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1 The Randall Centre, Guy's Campus, King's College London, London SE1 1UL, UK
2 Department of Physiological Sciences, Eastern Virginia Medical School, Norfolk, VA 23501, USA
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Abstract |
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50% and 10–35%, respectively, while shortening velocity was moderately reduced (by 20–30%). Phosphate also increased the rate of the fast component of force recovery. In contrast to Mn2+ and CTP, Ni·ATP and Mg·ITP did not support contraction well and caused striations to become disordered. The rates of force recovery and Me·NTPase activity were less than for Mg·ATP (by 40–80% and 50–85%, respectively), while shortening velocity was greatly reduced (by 80%). Dissociation of ADP from acto-S1 was little affected by Ni2+, suggesting that Ni·ADP dissociation does not account for the large reduction in shortening velocity. The different effects of Ni2+ and Mn2+ were also observed during brief activations elicited by photolytic release of ATP. These results confirm that at least one rate-limiting step is shared by acto-S1 ATPase activity and force development. Our results are consistent with a dual rate-limitation model in which the rate of force recovery is limited by both NTP cleavage and phosphate release, with their relative contributions and apparent rate constants influenced by an intervening rapid force-generating transition.
(Received 8 November 2004;
accepted after revision 9 December 2004;
first published online 20 December 2004)
Corresponding author J. Sleep: The Randall Centre, New Hunt's House, Guy's Campus, King's College London, London SE1 1UL, UK. Email: john.sleep{at}kcl.ac.uk
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Introduction |
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Brenner & Eisenberg (1986) compared the steady-state ATPase of cross-linked actomyosin-S1 over a range of temperatures to rates of force redevelopment under the same conditions in skinned single fibres from rabbit skeletal muscle following isotonic shortening at low load. Shortening was terminated by rapidly restretching the fibre to its original length, a procedure previously shown by Brenner (1983) to increase striation order in active skinned fibres. The rate of force redevelopment was found to be within a factor of two of acto-S1 ATPase activity over a range of temperatures at two ionic strengths, implying that the two processes are limited by the same step in the cross-bridge cycle.
Biochemical steps controlling the speed of unloaded shortening have also been the subject of several studies. Huxley (1957) postulated on theoretical grounds that the rate of cross-bridge detachment should limit the speed of shortening, while Bárány (1967) showed a correlation between actomyosin ATPase activity in solution and shortening velocity in different types of muscle. Steps which could slow detachment include substrate binding or product release. Evidence that product release limits shortening has been obtained from a comparison of several types of muscle in which ADP release and maximum velocity vary together over a large range (Siemankowski et al. 1985). However, UDP dissociates acto-S1 at a rate similar to ADP, while slowing shortening by 50% (Seow et al. 2001).
One approach to associating biochemical steps with mechanical events is to use the ability of myosin to hydrolyse a wide variety of divalent cation–nucleotide triphosphate substrates, which power work production in muscle to varying degrees (reviewed by Needham, 1971). In recent years several groups have used this property to relate actomyosin kinetics to muscle mechanics (Burton & Sleep, 1987; Pate et al. 1993; White et al. 1993; Wahr et al. 1997; Regnier et al. 1998; Regnier & Homsher, 1998; Seow et al. 2001). In this paper we have varied the substrate to compare steady-state and transient solution kinetics to rates of force recovery and fibre shortening. The velocity of unloaded shortening did not correlate either with nucleoside triphosphatase (NTPase) or the rate of nucleoside diphosphate (NDP) release, but did correlate with sarcomere disorder. We confirm Brenner & Eisenberg's (1986) observation of a modest correlation between acto-S1 NTPase activity in solution and the rate of force recovery. The effects of alternative substrates and inorganic phosphate suggest that force recovery is dependent on more than one step in the cross-bridge cycle, additional evidence for which is provided in a companion study in which fibres were activated by photoliberation of ATP (Sleep et al. 2005).
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Methods |
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Rabbit psoas fibres were isolated and mounted on the apparatus as described in the preceding paper (Sleep et al. 2005). Rabbits (2–2.5 kg) were killed, in accordance with the UK Animals (Scientific Procedures) Act 1986, by an overdose of sodium pentobarbitol (150 mg kg–1) administered intravenously in one ear followed by exanguination. Small bundles of muscle fibres were skinned in 0.5% Brij 35 detergent and either used within 3–4 days or glycerinated in 1: 1 (v/v) glycerol–skinning solution and stored at –20°C for up to 1 month. In the latter case, osmotic shock to the fibres was reduced by increasing the concentration of glycerol in two steps before lowering the temperature to –20°C. Fibres that had not been glycerinated were preferred (Yu & Brenner, 1989) as they were less stiff when relaxed, maintained greater striation order, and supported longer activations with higher shortening velocities and larger force recovery (see description of length change protocols below).
The composition of relaxing and activating solutions is given in Table 1. When inorganic phosphate was added to Mg·ATP solutions, potassium acetate concentration was adjusted to maintain ionic strength at 200 mM. Additional details of fibre preparation, apparatus and fibre handling, experimental protocol and data analysis are described by K. Burton et al. (in preparation).
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The experimental apparatus was built on an upright, fixed-stage microscope. Fibres were mounted in 40 µl drops of solution held on glass pedestals of the type previously described (Sleep, 1990; Sleep et al. 2005). Experiments were done at 5 ± 0.1°C. Temperature was measured by a small (200 µm) thermistor (Thermometrics, Edison, NJ, USA) placed near the fibre, and feedback-controlled by a Peltier cooler. In many experiments the thermistor was attached to a vibrating motor used to stir the drop to accelerate diffusion of substrate into fibres.
Fibres were attached to motor and transducer hooks by aluminium foil T-clips crimped onto the ends. Water-polymerizing cyanoacrylate (Histoacryl, Braun, Melsungen, FRG; Brenner & Eisenberg, 1986) was used to strengthen hook-clip and clip-fibre attachments. Sarcomere length in relaxed fibres on the experimental apparatus was measured with a x 20 water-immersion objective before the first activation, and during an experiment was estimated from the position of the first-order diffraction beam produced by laser illumination (HeNe laser, 632 nm wavelength).
The servomotor used for controlling fibre length was similar to that described by Ford et al. (1977). The signal controlling the servomotor was from a voltage nearly proportional to either fibre length (position of the motor; PM) or sarcomere length (position of the diffraction order; SL). Large step length changes were critically damped as underdamping introduced oscillations which greatly affected the size and rate of force redevelopment following a restretch (Burton, 1989). Additional details of mechanical and sarcomere length measurements can be found in Sleep et al. (2005) and K. Burton et al. (in preparation).
For most experiments the signals corresponding to tension, fibre length and the intensity and position of the first-order diffracted beam were recorded with a 100 kHz Tecmar board using software provided by Dr Lincoln Ford (SALT, Fenster & Ford, 1985; Wirth & Ford, 1986). The frequency of sampling was chosen to vary according to the rate of change of signals. Tension and temperature were recorded on a slow time base using a strip chart recorder.
Experimental protocol
Fibres were mounted on the experimental apparatus in relaxing solution (Table 1) at low temperature (0.0–0.5°C), and sarcomere length measured as described above. The temperature was raised to 5°C and the fibre transferred to Mg·ATP activating solution (Table 1). The striation pattern was stabilized by the technique of Brenner (1983) in which cycles of shortening at low load and rapid restretch to the initial length were applied at about 5 s intervals (Fig. 1). During the initial period of activation, the speed of ramp shortening was adjusted to bring load to near zero, a position on the fibre producing a suitable diffraction pattern was chosen, and sarcomere length measured. In experiments where sarcomere length control was to be used, the gain and offset of the sarcomere length signal were adjusted to match that of the PM signal, and then control of the servomotor was switched to the sarcomere length signal. Data were acquired during a series of length change protocols (Fig. 1) and the fibre was then either relaxed or another set of active experiments was carried out during the same activation (e.g. changing the type of length control or activating solution). In all experiments comparing different metal–nucleotides, fibres were activated in Mg·ATP before and after activation using an alternative substrate (Table 1 and Fig. 1), and results of the two ATP activations were averaged. In the text, identification of a substrate by reference to the nucleotide alone (e.g. CTP) means that Mg2+ was the metal complexed with the nucleotide; likewise, reference to a metal alone (e.g. Ni2+) means that ATP was the nucleotide.
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Two length change protocols were used for slack tests: the usual method (Edman, 1979) in which all step releases started from the same length and ended at various lengths (‘restretch slack tests’) or an alternative approach in which the releases started from various lengths and ended at the same length (‘prestretch slack tests’). In both protocols, a ramp–restretch was used to reset the length to the original value so that the final length was the same as the initial length, allowing the procedure to be repeated with various shortening steps during a single activation (Fig. 1). The advantage of the prestretch slack test protocol was that recovery always occurred at the same length, and the rate and magnitude of force recovery were independent of the amount of shortening. In the restretch slack test protocol recovery was smaller and slower at the shorter lengths reached after progressively longer releases, in agreement with previous observations (Ekelund & Edman, 1982; Brenner & Eisenberg, 1986; Vandenboom et al. 2002). However, a disadvantage of prestretch slack tests was that they greatly increased estimated unloaded shortening velocity and reduced series compliance. Although this observation is similar to that from intact frog fibres in which a non-linear length–time relation was attributed to passive compliance at long sarcomere lengths (Claflin et al. 1989), our length–time relations were linear (Fig. 3) and the effect was observed at short length. In this study absolute values of force recovery after unloaded shortening were usually obtained from prestretch slack tests, whereas restretch slack tests were used to estimate the absolute value of maximum shortening velocity (Fig. 3 and Table 2). See Supplementary Material for examples. The relative effects of different substrates on force recovery and shortening velocity were independent of slack test protocol.
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Analysis
For multiple-exponential fitting of force records a Fortran program was used that incorporated the routines of Provencher (1976; see also http://sprovencher.com/pages/discrete.shtml). The Provencher routine generated its own initial estimates, handled different sampling frequencies in a single record and was able to simultaneously fit up to five multiple functions to the record, ranking them in order of goodness of fit.
Results are presented as mean ± S.E.M., with n = number of fibres in the mechanics experiments unless otherwise stated. The values for each fibre usually were the result of replicates within a single continuous activation: 3–10 for force redevelopment, 7 for unloaded shortening velocity (representing 4–5 sizes of step release in a slack test; see Fig. 1), and 3–14 for isometric force. In some control experiments, each measurement was made in a single brief activation. The effects of alternative substrates on mechanical properties are expressed relative to the average value from Mg·ATP activations preceding and following the test activation.
Calculation of unloaded shortening velocity from slack test data used the slope of percentage shortening (expressed relative to a sarcomere length of 2.4 µm) versus slack time while the intercept on the percentage shortening axis provided an estimate of series compliance (Edman, 1979). Slack time was defined as the period between the shortening step and the time when force rose to 1% of the isometric level; additional precision in defining the end of the slack period (Julian et al. 1986) was not needed as the effects of alternative nucleotides on shortening velocity were large.
Since a double-exponential fit was nearly always a good description of force recovery, the degree to which a single-exponential fit differed from a double-exponential fit was taken to be one measure of the ‘bi-exponential’ nature of force recovery. We describe force recovery as being highly bi-exponential when the double–single difference curves are large relative to the magnitude of recovery. Figure 2 gives examples. These difference curves strongly correlated with the goodness of fit. Although the residuals of single- and double-exponential fits can be compared directly, they include noise which obscures the differences. Two exponentials have also been used by others to describe recovery after restretch (Swartz & Moss, 1992; Chase et al. 1994).
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Biochemical methods
Actin and myosin were prepared from rabbit back muscle by standard methods (Pardee & Spudich, 1982; Margossian & Lowey, 1982). Chymotryptic subfragment-1 (S1) was prepared by the methods of Weeds & Taylor (1975). Actin and Sl were cross-linked with 1-ethyl-3-(3-dimethylaminopropyl) carbodiimide (EDC) (Mornet et al. 1981). All experiments were done at 5°C.
NDP binding constant and rate of dissociation. This rate was determined by the inhibitory effect of NDP on the rate of acto-S1 dissociation by NTP. First the rate of dissociation by NTP was measured in the absence of NDP to establish the second-order rate constant, and then in the presence of a near-saturating concentration (in practice 1 mM, cf. a binding constant of 0.15 mM). The ratios of second-order rates of dissociation in the absence and presence of increasing concentrations of NDP give the fraction of acto-S1 with NDP bound, and the maximum rate directly gives the rate of NDP dissociation from acto-myosin-ADP (AM·D) (Siemankowski & White, 1984). A Kintek (Austin, TX, USA) stop flow was used, reactions being monitored by light scattering at 340 nm. The cell was 2 mm square and the dead time was about 2 ms.
The rate and equilibrium constant of the hydrolysis step. These parameters were measured using the single turnover method which in the case of Mg·ATP results in a large proportion being split in the burst phase (White et al. 1997). A Kintek stepper motor-driven quench-flow machine was used. The experiments used a ratio of [S1]/[ATP] of 5 and a wide range of S1 concentrations to ensure that conditions were found that distinguished the hydrolysis step itself from the NTP binding step. The A2 isozyme of myosin-S1 was used. Products Pi and NTP were separated by adsorption to activated charcoal (White et al. 1997).
Acto-S1 NTPase.
The rates were measured using cross-linked acto-S1 to avoid the need for the very high actin concentrations needed to achieve saturation at physiological ionic strength. In the case of the ATP metal–nucleotides, [
32P]ATP was used, the samples being treated with charcoal as above. In the case of ITP and CTP, rates were measured using the malachite green Pi assay (Kodama et al. 1986).
NTP regenerating system in the presence of alternative metal–nucleotides. The value of Vm/Km for the alternative Me·NDP complexes was checked at our standard concentration of phosphocreatine by using a low value of NDP (20 µM) and having an excess of cross-linked acto-S1 present so as to rapidly convert NTP back to NDP. The overall rate of the reaction was monitored by assaying for phosphate using the malachite green method (Kodama et al. 1986). Creatine kinase was found to be much less effective for all the alternative substrates.
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Results |
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Figure 2 shows examples of the ramp–restretch protocol and illustrates records obtained under sarcomere length and overall length (PM) control. Paired comparisons between sarcomere length control and PM control were made for six fibres using Mg·ATP as the substrate (see Supplementary Material): sarcomere length control increased the single-exponential rate constant by 12 ± 2%, and the magnitude of the fast component exhibited a small increase relative to the total recovery (9 ± 4%), but the rate constants of the slow and fast components were not significantly different (5 ± 5% and 6 ± 4%, respectively). The effect of sarcomere length control was small in part because the fibre ends were glued to metal clips, and the clips were glued to hooks. Both of these steps reduced sarcomere shortening during force recovery under PM control and increased the rate of recovery, similar to the improvements achieved by fixing the ends of fibres with glutaraldehyde (Chase & Kushmerick, 1988; Kraft et al. 1995). Sarcomere length control was used when feasible, but not for slack tests or when the diffraction pattern was disordered in the presence of some substrates (see below). The effects of alternative substrates on mechanical properties were not dependent on the type of length control used and so these data are usually grouped together.
Mechanical properties using Mn·ATP as substrate
Mean values of isometric force, unloaded shortening velocity, and exponential fits to force recovery are given in Table 2 for Mg·ATP as substrate. When Mn2+ was substituted for Mg2+ during activation, and the ramp–restretch protocol was used to elicit force redevelopment, three effects were immediately observed (Fig. 2): isometric force (Po) was reduced, the magnitude of recovery was reduced more than in proportion to Po, and the rate of recovery increased (Table 3). Po and striation order were well maintained during prolonged activations, and the effects of Mn2+ were reversible. Po fell by 27% on average while the tension minimum preceding recovery (Tmin) fell by only 7%
Po. Tmin estimated by extrapolating a double-exponential fit back to the time of the restretch was also reduced only slightly, to 95 ± 3% of its Mg2+ value (n
= 2 fibres, 2 comparisons between Mg2+ and Mn2+ for each fibre, one in PM and one in sarcomere length control; 27 force records in total). In long activations, Tmin usually rose and in these cases recovery could disappear completely in the presence of Mn2+. This smaller recovery reduced the signal to noise ratio of force recovery and the accuracy of double-exponential fits. An additional problem was the presence of a slow decline of force (rate 0.5 s–1) which tended to truncate the fitted force rise, making it appear faster (K. Burton et al. in preparation). The magnitude of this slow decline could be estimated from an overshoot in force recovery above the isometric level, and was not affected by substituting Mn2+ for Mg2+. In Fig. 2A and B the slow decline was 10% of Mg2+, but 40% of Mn2+ recovery, thus greatly increasing the apparent Mn2+ rate constant.
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35% (Table 4).
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1 min; Fig. 2B, n
= 2 fibres). One consequence of this procedure was that Tmin was lower and this was often accompanied by more sarcomere shortening after the restretch. The effects of Mn2+ were similar to those using long activations: for small magnitude recovery (no release after the restretch; Mn2+ recovery = 0.22Po, Mg2+
= 0.54Po), the single, slow and fast rates were 1.5 ± 0.6, 1.5 ± 0.8 and 1.8 ± 0.8 times the Mg·ATP value, respectively. For large magnitude recovery produced by step releases after the restretch (recovery = 67%
Po for Mn2+, 78% for Mg2+), the rates were 1.2 ± 0.2, 0.9 ± 0.1 and 1.5 ± 0.2 times the Mg·ATP value. As for the longer activations described above, Mn2+ had very little effect on Tmin or the magnitude of the slow decline of force estimated from the overshoot in recovery.
Large recovery following unloaded shortening (slack test) was also studied (Fig. 3). The effects of Mn2+ on force recovery following slack tests were similar to those following a ramp–restretch (Table 3): for the entire Mn2+ data set the single and slow rate constants decreased by 10% and 20%, respectively, and the fast rate constant increased by 50%. In the subset of Mn2+ data in which the slow rate constant for ramp–restretch was unchanged by Mn·ATP, the slow rate following a slack test was also unaffected (2 ± 12%) and the single and fast rates rose by 22 ± 4% and 87 ± 2.2%, respectively (n
= 2 fibres, each with 7 force records and 4 release sizes). Mn2+ had no effect on the relative amplitudes of the fast and slow components, and maximum shortening velocity was slowed to 82% of the Mg2+ value.
Mg·CTP
CTP increased the ATPase rate of cross-linked acto-S1 by about 10% (Table 4). Substituting CTP for ATP increased the rate of force redevelopment (Fig. 4, Table 3) and supported good striation order during activation. In contrast to Mn2+, Po was not reduced by CTP and the rates of both components of a double-exponential fit increased to a similar extent. The single- and double-exponential rates increased by 20–40% using slack tests (Fig. 4A) and 60–100% using the ramp–restretch protocol (Fig. 4B). Two effects of CTP on force recovery after unloaded shortening were not observed with the other substrates (Fig. 4A). The first was an increase in the magnitude of the fast component of a double-exponential fit, both in absolute terms and relative to Po (Table 3), which when combined with the increase in the rate constant made the faster rise of force more apparent. The second effect of CTP was a lag at the beginning of force recovery; such lags were not usually observed with ATP. This lag was consistently observed with CTP, but since it was not well fitted by a sum of exponentials and it occurred at a time when the fibre was just taking up the slack, the interpretation is complicated and this lag was not analysed in detail. An unfortunate practical consequence of this lag and its non-exponential form was that the exponential fits had to begin rather late, when force had risen to 25–30% of the isometric value. For the accompanying ATP activations, fits starting at 30% recovery did not differ significantly from those starting earlier (force at 5–10% isometric).
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58% of the ATP value (Fig. 4A). Pate et al. (1993) observed a somewhat smaller reduction to 70% (extrapolated to infinite [CTP]). They also reported that the Km of unloaded shortening velocity for CTP was large (1.9 mM, as compared to 0.15 mM for ATP), as determined by extrapolation of CTP concentration from 4 mM to infinity. Based on their data for the dependence of velocity on CTP concentration between 0.5 mM and 4 mM (their Fig. 2), the measured unloaded shortening velocity would increase by about 20% between 5 mM CTP (our conditions) and infinite CTP concentration, which accounts satisfactorily for the difference between our measurement and their extrapolated value. Ni·ATP
Figure 5 shows comparisons between activations in Ni·ATP and Mg·ATP. Ni2+ reduced isometric tension by about 20% and slowed force recovery to 30–60% of the Mg2+ value using all length change protocols (Table 3). The rate constant of the slow component of a double-exponential fit was reduced more than that of the fast component, so that the ratio of the fast to slow rate constants increased and recovery was somewhat more bi-exponential (Fig. 5A). Unloaded shortening velocity was greatly reduced (to 20% of the Mg2+ value) (Fig. 5A). The reduction in rate of force redevelopment was similar to the reduction in acto-S1 ATPase activity (Table 4).
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10% following Ni·ATP activation to increase striation order. This manoeuvre may have improved subsequent Mg·ATP activations, but reversibility of the Ni2+ effects on force remained poor. In an attempt to measure force recovery early during activation before the development of striation disorder, we rapidly activated several fibres from the rigor state by photolysing caged ATP complexed with Ni2+. An additional advantage of this experiment was that the initial development of force occurred in the absence of length changes, as it was not obvious that the ramp–restretch protocol improved active striation order in the presence of Ni·ATP. Initial force development after liberation of ATP slowed considerably when Ni2+ was substituted for Mg2+ (Fig. 5B). Hence the slowing caused by Ni2+ is present early in an activation, and is not the result of imposed length changes. In contrast to Ni2+, Mn2+ accelerated force development upon rapid liberation of ATP, similar to the effect of Mn2+ during steady activation (data not shown).
The striation disorder and low shortening velocity observed with Ni·ATP are similar to the effects of low ATP concentration or inhibition of ATP binding to cross-bridges (K. Burton & J. Sleep, unpublished observations). We tested the activity of creatine kinase (CK) in regenerating Ni·ATP from Ni·ADP and found that CK is 10 times less efficient with Ni2+ than with Mg2+ complexed to ATP. We carried out several control experiments for possible substrate limitation using Ni·ATP. Firstly, the concentration of CK was raised from 2.5 mg ml–1 (the concentration used with Mg·ATP) to 34 mg ml–1 and no significant improvement was noted with 5 mM Ni·ATP. An effect of CK concentration on maximum shortening velocity could be demonstrated by lowering Ni·ATP concentration (0.1 mM) or by reducing [CK] to less than 15 mg ml–1. We nevertheless used 20 mg ml–1 CK in activations with 5 mM Ni·ATP and additionally stirred the solution during activation (see Methods). We also activated fibres with a range of diameters using Ni·ATP (the smallest at 25 µm and one fibre at 130 µm and stripped sequentially to 78 and 37 µm) and did not observe improved mechanical performance in the thinner fibres. Higher concentrations of Ni·ATP were not used because of concern that excessive concentrations of Ni2+ ion are detrimental to fibres.
Mg·ITP
When ITP was substituted for ATP, there were substantial reductions in Po, rate of force redevelopment, and unloaded shortening velocity (Table 3 and Fig. 6). The 80% reduction in rate of force recovery compared to the ATP rate was similar to the 85% reduction in acto-S1 ATPase activity (Table 4). The striations were significantly disordered during activation, although they became reordered when the fibre was relaxed or when activated again using ATP. Force recovery after unloaded shortening showed a substantial lag using ITP, which was reversed by ATP (Fig. 6A). Following a shortening–restretch cycle force fell continuously towards the isometric level (Fig. 6B). The magnitude of the slow decline of force following the restretch (the difference between Po and force 1 s after the restretch) was, however, unaffected by ITP (3.3 mg for both ATP and ITP in Fig. 6B). The effects of ITP were observed in several activations in each of three fibres. As a test of the possibility that substrate limitation reduced shortening velocity, we doubled the concentration of Mg·ITP to 10 mM, but did not observe an increase in shortening velocity.
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Nucleotide structure has been shown to affect NTPase activity in solution via cross-bridge dissociation and NTP cleavage, while having less effect on product release (White et al. 1997). Phosphate (Pi) acts at a later step in a highly strain-dependent fashion (Bowater & Sleep, 1988), affecting several mechanical properties of fibres, including force development (Hibberd et al. 1985) and recovery (Wahr et al. 1997; Iwamoto, 1998; Regnier & Homsher, 1998). To ascertain whether Pi and the alternative nucleotides used here can affect the same step(s) in the cross-bridge cycle, we studied force recovery in the presence of 0–20 mM phosphate and fitted double-exponential functions to the data (Fig. 7).
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Rate of dissociation of metal–nucleotide diphosphates from acto-S1
For three ATP concentrations, the rates of dissociation of acto-S1 in the presence of 1 mM Mn·ADP are shown in Fig. 8A. The rates at the two highest concentrations of ATP (2.5 and 7 mM) were almost the same and the extrapolated rate, which corresponds to the ADP off-rate, was 325 s–1. The second-order rate constant in the presence of 1 mM ADP was 17% of that in its absence, which corresponds to a dissociation constant of 0.2 mM, so that about 83% of the acto-S1 had ADP bound. It can be seen that at the highest concentration the trace is not well fitted by a single exponential. Two exponentials are needed to provide a satisfactory fit and it is the rate of the fast phase that has been plotted against ATP concentration in Fig. 8B. The cause of the slow phase has not been established but the rate does not correspond with rates observed at lower ATP concentrations. The results of similar experiments for Mg2+ and Ni2+ and for CTP and ITP in the presence of Mg2+ are shown in Table 4.
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Plots of single turnovers of Mg·ATP and Mn·ATP by S1 at 5°C are shown in Fig. 9 for four different concentrations of S1. The ratio of S1: ATP was kept constant at 5: 1. The lines are the result of a global fit to the complete set of data and for Mn2+ correspond to a second-order rate of ATP binding of 0.6 ± 0.1 x 106 M–1 s–1, forward and reverse rates for the hydrolysis step of 8.8 ± 0.9 and 1.5 ± 0.3 s–1, and a rate of Pi release of 0.2 ± 0.04 s–1. The results of similar experiments for Mg2+ and Ni2+ are shown in Table 4, as are the Me·NTPase rates of cross-linked acto-S1 for the five species.
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Discussion |
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Interpretation of the form of force recovery
As observed by Brenner & Eisenberg (1986), force recovery after unloaded shortening was not well described by a single-exponential function. Force recovery after a ramp shortening with a restretch was also poorly described by a single exponential if Tmin was brought to a low level by a step release. A double exponential provided a good fit in most cases and there was little further improvement if more than three exponentials were fitted. In contrast to recovery from near zero force, recovery after a ramp–restretch without a release was often adequately described by a single-exponential function (Brenner & Eisenberg, 1986). We have shown that a restretch introduces a slow falling component into recovery which tends to truncate and accelerate the slow rising component, reducing the difference in rates between the slow and fast components and causing force recovery to appear more single exponential in form (K. Burton et al. in preparation). A step release following a restretch eliminates the slow falling component and reveals the double-exponential nature of recovery. Another motivation for introducing a step after a restretch was that alternative substrates that reduced isometric force reduced the magnitude of recovery and increased the relative contribution of the slow falling component, thus reducing the accuracy of the fit.
The rate of force recovery is thought to represent the sum of the rates of cross-bridge attachment and detachment (Huxley, 1957; Ford et al. 1977; Brenner & Eisenberg, 1986). Analysis of the origins of the exponential components of force recovery suggests that the fast component arises largely from cross-bridges attaching into force-generating states at moderate strain where the effective rate of attachment (f) dominates (K. Burton et al. in preparation), whereas the slow rising component results from cross-bridges attaching at high strain where the effective rate of detachment (g) dominates. A stretch introduces a slower falling component as highly strained bridges cycle to sites at lower strain. When strain is reduced to a low level 
, detachment is greatly accelerated. The present results provide additional support for these suggestions as discussed below.
Effects of intersarcomere dynamics
Correlations between fibre mechanical properties and steps in the cross-bridge cycle depend on several assumptions. One is that sarcomeres behave homogeneously and another is that the mechanical properties are attributable to cross-bridge activity and not passive sarcomeric structures. These assumptions are, however, never completely satisfied and depend on which substrate or mechanics protocol is used. A slow rise in force can result from shorter, stronger sarcomeres stretching longer, weaker sarcomeres in series (Hill, 1953; Julian & Morgan, 1979; Burton et al. 1989). This phenomenon might contribute to the slow component of force recovery, but several observations argue against it being the sole explanation: (1) the slow component was observed when sarcomere length control was used, (2) it occurred at short sarcomere lengths where the force–length relationship is stable, and (3) CTP increased the rate of the slow component of force redevelopment despite a reduction in maximum shortening velocity. In addition, there have been several previous reports of striation homogeneity in the presence of rates of force development similar to those studied here (e.g. Chase & Kushmerick, 1988; Chase et al. 1994).
Unloaded shortening velocity and rate of force recovery correlated strongly with striation order in the following sequence: Mg·ATP > Mg·CTP >Mn·ATP > Mg·CTP > Ni·ATP > Mg·ITP. An internal load resulting from slow cross-bridge dissociation could explain striation disorder and slowed shortening caused by Ni2+ and ITP, as the resistance to filament sliding could be variable within and between sarcomeres. Amitani et al. (2001) reported that ITP slowed cross-bridge dissociation and filament sliding velocity in vitro, and Regnier et al. (1998) also reported that ITP greatly reduced shortening velocity.
Correlation between mechanics and biochemistry
The first attempt to compare the rate of force redevelopment with a step of the biochemical cycle was made by Brenner & Eisenberg (1986). They found a correlation with the ATPase rate at saturating actin, Vm, which persisted with variations of ionic strength and temperature. We have extended this approach to alternative metal–nucleotides and can confirm that there is a modest correlation between force recovery and Vm using the alternative substrates (Table 4). This behaviour would be expected if the same biochemical step limited the two processes, which was the case for Eisenberg's refractory state model. In the current interpretation of the acto-S1 data the hydrolysis step to a significant extent plays the role of the refractory to non-refractory transition (Rosenfeld & Taylor, 1984). This scheme has been confirmed and extended by measurements of the rate of Pi release, which is considerably faster than the acto-S1 Vm (White et al. 1997). The Pi release experiments cannot be carried out at physiological ionic strength but small increases in ionic strength suggested that the rate was not very dependent on ionic strength and it is probable that Vm at this ionic strength remains limited by the hydrolysis step for myosin bound to actin (AM·ATP to AM·ADP·Pi). For fibres at physiological ionic strength the proportion of cross-bridges in these two states is thought to be small and thus it is unlikely that there is a direct correlation between the rate of force recovery and the acto-S1 Vm. As described in the preceding paper, it has become clear that the hydrolysis step while dissociated (M·ATP to M·ADP·Pi) is an important element in limiting the rate of force recovery and we find that the observed mechanical rate correlates better with M·ATP to M·ADP·Pi than with the acto-S1 Vm, although we suggest that the rate of Pi release is also critically involved in limiting the observed mechanical rate. However, the rate of the hydrolysis step while dissociated from actin is only 2 or 3 times faster than the rate while attached so that there are grounds for the originally observed correlation.
Shortening velocity has been shown to correlate with myosin and actin-activated myosin ATPase activities from several muscles (Bárány, 1967). Our results show that this correlation does not extend to alternative substrates, consistent with previous studies (Pate et al. 1993; White et al. 1993; Regnier et al. 1998; Regnier & Homsher, 1998), as well as with evidence from actin filament sliding in vitro (Waller et al. 1995).
Symmetrical rate-limitation model of force recovery
As described in the preceding paper (Sleep et al. 2005), analysis of force development after release of ATP from a caged precursor suggests a kinetic scheme in which its rate is limited by a combination of the hydrolysis and Pi release steps (rate constants refer to Mg·ATP in fibres at 5°C):
The rate constants of hydrolysis (step 2) and phosphate release (step 4) are within a factor of two of each other and combine to limit the rate of recovery. The pre- and posthydrolysis M (myosin) states are in rapid equilibrium with the respective AM (actomyosin) states. The two rate-limiting steps are separated by a fast force-generating transition (‘phase 2’, Ford et al. 1977) between force-generating and non-force-generating ADP·Pi states. The equilibrium constant of this transition, K3(x), can be treated as a strain-dependent rapid equilibrium which modulates the steady-state concentrations of AM·NDP·Pi and AM'·NDP·Pi, and therefore the apparent rate constants of reverse hydrolysis k'–2(x) = (k–2)[1/(K3(x) + 1)] and phosphate release k'+4(x) = (k+4)[K3(x)/(K3(x) + 1)]. The apparent rate constants of each step are the sum of the forward and reverse transitions, so that for the hydrolysis step, khydr(app) = k+2 + k'–2(x) and for the phosphate step, kPi(app) = k'+4(x) + k–4[Pi]. The results of computer simulations of the complete scheme are provided in Table 4 for ATP and CTP. Steps thought to be sensitive to alternative substrates and Pi are indicated in the boxes below the scheme and discussed further in the following sections. For comparison to the two-state mechanics model discussed above and in K. Burton et al. (in preparation), steps 2–4 largely control the rate constant of attachment (f) which is suggested to dominate the fast component, while steps 5 and 1 control detachment (g) which dominates the rate of the slow component. Regnier & Homsher (1998) also concluded that the rate of force recovery can be influenced by multiple steps, including NTP binding, hydrolysis and a slow force-generating isomerization associated with phosphate release.
CTP
Isometric force was the same in the presence of CTP and ATP, while CTP increased the rate of force recovery by 1.4–2 times (Table 3), results broadly in agreement with those of Wahr et al. (1997) and Regnier & Homsher (1998). Compared to acto-S1 NTPase activity, the acceleration in force recovery was greater, consistent with previous studies (White et al. 1993; Regnier et al. 1998). The forward rate and equilibrium constants of the hydrolysis step for CTP have been reported to be 2 times those for ATP (Table 4; White et al. 1997; Regnier et al. 1998), results consistent with the hydrolysis step contributing to the rate limitation of force recovery (Table 4). In contrast, CTP does not accelerate Pi release by acto-S1 (White et al. 1997). CTP increased the rate of the slow component, which as discussed above suggests more rapid cross-bridge detachment at high strain (g), consistent with increased fibre NTPase activity when CTP is substituted for ATP (Pate et al. 1993).
The velocity of unloaded shortening is less for CTP than ATP, even when extrapolated to infinite substrate concentration (Pate et al. 1993; see Results), whereas CDP release from acto-S1 is faster than ADP release (Robinson et al. 1993). This result appears inconsistent with the suggestion of Siemankowski et al. (1985) that NDP release uniquely limits unloaded shortening velocity. As previously suggested (Pate et al. 1993; White et al. 1993; Regnier et al. 1998; Regnier & Homsher, 1998), a more likely explanation is slow dissociation of acto-S1 by CTP, the first-order rate of which is much lower than that of ATP (Table 4; White et al. 1993; Regnier et al. 1998).
Mn2+ and Pi
Replacement of Mg2+ with Mn2+ increased the rate of the fast component by 50% (Table 3), and this compares with a 14% increase in the rate of forward hydrolysis but a decrease of 67% in the reverse rate (Table 4). As discussed above, the apparent rate of hydrolysis (khydr(app)) depends on K3, and using the value of 0.5 found to account for force development in the presence of Mg2+ (Table 4), khydr(app)
= 9.8 s–1 for Mn2+ and 10.8 s–1 for Mg2+. Decreasing the assumed value of K3 to 0.1 would only increase khydr(app) to 10.2 s–1. It therefore seems unlikely that changes in the rate of the hydrolysis step by Mn2+ can account for the observed increase in the rate of force development.
Mn2+ could also exert some of its effect by increasing the rate of Pi release and/or binding. This idea is supported by observations of the effect of alternative metal ions on the rate of Pi release from M·ADP·Pi (Peyser et al. 1996). In the absence of actin the ATPase rate is limited by Pi release and increases with the ionic radius of the cation such that the rate is 5 times faster for Mn2+ than Mg2+. In the presence of actin this correlation with the ATPase activity breaks down, but the rate is no longer limited by Pi release (White et al. 1997) and it seems plausible that Pi release remains faster for these alternative metal ions. An effect of Mn2+ on the interaction of Pi with AM'·ADP has also been observed by Martin Webb (London, Mill Hill; personal communication), who found that the rate of acto-S1 18O Pi water exchange was almost three times faster for Mn2+ than for Mg2+, an observation which is most simply interpreted in terms of an enhanced rate of Pi binding. We suggest that an increase in the rate of phosphate release (k+4 in scheme 1 above) caused by bound Mn2+ could contribute to acceleration of the fast component, while tighter Pi binding resulting from an increase in k–4 could account for reduced tension and also contribute to faster recovery.
Another similarity between the effects of Pi and Mn2+ was that both had little effect on Tmin, despite their large effects on isometric force. Tmin has been suggested to result from cross-bridges bound during shortening which when forcibly detached by a restretch rapidly reattach and then slip along the actin filament (Burton, 1992). Stiffness at the time of Tmin is little changed from that during shortening (Burton, 1992), and a reduction in ATP concentration increases both stiffness and Tmin (Regnier & Homsher, 1998; K. Burton, unpublished observations). Cross-bridge strain at Tmin is only slightly higher than at Po, implying that the average force per cross-bridge is similar (Burton, 1992). These observations can be accounted for in the scheme presented by Sleep et al. (2005) and shown above. During shortening at low load the state which contributes to stiffness is AM'·ADP·Pi and there is little AM'·ADP, the state to which Pi binds, because step 5 (ADP release) is very rapid at low strain (Sleep et al. 2005). During isometric contraction, ADP release is slow and AM'·ADP is the dominant bound state. Since the transition between these two states is relatively slow (23 s–1 at 5°C, White et al. 1997), little AM'·ADP appears within the 10 ms required for force to reach Tmin after a restretch. Pi therefore has little effect on Tmin as it does not bind to the dominant force-producing state, AM'·ADP·Pi. During isometric contraction Pi binds to AM'·ADP and drives the cross-bridges back towards AM'·ADP·Pi and the non-force-producing state AM·ADP·Pi. This shift in the steady-state cross-bridge distribution contributes to the widely observed reduction in Po (Altringham & Johnston, 1985; Bowater & Sleep, 1988; Millar & Homsher, 1990, 1992; Iwamoto, 1998; Regnier & Homsher, 1998). In this way a strain dependence in ADP release can explain the minimal effect of Pi on Tmin. The similarity in the effects of Mn2+ and Pi on Tmin and Po is consistent with Mn2+ affecting the phosphate-binding step.
However, two results suggest that Mn2+ also influences steps other than Pi release/binding: (1) Mn2+ reduced shortening velocity (Table 3) while Pi had no significant effect (this work, Pi data not shown; Altringham & Johnston, 1985), and (2) Mn2+
l/lo
= relative change in length) versus slack time for 4 release sizes using the restretch–slack test protocol (see Methods). The results of linear regression are shown on the graphs (y
= relative length change, x
= slack time, R
= correlation coefficient). The estimates of maximum shortening velocity are given by the slopes (muscle lengths per second): 0.85 and 0.72 for Mg2+ and Mn2+, respectively. In the tension records (lower graphs), single-exponential fits are indicated by short dashes and double-exponential fits by long dashes. Results of exponential fits to the slack test data for Mg·ATP: kr1
= 6.8, krs
= 2.8, krf
= 10.0, A'f
= 0.70, and for Mn·ATP: kr1
= 5.5, krs
= 2.0, krf
= 15.1, A'f
= 0.57. Sarcomere length (µm) and fibre cross-section (µm2) for Mg2+, Mn2+ activations, respectively, were 2.25, 2.42, and 6.63 x 103 in the shortening graphs and 2.55, 2.73, and 8.65 x 103 in the tension graphs. See Supplementary Material for additional details.
, 
) or ramp–restretch (•, 
). Error bars represent S.E.M. (n
= 2–20 fibres with 7 releases each for slack tests, and 5–8 fibres each for ramp–restretch cycles). D, isometric force (
, 10 µM; 
, 200 µM. In each case the ratio of S1 to ATP was 5: 1 and the experiments were carried out in 140 mM KAc, 50 mM imidazole, 2 mM MeCl2, pH 7. The lines represent a global fit to all the experimental data (continuous, 10 µM; dotted, 20 µM; dashed, 50 µM; dot-dashed, 200 µM). For Mg2+ (upper graph), the second-order rate constant of ATP binding was 0.2 x 106M–1 s–1 and the rate constants of forward and reverse hydrolysis were, respectively, 7.7 s–1 and 4.6 s–1. For Mn2+ (lower graph), the rate of ATP binding was 0.6 x 106M–1 s–1 and the rates of hydrolysis were 8.8 s–1 and 1.5 s–1. The ordinate represents percentage ATP split relative to that approached at t
=
.