Oxygen Exchange between Pi in the Medium and ... - Semantic Scholar

Val. 261, No. 33, Issue of November 25, pp. 15557-15564,1986 Printed in U.S.A.

T H EJ O U R N A L OF BIOLOGICAL CHEMISTRY 0 1986 by The American Society of Biological Chemists, [ne.

Oxygen Exchange between Pi in the Medium and Water during ATP Hydrolysis Mediated bySkinned Fibers from Rabbit Skeletal Muscle EVIDENCEFOR

Pi BINDING TO A FORCE-GENERATINGSTATE* (Received for publication, April 29, 1986)

Martin R. Webb$, Mark G. HibberdQY,Yale E. Goldman$,and David R. Trenthamt From the $Division of Physical Biochemistry, National Institutefor Medical Research, Mill Hill, London, NW7 lAA, United Kingdom and the $Department of Physiology, School of Medicine G4, University of Pennsylvania, Philadelphia, Pennsylvania19104

Oxygen exchange between (1804)Pi in the medium and water accompanies ATP hydrolysis catalyzed by the calcium-regulated MgATPase of vertebrate skeletal muscle. Exchange was observed in chemically skinned fibers from rabbit psoas muscle held isometrically and activated by 30 p~ free Ca2+.The rate of exchange was approximately proportional to Pi concentration (up to 10 mM) and was characterized by an apparent second order rate constant 2475 M” s” (pH 7.1, ionic strength 0.2 M, 22 “C). Much less exchange occurred in the absence ofCa2+ or when ATP was replaced by ADP. It has been inferred from mechanical experiments that Pi can bind to a force-generating ADP-bound state of actomyosin with resultant suppression of force (Hibberd,M. G., Dantzig, J . A., Trentham, D. R., and Goldman, Y. E. (1985) Science 228, 1317-1319). The oxygen exchangeresults support this inference by providing direct evidence that Pi in the medium bindsat the ATPase catalytic site in activated isometric fibers. The inter-relationship of these two effects involving Pi on mechanochemical coupling in muscle is discussed.

dissociation of M.ATP from actin (Step 2). ATP hydrolysis and actin binding (Steps 2,3,3a, and 4)readily are reversible. Inclusion of two bound ADP states was proposed by Sleep and Hutton (1980), who inferred that Pj can bind to AM’ . ADP during ATP hydrolysis by actomyosin, and that this state appears tobe different from theequilibrium state, AM. ADP, formed when ADP is added to actomyosin. It is not clear whether AM.ADP is on the ATPase pathway (Sleep and Hutton, 1980). It is probable that the rate-determining step for theATPase in Ca2+-activated muscle fibers held isometrically is associated with Steps5 and/or 6 (Ferenczi et at., 1984; Goldman et at., 1984b). “Intermediate” exchange, arising from oxygen exchange between Pi formed during ATP hydrolysis and the solvent water, has been demonstrated with Ca2+-activated skinned fibers (Hibberd et al., 1985b). This is evidence that ATP hydrolysis Steps 3 and/or 3a arereadily reversibleduring fiber ATPase activity as in isolated actomyosin (Rosenfeld and Taylor, 1984; Biosca et aL, 1985). Relaxed fibers show much more extensive intermediateexchange, comparable to thatof isolated myosin. Whether the binding of Pi (Step 5) is reversible may be tested by studying oxygen exchange between Pi in the medium and water during ATPase activity. If oxygen exchange occurs, Oxygen isotope exchange measurements are an established it implies protein-bound ATP formation through reversal of method to probe elementary steps of the myosin and acto- either Step 3a or Steps 4 and 3. Scheme 2 shows how this myosin ATPase mechanisms (Webb and Trentham, 1983, and could occur via reversal of Steps 5,4, and3, with filled circles references therein). In the present experiments we studied the representing ”0. Exchange depends on the water molecule MgATPase mechanism of Ca2+-activated skinnedfibers pre- formed during the condensation of ADP and Pi in Step 3 pared from vertebrate skeletal muscle through an investiga- being able t o escape from the ATPase catalytic site. Multiple tion of oxygen exchange between Pi in themedium and water reversals of Step 3, together with rotationof Pi in the catalytic during ATPhydrolysis. site, allow more than oneof the labeled phosphate oxygens to A mechanism for A T P hydrolysis in a muscle fiber during undergo exchange. contraction sufficient for our purposeis described in Scheme The reaction conditions used here resulted in low levels of 1, where A and M represent actin and myosin. This scheme oxygen exchange so that we may neglect multiple oxygen is based onsolutionstudies of actomyosin (Taylor, 1979; Eisenberg and Greene, 1980; Sleep and Hutton,1980; Hibberd exchangearisingdue to an exchanged Pi molecule in the and Trentham, 1986). K;(=k+Jk-J, k+i, and k-, are equilib- solvent rebinding toAM’ .ADP. This is indicated in Scheme rium and forward andreverse rate constants, respectively, of 2 by irreversible release of exchanged Pi. The presence of Pi in the medium accelerates the rate of 1) is followed by rapid theithstep.ATPbinding(Step ATP-induced activation and relaxationof vertebrate muscle * This work was supported by Grant HL 15835to the Pennsylvania fibers from rigor in the presence andabsence of Ca2+, respecMuscle Institute from the National Institutes of Health, by the tively (Hibberd et al., 1985a). Pi also attenuates the tension MuscularDystrophyAssociation of America, and by the Medical developed by anactivated isometric muscle (Hibberdand Research Council, United Kingdom. Parts of this work were presented Trentham, 1986, and references therein). These observations at the 1985 Annual Meeting of the Biophysical Society (Webbet al., can be explainedif Pi release during the ATP hydrolysis cycle 1985). The costs of publication of this article were defrayed in part is reversible and coupled to formation of a dominant forceby the payment of page charges. This article must therefore be hereby marked “nduertisement” in accordance with 18 U.S.C. Section 1734 generating cross-bridge state(Hibberd et al., 1985a). The oxygen exchange experiments described here enable the exsolely to indicate this fact. ll British-AmericanHeart Fellow. tent and a lower limit on the rate constant of Pi binding to

15557

15558

Medium Pi-Water Oxygen Exchange within Muscle Fibers

SCHEME 1

cAM.ATP If

cAM.ADP.P~+AM'.ADP 3a

1

AM + ATP

+

H,O

5

+

pi

B

LAM + ADP

A M.ATP + H,O

4

3

M.(l*O,)

2 M.ADI? Pi

5

t A

t

ATP 7 M . A D P . @-P-@ &AM.ADP. @-P-O=AM.'ADP

+

( '80,)Pi

0

H2.

M.ADP.

@ - L o&AM.ADP.

.-Lo

SCHEME2

O

A

M.ADP. @-b-O&

, L

0 AM.ADP. @-b-O--"AM.'ADP

c

+ (180,)Pi

I I

t Further Exchange

with ATP present, the fiber was removed from the medium before 20% ATP was hydrolyzed. For eachincubation a control solution was maintained on the experimental apparatus in the absence of fibers for an equal time to provide a measure of spontaneous ATP hydrolysis EXPERIMENTALPROCEDURES and oxygen exchange. The extent of fiber-catalyzed ATP hydrolysis Skinned fibers from rabbit psoasmuscle were prepared as described was determined by high performance liquid chromatography as deby Goldman et al. (1984a).Fibers were mounted isometrically in small scribed previously (Hibberd et al., 1985b). ATPase activities were troughscontaining 30-45 pl of incubation solution covered with calculated assuming that the myosin head concentration was154 silicone oil to prevent evaporation (Hibberd et aL, 1985b).Fibers were pmol/liter of fiber volume (Ferenczi et al., 1984). In some activating relaxed in a solution of 15 mM ATP, 15 mMMgCI,, 10 mM EGTA,' incubations the fibers broke after 5-30 min of contraction. Another 10 mM reduced glutathione, 100 mM TES, and 1-10 mM ("0,)P; (98% fiber was then incubated in the same solution to catalyze an accuenriched, prepared by the method of Hackney et al., 1980). The mulated 3-15% ATP hydrolysis. The sum of [(fiber volume) X (inactivating solution was the same except that theEGTA was replaced cubation time)] for each of the fibers in an experiment was used for by CaEGTA resulting in approximately 30 p M free Caz+.Rigor solu- calculation of kat of the ATPase. tion, + or - Ca", was the same as theactivating or relaxing solution, For each incubation the number of solvent oxygens exchanged into respectively, except that ATPwas not present, MgCL was reduced to the Pi was measured using a mass spectrometer (Hibberd et al., 2 mM, and ADP, when present, was added to 0.5 mM. Oligomycin and 1985b). The steps in this determination are outlined for one experiquercetin, when present, were at 1 pg/ml and 0.25 mM, respectively. ment in Table 1. Pi was converted to triethyl phosphate for the Each solution had an ionic strength of 200 mM, 1 mM free M p ,and analysis and theintensities of mass spectral peaks were integrated in was adjusted to pH 7.1 at 20-22 "C with KOH. the region m/e 153-163. For the unlabeled molecule, this range After fiber mounting, a short active contraction was elicited in a contains a fragment of major intensity at m/e 155, the molecular ion solution not containing Pi, fiber dimensions were measured (Goldman minus C2H3,and a minor fragment at m/e 153, the molecular ion and Simmons, 1984), and then the fiber was transferred to a stirred minus C2H6,with intensity approximately 5% of the major fragment. incubation solution containing (*sO,)Pi for 1-20 h. In experiments For the molecules containing "0 there are equivalent isotopically enriched fragments in identical ratios. The exact ratio of the major The abbreviations used are: EGTA, [ethylenebis(oxyethyl- to minor fragments was determined by obtaining the ratio of intenenenitri1o)Jtetraacetic acid; TES, N-tris[hydroxymeth~l]methyl- sities at m/e 153:155 for unlabeled triethyl phosphate. This ratio then applies to each isotopically enriched species. Three mass spectral 2-aminoethanesulfonic acid.

be measured and compared with the effects of Pi on transient and steady-statetension changes.

~~

Medium PiWater Oxygen Exchange within Muscle Fibers

repeatedly cycled through the four troughs until approximately 1 h of contraction time was accumulated in each of the two incubation troughs or it broke ( B ) .When this happened, the fiber was quickly removed from the sample trough, and additional fibers were cycled through the same solution troughs. Paired troughs were filled with 10 mM Pi and zero Pi activating media and left for the same time without fibers to serve as controls. The two sample troughs and paired blanks were analyzed for ADP by high performance liquid chromatography. There was always some decrease of isometric tension with time, as may be seen in Fig. 1. The following procedure was adopted to evaluate whether the relative ATPase rates and tensions with or without the addition of 10 mM Pi were different. First, theratios of ATPase rates for individual experiments were calculated. These ratios showedless scatter than the absolute values of the ATPase rates, presumably because fiber to fiber variation was avoided. The tension ratios were treated similarly. The complete data set was then subjected to the Student's paired-sample t test to obtain p , the probability that the relative ATPase and tension ratios were the same (Parker, 1973).

TABLE I Analysis of mass spectral data The data arefor the first experiment listed in Table 11. Relative composition of fragments at mle

153 155 157 159 161 163 ~~~

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~

0.9 17.3 0.9 1.3 10.6 69.0 A. Injection 1 0.8 17.2 0.8 1.3 10.6 69.3 Injection 2 0.9 17.1 0.9 1.2 10.6 69.3 Injection 3 0.9 17.2 0.9 1.2 10.6 69.2 B. Average 7.5 72.7 0 18.0 0.9 0.9 C. Correction for fragment at 153 77.8 2.6 18.0 0.7 0.9 D. Correction for 98.32% "0 enrichment 0 0.7 0.7 77.8 2.6 E. Subtraction of unlabeled phosphate" 0 0.9 0.8 3.2 95.1 F. Normalized Dercentaee "Allthe intensity at m/e 155 is subtracted together with the contribution at m/e 157 due to natural abundance of isotopes (see "Experimental Procedures").

RESULTS

ATP was hydrolyzed by fibers in solutions containing 10

measurements (line A) were averaged (line B), and the data were mM (lSO4)Pi,and the resulting Pi was analyzed for amount then corrected for the minor fragment (line C). and distributionof "0 using a mass spectrometer. The results, The data were then corrected for the lack of isotopic purity (line after correction for isotopic enrichment and removal of conD): the Pi starting material was approximately 98% enriched in '"0. tributions due to unlabeled Pi as outlined under "ExperimenThe exact enrichment for each incubation solution was found from the mass spectral data for the control solution in the absence of tal Procedures," are given in Table 11. The data show the presence of Pi containing 3, 2 , and 1 solvent oxygens per fibers, which reflects the lack of isotopic purityin thestarting material and any spontaneous loss of isotope due to exchange in molecule, whereas thecontrol solutions, incubated in the solution. The enrichment for the control Pi was calculated from the absence of fibers, show little exchange. The fibers have caused ratio of intensities at 161:163 (3:4 l80per Pi), assuming a random the ("04)Pito undergo oxygen exchange with water. distribution of "0in the four positions of Pi. The 161-163 peaks were Several general features of this phenomenon are apparent. chosen because their ratio is sensitive to the exact enrichment and they are unaffected by any Pi impurity arising from spontaneous ATP First, for all conditions studied, less than 10% of the Pi has hydrolysis. line D, therefore, represents the distribution if the enrich- undergone exchange with loss of 1, 2 , or 3 oxygens. Because no exchange information is obtained from the unlabeled Pi ment had been 100% rather than themeasured value of 98.32%. In the experiments unlabeled Pi (m/e 155) arises from several (loss of all 4 oxygens), the total amount of exchange may be sources. In most incubations the main contribution is due to fiber- higher than that shown in Table 11. The average rate of mediated ATP hydrolysis of unlabeled ATP. There may be some exchange (k') in Table I1 is 144 ( f l l S.E.) I"'s-', and the medium Pi that hasundergone total oxygen exchange as well as small amounts of unlabeled Pi impurity in solutions or glassware. Because average kcatfor the ATPase is 3.5 ( f O . l S.E.) s-'. If the distributions in Table I1 are averaged after normaliit is not possible to calculate the amount of unlabeled Pi formed by total oxygen exchange, all the unlabeled Pi was disregarded. The zation to loo%,their ratio is 63.9 (k2.6 S.E.):21.7 (f2.0):14.4 effect on our results of doing this is likely to be small because the (k1.2) for 1 2 3 solvent oxygens incorporated into Pi. We sum of P, molecules exchanging 2 or 3 oxygen atoms was half the return to theimplications of this distribution under "Discusnumber of those exchanging 1 oxygen atom, so only a small fraction sion." Scatter in the data arises chiefly from two factors. First, would be expected to exchange all 4 oxygen atoms. The percentage intensity at m/e 155 was therefore subtracted from the distribution the corrections to the data, as outlined in Table I, are large relative to the extentsof exchange (compare lines B and D in in line D, together with the contribution a t m/e 157 due to natural abundance of heavy isotope in the unlabeled Pi. Line E represents Table I), so that the distributions of exchanged oxygens are the Pi derived from the original ('"04)Pi, now containing 3, 2, 1, and not precise. Second, there is variability in performance of 0 solvent oxygens, which is then normalized to 100% (line F). different fibers that may be due in part to damage during The ATPase rate of fibers in the presence of 10 mM Pi was preparation or storage. compared to that in the absence of Pi using a different protocol. A The results of control experiments (Table 111, lines A and fiber was first activated briefly (10-15 s) in the absence of Pi and relaxed, and thenits dimensions were measured. It was then activated B) show that there is little exchange in incubations in which for alternating periods in troughs containing activating solution, as ADP replaced ATP or nucleotide was absent. above, with or without the addition of 10 mM unlabeled Pi. The ionic Several further tests are shown in Table I11 to determine strength, pH, and temperature were the same in the two solutions. whether any of the observed exchange was due to other The sequence of solution exchanges, illustrated in Fig. 1, were 1) zero Pi wash for 30 s ( W ) ,2) zero Pi sample incubation for 10 min ( S ) , 3) ATPases, in particular theea2+-pump ATPase of sarco10 mM Pi wash ( W ) for 30 s, and 4) 10 mM Pi sample incubation ( S ) plasmic reticulum and the mitochondrial ATPase, both of for 10 min. The 30-s wash periods between sample troughs were used which are known to catalyze medium Pi-water oxygen exto minimize contamination between sample troughs. The fiber was change in the presence of ADP (Hill and Boyer, 1967; Mc-

FIG. 1. Effect of 10 mM Pi on steady-state tension. After two washes in preactivating solutions(Pre), thefiber anwas transferred to activating solution for a brief wash ( W ) ,followed by incubation in an activated solution ( S ) while held isometrically. The fiber was then transferred via a wash solution between activating solutions with or without 10 mM Pi.

kN,d

-Pi

-Pi Stir Act

-

ns

us

2oo

f0 rnin

us UB

+IOmM Pi

Medium Pi- Water Oxygen Exchange within Muscle Fibers

15560

TABLE I1

TABLEIV Pi-water oxygen exchange by Ca2+-actiuatedfibers a t low concentrations of medium Pi

Pi-water oxygen exchange by Ca2+-activatedfibers in the presence of 10 mM (l8o4)P; Number of solkcatof ATPase s-l

vent Oxygens exchanged 3 2 1

distribution in

pi 3.3 0.9 0.8 3.5 1.0 4.3 3.10.6 0.9 0.10.6 3.46.4 3.5 0.5 0.7 0.4 3.2 0.2 3.6 0.6

0.7 0.3 0.4

Exchange in control

3.214.9 2.6 1.2 1.5 1.3 2.710.2

Myosin heads X time”

%

nmol .s

0.3 0.3 0.2

8.8 10.3

0.1 0.2 0.1

9.7 5.9

Exchange rate constant, k t b

Mr’ s” 108 159 192 140 121 131 158

(180r)P,

mM

3 3 3 3.2 3 1

1 1

katof ATPase

% exchange +fiber -fiber

S-1

3.3 5.9 4.4 0.3 5.8 4.2 7.8 3.3

4.3 122 0.6 1.5 0.5 4.4 0.2 3.4 3.4 3.3 0.4 6.2337 0.6 9.7 0.6

Myosin heads x time

Exchange rate constant, k’

nmol. s

hr’ s-1

10.7 1.7 11.5 9.7 29.9

259 164 441 379 136

1981). Table 111, line C shows that these inhibitorshave little effect on the ratesof oxygen exchange observed in Table 11. In contrast to the relatively fast exchange during ATP hydrolysis in the presence of Ca2+, there only is slow exchange in relaxed fibers in the absenceof Ca2+(cf. Tables I1 and 111, line D). A further control experimentwas the exclusion of nucleotide from the incubation medium also in the absenceof Ca2+. The actomyosin system is unlikely t o catalyze exchange in this case, because the mechanism for exchange presumes the synthesis of protein-bound ATP (Scheme 2 and Webb and Trentham, 1983). However, sarcoplasmicreticulum Ca2+pump ATPasecatalyzes Pi-water oxygen exchange by a mechanism involving the formation of an aspartyl phosphate intermediate (Dahms et al., 1973; Degani and Boyer, 1973). In the absence of both ATP and Ca2+, the rate of exchange is at. least 4-fold faster than in their presence (McIntoshBoyer, and TABLE I11 1983). It follows from the average exchange rate of 65 M” s-l observed in this test (Table 111, line E) that 16 M” s” is an Pi-water oxwen exchange controls upper limit for the contribution of the Ca*+-pump ATPase Experimental Ltof 7Z exchange Myosin Exchange rate toward k‘(=144 M” s-’) measured in Table 11. The fact that ~ heads b ~ X~ btime ~ constant, ~ k’ conditions” ATPase + ~- ~ the test incubation (Table111, line B) with no nucleotide but S” nmol .s M” s-l +Ca” has essentially no exchange is consistent with exchange 0.4 4 0.2 21.7 A. Rigor (+Ca2+,0.5 in the absence of nucleotide and Ca2+being due to the Ca2+0.2 0.3 14.9 0 mM ADP) pump ATPase (McIntosh andBoyer, 1983). Exchange promotedby the Ca2+-pump ATPase in the pres1 B. Rigor (+Ca2+,zero 0.2 0.1 34.6 ence of ATP but absenceof Ca2+is 15%of that when neither ADP) 1.7 0.1 39.1 18 0.4 0.1 130.7 1 ATP nor Ca’+ is present (McIntosh and Boyer, 1983). So it 52.70 0.1 0 is possible that most or all the exchange observed in Table 1 11, line D is due to Ca2+-pump ATPase, since its rate equals 184 8.8 3.7 3.7 0.1 C. Active (plus oligoM” s” recorded in Table 111, line E. We 15% of the 65 11.8 168 0.2 4.6 2.6 mycin + querciconclude that the rate of Pi-water oxygen exchange due to the 89 2.79.1 2.0 0.2 tin) myofibrillar ATPase of relaxed fibers is very low compared to D. Relaxed0.3 4.9 0.07 170.9 12 that observed with Ca’+-activated fibers. 0.06 7.2 0.2 9 346.8 Overall, the results from the control experiments listed in I11 strongly suggest that theobserved exchangein Table Table 39.3 7.4 0.1 84 E. Rigor (-Ca2+, zero I1 is almost entirely mediated by the Ca”-regulated ATPase 47.0 66 ADP) 6.9 0 116.0 58 15.0 0 of myofibrillar proteins. 52.7 51 6.1 0.1 Whether second order binding of Pi or a subsequent first oxygen exchange rate might be ” T h e concentration of Pi is 10 mM and of Ca2+ is 30 p M for order transition limits the deduced by determining whether the rate is saturated at 10 “+Ca2+,” and M for “-Ca2+.” Other components of the solutions are described under “Experimental Procedures.” mM Pi. Therefore, the rates of exchange in the presence of Ca” were studied at lower concentrations of (1804)Pi (Table IV). The rates show considerable scatter. In addition to variIntosh and Boyer,1983). Oligomycin inhibits the Pi-water oxygen exchange mediated by the submitochondrial particle able performance o f the individual fibers as described above, ATPase (Cross and Boyer, 1975). Quercetin inhibits several with low concentrations of Pi there areonly small amountsof partial reactions and the overall ATPase activities of sarco- Pi that have undergone exchange, leading to relatively large plasmic reticulum membranes and purified Ca2+-pump ATP- errors in the mass spectrometer data. The calculated second ase. In particular, ATP:Pi phosphate exchange and phospho- order rate constants of exchange increase 2-fold over a 10rylation of the enzyme by Pi are inhibited, suggesting that fold decrease in Pi concentration. (The increase would have quercetin would inhibitPi-water oxygen exchange during been IO-fold if 1 mM Pi was saturating.) Although the data are compatible with a Pi dissociation const.ant of about 10 Caz+-pumpATPaseactivity(ShoshanandMacLennan, The number of heads in the fibers was calculated from measurement of the fiber volume and assuming the head concentration within the fiber is 154 pM (Ferenczi et al., 1984). The exchange rate constant, K ’ , defined as lPi]”[Mo]-’ d[PT]/dt, is the fraction of labeled Pi undergoing exchange per second, divided by [M,]. P: indicates Pi with solvent oxygens. This i s calculated as follows, taking the first row as an example. The percent exchange is taken as the sum of Pi with 3, 2, and 1 solvent oxygens (0.9 + 0.8 + 3.2), corrected for the percent exchange in the control (0.3). This ignores the small amount of exchanged Pi with 4 solvent oxygens as explained in the text. The exchange due to the fiber, as a fraction of total Pi, is 0.046. The total myosin head concentration x time is equal to myosin heads X time divided by the incubation solution volume (35 p1 for this experiment). k’ is 0.046 X (35 X lob6)6 (14.9 X “1 s-l . Because the amount of Pi present due to ATP hydrolysis is an average less than 10% of the labeled Pi, no correction is made for inhibition of exchange by this Pi. a

Medium PiWater Oxygen Exchange mM, the imprecision of the data precludes any firm conclusion. In the calculations that follow, we make the simplifying assumption that Pi at 10 mM is only weakly associated to the protein. If the protein is half-saturated by 10 rnM Pi, the analysis would bemore complex, although the general conclusions are unaltered. The data in Tables I1 and IV show a small (although not statistically significant) decrease in fiber ATPase activity as the concentration of Pi is increased. This inhibition by Pi of ATPase activity in the isometric state was tested more precisely by monitoring ADP formation during incubations in activating solution with or without Pi, as described under "Experimental Procedures." The ATPaserate per myosin head in the presence of 10 mM Pi was 2.9 (kO.1 S.E., n = 10) s-l. The rate was 91% (+4% S.E., n = 10) of that at zero Pi. Tension at 10 mM Pi was measured as shown in Fig. 1 and was 78% (&2%S.E., n = 10) of that at zero Pi. Pi caused a significantly ( p < 0.001) greater reduction of tension than of steady-state ATPase activity, a result qualitatively similar to that of Kawai and Guth (1986). DISCUSSION

The above results areevidence that Pi in the medium binds at theATPase active site to anactomyosin-ADP state during fiber-mediated ATP hydrolysis and that reactions back to protein-bound ATP formation, the processes giving rise to oxygen exchange, are readily reversible. The rates of exchange in the presence of ATP compared to ADP show that this actomyosin-ADP state (AM' .ADP, Scheme 1) is not accessible via ADP binding to AM, consistent with the results of Sleep and Hutton (1980) for the isolated proteins. Evidence for AM' .ADP in skinned fibers has been also obtained by Dantzig and Goldman (1985) from studies of vanadate binding. Because the exchange depends on formation of proteinbound ATP, the kinetics of processes associated with ATP hydrolysis can be inferred from the distribution of solvent oxygens in the exchanged Pi. The distributions in Table I1 show that Pi,once condensed with ADP to form ATP and so losing 1 "0, has an 0.36 probability of undergoing further exchange. The average distribution of 1:2:3 solvent oxygens in Pi is 63.9:21.7:14.4and can be compared to thecorresponding ratio obtained from intermediate exchange experiments in activated fibers in which oxygen exchange occurs between water and productPi formed during ATP hydrolysis (Hibberd et al., 1985b). The ratio in those experiments averaged 62.5:24.2:13.3,well within the standard errors of the results reported here. It is probable that these are the same distributions, and so we may apply the information obtained from the intermediate exchange experiments to the experimental data described in this paper. In the following calculations we assume that equilibration of Steps 2 and 4 is rapid relative to the rate of Steps 3, 3a, and 5 in fibers, as found with isolated actomyosin subfragment 1 (Eisenberg and Greene, 1980; Sleep and Hutton, 1978). The distribution of exchanged oxygens is determined by the ratio of the rate constant controlling ATP formation, (k3,K4 k 3 ) / ( K 4+ l), to that controlling Pi release from AM.ADP. Pi, k+,K4/(K4+ 1). The equilibrium constant K4 is taken as dimensionless, in viewof the probable concentration independence of actin-myosin interactions in fibers. The ratio R = k+dC4/(k-3,K4 + k 3 ) is calculated from the distribution as described by Webb and Trentham (1981). The data from Hibberd et al. (1985b) are most simply described bytwo pathways of ATP hydrolysis differing in their value of R. The major flux (63%)leading to product Pi has R = 2.3. Since the

+

within Muscle Fibers

15561

ATPase rates associated with the different fluxes are unknown, we are unable to quantify what fraction of ATPase sites function with R = 2.3. We make the simplifying assumptions that all the sites do and, based on the similarity of the oxygen exchange distributions described above, that thevalue of R = 2.3 can be applied to the medium exchange data of this paper. A lower limit can be measured for the rate constant of Pi binding to AM' .ADP, k 5 in Scheme 1, from the rate of solvent oxygen incorporation into Pi (d[P*]/dt, where P* indicates Pi with solvent oxygens). d[P*]/dt equals the product of the rate of Pi binding (=k-,[AM'.ADP][Pi]) and the fraction of AM. ADP Pi that undergoes exchange by reforming M. ATP or AM. ATP, as in Scheme 1.This fraction equals (k3,K4 k"S)/(k+&4 k-,,K4 + k+,), which simplifies to ( R l)-'. It follows that e

+

+

+

d[P?]/dt = ( R + l)"kE-5[AM'.ADP][Pil.

[AM' .ADP] must be less than or equal to the total head concentration in the trough [M,]). Exchange rate constants, k ' , are calculated as described under Table I1 where k' = [Pi]"[h&]"d[P:]/dt

=

( R + ~)"~-~[AM'.ADP][~VL".

Taking k' = 144 M" s" from Table I11 and R = 2.3, ( R + 1)k' = 475 M" s-', and so k-5

=

475[Mo]/[AM'.ADP] M"

(1)

S-I.

Thus k 5 a 475 M-' s-' and, if AM'. ADP is the major steadystate intermediate, then k-5 = 475 "' s-'. A comparison can be made between this value of k 5 derived from oxygen exchange data with that estimated from the reduction of mechanical force by Pi. If in Scheme 1 "ADP. Pi, AM. ADP. Pi, andAM'. ADP are the dominant intermediates duringATP hydrolysis in an active fiber, then [AM'.ADP] = k:5[Mo]/(k:5

+ kc + k-,[Pi])

+

where hi5 = k+,K4/(K4 1) and kc is the rate constant limiting the turnover of the ATPase mechanism, probably controlling one or a combination of Steps 6, 7, and 8. If we assume that force is proportional to [AM' .ADP], then the ratio of the forces F and F, at two Pi concentrations, [Pi] and[Pilo,is:

which on rearrangement gives

To use this equation, values are needed for k:,, kc, and [Pi],. Cooke and Pate (1985) have estimated the average concentration of accumulated Pi inside chemically skinned psoas fibers contracting in Pi-free solution to be 200 PM, which we define as [Pilo and take as the standard state concentration of Pi. k:, can be estimatedas followsfrom intermediate oxygen exchange studies (Hibberd et al., 1985b) and from transient chemical changes in activatedfibers. Ferenczi (1986) has measured the transient rate of ATP hydrolysis when MgATP is rapidly released in a fiber held isometrically in the presence of Ca2+.The rate constant, kh, for the hydrolysis transient calculated from the data is 60 s-' at 12 "C, and is k-3a)K4 presumably about 120 s" at 22 "C. Also, kh = [(k,,. k+3 k - 3 ] / ( & -k 1). The equilibrium constants for the hydrolysis steps ( K3 and are in the range 5-10 in isolated proteins when extrapolated from low to physiological ionic strength (Bagshaw and Trentham, 1973; Rosenfeld and Taylor, 1984) and probably

+

15562

Medium Pi-Water Oxygen Exchange within Muscle

Fibers

have the samevalues in fibers. Combining these observations making k+, independent of cross-bridge strain. We show that it follows that (k--SaK4+ k-3)/(K4 1) = 10-20 s-l at 22 "C. simple assumptions concerning strain dependence of the AM. As noted above, k + a 4 / ( k - , , K 4 + k-J = R = 2.3, so that k:, = ADP.Pi + AM'.ADP + Pi equilibrium predictdifferent k+5K4/(K4+ 1)is 25-50 s" at 22 "C. values for k-5 measuredchemically and mechanically, and Taking kc = 3.9 s-' (since kCki5/(ke k:,) = kc,, = 3.5 s-', different degrees of ATPase inhibition and tension attenuaTable 11), and noting that in10 mM Pi tension is 75% of that tion by Pi. The formalism is expressed by describing the without added Pi, k-, = 1000-1800 M-' s-', from Equation 3. ATPase in termsof three key states of Scheme 2 and the rate This value is approximately 3-fold greater than thevalue for constants of their formation anddecay as in Equation4: k 5 estimatedfromthemedium exchange data,assuming AM' .ADP is the dominant intermediate of the ATPase mech(M.ADP.Pi; AM.ADP.Pi} anism, although the valuesagree if [M,]/[AM'.ADP] = 3 4 (see Equation 1). An alternate estimate of k-, comes from the effectof Pi on isometricmechanicaltransientsinitiated by photolysis of In Equation 4 M.ADP-Pi and AM.ADP.Pi are presumed to caged ATP within fibers in the presence of Ca2+ (Fig. 3 of be in rapid equilibrium and are represented as (M .ADP.Pi; of cross-bridges, Hibberd et al., 1985a). In the absenceof Pi, the rate constant AM.ADP. Pi). Thetotalconcentration [AM,], = [M.ADP.Pi] + [AM.ADP.Pi] + [AM'eADP]. Fig. of approach to the apparent steady tensionlevel is approxiPi;AM. ADP. mately 100 s-', but in the presence of 10 mM Pi, this transient 2 showsthe chemical potential, p, of (M. ADP. phase is accelerated typically to 150 s-'. This suggests that Pi) and AM'.ADP + Pi as a function of x, the normalized longitudinal strainof the cross-bridge. The potentialof AM'. the apparent rate constant of 10 mM Pi rebinding is 50 s-', which corresponds to a second order rate constant value for ADP Pi is drawn at two Pi concentrations, 10 mM and 200 k-5 Of 5000 M-' S-'. p~ (defined above as thestandardstateconcentration). The force reached after this rapid phase of tension devel- Cross-bridges in theisometric fiberare assumed to be attached opment was reduced by inclusion of Pi considerably morethan with a uniform distribution over values of x from 0 to 1 as in the 25% reduction of steady tension in an activated isometricthe model of Huxley (1957). The force exerted by a crossfiber. Further study of this effect has shown a slow phase of bridge a t a particular value of x is proportional to the slope tension development (tlh = 0.5 s) following the initial rapid of the curve. The curves are parabolas, since the force at any phase.' The presence of this slow phase, representing approx- x is proportional tox, as seemslikely from mechanical studies imately 25% of the total tension, means that the depression (Ford et al., 1977). The verticalposition of the curve forAM'. in tension measured from the steady and transient contraction Pi depends on Pi concentration. For simplicity the ADP experiments are now in close agreement. The events during ( M .ADP. Pi;AM .ADP. Pi)state is assumed to exert no force. this slow phase have not beenclarified, so it is presently Qualitatively, it can be seen from Fig. 2 that attenuation of unclear which of the values for k-5, 1000-1800 M" s-' (appro- tension by 10 mM Pi occurs because at elevated Pi concentrapriate for a tension reduction of 25%) or 5000 M" s-l (from tions the equilibrium between those AM'.ADP states generthe transient mechanical experiment), valid. is right of the diagram) ating the most force (i.e. those toward the These two mechanical estimatesof k-, are greater than thatand the corresponding (M . ADP. Pi; AM. ADP. Pi) states fafrom theoxygen exchange data. An explanation of this differvors the latter. Thus the AM'.ADP population is biochemik-, may lie in a hypothesis that presumes ence in estimates for that a wide range of forces is exerted by cross-bridges in the cally inhomogeneous with a range of Pi affinities, and the AM'.ADP states exerting the most positive force are those Pi only binds readily tothose AM'.ADP state, and that that have the largest Pi association constants. exerting the greatest force. Thus Pi might bind readily to The rate constants associated with transformation between AM'. ADP in only a small fraction of the cross-bridges, but those particularcross-bridges would exert a greater proportion ( M .ADP. Pi;AM .ADP. Pi)and AM' .ADP inisometric fibers of the force. The apparent second order rate constant for depend onx in a manner described by Hill's formalism (1974, medium oxygen exchange (Equation 1) is derived from the 1975). We define [AM'. ADP], as the concentrationof AM'. total AM'.ADP concentration rather than the fraction of ADP at a particular x, with k-5x the rate constant for Pi AM'. ADP that bindsPi readily. So this rate constantwould binding toAM' .ADP atx to give AM. ADP.Pi. The forward rateconstant, k:,, of the reaction step (M.ADP.Pi; AM. be expected to be less than that for Pi association to AM'. ADP-Pi) toAM' .ADP + Pi is taken to be independent of x ADP deducedfrom the mechanics in a calculation that is in this simple description. The breakdown of AM'.ADP, in independent of AM' .ADP concentration. In addition, this hypothesis would predict that the decrease in steady-state tension of isometric activated fibers in the presence of 10 mM Piis greater than the decrease in steady-state ATPase activity. If the hypothesis is correct that AM.ADP.Pi and AM'. ADP support different amounts of mechanical stress, it follows from the formalismdevelopedby Hill and Eisenberg (Hill 1974,1975; Eisenberg andHill, 1985) that the ratiok+5/ k-5 will vary with cross-bridge strain. It is useful to analyze the data obtained within the framework of this formalism. AM!ADP+ 200pM Pi 0 1 This has been done in a general way by Hibberd and TrenX tham (1986). We now analyze the specific data obtained here FIG. 2. Free energy profile for {M-ADP-Pi; AM-ADP-PJ in these terms. The available data are sufficiently sparse so and for AM'*ADP + Pi. Chemical potentials are shown as functions that, ofnecessity, any model is over-restrictive, and so various of x, the normalized displacement of the myosin head with respect to constraints are made on the rate constants, for example by a fixed point on the actin filament. The range of allowed values of x

+

+

+

+

1

J. A. Dantzig, D. R. Trentham, and Y. E. Goldman, unpublished observations.

is assumed to be from the intersection of the free energy profiles of {M.ADP.Pi; AM.ADP.Pi) and AM'.ADP 200 PM Pi to the minimum chemical potential of the latter.

+

M e d i u m Pi-Water Oxygen Exchange within Muscle Fibers the forward direction, is assumed to be rate-limiting for the whole cycle. At [Pilo, the standard state concentration of free Pi, the difference in chemical potential between {M.ADP.Pi; AM. ADP.PiJ and AM'-ADP atzero strain ( i e . x = 0) is h. The potential for AM' .ADP ata particular x and [Pi], equalshx2. At other [Pi],Q = [Pi]/[Pil0 andp = hx2 R T In Q. It follows that

+

k-5r[Pi] = k&exp[-(h - h? - R T In Q)/RT]

15563

decreases from 1150 to 800 M" s" over the range h = 30-40 kJ/mol. The elasticity of active cross-bridges is nearly linear (Ford et al., 1977), so the force generatedper cross-bridge at a particular x is defined as Kx, where K is thestiffness. Taking a as a constant relating the numberof cross-bridges to their concentration, the totalforce, F', produced in the rangex1 to x2 is F' =

(5)

6"

a[AM'.ADP],Kxdx.

(7)

= kL5Q exp[h(2 - l)/RT].

Combination of Equations 5, 6, and 7 gives In this analysis h is considered to be a constant but unknown quantity, and calculations are made for various values F ' = r aK[AM,]xdx/{l + k,/kL5 + Q exp[h(xz - l)/RT]). of h. Values of h between 30 and 40 kJ/mol are in the range expected from solutionbiochemistry(WhiteandTaylor, From this itfollows that 1976) but are some &fold greater than might be expected from cross-bridge stiffness measurements (Huxley and Simmons, 1971; Hibberd and Trentham, 1986). Considering first the chemical data, the rate constant for 1 + k,/k& + Q exp[h(x%Pi binding, based on oxygen exchange measurements, repre1 + k,/ki5 + Q exp[h(x: - l)/RT] sents thevalue obtained from the average flux of Pi exchange, &[AM' .ADP] [Pi].Recalling that the totalcross-bridge dis- For the rangex = 0-1, tribution along x is uniform, [AM'.ADP], = k&[AM,]/(k&

+ kc + k-5r[Pi]).

(6)

At each value of x, using Equations 5 and 6, thisflux is given by k-5r[AM'.ADP],[Pi]

and 1 + kc/k;5 +

F' -

"

=

kL5[AM01 (1

+

Q exp[h(x2 - l)/RT] k,/k& + Q exp[h(x2 - l ) / R T ] .

E

)

Q

+ kc/k;5 + Q exp[-h/RT] 2 + kc/kL, 1 + k,/k& + exp[-h/RT]

)).

(8)

Taking k&, = 50 s" and kc = 3.9 s-', an apparent rate constant where Fi is the total force at [Pilo. The apparent rate constant, for the chemical process ( k 6 of Equation 1) was calculated k-,, defined by the mechanical force reduction (combining from the ratio of k-,,[AM' .ADP], integrated over 0 s x s 1 Equations 3 and 8) is also plotted against h, also taking k:, divided by [AM' .ADP], also integrated over 0 s x s 1 by = 50 s" and kc = 3.9 s-'. k 5 decreases from 2100 to 1400 s-' using Equations 5 and 6. k-, is plotted againsth in Fig. 3. k-5 over the range h = 30-40 kJ/mol. The average chemicalk-, value is lower than themechanical value because the AM'.ADP states that bind Pi toward the right of Fig. 2 produce force in greater proportion than their number due to theirhigh strain. The relative value of the ATPase rate constant, k,,,, expected from the model is plotted over the same range of h in k-, (mechanical) Fig. 3 with the assumption thatkc, the rate constant controlling AM' .ADP breakdown is rate-limiting and independent of x, so that kc,, = kc [AM'. ADP]/[AM,]. The value for [AM'. ADP]/[AM,] averaged over x was calculated from Equations 5 and 6. For example at h = 35 kJ/mol, we find at 10mM Pi, 85% of attached cross-bridges exist as AM'.ADP and at200 p~ Pi, the figure is 97%. It follows that in the model the ATPase activity at 10 mM Pi is 87% of that in 200 MM Pi. On the other hand, the relative force, F'/FA (Equation 8), de0 1 , I I , creases to the 77% level of h = 35 kJ/mol (Fig. 3). Thus the model predicts that ATPase activity is reduced lessthan force by increasing concentrations of Pi. Two simplifying features of this model need further consideration. First, if AM.ADP.Pi were to have a chemical potential thatvaried with x then this statewould contribute to the force. However, qualitatively, theabove argument depends on 0.51 I I I I I the difference in chemical potential between AM.ADP.Pi 20 25 30 35 40 45 and AM' .ADPdecreasing as x increases and can thus accomh ( k J mol-') modate AM.ADP.Pi contributing to tension. FIG. 3. Dependence of kinetic and tension parameters at Second, k+s is assumedto be independent of x. Taken 20 "C in the presence of 10 mM Pi on h, the chemical potential together with other assumptions made above, this leads to between {M*ADP*Pi; AM-ADP-PiJ and AM'aADP + 200 p~ Pi at x = 0. T h e curves were calculated as described in the text. R[=k+5K4/(k-3sK4 + k 3 ) ] being independent of x . It is inter-

1

1

L

~

15564

Medium Pi-Water Oxygen Exchange within Muscle Fibers

esting that R is the same whether measured by intermediate or medium oxygen exchange. In this latter case, as we have seen, the exchanged Pi is derived mostly from cross-bridges to the right of the diagram in Fig. 2. In the former case we can expect the flux of the ATPase to be either uniform or else biased toward cross-bridges to the left of the diagram, since cross-bridges in the AM’. ADP state with no strain may be expected to correspond to theactin-subfragment 1interaction in solution that is associated with relatively high ATPase activity. Hence our assumptions made for simplicity that certain rates and equilibrium constants are independentof x are at least consistent with the invariance of R between the two methods of measurement. A caution that should be noted here is that the value of R we haveused for our kinetic calculations was derived from Pi formed by the major pathway observed in the intermediate exchange experiments rather than from all the Pi formed during fiber ATPase activity. The data of Schoenberg and Eisenberg (1985) provide another example in which a range of rate constants occurs as a function of cross-bridge strain. They showed that pyrophosphate- and (By-NH)ATP-induced relaxation of fibers from the rigor state have complex time courses, indicating a wide range of cross-bridge dissociation rate constants. We conclude that the oxygen exchange process observed here can be directly related to the mechanical effect of Pi on transient and steady-state tension of activated fibers. Oxygen exchange between solvent and medium P, implies that Pi binds directly to theactive site on myosin, and together with mechanical data, that Pi release during ATPase activity is coupled to theformation of a force-generating state. Acknowledgments-We thank Peter A. Fletcher and Mark Luttman for excellent technical assistance. REFERENCES Bagshaw, C. R., and Trentham, D. R. (1973) Biochem. J. 133,323328 Biosca, J. A., Travers, F., Barman, T. E., Bertrand, R., Audemard, E., and Kassab, R. (1985) Biochemistry 24,3814-3820 Cooke, R., and Pate,E. (1985) Biophys. J. 48,789-798 Cross, R. L., and Boyer, P. D. (1975) Biochemistry 14,392-398 Dahms, A. S., Kanazawa, T., and Boyer, P. D. (1973) J. Biol. Chem. 248,6592-6595 Dantzig, J. A., and Goldman, Y. E. (1985) J. Gen. Physiol. 8 6 , 305327 Degani, C., and Boyer, P. D. (1973) J. Biol. Chem. 2 4 8 , 8222-8226

Eisenberg, E., and Greene, L. E. (1980) Annu. Reu. Physiol. 42,293309 Eisenberg, E., and Hill, T. L. (1985) Science 227,999-1006 Ferenczi, M. A. (1986) Biophys. J. 5 0 , 471-477 Ferenczi, M. A., Homsher, E., and Trentham,D. R. (1984) J. Physiol. (Lond.)352,575-599 Ford, L. E., Huxley, A. F., and Simmons, R.M. (1977) J. Physiol. (Lond.)269,441-515 Goldman, Y. E., and Simmons, R. M. (1984) J. Physiol. (Lond.)3 5 0 , 497-518 Goldman, Y. E., Hibberd, M. G., and Trentham, D. R. (1984a) J. Physiol. (Land.) 3 5 4 , 577-604 Goldman, Y. E., Hibberd, M. G., and Trentham, D.R. (1984b) J. Physiol. (Lond.)3 5 4 , 605-624 Hackney, D.D., Stempel, K. E., and Boyer, P. D. (1980) Methods Enzymol. 64,60-63 Hibberd, M. G., and Trentham, D. R. (1986) Annu. Reu. Biophys. Biophys. Chem. 15, 119-161 Hibberd, M. G., Dantzig, J. A., Trentham, D. R., and Goldman, Y. E. (1985a) Science 228,1317-1319 Hibberd, M. G., Webb, M. R., Goldman, Y . E., and Trentham, D. R. (1985b) J. Biol. Chem. 260, 3496-3500 Hill, R. D., and Boyer, P. D. (1967) J. Biol. Chem. 242,4320-4323 Hill, T. L. (1974) Prog. Biophys. Mol. B i d . 28,267-340 Hill, T. L. (1975) Free Energy Transduction in Biology: The Steady State Kinetic and Thermodynamic Formalism, Academic Press, Inc., New York Huxley, A. F. (1957) Prog. Biophys. Biophys. Chem. 7, 255-318 Huxley, A. F., and Simmons, R. M. (1971) Nature 233,533-538 Kawai, M., and Guth, K. (1986) Biophys. J. 4 9 , 9 a McIntosh, D.R., and Boyer, P. D. (1983) Biochemistry 2 2 , 28672875 Parker, R. E. (1973) Introductory Statistics for Biology: Studies in Biology, No. 43, pp. 20-22, Edward Arnold (Publishers) Ltd., London Rosenfeld, S. S.,andTaylor, E. W. (1984) J. Bid. Chem. 259,1190811919 Schoenberg, M., and Eisenberg, E. (1985) Biophys. J. 48,863-871 Shoshan, V., and MacLennan, D. H. (1981) J. Biol. Chem. 256,887892 Sleep, J. A., and Hutton, R. L. (1978) Biochemistry 17,5423-5430 Sleep, J. A., and Hutton, R. L. (1980) Biochemistry 19, 1276-1283 Taylor, E. W. (1979) Crit. Reu. Biochem. 6 , 103-164 Webb, M. R., and Trentham,D. R. (1981) J.Biol. Chem. 256,1091010916 Webb, M. R., and Trentham,D. R. (1983) in Handbook of Physiology: Skeletal Muscle (Peachey, L. D., Adrian, R. H., and Geiger, S. R., eds) pp. 237-255, American Physiological Society, Washington, D. C. Webb, M. R., Hibberd, M. G., Goldman, Y. E., and Trentham, D. R. (1985) Biophys. J. 47,60a White, H.D., and Taylor, E. W. (1976) Biochemistry 1 5 , 5818-5826