured under conditions similar to those used here (Table 5). The value for step 3 was fitted, and the value for step 5 was found from these values and the known total enthalpy for the complete cycle.

The rate constant for the transition from AMADP to AM(k₅) is strain-dependent. In the model the value of k₅ depends on the ratio of force to (AMADP +AMADPPi), having a value 10 times greater at 0 force (0 strain, shortening at V_max) than for isometric force (maximum strain in these experiments). The rate of rise of force is calculated as stiffness of the series elasticity x velocity of filament sliding. The relationship between force/(AMADP +AMADPPi) and velocity of filament sliding is a hyperbolic function for which the curvature is the strain factor, sf, in the equation for shortening velocity in Table 5.

The maximum velocity of shortening, V_max= 3.8L₀ s^-1, has been measured under the conditions used here for intact fibres by Curtin & Woledge (1988). The stiffness of the series elasticity was assumed to be 20P₀/L₀(see Curtin et al. 1998). Work done in stretching the series elasticity was calculated as the time integral of force and velocity of filament sliding.

The model was fitted to the experimental data (intact fibre force and heat + work, permeabilized fibre force and P_i release) using Excel Solver (Microsoft). The rate constant for each step was the same for modelling intact and permeabilized fibres. During fitting the following parameters were adjusted without constraint: k₁, k_–1, k₄, k_–4, k₅, k_–5, H₃, activation rate constant for intact fibres, and the strain factor (sf). The value of k₂ was adjusted to be < = 150 s^-1, and the value of k_–2 was kept at one-tenth of the value of k₂. The rate constants for step 3 were fixed at the values shown in Table 5. The model was implemented in Excel using 0.2-ms time intervals, and the results were confirmed using MathCad (Mathsoft Engineering & Education, Inc.) with 0.02-ms time intervals.

The model when started from an equilibrium mixture of MATP and MADPPi, to simulate the intact fibre experiments, gives a satisfactory description of the entire time course of force and of energy output as heat + work during the 3.5-s contraction (Fig. 8A and C). Similarly, when started from rigor, AM, to simulate the permeabilized fibre experiments with MDCC-PBP, the model gives a good description of the time course of force and P_i release during 0.5 s of contraction (Fig. 8B and D). The model reproduces the experimental observation that the rate of the actomyosin cycle does not become constant (that is, a steady state is not reached) in either intact or permeabilized fibres. In contrast, the force is constant after the initial 0.2 s of contraction.

View larger version (25K): [in this window] [in a new window]   Figure 8.  Comparison of observations and predictions from the kinetic model of the actomyosin cycle during isometric contraction A, the observed (open symbols) and predicted (line) relative force during 3.5-s contraction of intact fibres activated from rest by electrical stimulation; and B, the corresponding relative force during 0.5-s contraction of permeabilized fibres activated from rigor by photolysis of NPE-caged ATP. C, the observed (open symbols) and predicted (line) heat + work for intact fibres. D, the observed (open symbols) and predicted (line) Pi release by the permeabilized fibres. See text, Fig. 7 and Table 5 for the model used for the prediction. For clarity only selected observed values are shown.

In the experiments on permeabilized fibres using the ADP–NADH linked enzyme assay, ADP does not accumulate, but after the fibre has been placed in oil, the P_i concentration increases in the fibre. So, assuming that the model is an accurate description, the cycle turnover in these fibres should be controlled by P_i accumulation. The fluorescence was measured a few seconds after transfer to oil, and so on the basis of the model we expect that the P_i concentration would be similar to that in intact fibres after 3.5 s of stimulation. The observed turnover rates, 0.89 mmol l^-1 s^-1 in intact fibres and 1.05 mmol l^-1 s^-1 in the permeabilized fibres (Table 4), are in fact similar.

See the Supplementary Material for more information about the time course of changes in the concentrations of the actomyosin states in the cycle, and the relative contributions of activation, work, ATP, ADP and P_i concentrations to the decline in turnover rate.

	Conclusion

Top Abstract Introduction Methods Results Discussion Conclusion Supplementary Material References

 
In conclusion, the results show a substantial reduction in the rate of energy turnover as both heat + work by actomyosin and ATP hydrolysis by actomyosin during isometric contraction. This effect is likely to be of physiological importance in reducing the energetic costs of muscle activity, as it indicates a substantial increase in the economy of force production. We used continuous stimulation, but an increase in economy also occurs with intermittent stimulation (Bronk, 1930). The fibres that we have studied power swimming by the live fish, and this activity requires intermittent stimulation of the muscles (Bone, 1966). Indeed, intermittent stimulation is the usual pattern for other animals using other forms of locomotion such as walking (Rose & Gamble, 1994), running (Novacheck, 1998), hopping (Biewener et al. 1998) and flying (Dial et al. 1988).

	Supplementary Material

Top Abstract Introduction Methods Results Discussion Conclusion Supplementary Material References

 
The online version of this paper can be found at: DOI:10.1113/jphysiol.2003.040089 and contains Appendix A1, consisting of Figs 9–11. This material can also be accessed at http://www.blackwellpublishing.com/products/journals/suppmat/tjp/tjp18/tjp18sm.htm

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Top Abstract Introduction Methods Results Discussion Conclusion Supplementary Material References

 
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