Analysis of the Interaction of Rabbit Skeletal Muscle Adenylate Deaminase with Myosin Subfragments A KINETICALLY REGULATED SYSTEM*

The interaction of rabbit skeletal muscle adenylate deaminase with myosin fragments (heavy meromyosin and subfragment-2) has been studied by analytical cen- trifugation, gel chromatography, and stopped flow light scattering. Formation the complex is highly cooperative with respect to addition of two molecules of adenylate deaminase/molecule of myosin fragment to form a ternary complex. complex formation is subfragment-2. pH 6.5, the dissociation constant for the heavy mero-myosin-deaminase complex is approximately the constants binary complexes deaminase heavy determined. anal- ysis the light while the in cells using an rotor at 20 In experiments performed on system of deaminase one myosin subfragments, schlieren determine of

The interaction of rabbit skeletal muscle adenylate deaminase with myosin fragments (heavy meromyosin and subfragment-2) has been studied by analytical centrifugation, gel chromatography, and stopped flow light scattering. Formation of the complex is highly cooperative with respect to addition of two molecules of adenylate deaminase/molecule of myosin fragment to form a ternary complex. Ternary complex formation is also highly pH-dependent with less complex formed at higher pH values, and the pH dependence is steeper with heavy meromyosin than with subfragment-2. At pH 6.5, the dissociation constant for the heavy meromyosin-deaminase complex is approximately 1.2 X M'. Over the pH range 6.5-7.0, rate constants for the formation and dissociation of both the ternary and binary complexes of adenylate deaminase with heavy meromyosin have been determined. From analysis of the time course of stopped flow light scattering, the association steps are found to be extremely rapid, while the rate constant for dissociation of the first molecule of adenylate deaminase from the ternary complex is quite slow. This rate constant increases as the pH increased, but is sufficiently low that the interacting system does not equilibrate on the time scale of mass transport experiments (sedimentation velocity and gel chromatography), and thus displays apparent "slow" behavior.
The kinetic regulatory properties of adenylate deaminase are influenced by heavy meromyosin and subfragment-2, particularly with respect to inhibition by GTP. The association and dissociation of adenylate deaminase and myosin fragments and the resultant changes in kinetic properties of the adenylate deaminase can markedly alter the time course of the enzymatic reaction. The time scale over which this interaction is modulated by changes in pH may have significance in the metabolism of exercising muscle.
Adenylate deaminase (AMP aminohydrolase, EC 3.5.4.6) is abundant in vertebrate skeletal muscle and has long been recognized as the enzyme responsible for ammonia production in exercising muscle (1). The exact physiological role of the enzyme is not yet clearly understood, although suggestions relating to its role include the control of glycolysis either by activating phosphofructokinase and pyruvate kinase by the ammonia produced (as shown in yeast (2)) or by altering nucleotide levels (AMP, IMP, ATP) which, in turn, influence the behavior of important regulatory enzymes. It is of interest that the muscle isozyme appears to be lacking in some individuals who experience muscle cramping following exercise (3), although other isozymes of the enzyme may be present in sufficient amounts to prevent serious effects. Thus, the clinical picture of these patients appears to be quite variable (4).
Since the enzyme is ubiquitous in all higher organisms, it would certainly appear to function in an important role in metabolism. Particularly important, however, with respect to muscle metabolism is the observation that adenylate deaminase is a dynamic component of the thick filament of vertebrate skeletal muscle. The deaminase binds to myosin, HMM,' and subfragment-:! (5), as well as to synthetic (6) and natural (7) thick filaments and has been found, by double immunofluorescence studies (8), to bind to the ends of the A band in isolated myofibrils and myotubes grown in culture. In the present paper, we will characterize the binding of adenylate deaminase to heavy meromyosin (and subfragment-2) and show that it is a highly cooperative process dependent on pH. We have determined the rate constants for the process and will show that these can be characterized as representing a "slow" protein:protein interaction. Thus, the results are of interest with respect to mass transport properties (e.g. sedimentation velocity, gel chromatography) since most treatments of those properties assume rapid equilibration.
In addition, as indicated above, adenylate deaminase is a highly regulated enzyme whose activity is influenced by purine nucleotide binding to both inhibitory and activating sites (9). While the activity of the enzyme in the absence of effectors is not affected by binding to myosin fragments, we have shown that the kinetic behavior with respect to these effectors (Le. GTP, ADP) is influenced by the interaction of the deaminase with subfragment-2 (9). We will show similar behavior with heavy meromyosin and explore this relationship to show that a time-dependent response of activity to effector binding (nucleotide and myosin) may also be important in the regulatory behavior. The overall picture which emerges is one of a highly complex regulated enzyme system.

MATERIALS AND METHODS
back and hind leg muscle of New Zealand White rabbits according to Protein Preparation-Adenylate deaminase was prepared from the the protocol of Smiley et al. (10). The native enzyme molecular weight is about 300,000. Polyacrylamide gel electrophoresis in the presence of sodium dodecyl sulfate shows multiple bands when frozen muscle was used as specified in the original protocol (lo), with two major bands of apparent M, = 80,000 and 75,000. We obtain a more homogeneous preparation when a rabbit is killed each time that the enzyme is prepared and when protease inhibitors are included (0.5 mg/ml of soybean trypsin inhibitor, 1 mM benzamidine, 1 mM phenylmethylsulfonyl fluoride). The adenylate deaminase preparations using fresh muscle generally show only a single band of apparent M, = 80,000, in keeping with the observation (11) that the rabbit muscle enzyme undergoes progressive fragmentation with storage. The four subunits of the native enzyme are probably identical.
Myosin was prepared by the method of Holtzer and Lowey (12). S-2 was prepared with soluble papain, following the technique of Lowey et al. (13). The tryptic and chymotryptic HMM subfragments were prepared according to the protocols of Lowey et al. (13) and Lowey and Cohen (14), respectively. Both forms of HMM were purified by ion exchange chromatography on diethylaminoethylene-cellulose (Whatman DE52), with a gradient between 0 and 0.5 M KCI. The HMM, which elutes as a sharp peak at a KC1 concentration of 0.14 M, was fractionated with ammonium sulfate, and the fraction precipitating between 43 and 55% saturated ammonium sulfate was used in experiments. The results in this study apply to both tryptic and chymotryptic HMM.
Analytical Ultracentrifugation-Analytical centrifugation was performed with a Beckman-Spinco model E ultracentrifuge. Sedimentation velocity experiments were carried out in 30-mm double sector cells using an An-E rotor at 20 "C. In experiments performed on the interacting system of adenylate deaminase and one of the myosin subfragments, the schlieren patterns were often complex, with up to three overlapping peaks. To determine the distribution of material among the boundaries, the schlieren curves were resolved by manual planimetry using tracings of projected enlargements (on a Nikon microcomparator) of the developed photographic plates. The resolved peak areas were corrected for radial dilution, and their transitions as a function of pH were analyzed in terms of an Adair-type transition, where the fractional transition, 8, is related to the coefficient of cooperativity, n, according to: Sedimentation equilibrium experiments were conducted with an An-H rotor using 10-mm cells equipped with Yphantis-style centerpieces. To prevent thermal convection during sedimentation equilibrium, the rotor temperature control unit was not used. These runs were thus performed without using the heating element, and the rotor temperature was allowed to equilibrate under refrigeration at between 5 and 12 "C. The partial specific volume of adenylate deaminase was taken as 0.731 (15) and that of HMM was assumed to be 0.728 (16). The molecular weight of S-2 was assumed to be 62,000.
Gel Chromatography-A column (30 X 1 cm) containing Sephacryl S-300 was equilibrated with buffer, and a protein sample of 0.4 ml was added to the top of the column and run as a small zone through the gel at a flow rate of 0.1 ml/min. Fractions of 0.26 ml were collected, and aliquots were assayed for adenylate deaminase and/or ATPase activity (measured as inorganic phosphate release).
Stopped flow Experiments-Data were acquired with a Durrum D-150 stopped flow spectrophotometer using a 75-watt xenon arc lamp as the light source. The photomultiplier signal was recorded with a digital oscilloscope, on line to a Digital Equipment Corporation VAX-11/780 computer. For enzymatic assays, the signal from the photomultiplier was converted to optical absorbance units. For kinetic light scattering experiments, the phototube was positioned at either 0 or 90" to the incident beam and the signal was converted to transmission units. For measurements of scattering at go", a light scattering stopped flow cuvette was used in which the tangential face of a 2-cm path length quartz cylinder was monitored from above. The reservoir syringes of the stopped flow device were maintained at 20 "C in a water bath. Adenylate deaminase activity was measured at 265 nm using the difference in absorbance of AMP and IMP under conditions indicated in the figure legends. The enzyme concentration was sufficiently high (H.01 mg/ml) so that no inactivation occurs over the time course of the experiment. Light scattering experiments required protein concentrations on the order of 1 mg/ml. Kinetic Sirnulotion-The full time courses of stopped flow experiments were analyzed using a computer method for simulation of reactions (17). The simulation system accepts a user's specification of a chemical reaction, typed in conventional chemical format, derives the tables of coefficients required for the kinetic differential equa-tions, and performs numerical integration of the equations. The user may also specify complex expressions for the output of the simulation. In the case of light scattering data, the output expression used gave the instantaneous weight average molecular weight of the system, offset and scaled. The application has previously been described (17).
Chemicals-Nucleotides were obtained from Sigma. All other compounds used were reagent grade.

RESULTS
Sedimentation Studies-We have shown previously (5) that adenylate deaminase binds to heavy meromyosin and subfragment-2, but does not bind to subfragment-1 (which contains the ATPase activity of myosin). We had previously found that at pH 6.5 in 0.15 M KC1 and 0.01 M imidazole buffer (20 "C), the stoichiometry with which adenylate deaminase binds HMM is 2:l (mol/mol). When a mixing ratio of 2:1 is used, sedimentation velocity patterns show (as previously reported (5)) a new peak with a sedimentation coefficient of 20 S. Fig. 1 shows that at any mixing ratio other than 2:1, a 20 S peak is observed as well as a slower peak which has the sedimentation coefficient of whichever species is present in excess of the 2:l stoichiometry (s& for HMM = 7.1 S, for adenylate deaminase = 12.0 S ) . Analysis  These results indicate that little or no 1:l complex is formed. Similar results are obtained when S-2 is substituted for HMM. It is of interest that the sedimentation coefficient for the deaminase:S-2 complex is approximately the same as that of the deaminase:HMM complex.
Sedimentation equilibrium experiments were performed to confirm that the molecular weight of the complex was that expected from a 2:l stoichiometry. The results were analyzed using the omega function of the concentration distribution of an interacting system (18). The experimental results (not shown) indicate no significant heterogeneity and, even in the presence of excess HMM, no significant amount of complexed species of molecular weight below that expected for a 2:l stoichiometry. However, further interpretations must be made with caution since there was an indication of material of higher molecular weight than expected, suggesting a small amount of a higher molecular weight aggregate. We believe, however, that the amount of higher aggregate is so small as not to influence any of the data analysis to be described below. In sedimentation equilibrium experiments on the individual proteins, the molecular weight of HMM was found to be 340,000 k 5,000, while that for deaminase was found to be 300,000 k 10,000 (data not shown).
Based on these observations and those presented below, we believe the reaction of adenylate deaminase and myosin subfragment to be where M is the myosin subfragment and A is adenylate deaminase. Furthermore, the results imply a high degree of cooperativity with respect to the binding of the 2 mol of deaminase.
Kinetic Studies of the Deaminase:HMM and Deaminase:S-2 Interaction-In order to determine rate constants for the steps shown in Mechanism I, the kinetics of the association and dissociation processes (Mechanism I) were studied by light scattering changes using a stopped flow apparatus (as described under "Materials and Methods"). To correlate the observed scattering changes with molecular weight changes,  Table I. Molecular weight values used were 300,000 for adenylate deaminase and 340,000 for HMM. Since the syringes of the stopped flow apparatus are of equal volume, the initial concentrations prior to mixing were 2-fold larger.
by guest on July 8, 2020 http://www.jbc.org/ Downloaded from the light scattering change for complete dissociation but also shows that between 300 and 500 nm the scattering change is proportional to X-4, suggesting that the change is, in fact, due to light scattering. It can also be shown that the light scattering change at 300 nm due to dissociation by phosphate is directly proportional to the total protein concentration (Fig.  2).
The top of Fig. 3 shows the light scattering changes associated with mixing adenylate deaminase and HMM at two different deaminase:HMM ratios. Also shown is the observed dissociation of the complex by a 2-fold dilution. The middle and bottom of Fig. 3 show similar data at pH 6.7 and 7.0, respectively. The solid lines given in the figure are those obtained using the mechanism given in Mechanism I with the stimulation method described under "Materials and Methods." The rate constants obtained from the fit of the real data are shown in Table I. Values of k,, and k-2 are uniquely determined from experiments of the type shown in Fig. 3. The values of k-, and k+2 shown are consistent with the values of k,, and k-2 used and give the best fit to the experimental data. For example, in order to fit the data, k+:! can not be less than k+, and therefore was chosen as equal to k+,. k-I can then be determined reasonably well from the data. These values will be discussed below (see "Discussion").
It can also be seen in Fig. 3 that the extent of the light scattering change decreases at the higher pH values. This observation suggests that the degree of interaction between adenylate deaminase and HMM is pH-dependent. In order to study this dependence, we performed sedimentation velocity experiments at a deaminase:HMM ratio of 2:l in 0.15 M KCl, 0.01 M TES buffer (20 "C) from pH 6.8 to 7.9. At each pH, a duplicate sample was run in the presence of 0.01 M phosphate to show the pattern of the completely dissociated material. Fig. 4 shows the patterns observed at four pH values in the presence and absence of phosphate. It can be seen that at the intermediate pH conditions, three peaks are obtained. Fig. 5 shows the pH dependence of the peak areas. The curves drawn through those data with HMM and using Equation 1 show the transitions expected for an Adair-type titration with an apparent pK for the dissociation of around 7.55 and a value of n = 2. The results of similar experiments using S-2 over the pH range of 6.5-7.3 are also shown in Fig. 5. The curves drawn through the data with S-2 are those expected for a transition with a pK of 7.0 and a value of n = 1 (see Equation 1). These results not only indicate that HMM binds adenylate deaminase more tightly than does S-2 over this range of pH but that the dissociation of the deaminase:HMM complex involves two protons, while that for the deaminase:S-2 complex involves only a single proton. At each pH value shown in Fig. 5, the loading molar ratio of adenylate deaminase to myosin subfragment was 2:1 and at each pH, regardless of how much complex is formed, the areas of the slow sedimenting peaks indicate a 2:l molar ratio of free adenylate deaminase to myosin subfragment. However, at all pH values where the complex is formed, there are 2 mol of deaminase bound per mol of either HMM or S-2.
The results of the sedimentation and light scattering ex-

Rate constants used in simulations
Simulations were using Mechanism I, with data shown in Fig. 3.  Fig. 4 for adenylate deaminase and HMM, and the curves drawn with solid symbols are from corresponding experiments using S-2 in place of HMM. Squares represent the area of the fast boundary, relative to the total area for the sample. Triangles represent the relative area of the 12 S peak (ascribed to adenylate deaminase), and circles represent the relative area of the peak ascribed to the myosin subfragment. Dashed and solid lines indicate the titration curves for Adair-type titrations using Equation 1 with n = 1 (for S-2 experiments) and n = 2 (for HMM experiments).
periments suggest that the binding of two deaminase molecules/HMM molecule is a highly cooperative process at pH 6.5, 6.7, or 7.0. In this regard, it was of interest that the sedimentation velocity experiments showed three clearly resolved peaks in the sedimentation pattern. Such behavior is not expected for a system of the type shown in Mechanism I if the protein:protein interactions reflect rapid equilibrium processes even when there is cooperative binding.' In order to examine the question of rapid or slow equilibration of the proteins, zonal gel filtration experiments were performed. The result of one such experiment is shown in Fig. 6. In this case, deaminase and HMM were mixed at pH 6.8 and passed as a small zone through a column of Sephacryl s-300. It can be seen that there is a bimodal elution pattern of the deaminase with one peak appearing at the same elution volume as adenylate deaminase alone but another eluting in the void volume of the column. This excluded adenylate deaminase activity corresponds with the HMM ATPase activity. The fact that the proteins remained associated to a considerable extent over the time scale of the gel filtration experiment (about 2 h) provides strong evidence that at pH 6.8 the rate of dissociation of the complex is slow in relation to the time of re-equilibration at each chromatographic plate. In an experiment in which the complex formed at pH 6.5 was chromatographed at pH 7.2, the deaminase activity eluted in a single peak at the volume expected for deaminase alone (data not shown). The question of rapid and slow dissociation of the 2:1 protein complex will be discussed below (see "Discussion").

Kinetic Studies Relevant to the Deaminase Activity in the Adenylate Deaminase:HMM Complex-We
have previously discussed the regulatory kinetic properties of adenylate deaminase (9). Briefly, the enzyme contains an active site, an inhibitory site (which primarily binds purine triphosphates), and an activating site (for mono-, di-, and triphosphates). The specificities of these sites overlap and the regulatory kinetic responses are therefore quite complex. In addition, the enzyme shows hysteretic behavior with respect to inhibition and activation (9).
We have also shown previously that S-2 affects the kinetic behavior of the deaminase only with respect to the regulatory behavior. Thus, GTP inhibition was lost in the presence of excess S-2 (9). Since deaminase is bound more tightly to HMM than to S-2, it was of interest to re-examine this question using HMM. Figs. 7 and 8 show some of the observed results. HMM, in the absence of nucleotide effectors, has little D. J. Cox, personal communication. or no effect on the adenylate deaminase activity, similar to the observation for 5-2 (line a in Fig. 7 or 8, see legend). However, HMM protects against G T P inhibition of deaminase. Fig. 7 shows that when enzyme is preincubated with HMM and then mixed with AMP and 10 ~L M GTP, the appearance of GTP inhibition is delayed (compare line c which is without HMM to line b in which the enzyme is preincubated with HMM). Fig. 8 shows that when deaminase alone is preincubated with 1 KM GTP and then mixed with AMP and HMM, activation of the enzyme by AMP is accelerated (compare line b (with HMM) to line c (without HMM)). In these experiments, the HMM is not present with GTP long enough to cause any significant hydrolysis to GDP.
Complete analysis of these and similar kinetic data is difficult, to say the least. Such an analysis would necessarily include 1) the hysteretic G T P inhibition and AMP activation, as well as 2 ) the GTP-dependent dissociation of the complex Interaction of Adenylate Deaminase with Myosin Subfragments (5) superimposed upon the complicated kinetic properties of the enzyme alone. However, the time dependence of the interaction of deaminase and myosin and the subsequent effects on the regulatory properties of the deaminase may very well be of fundamental importance in understanding the in vivo role of adenylate deaminase.

DISCUSSION
The adenylate deaminase:myosin subfragment system is unique among the systems of interacting proteins whose mass transport properties have been studied in detail. This system is notable in that it displays apparent cooperativity and an apparent slow time scale of the dissociation process. The values for the rate constants determined by stopped flow light scattering and shown in Table I are of considerable interest.
They show 1) that the interaction is cooperative for the binding of 2 mol of deaminase/mol of HMM, 2) that the association rate constants k+l and k+z are of the magnitude expected for diffusion control, and 3) that the rate-limiting step in dissociation of the complex is the dissociation of the first deaminase molecule from the ternary complex. Furthermore, the value of this rate constant is relevant to the question of the observed schlieren patterns as discussed below.
Schlieren Patterns of Interacting Systems: Relation to Slowness of Interaction-The shapes of concentration boundaries in mass transport experiments of interacting systems have been used to distinguish reaction mechanisms. Asymptotic expressions to describe the concentration boundaries can be derived when diffusion terms are ignored and when the interaction is assumed to be in rapid equilibrium (19). Complete description of the sedimentation patterns in interacting systems, including kinetically controlled reactions and diffusion, is only possible through computer simulation (20). Simulation studies, including the effects of diffusion, have been performed for a system such as outlined in Mechanism I, assuming rapid equilibration (21). Such simulations predict a maximum of two peaks in the schlieren pattern. The feature of the deaminase:myosin system which is most obviously inconsistent with the predictions for a rapidly equilibrating interaction (19, 21) is the presence of three peaks, rather than two. A likely explanation is that the rate of equilibration between the complex and its components is slow. Certainly, the bimodal elution of adenylate deaminase activity during zonal gel chromatography at pH 6.8 (Fig. 6) provides strong evidence that the dissociation may be considered to be slow. It is difficult to state the point at which an interaction would be expected to give rise to slow behavior in mass transport. Previous studies (22) on the effects of kinetically controlled reactions on the sedimentation patterns of interacting systems have been limited to cases of homogeneous association. It was the conclusion of those computer simulation studies (22) that for a ligand-mediated dimerization reaction, distinct differences from rapid equilibrium are observed only when half-times for dissociation exceed 60 s (for a sedimentation time of 1500 s). The rate constants determined from light scattering for the deaminase:HMM interaction ( Table I) predict half-times on that order under conditions of lower pH (20-30 s at pH 6.5), while at higher pH values the dissociation rates may be more than 1 order of magnitude greater (halftime of 1.8 s at pH 7.0). Even so, the sedimentation pattern still shows three clearly resolved peaks. Preliminary simulation studies performed recently' can generate trimodal patterns using the reaction mechanism of Mechanism I with the rate constants of Table I for pH 6.5-7. Further studies may help to clarify what exactly is the experimental parameter in relation to which an interaction may be said to be slow. Certainly the critical parameter is not simply the duration of the experiment, for the duration of the zonal chromatography experiment in Fig. 6 is on the order of hours. More likely, the critical parameter relates to the rate with which the complex is resolved from its components, and this is likely to be a complex function owing to the cooperation between transport of the components and the rate of formation of the complex.
Cooperatiuity of Interaction-The curves in Fig. 5 illustrate the two types of cooperativity may be involved in the interaction between adenylate deaminase and myosin. First, the interaction appears to be cooperative for the addition of the second molecule of adenylate deaminase to either HMM or S-2. When adenylate deaminase and HMM are combined at a 2:l stoichiometric ratio in sedimentation velocity experiments, the proportions of the slow peaks remain approximately constant a t 2:1, independent of the extent of association. When the proteins at pH 6.5 are combined at any other ratio, sedimentation velocity shows a fast boundary (20 S) and one slow boundary (with the sedimentation coefficient of whichever protein is present in excess of a 2:l deaminase:HMM ratio). It is extremely unlikely that a 1:l complex would sediment at the same rate as a 2:l complex, and thus the fact that the sedimentation coefficient of the fast peak remains constant even when the proteins are mixed at a deaminase:HMM ratio of 1:l suggests that the interaction is cooperative for the formation of the 2:l complex. Furthermore, there is no evidence of an appreciable amount of a 1:l complex in sedimentation equilibrium experiments, even in the presence of excess HMM. The maximal binding ratio determined by co-precipitation (5) is 2 mol of adenylate deaminase/mol of myosin. It is, however, uncertain that this cooperative feature is manifest in uiuo, since the observed maximal binding ratio has been observed to be 1 mol of adenylate deaminase/2 mol of myosin in native thick filaments (7) and this maximum is probably imposed by steric limitations (6). However, the observed cooperativity in uitro is interesting from the point of view of interchain interaction during conformational changes of the S-2 region (24) and the question of head-head interaction in myosin (23).
The dissociation curves in Fig. 5 also illustrate that with HMM the pH transition appears to be cooperative, involving two protons, whereas with S-2 the process more closely resembles a single ionization. We have no information to indicate which ionizable groups are involved, nor even on which protein they reside. The overall titration may involve groups on the myosin subfragment, deaminase, or both proteins. However, at least part of the pH dependence must be inherent in the myosin subfragment, since clear differences are observed between the pH dependence of deaminase binding to HMM and to S-2. The difference in pK between the HMM and S-2 titrations may relate to the absence of residues from the smaller S-2 fragment and/or to the presence of internal cleavages resulting from the use of papain.
Regulatory Effects-Several ligands have the effect of dissociating the deaminase:HMM complex. These effects are most likely mediated by their binding to adenylate deaminase, since the most effective dissociating ligands are inhibitors of adenylate deaminase. Phosphate, which inhibits adenylate deaminase with an inhibition constant in the range of 1 mM (25), dissociates the deaminase:HMM complex with a first order rate constant of about 50 s" a t concentrations of 5-10 mM (data not shown). GTP, which inhibits adenylate deaminase at concentrations below 10 p~, also dissociates the complex at low concentrations. It is of interest that the inhibitory effects of GTP are reversed when GTP is chelated with Mg2+ (26). We have alsu observed that the dissociating effect of the GTP analog, guanyl-5'-ylimidodiphosphate, is at least partly reversed by Mg2+ (data not shown).
As discussed previously (9), certain nucleotides (especially ADP) have a slight activating effect on adenylate deaminase. However, other nucleotides (such as GTP) show an inhibitory effect followed by activation as the nucleotide concentration is increased. The effect of a nucleotide such as ADP is more marked in reactivating the enzyme in the presence of inhibitory concentrations of GTP. The effects of myosin subfragments on the regulatory kinetics of adenylate deaminase are in many ways similar to the activating effects of this class of nucleotides. Thus, as shown in Figs. 7 and 8, HMM has minimal effects on the kinetics of adenylate deaminase in the absence of nucleotide, but it can have significant effects on the regulatory response to GTP. It is not known whether myosin binds to the same site on adenylate deaminase as do the reactivating nucleotides.
The inhibition observed a t low levels of GTP is a hysteretic (time-dependent) phenomenon on the time scale of stopped flow experiments. When adenylate deaminase is mixed with substrate and GTP, inhibition appears with time, so that the reaction rate decreases more quickly than expected from substrate depletion alone (compare lines a and c in Fig. 7). Conversely, when adenylate deaminase is preincubated with GTP and then mixed with substrate, the enzyme is reactivated in a time-dependent manner (Fig. 8, line c). Qualitatively, one might believe that it would be possible to determine something about the rates of deaminase:HMM interaction from the analysis of these kinetics, and in simple cases, this would be true. However, the kinetic properties of the deaminase are not simple. For example, our data suggest that AMP can reactivate GTP-inhibited enzyme and this reactivation, as well as the GTP inhibition itself, is time-dependent (Fig. 8,  line c). The analysis of the kinetics of adenylate deaminase is complex enough (9) but becomes even more complex in the presence of HMM because of the slow rate of dissociation of HMM from the deaminase. In spite of these complexities, we have made some estimates for the rate constants of association and dissociation of a 1:l deaminase:HMM complex based on computer simulation (17) of a model involving the complexities listed above. These values fall in the range of lo7-IO8 M-' s" and 1 s-', respectively. Although these computer simulations did not include the proper stoichiometry or the cooperative features of the protein:protein interaction, the estimated rate constants are in reasonable agreement with those determined from light scattering ( Table I).
It is clear, however, that adenylate deaminase i s refractory to the effects of endogenous nucleotide triphosphate inhibitors when it is bound to myosin or its subfragments. Since the extent of interaction is clearly regulated by pH (Fig. 5) and the transition occurs over the range measured in exercising muscle (27), the association of adenylate deaminase with the thick filament may vary with the exercise-recovery cycle, following the pH changes. The fraction of adenylate deaminase bound to thick filaments has been observed to increase after stimulation of rat muscles (28). What physiological role this may play is unclear at present.