The ATPase Mechanism of Skeletal and Smooth Muscle Acto-subfragment l*

Transcription

1 THE JOURNAL OF BIOLOGICAL CHEMISTRY by The American Society of Biological Chemists, Inc. Vol. 259, No. 19, Issue of October 10. pp ,1984 Printed in U.S.A. The ATPase Mechanism of Skeletal and Smooth Muscle Acto-subfragment l* (Received for publication, January 30, 1984) Steven S. Rosenfeld and Edwin. Taylor From the Department of Biophysics and Theoreticol Biology, The University of Chicago, Chicago, Illinois The transient and steady-state kinetic parameters nism of mechano-chemical coupling in muscle and other for the ATPase cycle of the complex of skeletal muscle motile systems. A simple model proposed by Lymn and Taylor actin with smooth or skeletal muscle subfragment 1 (S- (1) explained the available evidence by a scheme which pro- 1) were determined over a wide range of actin concen- posed the existence of two associated states, AM. T and AM. trations from measurements of protein tryptophan flu- DPi, and two dissociated states, M.T and M-DPi, where T, orescence, the transient hydrolysis step, and the D, and Pi refer to nucleotide triphosphate, nucleotide diphossteady-state rate. The properties of the completely as- phate, and inorganic phosphate, respectively. The simplicity sociated system were determined by using s-1 cova- of the model suggested a correlation of AM. T and AM. DPi lently cross-linking to actin. A four-state model was with two orientations of attached cross-bridges. Subsequent found to provide a good approximation to the kinetic studies from several laboratories have shown that other interand steady-state behavior: mediate states exist (2-4), that the equilibrium constant for AMo + T *A. K.1 k AM1.T 2 AMz-DP, hil AM0 + D + Pi ks $Kd Mo + TI- M1.T Mz DPI Mo + D + Pi where T, D, and Pi refer to ATP, ADP, and inorganic phosphate, respectively. The formation of AMIT and MIT occurs by a rapid equilibrium binding of T followed by a very fast step. Actin is in rapid equilibrium with M1T and MpDPI, with association constants Kz and K4. The three rate constants kl, k-l, and ka were obtained by fitting observed rate constants from transient state measurements and V, to the model using values of ks and k-s determined for S-1 alone. To fit the data for skeletal or smooth muscle acto-s-1, the calculated rate constant of the hydrolysis step k1 and the equilibrium constant K1 had to be 2-3 times smaller than the corresponding parameters (k3, K3) for S-1. The calculated effective rate constant for product release must be large for striated muscle (85 s at 20 OC, low ionic strength) and relatively small for smooth muscle (3 s- ). The difference in the actin-concentration dependence of association and of steady-state AT- Pase activity was predicted correctly from the rate constants fitted to the transient evidence. hile the proposed mechanism does not exclude the possibility of additional ATP or product intermediate states, the properties of such states cannot be deduced from the kinetic evidence. The mechanism of actomyosin ATPase has been extensively investigated to provide a basis for a molecular mecha-. T -+ M. DPi) is relatively small (equal the hydrolysis step (M to 1-10) (2,5), that association-dissociation steps are in rapid equilibrium (6, 7), and that the direct hydrolysis step (AM.T + AM.DPi) can make an appreciable contribution to the rate of hydrolysis (7, 8). It is, therefore, necessary to determine the number of important intermediate states, the dominant pathway in the more complex scheme, and the relation of this pathway to the cross-bridge cycle. The general kinetic scheme can be divided into three phases: the transitions between bound ATP states, the hydrolysis step, and the transitions between bound ADP.Pi states, as shown in Scheme 1. It is generally agreed that nucleotides initially form a collision complex with myosin or actomyosin (2, 4,9). Furthermore, it is assumed that the structure of myosin and its interaction with actin is not altered in forming a collision complex with nucleotide. The same subscript is used for the states Mo, AMo, Mo. T, AM,,. T, Mo. D, AMo. D to indicate that the myosin and actomyosin structures are essentially equivalent. The remaining transitions in the sequence will, in general, involve structural changes and the various intermediates may have different affinities for actin. The Lymn-Taylor model assumed that each box contained a single pair of states and that actomyosin hydrolysis (step 1) could be neglected because the rate of dissociation of the AMl.T state was an order of magnitude faster than the hydrolysis step. The findings that the association-dissocia- tions steps are rapid equilibria and that the equilibrium constant for the myosin hydrolysis step is small means that the pathway from AMl. T to M2. DPi is reversible. The contribution from step 1 could then only be neglected if the rate of step 1 is slow. This would lead to inhibition at high actin concentrations (10). which has not been detected at 15 C(7). Although a small inhibition may occur at low temperatures (ll), Mornet et al. (12) have shown that the covalently crosslinked complex of actin and myosin is fully activated. The experiments described here suggest that the covalent complex * This work was supported by Program Project Grant HL is a functional model of the associated state and the apparent from the Heart, Lung, and Blood Institute of the National Institutes rate of hydrolysis by the complex provides a minimum estiof Health and by the Muscular Dystrophy Association of America. mate of the rate of step 1. The experiments further suggest The costa of publication of this article were defrayed in part by the payment of page charges. This article must therefore be hereby that the direct pathway makes an appreciable contribution to marked advertisement in accordance with 18 U.S.C. Section 1734 the steady-state cycle. solely to indicate this fact. The kinetic scheme be may expanded by introducing further

2 ATPase Mechanism of Skeletal and Smooth Muscle Acto-S SCHEME 1 ATP and ADP. Pi intermediates. There is reasonable agreement that a fast transition with a large equilibrium constant occurs between ATP states of both myosin and actomyosin (4, 9, 13). This step is indicated by the transitions to the states AM1. T and MI. T. The association constant Kz for the binding of M1. T to actin is much smaller than the association constant of myosin alone and the transition from AMo-T to AM1. T is responsible for the very rapid dissociation of actomyosin by ATP. Thus, the first box contains at least two pairs of ATP states. Because the transitions to AM1. T and M1.T are an order of magnitude faster than the hydrolysis and subsequent steps in the cycle, the observed behavior following the very fast dissociation step might still be represented by a four-state model, as depicted by Scheme 2. k6 k1 AM, + ATP+AM1.T+AMz.DPi-A& 1 k4 k2 Mo+ATP-Ml~.T-Mz.DPi-Mo+D+Pi k SCHEME 2 + D + Pi In referring to this scheme as a four-state model, it is meant that states with subscript 0 are not counted because at a saturating ATP concentration these states are not present in appreciable amounts in the steady-state cycle. The purpose of the studies described here is to test the consistency of this general four-state model. It is similar in form to the Lymn-Taylor scheme in that only four intermediate states are shown explicitly. However, the actomyosin hydrolysis step is included here, and, therefore, the significance of the above scheme for muscle contraction models could be quite different from that for the Lymn-Taylor scheme. The approximation of the general scheme by four intermediates assumes that no other transitions between ATP states or between ADP. Pi states occur which could lead to the accumulation of other intermediates or which introduce rate-limiting steps in phase 1 or phase 3 of the general model (Scheme 1). This is the simplest modelwhichcouldbeexpected to account for the transient and steady-state behavior. Two alternatives are to introduce extra steps in phase 1 or phase 3. The first possibility has not been considered in detail (14), but Eisenberg and collaborators (7, 8) have extensively discussed the second possibility, i.e. that an extra transition between AM ADP. Pi states and M.ADP. Pi states occurs in phase 3. This transition is considered to be necessary to explain why the steady-state ATPase is fully activated at a low degree of association of myosin and actin (actin in large excess). This finding was the basis for the proposalof a refractory state, an M-DPi state which binds more slowly or more weakly to actin (3). The rate of the transition from the refractory to the nonrefractory state was taken to be the ratelimiting step in the cycle. Recent studies have failed to show the presence of such a weak binding state (7) and a new interpretation was proposed which retains the rate constants of the refractory state transition for myosin but which sup- poses that such a transition also occurs for actomyosin states. Thus, phase 3 would become: AMz. DPi - AMs. DPi %A& 1 1 L L M~.DP~.- M~.DP~ s ow-~ SCHEME 3 + D + Pi + D + pi The association constants of MZ.DPi, Ms-DPi, as well as MI. T, are taken to be approximately equal. The extra transitions account for the difference in concentration dependence of myosin binding and activation by actin. In the studies presented here, a comparison is made between acto-s-1 preparations from the fast striated muscle of rabbit and the slow smooth muscle of chicken gizzard. Significant differences in the kinetic parameters of the two preparations provides a more stringent test of whether a four-state model is a satisfactory description. A proper test of a kinetic scheme requires that the number of independent parameters that are measured should exceed the number of independent rate constants that are determined from the measurements. On the basis of measurements of the rate constants of the transient fluorescence signal and of the hydrolysis step, of the amplitudes of the fluorescence signal and phosphate burst, and of the steady-state rate and the degree of association as a function of actin concentration, it is concluded that the four-state model accounts satisfactorily for most of the properties of the system. A small but probably significant discrepancy between measured and calculated values suggests that additional states do contribute to the observable properties but a more complex model cannot be uniquely determined by the data. The evidence is difficult to reconcile with the type of contraction model proposed by Lymn and Taylor (1) in which the hydrolysis step is coupled to cross-bridge rotation. MATERIALS AND METHODS Striated muscle S-1 was prepared from rabbit back and leg muscles by the method of eeds and Taylor (15). S-1 was separated into two fractions, S-1A1 and S-1A2, by chromatography on DEAE-Sephacel. Smooth muscle S-1 waspreparedfrom smooth muscle myosin by papain digestion and purified by chromatography on DEAE-Sephacel (16). Actin was prepared from acetone powders of rabbit muscle as described by Taylor and eeds (17). Association of acto-s-1 in the presence of ATP was measured by centrifugation employing a Beckman airfuge essentially as described by Chalovich and Eisenberg (18). The fraction of S-1 remaining in the supernatant was determined from the ATPase activity in the presence of EDTA relative to an S-1 standard (18). A second method which proved to be more convenient was used in most of the later experiments. S-1 was labeled with 3H by reaction with [3H]succinimidyl propionate (Amersham). A 0.1-ml aliquot of the supernatant from the centrifugation experiment was added to Hydrofluor scintillation fluid (National Diagnostics) and counted in a Packard Tricarb scintillation counter. Specific activity of the S-1 was obtained from the radioactivity of the stock solution of known concentration. To The abbreviations used are: S-1, myosin subfragment 1; PIPES, 1,4-piperazinediethanesulfonic acid; MES, 4-morpholineethanesulfonic acid; HMM, heavy meromyosin; AMP-PNP, adenyl-5 yl 0,~imidodiphosphate.

3 11910 ATPase Mechanism of Skeletal and prepare radioactive S-1, a 10-p1 aliquot of the label in toluene was spotted on a wedge of filter paper, placed in an Eppendorf centrifuge tube, and the solvent was evaporated in a stream of nitrogen. A 1-ml aliquot of a solution of s-1 (10-50 pm) in 0.1 M KCl, 1 mm MgC12, 10 mm Pipes buffer (ph 7.5) was added, the tube was capped, and the reaction was allowed to proceed for 4 h. The reaction was carried out at room temperature, or at 4 "C, with similar results. The solution was dialyzed overnight against a large excess of the appropriate buffer and clarified by low-speed centrifugation. The extent of labeling was kept below 0.5 lysines/s-1 and was in most experiments. A total concentration of S-1 of 0.2 PM in the sedimentation experiment gave sufficient radioactivity for determination of concentrations. The binding curves obtained by the two methods were in good agreement (Fig. 1). Steady-state ATPase activity was determined using [Y-~~P]ATP (Amersham) by the method used in quench-flow experiments (4). Rates were calculated from at least three time points. Covalently cross-linked acto-s-1 was prepared essentially by the method of Mornet et al. (12). Actin at a concentration of p~ was reacted with 1 mm l-ethyl-3-(3-dimethylaminopropyl)-carbodi- imide in 200 mm MES buffer (ph 6), 0.1 M KC1, 1 mm MgCl, for 2 min at room temperature. S-1 was added in a ratio of 1 S-1 to 2 actin residues. The ph was adjusted to 8.5 with 0.5 M Na2C03. Magnesium pyrophosphate was added to give a final concentration of 5 mm and the acto-s-1 was pelleted by centrifugation for 2 h at 105,000 X g. The pellet was resuspended in the appropriate buffer and dialyzed overnight. The ratio of S-1 to actin residues was determined by difference from the protein concentration remaining in the supernatant after centrifugation. The ratio was also estimated by densitometry of sodium dodecyl sulfate-polyacrylamide gel electrophoresis tube gels stained with Coomasie Blue. In some experiments, the S-1 concentration was determined using [3H]S-1 prepared as described above and the results were in reasonable agreement with values obtained by concentration measurements. Transient State Measurements-The measurements of fluorescence and light scattering were performed as described previously (4). A new quench-flow apparatus was constructed during the course of these studies to meet the requirements of rapid mixing of concentrated acto-s-1 solutions. The apparatus was based on the design of Froehlich et al. (19). A three-syringe mixer was driven by a Sigma stepping motor connected to a lead screw. Linear velocity was measured by displaying the voltage output of a 15-turn potentiometer attached to the rotating shaft. The drive velocity and distance were controlled by a Sigma DMC-10 controller and bipolar chopper. Reaction times from ms were attained by inserting polypropy- 11 I ACTIN CONCENTRATION (pm) FIG. 1. Comparison of binding of S-1Al to actin in the presence of ATP as measured by ATPase assay and by radioactivity assay. Conditions: 3 mm PIPES buffer (ph 7, 20 "C, 1 mm MgC12, 2 mm MgATP, sedimentation for 20 min, 178,000 X g in Beckman airfuge. S-1 concentration in supernatant determined by EDTA ATPase activity (0) and by radioactivity of S-1 labeled with [3H]succinimidyl propionate (0). Each assay was run in duplicate; bars indicate the range of data. Solid curve is a hyperbola corresponding to a dissociation constant of 10 p ~ The. association constant (K) was determined by linear least-squares fit of all data points by a Scatchard plot O/[A] = K(l - e), where O is the degree of association and [A] is the actin concentration. The intercept on the 8 axis is P Smooth Muscle Acto-S-1 lene tubes of varying volumes between the mixers, and by varying the drive velocity. For longer reaction times a two-step drive mode was employed. In the first drive, a volume of approximately twice the volume of the delay line was passed through the system. The extra volume was sent to waste through an electromagnetic valve. This was done to avoid dilution of the reaction solution from mixing with the buffer initially present in the delay line. The valve was switched to the sample side when flow stopped. A second drive was initiated by a variable timer circuit interfaced with the DMC-10 controller. In the second drive, the volume in the delay line was mixed with acid or quenching solutions. The time delay between drives was obtained by displaying the position signal from the potentiometer on a memory oscilloscope. In some experiments, it was desired to initiate a reaction, quench after a predetermined time, and then stop the reaction after a second time interval. The second reaction time was obtained by storing the quenched solution in a second delay line. A second pair of syringes containing buffer and acid were used to expel the contents of the line and stop the reaction by mixing with acid in a third mixing chamber. The time interval was set by a second timer circuit triggered from the initial drive pulse, and the drive velocity was monitored by a linear potentiometer whose output was displayed on the second channel of a dual-beam memoryoscilloscope. The second pair of syringes was driven by gas pressure. The reactant syringes were thermostated by circulating fluid from a temperature bath. The apparatus was enclosed in a large lucite box and cooling of the delay line tubes was obtained by a stream of air which was passed through a heat exchanger connected to the cooling bath. Temperature of the reactants in the delay tube was determined with a digital thermocouple (BAT8, Bailey Instruments). The apparatus was calibrated by measuring the rate of hydrolysis of dinitrophenyl acetate (19). The mixing time for viscous solutions was investigated because of possible difficulties in the mixing of concentrated acto-s-1 solutions. The mixers used in the stop-flow and quench-flow machines are identical Berger mixers (19). At the same volume flow rate and tube diameter, the two machines have the same mixing properties. The mixing of 50% glycerol at one ph with aqueous buffers at a different ph was measured by the optical density change of bromthymol blue. Mixing was found to be 95% complete in 3 ms. The viscosity of the glycerol solution is greater than the high shear viscosity at 20 "c of 80 pm actin plus 10 pm s-1 (2-3 centipoise as measured in an Ostwald viscometer). In this viscosity range, the Reynolds number calculated from mixer dimensions and flow velocity exceeded the critical value necessary to maintain turbulence. Stopping the reaction with acid in the second mixer occurs at a lower viscosity and mixing should not be a limiting factor. The error arising from the rate of denaturation of the proteins was investigated by choosing conditions to give a rate constant of ATP hydrolysis by S-1 of approximately 200 s-'. The extent of reaction was measured using various concentrations of perchloric acid or HCI to stop the reaction. The extent of reaction was the same when stopped by mixing with 2 or 3 N perchloric acid but was 20-30% larger for 3 N HCI for a 5-10 ms reaction time. A concentration of 3 N perchloric acid was used for the experiments described here. The accumulation of errors in mixing and stopping the reaction limits the time resolution to approximately 5 ms. A further problem with quench-flow studies is that the reactants must traverse a length of tubing between mixers. The reaction time is calculated from the volume flow rate and tube volume and an error will occur in the calculated reaction time in a transient experiment if turbulence is not maintained in the tube. Flowvelocity and tube diameters were selected to exceed the critical Reynolds number of 2000 for the maintenance of turbulent flow (20). The effect of varying the Reynolds number between 1000 and 4000 was tested by using tubes of different diameter and length to give the same calculated reaction time. The degree of ATP hydrolysis by acto-s-1 during the transient phase increased for calculated Reynolds numbers less than An internal test of the ability of the apparatus to measure rapid ATP hydrolysis in viscous solutions was made by comparing the course of the hydrolysis reaction of 10 pm S-1 and 10 pm s-l plus 40 p~ actin (concentrations after mixing with ATP) in 0.12 M KCI. At this ionic strength, the acto-s-1 will be almost completely dissociated by ATP in the initial mixing, and the hydrolysis reaction should be essentially the same as that for S-1 alone. Both experiments gave an amplitude of the phosphate burst of 0.6 f 0.05 and the rate constant of the hydrolysis step was 125 s-' for s-1 in approximate agreement with the rate measured by fluorescence, and 150 S" for acto-s-1. The time course of the hydrolysis reaction for acto-s-1 did not show a lag,

4 ATPase Mechanism of Skeletal and Smooth Muscle Acto-S which would have been expected if the mixing time for acto-s-1 were significantly larger. Kinetic Equations-The simplest model was described in the Introduction (Scheme 2). At high ATP concentrations and at low ionic strength, the formation of the tightly bound nucleotide states AMI. T and MI. T and the establishment of an equilibrium between these states is complete in 2-3 ms. The conversion of this distribution to the steady-state distribution is described by Scheme 4. ks.i k i AM. 1 TAAM. DP~ - k-1 +A, KZ k3 K4 M.T M.DPi k-3 SCHEME 4 Subscripts 1 and 2 are omitted since the states are specified by T or DPi. Steps 2 and 4 are in rapid equilibrium, KZ = AM.T/(A)(M.T). Actin is in large excess over myosin and the free actin concentration changes by less than 10% during the transient phase. Under these conditions, the rate equations have a simple solution. Because there are two pairs of states and because the members of each pair remain in equilibrium with each other, this model is equivalent to a two-state system, X + Y, where X = AM. T + M.T, Y = AM.DPi + M.DPi, and X + Y = Mo, where M, is the total myosin concentration. It is convenient to normalize to the total myosin concentration &, hence X + Y = 1, Y = Y8(l - exp(-at)), where Y, is the steady-state value of Y and X = k+ + k-. In the general case, the rate and equilibrium constants are all different, 01 = K4/& =.TI/ K3. Let fz = Kz(A)/(l + Kz(A)), f4 = K(A)/(l + KAA)), AM.T = fzx and AM. DPi = f4y. The two rate constants are given by k+ = k3 + fz(kl - k3) and k- = k-3 + f4(k-1 - k-3 + k5). The term (1 - f4)$, where 4 is the forward rate constant for the M.DPi - M, transition, is omitted in the expression for k- because it is very small compared to the remaining terms. The measured parameters are simply expressed in terms of k+ and X. The rate constant describing the approach to a steady state is X, which is measured by the change in emission of fluorescence of protein tryptophans or by the rapid hydrolysis step. The steady-state concentration of bound products is Y. = k+/x. The steady-state rate is V = ksfrk+/x. The fractional association of myosin intermediates with actin is 0 = f z + ( f4 - fz) Y.. The production of phosphate by hydrolysis of ATP consists of two terms, the bound phosphate Y and free phosphate Pi. At time T, Pi = it f4k5ydt = f4k5y,t - f4k5y,/x + f4k5y, exp(-xt)/x The magnitude of the apparent phosphate burst B" is obtained by linear extrapolation of the steady rate of phosphate production back to zero time. Since the total phosphate formed at time T is Y#(l - exp(-at) + Pi, extrapolation from the time range where exp(-at) is essentially 0 gives the phosphate burst, B". Bo = Y, - f4ks Y,/X = Y. - V/X It should be noted that the size of the phosphate burst is less than Y., the steady-state concentration of product states, because of the recycling of the system. The correction term V/X is directly measurable. In the case of S-1 alone, the correction is negligible, and B" = K3/(K3 + 1). The amplitude of the fluorescence enhancement as a function of association depends on the intrinsic fluorescence enhancement of AM.T uersus M.T and AM.DPi uersus M.DPi. If the values are equal for AM and M states, the enhancement relative to M is Y,(K3 + I)/&. Other cases will be discussed in the experimental section. This simple procedure for deriving the measured parameters from the rate equations can be extended to more complex schemes. A six- state model consisting of three pairs of states in equilibrium gives two apparent rate constants, XI and Xz, but the experimental parameters can still be obtained in terms of the individual rate constants. Steady-state rate measurements with myosin in large excess over actin are described under "Results." A simple expression for the dependence of the rate of hydrolysis per actin residue on the myosin concentration cannot be given because the rate equations are nonlinear. Measurements were made by varying the myosin concentration at a constant myosin-to-actin ratio. In the limit of an infinite myosinto-actin ratio, the actin-activated cycle will not perturb the value of the ratio of M.DPi/M.T and M.DPi/M.T = k3/(k-3 + &) = K3, Since AM. T and AM. DPi are each in equilibrium with M.T and M. DPi, respectively, then AM.DPi/AM.T = K1 and V% = k5kl/(k1 + I), where V$ refers to the maximum rate per actin residue obtained by extrapolation to infinite S-1. (This expression has been given previously (IO).) In general, V% is larger than V& and, as the ratio of myosin-to-actin is reduced, the value of VM will decrease (21). To evaluate kinetic schemes at a finite myosin-to-actin ratio, the equations were solved by iteration using reasonable values for the second- order rate constants for association of myosin intermediates with actin ( M" s-i), together with the values obtained from fitting the remaining rate constants to a four-state model. The calculations indicated that a 50-to-1 ratio of myosin to actin would give a VM close to the value for an infinite ratio. RESULTS Rapid-hydrolysis Step-The rapid-hydrolysis step for S-1 and acto-s-1 was measured at low ionic strength for a range of actin concentrations (ph 7, 20 "C). Striated muscle S-1A1 gave a burst amplitude, B", of mol/site at a rate of s-l, which agreed with the rate constant for the second transition measured by protein tryptophan fluorescence (Fig. 2A). The amplitude was generally mol/site for S-1A2. The amplitude decreased as the preparation aged and, by this criterion, S-1A2 appeared to be more stable. To correct for inactive S-1, the hydrolysis of ATP was measured at 200 ms with S-1 in 5-fold excess over ATP. The fraction hydrolyzed is a measure of IC3/(& + l), which is independent of the presence of some inactive S-1 (2). The difference between the burst with ATP in excess and with S-1 excess in is determined by the fraction of inactive S-1 in the preparation. Freshly made S-1A1 was 85-90% active, but the active fraction declined to 50-60% over a period of a week to 10 days. The equilibrium constant for the hydrolysis step, K3, is approximately for S-lAl and 2-3 for S-1A2. Smooth muscle S-1 gave a burst of mol/site for fresh preparations (Fig. 2B), but the protein is less stable than striated muscle S-1. The rate constant of the hydrolysis step ranged from s-' for a dozen preparations. A similar variation was noted in a previous study (16). The range of values is much larger than the random experimental errors in the measurements and the variation appears to be caused by the proteolytic-digestion procedure. The rate constant of this step, as measured by tryptophan fluorescence, is more than twice as large for smooth muscle HMM, compared to S-1 independent of the degree of phosphorylation of the molecule. The rate constant decreases as S-1 is formed from the HMM by digestion with papain (22). Preparations of S-1 having a rate constant of 25 f 5 s-' were used in the experiments described below. The rate constant and amplitude of the rapid hydrolysis step of striated muscle acto-s-1 varied with actin concentration. Measurements were made in three buffer systems: imidazole, PIPES, and Tris-MES with or without added KC1. The degree of association of S-1 to actin is highly dependent on ionic strength, and is much smaller for S-1A2 than S-1A1 at the same ionic strength and actin concentration. To obtain a high degree of association, measurements were made in 3 mm imidazole or 3 mm PIPES buffer. An example of a burst experiment is shown in Fig. 2A (40 PM actin; degree of association, approximately 0.7). The magnitude of the burst obtained by extrapolation of the linear portion of the curve to zero time is 0.05, while that for S-1 in the same experiment was 0.52 (not corrected for inactive S-1). The small amplitude of the phosphate burst did not permit a measurement of X, the rate constant of the transient phase. However, X must be larger than the rate constant k, for the hydrolysis step of S-

5 11912 ATPase Mechanism of Skeletal and Smooth Muscle Acto-S-1 A 0.60 c w fn K a t fn E o a 2 n r fn t - C TIME(msec) TIME (msec) TIME (rnsec) FIG. 2. The transient and steady-state hydrolysis reaction of S-1 and acto-s-1 of striated and smooth muscle. A, striated S-1A1 and acto-s-1al. Conditions, 10 pm S-1A1 (0), 40 pm actin, 10 pm S-1A1 (e), 3 mm PIPES buffer (ph 7, 20"), 1 mm MgC12, 100 p~ MgATP. Concentrations given in all figure legends refer to concentrations after mixing. For S-1, X = 43 s-i; burst, 0.53 mol/site. For acto-s-1, the steady-state rate is 10.7 s-l; the transient rate constant was not measurable since a linear relation gave a satisfactory fit to all data points. The burst is less than 0.1 mol/site. Data were not corrected for inactive S-1. Vertical bars indicate range of duplicate measurements. B, smooth muscle s-1 and acto-s-1. Conditions: 15 pm S-1 (O), 15 pm s-1, 30 pm actin (from striated muscle) (O), 150 p~ MgATP; other conditions are as in A. For S-1, X = 18 s-i; burst, 0.52 mol/site. For acto-s-1, X = 15 s-'; burst, 0.39 mol/site; steady-state rate, 0.85 s-l. Data were not corrected for inactive S-1. C, covalently cross-linked smooth muscle acto-s-1. Conditions: 8.5 p~ S-1, 24 p~ actin, 75 p~ MgATP other conditions are as in A. X = 11 s-l; burst, 0.24 mol/site; steady-state rate, 0.6 s-'. Data were fitted to the equation Pi = B"[1- exp (-At)] + V,t where V. is the steady-state rate and B" is the apparent phosphate burst determined by linear extrapolation of the steady-state rate. X was determined by fitting Pi - Vat by a semi-log plot. The fraction of inactive S-1 was in various experiments. 1, since the reaction has reached a steady state at 15 ms. Measurements of ATP hydrolysis by acto-s-1 were also made over a range of times from 100 to 700 ms using the double-drive mode to verify that the steady state had been attained. The rate determined from the slope in the ms time range agreed with the steady-state rate measured in 1 mm ATP by hand mixing. Values for the amplitude of the burst are plotted in Fig. 3 as a function of the degree of association B determined from measurements of binding by the sedimentation method. The scatter in the data reflects the variability of a large number of preparations in addition to the error in the intercept of a single measurement. The amplitude decreases with 0 to a value of approximately 0.1 at 65-70% association. The burst was also measured for S-1 covalently cross-linked to actin by the method of Mornet et al. (12). The amplitude of the burst was small, but there is a relatively large error in the determination of the S-1 concentration, as mentioned above ("Materials and Methods"). The burst of cross-linked S-1 is approximately Smooth muscle acto-s-1 also showed a decrease in the amplitude of the burst (Fig. 2B), but the value of the burst was larger than that for striated muscle S-lAl at the same degree of association. In contrast to S-1A1, the rate constant X of the transient phase for the smooth muscle acto-s-1 was generally smaller than the value of ks for the hydrolysis step of S-1. Although the extent of the decrease varied with different preparations, in no case was there an increase in the rate constant. The dependence of the rate constant and amplitude of the burst is plotted in Fig. 4 as a function of the degree of association. The burst was also measured for covalently crosslinked acto-s-1 (Fig. 2C). Determination of the rate constant is not affected by errors in concentration and the value obtained was 13 & 3 s-', which shows a decrease in rate constant by roughly a factor of2, compared to S-1. The amplitude of the burst was in the range The Transient Rate Constant Measured by Protein Trypto- phan Fluorescence-The binding of ATP to S-1 gives a twostep fluorescence signal in which the rate constant of the second fluorescence transition is approximately equal to the hydrolysis step (4). hen acto-s-1 is mixed with ATP under conditions that lead to complete dissociation, the observed fluorescence transition can be described by a single exponential term, and the rate constant is equal to the second transition for S-1 (4, 16). Stein et al. (8) reported that the rate constant X of the fluorescence transition increased with actin concentration under conditions of partial association in the steady state, but the value of X for the hydrolysis transient was not reported because of instrument limitations. The present studies confirm their findings for striated muscle acto- S-1. Examples of fluorescence transients are shown in Fig. 5 for S-lAl and acto-s-1al. The rate constant for the fluorescence transition increased from 54 s-l for S-1 to 86 s-l for acto-s-1 at a degree of association of approximately The amplitude of the signal corrected for the increased turbidity of the acto-s-1 is approximately half as large as that for S-1. A decrease in amplitude is expected from the decrease in relative concentration of ADP. Pi intermediates compared to ATP intermediates in the steady-state cycle. The reaction of actin with a solution containing S-1 and ATP which had reached the steady-state distribution of intermediates shows a corresponding decrease in fluorescence emission (Fig. 5, curve C)) which accounts for the signal missing in curve B. The rate constant for the decrease in fluorescence emission was 77 s-l in this experiment, which is equal to the rate constant for the increase in fluorescence for the reaction of ATP with acto-s-1. This equality is predicted by a four-state rapid equilibrium model, since this mechanism has only one relaxation time. The apparent first-order rate constant for the fluorescence enhancement is plotted versus the degree of association in Fig. 3. The trend in the data points suggests that the apparent rate constant should be at least twice as large for complete association of acto-s-1 compared to S-1. The solid curve in the figure was calculated by fitting data to a particular model which predicts the increase in rate constant to be a factor of 2.4. Smooth muscle acto-s-1 did not yield an increase in the

6 ATPase Mechanism of Skeletal and Smooth Muscle Acto-S Y A 0 0 Y * re > c I- co a 3 rn k I a co 0 I n V z 0 v) 0 a 3 u. ti ASSOCIATION TIME ASSOCIATION (msec) FIG. 3 (left). Variation of kinetic parameters of striated acto-s-1 as a function of the degree of association. Apparent rate constant X of tryptophan fluorescence signal (0) and rapid hydrolysis step (A); amplitude of apparent phosphate burst E" (0). Points of association equal to 1 refer to covalently cross-linked acto-s-1. Conditions: 3 mm PIPES (ph 7,20 "C), 1mM MgClz and 1-2 mm MgATP for fluorescence measurements, p~ MgATP for hydrolysis measurements. Degree of association was calculated for acto-s-1 by using a dissociation constant of 17 p ~ The. experimental points were obtained from several protein preparations. The average values were used to fit VM and the variation of X and B" to the four-state model, described in the text, to obtain the rate constants, kt and k+ for hydrolysis by associated acto-s-1 and kg, the rate constant of product release. The solid curues were calculated from the kinetic model to give the best agreement of the rate constants with the data (for further details, see text). The curve labeled V is the normalized steady-state rate ( V/VM) calculated from the fitted-rate constants. Half-maximum rate occurs at a degree of association of 0.22 FIG. 4 (center). Variation of kinetic parameters of smooth muscle acto-s-1 as a function of the degree of association. Apparent rate constant X of tryptophan fluorescence signal (0) and rapid hydrolysis step (A); amplitude of apparent phosphate burst B" (0). Conditions are as in Fig. 3. The degree of association was calculated for acto-s-1 by using a dissociation constant of 50 p ~ The. solid curves were drawn as in Fig. 3. Half-maximum rate of hydrolysis occurs at a degree of association of FIG. 5 (right). Changes in tryptophan fluorescence emission for reactions of S-1 and acto-s-1 with ATP. Curve A, fluorescence enhancement for the reaction of 1 mm MgATP with 10 p~ S-1. The smooth curve was obtained by fitting the signal between 10 and 100 ms to a single exponential term, X = 54 s-'. The deviation of the fitted curve from the experimental curve over the first 10 ms shows the presence of a faster process. Curve B, fluorescence enhancement of acto-s-l,30 p~ actin, 10 pm s-1,l mm MgATP, X = 85 s-'. Curve C, fluorescence decrease for the reaction of a mixture of S-1 and ATP with actin to give the same final concentrations of reactants as in B, X = 77 s-'. To compare the amplitudes of signals B and C with A, the voltage gain for trace A was reduced to approximately correct for the difference in turbidity. Fluorescence is plotted in arbitrary units but 1 unit on the ordinate scale is approximately a 10% enhancement, relative to S-1. The smaller amplitude for trace B compared to trace A is accounted for by the decrease in fluorescence for the formation of the complex with actin (curue C). rate constant of the fluorescence signal with increasing asso- constant. From the final voltage at the end of the transient ciation. hile the change was small, there was a significant and the corrected voltage change, the emission at zero time decrease in the rate constant for most preparations. However, (fo) is obtained. The quantity Af/fo was converted to the in some cases the variation in rate constant was less than enhancement per S-1 in the complex from the ratio of actin- IO%, which is not significant. Fig. 4 shows the decrease in to-s-1 and from the relative molar fluorescence emission of rate constant together with rate measurements of the hydrol- actin and M T. The quantity obtained by this procedure ysis step made on the same preparations. Both measurements should be independent of tubidity and internal absorption. show a similar decrease and, based on the rate of the hydrol- The enhancement was expressed relative to the enhancement ysis step for cross-linked acto-s-1, the decrease in value of for the corresponding transition for S-1. Data for striated the rate constant is approximately a factor of 2. muscle acto-s-1 are shown in Fig. 6 as a function of the degree The amplitude of the tryptophan fluorescence signal pro- of association calculated from the association constant of 17 duced by the reaction of acto-s-1 with ATP is related to the PM. There is clearly a large decrease in the signal to distribution of substrate versw product intermediate states. over the accessible range. The dashed curve is the variation However, at high concentrations of acto-s-1, the observed in amplitude calculated from the same set of rate constants change in intensity has to be corrected for attenuation of the used in Fig. 3 to fit the transient and steady-state data. exciting light by scattering and by absorption, as well as for Although there is reasonably good agreement, the scatter in an internal absorption of the fluorescence. In turbid solutions, data points could lead to a value as large as 0.3 at complete it is also necessary to assess the contribution of the scattering association. of the incident light to the apparent fluorescence intensity Fluorescence measurements for covalently cross-linked arising from overlap of the pass bands of the optical filters. acto-s-1 were inconclusive. The actin-to-s-1 ratio of cross- The fluorescence emission in the stopped-flow apparatus was linked material was 2.5 or 3.0. Thus, an intercept of linear in concentration up to 25 PM acto-s-1 and the range corresponds to an actual fluorescence enhancement of 2.5%. could be extended by correcting for absorption from measure- The cross-linked material consisted of large aggregates based ments of the decrease in intensity of the transmitted beam. on its sedimentation behavior and high specific light-scatter- However, a relative measurement was considered to be more ing intensity. Electron microscopy of the preparations showed accurate. Measurements were made at a fixed actin-to-s-1 a preponderance of actin filament bundles (data not shown). ratio, usually 1.5 or 2. The observed signal was corrected for hile transient measurements gave a 3-4% enhancement, loss in the dead time of 1.5 ms using the measured rate the mixing artifact in the absence of ATP amounted to 2%.

7 11914 ATPase Mechanism of Skeletal and Smooth Muscle Acto-S-1 Therefore, cross-linked acto-s-1 was found to be unsuitable for determination of the amplitude of the fluorescence signal at complete association. In order to extend the data to a higher degree of association, a small number of measurements were made at 10 "C. The apparent dissociation constant of acto-s-1 in the presence of ATP is reduced to approximately 10 p~ at this temperature, permitting measurements at a degree of association up to 0.7. The relative fluorescence amplitude at 10 "C is plotted as the filkd circles in Fig. 6. It is evident that the decrease in relative amplitude is smaller than that at 20 "C for the same degree of association, and extrapolation to complete association would appear to give a value of approximately 0.3. The phosphate burst decreased from 0.45 for S-1 to 0.05 for acto-s-1 at 0 = 0.7, and the rate constant of the trypotphan fluores- cence signal increased from 8 s" for S-1 to 25 s-' for acto-s- 1 at 0 = 0.7. An approximate calculation for a four-state model based on this small data set predicts a relative fluorescence enhancement of approximately Thus, there may be a discrepancy at this temperature. There are difficulties in interpreting the relative amplitude of the fluorescence signal, which will be considered under "Discussion." The Slow-dissociation Step-Marston and Taylor (16) found that the ATP-induced dissociation of slow red muscle and smooth muscle acto-s-1 occurred in two steps as measured by light scattering or with a fluorescent probe attached to actin. The same effect was observed for striated and smooth muscle acto-s-1 in the present studies. The light-scattering signal showed a main step at a rate exceeding 1000 s-l at high ATP concentrations followed by a slow tail whose amplitude was 10-15% of the total signal (Fig. 7). The rate constant of the slow step was roughly equal to the rate of the fluorescence transition. In several experiments, the agreement was not quantitative even allowing for the errors in fitting a small light-scattering signal. However, both rate constants increased with actin concentration and differed by less than a factor of 2. It is concluded that a small additional dissociation step occurs at approximately the same rate as the protein fluorescence or hydrolysis steps. Quenching Experiments-The decrease in amplitude of the phosphate burst and tryptophan fluorescence signals with increasing degree of association suggest that in the steady state the associated states are predominantly AM. T states rather than AM.DPi states. Other explanations could be proposed on the basis of possible kinetic schemes. Consequently, this conclusion was tested by additional experiments whose interpretation does not depend on a detailed model. Striated muscle acto-s-lal was reacted with radioactive ATP at a ratio of 4-5 ATP/S-1 and at an actin concentration of 40 p ~ A. small phosphate burst was observed and the reaction appeared to reach a steady state in less than 30 ms (Fig. 8, curue I). At various times between 10 and 100 ms, the acto-s-1 intermediates were dissociated by mixing with KC1 plus a large excess of unlabeled ATP to give a KC1 concentration of 0.13 M. At this ionic strength, the complex is more than 95% dissociated, according to sedimentation measurements of binding. The major part of the dissociation induced by the ionic strength jump was complete in 2-3 ms as measured by the change in light scattering. This result verifies that the various actomyosin-intermediate states are in rapid equilibrium with myosin intermediates at physiological ionic strength. The reaction was stopped with acid at ms after the KC1 jump using the second drive system of the quench-flow machine. The extent of reaction is shown by curue 2 in Fig. 8. The line has approximately the same slope as the steady-state rate and extrapolates to 0.65 mol of phosphate/site at zero time. The reaction was also allowed to proceed for 10,60, and 120 s after mixing with KC1 and ATP. The amount of hydrolysis was corrected for the extra hydrolysis of the labeled ATP diluted with unlabeled ATP to give LL L I I ASSOCIATION FIG. 6. Variation in the amplitude of fluorescence enhancement of acto-s-1 with degree of association. The fractional change in fluorescence for acto-s-1 corrected for the instrument dead time (1.5 ms) was expressed relative to the fluorescence of the S-1 moiety. The value was divided by the fractional change for the second fluorescence transition of S-1 to obtain the relative fluorescence enhancement. Conditions: 3 mm PIPES buffer (ph 7), 1.67 mol of actinlmol of S-1, 1 mm MgC12, 1 mm MgATP and 20 "C(open circles) or 10 "C (closed circles). Degree of association calculated for a dissociation constant of 17 PM at 20 "C and 10 M at 10 "C. The dashed curue was calculated from the fit to a four-state model at 20 "C as in Fig TIMEhsec) FIG. 7. Comparison of the tryptophan fluorescence and light-scattering signals for the reaction of acto-s-1 with ATP. Conditions: 10 mm TRIS, 10 mm MES (ph 7), 1 mm MgCl,, 1 mm MgATP, 10 mm KCl, 20 PM acto-s-1. The very fast dissociation step is almost completed in the dead time of the apparatus and the trace shows only the final 10% of the signal. At this ionic strength, the degree of association is 10-15% as estimated by light-scattering amplitude. Both the slow dissociation step (decreasing signal) and the tryptophan fluorescence change (increasing signal) have apparent rate constants of 70 f 1 s-l (smooth curves), obtained by fitting the signal after the first 5 ms to a single exponential process.

8 ATPase Mechanism of Skeletal and Smooth Muscle Acto-S the total hydrolysis of the ATP bound prior to the ionic strength jump. The values are shown by curve 3, which extrapolates to 0.9 mol/s-1 site. The experiment shows that the sites are essentially saturated with tightly bound ATP at 30 ms. The value of 0.9 mol rather than 1 mol/site indicates some inactive S-1. In addition, there may be a small loss of ATP from the very small fraction of AM. T present at high ionic strength which can dissociate into ATP and AM (23). After dissociation of acto- S-1 nucleotide states by KC1, the ATP and ADP.Pi present on S-1 will first reach the steady-state ratio of M. T to M. DPi at a rate of 125 s-'. Thus, 50 ms after dissociation by KC1, the steady-state distribution of S-1 intermediates will be reached. Since curve 2 in Fig. 8 extrapolates to 0.65 mol/ site and the phosphate burst for S-1 was , as determined in the control experiment in the absence of actin, the increase in hydrolysis to the S-1 level indicates that the original acto-s-1 had attained a steady state with ATP bound but not hydrolyzed. At 100 ms, the difference between the acto-s-1 and the dissociated system is still 0.5 mol/site. Thus, the small phosphate burst and the decrease in amplitude of the tryptophan fluorescence signal for acto-s-1 is caused by a steady-state distribution in which AM. T is present at a high ratio relative to AM. DPi. If other intermediates, such as AM-ADP had accumulated in the steady state, the extent of rapid hydrolysis on dissociation would have been reduced accordingly. Steady-state ATPase and Actin Binding-The dependence of the steady-state rate and the degree of association on actin concentration defines apparent dissociation constants K$ and KO, respectively. These parameters are generally assumed to, &--' 0.1 I IO 50 IO0 TIME (MSEC) FIG. 8. Effect of quenching the acto-s-1 ATPase cycle by increase in ionic strength. The hydrolysis of ATP by acto-s-1 is shown by curue 1 (0) for the conditions of 40 pm actin, 10 pm s-1; 50 p~ [32P]ATP, 3 mm PIPES buffer (ph 7,20 "C); phosphate burst, approximately 0.13; steady-state rate, 4 s-'. At 10,30, 70, and 100 ms, the solvent conditions were changed by mixing with KC1 and unlabeled MgATP to give final concentrations of 0.13 M KC1 and 1.5 mm ATP. The reaction was stopped with acid in less than 100 ms to give curue 2 (0). The reaction was allowed to proceed for 50, 100, and 200 s, stopped with acid, and the hydrolysis was corrected for turnover of the diluted radioactive ATP to give the extent of hydrolysis of the ATP that was bound prior to the KC1 quench, curue 3 (0). Linear extrapolation of curues 2 and 3 back to zero time shows that the sites are saturated with tightly bound ATP in less than 30 ms since the phosphate burst corresponds to saturated S-1 and 90% of the sites are occupied with nondissociable nucleotide. The hydrolysis reaction for acto-s-1 had reached a steady state in less than 30 ms; consequently the small extent of hydrolysis must arise from a large ratio of bound ATP-to-ADP. Pi. refer to the dissociation constants obtained by fitting experimental data to a hyperbola. This assumption is satisfactory for binding measurements as illustrated in Fig. 9. However, a general kinetic scheme does not predict a hyperbolic dependence of the steady-state rate on actin concentration and, for some values of the rate and equilibrium constants of the ATPase cycle, very high concentrations of actin could begin to inhibit the steady-state rate of hydrolysis (10). No inhibi- tion was detected by Stein et al. (7,s) at 15 "C. In the present experiments with S-1A1, a maximum rate was reached at a relatively low actin concentration and the rate was essentially constant in the range of actin concentrations from p ~ hile. some experiments did show a decrease in rate in this range, the average slope of the activity versus actin concentration curve did not differ significantly from 0 for a mean error in data points of &5%. However, the data did show a small deviation from a fit to a hyperbola. An example of a double reciprocal plot of rate and actin concentration is shown in Fig. 10. The data points at high actin concentrations deviated from the straight line fitted to the data for actin concentrations of less than 40 pm. The parameters V& and K$ given in Table I were obtained from the observed maximum rate and the concentration of actin at half-maximum rate for S-1A1 and S-1A2. In the case of smooth muscle, the maximum rate was not reached at accessible actin concentrations, and the parameters had to be determined by extrapolation assuming a fit to a hyperbola (Fig. 9B). The values of V& and K$ for S-1 are in moderate agreement with previous reports (24) in showing that V& is larger for S- 1A2 by a factor of at low ionic strength, and that K$ is 2-4 times greater for S-1A2 compared to S-1A1. Previous studies have shown that K$ is less than KO, particularly at low temperature, while at "C, values reported in the literature are not in agreement (7, 24). Our results support the findings of Stein et al. (7) that K$ is 3-4 times smaller than K@ (Table I). Measurements were made on more than 10 preparations and the standard deviation of the mean includes the variability in protein preparations. Both parameters are very dependent on ionic strength. For the lowest ionic strength employed, the average values are KO = 16 f 5 p~ and K$ = 6 f 2 p~ for acto-s-1al. In individual experiments, the ratio KO/K$ ranged from with an [ACTIN-IJ(~M-I) [ACTIN-! (,,"I) FIG. 9. Degree of association (0) and ATPase activity (V) of smooth muscle acto-8-1 as a function of actin concentration. Data are presented as a double-reciprocal plot. Solid lines were obtained by linear least-squares fit. For association, KO = 52 p ~ ; intercept of the plot is 0.8. For ATPase activation, Kv = 37 p ~ VM, = 0.72 s-'. Conditions: 3 mm PIPES buffer (ph 7, 20 "C), 1 mm MgC12,2 mm MgATP.

9 11916 ATPase Mechanism of Skeletal and Smooth Muscle Acto-S-1 average value of 2.7. For acto-s-1a2, both constants are larger at the same ionic strength but the ratio was 3-4, while for smooth muscle the ratio is less than 2 (Table I), in disagreement with Greene et al. (25). The activation of the ATPase was also determined by varying the S-1 concentration and measuring the ATPase activity per actin residue with S-1 in large excess. This procedure defines two additional parameters, V$ and Kt. The value of Kt is much larger than Kt and was not determined accurately. V$ was obtained by extrapolation assuming a hyperbolic dependence on S-1 concentration. It has been reported (21) that V& depends on actin concentration. Since this complication is expected even for the simplest kinetic scheme, measurements were made at fixed S-1-to-actin ratios of 10,25,40, and 50. V$ increased with the S-1-to-actin ratio but appeared to reach a maximum at a ratio of The figures given in Table I refer to measurements in this range but it is possible that the maximum rate has been underestimated. A large difference in the two parameters V& and vsm has been reported at low temperature (21). Our results showed v", to be approximately twice as large as V& at 20 "C and an S-1-to-actin ratio of An example of a set of measurements of the acto-s-1 ATPase activity with S-1A1 in excess is shown in Fig. 10 in which the data are plotted as reciprocal rate uerszu reciprocal of S-1 concentration for comparison with the behavior for actin in excess. The results for acto-s-1 are in approximate agreement with those of agner et al. (26) for the change in maximum rate although they obtained a lower value for Kt. They did not find a difference in v"m and V$ for S-1A2, while our measurements showed a ratio of approximately 2. However, the extrapolated value is subject to large errors because of the large value of Kt. In the case of smooth muscle S-1, the activation is small and increases linearly with concentrations up to 150 p~ S-1, and V$ could not be measured. DISCUSSION (ACTIN)-1 or (SF-II-~ (p~1-1 FIG. 10. Dependence of the ATPase activity V on concentration for actin in excess and S-1A1 in excess. Solid circles, actin concentration varied for an actin-to-s-1 ratio of at least 20. Open circles, S-1 concentration varied for constant S-1-to-actin ratio of 40. The ATPase activity of S-1 in the absence of actin was subtracted for each data point. The solid curve for actin in excess is a linear least-squares fit to the range of concentrations up to 40 pm. The data show a deviation from a hyperbola for actin concentrations larger than 75 MM. The solid curve for S-1 in excess is a linear leastsquares fit to all data points. Conditions: 1 mm MgC12,2 mm MgATP (ph 7,20 "C). 3 mm PIPES buffer for actin in excess, 3 mm imidazole buffer for S-1 in excess. K% obtained from the actin concentration at one-half the maximum observed rate is 10 p ~ Kt. obtained from the fit to a hyperbola is 70 p ~. TABLE I Steady-state parameters of striated and smooth muscle acto-s-1 Conditions: 3 mm PIPES or 3 mm imidazole buffer (ph 7), 1 mm MgCIz, 2 mm MgATP, 20 "C. V$ is the maximum rate obtained by varying the actin concentration. For S-lAl and S-1A2, V$ is the actual plateau value and K$ is the actin concentration at halfmaximum rate. For smooth muscle, acto-s-1 V$ and K$ were obtained by least-squares fit to a hyperbola. v",is the maximum rate per actin residue obtained by varying the S-1 concentration at a constant S-1-to-actin ratiof 40- or 50-to-1. v",and Kt were obtained by the fit to a hyperbola. KS is the dissociation constant of acto-s-1 in the presence of MgATP. Striated muscle actin was used in all experiments. Protein Vb V% KC pv s" pm pm pm Acto-S-1Al 6.7 f0.6 19f 4 6-C f5 Acto-S-lA f f Smooth muscle 1.0 & f 5 52 f 5 acto-s-1 This series of experiments was undertaken to provide data with which to test models of the acto-s-1 ATPase cycle. However, certain conclusions can be drawn which do not depend on a detailed model. The evidence shows that a direct hydrolysis step occurs, since the transient and steady-state rate parameters do not approach 0 as the association between actin and S-1 approaches unity. Mornet et al. (12) have shown that S-1 covalently cross-linked to actin is a fully activated ATPase which places a lower limit on the rate of direct hydrolysis. The amplitude of the phosphate burst of the crosslinked material appeared to agree approximately with the amplitude expected by extrapolation of the data for noncrosslinked acto-s-1 to complete association, providing evidence that cross-linked acto-s-1 is a reasonable model of completely associated actomyosin. Qualitatively, the results are in agreement with the conclusion of Tonomura (27) and of Stein et al. (7,8) that the direct hydrolysis pathway contributes to the actomyosin ATPase cycle. A second conclusion is that, for striated muscle acto-s-1, the predominant acto-s-1 interme- diate is an ATP state rather than a product state. The low ratio of ATP to products could be attributed to a smaller equilibrium constant of the hydrolysis step of acto-s-1 compared to S-1, to a large rate coristant for product release which would lower the steady-state concentration of the product state, or to a combination of both factors. It must be emphasized that the rate constants or equilibrium constant of the hydrolysis step of the acto-s-1 state cannot be measured directly since the observable parameters depend on all of the rate constants of the cycle. Consequently, the rate of this step is inferred from a particular model. It is logical to begin with a model containing the smallest number of intermediates and determine whether the model is consistent with the measured parameters. The equations for testing the simplest model are given in the section, "Kinetic Equations." The first transition to the AM. T state and the partial dissociation of this complex occurs at a sufficiently large rate that these steps can reach equilibrium a few milliseconds after mixing with ATP. At

10 +A, KZ 1 ATPase Mechanism of Skeletal and Smooth Muscle Acto-S kg 1 kl k-1 k3 AM.T-AM.DPi I K4 M.T- M.DPi k-3 SCHEME 5 very low ionic strength, and at ATP concentrations of 100 pm or larger, these steps are completed in less than 5 ms. Thus, a reasonable approximation is provided by a four-state model. The steps from AM.DPi, in which ADP and Pi are released, ATP is rebound, and the AM.T state is regenerated, are described by a single effective rate constant kg. The assumption that no intermediates accumulate except those in equilibrium with M. T and M. DPi was tested by the quenching experiment (Fig. 8). The rate constants k3 and k3 were measured separately for S-1. A test of the four-state model can be made by determining whether all of the experimental parameters can be fitted within the limits of experimental error by a unique set of values of the three rate constants Itl, k-,, and kg. It is easily shown that the special case of Kz = K4 is not consistent with the data for striated muscle or smooth muscle. In this case, fz = f4 = 8, and the parameters V&, X, and B" provide three equations for kl, kel, and k6. For this situation, solution of the equation for a range of values of 0 gives kl/kl approximately equal to while the hypothesis requires Kl = K3 = 1.5 for striated muscle. Also, in this case, X would be a linear function of e while the experimental data fitted a curve of increasing slope (Fig. 3). Stein et al. (7) also concluded that this special case of the four-state model was not consistent with their data. The general case was tested by using the values of V& and the variation in B" and X to determine values of kl, k-,, and k5 which would give a satisfactory fit to this subset of the data (Fig. 3). For straited muscle, the values are kl = 12 s-l, k-l = 28 s-l, k3 = 30 s-', = 20 s-', k5 = 85 s-'. Thus, the direct hydrolysis step of actomyosin calculated from a four-state model has a smaller rate constant and a smaller equilibrium constant than the corresponding myosin step, K, = 0.43, while K3 = 1.5. Consequently, the ratio Kz/K4 is 3.5, which would mean that M. T is more strongly bound to actin than M. DPi. The concentration dependence of the steady-state ATPase calculated from these parameters is plotted in Fig. 3. If the apparent dissociation constants for the ATPase (Kt) and the actomyosin complex (KO) were equal, the curve in Fig. 3 would be a straight line of unit slope. The plot shows appreciable curvature and reaches half of the maximum rate at 8 = 0.22 which corresponds to K8/K$ = 3.6. Experimental values of this ratio (Table I) ranged from with an average value of 2.7. Thus, the kinetic parameters predict a property of the system which has been regarded as strong evidence for the presence of extra intermediates (7,8). The actin concentration dependence of the ATPase activity calculated from these parameters does pass through a maximum value but the decrease in rate is only 1.5% at 0 = Even for S-1A1, which has the highest affinity for actin among the proteins examined, the decrease is much less than experimental error, up to a concentration of 300 p~ actin. However, the predicted concentration dependence does not fit a hyperbola, and this is consistent with the observed deviation of a double-reciprocal plot from linearity for acto-s-1al (Fig. 10). The difference in association constants Kz and K4 requires two-step dissociation of acto-s-1. The slower step has rate constant X but the extra dissociation is, at most, 10-15% of the magnitude of the total change. The slow step was observed here (Fig. 7), and in previous studies (16); however, agreement between the rate constant for dissociation and the value obtained from tryptophan fluorescence was not satisfactory. hile both rate constants increased with the degree of association, the values differed by as much as a factor of 2 in some experiments. Although the measurement of the rate constant of a small light-scattering signal is subject to large errors, the model can only be considered to be in qualitative agreement with experiments. The amplitude of the tryptophan fluorescence signal versus the degree of association is shown in Fig. 6. The dashed curve was calculated from the same set of rate constants at 20 "C and it does give a reasonable fit to the data. A smaller set of measurements was made at 10 "C, which permitted a higher degree of association to be examined, and there does appear to be a discrepancy in that the fluorescence signal is larger than predicted. In addition to experimental errors which are large at high concentrations of acto-s-1, there is some uncertainty in the interpretation of the fluorescence signal. The actual fluorescence enhancements for AM.T and AM.DPi are unknown and the calculated curve is based on the simplest assumption that the intrinsic enhancements of AM.T and AM. DPi are equal to the enhancements of M' T and Ma DPi, respectively. However, there appears to be an enhancement of 0.1 for the formation of the acto-s-1 complex (4) and the enhancement of AM. T could be correspondingly larger than that for M.T. In viewof these difficulties, it is safest to conclude that there is a small discrepancy among the observed amplitudes of the fluorescence signal and the phosphate burst and the calculated values for a four-state model. The model predicts V% = k5kl/(kl + 1) and Kt = (1/ + a)/( Kl + l), where v", K4)( Kl and Kt are the parameters which describe activation of the ATPase with S-1 in large excess over actin and a = KJK3. The experiments were carried out at a S-1-to-actin ratio which may still have underestimated the values. V% is 19 k 4 s-l for S-1A1, compared to 26 s-* calculated from the model, which constitutes reasonable agreement. However, the concentration de- pendence at an infinite ratio of S-l to actin gives Kt equal to 20 p ~ while, experimental values were at least twice as large. It is difficult to determine V% accurately because the large value of KF requires extrapolation to infinite S-1. The values of V% and V& couldbeused to determine kl since kl = V$V&/(V% - V&) whichgives a value of10-12 s-'. This approach was not followed because of fairly large errors in determination of V$ - V&, but the value of k, which gave the best fit to the transient data is in this range. The smaller amount of data on S-1A2 could be explained satisfactorily by the four-state model. The errors are larger because of weaker binding to actin. There does appear to be a real difference in the association constants, Kz and K4, for the two isozymes, which may be a consequence of interaction of the extra peptide of the A1 light chain with actin. The results obtained for smooth muscle acto-s-1 were significantly different from those for skeletal acto-s-1. The rate constants of the fluorescence transition and the hydrolysis step decreased slightly with the degree of association. The rate constant for cross-linked acto-s-1 was reduced by almost a factor of 2 compared to S-1 alone. The evidence could be approximately fitted by a four-state model. Since the limiting value of X for complete association is X = kl + +

11 11918 ATPase Mechanism of Skeletal and Smooth Muscle Acto-S-1 k5, the direct hydrolysis step for acto-s-1 must be slower than for S-1. The highest degree of association that could be reached was smaller than that for striated acto-s-1, and the variation in the phosphate burst and rate constant of hydrolysis was nearly a linear function of the degree of association over the accessible range. This data could be fitted by a fairly wide range of values for the three rate constants of a fourstate model. However, the experiments on cross-linked acto- S-1 allows the individual rate constants to be calculated from the values of X, B", and VM. The danger in basing a fit only on cross-linked material is that the reagent is not specific and the presence of S-1 which is cross-linked but not activated by actin would lead to an overestimate of the size of the phosphate burst. Therefore, the rate constants were determined by varying kl, kl, and k5 to obtain the best fit to noncrosslinked and cross-linked preparations. The theoretical curves (Fig. 4) are satisfactory for X but overestimate the size of the burst slightly. The values of the set of rate constants are: kl = 4.3 s-', k-l = 5.4 s-', k3 = 15 s-', k 3 = 10 s-', and k5 = 3 s-'. The values are not altered by more than 10% by using only the data from cross-linked acto-s-1. The concentration dependence of the steady-state rate calculated from these parameters is shown in Fig.4. The calculated ratio Ko/KV is The measured ratio is 1.5 f 0.2, which is in reasonable agreement. The general conclusion from this extensive series of measurements is that a four-state model provides a good approximation to the kinetic and steady-state behavior of acto-s-1 from striated or smooth muscle. In the case of striated muscle, more quantities were measured than are needed to fix the values of the kinetic parameters. Consequently, it was possible to rigorously test the model. The set of rate constants predicts the values of K8/Kv, two-step dissociation, the variation in amplitude of the fluorescence signal, and the difference in V& and V& at 20 "C. There may be a small discrepancy at 20 "C in the amplitude calculated for the fluorescence signal, depending upon the interpretation of intrinsic enhancements, but the discrepancy is probably significant at 10 "C. In the case of smooth muscle acto-s-1, only one independent prediction is made from the rate constants, namely, the value of KO/ Kv, and this prediction agrees with the measurements within experimental error. The values of the rate constants obtained from the data are determined by the model, since different values could be assigned to a particular transition if additional states are included in the model. The four-state model is a sufficiently good approximation that the values of the rate constants are significant, since they would not be greatly altered by adding extra states. Two general conclusions can be drawn from the results. First, a direct hydrolysis step must make an apprecia- ble contribution to the hydrolysis cycle for striated and smooth muscle acto-s-1. The calculated rate constant for hydrolysis is 3 times smaller and the equilibrium constant is also reduced by a similar factor for acto-s-1, compared to S- 1. This represents a very small perturbation of the hydrolysis step by the binding of actin. By comparison, the transitions induced by the binding of ATP, ADP, AMP-PNP, and the.dissociation of ADP.Pi and ADP.Vi, where V6 is vanadate ion, show perturbations on the order of in rate and equilibrium constants by the binding of actin (28). The calculated equilibrium constant of the direct hydrolysis step is less than 1 at low ionic strength, although it is probably somewhat larger at physiological ionic strength. It is a reasonable hypothesis that a step in the cycle which is involved in force generation will involve a change in structure of myosin which would in turn alter its interaction with actin. Hence, the rate and equilibrium constants of such a transition in solution should be perturbed by actin binding. In addition, the equilibrium constant for such a transition should be large in order to drive the reaction in the presence of mechanical forces. Therefore, it is unlikely that the hydrolysis step is directly coupled to cross-bridge rotation or force generation. However, the occurrence of direct hydrolysis at a rate comparable to that of the dissociated state is not by itself a strong argument against a model which assumes different orientations for AM.T and AM.DPi states. If the system is 50% associated, then a simple calculation from the rate constants shows that approximately one-third of the flux around the cycle occurs via the direct pathway. In a muscle lattice, the relative contribution of the direct pathway could be much smaller if rotation of the bridge does work against mechanical forces while the dissociation-hydrolysis-reassociation pathway permits rebinding to a different actin. The comparison of smooth and striated acto-s-1 suggests that there is a significant difference in the kinetic properties. The calculated rate constant of product release is much smaller for smooth uersus striated muscle (k5 = 3-4 s-l for smooth and s-l for striated acto-s-1 at 20 "C). hile smooth muscle S-1 may not be a good model system since it is not regulated, preliminary results with acto-hmm gave an even smaller ratio for k5/k1. A smaller value of k5 is expected since the cycling rate is smaller for smooth muscle. The low ratio of k5/kl for smooth muscle compared to skeletal muscle means that the product intermediate state has a relatively longer lifetime compared to the substrate intermediate state for smooth muscle versus striated muscle. This difference may be related to the physiological differences of greater economy in force production and a larger force per attached crossbridge (29). Stein et al. (7, 8) have concluded from kinetic measurements that two additional states are necessary to account for the ratio of KB to Kv. These authors obtained a larger phosphate burst and a larger tryptophan fluorescence signal for acto-s-1. hile the difference between their values and those reported here are small, they are sufficient to lead to a significant disagreement between their value of K@/KV and the value calculated from transient measurements using a four-state model. Measurements at 4 "C show a smaller value of K$ and a larger rat0 of V&/V& (21) which may not be consistent with a four-state model, although transient state measurements are not available to test this possibility. Studies by Sleep and Hutton (23, 30) of ATP dissociation from acto- S-1 and of oxygen exchange indicate that extra states are necessary. e do not conclude that additional states are absent or unimportant but rather that a four-state model provides a sufficiently good description of the transient and steady-state mechanism that the properties of transitions between additional intermediates cannot be inferred from our data. A six-state model has four additional kinetic parameters which are not fixed by the data. Stein et al. (7,s) introduced plausible assumptions to determine the unknown rate con- stants and interpreted their evidence in terms of an additional AM. DPi and M.DPi state. In our case, it would be equally plausible to introduce an additional AM.T and M. T state to account for the small discrepancy in the amplitude predicted for the tryptophan fluorescence signal (Fig. 6). A more direct method for detecting additional intermediates is required. Evidence for an additional transition between nucleotide triphosphate states and probably also between nucleotide diphosphate states in the cycle has been obtained by employing the fluorescent ligands, 1-N'-ethenoadenosine nucleotide triphosphate and diphosphate (31).

12 ATPase Mechanism of Skeletal and Smooth Muscle Acto-S Acknowledgment-e wish to thank Aldona Rukuiza for her tech- 16. Marston, S. B., and Taylor, E.. (1980) J. Mol. Biol. 139,573- nical assistance Taylor, R. S., and eeds, A. G. (1976) Biochem. J. 159, Chalovich, J. M., and Eisenberg, E. (1982) J. Biol. Chem. 257, REFERENCES Lymn, R.., and Taylor, E.. (1971) Biochemistry 10, Eroehlich, J. P., Sullivan, J. V., and Berger, R. L. (1976) Anal Biochem. 73, Bagshaw, C. R., and Trentham, D. R. (1974) Biochem. J. 141, 20. Vennard, J. K., and Street, R. L. (1975) Elementary Fluid Me chanics, pp ,a. iley and Sons, New York 3. Chock, S. P., Chock, P. B., and Eisenberg, E. (1976) Biochemistry 21. Eisenberg, E., and Kielley,.. (1972) Cold Spring Harbor 15, Symp. Quant. Biol. 27, Johnson, K. A., and Taylor, E.. (1978) Biochemistry 17, Rosenfeld, S. S., and Taylor, E.. (1982) Biophys. SOC. Abstr ,43a 5. Taylor, E.. (1977) Biochemistry 16, Sleep, J. A., and Hutton, R. L. (1978) Biochemistry 17, hite, H. D., Taylor, E.. (1976) Biochemistry 15, Stein, L. A,, Schwarz, R. P., Jr., Chock, P. B., and Eisenberg, E. 24. agner, P. D., and eeds, A. G. (1979) Biochemistry 18, (1979) Biochemistry 18, Stein, L. A., Chock, P. B., and Eisenberg, E. (1981) Proc. Natl. 25. Greene, L. E., Sellers, J. R., Eisenberg, E., and Adelstein, R. S. Acad. Sci. U. S. A. 78, (1983) Bi~~hemistry 22, Chock, S. P., and Eisenberg, E. (1979) J. Biol. Chem. 254, agner, P. D., Slater, C. S., Pope, B., and eeds, A. G. (1979) 3235 Eur. J. Biochem. 99, Taylor, E.. (1979) CRC Crit. Reu. Biochem. 6, Inoue, A., Ikebe, M., and Tonomura, Y. (1980) J. Biochem. 88, 11. Marston, S. (1978) FEBS Lett. 92, Mornet, D., Bertrand, R., Pantel, P., Audemard, E., and Kassab, 28. Goodno, C. C., and Taylor, E.. (1982) Proc. Natl. Acad. Sci. U. R. (1981) Nature (Lond.) 292, S. A. 79, Geeves, M.A., and Trentham, D. R. (1982) Biochemistry 21, 29. Butler, T. M., Siegman, M. J., and Mooers, S. U. (1983) Am. J Physiol. 244, Trybus, K. M., and Taylor, E.. (1982) Biochemistry 21, Sleep, J. A., and Hutton, R. L. (1980) Biochemistry 19, eeds, A. G., and Taylor, R. S. (1975) Nature (Lond.) 257, Rosenfeld, S. S., and Taylor, E.. (1984) J. Biol. Chem. 259,