Kinetics of muscle contraction and actomyosin NTP hydrolysis from rabbit using a series of metal–nucleotide substrates

J Physiol 563.3 (2005) pp 689–711 689

Kinetics of muscle contraction and actomyosin NTPhydrolysis from rabbit using a seriesof metal–nucleotide substrates

Kevin Burton1, Howard White2 and John Sleep1

1The Randall Centre, Guy’s Campus, King’s College London, London SE1 1UL, UK2Department of Physiological Sciences, Eastern Virginia Medical School, Norfolk, VA 23501, USA

Mechanical properties of skinned single fibres from rabbit psoas muscle have been correlatedwith biochemical steps in the cross-bridge cycle using a series of metal–nucleotide (Me·NTP)substrates (Mn2+ or Ni2+ substituted for Mg2+; CTP or ITP for ATP) and inorganic phosphate.Measurements were made of the rate of force redevelopment following (1) slack tests in whichforce recovery followed a period of unloaded shortening, or (2) ramp shortening at low loadterminated by a rapid restretch. The form and rate of force recovery were described as the sumof two exponential functions. Actomyosin-Subfragment 1 (acto-S1) Me·NTPase activity andMe·NDP release were monitored under the same conditions as the fibre experiments. Mn·ATPand Mg·CTP both supported contraction well and maintained good striation order. Relative toMg·ATP, they increased the rates and Me·NTPase activity of cross-linked acto-S1 and the fastcomponent of a double-exponential fit to force recovery by ∼50% and 10–35%, respectively,while shortening velocity was moderately reduced (by 20–30%). Phosphate also increased therate of the fast component of force recovery. In contrast to Mn2+ and CTP, Ni·ATP and Mg·ITPdid not support contraction well and caused striations to become disordered. The rates offorce 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 ADPfrom acto-S1 was little affected by Ni2+, suggesting that Ni·ADP dissociation does not accountfor the large reduction in shortening velocity. The different effects of Ni2+ and Mn2+ were alsoobserved during brief activations elicited by photolytic release of ATP. These results confirmthat 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 recoveryis limited by both NTP cleavage and phosphate release, with their relative contributions andapparent rate constants influenced by an intervening rapid force-generating transition.

(Resubmitted 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, LondonSE1 1UL, UK. Email: [email protected]

An important property of contractile function is forcedevelopment at the start of contraction or after shortening(Ekelund & Edman, 1982; Brenner & Eisenberg, 1986;K. Burton et al. in preparation), the rate of which isthought to be limited by attachment and detachmentreactions of cross-bridges. Identification of the step(s) inthe cross-bridge cycle which control this rate is importantin the understanding of several properties of active muscle,including stiffness and the curvature of the force–velocityrelation.

Brenner & Eisenberg (1986) compared the steady-stateATPase of cross-linked actomyosin-S1 over a range oftemperatures to rates of force redevelopment under thesame conditions in skinned single fibres from rabbit

skeletal muscle following isotonic shortening at low load.Shortening was terminated by rapidly restretching the fibreto its original length, a procedure previously shown byBrenner (1983) to increase striation order in active skinnedfibres. The rate of force redevelopment was found to bewithin a factor of two of acto-S1 ATPase activity over arange of temperatures at two ionic strengths, implyingthat the two processes are limited by the same step in thecross-bridge cycle.

Biochemical steps controlling the speed of unloadedshortening have also been the subject of several studies.Huxley (1957) postulated on theoretical grounds that therate of cross-bridge detachment should limit the speedof shortening, while Barany (1967) showed a correlation

C© The Physiological Society 2004 DOI: 10.1113/jphysiol.2004.078907

690 K. Burton and others J Physiol 563.3

between actomyosin ATPase activity in solution andshortening velocity in different types of muscle. Stepswhich could slow detachment include substrate bindingor product release. Evidence that product release limitsshortening has been obtained from a comparison of severaltypes of muscle in which ADP release and maximumvelocity vary together over a large range (Siemankowskiet al. 1985). However, UDP dissociates acto-S1 at a ratesimilar to ADP, while slowing shortening by ∼50% (Seowet al. 2001).

One approach to associating biochemical steps withmechanical events is to use the ability of myosin tohydrolyse a wide variety of divalent cation–nucleotidetriphosphate substrates, which power work production inmuscle to varying degrees (reviewed by Needham, 1971).In recent years several groups have used this property torelate actomyosin kinetics to muscle mechanics (Burton& Sleep, 1987; Pate et al. 1993; White et al. 1993; Wahret al. 1997; Regnier et al. 1998; Regnier & Homsher,1998; Seow et al. 2001). In this paper we have varied thesubstrate to compare steady-state and transient solutionkinetics to rates of force recovery and fibre shortening.The velocity of unloaded shortening did not correlateeither with nucleoside triphosphatase (NTPase) or therate of nucleoside diphosphate (NDP) release, but didcorrelate with sarcomere disorder. We confirm Brenner& Eisenberg’s (1986) observation of a modest correlationbetween acto-S1 NTPase activity in solution and the rateof force recovery. The effects of alternative substratesand inorganic phosphate suggest that force recovery isdependent on more than one step in the cross-bridge cycle,additional evidence for which is provided in a companionstudy in which fibres were activated by photoliberation ofATP (Sleep et al. 2005).

Methods

Materials

Rabbit psoas fibres were isolated and mounted on theapparatus as described in the preceding paper (Sleepet al. 2005). Rabbits (2–2.5 kg) were killed, in accordancewith the UK Animals (Scientific Procedures) Act 1986,by an overdose of sodium pentobarbitol (150 mg kg−1)administered intravenously in one ear followed byexanguination. Small bundles of muscle fibres wereskinned in 0.5% Brij 35 detergent and either used within3–4 days or glycerinated in 1 : 1 (v/v) glycerol–skinningsolution and stored at −20◦C for up to 1 month. In thelatter case, osmotic shock to the fibres was reduced byincreasing the concentration of glycerol in two steps beforelowering the temperature to −20◦C. Fibres that had notbeen glycerinated were preferred (Yu & Brenner, 1989)as they were less stiff when relaxed, maintained greaterstriation order, and supported longer activations with

higher shortening velocities and larger force recovery (seedescription of length change protocols below).

The composition of relaxing and activating solutions isgiven in Table 1. When inorganic phosphate was added toMg·ATP solutions, potassium acetate concentration wasadjusted to maintain ionic strength at 200 mm. Additionaldetails of fibre preparation, apparatus and fibre handling,experimental protocol and data analysis are described byK. Burton et al. (in preparation).

Apparatus

The experimental apparatus was built on an upright,fixed-stage microscope. Fibres were mounted in 40 µldrops of solution held on glass pedestals of the typepreviously described (Sleep, 1990; Sleep et al. 2005).Experiments were done at 5 ± 0.1◦C. Temperature wasmeasured by a small (200 µm) thermistor (Thermo-metrics, Edison, NJ, USA) placed near the fibre,and feedback-controlled by a Peltier cooler. In manyexperiments the thermistor was attached to a vibratingmotor used to stir the drop to accelerate diffusion ofsubstrate into fibres.

Fibres were attached to motor and transducer hooksby aluminium foil T-clips crimped onto the ends.Water-polymerizing cyanoacrylate (Histoacryl, Braun,Melsungen, FRG; Brenner & Eisenberg, 1986) was usedto strengthen hook-clip and clip-fibre attachments.Sarcomere length in relaxed fibres on the experimentalapparatus was measured with a × 20 water-immersionobjective before the first activation, and duringan experiment was estimated from the position ofthe first-order diffraction beam produced by laserillumination (HeNe laser, 632 nm wavelength).

The servomotor used for controlling fibre length wassimilar to that described by Ford et al. (1977). The signalcontrolling the servomotor was from a voltage nearlyproportional to either fibre length (position of the motor;PM) or sarcomere length (position of the diffractionorder; SL). Large step length changes were criticallydamped as underdamping introduced oscillations whichgreatly affected the size and rate of force redevelopmentfollowing a restretch (Burton, 1989). Additional detailsof mechanical and sarcomere length measurements canbe found in Sleep et al. (2005) and K. Burton et al. (inpreparation).

For most experiments the signals corresponding totension, fibre length and the intensity and position of thefirst-order diffracted beam were recorded with a 100 kHzTecmar board using software provided by Dr Lincoln Ford(SALT, Fenster & Ford, 1985; Wirth & Ford, 1986). Thefrequency of sampling was chosen to vary according to therate of change of signals. Tension and temperature wererecorded on a slow time base using a strip chart recorder.

C© The Physiological Society 2004

J Physiol 563.3 Substrate effects on muscle and actomyosin kinetics 691

Table 1. Experimental solutions

Relaxing solutionsa

Activating solutionsLow Mg2+,

Component Skinning low EGTA ATP CTP ITP Mn2+ Ni2+

ATP 7 8 5 — — 5.8 5 (10)CTP — — — 5 — — —ITP — — — — 5 (10) — —MgAc 8 0.01 7 — 7 (12) — —MnCl2 — — — — — 6 —NiAc — — — — — — 5KAc — 73.2 85 85 85 (59) 112.4 89.8 (47.9)KProp 70 — — — — — —EGTA 5 0.5 — — — — —CaEGTA — — 10 10 10 — —CaCl2 — — — — — 0.285 0.15Imidazole 6 50 50 50 50 50 50Phosphocreatine — 20 10 10 10 10 20CK (mg ml−1) — 2.5 2.5 2.5 2.5 2.5 20 (40)

Ac, acetate; Prop, propionate; CK, creatine kinase. Concentrations are millimolar, except for CK which is inmg ml−1 (125–250 units mg−1). In some experiments using Ni·ATP, the concentration of CK added to thesolution was raised to 40 mg ml−1; the solubility of CK was measured to be 34 mg ml−1. pH was 7.0 at 5◦C andionic strength 200 mM for all solutions except skinning, which was pH 7.0 at 0◦C and ionic strength 126 mM.Proteases added to skinning solution: leupeptin (8 µg ml−1), phenylmethylsulphonyl fluoride (0.1 mM), trypsininhibitor (0.1 mg ml−1). aThe low Mg2+, low EGTA relaxing solution was used before activations with Ni·ATPand Mn·ATP because of the strong affinity of Ni2+ and Mn2+ for EGTA, thus making it impractical to maintainlow calcium and high metal–nucleotide concentrations; additionally EGTA was not used in the activationsolutions for these two substrates; the concentration of EGTA in the relaxing solution was reduced as muchas possible while still keeping the fibre relaxed. CTP, ITP and ATP relaxing solutions were identical to thecorresponding activating solutions, but with EGTA substituted for Ca·EGTA. Values in parentheses indicateconcentrations used in control experiments for Mg·ITP and Ni·ATP (see text). Free Mg2+ was usually ∼2 mM,except for activations comparing Mn·ATP with Mg·ATP in which 1 mM free Mn2+ or Mg2+ (6 mM total) wereused. Free Mn2+ was minimized as it is known to bind the regulatory light chain with high affinity (Bagshaw,1977) and has been reported to activate smooth muscle (Hoar & Kerrick, 1988). Ten millimolar free ATP wasused with 5 mM NiAc in control experiments to minimize free Ni2+. pCa was 4 in the Mn·ATP and Ni·ATPactivating solutions and about 4.5 otherwise. The concentration of the metal–nucleotide complexes was4.9–5 mM except in control solutions using 10 mM Mg·ITP. Total and free concentrations were calculated fromequations for multiple-binding equilibria using the program of Fabiato (1988) and the apparent stabilityconstants therein, as well as from Godt & Lindley (1982), Sillen & Martell (1970) and Smith & Martell (1989).Variation in stability constants with temperature was taken into account. All chemicals were obtained fromSigma (UK).

Experimental protocol

Fibres were mounted on the experimental apparatusin relaxing solution (Table 1) at low temperature(0.0−0.5◦C), and sarcomere length measured as describedabove. The temperature was raised to 5◦C and the fibretransferred to Mg·ATP activating solution (Table 1). Thestriation pattern was stabilized by the technique of Brenner(1983) in which cycles of shortening at low load and rapidrestretch to the initial length were applied at about 5 sintervals (Fig. 1). During the initial period of activation,the speed of ramp shortening was adjusted to bring loadto near zero, a position on the fibre producing a suitablediffraction pattern was chosen, and sarcomere lengthmeasured. In experiments where sarcomere length controlwas 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 thesarcomere length signal. Data were acquired during aseries of length change protocols (Fig. 1) and the fibre wasthen either relaxed or another set of active experimentswas carried out during the same activation (e.g. changingthe type of length control or activating solution). Inall experiments comparing different metal–nucleotides,fibres were activated in Mg·ATP before and after activationusing an alternative substrate (Table 1 and Fig. 1), andresults of the two ATP activations were averaged. Inthe text, identification of a substrate by reference to thenucleotide alone (e.g. CTP) means that Mg2+ was the metalcomplexed with the nucleotide; likewise, reference to ametal alone (e.g. Ni2+) means that ATP was the nucleotide.



Length change protocols used were (1) slack tests inwhich step shortening of 3–15% of the fibre length (lo) wasapplied, and (2) variations on the technique introducedby Brenner (1983) in which ramp shortening of 7–15%lo was terminated by a rapid restretch (< 0.5 ms) to theinitial length. Ramp shortening was preceded in manyexperiments by a step release to quickly bring load to alow level, and the restretch was in some cases followedwithin 2 ms by a step release of a few per cent.

Two length change protocols were used for slack tests:the usual method (Edman, 1979) in which all step releasesstarted from the same length and ended at various lengths(‘restretch slack tests’) or an alternative approach in whichthe releases started from various lengths and ended at thesame length (‘prestretch slack tests’). In both protocols, aramp–restretch was used to reset the length to the originalvalue so that the final length was the same as the initiallength, allowing the procedure to be repeated with variousshortening steps during a single activation (Fig. 1). Theadvantage of the prestretch slack test protocol was thatrecovery always occurred at the same length, and the rateand magnitude of force recovery were independent of theamount of shortening. In the restretch slack test protocolrecovery was smaller and slower at the shorter lengthsreached after progressively longer releases, in agreementwith previous observations (Ekelund & Edman, 1982;Brenner & Eisenberg, 1986; Vandenboom et al. 2002).However, a disadvantage of prestretch slack tests wasthat they greatly increased estimated unloaded shorteningvelocity and reduced series compliance. Although thisobservation is similar to that from intact frog fibres inwhich a non-linear length–time relation was attributedto passive compliance at long sarcomere lengths (Claflinet al. 1989), our length–time relations were linear (Fig. 3)and the effect was observed at short length. In thisstudy absolute values of force recovery after unloadedshortening were usually obtained from prestretch slacktests, whereas restretch slack tests were used to estimatethe absolute value of maximum shortening velocity (Fig. 3and Table 2). See Supplementary Material for examples.The relative effects of different substrates on force recoveryand shortening velocity were independent of slack testprotocol.

The protocols for caged ATP are described in thepreceding paper (Sleep et al. 2005).

Figure 1. Chart recordTension is shown during three activations using, respectively, ATP, CTPand ATP solutions (Table 1). Vertical deflections result from periodicramp–restretch cycles used to maintain striation order. A series of slacktests was applied at the end of each activation after initial tests of thelength change protocol and other procedures as described inMethods. Active sarcomere length = 2.2 µm, fibre length = 2.49 mm,cross-section = 9.8 × 103 µm2.



Table 2. Mechanics using Mg·ATPForce and shortening velocity

Diameter Force Vo

(µm) (nN µm−2) (L s−1)a

78 ± 2.4 98 ± 7.8 0.88 ± 0.04(22) (22) (19)

Force recovery: ramp–stretch cycle and slack tests

Shortening kr1 krs krf A′f krf/krs

protocol (s−1) (s−1) (s−1)

Ramp– 5.9 ± 0.28 3.6 ± 0.34 10.6 ± 0.62 0.54 ± 0.03 3.1 ± 0.1restretch (26) (13) (13) (13) (13)

Prestretch 5.0 ± 0.34 2.3 ± 0.18 8.2 ± 0.52 0.66 ± 0.02 3.6 ± 0.2slack tests (9) (7) (7) (7) (7)

Means ± S.E.M. Values in parentheses refer to number of fibres in mechanics experiments. Thenumber of repeats per fibre is discussed in Methods. Temperature = 5◦C. aUnloaded shorteningvelocity (Vo) obtained from restretch–slack tests. L s−1 = lengths per second at sarcomere length(SL) = 2.4 µm. Mechanical properties are from the first Mg·ATP activation for each of n fibres.Magnitudes of exponential components were calculated by extrapolating back to the time ofthe restretch in the case of a ramp–restretch protocol, the step release applied after a restretch,or zero force in a slack test. Symbols: kr = rate constant of an exponential component fitted totension recovery, where r1 = single exponential, rs = slow component of double exponential,rf = fast component, A′

f = amplitude of the fast component of a double-exponential fit relativeto total force recovery (amplitudes extrapolated to the beginning of recovery as discussed inMethods). The rate constants for ramp–stretch cycles are averages of SL and fibre length (PM)control protocols as the two groups of data were within 5–12% of each other as discussed in thetext. All slack tests were in PM control. The rate constants for slack tests are average values for allrelease sizes, which did not vary significantly for prestretch slack tests as discussed in Methods.

Analysis

For multiple-exponential fitting of force records aFortran program was used that incorporated theroutines of Provencher (1976; see also http://s-provencher.com/pages/discrete.shtml). The Provencherroutine generated its own initial estimates, handleddifferent sampling frequencies in a single record and wasable to simultaneously fit up to five multiple functions tothe 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 unlessotherwise stated. The values for each fibre usually were theresult of replicates within a single continuous activation:3–10 for force redevelopment, 7 for unloaded shorteningvelocity (representing 4–5 sizes of step release in a slack test;see Fig. 1), and 3–14 for isometric force. In some controlexperiments, each measurement was made in a singlebrief activation. The effects of alternative substrates onmechanical properties are expressed relative to the averagevalue from Mg·ATP activations preceding and followingthe test activation.

Calculation of unloaded shortening velocity from slacktest data used the slope of percentage shortening (expressedrelative to a sarcomere length of 2.4 µm) versus slacktime while the intercept on the percentage shortening

axis provided an estimate of series compliance (Edman,1979). Slack time was defined as the period between theshortening step and the time when force rose to ∼1% ofthe isometric level; additional precision in defining the endof the slack period (Julian et al. 1986) was not needed asthe effects of alternative nucleotides on shortening velocitywere large.

Since a double-exponential fit was nearly always agood description of force recovery, the degree to which asingle-exponential fit differed from a double-exponentialfit was taken to be one measure of the ‘bi-exponential’nature of force recovery. We describe force recoveryas being highly bi-exponential when the double–singledifference curves are large relative to the magnitude ofrecovery. Figure 2 gives examples. These difference curvesstrongly correlated with the goodness of fit. Although theresiduals of single- and double-exponential fits can becompared directly, they include noise which obscures thedifferences. Two exponentials have also been used by othersto describe recovery after restretch (Swartz & Moss, 1992;Chase et al. 1994).

The kinetics of the force rise of interest here were insome cases isolated from faster or slower componentseither by explicitly fitting a large number of exponentialsover the entire force record. The rate constants of the earlyforce transients were, however, sufficiently well separated



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(more than tenfold) from subsequent force recovery forit not to be necessary to include them. During recoveryafter slack tests, fitting started after an initial periodin which force rose in a variable way before becomingexponential in form. This behaviour may be explained byslack fibres straightening out with different time courses,depending on their shape and/or twist (Julian et al.1986). Three exponential components were occasionallya better fit to the force rise following unloaded shortening,but the improvement was small, so a maximum of twocomponents is reported here. The period over whichexponential functions were fitted is shown superimposedon experimental records in the figures.

Biochemical methods

Actin and myosin were prepared from rabbit backmuscle 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 with1-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 ratewas determined by the inhibitory effect of NDP on therate of acto-S1 dissociation by NTP. First the rate ofdissociation by NTP was measured in the absence of NDPto establish the second-order rate constant, and then in thepresence of a near-saturating concentration (in practice1 mm, cf. a binding constant of 0.15 mm). The ratiosof second-order rates of dissociation in the absence andpresence of increasing concentrations of NDP give thefraction of acto-S1 with NDP bound, and the maximumrate directly gives the rate of NDP dissociation fromacto-myosin-ADP (AM·D) (Siemankowski & White,

Figure 2. Comparison of force recovery in Mg2+ and Mn2+ activationsRamp–restretch protocol. Fibre length, sarcomere length and tension are given in the top three graphs (panelsa–c). Superimposed on the tension records (panel c) are double (long dashes) and single (short dashes) exponentialfits to force recovery. The goodness of fit is better revealed by residuals of the fits shown in the 4th and 5thgraphs from the top (panels d and e). The differences between the double- and single-exponential fits areshown in the bottom graph (panel f ) as discussed in Methods. The residuals and single–double difference dataare normalized by the observed magnitude of force recovery. A shortening step was applied at the beginningof ramp shortening to rapidly bring tension to a low level. Length and force records are in pairs: one recordincludes an overshoot on the restretch followed by a return to the original length, thereby reducing Tminand increasing recovery magnitude. Insets in panels a–c show 10 ms records during and after the restretch.A, continuous activation in sarcomere length (SL) control. In the middle graph (panel c), the pair of high forcerecords was acquired in the presence of Mg·ATP, and the low force pair in Mn·ATP; the length, residualsand single–double difference records are from the Mg2+ activation (see B for equivalent Mn2+ records). Forthe Mg2+ activation, the exponential constants fitted to force recovery (kr1, krs, krf and A′

f; see Table 2)following a ramp–restretch without step release were, respectively, 6.8, 4.8, 11.0 s−1, and 0.50, and when astep release was included were 5.6, 2.9, 9.1 and 0.65, respectively (n = 3 repeats). For Mn2+, the exponentialconstants were 13, 7.1, 22 and 0.67 without a step release, and 6.0, 3.1, 17.4 and 0.60 with a release.B, single activations in fibre length (PM) control with data acquired within 1 min of activation. All records are fromMn2+ activations except for high force pair acquired with Mg2+. Mg2+ exponential constants for the experimentwithout a step release were 5.5, 3.3, 8.8 and 0.57, and with a release were 4.7, 2.8, 9.2 and 0.50. For Mn2+without a step release: 10.5, 7.4, 21.4 and 0.54; with a release: 6.1, 2.8, 15.8 and 0.62. All the experiments shownin this figure used the same fibre; the activations in B preceded those in A. Fibre cross-section = 5.09 × 103 µm2.

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 about2 ms.

The rate and equilibrium constant of the hydrolysisstep. These parameters were measured using the singleturnover method which in the case of Mg·ATP results ina large proportion being split in the burst phase (Whiteet al. 1997). A Kintek stepper motor-driven quench-flowmachine was used. The experiments used a ratio of[S1]/[ATP] of 5 and a wide range of S1 concentrationsto ensure that conditions were found that distinguishedthe hydrolysis step itself from the NTP binding step. TheA2 isozyme of myosin-S1 was used. Products Pi and NTPwere separated by adsorption to activated charcoal (Whiteet al. 1997).

Acto-S1 NTPase. The rates were measured usingcross-linked acto-S1 to avoid the need for the veryhigh actin concentrations needed to achieve saturationat physiological ionic strength. In the case of the ATPmetal–nucleotides, [γ 32P]ATP was used, the samples beingtreated 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 alternativemetal–nucleotides. The value of V m/K m for thealternative Me·NDP complexes was checked at ourstandard concentration of phosphocreatine by using a lowvalue of NDP (20 µm) and having an excess of cross-linkedacto-S1 present so as to rapidly convert NTP back to NDP.The overall rate of the reaction was monitored by assayingfor phosphate using the malachite green method (Kodamaet al. 1986). Creatine kinase was found to be much lesseffective for all the alternative substrates.



Table 3. Effect of metal–nucleotides on mechanical parameters: ratios of Me·NTP/Mg·ATPForce and shortening

ShorteningSubstrate Force velocity Striations

Mn·ATP 0.73 ± 0.06 0.82 ± 0.05 Ordered(8) (6)

Ni·ATP 0.79 ± 0.9 0.19 ± 0.02 Disordered(7) (8)

Mg·CTP 1.02 ± 0.06 0.58 ± 0.05 Ordered(7) (5)

Mg·ITP 0.35 0.15 Disordered(2) (2)

Force recovery: ramp–restretch cycle (large recovery) and slack test

Substrate Protocol kr1 krs krf A′f krf/krs

Mn·ATP Ramp– 0.89 ± 0.07 0.82 ± 0.06 1.47 ± 0.06 1.05 ± 0.03 1.83 ± 0.09restretch (8) (8) (8) (8) (8)Slack 0.91 ± 0.11 0.80 ± 0.09 1.56 ± 0.13 0.93 ± 0.05 1.98 ± 0.07test (6) (6) (6) (6) (6)

Ni·ATP Ramp– 0.62 ± 0.04 0.30 ± 0.01 0.57 ± 0.03 1.27 ± 0.05 1.90 ± 0.02restretch (7) (2) (2) (2) (2)Slack 0.61 ± 0.05 0.48 ± 0.05 0.68 ± 0.04 0.95 ± 0.04 1.46 ± 0.17test (8) (5) (5) (5) (5)

Mg·CTP Ramp– 1.65 ± 0.07 2.01 ± 0.19 1.80 ± 0.30 1.05 ± 0.14 0.89 ± 0.08restretch (6) (3) (3) (3) (3)Slack 1.39 ± 0.06 1.24 ± 0.15 1.34 ± 0.09 1.31 ± 0.16 1.09 ± 0.06test (5) (3) (3) (3) (3)

Mg·ITP Slack 0.20 0.34 0.21 0.35 0.66test (2) (1) (1) (1) (1)

All values are given as ratios of Me·NTP to Mg·ATP results (mean ± S.E.M.). The Mg·ATP values are an average fromactivations before and after the alternate Me·NTP activation in each fibre. Values in parentheses refer to numberof fibres in mechanics experiments. For Mn·ATP, the ramp–restretch protocol included an overshoot and returnstep on the restretch to increase the size of recovery. See also legend to Table 2.

Results

Force recovery in fibre length and sarcomerelength control

Figure 2 shows examples of the ramp–restretch protocoland illustrates records obtained under sarcomere lengthand overall length (PM) control. Paired comparisonsbetween sarcomere length control and PM control weremade for six fibres using Mg·ATP as the substrate(see Supplementary Material): sarcomere length controlincreased the single-exponential rate constant by 12 ± 2%,and the magnitude of the fast component exhibited asmall increase relative to the total recovery (9 ± 4%),but the rate constants of the slow and fast componentswere not significantly different (5 ± 5% and 6 ± 4%,respectively). The effect of sarcomere length control wassmall in part because the fibre ends were glued to metalclips, and the clips were glued to hooks. Both of thesesteps reduced sarcomere shortening during force recovery

under PM control and increased the rate of recovery,similar to the improvements achieved by fixing the endsof fibres with glutaraldehyde (Chase & Kushmerick,1988; Kraft et al. 1995). Sarcomere length control wasused when feasible, but not for slack tests or when thediffraction pattern was disordered in the presence of somesubstrates (see below). The effects of alternative substrateson mechanical properties were not dependent on thetype of length control used and so these data are usuallygrouped together.

Mechanical properties using Mn·ATP as substrate

Mean values of isometric force, unloaded shorteningvelocity, and exponential fits to force recovery aregiven in Table 2 for Mg·ATP as substrate. WhenMn2+ was substituted for Mg2+ during activation, andthe ramp–restretch protocol was used to elicit forceredevelopment, three effects were immediately observed(Fig. 2): isometric force (Po) was reduced, the magnitude



of recovery was reduced more than in proportion toPo, and the rate of recovery increased (Table 3). Po andstriation order were well maintained during prolongedactivations, and the effects of Mn2+ were reversible. Po

fell by 27% on average while the tension minimumpreceding recovery (Tmin) fell by only ∼7% Po. Tmin

estimated by extrapolating a double-exponential fit backto the time of the restretch was also reduced only slightly,to 95 ± 3% of its Mg2+ value (n = 2 fibres, 2 comparisonsbetween Mg2+ and Mn2+ for each fibre, one in PM andone in sarcomere length control; 27 force records intotal). In long activations, Tmin usually rose and inthese cases recovery could disappear completely in thepresence of Mn2+. This smaller recovery reduced thesignal to noise ratio of force recovery and the accuracyof double-exponential fits. An additional problem was thepresence of a slow decline of force (rate ∼0.5 s−1) whichtended to truncate the fitted force rise, making it appearfaster (K. Burton et al. in preparation). The magnitude ofthis slow decline could be estimated from an overshootin force recovery above the isometric level, and was notaffected by substituting Mn2+ for Mg2+. In Fig. 2A and Bthe slow decline was ∼10% of Mg2+, but 40% of Mn2+

recovery, thus greatly increasing the apparent Mn2+ rateconstant.

This problem could be reduced by increasing themagnitude of force recovery in the presence of Mn2+, andin order to achieve this, Tmin was brought to a low levelby applying step releases 2 ms after the restretch (insets toFig. 2A). This length change protocol provided for largemagnitude recovery in the presence of both Mg2+ andMn2+, which made the double-exponential form ofrecovery more apparent (Fig. 2A and B; see residuals anddouble–single difference curves). In this case there wasmuch less slow decline following force recovery, both inabsolute magnitude as well as relative to the magnitudeof the force rise. We compared this ramp–restretch + stepprotocol to the standard ramp–restretch protocol duringsingle activations of two fibres: Mn2+ increased thesingle-exponential rate by only 12 ± 2%, compared to85 ± 21% without a step release (n = 2 fibres, 16 records),and the fast component of a double-exponential fit roseby 67 ± 9%, compared to 87 ± 9% without a release.However, the slow component was unaffected by Mn2+

when a step release was applied (3 ± 9% compared to58 ± 3% without a release). The actual rate constants forMg·ATP from this data set were (s−1): 5.7 ± 0.5, 3.1 ± 0.1and 9.1 ± 0.6 for the single, slow, and fast components,respectively. In an earlier set of experiments (n = 6 fibres),Mn2+ produced a smaller increase in the fast rate, thesingle and slow rates slowed, and force was reduced byonly 15% compared to a 50% reduction for the two fibresabove; the reasons for these differences are not clear. Forthe combined data set given in Table 3, the single and slowrates were 80–90% of the Mg·ATP value, while the fast

rate rose by about 50%. Mn2+ also increased the acto-S1ATPase by ∼35% (Table 4).

In most experiments, fibres were activated for manyminutes (Fig. 1) at 5◦C and striation order maintainedusing cycles of ramp–restretch. To ensure that the effectsof Mn2+ were not influenced by the duration of activation,we did a series of experiments in which data were acquiredin single activations of short duration (∼1 min; Fig. 2B,n = 2 fibres). One consequence of this procedure was thatTmin was lower and this was often accompanied by moresarcomere shortening after the restretch. The effects ofMn2+ were similar to those using long activations: forsmall magnitude recovery (no release after the restretch;Mn2+ recovery = 0.22Po, Mg2+ = 0.54Po), the single, slowand fast rates were 1.5 ± 0.6, 1.5 ± 0.8 and 1.8 ± 0.8times the Mg·ATP value, respectively. For large magnituderecovery produced by step releases after the restretch(recovery = 67% Po for Mn2+, 78% for Mg2+), the rateswere 1.2 ± 0.2, 0.9 ± 0.1 and 1.5 ± 0.2 times the Mg·ATPvalue. As for the longer activations described above,Mn2+ had very little effect on Tmin or the magnitude ofthe slow decline of force estimated from the overshoot inrecovery.

Large recovery following unloaded shortening (slacktest) was also studied (Fig. 3). The effects of Mn2+ onforce recovery following slack tests were similar to thosefollowing 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 increasedby ∼50%. In the subset of Mn2+ data in which the slow rateconstant 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 forcerecords and 4 release sizes). Mn2+ had no effect on therelative amplitudes of the fast and slow components, andmaximum shortening velocity was slowed to 82% of theMg2+ value.

Mg·CTP

CTP increased the ATPase rate of cross-linked acto-S1 byabout 10% (Table 4). Substituting CTP for ATP increasedthe rate of force redevelopment (Fig. 4, Table 3) andsupported good striation order during activation. Incontrast to Mn2+, Po was not reduced by CTP and the ratesof both components of a double-exponential fit increasedto a similar extent. The single- and double-exponentialrates increased by 20–40% using slack tests (Fig. 4A) and60–100% using the ramp–restretch protocol (Fig. 4B). Twoeffects of CTP on force recovery after unloaded shorteningwere not observed with the other substrates (Fig. 4A).The first was an increase in the magnitude of the fastcomponent of a double-exponential fit, both in absoluteterms and relative to Po (Table 3), which when combined



Table 4. Comparison of mechanics and biochemistry: potential rate-limiting steps

Fibre shortening and cross-bridge dissociationPredicted

Substrate Velocity NDP koff velocity k′ (AM)(L s−1)a (s−1)b (L s−1)c (µM−1 s−1)

Mg·ATP 0.88 ± 0.04 300 ± 50 1.8 1.2 ± 0.1(19) (4) (6)

Mn·ATP 0.73 ± 0.04 300 ± 50 1.8 1.2 ± 0.2(6) (4) (4)

Ni·ATP 0.17 ± 0.02 150 ± 40 0.9 0.2 ± 0.05(8) (4) (4)

Mg·CTP 0.51 ± 0.04 > 300d > 1.8 0.14, 0.07e

(5)Mg·ITP 0.13 ? ? ?

(2)

Force recovery, ATP hydrolysis and phosphate release

kr1 k+hyd Khyd kPi-off Predicted kr1f NTPase

Substrate (s−1)a (s−1) (s−1) (s−1) (s−1)

Mg·ATP 5.2 ± 0.3 7.7 ± 0.9 1.7 23h 5.2 1.9 ± 0.2(46) (8) (8) (11)

Mn·ATP 4.6 ± 0.2 8.8 ± 0.9 5.8 ? ? 2.5 ± 0.2(14) (8) (8) (8)

Ni·ATP 3.2 ± 0.2 > 0.6g > 0.006g ? ? 0.7 ± 0.2(15) (8) (8) (4)

Mg·CTP 7.8 ± 0.4 15.4h 3.3h 18h 7.8 2.2 ± 0.1(11) (5)

Mg·ITP 1.0 ± 0.1 0.15i ∼0.5i ? ? 0.15 ± 0.04(2) (5)

Values are mean ± error, where error is S.E.M. for mechanics and S.D. for biochemistry. Number of replicates (n)shown in parentheses (= fibres in mechanics experiments). NDP koff, first-order rate constant of ADP dissociationfrom actomyosin (n indicates replicates at each [ATP]); k′, second-order rate constant of Me·NTP binding toactomyosin; kr1, single-exponential rate constant of force recovery; k+hyd and Khyd, forward rate and equilibriumconstants, respectively, of the NTP hydrolysis step of myosin S1. NTPase, steady-state NTPase activity of cross-linkedacto-S1. aFor Mg·ATP, shortening velocity and kr1 are taken from Table 2. The mean ± S.E.M. for the alternativesubstrates was obtained by multiplying the Mg·ATP values by the relative effects given in Table 3. L s−1, fibrelengths per second. bEquilibrium constant for ADP binding to actomyosin = 0.13 mM for Mg·ATP. n number oftraces at each [ATP]. cLengths per second calculated assuming 5 nm working stroke estimated from shorteningvelocity at low [ATP] (White et al. 1993). dRate of CDP release reported by Robinson et al. (1993) was higher thanfor ADP release (taken from this study). eWhite et al. (1993) using actomyosin-S1 and Regnier et al. (1998) usingacto-heavy meromyosin (acto-HMM), respectively; 10◦C. fPredicted kr1 is from single-exponential functions fittedto simulated force records obtained from the kinetic scheme presented in Discussion, where hydrolysis is step 2and Pi release is step 4. For Mg·ATP, the rate constants are given there and above, with K 3 = 0.5. For Mg·CTP,K3 = 1, and in addition to the rates given above, k1 = 240 s−1 (White et al. 1993) and k5 = 0.7 s−1 (taken from fibreCTPase; Pate et al. 1993). k1 and k5 have been corrected for temperature. gk+hyd for Ni·ATP is a lower estimate asthe maximum rate was not reached within the accessible [S1]. hWhite et al. (1997). Khyd is that reported for S1 at10◦C; k+hyd has been extrapolated from 10 to 5◦C using a Q10 of 5 and correcting for ionic strength. The Pi releaserate for CTP assumes that the ratio of rates using CTP and ATP is the same at 20◦C (their study) and 5◦C. ik+hyd forITP was estimated from Khyd and steady-state ITPase activity at 20◦C, where the hydrolysis step is rate limiting.k+hyd and Khyd have been corrected for temperature and ionic strength.

with the increase in the rate constant made the faster riseof force more apparent. The second effect of CTP wasa lag at the beginning of force recovery; such lags werenot usually observed with ATP. This lag was consistentlyobserved with CTP, but since it was not well fitted by a sumof exponentials and it occurred at a time when the fibre was

just taking up the slack, the interpretation is complicatedand this lag was not analysed in detail. An unfortunatepractical consequence of this lag and its non-exponentialform was that the exponential fits had to begin rather late,when force had risen to 25–30% of the isometric value. Forthe accompanying ATP activations, fits starting at 30%



recovery did not differ significantly from those startingearlier (force at 5–10% isometric).

Although force recovery was faster with CTP than withATP, maximum shortening velocity was reduced to ∼58%of the ATP value (Fig. 4A). Pate et al. (1993) observeda somewhat smaller reduction to ∼70% (extrapolatedto infinite [CTP]). They also reported that the K m ofunloaded shortening velocity for CTP was large (1.9 mm,as compared to 0.15 mm for ATP), as determined byextrapolation of CTP concentration from 4 mm to infinity.Based on their data for the dependence of velocity on CTPconcentration between 0.5 mm and 4 mm (their Fig. 2),the measured unloaded shortening velocity would increaseby about 20% between 5 mm CTP (our conditions) andinfinite CTP concentration, which accounts satisfactorily

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Figure 3. Slack tests using Mg·ATP and Mn·ATPLeft, Mg2+; right, Mn2+. The upper graphs show release size (�l/lo = relative change in length) versus slacktime for 4 release sizes using the restretch–slack test protocol (see Methods). The results of linear regression areshown on the graphs (y = relative length change, x = slack time, R = correlation coefficient). The estimates ofmaximum shortening velocity are given by the slopes (muscle lengths per second): 0.85 and 0.72 for Mg2+ andMn2+, respectively. In the tension records (lower graphs), single-exponential fits are indicated by short dashes anddouble-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 × 103

in the shortening graphs and 2.55, 2.73, and 8.65 × 103 in the tension graphs. See Supplementary Material foradditional details.

for the difference between our measurement and theirextrapolated value.

Ni·ATP

Figure 5 shows comparisons between activations inNi·ATP and Mg·ATP. Ni2+ reduced isometric tensionby 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 ofa double-exponential fit was reduced more than that ofthe fast component, so that the ratio of the fast to slowrate constants increased and recovery was somewhat morebi-exponential (Fig. 5A). Unloaded shortening velocitywas greatly reduced (to 20% of the Mg2+ value) (Fig. 5A).



The reduction in rate of force redevelopment was similarto the reduction in acto-S1 ATPase activity (Table 4).

Striations during activation were usually disorderedwhen Ni·ATP was the substrate. Part of the reduction

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Figure 4. Effects of CTPA, slack tests using ATP (left column) versus CTP (right column). The restretch–slack test protocol was used. Thegraphs are otherwise as described in Fig. 3. The ATP activation followed the CTP activation. Exponential constants(kr1, krs, krf and A′

f; n = 2–3) for CTP were, respectively, 6.5, 2.7, 9.7 s−1, and 0.71, and for ATP were 4.5, 2.4,7.4 and 0.56. B, ramp–restretch cycles in ATP and CTP. The spike of tension during the restretch was not recordedat the sampling frequency used. Exponential constants were 5.0, 3.6, 9.5 and 0.44 for ATP and 9.0, 5.6, 14.0 and0.62 for CTP. The data in A and B were acquired from the same fibre; sarcomere length = 2.5 µm in A and 2.4 µmin B; fibre cross-section = 4.9 × 103 µm2.

in tension probably resulted from the presence ofextremely lengthened and shortened sarcomeres. Becauseof striation disorder, sarcomere length control was usuallyunsatisfactory. Another disadvantage of activations with



Ni·ATP was that its effects on force were not soreversible as with Mn·ATP or Mg·CTP. Similar effectswere reported by Stephenson & Thieleczek (1986), whoactivated frog skinned fibres with Ni2+ instead of Ca2+.To test the possibility that free Ni2+ ion contributed tothe effects attributed to Ni·ATP, we reduced free Ni2+ byadding ATP in 5 mm excess (Table 1) and found nosignificant difference in results. However, the converseapproach of increasing free Ni2+ reduced both forceand rate of recovery. These results suggest that Ni2+

complexed with ATP could have contributed to theobservations of Stephenson & Thieleczek (1986). We alsoregularly stretched and released relaxed fibres by ∼10%following Ni·ATP activation to increase striation order.This manoeuvre may have improved subsequent Mg·ATPactivations, but reversibility of the Ni2+ effects on forceremained poor.

In an attempt to measure force recovery early duringactivation before the development of striation disorder,we rapidly activated several fibres from the rigor stateby photolysing caged ATP complexed with Ni2+. Anadditional advantage of this experiment was that the initialdevelopment of force occurred in the absence of lengthchanges, as it was not obvious that the ramp–restretchprotocol improved active striation order in the presenceof Ni·ATP. Initial force development after liberation ofATP slowed considerably when Ni2+ was substituted forMg2+ (Fig. 5B). Hence the slowing caused by Ni2+ ispresent early in an activation, and is not the resultof imposed length changes. In contrast to Ni2+, Mn2+

accelerated force development upon rapid liberation ofATP, similar to the effect of Mn2+ during steady activation(data not shown).

The striation disorder and low shortening velocityobserved with Ni·ATP are similar to the effects oflow ATP concentration or inhibition of ATP bindingto cross-bridges (K. Burton & J. Sleep, unpublishedobservations). We tested the activity of creatine kinase(CK) in regenerating Ni·ATP from Ni·ADP and foundthat CK is 10 times less efficient with Ni2+ thanwith Mg2+ complexed to ATP. We carried out severalcontrol experiments for possible substrate limitation usingNi·ATP. Firstly, the concentration of CK was raised from2.5 mg ml−1 (the concentration used with Mg·ATP) to34 mg ml−1 and no significant improvement was notedwith 5 mm Ni·ATP. An effect of CK concentration onmaximum shortening velocity could be demonstratedby lowering Ni·ATP concentration (∼0.1 mm) or byreducing [CK] to less than 15 mg ml−1. We neverthelessused 20 mg ml−1 CK in activations with 5 mm Ni·ATPand additionally stirred the solution during activation(see Methods). We also activated fibres with a rangeof diameters using Ni·ATP (the smallest at 25 µm andone fibre at 130 µm and stripped sequentially to 78and 37 µm) and did not observe improved mechanicalperformance in the thinner fibres. Higher concentrations

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Figure 5. Effects of Ni2+

A, slack test protocols. See Fig. 3 for description of graphs. The forcerecords were obtained from the prestretch–slack test protocol: theinitial value is at the plateau of force recovery following aramp–prestretch prior to the slack test (release 0.86 s after restretchfor Mg2+, 1.66 s for Ni2+). For the tension records, the exponentialconstants (kr1, krs, krf and A′

f) for Mg·ATP were 5.4, 2.5, 8.6 s−1, and0.64, and for Ni·ATP were 2.2, 1.0, 5.5 and 0.60 (n = 2); sarcomerelength = 2.6 µm and fibre cross-section = 8.63 × 103 µm2.B, activations by photolysis of caged ATP complexed with Ni2+ orMg2+.



of Ni·ATP were not used because of concern that excessiveconcentrations of Ni2+ ion are detrimental to fibres.

Mg·ITP

When ITP was substituted for ATP, there were sub-stantial reductions in Po, rate of force redevelopment,and unloaded shortening velocity (Table 3 and Fig. 6). The80% reduction in rate of force recovery compared to theATP rate was similar to the 85% reduction in acto-S1ATPase activity (Table 4). The striations were significantlydisordered during activation, although they becamereordered when the fibre was relaxed or when activatedagain using ATP. Force recovery after unloaded shorteningshowed a substantial lag using ITP, which was reversed byATP (Fig. 6A). Following a shortening–restretch cycle forcefell continuously towards the isometric level (Fig. 6B).The magnitude of the slow decline of force following the

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Figure 6. Effects of ITPA, force recovery following unloaded shortening in ATPactivations before and after an activation using ITP. Thetime scale is expanded before 1 s to facilitatecomparison of the ATP and ITP records. B, the forceresponse to the ramp–restretch protocol in ATP and ITPactivations. The size of the shortening ramp was thesame in the ATP and ITP activations, but was muchslower in ITP. The data from the ramp–restretch andslack release experiments were from different fibres.Sarcomere length = 2.5 µm, fibre cross-section =4.49 × 103 µm2. Exponential constants (kr1, krs, krfand A′

f) for the fits to force recovery following slackreleases (n = 1–3) for the first ATP activation were,respectively, 4.9, 2.5, 9.6 s−1, and 0.71, and for the ITPactivation 0.9, 0.9, 2.0 and 0.25, and for second ATPactivation they were 4.2, 2.6, 9.0 and 0.66.

restretch (the difference between Po and force 1 s after therestretch) was, however, unaffected by ITP (3.3 mg for bothATP and ITP in Fig. 6B). The effects of ITP were observedin several activations in each of three fibres. As a test ofthe possibility that substrate limitation reduced shorteningvelocity, we doubled the concentration of Mg·ITP to10 mm, but did not observe an increase in shorteningvelocity.

Inorganic phosphate

Nucleotide structure has been shown to affect NTPaseactivity in solution via cross-bridge dissociation andNTP cleavage, while having less effect on productrelease (White et al. 1997). Phosphate (Pi) acts at alater step in a highly strain-dependent fashion (Bowater& Sleep, 1988), affecting several mechanical propertiesof 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 thesame step(s) in the cross-bridge cycle, we studied forcerecovery in the presence of 0–20 mm phosphate and fitteddouble-exponential functions to the data (Fig. 7).

High Pi concentration did not alter either Tmin followinga ramp–restretch or the tension spike during the restretch,despite a large reduction in Po (Fig. 7A and D). As aconsequence, recovery became so small that it couldnot reliably be fitted with multiple functions. Threeapproaches were therefore taken to ensure force developedfrom a low level, thus ensuring a large signal. First, weapplied a shortening step immediately after the restretchto bring force to near zero, as was done above in theexperiments using Mn2+ (Fig. 7A). Phosphate acceleratedthe rate constant of the fast component while having littleeffect on the rate of the slow component (Fig. 7C). Theamplitudes of the fast and slow components were reducedto a similar extent. Second, we fitted force recovery afterslack tests (Fig. 7B), and the effect of phosphate on rate ofrecovery was similar to that after ramp–restretch + steprelease (Fig. 7C). Third, we elicited force developmentfrom rigor by rapid release of ATP in the presence ofsaturating calcium (Fig. 7E), where it is shown in acompanion paper that initial force development is similarto that after shortening and restretch (Sleep et al. 2005).We minimized rigor force so that force development wasbetter isolated from a rapid decline which occurs duringinitial cross-bridge detachment at high rigor force, thusfacilitating detection of multiple exponential componentsin the force rise. The kinetics of this kind of forcedevelopment varied with phosphate in the same way asfor the other protocols: the fast rising component wasaccelerated while the slow component did not changesignificantly, so that recovery became significantly morebi-exponential at high Pi concentration (Fig. 7F). The rateconstants were most similar to those of slack tests, whichmay be the result of both protocols eliciting force fromvery low levels.

Rate of dissociation of metal–nucleotidediphosphates from acto-S1

For three ATP concentrations, the rates of dissociation ofacto-S1 in the presence of 1 mm Mn·ADP are shown inFig. 8A. The rates at the two highest concentrations of ATP(2.5 and 7 mm) were almost the same and the extrapolatedrate, which corresponds to the ADP off-rate, was 325 s−1.The second-order rate constant in the presence of 1 mmADP was 17% of that in its absence, which correspondsto a dissociation constant of 0.2 mm, so that about 83%of the acto-S1 had ADP bound. It can be seen that at thehighest concentration the trace is not well fitted by a singleexponential. Two exponentials are needed to provide asatisfactory fit and it is the rate of the fast phase that has

been plotted against ATP concentration in Fig. 8B. Thecause of the slow phase has not been established but therate does not correspond with rates observed at lowerATP concentrations. The results of similar experimentsfor Mg2+ and Ni2+ and for CTP and ITP in the presenceof Mg2+ are shown in Table 4.

The rate and equilibrium constantof the hydrolysis step

Plots of single turnovers of Mg·ATP and Mn·ATP by S1 at5◦C are shown in Fig. 9 for four different concentrations ofS1. The ratio of S1 : ATP was kept constant at 5 : 1. The linesare the result of a global fit to the complete set of data andfor Mn2+ correspond to a second-order rate of ATP bindingof 0.6 ± 0.1 × 106 m−1 s−1, forward and reverse rates forthe hydrolysis step of 8.8 ± 0.9 and 1.5 ± 0.3 s−1, and arate of Pi release of 0.2 ± 0.04 s−1. The results of similarexperiments for Mg2+ and Ni2+ are shown in Table 4, asare the Me·NTPase rates of cross-linked acto-S1 for thefive species.

Discussion

In order to probe steps in the cross-bridge cycle in activesingle skinned muscle fibres we have compared the effect offour alternative metal–nucleotides with the native Mg·ATP.We have concentrated on two mechanical properties offibres: (1) the rate and magnitude of force redevelopmentafter shortening, and (2) unloaded shortening velocity.The first is thought to be a probe of the flux of cross-bridgesinto attached force-generating states, which Brenner &Eisenberg (1986) proposed was limited by the same step asacto-S1 ATPase activity. The second, unloaded shorteningvelocity, is thought to be a measure of detachment ofcross-bridges under negative strain (Huxley, 1957), whichcould be limited by NDP release (Siemankowski et al. 1985)or NTP binding (Pate et al. 1993; Regnier et al. 1998).

Interpretation of the form of force recovery

As observed by Brenner & Eisenberg (1986), force recoveryafter unloaded shortening was not well described by asingle-exponential function. Force recovery after a rampshortening with a restretch was also poorly describedby a single exponential if Tmin was brought to a lowlevel by a step release. A double exponential provideda good fit in most cases and there was little furtherimprovement if more than three exponentials were fitted.In contrast to recovery from near zero force, recovery aftera ramp–restretch without a release was often adequatelydescribed by a single-exponential function (Brenner& Eisenberg, 1986). We have shown that a restretchintroduces a slow falling component into recovery whichtends to truncate and accelerate the slow rising component,reducing the difference in rates between the slow and fast



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Figure 7. Effects of inorganic phosphate (Pi) on force recoveryA, ramp–restretch protocol with 0, 5, 10, or 20 mM Pi in five separate activations. One record at each [Pi] isshown with no step release after the restretch (Tmin 0.4Po), and at 0 and 20 mM Pi (dotted lines), records are alsoshown with a step release 2 ms after the restretch (low Tmin; see Fig. 2). The latter record from each pair at 0 and20 mM Pi was scaled up by ∼10% to match the isometric force of the first record. B, unloaded shortening with 0(high force) or 20 mM Pi added to the activating solution. Single- and double-exponential fits are shown with theforce records as in Fig. 2. C, D and F, [Pi] on the abscissa refers to phosphate concentration above backgroundlevels (∼0.7 mM; Millar & Homsher, 1990). C, rate constants from double-exponential fits to recovery after unloaded



components and causing force recovery to appear moresingle exponential in form (K. Burton et al. in preparation).A step release following a restretch eliminates the slowfalling component and reveals the double-exponentialnature of recovery. Another motivation for introducinga step after a restretch was that alternative substrates thatreduced isometric force reduced the magnitude of recoveryand increased the relative contribution of the slow fallingcomponent, thus reducing the accuracy of the fit.

The rate of force recovery is thought to representthe sum of the rates of cross-bridge attachment anddetachment (Huxley, 1957; Ford et al. 1977; Brenner &Eisenberg, 1986). Analysis of the origins of the exponentialcomponents of force recovery suggests that the fastcomponent arises largely from cross-bridges attachinginto force-generating states at moderate strain where theeffective rate of attachment (f ) dominates (K. Burtonet al. in preparation), whereas the slow rising componentresults from cross-bridges attaching at high strain wherethe effective rate of detachment (g) dominates. A stretchintroduces a slower falling component as highly strainedbridges cycle to sites at lower strain. When strain is reducedto a low level (∼< 0), detachment is greatly accelerated.The present results provide additional support for thesesuggestions as discussed below.

Effects of intersarcomere dynamics

Correlations between fibre mechanical properties andsteps in the cross-bridge cycle depend on severalassumptions. One is that sarcomeres behave homo-geneously and another is that the mechanical propertiesare attributable to cross-bridge activity and not passivesarcomeric structures. These assumptions are, however,never completely satisfied and depend on whichsubstrate or mechanics protocol is used. A slow rise in forcecan result from shorter, stronger sarcomeres stretchinglonger, weaker sarcomeres in series (Hill, 1953; Julian &Morgan, 1979; Burton et al. 1989). This phenomenonmight contribute to the slow component of force recovery,but several observations argue against it being the soleexplanation: (1) the slow component was observed when

shortening ( ❡, �) or ramp–restretch (•, �). Error bars represent S.E.M. (n = 2–20 fibres with 7 releases each forslack tests, and 5–8 fibres each for ramp–restretch cycles). D, isometric force (�, ❡) and Tmin (×) versus [Pi] for theramp–restretch protocol. The dashed line represents Tmin independent of [Pi]. At 20 mM Pi, Tmin was ill defined(note large S.E.M.) because force usually fell monotonically after a restretch (see B). Force is represented by thesteady value before ramp shortening (�) and the force reached after recovery ( ❡, dotted line). In A, sarcomerelength = 2.30 µm and fibre cross-section = 8.48 × 103 µm2, and in B, sarcomere length = 2.15 µm and fibrecross-section = 5.52 × 103 µm2. E and F, effects of Pi on force development following photolytic release of ATPinto a rigor fibre. E, ATP was released at 0.1 s (downward spike on force record). The two force records were fromsequential activations with added Pi = 20 mM (2.47 µm sarcomere length in rigor) and Pi = 0 mM (2.44 µm SL).Force records were fitted with multiple-exponential functions that included a double-exponential rise and a rapidfalling component to describe an initial lag that gave the force rise a sigmoid shape. F, as in C. n = 11, 5, 5, 8 and4 force records from 10 fibres at 0, 2, 5, 10 and 20 mM Pi, respectively. Fibre cross-section = 2.09 × 103 µm2.

sarcomere length control was used, (2) it occurred at shortsarcomere lengths where the force–length relationshipis stable, and (3) CTP increased the rate of the slowcomponent of force redevelopment despite a reductionin maximum shortening velocity. In addition, there havebeen several previous reports of striation homogeneity inthe presence of rates of force development similar to thosestudied here (e.g. Chase & Kushmerick, 1988; Chase et al.1994).

Unloaded shortening velocity and rate of forcerecovery correlated strongly with striation orderin the following sequence: Mg·ATP > Mg·CTP >

Mn·ATP > Mg·CTP > Ni·ATP > Mg·ITP. An internalload resulting from slow cross-bridge dissociation couldexplain striation disorder and slowed shortening causedby Ni2+ and ITP, as the resistance to filament sliding couldbe variable within and between sarcomeres. Amitani et al.(2001) reported that ITP slowed cross-bridge dissociationand filament sliding velocity in vitro, and Regnier et al.(1998) also reported that ITP greatly reduced shorteningvelocity.

Correlation between mechanics and biochemistry

The first attempt to compare the rate of forceredevelopment with a step of the biochemical cycle wasmade by Brenner & Eisenberg (1986). They found acorrelation with the ATPase rate at saturating actin,V m, which persisted with variations of ionic strengthand temperature. We have extended this approach toalternative metal–nucleotides and can confirm that there isa modest correlation between force recovery and V m usingthe alternative substrates (Table 4). This behaviour wouldbe expected if the same biochemical step limited the twoprocesses, which was the case for Eisenberg’s refractorystate model. In the current interpretation of the acto-S1data the hydrolysis step to a significant extent plays the roleof the refractory to non-refractory transition (Rosenfeld& Taylor, 1984). This scheme has been confirmed andextended by measurements of the rate of Pi release, whichis considerably faster than the acto-S1 V m (White et al.1997). The Pi release experiments cannot be carried out at



physiological ionic strength but small increases in ionicstrength suggested that the rate was not very dependenton ionic strength and it is probable that V m at thisionic strength remains limited by the hydrolysis step formyosin bound to actin (AM·ATP to AM·ADP·Pi). Forfibres at physiological ionic strength the proportion ofcross-bridges in these two states is thought to be small andthus it is unlikely that there is a direct correlation betweenthe rate of force recovery and the acto-S1 V m. As describedin the preceding paper, it has become clear that thehydrolysis step while dissociated (M·ATP to M·ADP·Pi)is an important element in limiting the rate of force

Figure 8. Rate of dissociation of metal–nucleotide diphosphatesfrom acto-S1A, the time course of decrease in light scattering upon addition of7 µM, 35 µM and 3.5 mM ATP (final concentrations; two traces at3.5 mM ATP) to a solution of 6 µM actin, 4 µM S1 and 1 mM ADP(initial syringe concentrations) at 5◦C. The basic buffer was 100 mM

potassium acetate (KAc) and 20 mM Mops pH 7. The acto-S1 solutioncontained 2 mM MnCl2 and the ATP solution contained 5 mM Mg2+(initial syringe concentrations). B, plot of rate as a function of ATPconcentration. The maximum rate of the fitted curve was 325 s−1.

recovery and we find that the observed mechanical ratecorrelates better with M·ATP to M·ADP·Pi than withthe acto-S1 V m, although we suggest that the rate of Pi

release is also critically involved in limiting the observedmechanical rate. However, the rate of the hydrolysis stepwhile dissociated from actin is only 2 or 3 times faster thanthe rate while attached so that there are grounds for theoriginally observed correlation.

Shortening velocity has been shown to correlate withmyosin and actin-activated myosin ATPase activities fromseveral muscles (Barany, 1967). Our results show that

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Figure 9. Rate and equilibrium constants of the hydrolysis stepSingle Me·ATP turnover of S1 at a range of S1 concentrations: �,10 µM; ❡, 20 µM; �, 50 µM; �, 200 µM. In each case the ratio of S1 toATP 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 toall the experimental data (continuous, 10 µM; dotted, 20 µM; dashed,50 µM; dot-dashed, 200 µM). For Mg2+ (upper graph), thesecond-order rate constant of ATP binding was 0.2 × 106 M−1 s−1 andthe 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 bindingwas 0.6 × 106 M−1 s−1 and the rates of hydrolysis were 8.8 s−1 and1.5 s−1. The ordinate represents percentage ATP split relative to thatapproached at t = ∞.



this correlation does not extend to alternative substrates,consistent with previous studies (Pate et al. 1993; Whiteet 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 acaged precursor suggests a kinetic scheme in which its rateis limited by a combination of the hydrolysis and Pi releasesteps (rate constants refer to Mg·ATP in fibres at 5◦C):

Scheme 1

The rate constants of hydrolysis (step 2) and phosphaterelease (step 4) are within a factor of two of each otherand combine to limit the rate of recovery. Thepre- and posthydrolysis M (myosin) states are inrapid equilibrium with the respective AM (actomyosin)states. The two rate-limiting steps are separated by afast force-generating transition (‘phase 2’, Ford et al.1977) between force-generating and non-force-generatingADP·Pi states. The equilibrium constant of this trans-ition, K 3(x), can be treated as a strain-dependentrapid equilibrium which modulates the steady-stateconcentrations of AM·NDP·Pi and AM′·NDP·Pi, andtherefore the apparent rate constants of reverse hydrolysisk ′–2(x) = (k–2)[1/(K 3(x) + 1)] and phosphate releasek ′+4(x) = (k+4)[K 3(x)/(K 3(x) + 1)]. The apparent rateconstants of each step are the sum of the forwardand reverse transitions, so that for the hydrolysisstep, khydr(app) = k+2 + k′−2(x) and for the phosphatestep, kPi(app) = k′+4(x) + k−4[Pi]. The results of computersimulations of the complete scheme are provided inTable 4 for ATP and CTP. Steps thought to be sensitiveto alternative substrates and Pi are indicated in the boxesbelow the scheme and discussed further in the followingsections. For comparison to the two-state mechanicsmodel discussed above and in K. Burton et al. (inpreparation), steps 2–4 largely control the rate constantof attachment (f ) which is suggested to dominate the fastcomponent, 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, includingNTP binding, hydrolysis and a slow force-generating iso-merization associated with phosphate release.

CTP

Isometric force was the same in the presence of CTP andATP, while CTP increased the rate of force recovery by1.4–2 times (Table 3), results broadly in agreement withthose of Wahr et al. (1997) and Regnier & Homsher (1998).Compared to acto-S1 NTPase activity, the accelerationin force recovery was greater, consistent with previousstudies (White et al. 1993; Regnier et al. 1998). The forwardrate and equilibrium constants of the hydrolysis step forCTP have been reported to be ∼2 times those for ATP(Table 4; White et al. 1997; Regnier et al. 1998), resultsconsistent with the hydrolysis step contributing to the ratelimitation of force recovery (Table 4). In contrast, CTPdoes 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-bridgedetachment at high strain (g), consistent with increasedfibre NTPase activity when CTP is substituted for ATP(Pate et al. 1993).

The velocity of unloaded shortening is less for CTPthan ATP, even when extrapolated to infinite substrateconcentration (Pate et al. 1993; see Results), whereas CDPrelease from acto-S1 is faster than ADP release (Robinsonet al. 1993). This result appears inconsistent with thesuggestion of Siemankowski et al. (1985) that NDP releaseuniquely limits unloaded shortening velocity. As pre-viously suggested (Pate et al. 1993; White et al. 1993;Regnier et al. 1998; Regnier & Homsher, 1998), a morelikely explanation is slow dissociation of acto-S1 by CTP,the first-order rate of which is much lower than that ofATP (Table 4; White et al. 1993; Regnier et al. 1998).

Mn2+ and Pi

Replacement of Mg2+ with Mn2+ increased the rateof the fast component by ∼50% (Table 3), and thiscompares with a 14% increase in the rate of forwardhydrolysis but a decrease of 67% in the reverse rate(Table 4). As discussed above, the apparent rate ofhydrolysis (khydr(app)) depends on K 3, and using the valueof 0.5 found to account for force development in thepresence of Mg2+ (Table 4), khydr(app) = 9.8 s−1 forMn2+ and 10.8 s−1 for Mg2+. Decreasing the assumedvalue of K 3 to 0.1 would only increase khydr(app) to 10.2 s−1.It therefore seems unlikely that changes in the rate of thehydrolysis step by Mn2+ can account for the observedincrease in the rate of force development.

Mn2+ could also exert some of its effect by increasing therate of Pi release and/or binding. This idea is supported byobservations of the effect of alternative metal ions on therate of Pi release from M·ADP·Pi (Peyser et al. 1996). In



the absence of actin the ATPase rate is limited by Pi releaseand increases with the ionic radius of the cation suchthat the rate is 5 times faster for Mn2+ than Mg2+. In thepresence of actin this correlation with the ATPase activitybreaks down, but the rate is no longer limited by Pi release(White et al. 1997) and it seems plausible that Pi releaseremains faster for these alternative metal ions. An effect ofMn2+ on the interaction of Pi with AM′·ADP has also beenobserved by Martin Webb (London, Mill Hill; personalcommunication), who found that the rate of acto-S118O Pi water exchange was almost three times faster forMn2+ than for Mg2+, an observation which is most simplyinterpreted in terms of an enhanced rate of Pi binding. Wesuggest that an increase in the rate of phosphate release(k+4 in scheme 1 above) caused by bound Mn2+ couldcontribute to acceleration of the fast component, whiletighter Pi binding resulting from an increase in k–4 couldaccount for reduced tension and also contribute to fasterrecovery.

Another similarity between the effects of Pi andMn2+ was that both had little effect on Tmin, despite theirlarge effects on isometric force. Tmin has been suggested toresult from cross-bridges bound during shortening whichwhen forcibly detached by a restretch rapidly reattachand then slip along the actin filament (Burton, 1992).Stiffness at the time of Tmin is little changed from thatduring shortening (Burton, 1992), and a reduction in ATPconcentration increases both stiffness and Tmin (Regnier& Homsher, 1998; K. Burton, unpublished observations).Cross-bridge strain at Tmin is only slightly higher thanat Po, implying that the average force per cross-bridgeis similar (Burton, 1992). These observations can beaccounted for in the scheme presented by Sleep et al. (2005)and shown above. During shortening at low load the statewhich contributes to stiffness is AM′·ADP·Pi and thereis little AM′·ADP, the state to which Pi binds, becausestep 5 (ADP release) is very rapid at low strain (Sleepet al. 2005). During isometric contraction, ADP releaseis slow and AM′·ADP is the dominant bound state. Sincethe transition between these two states is relatively slow(∼23 s−1 at 5◦C, White et al. 1997), little AM′·ADP appearswithin the ∼10 ms required for force to reach Tmin after arestretch. Pi therefore has little effect on Tmin as it does notbind to the dominant force-producing state, AM′·ADP·Pi.During isometric contraction Pi binds to AM′·ADP anddrives the cross-bridges back towards AM′·ADP·Pi andthe non-force-producing state AM·ADP·Pi. This shiftin the steady-state cross-bridge distribution contributesto the widely observed reduction in Po (Altringham &Johnston, 1985; Bowater & Sleep, 1988; Millar & Homsher,1990, 1992; Iwamoto, 1998; Regnier & Homsher, 1998). Inthis way a strain dependence in ADP release can explain theminimal effect of Pi on Tmin. The similarity in the effectsof Mn2+ and Pi on Tmin and Po is consistent with Mn2+

affecting the phosphate-binding step.

However, two results suggest that Mn2+ also influencessteps other than Pi release/binding: (1) Mn2+ reducedshortening velocity (Table 3) while Pi had no significanteffect (this work, Pi data not shown; Altringham &Johnston, 1985), and (2) Mn2+ increased acto-S1 ATPaseactivity (Table 4) while Pi had no effect (Ma & Taylor,1994). The affected steps are currently unknown, as Mn2+

does not appear to alter those usually thought to limitthe two processes (Table 4; Regnier et al. 1995), ATPhydrolysis in the case of acto-S1 ATPase activity (Rosenfeld& Taylor, 1984) and ADP release or ATP binding in the caseof shortening velocity.

Acceleration of force recovery by Pi has been reportedpreviously for step releases (Altringham & Johnston,1985), ramp shortening to a stop (Iwamoto, 1998),ramp–restretch cycles (Regnier & Homsher, 1998; Tesiet al. 2000), and force development after release of ATPinto a rigor fibre (Hibberd et al. 1985). Our results weresimilar, but the acceleration was observed solely in thefast component of recovery, which was ∼2-fold fasterthan a single-exponential fit. Biphasic behaviour in thepresence of phosphate can also be seen in the data ofIwamoto (1998), Regnier & Homsher (1998) and Tesiet al. (2000). The rate constant of the fast componentis similar to other Pi-sensitive measures of cross-bridgeattachment into force-generating states (K. Burton et al.in preparation), including the rate constant of force trans-ients in response to a Pi jump at low Pi concentration(Regnier & Homsher, 1998), and a slow phase of tensiondecline following step stretches (Ranatunga et al. 2002).Force development following step changes in pressure(Fortune et al. 1994) and temperature (Ranatunga, 1999)shares many features of those reported here, includingbeing biphasic with phosphate increasing the rate of thefast component while having little effect on the rate ofthe slow component. Since phosphate is thought to affectattachment and force generation, our results are consistentwith a Huxley-type model (Huxley, 1957) in which the rateof the fast component is dominated by f (K. Burton et al.in preparation).

ITP and Ni2+

Both ITP and Ni2+ greatly reduced isometric forceand slowed acto-S1 ATPase activity, force recoveryand unloaded shortening velocity. They were thereforegenerally poor substrates for contraction, and in additioncaused the striations to become disordered. ITP is oneof a class of ATP analogues which include ATPγ S andGTP for which the hydrolysis rate in solution is more than10 times slower than for ATP (Table 4). A second featureis that the equilibrium constant of the hydrolysis step insolution is only 0.5, over 3-fold less than for Mg2+, whichpresumably is also true of fibres. The hydrolysis step is alsostrongly affected by Ni·ATP, with the forward rate slowed



by a factor of ∼10 and the equilibrium constant reduced byabout two orders of magnitude (Table 4). The member ofthe class that has received the most detailed investigationis ATPγ S, and the major effect of it on a muscle fibreis to cause relaxation (Kraft et al. 1992). GTP and ITPdo yield some tension, but its low value is probably dueto the slow hydrolysis step (step 2 in scheme 1, k+hyd inTable 4) which results in a large fraction of the heads beingheld up in the myosin·NTP state which (1) is not thoughtto generate force, and (2) does not support completeactivation owing to the requirement for strongly boundheads in addition to Ca2+. We suggest that such incompleteactivation may in part be responsible for the observedstriation disorder because force is extremely sensitive toactivation, and small variations among sarcomeres inseries would lead to the stronger sarcomeres contractingagainst the weaker. The slow rate of the hydrolysis stepreadily accounts for the slow observed rates of forcerecovery, although they may be further slowed by anyeffects on the Pi release step, and additionally by sarcomereinhomogeneity. Peyser et al. (1996) and Amitani et al.(2001) reported that Ni2+ greatly reduces acto-S1 ATPaseactivity.

The reduction in unloaded shortening velocity causedby Ni2+ has also been observed for actin filamentmovement in vitro by Amitani et al. (2001). Thedissociation of Ni·ADP occurs at a rate of more than100 s−1 which should allow a velocity of filament sliding of> 0.6 µm s−1 (Table 4). Since ADP dissociation occurs atcomparable rates in the presence of Mg2+ or Ni2+, Ni·ADPrelease does not appear to limit shortening velocity. Asimilar conclusion can be drawn from a comparisonof shortening velocity and acto-S1 dissociation by UDP(Seow et al. 2001). Siemankowski et al. (1985) havemade a convincing case for shortening velocity in cardiacmuscle being limited by the rate of ADP dissociation,but the link is much less convincing for rabbit psoasmuscle with Mg·ATP, a point made more decisively byour Ni·ATP results. As with CTP discussed above, analternative possibility is that the low rate of Ni·ATP bindingand cross-bridge dissociation limits shortening velocity(Table 4).

Conclusions

We interpret our data on the basis of the scheme presentedabove (scheme 1), which as discussed in the precedingpaper (Sleep et al. 2005) is distinct from previous models inthree ways: (1) the hydrolysis step is at least as important asthe Pi release step in limiting the rate of force development,(2) the fast force-generating, Huxley-Simmons transitionis explicitly located between two slow biochemical steps(ATP hydrolysis and Pi release), and (3) solution valuesare used for the key biochemical rate constants (binding,hydrolysis and Pi release). On this basis the rate of force

recovery is altered by changes in (1) the NTP hydrolysisstep (step 2 in the scheme) in the presence of CTP, ITP andNi2+, and (2) the Pi release step (step 4) in the presenceof phosphate itself, and probably also in the presence ofMn2+, while unloaded shortening is slowed by a reductionin the rate of cross-bridge dissociation (step 1) in thepresence of CTP and Ni2+.

References

Altringham JD & Johnston IA (1985). Effects of phosphate onthe contractile properties of fast and slow muscle fibres froman antarctic fish. J Physiol 368, 491–500.

Amitani I, Sakamoto T & Ando T (2001). Link between theenzymatic kinetics and mechanical behavior in anactomyosin motor. Biophys J 80, 379–397.

Bagshaw CR (1977). On the location of the divalent metalbinding sites and the light chain subunits of vertebratemyosin. Biochemistry 16, 59–67.

Barany M (1967). ATPase activity of myosin correlated withspeed of muscle shortening. J Gen Physiol 50,197–216.

Bowater R & Sleep J (1988). Demembranated muscle fiberscatalyze a more rapid exchange between phosphate andadenosine triphosphate than actomyosin subfragment 1.Biochemistry 27, 5314–5323.

Brenner B (1983). Technique for stabilizing the striationpattern in maximally calcium-activated skinned rabbit psoasfibers. Biophys J 41, 99–102.

Brenner B & Eisenberg E (1986). Rate of force generation inmuscle: Correlation with actomyosin ATPase activity insolution. Proc Natl Acad Sci U S A 83, 3542–3546.

Burton K (1989). The magnitude of the force rise after rapidshortening and restretch in fibres isolated from rabbit psoasmuscle. J Physiol 418, 66P.

Burton K (1992). Stiffness and cross-bridge strain followinglarge step stretches at the end of rapid shortening in rabbitpsoas skinned single fibers. Biophys J 61, A267.

Burton K & Sleep J (1987). Effect of different metal-nucleotidecomplexes on actomyosin kinetics in fibers and in solution.Biophys J 51, 6a.

Burton K, Zagotta WN & Baskin RJ (1989). Sarcomere lengthbehaviour along single frog muscle fibres at different lengthsduring isometric tetani. J Muscle Res Cell Motil 10, 67–84.

Chase PB & Kushmerick MJ (1988). Effects of pH oncontraction of rabbit fast and slow skeletal muscle fibers.Biophys J 53, 935–946.

Chase PB, Martyn DA & Hannon JD (1994). Isometric forceredevelopment of skinned muscle fibers from rabbitactivated with and without Ca2+. Biophys J 67, 1994–2001.

Claflin DR, Morgan DL & Julian FJ (1989). Effects of passivetension on unloaded shortening speed of frog single musclefibers. Biophys J 56, 967–977.

Edman KAP (1979). The velocity of unloaded shortening andits relation to sarcomere length and isometric force invertebrate muscle fibres. J Physiol 291, 143–156.

Ekelund MC & Edman KAP (1982). Shortening induceddeactivation of skinned fibres of frog and mouse striatedmuscle. Acta Physiol Scand 116, 189–199.



Fabiato A (1988). Computer programs for calculating totalfrom specified free or free from specified total ionicconcentrations in aqueous solutions containing multiplemetals and ligands. Methods Enzymol 157, 378–417.

Fenster SD & Ford LE (1985). SALT: a threaded interpretivelanguage interfaced to BASIC for laboratory applications.Byte 10, 147–164.

Ford LE, Huxley AF & Simmons RM (1977). Tension responsesto sudden length change in stimulated frog muscle fibresnear slack length. J Physiol 269, 441–515.

Fortune NS, Geeves MA & Ranatunga KW (1994). Contractileactivation and force generation in skinned rabbit musclefibres: effects of hydrostatic pressure. J Physiol 474,283–290.

Godt RE & Lindley BD (1982). Influence of temperature uponcontractile activation and isometric force production inmechanically skinned muscle fibers of the frog. J Gen Physiol80, 279–297.

Hibberd MG, Dantzig JA, Trentham DR & Goldman YE (1985).Phosphate release and force generation in skeletal musclesfibers. Science 228, 1317–1319.

Hill AV (1953). The mechanics of active muscle. Proc R SocLond B Biol Sci 141, 104–117.

Hoar PE & Kerrick WGL (1988). Mn2+ activates skinnedsmooth muscle cells in the absence of myosin light chainphosphorylation. Pflugers Arch 412, 225–230.

Huxley AF (1957). Muscle structure and theories ofcontraction. Prog Biochem Biophys 7, 255–318.

Iwamoto H (1998). Thin filament cooperativity as a majordeterminant of shortening velocity in skeletal muscle fibers.Biophys J 74, 1452–1464.

Julian FJ & Morgan DL (1979). Intersarcomere dynamicsduring fixed-end tetanic contractions of frog muscle fibres.J Physiol 293, 365–378.

Julian FJ, Rome LC, Stephenson DG & Striz S (1986). Themaximum speed of shortening in living and skinned frogmuscle fibres. J Physiol 370, 181–199.

Kodama T, Fukui K & Kometani K (1986). The initialphosphate burst in ATP hydrolysis by myosin andsubfragment-1 as studied by a modified malachite greenmethod for determination of inorganic phosphate. J Biochem(Tokyo) 99, 1465–1472.

Kraft T, Chalovich JM, Yu LC & Brenner B (1995). Parallelinhibition of active force and relaxed fibre stiffness bycaldesmon fragments at physiological ionic strength andtemperature conditions: Additional evidence that weakcross-bridge binding to actin is an essential intermediate forforce generation. Biophys J 68, 2404–2418.

Kraft T, Yu LC, Kuhn HJ & Brenner B (1992). Effect of Ca2+ onweak cross-bridge interaction with actin in the presence ofadenosine 5

′-[γ -thio]triphosphate. Proc Natl Acad Sci U S A

89, 11362–11366.Ma Y-Z & Taylor EW (1994). Kinetic mechanism of myofibril

ATPase. Biophys J 66, 1542–1553.Margossian SS & Lowey S (1982). Preparation of myosin and its

subfragments from rabbit skeletal muscle. Methods Enzymol85, 55–71.

Millar NC & Homsher E (1990). The effect of phosphate andcalcium on force generation in glycerinated rabbit skeletalmuscle fibers. J Biol Chem 265, 20234–20240.

Millar NC & Homsher E (1992). Kinetics of force generationand phosphate release in skinned rabbit soleus muscle fibers.Am J Physiol 262, C1239–C1245.

Mornet D, Bertrand R, Pantel P, Audemard E & Kassab R(1981). Structure of the actin–myosin interface. Nature 292,301–306.

Needham DM (1971). Machina Carnis. The Biochemistry ofMuscular Contraction in its Historical Development .Cambridge University Press, UK.

Pardee JD & Spudich JA (1982). Purification of muscle actin.Methods Enzymol 85, 164–181.

Pate E, Franks-Skiba K, White HD & Cooke R (1993). The useof differing nucleotides to investigate cross-bridge kinetics.J Biol Chem 268, 10046–10053.

Peyser YM, Ben-Hur M, Werber MM & Muhlrad A (1996).Effect of divalent cations on the formation and stability ofmyosin subfragment 1-ADP-phosphate analog complexes.Biochemistry 35, 4409–4416.

Provencher SW (1976). A Fourier method for the analysis ofexponential decay curves. Biophys J 16,27–41.

Ranatunga KW (1999). Effects of inorganic phosphate onendothermic force generation in muscle. Proc R Soc Lond BBiol Sci 266, 1381–1385.

Ranatunga KW, Coupland ME & Mutungi G (2002). Anasymmetry in the phosphate dependence of tensiontransients induced by length perturbation in mammalian(rabbit psoas) muscle fibres. J Physiol 542,899–910.

Regnier M, Bobkova A, Kim B, Reisler E & Homsher E (1995).Effects of replacement of Mg·ATP with Mn·ATP onacto-HMM ATPase, actin filament sliding velocity andunloaded shortening velocity of rabbit skeletal muscle.Biophys J 68, A70.

Regnier M & Homsher E (1998). The effect of ATP analogs onposthydrolytic and force development steps in skinnedskeletal muscle fibers. Biophys J 74,3059–3071.

Regnier M, Lee DM & Homsher E (1998). ATP analogs andmuscle contraction: Mechanics and kinetics of nucleosidetriphosphate binding and hydrolysis. Biophys J 74,3044–3058.

Robinson A, Jiang W, Zhang XZ & White HD (1993).Measurement of the rate and equilibrium constants of thebinding of nucleoside diphosphate products of ADP, CDP,aza-ADP, and GDP to rabbit skeletal and bovine cardiacactomyosin-S1. Biophys J 64, A361.

Rosenfeld SS & Taylor EW (1984). The ATPase mechanism ofskeletal and smooth muscle acto-subfragment 1. J Biol Chem259, 11908–11919.

Seow CY, White HD & Ford LE (2001). Effects of substitutinguridine triphosphate for ATP on the crossbridge cycle ofrabbit muscle. J Physiol 537, 907–921.

Siemankowski RF & White HD (1984). Kinetics of theinteraction between actin, ADP, and cardiac myosin-S1.J Biol Chem 259, 5045–5053.

Siemankowski RF, Wiseman MO & White HD (1985). ADPdissociation from actomyosin subfragment 1 is sufficientlyslow to limit the unloaded shortening velocity in vertebratemuscle. Proc Natl Acad Sci U S A 82, 658–662.



Sillen LG & Martell AE (1970). Stability Constants of Metal-IonComplexes. Suppl. no. 1. Special Publication no. 25. TheChemical Society, Burlington House, London.

Sleep J (1990). Temperature control and exchange of thebathing solution for skinned muscle fibres. J Physiol 423, 7P.

Sleep J, Irving M & Burton K (2005). The ATP hydrolysis andphosphate release steps control the time course of forcedevelopment in rabbit skeletal muscle. J Physiol 563,671–687.

Smith RM & Martell RA (1989). Critical Stability Constants.Inorganic Complexes, vol. 6. Plenum Press, New York.

Stephenson DG & Thieleczek R (1986). Activation of thecontractile apparatus of skinned fibres of frog by the divalentcations barium, cadmium and nickel. J Physiol 380, 75–92.

Swartz DR & Moss RL (1992). Influence of a strong-bindingmyosin analogue on calcium-sensitive mechanical propertiesof skinned skeletal muscle fibers. J Biol Chem 267,20497–20506.

Tesi C, Colomo F, Nencini S, Piroddi N & Pogessi C (2000).The effect of inorganic phosphate on force generation insingle myofibrils from rabbit skeletal muscle. Biophys J 78,3081–3092.

Vandenboom R, Hannon JD & Sieck GC (2002). Isotonic forcemodulates force redevelopment rate of intact frog musclefibres: evidence for cross-bridge induced thin filamentactivation. J Physiol 543, 555–556.

Wahr PA, Cantor HC & Metzger JM (1997). Nucleotide-dependent contractile properties of Ca2+-activated fast andslow skeletal muscle fibers. Biophys J 72, 822–834.

Waller GS, Ouyang G, Swafford J, Vibert P & Lowey S (1995).A minimal motor domain from chicken skeletal musclemyosin. J Biol Chem 270, 15348–15352.

Weeds AG & Taylor RS (1975). Separation of subfragment-1isoenzymes from rabbit skeletal muscle myosin. Nature 257,54–56.

White HD, Belknap B & Jiang W (1993). Kinetics of bindingand hydrolysis of a series of nucleoside triphosphates byactomyosin-S1. J Biol Chem 268, 10039.

White HD, Belknap B & Webb M (1997). Kinetics of nucleosidetriphosphate cleavage and phosphate release steps byassociated rabbit skeletal actomyosin, measured using anovel fluorescent probe for phosphate. Biochemistry 36,11828–11836.

Wirth P & Ford LE (1986). Five laboratory interfacingpackages. Byte 11, 303–312.

Yu LC & Brenner B (1989). Structures of actomyosincrossbridges in relaxed and rigor muscle fibers. Biophys J 55,441–453.

Acknowledgements

We wish to thank Mr Kevin Eason, Mr Peter Stoneham, andMr Barry McCarthy for expert technical assistance. K. Burtonis grateful to the European Molecular Biology Organization fora short-term fellowship to visit the laboratory of Dr BernhardBrenner and to Dr Brenner for helpful suggestions. This work wassupported by the Medical Research Council (UK) through theMRC Muscle and Cell Motility Unit. K.B. was also supported bypersonal fellowships from the Muscular Dystrophy Association(USA) and National Institutes of Health (NIH, USA) during theperiod of this study. H.W. was supported by NIH (NIBIB) grantEB00209.

Supplementary material

The online version of this paper can be accessed at:DOI: 10.1113/jphysiol.2004.078907http://jp.physoc.org/cgi/content/full/jphysiol.2004.078907/DC1and contains supplementary material entitled:Muscle fibre preservation during storage and preparation; T-clipfabrication and attachment; Force recovery in PM and sarcomerelength control; Slack test protocols. Figure S1: Length controlduring force recovery; Figure S2: Slack test protocols.This material can also be found at:http://www.blackwellpublishing.com/products/journals/suppmat/tjp/tjp711/tjp711sm.htm


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