- Email: [email protected]
[22] The use of pH studies to determine chemical mechanisms of enzyme-catalyzed reactions
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important test of the model is the prediction of the outcome of new experiments. Completion of the cycle in Fig. 5 usually does not constitute the end of the investigation. If the primary problem is the discrimination between rival models, a new cycle of steps emphasizing parameter estimation may be required. In fact, the proper execution of the steps in Fig. 5 could not be performed without some prior inform.ation about possible mathematical models, parameter values, and the experimental error. Preliminary information on all these issues could be obtained if replicate measurements were made in (p + 1) experimental points. For example, if the MichaelisMenten equation were considered (p =2), replicates (t> 5) could be obtained at low, intermediate, and high substrate concentrations. If measurements at the three levels appear to belong to a rectangular hyperbola, the model seems appropriate; otherwise, an alternative model must be considered. The data also permit calculations of preliminary values of the parameters, and from the replicate measurements the local variance of the data can be estimated in the points of experimentation. On the basis of these variance estimates, the design of further experiments can be made and a preliminary value of a (cf. Ref. 26) be calculated and used in the weighting function [Eq. (13)]. Consequently, a typical investigation is characterized by a sequential design in which the cycle of steps in Fig. 5 may be repeated with successive shifts of emphasis from model to model, and from model identification to parameter estimation. In this manner the analysis proceeds by consecutive steps of refinements until a satisfactory result has been obtained.
Acknowledgments The work from the author's laboratory described in this article was supported by the Swedish Natural Science Research Counciland the Swedish Cancer Society.
[22] T h e U s e o f p H S t u d i e s t o D e t e r m i n e C h e m i c a l Mechanisms of Enzyme-Catalyzed Reactions
By
W.
WALLACE
CLELAND
The use of pH studies specifically to determine chemical mechanisms of enzyme-catalyzed reactions is fairly new, and since many studies have been carried out very recently, it is useful to provide a short summary of the principles involved and of recent findings as a supplement to previous METHODS IN ENZYMOLOGY, VOL. 87
Copyright © 1982 by Academic Press, Inc. All rights of reproduction in any form reserved. 1SBN 0-12-181987-6
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articles ~ on the effect of p H on enzymatic reactions (see this series, Vol. 63, Article [9]). W h i c h p H Profiles D o W e L o o k At? The p H profiles that will be of the m o s t value will be pKi for competitive inhibitors or for metal-ion activators, log(V/K) for one or m o r e slow, nonsticky substrates, and isotope effects on V / K for these same substrates. Profiles for log V or for isotope effects on V require more knowledge o f the kinetic m e c h a n i s m for interpretation, although they do provide very useful information not present in the other profiles. The pKm profile for a substrate is not simple to interpret by itself, since it is merely the difference between the log(V/K) and log V profiles. We shall consider each of these profiles in turn, and see what it can tell us. p K i for C o m p e t i t i v e Inhibitor, or M e t a l A c t i v a t o r The Ki values used for these profiles represent equilibrium dissociation constants f r o m the e n z y m e f o r m present under the reaction conditions, since one extrapolates the variable substrate to zero in order to determine K~ .2 The p K values seen in these profiles are thus the correct ones in either the molecule whose Ki is being determined, or the e n z y m e form it combines with. The profile m a y either show a change to a slope of -+ 1 at the p K , if the incorrectly protonated f o r m can not bind at all, or after initially decreasing with +- 1 slope, the curve m a y plateau at a new level if the incorrectly protonated f o r m can bind less strongly. In this case, the point at which the curve levels out is the p K in the bound complex. If protonation decreases binding, the equation for the apparent Ki is thus Eq. (1) or Eq. (2) for the two cases: app K~ = K~(1 + H/K1)
(1)
app K~ = K~(1 + H/KO/(I + H/K~)
(2)
where Ki is the optimal Ki value, H is [H+], and K1 and K2 are acid dissociation constants of the group in free e n z y m e or inhibitor, and in the com1 W. W. Cleland, Adv. Enzymol. 45, 273 (1977). 2 In mechanisms where the dissociation constant of a substrate can be determined by initial velocity or product-inhibition studies, the profile of pKl versus pH gives the same information as those discussed here. Care must be taken when using Ki values from initial velocity patterns, however, as the observed value is not always a correct measure of the true dissociation constant. With yeast hexokinase, a for example, the Kl for ATP appears to be 100/zM, but the true value is 5 mM. a The reason for the discrepancy is explained in K. D. Danenberg and W. W. Cleland, Biochemistry 14, 28 (1975).
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2 pK i
~
. . . . .
I
I
Log V/K Log V
I
I
I
pH FIG. I. Possible shapes o f p H profiles when protonation decreases activity. A pKi profile has shape 1 if protonation does not allow binding at all, but levels out as shown by 4 if binding is decreased but not prevented. LogV/K profiles can have shapes 1, 2 (hump), or 3 (hollow), but shapes 2 and 3 are seen only when the substrate is sticky and certain ratios of rate constants occur. Log V profiles can have shapes 1 or 3, but shape 3 is seen only when both the substrate that dissociates most rapidly from the central complex and the proton in the protonated central complex are sticky. Leveling off as in shape 4 is rare in V/K profiles, but sometimes occurs in V profiles.
plex, respectively. If the group represented by pKI must be protonated for optimal binding, the terms in these equations are (1 + KI/H) and (1 +
K2/H). Profiles of pKi have the virtue of always having simple shapes, like those corresponding to Eq. (1) and (2) and illustrated in Fig. 1, but they detect only groups whose protonation state affects binding. A group necessary for catalysis but not directly participating in the binding process will not show up, or will show only a small change in affinity with change in protonation state; this is true of many acid-base catalytic groups, especially those that do not hydrogen-bond to the substrate. Even a catalytic group that hydrogen-bonds to the substrate will be likely to have its pK shifted no more than a pH unit by binding of the substrate or inhibitor. However, if the hydrogen bond is between positively and negatively charged groups (phosphate or carboxyl with arginine or lysine), the pK will be displaced at least 2 pH units by binding and formation of the hydrogen bond. A group whose pK is seen in a pKi profile may or may not act as an acid-base catalyst in the reaction, but its state of protonation clearly affects binding. Profiles of pK~ for a series of inhibitors of glutamate dehydrogenase that were competitive versus ot-ketoglutarate showed that groups with pK values of 5.2 and 8 both had to be protonated for binding to E - T P N H . 4 All dicarboxylic acids showed this behavior, as did glycolylglycine, which has C-1 altered to a hydroxymethyl group and binds only a factor of l0 less tightly than oxalylglycine and ot-ketoglutarate. (This alteration of COO- to CH2OH without serious loss of binding proves that 4 j. E. Rife and W. W. Cleland, Biochemistry 19, 2328 (1980).
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binding is not to arginine or lysine, but by hydrogen bonds to formally neutral groups such as amide N H groups.) Since inhibitors with C-5 absent or altered to a methyl group bound more weakly, and the profile showed that only one group on the enzyme needed to be protonated for binding, it was postulated that the group with pK 8 had to be protonated for binding of a carboxyl at C-5, but neutral to allow a monocarboxylic inhibitor to bind. This group is probably a lysine, and thus C-5 of a-ketoglutarate is bound by an ion-pair bond to lysine, but C-1 is not. The group with pK 5.2 has to be protonated for binding of all inhibitors and was postulated to play a catalytic role in the reaction. Note that since the group with pK 5.2 has to be protonated, and the lysine with pK 8 had to be neutral for binding of monocarboxylic inhibitors or substrates, it is only that portion of the enzyme which has this reverse protonation that participates in binding in this case. The observed binding is thus weak, and occurs only between the two pK values, which is the pH region where the reverse protonation form of enzyme occurs (1 part in 630 of the enzyme will show this reverse protonation rather than protonation of the lysine and deprotonation of the group with pK 5.2, since the pK values are 2.8 pH units apart and antilog 2.8 = 630). An example of reverse protonation in pH profiles is the pKi profile for phosphoglycolate with triose-P isomerase.5 Competitive inhibitors of the enzyme show binding only of the dianion, and thus pKi decreases below the phosphate pK around 6. Phosphoglycolohydroxamate, for example, shows a decrease in pKi with pK values of 5.7 and 9.5 (the latter pK being for the hydroxamate group). Inorganic sulfate binds well, while sulfate esters of analogs of the substrates (containing only a single negative charge) do not bind at all. Phosphoglycolate, however, binds only below a pK of 6.8, showing that the active species is H O O C - - C H 2 - - O - - P O a 2-, although there is 1600 times as much of the inhibitor in the form - O O C - - C H 2 - - O - - P O a H - . Above the pK of 6.8, the inhibitor is all the trianion, which is not absorbed, and thus it is clear that the phosphate portion of any substrate analog must be a dianion and the other end uncharged in order for binding to occur. 6 The pK~ profiles for metal activators provide evidence concerning the ligands of the metal. The pK values of these ligands should be perturbed by at least 2 pH units by coordination with the metal, and thus should show in the pK~ profiles except for carboxyls with pK values too low to observe. These pK values will not normally appear in the V profile, be5 F. C. Hartman, G. M. LaMuraglia, Y. Tomozawa, and R. Wolfenden, Biochemistry 14, 5274 (1975). 6 After binding, the carboxyl of phosphoglycolate apparently does transfer the proton to the catalytic glutamate residue [I. D. Campbell, R. B. Jones, P. A. Kiener, E. Richards, S. G. Waley, and R. Wolfenden, Biochem. Biophys. Res. Commun. 83, 347 (1978)].
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cause o f the large displacement in p K caused by coordination to the metal. Such a p K o f 8.7 is seen for Mg 2+ with malic enzyme, but the nature o f the group involved has not been determined, r Two ligands of Mg z÷ show in the pKi profile for enolase, while neither is seen in the V profile. 8 More use should be made of this method for determining the metal ligands for enzyme-catalyzed reactions.
Log(V/K) Profiles The V/K for a substratc is the apparent flrst-ordcr rate constant for reaction of the variable substrate with the enzyme when the variable substratc is at near-zero levels, and is the product of four factors: (I) The proportion of the substratc in the correct form to react. This will bc pHdependent if a certain protonation form is required for binding and/or activity. (2) The proportion of the enzyme in the correct form to react. This is pH-depcndent when only one protonation state of a group allows binding and/or catalysis. (3) The bimolecular rate constant for combination of enzyme and substrate. This will probably not bc pH-dcpendent, and will often bc limited by diffusion. (4) The fraction of the collision complex that reacts to give products, as opposed to dissociating. This will bc pH-dcpendent whenever binding is not pH-depcndcnt (or is only partly so), but the catalytic reaction requires one or more groups on enzyme or substratc to be in a given protonation state. Thus, if a p K is sccn in both the V and V/K profiles, (4) is probably responsible, while if it is seen only in the V/K profile, and not in the V profile, (I) or (2) is likely to bc the cause. Since the p K values of the substrate arc known, it is usually simple to tell whether itis incorrect protonation of enzyme or substratc that leads to the observed pK. In case of doubt, use of an alternate substrate with a different p K will resolve the issue. If a substrate is not sticky (that is, dissociates from the collision complex faster than it reacts to give products), the V / K profile shows the correct p K values o f e n z y m e or substrate, and the curve has a simple algebraic form. Thus, if protonation destroys activity, we have
V I K = (VIK)o/(1 + t-IIKI)
(3)
where ( V / K ) o is the pH-independent value, H is [H+], and K1 is the acid dissociation constant of the group which must be unprotonated. If the group must be protonated for activity, the denominator of Eq. (3) is (1 + K1/H), while if there are two groups, one o f which must be protonated and the other unprotonated, the denominator is (1 + H / K I + K2/H). r M. I. Schimerlik and W. W. Cleland, Biochemistry 16, 576 (1977). s UnpubliShed experiments in this lab by V. Anderson.
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More complicated profiles are often observed with two or more pK values on one limb. 4 If a substrate is sticky (that is, dissociates more slowly than it reacts to give products), the pK values will not be seen in the correct position on the profile, but will be displaced outward (that is, to lower pH when protonation decreases activity, and to higher pH when deprotonation lowers V/K) by log(1 + k3/k2), where k3 is the net rate constant for reaction of the collision complex to yield products, and k2 is for dissociation. 1 (This displacement occurs only in the first pK to decrease activity; subsequent pK values on the same limb of the profile are not displaced.) With a sticky substrate the displacement can be a pH unit or more, although values of 0.3 to 0.5 pH unit are more common. The displacement of 0.9 units between the pK values seen in V/K profiles for L-serine (a slow, nonsticky substrate) and L-alanine (fast, sticky) as substrates of alanine dehydrogenase is a clear example. 9 The stickiness of a substrate may be checked in several ways. The isotope partition method of Rose can be used for any substrate in a random mechanism. TM With creatine kinase, H ka/k2 was 6 for phosphocreatine at the pH optimum of 7. When there is a measurable isotope effect on V/K, the pH variation of this isotope effect will detect the stickiness, since the isotope effect at the pH optimum will be lower than that on the limb of the V/K profile for a sticky substratelZ; this is the case for alanine, but not for serine with alanine dehydrogenase.a Finally, a comparison of the apparent pK in the V/K profile with the actual one for the substrate, or with one determined from a pKi profile, or with a slow nonsticky substrate (as in the alanine dehydrogenase case 9) will detect the displacement. While the displacement of the pK is a sufficient problem, a further difficulty with sticky substrates is the alteration in shape of the pH profile in the vicinity of the pK, which can occur with certain values of the rate constants. This alteration in shape can take the form of a hollow or hump in the vicinity of the apparent pK (Fig. 1). 1 The hollow results when proton movement into and out of the active site is restricted, so that the state of protonation of the enzyme-substrate complex is not equilibrated rapidly with respect to the rates of reaction to give products or the rate of substrate dissociation. The hump pattern results when protonation increases 9 C. E. Grimshaw, P. F. Cook, and W. W. Cleland, Biochemistry 20, 5655 (1981). 10 I. A. Rose, E. L. O'Connell, S. Litwin, andJ. Bar-Tana, J. Biol. Chem. 249, 5163 (1974). 11 p. F. Cook, G. L. Kenyon, and W. W. Cleland, Biochemistry 20, 1204 (1981). 12 At the pH optimum, the isotope effect will generally be: (Dk + ka/k2)/(l + ka//~), where Dk is the value seen beyond the pK, and ka and k2 are the same rate constants used in the expression for displacement of the pK. For a complete discussion of the theory for the pH variation of isotope effects, see P. F. Cook and W. W. Cleland, Biochemistry 20, 1797, 1805 (1981).
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the biomolecular rate constant for addition of substrate. No pattern with a hump has yet been identified, but the V/Kp...ereatine profile with creatine kinase it shows a distinct hollow at 12 and 24°, but not at 35°, although phosphocreatine is still somewhat sticky at 35°. The stickiness varies with temperature, with ka/k2 being 11,4, and 1.6-3 at 12, 25, and 35°, respectively. The hollow is greater at 12 than at 25°, so it appears that the rate of proton equilibration with the acid-base catalyst in the enzyme-substrate complex is more temperature-sensitive than the rate of stlbstrate dissociation, which in turn is more so than the rate of reaction to give products. This study with creatine kinase H clearly shows the problems of dealing with a sticky substrate. Not only did the degree of stickiness vary with temperature, thus making it very difficult to determine the temperature coefficient of the pK itself, but also 25% dimethylformamide, which was used in solvent perturbation experiments to determine whether the group on the enzyme was a cationic or neutral acid, eliminated the stickiness, so that this pK shift was superimposed on that caused by solvent perturbation. Although it was possible to dissect the effects in this case by comparing the size of the solvent-induced pK shifts in cationic and neutral acid buffers ( - 0 . 8 and - 1.20 pH units, respectively), and thus to show that the group on the enzyme was a cationic acid, it would be much easier to use a substrate with a low enough maximum velocity that it was not sticky. Thus, one should use the V/K profiles for nonsticky substrates to determine the pK values and nature of the catalytic groups by solvent perturbation and temperature variation of the pK values, and then by comparison with the V/K profile of the normal sticky substrate determine the stickiness and, from the shape of the profile in the vicinity of the pK, how rapidly the protonation state of the group is equilibrated when substrate is present. Substrates are normally sticky only in the reaction direction with the higher maximum velocity, and not always then. (Isocitrate is very sticky from isocitrate dehydrogenase, TM while malate is not sticky with the closely related malic e n z y m e ) 4) In the direction with the lower maximum velocity, substrates cannot normally be sticky because their release rates from the enzyme must exceed the more rapid maximum velocity in the reverse direction. Thus, one needs to use the pH profiles of slow substrates only in the direction with the fastest maximum velocity; in the reverse reaction, one can use the profiles of the normal substrates for comparison. 13 p. F. Cook and W. W. Cleland, Biochemistry 20, 1797 (1981). ~4 M. I. Schimerlik, C. E. Grimshaw, and W. W. Cleland, Biochemistry 16, 571 (1977).
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Log V Profiles Here again the profile for a slow substrate, especially if sizeable isotope effects indicate that the chemical reaction is at least partly rate-limiting, is likely to be more easily interpreted, since portions of the reaction mechanism that do not affect V/K (such as the release of a second or third product) are not likely to be rate-limiting, even at the pH optimum. With a fast substrate (and especially in the direction with the faster maximum velocity), however, such product-release steps are often rate-limiting, or partly so. This displaces pK values outward on the pH profile until the portion of the reaction involving the chemical reaction does become ratelimiting. This effect is seen clearly with malic e n z y m e / w h e r e the pK values are displaced 1.5 pH units because TPNH release is rate-limiting at the pH optimum, If an isotope effect is seen on V/K and not on V, then later product release (or some prior step such as E - D P N isomerization) is rate-limiting for V, while if isotope effects are seen on both V and V/K, later product release is not a problem. If altering pH makes the portion of the mechanism containing the chemical reaction solely rate-limiting, both V and V/K should decrease outside of the pK values, and the V/K and V isotope effects should become equal, although their values at the pH optimum may be different. 15 This is the case at low pH with isocitrate dehydrogenase, malic enzyme, and yeast alcohol dehydrogenase with isopropanol as substrate. 13 In several recent studies, however, the isotope effects on V and V/K did not become equal outside of the pK values, but rather the isotope effect on V increased only to a portion of that on V/K. In the case of alanine dehydrogenase, this effect has been traced to the pH-dependent isomerization of the initially formed E - D P N complex to the form capable of productively binding alanine. 9 This isomerization is the major, but not sole, rate-limiting step for the maximum velocity of oxidation of alanine, and since it is sensitive to the state of protonation of the same group that affects V/Kalanine,the ratio between its rate constant and that for the chemical reaction becomes constant below the pK in the V profile. The isotope effect thus remains less than that on the chemical step itself, although it is somewhat higher a t l o w pH that at the pH optimum. While V/K profiles usually show total loss of activity when groups are 15 As noted above, the V / K isotope effect is reduced by an external commitment (k3/k2) when the substrate is sticky. The V isotope effect can similarly be expressed as: °V = (Dk + k3/kg)/(l + k3/kg) where ka is a step such as later product release which is slower than k 3 . If k9 is pH-independent, °V becomes Dk beyond the pK in the V profile; but if k9 is also pH-dependent--so that beyond the pK, k3/ka does not vary with p H - - t h e n °V will not become equal to °k, but will still depend on the value ofk3/k 9.
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incorrectly protonated, V profiles may show changes to a new plateau level when ionization o f a group increases the rate o f a step that is normally rate-limiting. With glucose-6-P dehydrogenase, for example,16 the V profile shows a small increase above a p K o f 8.7 to a new plateau level, and a corresponding increase in the isotope effect on V suggests that release o f D P N H or isomerization o f E - D P N has.become faster above p H 8.7, and no longer partly rate-limiting. In addition to being perturbed by the fact that the chemical reaction is not rate-limiting, p K values seen in V profiles may be perturbed as the result o f formation of the e n z y m e - s u b s t r a t e complex. When no hydrogen bonds form to the group in question, binding o f the substrate often rem o v e s the group from contact with solvent, and thus leads to what is in effect a solvent perturbation. For example, the p K o f the carboxyl group on fumarase is elevated by 0.5 p H unit by the binding o f malate, and by I. 1 units by the binding o f fumarate, 17 which is the change expected for a neutral acid group. The p K o f a cationic acid such as histidine should not be much altered by substrate binding unless it hydrogen-bonds specifically to the substrate. With fumarase, the histidine p K is elevated by 2 p H units by binding of malate, and lowered by 2.2 units by the binding of fumarate. 17 Malate hydrogen-bonds to protonated histidine, while the specifically absorbed water molecule hydrogen-bonds to unprotonated histidine. When binding only occurs with a group on the e n z y m e or substrate in one protonation state, the corresponding p K does not appear in the V profile at all. This is c o m m o n for phosphate esters, many of which are adsorbed only as the dianion. TM These are really cases in which the p K has been shifted so far to the outside of the p H profile that it is not observeable. While the stickiness of a substrate does not displace the p K values in V profiles, it can lead to more complex shapes than the simple one corresponding in algebraic form to Eq. (3) if proton access to the groups involved is restricted in the central complex o f e n z y m e and substrates. 1 When both the substrate that dissociates most rapidly from the central complex and the proton on the group in question are sticky, the curve will have a hollow in the vicinity of the p K (Fig. 1), but the hump pattern is not possible. (For groups that must be protonated for activity, it is access of O H - to the site, rather than H +, that must be restricted.)
16Unpublished experiments by Dr. Ronald Viola in this laboratory. 17D. A. Brandt, L. B. Barnett, and R. A. Alberty, J. Am. Chem. Soc. 85, 2204 (1963). i s Examples: triose-P isomerase,5 creatine kinase, 11and glucose-6-P dehydrogenase.TM
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S u m m a r y of Procedure to Follow for p H Studies At this point we will summarize what we have said above in terms of the steps one takes to carry out a pH study of an enzymic mechanism. While some of these steps may be omitted in certain cases, the possible ambiguities in these studies are such that one normally needs all of the following information to obtain an unequivocal picture of the chemical mechanism. In most cases, however, one can make definite conclusions once sufficient data are in hand. 1. Profiles of pKi for competitive inhibitors will show the required state of protonation of the inhibitor or of groups on the enzyme for binding. Correct pK values are seen, and such profiles are good candidates for temperature variation or solvent perturbation studies to identify the groups involved. Since one is running competitive inhibition patterns at various pH values, one also gets V/K and V values at the same time if one keeps track of the levels of enzyme used in the patterns. (Both V and V/K are proportional to enzyme level, but Ki is not.) 2. The log(V/K) versus pH profile for a nonsticky substrate shows the correct pK values of groups necessary both for binding and catalysis. Those pK values not present in the pKi profiles are groups that act as acid-base catalysts during the reaction, or whose protonation state is important for the chemical reaction, but not for binding. Profiles of V/K for nonsticky substrates can also be used in temperature-variation and solvent-perturbation studies to determine the nature of the groups involved. When there is more than one substrate, the one whose V/K profile will best show the catalytic groups must be determined by experiment. In an ordered mechanism, V/K for the first substrate normally equals the bimolecular rate constant for combination with the enzyme and shows only binding information, so V/K for the second substrate is the one of interest. In a random mechanism, however, it often cannot be predicted which profile will give the most information, since the binding of one substrate may perturb the pK values of the catalytic groups, or the pK may be hidden under others important only for binding. With hexokinase, for example, V/Kg~ucosedrops very rapidly at low pH, since protonation of a large number of groups on the enzyme prevents its binding. TM The V/KMgAT P profile (with glucose now saturating, and preventing the protonation of these groups) shows only the pK of the carboxyl group that is the acidbase catalyst. With glucose-6-P dehydrogenase, TM the V/K profile for glucose 6-phosphate shows pK values at low pH both for the phosphate of the substrate and for the acid-base catalyst, but the V/K profile for the 19R. E. Violaand W. W. Cleland,Biochemistry17, 4111 (1978).
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very slow substrate glucose 6-sulfate shows only the pK of the acid-base catalyst, since the sulfate group is not protonated in the accessible pH range. (Glucose 6-sulfate has a very low V/K value because it is a monoanion, and the enzyme has a preference for binding of dianions of at least 5 orders of magnitude.) The V/K profiles for sticky substrates are not easy to use for study of the chemical mechanism, but will indicate the degree of stickiness, and from the shape of the profile one may determine any restrictions to the rate of proton transfer in and out of the active site while the substrate is present. 3. The V profile will fail to show the pK values of groups that allow binding only when correctly protonated, while conversely, when the pK is seen in the V profile, one knows that binding is not totally pH-dependent, but that the group must be correctly protonated for catalysis. The displacement of the pK from its value in the V/K or pKi profiles carries information on the relative rates of steps in the mechanism and on the environment in the enzyme-substrate complex. When there is more than one substrate and product, however, remember that V/K involves only part of the overall mechanism (from variable substrate addition to release of the first product, or other irreversible step), and the pH-dependence of steps in the rest of the mechanism will show up in V and not V/K. This problem will be less when V is determined for a slow substrate giving a large isotope effect, since the portion of the mechanism containing the chemical reaction is now largely rate-limiting, and V is no longer sensitive to steps not included in the calculation of V/K. 4. Profiles must be determined in both directions of the reaction. If the overall reaction involves a proton, as do many kinase and dehydrogenase reactions, the V/K profiles will show the pK of the acid-base catalytic group with different required protonation states in the two directions, and this pattern will tell which pK is that of the acid-base catalyst. Groups showing identical pH-dependence in both directions may still act as acidbase catalysts, but always end up in the same protonation state as the one they started in. Their required protonation state may simply be required to allow conformation changes leading to catalysis to occur, however. When no proton is involved in the overall reaction, the V/K profiles should have similar shapes in forward and reverse reactions. One must keep in mind the possibility of reverse protonation, however. Thus, the V/K profiles for fumarase in both directions show the carboxyl pK at 5.9 and the imidazole one at 7.1, but the carboxyl must be ionized and the imidazole protonated for reaction of malate, while the carboxyl is protonated and the imidazole unprotonated for the reaction of fumarate and water. 17
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5. The identity of catalytic groups when p K values are seen in pH profiles is established kinetically by temperature variation and solvent perturbation studies. The observed AHion o f a p K is a maximum value, since the observed value will be too high if conformation changes in the p r o t e i n - changes that usually have high temperature c o e f f i c i e n t s - - a r e coupled to the ionization of the group. Thus, a AHion value near zero suggests a carboxyl or phosphate rather than a histidine, while a value near 6 kcal/mol could be a histidine, or a carboxyl accompanied by a conformation change, but is unlikely to be a lysine, for which the normal value would be 12 kcal/mol. Solvent perturbation studies when properly done 2° are less ambiguous, but in cases where one is observing a global pK for a hydrogen-bonded system in the active site, one sees the acid type o f the group exposed to the solvent, and not of any groups buried in the protein. Thus, the Asp-His charge relay system o f c h y m o t r y p s i n acts as a cationic acid in solvent perturbation studies? 1 although the system is neutral at low p H and negatively charged in the active form at neutral pH, and thus might be expected to act as neutral acid. One should o f course make use o f all information that can be obtained by other nonkinetic means (X-ray, modification studies, etc.) to identify the groups in the active site and the roles they play in the chemical mechanism. Experimental Notes We should comment on several matters that are important for obtaining good experimental results in p H studies. B u f f e r s . One can either switch from one buffer to another to c o v e r different portions of the p H profile, or use a mixture of buffers in which each one buffers in a different portion of the p H range. The p K spacing should be no more than 1.5-2 units between the pK values of the buffers used, and each buffer must be tested for inhibition o f both the protonated and unprotonated components by testing several levels o f buffer 0.5 p H unit or so above and below the pK, One must also use p H overlaps when different buffers are used for different portions o f the profile. It is best to keep ionic strength as constant as possible, especially if the e n z y m e is sensitive to ionic strength, but it must be remembered that p H profiles involve changes of a factor of 10 per p H unit, and 5 or 10% changes in rate 20One should use both neutral acid and cationic acid buffers and run profiles with and without solvent, measuring pH values before addition of the solvent [see D. Findley, A. P. Mathias, and B. R. Rabin, Biochem. J. 85, 139 (1962)]. No change in pK shows a group of acid type similar to the buffer, while an increase in the pK in cationic acid buffer, or decrease in pK in neutral acid buffer, shows the opposite acid type. 21T. Ingami and J. M. Sturtevant, Biochim. Biophys. Acta 38, 64 (1960).
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resulting from changes in ionic strength or other causes do not result in serious errors. For solvent perturbation studies, one needs one set of neutral acid buffers, and one set of cationic acid buffers. Again, each buffer must be tested for inhibition, and the pH profile should be identical in the two buffer systems in the absence of solvent. Enzyme Stability. When reactions are followed by continuous spectroscopic recording, enzyme instability at the pH extremes is obvious from the rapidly decreasing rates. The pH profiles can be pushed as far as it is still possible to determine initial rates, and if the enzyme stock solution is at a comfortable pH and enzyme is added last to the reaction mixture, one can get data at pH values where the half-life of the enzyme is only several minutes. Substrate instability may also be a problem. For example, the rate of DPNH breakdown may limit how low a pH can be used, although pH 4 has been reached in some studies. 7 A higher enzyme level will increase the difference between enzymic and nonenzymic reactions, and a lower temperature will help. (This is one reason why 25° is better than higher temperatures for routine kinetic study.) pH Measurement. Values of pH should be determined prior to adding enzyme, rather than being assumed from the pH of the buffer, or measured after reaction for several minutes. Since some reactions generate or use up protons, the pH may shift, but the initial velocity corresponds to the initial pH. Experimental Design. To determine V/K and V profiles, one tries to run single reciprocal plots as a function of pH, with other reactants saturating. This may involve different levels of the nonvaried substrates or metal activators at different pH values, and may even require full initial velocity patterns at the pH extremes if Michaelis constants for the nonvaried reactants get too large. Two reciprocal plots at different levels of the nonvaried substrate will usually suffice, however. (Remember, in pH profiles one is looking for changes of factors of l0 per pH unit.) If the Km of the variable substrate changes with pH, the concentrations used for the reciprocal plots must also be changed in order to determine V and V/K properly. With pH profiles that change one or more factors of l0 per pH unit, one must use different enzyme levels for different portions of the pH profile in order to measure the rates. One should check to be sure that activity does not change on dilution, however, and use overlaps between the various enzyme levels. To determine pK~ profiles, a competitive inhibition pattern must be run at each pH. If 1/v versus 1/I plots are linear at key pH values, including the extremes, only one reciprocal plot with and one without the inhibitor at each pH value suffices. Be sure the reciprocal plot without inhibitor has
[22]
USE OF p H STUDIES TO DETERMINE MECHANISMS
403
an adequate slope; otherwise, you cannot get an accurate value of Kl, but only the ratio of Km and Ki. Statistical Analysis. All reciprocal plots and patterns should be fitted to appropriate rate equations by the least squares method, and the resulting K~, V/K, or V values then fitted to the appropriate equations. 22 Computer programs for doing these calculations are in this series (Vol. 63, Article [6], of this series). 22a The pH:profiles themselves must be fitted in the log form, since the values may change by several orders o f magnitude o v e r the profile. We have found that it is usually better to use an unweighted fit to the p H profiles. (The programs allow the use of weights, however.) Weights should probably be used only if one has run each reciprocal plot a number of times and thus has adequate data for proper evaluation of the weighting factors for the kinetic parameters. Otherwise, there is considerable scatter in the standard errors of the parameters, and thus in the weights, and this scatter biases the end result. Finally, we must emphasize that although statistical analysis is essential, it must be the right sort o f statistical analysis as described in this series, Vol. 63, Article [6]. The use of the least squares method on reciprocal plots without proper weights, or for fitting p H profiles not in the log form, will do more harm than good. E x a m p l e s of the M e t h o d We shall give several recent examples of p H studies in which the intent was to determine the chemical mechanism. We shall not review older literature or be exhaustive. Both frnctokinase z3 and hexokinase TM show V / K profiles in which a carboxyl group must be ionized to accept the proton from the hydroxyl group being phosphorylated, and protonated for the reverse reaction. F o r hexokinase, this group is seen in X-ray studies as an aspartate hydrogen bonded to the 6-hydroxyl of glucose. 24 In contrast, the a c i d - b a s e catalyst with creatine kinase is a cationic acid, probably histidine. ~1The binding of creatine in a binary complex with e n z y m e is prevented by protonation of this group, but ternary complexes with e n z y m e - n u c l e o t i d e form even with this group protonated. A carboxyi group must be ionized for binding o f either creatine or creatine P in any complex, and was postulated to in22 w. w. Cleland, Adv. Enzymol. 29, (1967). 22aThere is an error in these programs for fitting pH profiles. In BELL, HABELL, and HBBELL the statement evaluating DXl should be changed to DX1 = (X2-X3)*2.3026. In WAVL, the corresponding statement is DX = (X1-X2).2.3026. As printed, the programs give standard errors too small by In 10, since base-10 logs are used to compare experimental and calculated points, but natural logs are used for the least-squares fit. 23 F. M. Raushel and W. W. Cleland, Biochemistry 16, 2176 (1977). 24C. M. Anderson, R. E. Stenkamp, R. C. McDonald, and T. A. Steitz, J. Mol. Biol. 123, 207 (1978).
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teract with the tertiary nitrogen of the guanidinium group; thus the positive charge was concentrated on this nitrogen and the primary amino group being phosphorylated would not carry any of the charge of the guanidinium group. With malic enzyme, T M the deuterium isotope effect o n V/gmalate (1.5) was independent of pH, and thus malate is not sticky. The V/Kma~ate profile showed pK values of 6 and 8, although the binding of competitive inhibitors was only slightly affected by the ionization of these groups. Decarboxylation of oxaloacetate in the presence of TPN (an alternate reaction of this enzyme) occurred only below the pK of 6; it was therefore postulated that the group with pK 6 was the acid-base catalyst for the dehydrogenation, accepting the proton from the hydroxyl of malate, but requiring this proton for general acid catalysis of subsequent decarboxylation of oxaloacetate, which was either adsorbed as such or produced by dehydrogenation. Unfortunately, this group could not be identified because a conformation change apparently accompanies its ionization (AH~on = 22 kcal/mol), and the enzyme was sensitive in this pH range to solvents. (The data with 10% dimethylformamide suggested a neutral acid, but a higher solvent level would be needed to establish this definitely.) Hsu et al. 25 have suggested that this group was water-coordinated to the metal ion required for the reaction, but this is a very low pK for water coordinated to magnesium! The group with pK 8 is a neutral acid with AH~on = 9 kcal/mol, and Schimerlik and Cleland r suggested that this group might be metal-bound water, but further work is clearly needed to identify it. The role of the group with pK 8 is presumably to protonate C-3 of enolpyruvate formed by decarboxylation of oxaloacetate. Glutamate dehydrogenase 4 appears to have two lysines in the active site, one of which binds C-5 of glutamate or ot-ketoglutarate by an ion-pair bond, and the other of which acts as an acid-base catalyst, donating one proton to the carbonyl oxygen of ot-ketoglutarate during the addition of ammonia, which reacts as NH3 to form a carbinolamine. Transfer of a proton from nitrogen to oxygen in the carbinolamine allows release of water to give iminoglutarate, which is then reduced by TPNH. A group with pK 5.2 must also be protonated for binding of o~-ketoglutarate or inhibitors to E - T P N H , but unprotonated for oxidation of amino acids, which react in their zwitterionic form. (This group presumably removes the proton from the amino group to allow its oxidation.) The lysine, which must be protonated to allow binding of glutamate and a-ketoglutarate, must be neutral for binding of monocarboxylic acids, and thus the pH optimum for oxidation of norvaline is much higher than that for glutamate, although the maximum velocities at the pH optima are similar. 25 R. Y. Hsu, A. S. Mildvan, G.-G. Chang, and C.-H. Fung,J. Biol. Chem. 251, 6574 (1976).
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PROCESSES
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Alanine dehydrogenase 9 catalyzes a very similar reaction (in fact, glutamate dehydrogenase shows very weak alanine dehydrogenase activity), with free NHa as the substrate, and carbinolamine and iminopyruvate intermediates, but there are important differences. First, the nucleotide specificity is A side, rather than B as with glutamate dehydrogenase. Second, alanine reacts as the monoanion, instead of zwitterion. Third, the acid-base catalyst that must be protonated for binding of pyruvate but neutral for reaction of alanine has a pK near 7 and is probably histidine, rather than lysine. In E - D P N this group is not within hydrogen-bonding distance of an L-hydroxy group, but will hydrogen-bond to a carbonyl or D-hydroxy group. In E - D P N H complexes, however, it hydrogen-bonds to both D- and L-hydroxyls, as well as carbonyl groups. (These deductions came from an extensive series of pKi profiles.) Finally, the stereochemistry of the intermediate carbinolamine appears to be opposite thaf for glutamate dehydrogenase, based on K~ values for D- and L-hydroxy analogs. In closing, we should mention the pH studies of the deuterium isotope effects with liver alcohol dehydrogenase,Z6 which have clearly shown that aldehydes or ketones can be reduced by DPNH to alkoxide intermediates regardless of the protonation state of the acid-base catalyst (presumably His-51). Release of alcohol from E - D P N alkoxide requires protonation of His-51, however, and thus the partition ratio for this intermediate for hydride transfer and alcohol release is pH-dependent, as are the V/K isotope effects. As the above examples show, it has proven possible to extract a great deal of information about the kinetic and chemical mechanisms of enzyme-catalyzed reactions by carefully planned and thorough pH studies. The principles involved and the proper experiments to run are now clear, and as soon as more workers begin to use the techniques, our knowledge of enzyme mechanisms should increase greatly. 26 p. F. Cook and W. W. Cleland,
Biochemistry 20,
1805 (1981).
[23] Buffers of Constant Ionic Strength pH-Dependent Processes
By
KEITH J. ELLIS and
JOHN F.
for Studying
MORRISON
Over the past few years there has been increasing interest in the use of pH studies for gaining insights into the chemical mechanisms of enzymecatalyzed reactions. Thus studies of the variation with pH of the V and V/K values for substrates and of the Ki values for competitive inhibitors have led to the identification of groups on enzymes that are involved with METHODS IN ENZYMOLOGY, VOL. 87
Copyright © 1982by Academic Press, Inc. All rightsof reproductionin any form reserved. ISBN 0-12-181987-6
INITIAL
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important test of the model is the prediction of the outcome of new experiments. Completion of the cycle in Fig. 5 usually does not constitute the end of the investigation. If the primary problem is the discrimination between rival models, a new cycle of steps emphasizing parameter estimation may be required. In fact, the proper execution of the steps in Fig. 5 could not be performed without some prior inform.ation about possible mathematical models, parameter values, and the experimental error. Preliminary information on all these issues could be obtained if replicate measurements were made in (p + 1) experimental points. For example, if the MichaelisMenten equation were considered (p =2), replicates (t> 5) could be obtained at low, intermediate, and high substrate concentrations. If measurements at the three levels appear to belong to a rectangular hyperbola, the model seems appropriate; otherwise, an alternative model must be considered. The data also permit calculations of preliminary values of the parameters, and from the replicate measurements the local variance of the data can be estimated in the points of experimentation. On the basis of these variance estimates, the design of further experiments can be made and a preliminary value of a (cf. Ref. 26) be calculated and used in the weighting function [Eq. (13)]. Consequently, a typical investigation is characterized by a sequential design in which the cycle of steps in Fig. 5 may be repeated with successive shifts of emphasis from model to model, and from model identification to parameter estimation. In this manner the analysis proceeds by consecutive steps of refinements until a satisfactory result has been obtained.
Acknowledgments The work from the author's laboratory described in this article was supported by the Swedish Natural Science Research Counciland the Swedish Cancer Society.
[22] T h e U s e o f p H S t u d i e s t o D e t e r m i n e C h e m i c a l Mechanisms of Enzyme-Catalyzed Reactions
By
W.
WALLACE
CLELAND
The use of pH studies specifically to determine chemical mechanisms of enzyme-catalyzed reactions is fairly new, and since many studies have been carried out very recently, it is useful to provide a short summary of the principles involved and of recent findings as a supplement to previous METHODS IN ENZYMOLOGY, VOL. 87
Copyright © 1982 by Academic Press, Inc. All rights of reproduction in any form reserved. 1SBN 0-12-181987-6
[22]
USE OF p H STUDIES TO DETERMINE MECHANISMS
391
articles ~ on the effect of p H on enzymatic reactions (see this series, Vol. 63, Article [9]). W h i c h p H Profiles D o W e L o o k At? The p H profiles that will be of the m o s t value will be pKi for competitive inhibitors or for metal-ion activators, log(V/K) for one or m o r e slow, nonsticky substrates, and isotope effects on V / K for these same substrates. Profiles for log V or for isotope effects on V require more knowledge o f the kinetic m e c h a n i s m for interpretation, although they do provide very useful information not present in the other profiles. The pKm profile for a substrate is not simple to interpret by itself, since it is merely the difference between the log(V/K) and log V profiles. We shall consider each of these profiles in turn, and see what it can tell us. p K i for C o m p e t i t i v e Inhibitor, or M e t a l A c t i v a t o r The Ki values used for these profiles represent equilibrium dissociation constants f r o m the e n z y m e f o r m present under the reaction conditions, since one extrapolates the variable substrate to zero in order to determine K~ .2 The p K values seen in these profiles are thus the correct ones in either the molecule whose Ki is being determined, or the e n z y m e form it combines with. The profile m a y either show a change to a slope of -+ 1 at the p K , if the incorrectly protonated f o r m can not bind at all, or after initially decreasing with +- 1 slope, the curve m a y plateau at a new level if the incorrectly protonated f o r m can bind less strongly. In this case, the point at which the curve levels out is the p K in the bound complex. If protonation decreases binding, the equation for the apparent Ki is thus Eq. (1) or Eq. (2) for the two cases: app K~ = K~(1 + H/K1)
(1)
app K~ = K~(1 + H/KO/(I + H/K~)
(2)
where Ki is the optimal Ki value, H is [H+], and K1 and K2 are acid dissociation constants of the group in free e n z y m e or inhibitor, and in the com1 W. W. Cleland, Adv. Enzymol. 45, 273 (1977). 2 In mechanisms where the dissociation constant of a substrate can be determined by initial velocity or product-inhibition studies, the profile of pKl versus pH gives the same information as those discussed here. Care must be taken when using Ki values from initial velocity patterns, however, as the observed value is not always a correct measure of the true dissociation constant. With yeast hexokinase, a for example, the Kl for ATP appears to be 100/zM, but the true value is 5 mM. a The reason for the discrepancy is explained in K. D. Danenberg and W. W. Cleland, Biochemistry 14, 28 (1975).
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2 pK i
~
. . . . .
I
I
Log V/K Log V
I
I
I
pH FIG. I. Possible shapes o f p H profiles when protonation decreases activity. A pKi profile has shape 1 if protonation does not allow binding at all, but levels out as shown by 4 if binding is decreased but not prevented. LogV/K profiles can have shapes 1, 2 (hump), or 3 (hollow), but shapes 2 and 3 are seen only when the substrate is sticky and certain ratios of rate constants occur. Log V profiles can have shapes 1 or 3, but shape 3 is seen only when both the substrate that dissociates most rapidly from the central complex and the proton in the protonated central complex are sticky. Leveling off as in shape 4 is rare in V/K profiles, but sometimes occurs in V profiles.
plex, respectively. If the group represented by pKI must be protonated for optimal binding, the terms in these equations are (1 + KI/H) and (1 +
K2/H). Profiles of pKi have the virtue of always having simple shapes, like those corresponding to Eq. (1) and (2) and illustrated in Fig. 1, but they detect only groups whose protonation state affects binding. A group necessary for catalysis but not directly participating in the binding process will not show up, or will show only a small change in affinity with change in protonation state; this is true of many acid-base catalytic groups, especially those that do not hydrogen-bond to the substrate. Even a catalytic group that hydrogen-bonds to the substrate will be likely to have its pK shifted no more than a pH unit by binding of the substrate or inhibitor. However, if the hydrogen bond is between positively and negatively charged groups (phosphate or carboxyl with arginine or lysine), the pK will be displaced at least 2 pH units by binding and formation of the hydrogen bond. A group whose pK is seen in a pKi profile may or may not act as an acid-base catalyst in the reaction, but its state of protonation clearly affects binding. Profiles of pK~ for a series of inhibitors of glutamate dehydrogenase that were competitive versus ot-ketoglutarate showed that groups with pK values of 5.2 and 8 both had to be protonated for binding to E - T P N H . 4 All dicarboxylic acids showed this behavior, as did glycolylglycine, which has C-1 altered to a hydroxymethyl group and binds only a factor of l0 less tightly than oxalylglycine and ot-ketoglutarate. (This alteration of COO- to CH2OH without serious loss of binding proves that 4 j. E. Rife and W. W. Cleland, Biochemistry 19, 2328 (1980).
[22]
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393
binding is not to arginine or lysine, but by hydrogen bonds to formally neutral groups such as amide N H groups.) Since inhibitors with C-5 absent or altered to a methyl group bound more weakly, and the profile showed that only one group on the enzyme needed to be protonated for binding, it was postulated that the group with pK 8 had to be protonated for binding of a carboxyl at C-5, but neutral to allow a monocarboxylic inhibitor to bind. This group is probably a lysine, and thus C-5 of a-ketoglutarate is bound by an ion-pair bond to lysine, but C-1 is not. The group with pK 5.2 has to be protonated for binding of all inhibitors and was postulated to play a catalytic role in the reaction. Note that since the group with pK 5.2 has to be protonated, and the lysine with pK 8 had to be neutral for binding of monocarboxylic inhibitors or substrates, it is only that portion of the enzyme which has this reverse protonation that participates in binding in this case. The observed binding is thus weak, and occurs only between the two pK values, which is the pH region where the reverse protonation form of enzyme occurs (1 part in 630 of the enzyme will show this reverse protonation rather than protonation of the lysine and deprotonation of the group with pK 5.2, since the pK values are 2.8 pH units apart and antilog 2.8 = 630). An example of reverse protonation in pH profiles is the pKi profile for phosphoglycolate with triose-P isomerase.5 Competitive inhibitors of the enzyme show binding only of the dianion, and thus pKi decreases below the phosphate pK around 6. Phosphoglycolohydroxamate, for example, shows a decrease in pKi with pK values of 5.7 and 9.5 (the latter pK being for the hydroxamate group). Inorganic sulfate binds well, while sulfate esters of analogs of the substrates (containing only a single negative charge) do not bind at all. Phosphoglycolate, however, binds only below a pK of 6.8, showing that the active species is H O O C - - C H 2 - - O - - P O a 2-, although there is 1600 times as much of the inhibitor in the form - O O C - - C H 2 - - O - - P O a H - . Above the pK of 6.8, the inhibitor is all the trianion, which is not absorbed, and thus it is clear that the phosphate portion of any substrate analog must be a dianion and the other end uncharged in order for binding to occur. 6 The pK~ profiles for metal activators provide evidence concerning the ligands of the metal. The pK values of these ligands should be perturbed by at least 2 pH units by coordination with the metal, and thus should show in the pK~ profiles except for carboxyls with pK values too low to observe. These pK values will not normally appear in the V profile, be5 F. C. Hartman, G. M. LaMuraglia, Y. Tomozawa, and R. Wolfenden, Biochemistry 14, 5274 (1975). 6 After binding, the carboxyl of phosphoglycolate apparently does transfer the proton to the catalytic glutamate residue [I. D. Campbell, R. B. Jones, P. A. Kiener, E. Richards, S. G. Waley, and R. Wolfenden, Biochem. Biophys. Res. Commun. 83, 347 (1978)].
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cause o f the large displacement in p K caused by coordination to the metal. Such a p K o f 8.7 is seen for Mg 2+ with malic enzyme, but the nature o f the group involved has not been determined, r Two ligands of Mg z÷ show in the pKi profile for enolase, while neither is seen in the V profile. 8 More use should be made of this method for determining the metal ligands for enzyme-catalyzed reactions.
Log(V/K) Profiles The V/K for a substratc is the apparent flrst-ordcr rate constant for reaction of the variable substrate with the enzyme when the variable substratc is at near-zero levels, and is the product of four factors: (I) The proportion of the substratc in the correct form to react. This will bc pHdependent if a certain protonation form is required for binding and/or activity. (2) The proportion of the enzyme in the correct form to react. This is pH-depcndent when only one protonation state of a group allows binding and/or catalysis. (3) The bimolecular rate constant for combination of enzyme and substrate. This will probably not bc pH-dcpendent, and will often bc limited by diffusion. (4) The fraction of the collision complex that reacts to give products, as opposed to dissociating. This will bc pH-dcpendent whenever binding is not pH-depcndcnt (or is only partly so), but the catalytic reaction requires one or more groups on enzyme or substratc to be in a given protonation state. Thus, if a p K is sccn in both the V and V/K profiles, (4) is probably responsible, while if it is seen only in the V/K profile, and not in the V profile, (I) or (2) is likely to bc the cause. Since the p K values of the substrate arc known, it is usually simple to tell whether itis incorrect protonation of enzyme or substratc that leads to the observed pK. In case of doubt, use of an alternate substrate with a different p K will resolve the issue. If a substrate is not sticky (that is, dissociates from the collision complex faster than it reacts to give products), the V / K profile shows the correct p K values o f e n z y m e or substrate, and the curve has a simple algebraic form. Thus, if protonation destroys activity, we have
V I K = (VIK)o/(1 + t-IIKI)
(3)
where ( V / K ) o is the pH-independent value, H is [H+], and K1 is the acid dissociation constant of the group which must be unprotonated. If the group must be protonated for activity, the denominator of Eq. (3) is (1 + K1/H), while if there are two groups, one o f which must be protonated and the other unprotonated, the denominator is (1 + H / K I + K2/H). r M. I. Schimerlik and W. W. Cleland, Biochemistry 16, 576 (1977). s UnpubliShed experiments in this lab by V. Anderson.
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More complicated profiles are often observed with two or more pK values on one limb. 4 If a substrate is sticky (that is, dissociates more slowly than it reacts to give products), the pK values will not be seen in the correct position on the profile, but will be displaced outward (that is, to lower pH when protonation decreases activity, and to higher pH when deprotonation lowers V/K) by log(1 + k3/k2), where k3 is the net rate constant for reaction of the collision complex to yield products, and k2 is for dissociation. 1 (This displacement occurs only in the first pK to decrease activity; subsequent pK values on the same limb of the profile are not displaced.) With a sticky substrate the displacement can be a pH unit or more, although values of 0.3 to 0.5 pH unit are more common. The displacement of 0.9 units between the pK values seen in V/K profiles for L-serine (a slow, nonsticky substrate) and L-alanine (fast, sticky) as substrates of alanine dehydrogenase is a clear example. 9 The stickiness of a substrate may be checked in several ways. The isotope partition method of Rose can be used for any substrate in a random mechanism. TM With creatine kinase, H ka/k2 was 6 for phosphocreatine at the pH optimum of 7. When there is a measurable isotope effect on V/K, the pH variation of this isotope effect will detect the stickiness, since the isotope effect at the pH optimum will be lower than that on the limb of the V/K profile for a sticky substratelZ; this is the case for alanine, but not for serine with alanine dehydrogenase.a Finally, a comparison of the apparent pK in the V/K profile with the actual one for the substrate, or with one determined from a pKi profile, or with a slow nonsticky substrate (as in the alanine dehydrogenase case 9) will detect the displacement. While the displacement of the pK is a sufficient problem, a further difficulty with sticky substrates is the alteration in shape of the pH profile in the vicinity of the pK, which can occur with certain values of the rate constants. This alteration in shape can take the form of a hollow or hump in the vicinity of the apparent pK (Fig. 1). 1 The hollow results when proton movement into and out of the active site is restricted, so that the state of protonation of the enzyme-substrate complex is not equilibrated rapidly with respect to the rates of reaction to give products or the rate of substrate dissociation. The hump pattern results when protonation increases 9 C. E. Grimshaw, P. F. Cook, and W. W. Cleland, Biochemistry 20, 5655 (1981). 10 I. A. Rose, E. L. O'Connell, S. Litwin, andJ. Bar-Tana, J. Biol. Chem. 249, 5163 (1974). 11 p. F. Cook, G. L. Kenyon, and W. W. Cleland, Biochemistry 20, 1204 (1981). 12 At the pH optimum, the isotope effect will generally be: (Dk + ka/k2)/(l + ka//~), where Dk is the value seen beyond the pK, and ka and k2 are the same rate constants used in the expression for displacement of the pK. For a complete discussion of the theory for the pH variation of isotope effects, see P. F. Cook and W. W. Cleland, Biochemistry 20, 1797, 1805 (1981).
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the biomolecular rate constant for addition of substrate. No pattern with a hump has yet been identified, but the V/Kp...ereatine profile with creatine kinase it shows a distinct hollow at 12 and 24°, but not at 35°, although phosphocreatine is still somewhat sticky at 35°. The stickiness varies with temperature, with ka/k2 being 11,4, and 1.6-3 at 12, 25, and 35°, respectively. The hollow is greater at 12 than at 25°, so it appears that the rate of proton equilibration with the acid-base catalyst in the enzyme-substrate complex is more temperature-sensitive than the rate of stlbstrate dissociation, which in turn is more so than the rate of reaction to give products. This study with creatine kinase H clearly shows the problems of dealing with a sticky substrate. Not only did the degree of stickiness vary with temperature, thus making it very difficult to determine the temperature coefficient of the pK itself, but also 25% dimethylformamide, which was used in solvent perturbation experiments to determine whether the group on the enzyme was a cationic or neutral acid, eliminated the stickiness, so that this pK shift was superimposed on that caused by solvent perturbation. Although it was possible to dissect the effects in this case by comparing the size of the solvent-induced pK shifts in cationic and neutral acid buffers ( - 0 . 8 and - 1.20 pH units, respectively), and thus to show that the group on the enzyme was a cationic acid, it would be much easier to use a substrate with a low enough maximum velocity that it was not sticky. Thus, one should use the V/K profiles for nonsticky substrates to determine the pK values and nature of the catalytic groups by solvent perturbation and temperature variation of the pK values, and then by comparison with the V/K profile of the normal sticky substrate determine the stickiness and, from the shape of the profile in the vicinity of the pK, how rapidly the protonation state of the group is equilibrated when substrate is present. Substrates are normally sticky only in the reaction direction with the higher maximum velocity, and not always then. (Isocitrate is very sticky from isocitrate dehydrogenase, TM while malate is not sticky with the closely related malic e n z y m e ) 4) In the direction with the lower maximum velocity, substrates cannot normally be sticky because their release rates from the enzyme must exceed the more rapid maximum velocity in the reverse direction. Thus, one needs to use the pH profiles of slow substrates only in the direction with the fastest maximum velocity; in the reverse reaction, one can use the profiles of the normal substrates for comparison. 13 p. F. Cook and W. W. Cleland, Biochemistry 20, 1797 (1981). ~4 M. I. Schimerlik, C. E. Grimshaw, and W. W. Cleland, Biochemistry 16, 571 (1977).
[22]
USE OF pH STUDIES TO DETERMINE MECHANISMS
397
Log V Profiles Here again the profile for a slow substrate, especially if sizeable isotope effects indicate that the chemical reaction is at least partly rate-limiting, is likely to be more easily interpreted, since portions of the reaction mechanism that do not affect V/K (such as the release of a second or third product) are not likely to be rate-limiting, even at the pH optimum. With a fast substrate (and especially in the direction with the faster maximum velocity), however, such product-release steps are often rate-limiting, or partly so. This displaces pK values outward on the pH profile until the portion of the reaction involving the chemical reaction does become ratelimiting. This effect is seen clearly with malic e n z y m e / w h e r e the pK values are displaced 1.5 pH units because TPNH release is rate-limiting at the pH optimum, If an isotope effect is seen on V/K and not on V, then later product release (or some prior step such as E - D P N isomerization) is rate-limiting for V, while if isotope effects are seen on both V and V/K, later product release is not a problem. If altering pH makes the portion of the mechanism containing the chemical reaction solely rate-limiting, both V and V/K should decrease outside of the pK values, and the V/K and V isotope effects should become equal, although their values at the pH optimum may be different. 15 This is the case at low pH with isocitrate dehydrogenase, malic enzyme, and yeast alcohol dehydrogenase with isopropanol as substrate. 13 In several recent studies, however, the isotope effects on V and V/K did not become equal outside of the pK values, but rather the isotope effect on V increased only to a portion of that on V/K. In the case of alanine dehydrogenase, this effect has been traced to the pH-dependent isomerization of the initially formed E - D P N complex to the form capable of productively binding alanine. 9 This isomerization is the major, but not sole, rate-limiting step for the maximum velocity of oxidation of alanine, and since it is sensitive to the state of protonation of the same group that affects V/Kalanine,the ratio between its rate constant and that for the chemical reaction becomes constant below the pK in the V profile. The isotope effect thus remains less than that on the chemical step itself, although it is somewhat higher a t l o w pH that at the pH optimum. While V/K profiles usually show total loss of activity when groups are 15 As noted above, the V / K isotope effect is reduced by an external commitment (k3/k2) when the substrate is sticky. The V isotope effect can similarly be expressed as: °V = (Dk + k3/kg)/(l + k3/kg) where ka is a step such as later product release which is slower than k 3 . If k9 is pH-independent, °V becomes Dk beyond the pK in the V profile; but if k9 is also pH-dependent--so that beyond the pK, k3/ka does not vary with p H - - t h e n °V will not become equal to °k, but will still depend on the value ofk3/k 9.
398
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[22]
incorrectly protonated, V profiles may show changes to a new plateau level when ionization o f a group increases the rate o f a step that is normally rate-limiting. With glucose-6-P dehydrogenase, for example,16 the V profile shows a small increase above a p K o f 8.7 to a new plateau level, and a corresponding increase in the isotope effect on V suggests that release o f D P N H or isomerization o f E - D P N has.become faster above p H 8.7, and no longer partly rate-limiting. In addition to being perturbed by the fact that the chemical reaction is not rate-limiting, p K values seen in V profiles may be perturbed as the result o f formation of the e n z y m e - s u b s t r a t e complex. When no hydrogen bonds form to the group in question, binding o f the substrate often rem o v e s the group from contact with solvent, and thus leads to what is in effect a solvent perturbation. For example, the p K o f the carboxyl group on fumarase is elevated by 0.5 p H unit by the binding o f malate, and by I. 1 units by the binding o f fumarate, 17 which is the change expected for a neutral acid group. The p K o f a cationic acid such as histidine should not be much altered by substrate binding unless it hydrogen-bonds specifically to the substrate. With fumarase, the histidine p K is elevated by 2 p H units by binding of malate, and lowered by 2.2 units by the binding of fumarate. 17 Malate hydrogen-bonds to protonated histidine, while the specifically absorbed water molecule hydrogen-bonds to unprotonated histidine. When binding only occurs with a group on the e n z y m e or substrate in one protonation state, the corresponding p K does not appear in the V profile at all. This is c o m m o n for phosphate esters, many of which are adsorbed only as the dianion. TM These are really cases in which the p K has been shifted so far to the outside of the p H profile that it is not observeable. While the stickiness of a substrate does not displace the p K values in V profiles, it can lead to more complex shapes than the simple one corresponding in algebraic form to Eq. (3) if proton access to the groups involved is restricted in the central complex o f e n z y m e and substrates. 1 When both the substrate that dissociates most rapidly from the central complex and the proton on the group in question are sticky, the curve will have a hollow in the vicinity of the p K (Fig. 1), but the hump pattern is not possible. (For groups that must be protonated for activity, it is access of O H - to the site, rather than H +, that must be restricted.)
16Unpublished experiments by Dr. Ronald Viola in this laboratory. 17D. A. Brandt, L. B. Barnett, and R. A. Alberty, J. Am. Chem. Soc. 85, 2204 (1963). i s Examples: triose-P isomerase,5 creatine kinase, 11and glucose-6-P dehydrogenase.TM
[22]
USE OF pH STUDIES TO DETERMINE MECHANISMS
399
S u m m a r y of Procedure to Follow for p H Studies At this point we will summarize what we have said above in terms of the steps one takes to carry out a pH study of an enzymic mechanism. While some of these steps may be omitted in certain cases, the possible ambiguities in these studies are such that one normally needs all of the following information to obtain an unequivocal picture of the chemical mechanism. In most cases, however, one can make definite conclusions once sufficient data are in hand. 1. Profiles of pKi for competitive inhibitors will show the required state of protonation of the inhibitor or of groups on the enzyme for binding. Correct pK values are seen, and such profiles are good candidates for temperature variation or solvent perturbation studies to identify the groups involved. Since one is running competitive inhibition patterns at various pH values, one also gets V/K and V values at the same time if one keeps track of the levels of enzyme used in the patterns. (Both V and V/K are proportional to enzyme level, but Ki is not.) 2. The log(V/K) versus pH profile for a nonsticky substrate shows the correct pK values of groups necessary both for binding and catalysis. Those pK values not present in the pKi profiles are groups that act as acid-base catalysts during the reaction, or whose protonation state is important for the chemical reaction, but not for binding. Profiles of V/K for nonsticky substrates can also be used in temperature-variation and solvent-perturbation studies to determine the nature of the groups involved. When there is more than one substrate, the one whose V/K profile will best show the catalytic groups must be determined by experiment. In an ordered mechanism, V/K for the first substrate normally equals the bimolecular rate constant for combination with the enzyme and shows only binding information, so V/K for the second substrate is the one of interest. In a random mechanism, however, it often cannot be predicted which profile will give the most information, since the binding of one substrate may perturb the pK values of the catalytic groups, or the pK may be hidden under others important only for binding. With hexokinase, for example, V/Kg~ucosedrops very rapidly at low pH, since protonation of a large number of groups on the enzyme prevents its binding. TM The V/KMgAT P profile (with glucose now saturating, and preventing the protonation of these groups) shows only the pK of the carboxyl group that is the acidbase catalyst. With glucose-6-P dehydrogenase, TM the V/K profile for glucose 6-phosphate shows pK values at low pH both for the phosphate of the substrate and for the acid-base catalyst, but the V/K profile for the 19R. E. Violaand W. W. Cleland,Biochemistry17, 4111 (1978).
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INITIAL RATE AND INHIBITOR METHODS
[22]
very slow substrate glucose 6-sulfate shows only the pK of the acid-base catalyst, since the sulfate group is not protonated in the accessible pH range. (Glucose 6-sulfate has a very low V/K value because it is a monoanion, and the enzyme has a preference for binding of dianions of at least 5 orders of magnitude.) The V/K profiles for sticky substrates are not easy to use for study of the chemical mechanism, but will indicate the degree of stickiness, and from the shape of the profile one may determine any restrictions to the rate of proton transfer in and out of the active site while the substrate is present. 3. The V profile will fail to show the pK values of groups that allow binding only when correctly protonated, while conversely, when the pK is seen in the V profile, one knows that binding is not totally pH-dependent, but that the group must be correctly protonated for catalysis. The displacement of the pK from its value in the V/K or pKi profiles carries information on the relative rates of steps in the mechanism and on the environment in the enzyme-substrate complex. When there is more than one substrate and product, however, remember that V/K involves only part of the overall mechanism (from variable substrate addition to release of the first product, or other irreversible step), and the pH-dependence of steps in the rest of the mechanism will show up in V and not V/K. This problem will be less when V is determined for a slow substrate giving a large isotope effect, since the portion of the mechanism containing the chemical reaction is now largely rate-limiting, and V is no longer sensitive to steps not included in the calculation of V/K. 4. Profiles must be determined in both directions of the reaction. If the overall reaction involves a proton, as do many kinase and dehydrogenase reactions, the V/K profiles will show the pK of the acid-base catalytic group with different required protonation states in the two directions, and this pattern will tell which pK is that of the acid-base catalyst. Groups showing identical pH-dependence in both directions may still act as acidbase catalysts, but always end up in the same protonation state as the one they started in. Their required protonation state may simply be required to allow conformation changes leading to catalysis to occur, however. When no proton is involved in the overall reaction, the V/K profiles should have similar shapes in forward and reverse reactions. One must keep in mind the possibility of reverse protonation, however. Thus, the V/K profiles for fumarase in both directions show the carboxyl pK at 5.9 and the imidazole one at 7.1, but the carboxyl must be ionized and the imidazole protonated for reaction of malate, while the carboxyl is protonated and the imidazole unprotonated for the reaction of fumarate and water. 17
[22]
USE OF
pH
S T U D I E S TO D E T E R M I N E M E C H A N I S M S
401
5. The identity of catalytic groups when p K values are seen in pH profiles is established kinetically by temperature variation and solvent perturbation studies. The observed AHion o f a p K is a maximum value, since the observed value will be too high if conformation changes in the p r o t e i n - changes that usually have high temperature c o e f f i c i e n t s - - a r e coupled to the ionization of the group. Thus, a AHion value near zero suggests a carboxyl or phosphate rather than a histidine, while a value near 6 kcal/mol could be a histidine, or a carboxyl accompanied by a conformation change, but is unlikely to be a lysine, for which the normal value would be 12 kcal/mol. Solvent perturbation studies when properly done 2° are less ambiguous, but in cases where one is observing a global pK for a hydrogen-bonded system in the active site, one sees the acid type o f the group exposed to the solvent, and not of any groups buried in the protein. Thus, the Asp-His charge relay system o f c h y m o t r y p s i n acts as a cationic acid in solvent perturbation studies? 1 although the system is neutral at low p H and negatively charged in the active form at neutral pH, and thus might be expected to act as neutral acid. One should o f course make use o f all information that can be obtained by other nonkinetic means (X-ray, modification studies, etc.) to identify the groups in the active site and the roles they play in the chemical mechanism. Experimental Notes We should comment on several matters that are important for obtaining good experimental results in p H studies. B u f f e r s . One can either switch from one buffer to another to c o v e r different portions of the p H profile, or use a mixture of buffers in which each one buffers in a different portion of the p H range. The p K spacing should be no more than 1.5-2 units between the pK values of the buffers used, and each buffer must be tested for inhibition o f both the protonated and unprotonated components by testing several levels o f buffer 0.5 p H unit or so above and below the pK, One must also use p H overlaps when different buffers are used for different portions o f the profile. It is best to keep ionic strength as constant as possible, especially if the e n z y m e is sensitive to ionic strength, but it must be remembered that p H profiles involve changes of a factor of 10 per p H unit, and 5 or 10% changes in rate 20One should use both neutral acid and cationic acid buffers and run profiles with and without solvent, measuring pH values before addition of the solvent [see D. Findley, A. P. Mathias, and B. R. Rabin, Biochem. J. 85, 139 (1962)]. No change in pK shows a group of acid type similar to the buffer, while an increase in the pK in cationic acid buffer, or decrease in pK in neutral acid buffer, shows the opposite acid type. 21T. Ingami and J. M. Sturtevant, Biochim. Biophys. Acta 38, 64 (1960).
402
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[22]
resulting from changes in ionic strength or other causes do not result in serious errors. For solvent perturbation studies, one needs one set of neutral acid buffers, and one set of cationic acid buffers. Again, each buffer must be tested for inhibition, and the pH profile should be identical in the two buffer systems in the absence of solvent. Enzyme Stability. When reactions are followed by continuous spectroscopic recording, enzyme instability at the pH extremes is obvious from the rapidly decreasing rates. The pH profiles can be pushed as far as it is still possible to determine initial rates, and if the enzyme stock solution is at a comfortable pH and enzyme is added last to the reaction mixture, one can get data at pH values where the half-life of the enzyme is only several minutes. Substrate instability may also be a problem. For example, the rate of DPNH breakdown may limit how low a pH can be used, although pH 4 has been reached in some studies. 7 A higher enzyme level will increase the difference between enzymic and nonenzymic reactions, and a lower temperature will help. (This is one reason why 25° is better than higher temperatures for routine kinetic study.) pH Measurement. Values of pH should be determined prior to adding enzyme, rather than being assumed from the pH of the buffer, or measured after reaction for several minutes. Since some reactions generate or use up protons, the pH may shift, but the initial velocity corresponds to the initial pH. Experimental Design. To determine V/K and V profiles, one tries to run single reciprocal plots as a function of pH, with other reactants saturating. This may involve different levels of the nonvaried substrates or metal activators at different pH values, and may even require full initial velocity patterns at the pH extremes if Michaelis constants for the nonvaried reactants get too large. Two reciprocal plots at different levels of the nonvaried substrate will usually suffice, however. (Remember, in pH profiles one is looking for changes of factors of l0 per pH unit.) If the Km of the variable substrate changes with pH, the concentrations used for the reciprocal plots must also be changed in order to determine V and V/K properly. With pH profiles that change one or more factors of l0 per pH unit, one must use different enzyme levels for different portions of the pH profile in order to measure the rates. One should check to be sure that activity does not change on dilution, however, and use overlaps between the various enzyme levels. To determine pK~ profiles, a competitive inhibition pattern must be run at each pH. If 1/v versus 1/I plots are linear at key pH values, including the extremes, only one reciprocal plot with and one without the inhibitor at each pH value suffices. Be sure the reciprocal plot without inhibitor has
[22]
USE OF p H STUDIES TO DETERMINE MECHANISMS
403
an adequate slope; otherwise, you cannot get an accurate value of Kl, but only the ratio of Km and Ki. Statistical Analysis. All reciprocal plots and patterns should be fitted to appropriate rate equations by the least squares method, and the resulting K~, V/K, or V values then fitted to the appropriate equations. 22 Computer programs for doing these calculations are in this series (Vol. 63, Article [6], of this series). 22a The pH:profiles themselves must be fitted in the log form, since the values may change by several orders o f magnitude o v e r the profile. We have found that it is usually better to use an unweighted fit to the p H profiles. (The programs allow the use of weights, however.) Weights should probably be used only if one has run each reciprocal plot a number of times and thus has adequate data for proper evaluation of the weighting factors for the kinetic parameters. Otherwise, there is considerable scatter in the standard errors of the parameters, and thus in the weights, and this scatter biases the end result. Finally, we must emphasize that although statistical analysis is essential, it must be the right sort o f statistical analysis as described in this series, Vol. 63, Article [6]. The use of the least squares method on reciprocal plots without proper weights, or for fitting p H profiles not in the log form, will do more harm than good. E x a m p l e s of the M e t h o d We shall give several recent examples of p H studies in which the intent was to determine the chemical mechanism. We shall not review older literature or be exhaustive. Both frnctokinase z3 and hexokinase TM show V / K profiles in which a carboxyl group must be ionized to accept the proton from the hydroxyl group being phosphorylated, and protonated for the reverse reaction. F o r hexokinase, this group is seen in X-ray studies as an aspartate hydrogen bonded to the 6-hydroxyl of glucose. 24 In contrast, the a c i d - b a s e catalyst with creatine kinase is a cationic acid, probably histidine. ~1The binding of creatine in a binary complex with e n z y m e is prevented by protonation of this group, but ternary complexes with e n z y m e - n u c l e o t i d e form even with this group protonated. A carboxyi group must be ionized for binding o f either creatine or creatine P in any complex, and was postulated to in22 w. w. Cleland, Adv. Enzymol. 29, (1967). 22aThere is an error in these programs for fitting pH profiles. In BELL, HABELL, and HBBELL the statement evaluating DXl should be changed to DX1 = (X2-X3)*2.3026. In WAVL, the corresponding statement is DX = (X1-X2).2.3026. As printed, the programs give standard errors too small by In 10, since base-10 logs are used to compare experimental and calculated points, but natural logs are used for the least-squares fit. 23 F. M. Raushel and W. W. Cleland, Biochemistry 16, 2176 (1977). 24C. M. Anderson, R. E. Stenkamp, R. C. McDonald, and T. A. Steitz, J. Mol. Biol. 123, 207 (1978).
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INITIAL RATE AND INHIBITOR METHODS
[22]
teract with the tertiary nitrogen of the guanidinium group; thus the positive charge was concentrated on this nitrogen and the primary amino group being phosphorylated would not carry any of the charge of the guanidinium group. With malic enzyme, T M the deuterium isotope effect o n V/gmalate (1.5) was independent of pH, and thus malate is not sticky. The V/Kma~ate profile showed pK values of 6 and 8, although the binding of competitive inhibitors was only slightly affected by the ionization of these groups. Decarboxylation of oxaloacetate in the presence of TPN (an alternate reaction of this enzyme) occurred only below the pK of 6; it was therefore postulated that the group with pK 6 was the acid-base catalyst for the dehydrogenation, accepting the proton from the hydroxyl of malate, but requiring this proton for general acid catalysis of subsequent decarboxylation of oxaloacetate, which was either adsorbed as such or produced by dehydrogenation. Unfortunately, this group could not be identified because a conformation change apparently accompanies its ionization (AH~on = 22 kcal/mol), and the enzyme was sensitive in this pH range to solvents. (The data with 10% dimethylformamide suggested a neutral acid, but a higher solvent level would be needed to establish this definitely.) Hsu et al. 25 have suggested that this group was water-coordinated to the metal ion required for the reaction, but this is a very low pK for water coordinated to magnesium! The group with pK 8 is a neutral acid with AH~on = 9 kcal/mol, and Schimerlik and Cleland r suggested that this group might be metal-bound water, but further work is clearly needed to identify it. The role of the group with pK 8 is presumably to protonate C-3 of enolpyruvate formed by decarboxylation of oxaloacetate. Glutamate dehydrogenase 4 appears to have two lysines in the active site, one of which binds C-5 of glutamate or ot-ketoglutarate by an ion-pair bond, and the other of which acts as an acid-base catalyst, donating one proton to the carbonyl oxygen of ot-ketoglutarate during the addition of ammonia, which reacts as NH3 to form a carbinolamine. Transfer of a proton from nitrogen to oxygen in the carbinolamine allows release of water to give iminoglutarate, which is then reduced by TPNH. A group with pK 5.2 must also be protonated for binding of o~-ketoglutarate or inhibitors to E - T P N H , but unprotonated for oxidation of amino acids, which react in their zwitterionic form. (This group presumably removes the proton from the amino group to allow its oxidation.) The lysine, which must be protonated to allow binding of glutamate and a-ketoglutarate, must be neutral for binding of monocarboxylic acids, and thus the pH optimum for oxidation of norvaline is much higher than that for glutamate, although the maximum velocities at the pH optima are similar. 25 R. Y. Hsu, A. S. Mildvan, G.-G. Chang, and C.-H. Fung,J. Biol. Chem. 251, 6574 (1976).
[23]
B U F F E R S FOR S T U D Y I N G p H - D E P E N D E N T
PROCESSES
405
Alanine dehydrogenase 9 catalyzes a very similar reaction (in fact, glutamate dehydrogenase shows very weak alanine dehydrogenase activity), with free NHa as the substrate, and carbinolamine and iminopyruvate intermediates, but there are important differences. First, the nucleotide specificity is A side, rather than B as with glutamate dehydrogenase. Second, alanine reacts as the monoanion, instead of zwitterion. Third, the acid-base catalyst that must be protonated for binding of pyruvate but neutral for reaction of alanine has a pK near 7 and is probably histidine, rather than lysine. In E - D P N this group is not within hydrogen-bonding distance of an L-hydroxy group, but will hydrogen-bond to a carbonyl or D-hydroxy group. In E - D P N H complexes, however, it hydrogen-bonds to both D- and L-hydroxyls, as well as carbonyl groups. (These deductions came from an extensive series of pKi profiles.) Finally, the stereochemistry of the intermediate carbinolamine appears to be opposite thaf for glutamate dehydrogenase, based on K~ values for D- and L-hydroxy analogs. In closing, we should mention the pH studies of the deuterium isotope effects with liver alcohol dehydrogenase,Z6 which have clearly shown that aldehydes or ketones can be reduced by DPNH to alkoxide intermediates regardless of the protonation state of the acid-base catalyst (presumably His-51). Release of alcohol from E - D P N alkoxide requires protonation of His-51, however, and thus the partition ratio for this intermediate for hydride transfer and alcohol release is pH-dependent, as are the V/K isotope effects. As the above examples show, it has proven possible to extract a great deal of information about the kinetic and chemical mechanisms of enzyme-catalyzed reactions by carefully planned and thorough pH studies. The principles involved and the proper experiments to run are now clear, and as soon as more workers begin to use the techniques, our knowledge of enzyme mechanisms should increase greatly. 26 p. F. Cook and W. W. Cleland,
Biochemistry 20,
1805 (1981).
[23] Buffers of Constant Ionic Strength pH-Dependent Processes
By
KEITH J. ELLIS and
JOHN F.
for Studying
MORRISON
Over the past few years there has been increasing interest in the use of pH studies for gaining insights into the chemical mechanisms of enzymecatalyzed reactions. Thus studies of the variation with pH of the V and V/K values for substrates and of the Ki values for competitive inhibitors have led to the identification of groups on enzymes that are involved with METHODS IN ENZYMOLOGY, VOL. 87
Copyright © 1982by Academic Press, Inc. All rightsof reproductionin any form reserved. ISBN 0-12-181987-6