Kinetic Studies on the Association and Dissociation of Myosin Subfragment 1 and Actin*

The reactions of pyrene-labeled actin with myosin subfragment 1 (Sl) and S1-ligand complexes at low ionic strength are described by the schemes where M refers to a myosin head; A is actin; L is ligand; the asterisk refers to a high fluorescence state of actin; and K1 and K3 are association constants. K1 is reduced approximately 10-fold for “ADP or Mopyrophos- phate versus M alone. The rate constant of the isomerization step (k2) is 150-200 s” for A*M, A*M*ADP, and A*M-pyrophosphate (20 “C). The interaction between the ligand the actin binding sites reduces Kz from 2,000 for A*M to 50-100 for A*M*ADP and to approximately unity for A*M-pyrophosphate. The A*M*ADP state is equated with the AM’sADP state of Sleep and Hutton (Sleep, J., A., and Hutton, R. L. (1980) Biochemistry 19, 1276-1283). The actomyosin ATPase cycle been studied extensively basis for models of muscle contraction and motility The mechanism is usually represented by a two-line “linear” scheme. A somewhat simplified form of the scheme is

different conformations to the strongly (Ka, Kd) versus weakly (Kb, Kc) bound states (5) or by postulating intrinsic conformations of myosin or myosin-nucleotide complexes which are weakly or strongly bound to actin (6,7). Force generation or movement is generally attributed to the change(s) in conformation of the actoymyosin complex which accompanies the dissociation of phosphate and ADP. At least in the case of ADP an isomerization appears to precede the actual release of the ligand (8). In previous studies it was shown that the binding of S1' to actin is also a two-step reaction (9), which means that the actin-S1 complex undergoes an isomerization even in the absence of nucleotide ligands. The reaction has been studied further by Geeves and collaborators using pyrene-labeled actin (10,11).
The occurrence of isomerization steps for actomyosin and actomyosin-ligand complexes affects the interpretation of the actin association constants in Scheme 1. K. is the product of the two equilibrium constants for the formation of an initial complex and an isomerization whereas Kb and Kc refer only to the initial complex. It is an attractive hypothesis that the association constant for the initial step in myosin binding is equal to Kb or Kc. Unfortunately Kd has been given different meanings depending on whether the authors are referring to the initial complex (2, 8,9) or to the overall equilibrium (5, 12). These ambiguities can be avoided by using a three-line mechanism as discussed by Geeves et al. (7) in which an initial complex with actin is assigned to all of the myosin and myosin-ligand states, but the simpler formulation will be retained here.
The present study was undertaken to characterize the initial binding and the isomerization steps in the interaction of myosin and myosin-ligand complexes with actin. It is shown that the isomerization step has similar rate constants for myosin and myosin-ligand complexes, but the equilibrium constant is reduced by interaction with ligand. The initial complex formed between actin and M. D is identified with the AM' .D state proposed by Sleep and Hutton (13). On this basis the steps in product release are reevaluated.
The labeled F-actin was stored at a high protein concentration in a low ionic strength buffer (10 mM NaCI, 3 mM PIPES, pH 7, 1 mM MgCl,, 0.1 mM CaCl,, 2 mM dithiothreitol). The polymer was less stable than unlabeled actin under these conditions. Depolymerized actin was removed by sedimentation and resuspension. For solutions stored for several days, depolymerization was largely prevented by adding MgATP at intervals in a 1:l ratio to protein. Free nucleotide was removed by overnight dialyses before use. In some experiments in which the binding of S1 was measured at a low ratio of SI to actin the presence of nucleotide in the actin solution could affect the results. Nucleotides were removed by two cycles of batch adsorbtion of the actin stock solution with Dowex 2. In this case the actin was used immediately after dilution since there was appreciable depolymerization in 30 min at concentrations less than 5 p~. Fluorescence and 90" light scattering were measured in the stopped flow apparatus described previously (4). Fluorescence excitation and emission wavelengths are isolated using interference filters (365 nm excitation and 405 nm emission for pyrene; 295 or 310 nm excitation and 410 nm emission for etheno-ADP). The data collection and analysis system was modified during the course of these experiments.
where a, is positive and a2 is negative. The first exponential term arises from the lag in passing through the A*M state. Data were fitted to a lag plus the main exponential term as shown in Fig. 1 of the observed rate constant on concentrations was calculated from the values of k,, k-l, and kz, and these values were adjusted if necessary to improve the fit to the experimental curve.
The apparent rate constant of dissociation, kd, as determined by trapping free M with excess unlabeled actin, is obtained from the same equation by letting k,M approach zero. In this case, the square root can he expanded to give X p = kd = k-1 k-,/(k-l + k2 + k-2). The ratio kJkd gives the overall equilibrium constant Kl(K2 + 1).
The association of actin and myosin measured by light scattering fits the same equation as the fluorescence signal with the same rate constants X1 and X2 except that both states contribute to the increase in light scattering, al and a2 are negative, and the time course fits two exponential terms.
The reactions of SI-ligand complexes with actin, in which the ligands are ADP, AMP-PNP, and pyrophosphate were analyzed in terms of the scheme 1/K, = ka/k--3 is the dissociation constant for the first step in the binding of ligand to AM (greater than 0.2 mM). The relation between the observed rate constant and the individual rate constants is the same as for the binding of S1 under conditions such that ligand dissociation is irreversible (L << 1/K-3) and k3 >> 122. In other cases the equations were modified as described in the text.

RESULTS
Formation of the Actin-SI Complex-The rate of complex formation was measured by the increase in light scattering and by the decrease in actin fluorescence. At low ionic strength (15-20 mM) the fluorescence signal fitted a single exponential term after a very short lag phase of 2-3 ms. The time course of a fluorescence transient is shown in Fig. 1, which is typical of the signals obtained for the binding of S1 or S1. ADP to actin. The curve obtained by fitting the data to a lag plus one exponential term is also drawn in the figure, but it is distinguishable from the experimental curve for only the first 1-2 ms. The light scattering signal did not show a lag phase and gave a satisfactory fit to a single exponential term which agreed approximately with the value obtained by fluorescence.
Increasing the concentration of S1 increased the apparent rate constant of the fluorescence signal, but a maximum rate of approximately 200 s" was attained at high S1 concentrations (Fig. 2). The amplitude of the observed fluorescence change decreased slightly in accord with the prediction from the rate constant and the dead time of the apparatus. Most FIG. 2. Apparent rate constant for the binding of S1 to labeled actin as a function of S1 concentration. Conditions: 20 "C, buffer as for Fig. 1 except no ADP; the S1 to actin molar ratio was 10 or larger except for the lowest S1 concentration for which the ratio was 5. The apparent rate constant is the value obtained by fitting data to a lag plus a single exponential term as illustrated in (1) (2) of the increase in light scattering was lost in the dead time of the apparatus (1.5 ms) at high S1 concentrations, but the remainder of the signal gave approximately the same rate constant as the fluorescence signal. The results are consistent with the scheme

A * + M -A * M + A M
in which there is no measurable change in fluorescence in the formation of the initial complex as already described in Geeves and associates (10). The rate constant of the lag exceeds 1000 s-l at high S1 concentrations, which would lead to the loss of most of the light scattering signal. The data shown in Fig. 2 do not fit a hyperbolic dependence of the observed rate constant on S1 concentration. Therefore the concentration at half-maximum rate does not measure the association constant Kl. The maximum value of the apparent rate constant is kz + k+, which is essentially kz since k-2 is very small. kl and k l were calculated by the procedure described under "Kinetic Equations." The values are 8 x lo7 M" s-' and 50 s-' for the experiment shown in Fig. 2.  Tables I and 11.
The association reaction was also examined by varying the actin concentration at an actin to S1 ratio of at least 51. The relative signal amplitude is much smaller than for the experiments with S1 in excess, and a correction was made for bleaching of the fluorescence. The behavior was similar and gave a maximum rate of 200-250 s-'. Consequently, the observation that the reaction reaches a maximum rate is not explained by an interaction arising at high occupancy of the actin binding sites.
The apparent rate constant of dissociation of the actin S1 complex kd was measured by mixing labeled action-S1 with a 10-20-fold excess of unlabeled actin. The fluorescence signal fitted a single exponential term with a value of 0.025 f 0.003 s-' at very low ionic strength. The rate constant k-z was calculated from the relation kd = k-' k-z/(k-l + k~) , which gave a value of approximately 0.1 s-'. Therefore, Kz is 2,000. The value of kd increased with ionic strength, and at 0.1 M the value of 0.16 s-l is in reasonable agreement with 0.1 s-' given by Criddle et al. (10).
The value of kd for unlabeled actin was obtained by the reciprocal experiment of displacement of S1 from the normal actin431 complex by an excess of pyrene labeled actin. The rate constant was measured for a range of ratios of labeled to unlabeled actin from 2 to 8, and the limiting value was obtained by plotting the rate constant uersus the reciprocal ratio. The value was 30% smaller for normal actin than for labeled actin.
The modification of actin by labeling with a bulky pyrene group may be expected to affect the association with myosin. The value of k. measured by light scattering was approximately equal for normal and labeled actin, but the maximum rate could not be determined accurately. Criddle et al. (10) estimated that the association constant was reduced by less than a factor of 2 by labeling of the actin.
The quantity ka is equal to klkZ/(k-' + kz). If kl and k 1 are unchanged but kz is twice as large for normal actin, then k.
would increase by only 10-20%, which is consistent with the finding that k. is similar for normal and labeled actin. Since k d = k-lk-z/(k"l + kz) a 2-fold increase in kz would reduce the value of kd by 30% to 50% for normal actin if k-2 remained unchanged. Therefore the perturbation by labeling is consistent with at most a 2-fold reduction in kz with very little change in the other rate constants.
The observed quantities k, and kd give the value of the The relationship is not sensitive to the number of steps in the mechanism. The values of the individual constants Kl and K2 are subject to the errors introduced in fitting individual rate constants, but the overall association constant of 2 x lo9 M" is obtained directly from the observed quantities. The binding of Sl(A2) to actin gave similar values for the kinetic constants. The association constant was reduced by a factor of 3 primarily by an increase in k 2 . Cleavage of the S1 heavy chain by trypsin into the 25-,50-, and 20-kDa segments reduced the association constant by 6-7-fold but had little or no effect on the isomerization step (kz). The concentration dependence did not deviate sufficiently from a hyperbola to permit fitting of kl and k-, separately. From the approximate relation, k, = Klkz, the value of Kl was reduced about 10-fold by tryptic digestion.
The association constant of Sl(A1) to regulated actin in the presence of calcium ion was increased approximately 7fold compared with nonregulated actin. Since the ionic strength was higher in the experiments with regulated actin  Tryptic S1 refers to S1 digested to give 25-, 50-, 20-kDa polypeptide chains. S1 to actin ratio was at least 8 1 . The fluorescence signal was fitted by a single exponential term plus a short lag phase except for measurements at 155 mM which gave a deviation from one exponential. k. is the initial slope of the plot of observed rate constant versus S1 concentration. Apparent dissociation constant is the rate constant obtained for dissociation of pyrene-labeled actin-S1 in the Dresence of excess unlabeled actin: the eauilibrium constant is k,lkd.   Table I. Rate constants k, and k-, were fitted to data as described under "Kinetic Equations"; k-* = kd (1 + k2/k-,). At higher ionic strength and low temperature the concentration dependence fitted a hyperbola, and kl and k-I could not be determined. To obtain k-, at higher ionic strengths it was assumed that k , decreased and k-l increased by the same factor with increasing ionic strength. the increase in binding constant is closer to 10-fold at the same ionic strength in agreement with the findings of Geeves and Halsall (16). The rate constant of the isomerization step kZ was not affected; the main difference was a 3-4-fold reduction in k-, . A significant result of this series of experiments is that the rate constant k, of the isomerization step is essentially constant for Sl(Al), Sl(A2), tryptic-digested S1 and for the addition of regulatory proteins to the actin.
This rate constant has a large temperature dependence as might be expected for an isomerization step. At 6 "C the rate constant kz was reduced to 25 s-'. The concentration dependence gave an approximate fit to a hyperbola. The value of Kl was reduced 2-3-fold. Although kl and k-, could not be determined separately in this case the results are consistent with a small decrease in kl and increase in k-l. The large decrease in k, arises from the increase in the ratio of k l to kp, since k, Increasing the ionic strength decreased k,, and the concentration dependence gave an increasingly better fit to a hyperbola. In 55 mM ionic strength Kl was reduced by 10-fold. kz increased slightly with ionic strength. At ionic strengths larger than 100 mM the fluorescence signal no longer gave a satisfactory fit to a single exponential term. At 155 mM ionic strength the rate constant of the main component extrapolated to a maximum rate of 350 f 50 s-', but 30% of the amplitude fitted a second exponential term with maximum rate constant of 80 s-'. A sequential mechanism is not consistent with both rate constants showing a dependence on S1 concentration. If S1 were a mixture of two different states at high ionic strength and the transition between these states had a smaller rate constant than the effective rate of binding to actin, the concentration dependence could be explained. However, this possibility was eliminated by mixing S1 at low ionic strength with actin at high ionic strength to give a final ionic strength of 155 mM. Both rate constants were observed, and the values were unchanged. The significance of a second rate process is not clear, and this aspect of the problem was not investigated further in the present work.
The main conclusions from investigating ionic strength effects are that the initial binding constant Kl is markedly reduced by increasing ionic strength whereas the isomerization step shows only a small dependence on ionic strength.
There was a small increase in kz and although kd increased, most of the change could be accounted for by the increase in k-I rather than k-*. =

kl/(l + k--l/kp).
Reaction of SI -Ligand Complexes with Actin-The reactions of SI-nucleotide and S1-pyrophosphate complexes with actin were investigated to determine the effect of the ligand on the rate and equilibrium constants of the mechanism established for the binding of S1 alone. The reaction has been studied previously using light scattering and fluorescent nucleotide analogues to determine the time course of association (2,8,17). The reaction was investigated using the change in pyrene fluorescence of labeled actin and compared with results obtained by light scattering. The kinetic behavior satisfied the same mechanism as the reaction with S1 alone. An extra step is added for the dissociation of the ligand where Kl and K3 are association constants, and k3 is the first order rate constant of ligand dissociation. The choice of ligand concentration in the S1 solution is a compromise. It has to be large enough to nearly saturate S1 because free S1 binds with a larger rate constant than S1ligand. However, it must be small enough to dissociate from actin31 to prevent step 3 from affecting the apparent rate constant of the binding reaction. The ligand dissociation constants are 1 p~ for SI, and 200-1000 WM for actin-SI. Ligand concentrations in the S1 solution before mixing were in the range of 10-40 pM in excess over the S1 concentration.
The reaction of S1-pyrophosphate or S1. ADP with labeled actin gave a short lag in the fluorescence signal, and the remainder gave a good fit to a single exponential term. The light scattering signal was fitted approximately by one exponential term, but an increasing fraction of the total signal was lost in the dead time of the apparatus as the protein concentration was increased (12). Thus the behavior is essentially the same as for the binding of S1; the formation of an initial complex by a rapid reaction is followed by an isomerization detected by the pyrene label (Fig. 1). The dependence of the rate constant on the S1-ligand concentration gave a better fit to a hyperbola than for S1 alone. Data for two different protein preparations are shown in Fig. 3. The results for S1. ADP (circles) could be fitted by hyperbolas giving maximum rate constants of 150-165 s-l and dissociation constants of 13-11 pM. The data points for S1-pyrophosphate are not significantly different than those of S1 .ADP and yield a maximum rate of 155 s-'. The average values are given in Table 111.
The reaction of S1.AMP-PNP with actin was complex. and S1-pyrophosphate to labeled actin as a Function of S1ligand concentration. Data are shown for two different protein preparations: 0, 0, S1.ADP (A, A) S1-pyrophosphate. Conditions: 5 mM PIPES buffer, pH 7, 20 "C, 10 mM NaCl, 2 mM MgC12, ligand concentrations before mixing S1-ligand with actin are 10-40 p~ in excess of S1 concentration. The S1 to actin ratio is 8 or larger except for the lowest concentration for which the ratio is 5. The two curves are hyperbolas fitted to the S1. The fluorescence signal fitted two exponential terms over a range of concentrations. The maximum rate for the faster process was 100 s-'. The reverse reaction, the dissociation of the actin-S1-ligand complex into actin and S1-ligand, was measured in order to determine the value of L 2 . In the case of pyrophosphate the rate of dissociation was measured as a function of pyrophosphate concentration. The rate constant measured by light scattering or pyrene fluorescence gave a hyperbolic dependence on pyrophosphate concentration, K3 = 2 X lo3 "' , and a maximum rate of 210 f 20 s-' from fluorescence and 275 f 40 s" by light scattering (data not shown). Since the rate of association of S1-pyrophosphate with actin fitted a hyperbola, k-' is larger than k2. An estimate of k 1 was made by assuming that kl has approximately the same value as for S1 alone (10' M-' s-I). From Kl = lo5 M-', the value of k 1 is approximately 500-1000 s-I. Therefore the maximum rate of dissociation is determined primarily by k 2 . The maximum rate constants obtained by extrapolation for pyrophosphate-induced dissociation and for S1-pyrophosphate binding are approximately equal to k-* and k2, respectively. However, these values are similar, and the observed rate constants also depend on k-J k2 for dissociation by pyrophosphate and k3/k-2 for Sl-pyrophosphate binding. Since the ratios are the order of 10 or larger, calculations based on the complete rate equation show that kp and k 2 are about 10% larger than the observed maximum rate constants (kp = 165 s-', k--P = 250 s-I). The results are summarized in Table 111. The values are in approximate agreement with equilibrium measurements (12) taking into account differences in ionic strength. The association constant of SI-pyrophosphate, Kl (1 + Kz), is approximately 1.5 X lo5 M-' at 10 mM ionic strength compared with 2 X lo4 "' at 80 mM from equilibrium measurements. The binding constant of pyrophosphate to actin-Sl is 2 X lo3 M" at 10 mM ionic strength uersus 0.4 X lo3 M" at 20 mM from equilibrium data. The rate of dissociation of S1. ADP from its complex with actin was determined by mixing labeled actin-S1 .ADP with excess unlabeled actin. We have reported previously an apparent rate constant of dissociation of S1 .ADP of 1-2 s" (2). Labeled actin31 at a concentration of 5 @I and range of MgADP concentrations from 1 to 4 mM was mixed with 40 PM unlabeled actin. The increase in fluorescence fitted a single exponential term. The apparent rate constant increased with MgADP concentration as expected since the reaction scheme is where A,, refers to normal (unlabeled) actin. The AM.D complex is essentially in rapid equilibrium with ADP, and the observed rate constant of the fluorescence signal is given by term in the first square bracket accounts for the dependence on MgADP concentration. The observed rate constant extrapolated to a value of 1.1 s" with an apparent dissociation constant l/K3 of 0.5-1 mM. As discussed above for Sl-pyrophosphate, k-' is expected to be approximately IO3 s-I, which gives for k-2 a value of 2 s" at an ionic strength of 15 mM. At 120 mM, k-2 is 4-5 s-', and l/K3 is approximately 2 mm.
The apparent rate constant can also be determined from the maximum rate of dissociation of actin-S1 by MgADP. The method can be used only at high ionic strength and low protein concentration for which nearly complete dissociation can be obtained. The MgADP solution was preincubated with 0.5 p M S1 to hydrolyze any ATP present. At 100 mM ionic strength the increase in fluorescence gave a reasonable fit to a single exponential term although 10-15% of the amplitude fitted a larger rate constant. The maximum rate was 4-5 s-' at 3 p~ actin. Measurements of the maximum rate over a

TABLE I11
Kinetic constants for S1 -ligand reactions with actin Conditions: 20  range of actin concentrations from 7.5 to 2.5 ~L M extrapolated to a value of 3-4 s" at 0 protein concentration. Although the experiment is subject to error from extrapolation and to the problem of rembving traces of ATP from the ADP solution the results confirm the value obtained by the displacement method.
The measurements of kz and k 2 yield an equilibrium constant of 50-100 for the isomerization step at very low ionic strength.
Comparison with Direct Measurements of ADP Dissociation from Actin-SI-The kinetic scheme may appear to contradict previous studies since kp determines the rate of ADP dissociation. The rate constant of ADP dissociation from an equilibrium complex with actin-S1 as measured by the rate of dissociation of the complex by ATP is larger than 500 s-' (18) whereas kz is approximately 150 s-'. However, K2 is approximately 100, and at equilibrium the complex is essentially in the AM. D state, in terms of the simple kinetic scheme. Thus the rate constant measured for the equilibrium mixture is k3 which is expected to be large. An estimate of the magnitude of k3 was made by mixing S1. ADP with labeled actin plus a range of Concentrations of ATP. The quenching of fluorescence in the formation of AM-D should be reversed at a rate determined by the dissociation of ADP and the binding of ATP to produce A* plus M-T. The fluorescence signal F, normalized to the value for the complete association of S1 The rate constant for the dissociation of the fluorescent analogue etheno-ADP was measured previously in a similar type of experiment in which S1. etheno-ADP was reacted with excess actin containing MgATP (8). This experiment should measure k2, but over the range of concentration from 15 to 70 p M actin the rate constant was approximately 400 s" (Fig. 1  There are a number of possible explanations of this discrepancy: a different rate constant for dissociation of etheno-ADP versus ADP; a different rate constant for normal versus pyrene-labeled actin; a difference in maximum rate for actin in excess versus S1 .ADP in excess; a different step in the mechanism is measured by the quenching of actin fluorescence versus etheno-ADP fluorescence.
Eight data sets are necessary to test these possibilities. The results are summarized in Table IV. The errors are large for some combinations that necessarily produce small signals against a large background and a correction has to be made for bleaching of the fluorophor. Rate constants obtained from the fluorescence change of pyrene actin reacted with S1 .ADP and S1 .ethene-ADP agreed within 10-20%. Etheno-ADP does not contribute to the change in fluorescence for excitation at 365 nm in the absence of acrylamide. However, with actin in excess the signal was fitted to one exponential plus a linear term to correct for bleaching. A deviation from a single exponential was also expected since measurements were made at an actin to S1 ratio of 4 in order to increase the relative change in fluorescence, and the reaction is not accurately first order. However, it is clear that ADP and etheno-ADP have essentially the same rate constant and that the rate constants for actin in excess are approximately the same as for S1 in excess.
The rate constant obtained from the quenching of etheno-ADP fluorescence was approximately twice as large for normal actin than for pyrene-labeled actin. The pyrene actin contributes a large background fluorescence which reduces the accuracy of the measurement. The experiment with normal actin in excess is in agreement with our previous results (8) except that the signal showed a small deviation from a single exponential term of about 10% of the total amplitude. In the previous study a deviation was found only at low temperatures.

TABLE IV
Comparison of rate constants of signals from etheno-ADP and pyrene actin Reaction: S1.ADP or S1-etheno-ADP mixed with actin or pyrenelabeled actin, 20 "C, pH 7, 10 mM NaC1, 3 mM PIPES buffer, 2 mM MgCl,, 20-40 g M nucleotide in excess of S1 concentration, actin or S1 in excess at concentrations of 25-40 FM. The observed rate constant is essentially equal to the maximum rate (k2). Molar ratio of the proteins was 4 in cases in which both fluorophors are present, which could cause a deviation of the signal from a single exponential term. The signal fitted a single exponential plus a lag phase for S1 in excess and pyrene actin. In other cases the signal was fitted by a single exponential plus a linear term to correct for bleaching. The fit to two exponential terms is also given in parentheses. For measurements of the change in etheno-ADP fluorescence 200 mM acrylamide was present. To measure the change in etheno-ADP fluorescence with pyrene actin in excess, 2 mM MgATP was present in the actin solution to prevent a change in fluorescence from pyrene actin. In the case of S1-etheno-ADP in excess reacted with pyrene actin; ATP could not be added, and approximately 30% of the signal amplitude was contributed by the pyrene actin. Excitation of etheno-ADP was at 295 or 310 nM, and emission was measured at 410 nm. Pyrene actin was excited at 365 nm, and emission was measured at 405 nm. Rate or S1-etheno-ADP. ATP was present in the actin solution in the earlier experiments (8) to block rebinding of etheno-ADP and also to reduce changes in light scattering by dissociating the actoS1 complex. This procedure gives a small improvement in the precision of the experiments, but the same values were obtained for the rate constants in the absence of ATP. It was omitted from this series of experiments in order to compare the two fluorescence signals under the same conditions. This series of measurements is consistent with the simple scheme in which a single isomerization is detected by the change in actin or substrate fluorescence. A difficulty in the interpretation of these rate measurements is that a small contribution from a second exponential term that has a 10 times smaller rate constant is difficult to separate from an approximately linear term arising from bleaching of the fluorescence. The rate constant fitted to the main signal will be larger if the data are fitted by two exponentials rather than one exponential plus a linear term. Consequently the value of the rate constant kz may be overestimated, and a value of 300 s-l will be assigned to the rate constant for normal actin.

DISCUSSION
Earlier studies (2,17) led to the proposal that the minimum kinetic scheme must include one isomerization of actin31 or actin-S1-ligand complexes where the asterisk refers to the high fluorescence state of actin, and Kl and K3 are association constants. The scheme accounts for most of the kinetic behavior. Although there are some deviations from the predictions of this model which will be considered below, the simple model permits all of the rate or equilibrium constants to be determined from the data. A comparison of the values for actin-S1 alone and for three ligands, ADP, pyrophosphate, and AMP-PNP, allows some generalizations to be made. For the binding of S1 alone Kl is large at low ionic strength (lo6 M-'), and kl is approximately lo8 M" s-'. The rate constant is in the range expected for a diffusion limited reaction of large proteins (19). However, electrostatic attractions in the binding site could increase k1 relative to the value for simple diffusion, and some structural changes in the initial complex cannot be ruled out.
Step 2 is an isomerization of the complex, detected by a change in environment of the fluorophor on Cys374 of actin. kZ decreased about 10-fold from 200 s" at 20 "C to 20 s-l at 6 "C but showed only a small increase with ionic strength.
The results indicate a conformational change of the actomyosin complex in the transition to the "rigor" state.
The binding of the ligands ADP, pyrophosphate, and AMP-PNP at the active site reduces the association constant Kl by about 10-fold to lo5 M-'. A value of 2 X lo5 M" was obtained for normal actin and S1.ADP (2) uersus 1.1 k 0.2 X lo5 "' in this work; consequently, K , may be reduced slightly by labeling the actin. In the case of ATP or reaction products bound at the active site, the association constant is 2-3 X lo4 M (4). K 1 for S1 and for S1 products (20) is reduced by a similar factor by increasing the ionic strength; consequently the electrostatic contribution to the association constant is probably not affected. The results do not support the hypothesis that the initial complex formed with S1 has the same affinity as the "weakly" bound states. Rather there is a set of binding constants for S1 and its complexes with ATP, reac-tion products, and ADP which covers a range of about 50fold.
Scheme 2 asserts that step 2 is a concerted change in structure which alters the environment of Cys374 of actin and of the base portion of etheno-ADP, two regions that are widely separated in the complex (21). It is difficult to test this interpretation by showing that the fluorescence signals from both labels give the same value of the rate constant because modification of the actin reduces the rate constant by up to a factor of 2. However within the limitations of the measurements both rate constants agree within 10-20% (Table IV) ED, where asterisks refer to high fluorescence states of actin and nucleotide and E refers to etheno, is that the rate constants measured for the two fluorescence signal are nearly equal, and a sequential process would lead to an appreciable lag in the second transition. Particularly in the case of the pyrene signal the measurement is made with high accuracy (see Fig. l), and the curve cannot be fitted by two sequential steps with similar rate constants. This is an important point, and further studies of this problem using a label on Cys707 of S1 (the "SH-1 sulfhydryl group) will be described elsewhere.
The rate constant of the transition (kz) is not greatly affected by ligands bound at the active site, which is some distance from the actin-S1 contact region. The interaction between the ligand site and the actin site is expressed primarily by the increase in k-z. The value of Kz at very low ionic strength is about 2000 in the absence of ligand, 50-100 for ADP, and somewhat less than 1 for pyrophosphate and AMP-PNP. If the dissociation of a c t i n 4 1 by ATP is described by Scheme 2, the value of K2 would have to be less than IO-' to account for dissociation.
Geeves (22)  and (kz + k-J decreased, and kd increased with increasing ionic strength, but the change was less than a factor of 2-3fold at an ionic strength of 65 mM compared with 15 mM. However, at higher ionic strengths the fluorescence transient for the association of S1 .ADP with actin deviated from a single exponential term. A satisfactory fit was obtained to one exponential plus a linear term, and a better fit was given by two exponentials. In either case, k,, is equal to or greater than lo6 M-' s-', and the maximum rate was 60-70 s" fitted to one exponential or 25 s-l and 100 s-l fitted to two exponentials. The disagreement between the stop flow results and the pressure relaxation results (24) is so large that the two experiments cannot be measuring the same process. In our earlier studies (2, 8 ) as well as in the present work, the effective rate of ADP dissociation has been shown to be large; consequently the slow step proposed by Geeves cannot be on the pathway described by Scheme 2. Although Scheme 2 is oversimplified and we cannot rule out a branch of the pathway which might account for the small change in association following the release of pressure, the very low value of k, and the linear dependence of the rate constant on protein concentration suggest that a very weakly bound intermediate state is responsible for the signal. For example, the value of k,, is approximately equal to the value for the association of the M. D. P complex with actin (20).
The proposal (22) that A*M.D dissociates slowly (k-, small) is not compatible with our data because of the much larger value we obtained for k,. A further complication is that in (22) k 1 was obtained from k d using the approximation that the isomerization step is in equilibrium ( k d = k-]/(1 + K z ) = k--lk"P/(kz + k J ) . If k-l is equal or greater than kz as appears to be the case, the complete equation ( k d = k-lk-?/(k-l + kz + k-*) should be used which leads to significantly different results.
An important question is whether the isomerization of A*M.D is a step in the hydrolysis cycle. Sleep  where an asterisk is added to their notation to indicate the relation to this study and we have retained the numbering for the steps measured here. AM.D and M.D are collision complexes in equilibrium with free ADP. We have already discussed the evidence that step 2 is a concerted transition to AM.D. The ADP reactions have to satisfy detailed balance; In a previous study the effective rate of product dissociation was calculated to be 80 s-' although the value is model dependent (4). Since k3 >> kz, the effective rate constant of product dissociation is k4k2/(k4 + k2). A value of 300 s" for kp gives roughly 100 s-l for k4. The value of KJK5 is 5-10. For these values of the constants A*". D will be present in much larger amounts during the cycle than at equilibrium as required by Sleep and Hutton. The scheme still retains the property that the apparent dissociation constant of actin is larger than the K,,, of actin activation of the ATPase (3,4).
The dissociation constant of phosphate ( K 4 ) is K a 1 / K 5 or roughly 500 mM (Ks is approximately 50 mM based on ATP t* Pi and Pi cf H 2 0 exchange measurements (13,23,24) and an equilibrium constant of three for the hydrolysis step for Sl). A value of 1 M can be calculated from data of Bowater and Sleep (25) for K2 = 100 and a hydrolysis equilibrium constant of three for actin-S1. The ATPase activity of crosslinked actin-S1 or myofibrils is barely inhibited by 100 mM of phosphate (data not shown) which is consistent with a value of K4 of at least 200 mM.
The scheme accounts for most of the kinetic and isotope exchange data, but it is not intended to be a complete description. Some kinetic studies of nucleotide association and dissociation cannot be explained by a single isomerization step (2,8,26), and a second isomerization might occur in the absence of nucleotide (9,11). Although the scheme explains the increase in rate of nucleotide dissociation from actin-Sjl (kz >> k7) by the coupling of this step to an isomerization of the actin-S1 complex, it does not explicitly account for the increase in rate of phosphate dissociation (k4 >> ks). A logical extension of the mechanism is to include a second isomerization to drive phosphate dissociation. Also the scheme would not explain the inhibition of tension in muscle by phosphate in the 5 mM concentration range (27), which implies that some intermediate has a phosphate dissociation constant in this range. If step 4 is expanded to include an isomerization followed by rapid dissociation of phosphate this requirement would be met. For example if step 4 is replaced by A*M".D.P -A*M'.D .P -A*M'.D + P an equilibrium constant of 100 for the isomerization step would give a dissociation constant of 5 mM for phosphate. In an isometric fiber the A*M' .D state is expected to accumulate, and a phosphate dissociation constant of 3 mM was obtained by Bowater and Sleep (25).
Two actin-Sl. ADP. P states have been invoked to explain steady-state properties (3), but the rate and equilibrium constants are different from those needed to explain phosphate binding to fibers. The similarity in kinetic properties for the binding of myosin uersus myosin-ligand complexes suggests that formation of an initial complex followed by one or more isomerization is an intrinsic property of the mechanism. The isomerization step or steps presumably corresponds to the change in structure of the complex which produces motion or tension. The isomerization of A*". D is a global conformation change which is detected by labels placed in various regions of the complex. The isomerization of this state to give the rigor complex may contribute to tension. However, the A*M' .D state is probably itself a tension-generating state, and further evidence is needed to define the steps from the product intermediate state to A*". D.