velick vavra 1962l

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THE JOURNAL OF BIOLOGICAL CHEMISTRYVol. 237, No. 7,July 1962Printed in U.S .A.

A Kinetic and Equilibrium Analysis of the GlutamicOxaloacetate Transaminase Mechanism*

SIDNEY F. VELICK AND JOHN VAVRA

From the Department of Biological Chemistry, Washington Universi ty School of Medicine, St. Louis IO, Missouri(Received for publication, January 22, 1962)

The amino group carrier function of the coenzyme of trans-amination was postulated on the basis of coenzyme propertiesand model experiments (1, 2) and was established for the en-zymatic reaction by the observation that pyridoxal and pyri-doxamine phosphates exhibit equivalent act ivi ty in the reactiva-tion of crude apoglutamate oxaloacetate transaminase (3) andby direct spectrophotometric observation of the coenzyme inter-conversion in experiments on the purified enzyme (4). Theenzyme is stable and highly active and catalyzes a reaction thatis susceptible to detailed kinetic analysis by continuous opticalmethods. Moreover, the bound coenzyme exhibits spectralchanges that make it an indicator of events occurring in experi-ments carried out with substrate level concentrations of enzyme.It is therefore possible to attempt the correlation of mechanismand intermediary reaction equilibria, deduced kinetica lly, withresults obtained by examination of the bound coenzyme itselfunder various conditions. The glutamate oxaloacetate enzymeis a mechanistic prototype for a large number of experimentallyless accessible transaminases and also for the general class ofgroup-transferring enzymes, which operate exclusively throughbinary enzyme substrate complexes.

Experimental ProcedureEnzyme and Substrates-Pig heart enzyme preparations weremade by the method of Jenkins, Yphantis, and Sizer (4) and by

modifications thereof, which yielded additional purification andproduced an enzyme that approached homogeneity. Purifica-tion steps beyond the ammonium sulfate fractionation of theheated extract did not af fect the kinetic behavior of the enzyme,nor was purification beyond the level obtained by these workersessential for the spectrophotometric analysis o f the bound coen-zyme. A physical and chemical description of the enzyme willtherefore be reserved for a separate communication. The sub-stra tes were of reagent grade and were checked chromato-graphically for amino and keto acid contaminants. Except foroxaloacetate, solutions of which were prepared shortly beforeuse, concentrated stock solutions of the substrates could beneutralized and stored in the frozen state. Stock enzyme solu-tions, dialized against 0.025 M arsenate buf fer, pH 7.4, werestable for long periods of time. The amount of enzyme used in akinetic test was of the order of 0.04 pg per ml.

Initial Velocity Measurements-The transaminase catalyzesthe equilibrium of Equation 1,

* Th is work wa s supported in part by Research Grants H-2732and H-22 of the United States Public Health Service.

Aspartate + ketoglutarate F;(1)glutamate + oxaloacetate

which may be studied kinetical ly in either reaction direction bymeasuring the increase or decrease of absorbancy in the 260 rnpabsorption band of oxaloacetate. In the neutral pH region andin the absence of metal ion contaminants, the absorption coef fi-cient of oxaloacetate is 0.57 rnM-l cm-l, at 280 m,u, based uponweighed samples of the substrate and also upon enzymatic assaywith an excess of reduced diphosphopyridine nucleotide andmalic dehydrogenase at pH 6.8. Since the absorption coef fi-cient is relat ively small, i t was necessary to use reaction cuvet tesof lo-cm light path and a strip chart recorder with compensatingcircuits and a 5-fold expanded scale in order to obtain reliableinitial velocities at low substrate concentration. By thesedevices, an absorbancy change of 0.02 gives a full scale (11-inch)recorder deflect ion. This sens itiv ity was more than adequateto cover the required range of amino acid substrate concentra-tions and just barely suf ficed for the keto acids, which haveMichaelis constants in the range from 0.03 to 0.1 mM. Reactionmixtures were made up to 25 ml, and reaction was initiated byaddition of 0.05 ml or less of a standardized enzyme solution.Initial velocities were based upon the early linear portions of thereaction curve, usually involving the first few per cent of thetotal reaction. Brief initial lags were observed. These weremost pronounced at very low substrate concentrations and atextreme pH values. They could not be accounted for consist-ently by the occurrence of rate-limiting enolizations of oxaloace-tate, since they occurred in both reaction directions. Essentiallythe same Michaelis constants for aspartate and ketoglutaratewere obtained by the assay system described above and also bymeasurement of oxaloacetate production at 340 rnp with anexcess of malic dehydrogenase and reduced pyridine nucleotide,although the apparent maximal velocities in the latter case weresomewhat larger.

Kinetic TheoryFormulation of Reaction-The general formulation of the reac-tion is based upon the following observations. (a) The bound

coenzyme undergoes cyclic interconversions between the aminoand aldehyde form s, and (b) the enzyme catalyzes amino groupexchange between glutamate-CL4 and unlabeled ketoglutaratein the total absence of the aspartate oxaloacetate pair (5, 6).These results indicate that the reversible amino group transferbetween aspartate and ketoglutarate is the sum of two half-reactions (Equation 2).

2109


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2110 Glutamic Oxaloacetate Transaminase Mechanism Vol. 237, No. 7Aspartate + aldehyde enzyme $ @a)oxaloacetate + amino enzymeAmino enzyme + ketoglutarate $ @b)glutamate + aldehyde enzymeThe sequences of intermediates begin with the formation of acomplex between substrate and enzyme protein and proceedthrough the intramolecular formation of a Sch iff base betweensubstrate and bound coenzyme, a shi ft o f the double bond to theopposite side of the imino nitrogen in the Schi ff base, cleavageof the isomerized Sch iff base, and dissociation of amino or ketoacid product from the protein. The simplest hypothesis con-cerning the intermediary complexes is that the substrates occupythe same catalytic site one at a time in sequence, forming binaryenzyme-substrate complexes exclusively. This is the mecha-nism that is supported by the experimental results.Derivation of Rate Equations-Since both half-reactions arefreely reversible, the general formulation of the kinetic mecha-nism with four intermediates in each half-reaction involves theexplicit use of 20 individual rate constants. Derivations for thiscase have been made by the schematic matrix method of Kingand Altman (7) for the condition that involves the minimalassumptions concerning the rate constants, namely, that the

TABLE IMichaelis constants and maximal velocities in terms of rate constantsof minimal mechanism oj transaminase reaction

KA

Vfh + kd

klh

Kl

Vr(ks + k7)

ksk,

Vr(ks + k7) Vr(kz + kdk&s k&4

kzksv, = ___kz+ kg

FIG. 1. Double reciprocal plot of initial velocities againstketoglutarate concentration at a series of fixed concentrations ofaspartate at pH 7.3 in 0.04 M sodium arsenate at 26.

reactive enzyme species are in a steady state during initialvelocity measurements. Derivations have also been made forthe cases in which fewer intermediates are explici tly postulatedin the half-reactions. It turns out that the form of the rateequations is independent of the number of postulated inter-mediates. For this reason, and because the algebra will begreatly simplified, the initial treatment of the experimentalresults will be based on what we term the minimal mechanism(Equation 3)) in which only one intermediate is explici tly postu-lated in each half-reaction. The symbols, A, QI, G, and Ox referto concentrations of aspartate, ketoglutarate, glutamate, andoxaloacetate, respectively. E and E are the functionally non-dissociable complexes of pyridoxal and pyridoxamine phosphatewith enzyme, and EX and EY are symbols for sequences ofintermediates.

klA+.?#----+ Jakz EX - Ox + Eh (3a)ksol+E- hkG EY-G+E ks (3b)

The forms taken by the rate equations for the forward andreverse reactions are the same, since the equilibrium is sym-metrical, and are given in reciprocal form in Equation 4

EO-=-Vf ; %+?+If ( 01 >

EO-=- ; z+K&+lvr r ( >

(44

Mb)where v and V are initial and maximal velocit ies, the subscripts,f and,, refer to forward and reverse reaction directions, and theKs are Michaelis constants. As stated previously, Equation 4is obtained both for the minimal mechanism and for the expandedmechanism containing any number of intermediates. Thedifferences arise only in the expressions obtained for the Ks andVs in terms of the individual rate constants. These expressionsfor the minimal mechanism are summarized in Table I . It sohappens that the apparent association or dissociation constantsof the enzyme-substrate complexes, corresponding to rate con-stant ratios of the type, k&, k&, etc., can be evaluatedexperimentally. At a later point in the discussion, we shallconsider the meaning of these ratios in terms of the expandedkinetic mechanisms. It should be noted here that since thereaction is a cycl ic one it makes no difference which of the twohalf-reactions is written fir st. Changing the order puts differentnumerical subscripts on the ks, but the proper ident ification ofthe Its is automatic in the analysis of the experimental data.

Kinetic ParametersForward and Reverse eactions-According to Equation 4, a

double reciprocal plot of initial velocity against the concentra-tion of one substrate, 81, at a series of fixed concentrations of thesecond substrate, &, should yield a set of parallel lines, one foreach concentration of 82. This is observed for both reactiondirections (Figs. 1 and 2). Similar plots from the same sets ofdata are obtained with either substrate as the independentvariable. The intercepts on the ordinates are reciprocals ofapparent maximal velocit ies, l/V, and the intercepts on theabscissas are negative reciprocals of apparent Michaelis con-


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July 1962 X. F. Velick and J. Vavra 2111

I I I I I I I I I40 80 120 160

/OXALACETATEhnM)FIG. 2. Double reciprocal plot of initial velocity against oxalo-acetate concentration at a series of fixed concentrations of glu-tamate, pH 7.3, in 0.04 M sodium arsenate at 26.

slants, 1 /K,, . These quantities are related to the concentra-tion independent constants by Equation 5.1and - = -G,

Accordingly, a plot of 1 /V against l/(Sz) yields V and Ksz, anda plot of l/Ks, against l/(82) yields K,, (Figs. 3 and 4). Dataobtained in this manner for all four substrates are summarizedin Table II. It is noted that the enzyme reacts more rapidlywith glutamate and oxaloacetate than with aspartate plusketoglutarate and that the Michaelis constants for the keto acidsare much smaller than those for the amino acids. The con-cordance of the graphical form of the results with the require-ments of Equation 4 established the validity of the kineticmechanism of Equation 3 or of the equivalent expanded mecha-nisms. If ternary complexes between enzyme and two sub-strates were formed, then the rate equations would contain termsof the type, Ks,Ks,/(X1)/(S2), and the plots corresponding toFigs. 1 and 2 would be not sets of parallel lines but sets of linesthat intersected in a left-hand quadrant. This is what occurswith pyridine nucleotide-linked dehydrogenases, which formternary complexes in which the coenzyme behaves as a seconddissociable substrate. The reactive complex in transaminationis actually ternary if we include the coenzyme, but the coenzymein this case is not dissociable and hence is not an independentvariable. The above interpretation of the kinetic mechanismis also supported by the experiments described in the followingsections, which deal with substrate and product inhibition,equilibria, and various kinds of competit ive inhibitors.

EquilibriaOver-all Reaction-The equilibrium constant of the over-allreaction, determined by chemical and enzymatic analyses of the

substrate concentrations at equilibrium, is 7 i 1 (8, 9). Wemay , according to Equation 3 and Table I, formulate the reac-tion equilibrium as in Equation 6.

(6)The term on the right is the Haldane relation for this particularmechanism (10, 11) and may be verif ied by substituting for theVs and Ks the corresponding expressions in terms o f rate con-

stants from Table I. Substitution of the numerical values ofthe maximal velocities and rate constants from Table II givesK = 6.2, which is in good agreement with the direct ly determinedvalue and provides an independent test for the type of kineticmechanism and the self-consis t.ency of the kinetic parameters.The occurrence of Vf and Vr to the second power makes theHaldane relation a fai rly sensitive criterion for this mechanism.Half-reactions-A distinc tive property of the transaminasereaction is the sequential occurrence of two mutually invertedhalf-reactions. The occurrence of the half-reactions in thecomplete reacting system is established by the over-all kinetics,

-10 -5 5 IO 15 20 25k KETOGLUTARATEhnM)

FIG. 3. Secondary plots from data of Fig. 1. I, Graphicalanalysis yielding l/K, as intercept on the ordinate. KA is thequotient, slope/intercept (Equation 5). II, Graphical analysisyielding l/Vr as intercept on the ordinate at two different enzymeconcentrations and -1/K, as intercept on the abscissa. The samedata, replotted as in Fig. 1 with aspartate as the independen tvariable and anal.yzed as in Fig. 311, .yield -l/K* and the samel/VI.

I 2 3I/GLUTAMATE (mM)FIG. 4. Secondary plot from the intercepts of Fig. 2 showing

the extrapolations for l/V, and -l/Kc. The data may also beplotted to yield Koz.

TABLE IIMichaelis constants and relative maximal velocities,

experimental valuesThe experiment was carried out at pH 7.4 in 0.04 M arsenate at

26.KA K? KG Koz VrPf9n.M m.u ?nM 9n.u0.9 0.1 4 0.04 5/1.5


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2112 Glutamic Oxaloacetate Transaminase Mechanism Vol. 237, No. 7and the same data may be utilized in computing the equilibriumconstants of the half-reactions. Thus we may write

(A)(E) k&4 KAV,KI=o(E')=-=- k&3 KozVr(G) (El k&k; KGVrK1r=o(E)=kslcs=K,V,

(74

Substitution into Equation 7 of the numerical values for the Ksand Vs from Table II gives Kr = 74 and Krr = 12. The ratioof these K values is 74/12 = 6.2, which is merely a restatementof Equation 6. In both of the half-reactions, the equilibria favorthe formation of aldehyde enzyme and free amino acid, and thistendency is more marked with the aspartate than with theglutamate system. By virtue o f the carboxyl groups both crand fl to the keto function, oxaloacetate is both kinetically andthermodynamically less stable than ketoglutarate, and it is

.40-

$ .30-5g .20-cn:

.lO-

I I I I I I I I I320 340 360 380WAVELENGTH (rnp)

FIG. 5. Spectral changes in the conversion of the transaminasefrom the pyridoxal to the pyridoxamine phosphate form by titra-tion with aspartate.

KETOGLUTARATE, micromolarFIG. 6. Spectrophotometric equilibrium titration of the trans-aminase in the pyridoxamine phosphate form with ketoglutaratein 0.04 M sodium arsenate, pH 7.3, at 26. The intersection of theextrapolated initial slope with the limiting absorbancy gives theconcentration of the bound coenzyme.

140- 1 I I 85 4 3 2-log [G or A] (molar )

FIG. 7. Spectrophotometric equilibrium titration of phos-phopyridoxal enzyme with glutamate and with aspartate in 0.04M sodium arsenate, pH 7.3. The enzyme concentration may bedetermined from (AA860)max with a molar absorption coeff icientcalculated from Fig. 6.therefore to be expected that its amination equilibrium proceedfarther toward completion. The relat ively large equilibriumconstants are due in part to the fac t that the aldehyde group ofpyridoxal phosphate in its enzyme complex is not free but occursin Sch iff base linkage with the e-amino group of an adjacentlysine side chain (12). The tendency of the coenzyme to formthis internal bond serves to promote the elimination of substratein the amino acid form from the Schif f base enzyme-substrateintermediate. The enzyme-coenzyme complex thus has a some-what smaller amino group-accepting potential than do the aminoacid-keto acid pairs.SpectrophotometricTitration-Bound pyridoxal phosphateexhibits an absorption maximum at 362 rnp in neutral andalkaline solvents, and the band sh ifts to 333 rnp upon conversionto the pyridoxamine phosphate form. The spectral changeswith successive additions of aspartate to the aldehyde enzymeare illustrated in Fig. 5. Titration curves of the amino andaldehyde forms of the enzyme with keto and amino acid, respec-tively, are shown in Figs. 6 and 7, where absorbancy changes at362 mp are used as the indicator. As expected from the kineticanalysis of the half-reaction equilibria, a large molar excess ofamino acid is needed for complete conversion of aldehyde toamino enzyme, and glutamate is a better amino donor thanaspartate. In the reverse titrations, the conversion of amino toaldehyde enzyme proceeds nearly stoichiometrically with addi-tions of keto acid at micromolar concentrations. There is littlequestion concerning the qualitative interpretation of theseresults. They represent predominantly the equilibria of thehalf- reactions corresponding to Equations 7a and 7b. A quanti-tati ve interpretation requires the proper assignment of molecularspecies on the basis of the absorption changes observed. Inparticular, the possibility must be considered that the apparentequilibria are shifted by the accumulation in significant amountsof enzyme-substrate intermediates. Since the spectra of theamino and aldehyde enzymes are not markedly altered by dialy-sis, we may as a first approximation assume that intermediatesdo not accumulate, although we cannot exclude the possibilitythat they occur in forms that are not spectrally distinguished


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July 1962 X. F. Velick and J. Vavra 2113from those of the free enzyme coenzyme complex. On theassumption of no accumulated substrate complex, the reactionsconsidered are described by Equation 2, and the equilibria arethose of the half-reactions (Equation 7). We find from themid-points of the curves of Fig. 7 and the known concentrationsof added amino acid that the aspartate oxaloacetate enzymeequilibrium constant is K1 = 150 and that the glutamate keto-glutarate enzyme equilibrium constant is KII = 40. Bothvalues are larger than the corresponding numbers obtainedkinetically, and the ratio, KI/KI I = 3.7, is less than half ofthe correct value. The discrepancy might be attributed to theaccumulation of amino acid enzyme complexes, since the aminoacid concentrations exceeded 1 mM. However, the value of KIIcomputed from Fig. 6, where the ketoglutarate concentrationand the formed glutamate were in the micromolar range, is alsoin the vic ini ty of 40. Titrations of the amino enzyme withoxaloacetate give values of K1 between 80 and 200 and are dif fi-cult to control precisely . The discrepancies are not quantita-tive ly accounted for at the present time.

ZnhibitionSubstrate Analogues-The transaminase is inhibited by sub-strate analogues that are incapable of undergoing transamina-

tion. Several such compounds, all aliphatic dicarboxylic acids,have been examined by Jenkins, Yphantis, and Sizer (4), whofound that those compounds that were inhibitory at one arbitraryconcentration also formed an enzyme complex in which the pHdependence of the absorption spectrum of the bound pyridoxalphosphate was altered. In this section, we derive the rateequations for the inhibited systems, establish experimentallythat the substrate analogues are competit ive with all four sub-strates, derive the dissociation constants of the enzyme-inhibitorcomplexes both kinetical ly and by spectrophotometric equilib-rium titration, and show that the substrate analogues do notdiscriminate between the pyridoxal and pyridoxamine phosphateforms of the enzyme-coenzyme complex.Rate Equation for Competitive Znhibition-If a competitiveinhibitor acts by occupying a site on the enzyme that is utilizedsingly by all four substrates, then only two inhibited complexesneed be considered, namely, those formed by the inhibitor withthe amino and aldehyde forms of the enzyme-coenzyme com-plex, respectively. The numerical indices of the rate constantsof the equilibria of Equation 8 are continued in sequence fromthose of the minimal mechanism (Equation 4).

E+I- kg EIkm and E + I -$ EI (8)The initial velocity expression takes the form of Equation 9.

In a plot of l/v i against l/(A) or l/(a) at a series of inhibitorconcentrations, the inhibitor aff ect s both the slope and theintercept, and the lines will not intersect on the ordinate. Thus,although in this case the inhibition may be str ictl y competi tive,the usual simple criterion of competit ive inhibition is lacking.

The dissociation constants of the enzyme-inhibitor complexesare evaluated by plotting l/ v against (I) at a series of fixedconcentrations of one substrate and a single arbitrary concentra-tion of the second substrate. Such graphs for maleate inhibition

7v , ASPARTATE4- (mM)0.4 a,b,c,d

1.6 e, f ,g3-

I I I I I I / 1-2 -I 0 I 2 3 4 --eMALEATE (mM)

FIG. 8. Plot of the data for maleate inhibitio n of the aspartateketoglutarate transamin ation to yield, at the intersec tion point,the dissociation constant of the complex between maleate andthe pyridoxal phosphate form of the enzyme.

at a series of aspartate concentrations are shown in Fig. 8. Aset of straight lines is obtained that intersect in the upper left -hand quadrant. One may solve Equation 9 for the intersectionpoint, projected on the (-I) axis. It is found to occur atC-0 = holks, which, from Equation 8, is the dissociationconstant of the complex between maleate and aldehyde enzyme.This constant is found to be 2.3 mM. A corresponding plot of1 /Vi against (I) at a series of fixed concentrations of ketoglutarateand an arbitrary fixed concentration of aspartate also yields aset of lines that intersect in a left-hand quadrant (Fig. 9). Itmay be shown that the intersection point in this case is (-I) =&/i&, which, according to Equation 8, is the dissociation con-stant of the complex between maleate and the pyridoxamineform of the enzyme. In this case also, the intersection occurs at(-I) = 2.3 mM and is independent of the arbitrary fixed concen-tration of A. The combination of maleate with enzyme is thusindependent of the form of the coenzyme and is determinedexclusively by the specifici ty of the protein. Similar results areobtained when the inhibition is studied with glutamate andoxaloacetate as substrates. These observations provide addi-tional support for the idea that all four substrates utilize thesame catalytic site on the protein.

Equation 9 may also be solved for the intersection pointprojected on the l/v i axis. Thus, by substituting -i&/kg for(I) in Equation 9, we obtain Equation 10.

KETOGLUTARATE ASPb. - 0.08mM CmM)J. o--o 0.64mM 0. 4 /-I

MALEATE (mM)FIG. 9. The kinetics of the maleate inhibition of the aspartate

ketoglutarate transam ination, plotted to yield, at the intersec-tion point, the dissociation constant of the complex betweenmaleate and the pyridoxamine phosphate form of the enzyme.


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2114 Glutamic Oxaloacetate Transaminase Mechanism Vol. 237, Xo. 7

The value of l/v i at the intersection point may thus be eithergreater or less than the reciprocal of the maximal velocity , de-pending on the ratio of the dissociation constants in the lastterm on the right. In the special case that the inhibitor com-plexes of the two forms of the enzyme exhibit equal dissociationconstants, the factor in brackets equals unity , and l/v i = l/Vr.This was actually observed in Fig. 8, where the intersectionpoint is independent of the concentrations of both substrates,and is in accord with the fact that the two dissociation constantsare equal. Moreover, the value of Vf obtained from Fig. 9 isthe same as that obtained by the method of Fig. 3 in the absenceof inhibitor. This unusual way of obtaining a maximal velocityis restricted to kinetic mechanisms of the transaminase type.

Xpectrophotornetric Titration of Enzyme with Maleate-Anindependent value for the enzyme-maleate dissociation constantmay be obtained by an equilibrium titration of the enzyme. AtpH 7.4, the pH of the kinetic experiments, the enzyme-pyridoxalphosphate complex exhibits a strong 362 rnp absorption maxi-mum arising from the alkaline form of the bound pyridoxalphosphate and a weak maximum at 430 rnp arising from a smallequilibrium concentration of the acid form. Formation of themaleate enzyme complex raises the pK of the hydrogen iondissociation that controls the spectrum of the bound coenzymeand hence causes a weakening of the 362 rnp band and a strength-ening of the 430 rnp band. The concentration of the complex isproportional to the magnitude of the spectral change. Ab-sorbancy at 360 rnp plotted against the log maleate concentrationgives a typical sigmoid dissociation curve (Fig. 10). Sinceinhibitor concentration is greatly in excess of enzyme concentra-tion, the dissociation constant of the complex is given by themaleate concentration at the inflection point. The numberobtained is 2.3 mM, in close agreement with the result of thekinetic analysis. A sensitive spectral indicator is not availablefor a similar equilibrium titration of the pyridoxamine form of theenzyme, but in view of the above results we would expect thesame type o f agreement with the kinetic analysis.Xpeci$city of Inhibitor-Dissociation constants of enzyme-inhibitor complexes for a number of substrate analogues havebeen determined by the methods described above and are listedin Table III . In all cases, the inhibitors behave like maleatein that they are competitive with both the amino and keto acidsubstrates and interact identically with the amino and aldehyde

I I I I I I2 3 4 5

LOG [ MALEAT~J mMFIG. 10. Spectrophotometric equilibrium titration of thepyridoxal phosphate form of the transaminase with maleate. Thedissociation constant of the complex, given by the maleate con-centration at the mid-point, is the same as the values determinedkinetically.

TABLE IIIDissociation constants of inhibitor complexes between

transaminase and competitive substrate analoguesThe experiment was carried out at pH 7.4 in 0.04 M arsenate at

26.Inhibitor K

Succinate...........................Maleate.............................Fumarate........ .._.Glutarate...........................Adipate................Pimelate..........o-Phthalate.........................m-Phthalatep-Phthalate ,.........._ I:..::::::::

182.3Large35Large58

10

forms of the enzyme-coenzyme complex. In order to study thekinetics of the inhibition by the aromatic dicarboxylic acids, itwas necessary, because o f optical interference in the 260 to 280rnp region, to measure oxaloacetate production in a coupledenzyme system with an excess of malic dehydrogenase andreduced pyridine nucleotide. Although the phthalate isomersare also substrate analogues for the malic dehydrogenase, theydid not inhibit this enzyme in the concentration region employed.It is clear from the results that the protein-inhibitor interactionis strongly influenced by planarity, intercarboxyl group distance,and other factors. There is a greater conformational flexibili tyin the Cs and Cg acids than in succinate, and they are boundmore strongly. Pimelate is flexible, but the fold in the methylenechain is presumably too bulky when the carboxyl groups are inthe favored orientation for binding. It is not possible to makeany easy correlation between the behavior of the aliphatic andaromatic series of inhibitors.

Inhibition by Hydroxyylamine-This reagent dif fers from thepreviously described inhibitors in that i t should have no stereo-specif ic interaction with the protein portion of the substrate-binding site of the enzyme but should react exclusively with thealdehyde form of the bound coenzyme. I f the enzyme-in-hibitor compound is formed revers ibly, then the rate equationfor transamination in the presence of hydroxylamine should beobtained from Equation 9 by striking out the term containingkn/klz, which becomes zero since no amino enzyme-inhibitorcomplex would be formed (Equation 11).

_ _ U)KAh 1O Ka Kc, (11)Vi Vr(A)ho +Ff l+o+o( >If , as in the case of the substrate analogues, one plots 1 /v i againstthe inhibitor concentration, (I), at a fixed value of OLand a seriesof fixed concentrations of A, then a set of lines should be ob-tained that intersect in the upper left-hand quadrant. As before,the intersection point projected on the abscissa is ( -I) = klo/lcs,the dissociation constant of the enzyme-hydroxylamine com-pound. The experimental data so plotted are shown in Fig. 11Z.The apparent dissociation constant is unexpectedly small, ofthe order of 10 PM.

When the complementary set of data is plotted, l/v i against(I) at an arbitrary fixed concentration of A and a series of con-centrations of OL, hen a set of parallel lines should be obtained,


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July 1962 S. F. Veliclc and J. Vavra

A= 4.0mM

- .Ol 0 .Oi .02 ,005 ,010 ,015 ,020NH20H hM) N&OH (mM)

FIG. 11. Inhibition of the transamina se by hydroxylamine.I, Comp etition of hydroxylamine with aspartate for the boundpyridoxal phosphate of the enzyme at 0.5 mM ketoglutarate, pH7.3. The intersection point, projected on theabscissa, correspondsto a dissociation constant of 10 PM for the enzyme-inhibitor com-plex. II, The noncom petitive inhibit ion of the enzyme by hy-droxylamine with respect to ketoglutarate concentration.one line for each value of (Y. As shown in Fig. llZZ, this is theresult actually observed. We therefore conclude from the kineticanalysis that the primary inhibition by hydroxylamine occurs,as expected, by reaction with the aldehyde group of the boundcoenzyme and that the enzyme in the amino form is inert to thereagent. A spectrophotometric analysis of the ef fect follows.Xpectrophotometric Analysis of Enzyme-Hydroxylamine Com-pound-Fig. 12 illustrates the spectral shift that occurs whenhydroxylamine is added to the phosphopyridoxal form of theenzyme. The absorption bands of both the acid and alkalineforms of the bound coenzyme, pH 5.5 and 8.5, shif t to the regionof 380 mp, corresponding to the formation of the hydroxylamineadduct. In accord with the kinetic analysis, 50% conversionoccurs at hydroxylamine concentrations in the range from 10 to20 PM.

Also in accord with kinetic analysis, the spectrum of the phos-phopyridoxamine enzyme is unaffected by hydroxylamine. Itis necessary for such a test to dialyze the amino enzyme freefrom any traces of keto acid. If , for example, in the presenceof stoichiometric concentrations of ketoglutarate, the enzymeis maintained predominantly in the amino form by a high con-centration of glutamate, the addition of hydroxylamine in themillimolar concentration range suffi ces to pull the equilibriumtoward the aldehyde form by formation of the hydroxylaminealdehyde adduct. This is illustrated in Fig. 13. The apparentconversion of amino enzyme to aldehyde enzyme hydroxylamineadduct is mediated by the trace of ketoglutarate formed in theoriginal conversion of aldehyde to amino enzyme and proceedsto an extent that is limited by the amount of ketoglutaratepresent.The formation of the hydroxylamine enzyme adduct is reversi-ble. Thus, if the dialyzed aldehyde enzyme in the presence of10 to 20 PM hydroxylamine is treated with glutamate at a finalconcentration of 10 mM or higher, the 380 rnp absorption banddeclines and the 335 rnp band of the amino enzyme appears.Therefore, as indicated by the kinetic analysis, the enzymeinhibitor compound is dissociable. The hydroxylamine reac-tion with the bound coenzyme presumably occurs by displa cingthe internal lysine bond and is thus expected to go directly tothe oxime. In the nonenzymatic case, oxime formation involvesaddition followed by elimina tion of the elemen ts of water andproceeds toward comple tion only at much higher concentration sof reactants.Inhibition by Excess Substrate-As in the case of the substrate

analogues, the individual substrates should bind both to theamino and aldehyde forms of the enzyme-coenzyme complex.In addition to the reactive complexes, one should also obtain,at suitably high concentrations, the abortive or nonreactivecomplexes of the type , keto acid-aldehyde enzyme and aminoacid-amino enzyme. Formation of such complexes shouldresult in inhibitions that are compet itively overcome by thecomplementary substrates. Inhibitions of this type were notobserved in the double reciprocal plots of Figs. 1 and 2 becausethe concentration range covered was too low, but they are ob-served in Fig. 14, where the substrate concentrations are elevatedto levels of the order of 10 x Ks. The competitive nature ofthe effect is indicated by the fact that the concentration of thefirst or independently varied substrate at which the upwardinflection of the curves occurs increases as the concentration ofthe second or fixed substrate is increased. Although the analysisis rather cumbersome, it can be shown that the inhibition con-stants of amino and keto acids are much more near ly equal thantheir respective Michaelis constants. The dissociation con-stants of the abortive complexes, determined by spectrophoto-

or 60 400 320 360 400 440 460WAVELENGTH, my

FIG. 12. Spectra of the bound pyridoxal phosphate in thenresence and absence of hydroxylamine. I, At pH 8.5; 11, at pH5.5.

a

0 t

2

I I I I I I I I I I I420 380 340WAVELENGTH, m/c

FIG. 13. Curve 1, absorption spectrum of a dialyzed mixture ofthe amino and aldehyde forms of the transamin ase. Curve 2,absorption spectrum of the same mixture after addition of excessglutamate showing ostensibly complete conversion to the aminoform. Ketoglutarate is now present at a concentra tion equalto that of the aldehyde enzyme, which has disappeared. Curve 3,effect of hydroxylamine addition to the system of Curve 2. Bycombin ing with the extremely low equilibrium concentra tion ofaldehyde enzyme, the inhibitor has pulled the amino and aldehydeenzyme concen trations back to the original level limited by theamount of ketoglutarate formed in the original conversion. Inthe absenc e of ketoglutarate, the amino enzyme is unaffectedspectrally by hydroxylamine.


8/14

2116 Glutamic Oxaloacetate Transaminase Mechanism Vol. 237, No. 7

1 I I I I I0 I 2 3 4I/KETOGLUTARATEhnM)

FIG. 14. Substrate inhibition by ketoglutarate as a functionof aspartate concentration at pH 7.3. Inhibition, as indicatedby the upward inflection of the curves, begins at higher keto-glutarate concent,rations as the aspartate concentration is in-creased.metric equilibrium titration, are utilized in a later section in theevaluation of individual rate constants. They are consideredalso in the study of the pH dependence of maximal velocit ies,since their pH dependence is different from the pH dependenceof the reaction steps and cause arti facts which must be controlled.Aspects of substrate and product inhibition are utilized for otherpurposes in the following section, which treats the behavior ofthe so-called three-substrate systems.

Three-substrate ystemsTheory-An independent kinetic determination of the equilib-

rium constants of the half-reactions and a further separation ofthe individual rate constants is obtained by analysis of initialvelocities measured in the presence of one reaction product.There are four three-substrate cases that may be examined,corresponding to the substrate combinations, A-or-G, G-Ox-A,Ox-G-a, and a-A-Ox. In each instance, the inhibitor is writtenon the right, and the substrate with which it competes, on the lef t.The inhibitors actually engage in transaminations, but underinitial velocity conditions they can only react with the centralmembers of the trios by reactions in which both partners areregenerated. The net ef fect is withdrawal of enzyme from thereaction being directly observed and an apparent inhibition.Initial velocity equations for these systems have been derivedfor the steady-state condition and for both the minimal and theexpanded kinetic mechanisms. As before, expansion of themechanism does not alter the form of the results, and we there-fore present the equations for the minimal mechanism involvingonly one explicit intermediate per half-reaction.

Wa)(13a)

1 b) Koz 4 ksh 1-=-vi vr (02) i + E (G) (14a)6 6 8I (OS)-=- Vfi (15a)

These equations, which correspond to the four three-substratecases, are all of the same form, and examination of them revealsthat equivalent information may be obtained by the analysisof either of two pairs, Equations 12a and 13a or Equations 14~and 15a. In order to condense the equations, we have substi-tuted for the appropriate aggregates of individual rate constantsthe symbols for the equivalent Michaelis constants and maximalvelocit ies, leaving in explicit form only those rate constants orratios thereof to be evaluated experimentally.

Experimental Procedure-The experimental results are treatedby two success ive graphical analyses. With Ox-G-o! system(Equation 14a) as an example, ai is measured as a function ofthe inhibitor concentration, (a!), at fixed concentrations of 0%and G. A plot of l/v i against (a) yields a straight line. With(G) kept constant, the measurements are repeated at a series offixed concentrations of Ox. Plots of these results yield a seriesof straight lines, one for each concentration of Ox, and the linesare found to intersect in a left-hand quadrant. Several similarseries of measurements are made at different fixed concentrationsof G. The intersection points, projected on the abscissa or (o()axis, are functions of (G). Two such sets are illustrated in Fig.15. The data for the other three-substrate cases are obtainedand treated in the same way with similar results.

One may solve Equations 12a to 15a for the intersectionpoints obtained in graphs of the above type . The relations areexpressed in reciprocal form, with the inhibitory product ineach case written on the left (Equations 12Z1 o 15b).7J

I~LIJ CURVE [OXALACJ

m M flbM4 0 0.020.4 b 0.04

c 0.12

td 0.026.4 e 0.043 f 0. I2

I II-

.1 I I I I I I-0.3 - 0.2 -0.1 0 0.1 0.2 OS3

[ KETOGLUTARATE] muFIG. 15. Inhibition of the glutamate oxaloacetate reaction at

pH 7.3 by ketoglutarate. Reciprocal initial velocities are plottedagainst ketoglutarate concentration at three oxaloacetate concen-trations, each at two different concentrations of glutamate, ac-cording to Equation 14~.Iq OXALACETATE 0.06mM GLUmM l

3- /A /

I I3 I I I I I 89 I ! 9 I I I I-1.2 -0.8 -0.4 0 0.4 0 .8 1.2

ASPARTATE (mM)FIG. 16. Inhibition of the glutamate oxaloacetate transamina-tion by aspartate at pH 7.3, plotted according to Equation 13a.


9/14

July 1962 X. F. Velick and J. Vavra 2117

WI(14b)(15b)

Thus, for the case we are examining in detail, Equations 14~ and14b, a plot o f the reciprocal of the intersection points, - (1 /cr) a,against the corresponding reciprocal concentration of G gives astraight line (Fig. 17)) the slope of which is k&,/i&&, the equilib-rium constant of the glutamate half-reaction, and the interceptof which on the ordinate is k5/&. From these quantities onemay calculate k,/Jcs. The latter ratios are, respectively, theequilibrium constant for formation of intermediate from aminoenzyme and ketoglutarate and the equilibrium constant for thedissociation of intermediate to form aldehyde enzyme andglutamate.

k GLUTAMATE (m M 1

-75j i0.6

IO 20 30bOXALACETATE (mM)

FIG. 17. Left, reciprocal intersection points, with respect tothe abscissa, for the system of Fig. 15, plotted against the cor-responding reciprocal glutamate concentrations (Equation 14b).Right, reciprocal intersection points fo r the system of Fig. 16plotted against the corresponding reciprocal concentrations ofoxaloacetate. The intercepts on the ordinates are, respectively ,ka/ka and kl/kp, and the slopes are as indicated.

All o f the three substrate cases have been studied, and theresults are summarized in Table IV. The equilibrium con-stants of the half-reactions, obtained by this method, are inessential agreement with the results calculated from the Michaelisconstants and maximal velocities of the two substrate systems.The apparent dissociation constants, k&r, etc., are furtheranalyzed in the following section.

Dissociation ConstantsExpanded Mechanism-The theoretical treatment of the

kinetic experiments in the preceding sections was based uponthe minimal mechanism, both for algebraic simplicity and be-cause additional constants could not be resolved solely by themethods of over-all kinetics. Insofar as the over-all equilibriaand the equilibria of the half-reactions are concerned, the minimalmechanism introduces no ambiguity. On the other hand, theapparent dissociation constants of the enzyme-substrate com-plexes, as defined by the minimal mechanism and listed in TableIV, are not microscopic constants but involve intramolecularreactions in addition to the association and dissociation processes.

A more detailed analysis o f the product inhibition experimentscorresponding to Fig. 17 and Table IV requires consideration ofan expanded kinetic mechanism. For this purpose, a partialexpansion to two intermediates per half-reaction will suf fice(Equation 16).

& ka ksA+EyEA kz Z EOx e E + Oxk kg (16a)

The rate constants for the expanded mechanism are in bold facetype to distinguish them from those of the minimal mechanism.Since there are, in fac t, at least twice as many intermediates asthose formulated in Equation 16, it may appear arbitrary todesignate the two intermediates per half-reaction explicit ly asenzyme-substrate and enzyme-product complexes. Justificationfor this procedure is provided in the following paragraph.

TABLE IVIntermediate equilibria from kinetic analysis of compe tition in three-substrate systems

Al l measurements are based on conditions of 0.04 M sodium arsenate, pH 7.3, 25.

EquationHalf-reaction equilibrium

From slope or its reciprocalFrom K, and v,,, (Equation 7)

Apparent association constant

From intercept (equation above)Calculated*

A-a-G I 0x-G-a

12b I 14b

8.8 I 11.4 55 I 7212 74ks EY-=__h G.E

ks EY-=-ks ol.E0.20.15

1.70.6

G-0x-A I a-A-Ox

136 15b

h EX-=-kz A-Ekd EX-=-b 0x.E

0.5I

280.38 28

* Calculate d from intercept and slope of the paired system. The discrep ancies are within the probable errors o f the primary andsecondary plots.


10/14

2118 Glutamic Oxaloacetate Transaminase Mechanism Vol. 237, h-o. 7The rate equations corresponding to Equation 16 are identicalwith Equation 4, but the expressions for the Michaelis constants

and maximal velocities in terms of individual rate constants aremore complicated (Table V). Similarly, the equations fo r thethree-substrate systems (Equations 12 to 15) are enlarged butretain the same form. We will not present the expansion of theseequations in full , but the reinterpretation of the slopes andintercepts of the secondary plots corresponding to Equations12b to 15b and Fig. 17 are summarized in Table VI. It may beseen that the slopes are still the equilibrium constants of thehalf-reactions, but the intercepts now contain two terms, whichmay be factored. In each case, the factor outside the paren-theses is the equilibrium constan t for the initia l or terminal stepin a half-reaction. The same type of factored intercept is ob-tained regardless of the number of additional intermediates

TABLE VMichaelis constants and maximal velocities in terms of

rate consta nts of partially expanded mech anismK _ Vr(kzks + ksks + knkr)A- K a = Vr(k&lo f k&l + k&l)W&s k?kokn

kzkakskm = ksklo(kz + k, + k4) + kekr(ks + ks + kd

TABLE VIInterpretation of secondary plots of three-substrate kinetics

(Table IV) in terms of partially expanded mecha nism

Slope

Intercept

TA-a-G 0x-G-a G-0x-A a-A-Ox

I

I I --1-

FIG. 18. Spectrophotometric equilibrium titration of pyridoxalphosphate enzyme with ketoglutarate and oxaloacetate. Theconcentrations of the keto acids at the mid-points are the dissocia-tion consta nts of the respective abortive complexe s, E-a and E-Ox.

4-x-

k3--c

\,,,s5I

2:,, . ../

,,_!..\ ,.*,+H +

k, k,- - ho

4 i%_ -.,::

2:

: \. .,,I .,,,*I.I ._ I.0

(1SSOC + dlsplocement -H+xiz

+ H, O dissoc.-displacement - -H + 5-c 2 assoc.+H +

FIG. 19. Diagram of the mecha nism of a half-reaction withfour intermediate s showing the enzyme-substrate and enzyme-product complexes and the two isomeric Sch iff base intermediates.Supe rposition of substrate and bound coenzyme show s one way inwhich the proximity effect of a substrate or substrate analoguecarboxyl group could influen ce the spectrally linked p K of thecoenzyme. The amino group of the substrate and the e-aminogroup of the adjacent lysine side chain competitively displace eachother from azomethine bonds to the carbonyl group of the co-enzyme. On the other side of the sequen ce, the isome ric Schif fbase is reversibly formed and cleaved by the elimin ation andaddition of the elements of water. As the figure is drawn, theamino group of the lysine and the phen olic group of the coenzymecould catalyze the hydrogen shift in the isomerization of theintermediate, but the results and arguments summarized inNume rical Evaluation of Individual Rate Constants provideno direct evidence for such an interpretation.

postulated in the kinetic mechanism. In the general case, thefactor outside the parentheses is always the equilibrium constantof an initial or final step, and the constants within the paren-theses correspond exclusively to intramolecular reactions withinthe complex. Analysis of over-all kinetics does not enable us toseparate the bimolecular from the intramolecular factors, butif the pure association or dissociation constants of two of theenzyme-substrate complexes can be determined by independentmeans, then the corresponding constants for the other two com-plexes may be computed, and in addition one may obtain thesteady state equilibrium ratios of the two macroscopic intra-molecular rate constants of each half-reaction, namely, ks /kloand k4/ks . It will be shown that this can be done, at least to afirst approximation, and that the results taken together withother kinetic information permit the numerical evaluation ofk3, k4, kg, and km

Approximation of Dissociation Constants-The two enzyme-substrate dissociation constants that may be determined ex-perimentally are those of the nonreactive complexes betweenphosphopyridoxal enzyme and the two keto acids. These aredetermined by equilibrium titrations, which are based uponobservations of the same spectral shi fts that are produced in thecomplexes between enzyme and the compe titive substrateanalogues such as maleate. The two titration curves are shownin Fig. 18 and yield dissociation constants of 3 and 6.7 mM forE-a, and E-Ox. In order to equate these values, respectively,with ks/k7 and k5/k6 of the expanded mech anism, it is necessaryto assume that the keto acids, like the substrate analogues, arenot strongly affected by the state of the functional group of thecoenzymes in their initial interaction with the protein. Thisassumption would appear, at fir st, to involve neglect o f thefundamental nature of the catalysis. It may be rationalizedin the case of the amino acid substrates because the carbonylgroup of the coenzyme is in azomethine linkage to a lysine sidechain and is pulled to one side, as illustrated diagrammatically inFig. 19. In the case of the active keto acid complex, the free


11/14

July 1962 S. F. Velick and J. Vauraamino group of the coenzyme can cause steric interference, butit also has some degree of rotational freedom, and the inter-ference, energetically, may therefore not be large. If we acceptthese arguments provisionally, then multiplication of the numeri-cal value of kg/kT, so obtained, by the experimental value ofkF/ks( l + kg/km) from Table VI gives us the numerical valueof the factor in parentheses from which we obtain the value ofks/km The latter number turns out to be 4.0. Substitutionof the reciprocal of this number in the appropriate parentheticalterm of Table VI gives us the numerical value of klz/kn, theassociation constant of the enzyme-glutamate complex. Thesame sequence of operations with ks/kc from the abortiveoxaloacetate complex gives us k4/k3, the intramolecular equilib-rium of the first half-reaction, and kl/kz, the association con-stant of the enzyme-aspartate complex. The numbers so ob-tained are listed in Table VII .

Numerical Evaluation of Individual Rate Constan tsThe analysis up to this point yields simple ratios of rate con-stants . Those ratios corresponding to initial or final steps of

the half-reactions are clearly defined as association and dissocia-tion equilibria, provided only that two or more intermediatesare postulated per half-reaction, as in Equation 16. Theyremain so defined, with the numerical values in Table VII,regardless of any further expansion of the kinetic mechanism.Mechanistically they apply to those events that occur beforeSchi ff s base formation between substrate and coenzyme or theevents that occur after the cleavage of the intermediate. Towhat extent they correspond to elementary processes is of interestbut is irrelevant to the present argument. On the other hand,the so-called intramolecular rate constants, ks, kh, kg, and klo,are defini tely macroscopic constants in the sense that eachdescribes a sequence of elementary processes. It is thereforepossible to describe each of them as a function of a still largernumber of specif ic intramolecular rate processes, but it is point-less to do so for the treatment of over-all kinetic and equilibriumdata because they could not be evaluated from such information.Each macroscopic k nevertheless describes the rate of a particu-lar intramolecular sequence in the direction indicated. More-over, in a special case, of which the transaminase appears to bean example, they may be evaluated numerically from the dataat hand. The special case is that the bimolecular steps invo lv-ing the association of substrate with enzyme are not rate-limitingand are of the order of diffusion controlled values.

The experimental support for the argument that kl, kg, k?,and kIz are extremely large is provided by the fac ts (a) that onsuch an assumption one may derive values of the four intra-molecular ks that predict the observed rates of isotopic exchangein the isolated half-reactions and (b) that even if it is rate-limit-ing, kg, for example, would have to be of the order of 10M-I see-l to account for the observed V, under the conditionsat which it is attained. If the intramolecular steps were notrate-limiting, they would have to be improbably large. It ispertinent to point out that the observed resul ts are describedby the steady state approximation and that in the steady stateapproximation the bimolecular rate constants do not appear inthe expressions for the maximal velocit ies. This is a generalproperty of such mechanisms, although it is usually stated thatthe steady-s tate approximation makes no assumptions aboutrate constants. It is also pertinent to mention that the associa-tion of fumarase with its dicarboxylic acid substrates, which aresimilar to those of the transaminase, also approaches diffusion

controlled rates according to the analysis of Alberty and Pierce(13). If we are dealing with rates of this order of magnitude,then IQ, kg, kg, and kll are also large, since the dissociationconstants are all between 10e2 and lop3 M. Accordingly, theexpressions for maximal velocity in the expanded mechanism(Table V) reduce to a simpler form (Equation 17).

k&sVf = __ lcakmk3 + ks and v, = -1~ + ho (17)These relations, together with the equilibria of the type, kI/k2,etc. , of Table IV complete the number of independent relationsrequired for the algebraic solution of the intramolecular rateconstants of the partially expanded mechanism.

Thus, i f kr/ks = a and ks/klo = b, it may be shown (Equation18) thatk 3 = Cab - l)VfV,

Wrb - Vfhand klo = (1 - ab)VfV,

(Vr - aVr)b(18)

The other two intramolecular constants, k4 and ks, may also berelated to a, b, and the maximal velocities or may be obtainedfrom kt and klo by simple relations which have already beengiven. Substitution of the appropriate numerical values of aand b and the maximal velocities from Table VII into Equation18 give us the numerical values of the intramolecular rate con-stants listed in Table V III. According to these results, therate-limiting step in the transamination of ketoglutarate byaspartate occurs in the first half-reaction and is described by k3,the rate of conversion of bound aspartate and pyridoxal phos-phate to bound oxaloacetate and pyridoxamine phosphate.Similarly, the rate-limiting step in the reverse reaction is de-scribed by klo, the intramolecular conversion of glutamate toketoglutarate. The large numerical value of k4 is required bythe equilibrium of the fir st half-reaction.Isotopic Equilibration-It is possible, on the basis of the resultsin Table VIII , to predict the rate of the steady state isotopicequilibration reaction (Equation 19)Glutamate-W + ketoglutarate-CY fglutamate-C* + ketoglutarate-Cl4 (19)compared to the initial maximal velocity, Vf, of the over-alltransamination.The exchange rate is given by a standard expression, Equation20 (14), which is independent of the reaction mechanism

(G) (c40.693Vex = [(G) + (a)lt;

TABLE VIIDissociation constants of enzyme-substrate complexes

(20)

kz l3.A-=_kg (EA)kc EJ.0.Xkc = @Or)

ks E.o:k7 = (Ea)

w&M mu ,?LM

2 6.7 3

ku E.G-=-kn (EG)VZM

8.3

TABLE VIIIRate constants for intramolecular reaction sequences of

ylutamic oxaloacetate transaminaseka

seco323

kase0

59,100

kssec9

4170

kmMC-1020


12/14

2120 Glutamic O.raloacetate Transaminase Mechanism Vol. 237, No. 7where ti is the half-time for complete isotopic equilibration. I fthe experiment is carried out at substrate concentrations thatgive approximate maximal velocity, then, purely by symmetryconsiderations, the exchange veloci ty, V,,, is a maximal velocitygiven by the expression (Equation 21)

k&mv,, = ~ks + ho (21)Substitution into Equation 21 of the numerical values of therate constants from Table VIII gives V,, = 800, which we maycompare with Vf = 300, and which gives the theoretical ratio,V,, /Vf = 2.7. Jenkins and Sizer (6) have actually measuredthe rate of equilibration of glutamate and ketoglutarate andmention the fact that i t occurs at approximately twice the rateof the over-all transamination of ketoglutarate by aspartate atthe same concentrations of enzyme and substrate. In the lightof the present work, the amino acid concentrations they em-ployed approached saturation levels and the keto acid concen-trations were in the range that produced substrate inhibition,but the latter ef fect should cancel out approximately in theratio. In view of the facts that no claims were made concerningthe precision of the experimental ratio, that an unspecified anduncertain absorption coeff icient was involved, and that thereare approximations in the theoretical ratio, the agreement be-tween theory and experiment must be considered to be good.

PHFIG. 20. Plots of Vf, Vi/K*, and Vf/K, as functions of PH.

Vr is in units of turnover number per molecule of bound coenzvme.In the acid region, the buffer is acetate with Tris as the cation.In the middle and alkaline regions. the buffer is either sodiumarsenate or Tris, with acetate or chloride as the cation. Resultswith carbonate-bicarbonate and with glycine buffers were erratic.

TABLE IXpH dependence of kinetic parameters of glutamicoxaloacetic transaminase

PH vf* KASIG-

70185260300300310300320310330

4.55.05.56.06.57.07.58.08.59.09.5

3.52.02.41.21.00.91.01.21.92.5

--

-

0.020.040.050.10.10.090.090.130.14

vf /K~

53130130250310330310260170120

-

* In units of turnover per mole of bound coenayme.

Vi/&

13,0007,5006,0003,1003,0003,5003,0002,6002,200

pH Dependence of Enzyme ActivityMaximal Velocity pH Dependence-With the methods de-scribed in Kinetic Parameters, the maximal velocities of the

forward and reverse reactions were studied over the pH rangefrom 5.0 to 10.0. In order to cover this range, it was necessaryto establish the absence of specific ion eff ects from the differentbuffers employed, to make corrections for the changes in absorp-tion coefficient of oxaloacetate as a function of pH, and to copewith possible irreversible or secondary changes in the moreextreme pH conditions. The various complications were mosttroublesome above pH 9, and we have not succeeded in obtaininga reliable estimate of a rate-controlling pK in the alkaline region,although we believe one to occur in the vicinity of pH 10. Theresults for the forward reaction are summarized in Fig. 20 andTable IX. Diffi cul ties were encountered in the acid regionbecause the Michaelis constant for ketoglutarate decreases withpH, and the sensitive concentrations become too small for opti-mal treatment even by the expanded scale optical method.Close analysis was particularly important because deviations indouble reciprocal plots due to inhibition by excess keto acid aremore marked in the acid region. It was possible to check themaximal velocities and to circumvent both difficult ies by makinguse of a relation observed in connection with maleate inhibition(Figs. 6, 7, and 8). It was shown in the latter analysis that theintersection points of l/Vi against (maleate) plots at a series ofdiffe rent aspartate concentrations and a single fixed ketoglutarateconcentration give not only the dissociation constant of themaleate-enzyme complex but also a true, uninhibited, maximalvelocity (Equation 10). The latter curves may be run at thelowest fixed ketoglutarate concentration that gives measurableinitial velocities and have been utilized to check the maximalvelocities at pH 5.0, 5.5, and 6.0. The results also explain theincreased inhibition by ketoglutarate at acid pH, since thedissociation constant of the maleate-enzyme complex, whichinhibits exactly like the abortive ketoglutarate-enzyme complex,decreases from 2.3 mM at pH 7.4 to 0.36 mM at pH 5.

Attempts to measure veloci ty-pH functions at high fixedsubstrate concentrations lead to erroneously high and variablepK values in the pH activit y curves because of the pH depend-ence of inhibition by ketoglutarate. Thus, at aspartate andketoglutarate concentrations of 6.7 DIM, there is an apparentrate-controlling pK around pH 7 (4). Any correlation of sucha pK with the protolyt ic pK of the abortive ketoglutarate-enzyme complex is coincidental. One may, however, obtain afair approximation of the present results by running the pH-activ ity curve at fixed substrate concentrations of aspartate,(20 mm) and ketoglutarate (0.5 mm). These concentrationsgive a good approximation of maximal velocity, and at the sametime any competit ive substrate inhibition is eliminated.

The same type of broad pH-maximal velocity plateau is ob-tained for the transaminase reaction studied in the reversedirection with oxaloacetate and glutamate as substrates. How-ever, oxaloacetate is more dif ficult to cope with in the acid regionthan is ketoglutarate, and we have not attempted to extend theanalysis with th is substrate. Because of the degree of symmetryof the forward and reverse reactions, the absence of these datadoes not seriously handicap us.

pH Dependence o f ka and kio--When two rate constants are inseries, the over-all rate is dominated by the smaller of the twoconstants. Thus the maximal velocities and pH dependence ofthe forward and reverse reactions are determined, respectively,


13/14

July 1962 S. F. Velick and J. Vavra 2121by ks and klo and by their respective pH dependencies. The linked group is appreciably raised in the enzyme-substrate orrate-controlling pK of 5.1 for Vf , therefore, corresponds to the enzyme-inhibitor complex (as utilized under Three-substratedissociation of a hydrogen ion from a group in the enzyme-as- Systems and Dissociation Constants), it could not be thispartate complex or in one of the associated intermediates. If group, as modified by substrate in the enzyme-substrate com-the pK is that of a group of the protein or coenzyme, it is not plex, which is responsible for the pK of 5.1 that controls Vf andnecessarily identical with the pK of the same group in the ka. The latter pK may correspond to a carboxyl ionization ofabsence o f substrate. the substrate itse lf or of a protein side chain.A feature of a transaminase mechanism involving a Sch iff baseintermediate is that an isomerization is required in which thedouble bond o f the Sch iff base is moved revers ibly from thesubstrate side to the coenzyme side of the imino nitrogen. Sucha shi ft involves both a gain and a loss of protons from the inter-mediate and is enzyme-catalyzed, since it does not occur rapidlyin nonenzymatic systems. I f the proton reactions are promotedby specif ically oriented proton-donating and -accepting groups ofthe enzyme, then these groups would be expected to function inthe vic ini ty of their respective pK values, because a group thatdonates a proton in the fir st half-reaction must accept a protonin the inverted second half-reaction. One would therefore expectto observe a sharp optimum in the pH-maximal velocity curve.The absence o f a sharp optimum would occur in such a mech-anism only under the conditions that have been defined, namely,that the maximal velocity in each reaction direction is dominatedby one of the two hal f-reactions.

SummaryGlutamic oxaloacetate transaminase has been prepared in a

state approaching purity. From a spectrophotometric analysisof the experimentally accessible equilibria between enzyme,bound coenzyme, substrates, and inhibitors, and by a systemat icanalysis of the initial velocity kinetics of the transamination inboth reaction directions in the presence and absence of oneproduct, the following information has been obtained.1. The reaction proceeds kinetically through two mutuallyinverted half-reactions with exclusively binary complexes be-tween substrate and the functionally nondissociable enzyme-coenzyme complex.

pH Dependence of kl, ke, k7, and kn-Whereas the pH de-pendence of the maximal velocity is determined by ionizationsin the enzyme-substrate complex, a pH plot of Vmax/Ks, whereKs is a Michaelis constant, gives the pK values of dissociablegroups in the enzyme itse lf which af fect the rate constants of therapid bimolecular association reactions between enzyme andsubstrate (15). Thus, if we consider the expanded mechanismof the transaminase reaction (Table V), the functions, KA/Vfand Ka/Vf , may be written in the form of Equation 20.

2. In accord with previous chemical information, the boundcoenzyme acts as an amino group carrier.3. The four substrates are mutually competit ive and occupythe single cata lytic binding site on the protein one at a time, in

sequence.4. The equilibrium constants of the over-all reaction and ofthe two half-reactions may be derived kinetically by two inde-

pendent methods.5. The theory of competit ive inhibition for the transaminasemechanism has been developed and applied to the inhibitions

produced by a series of substrate analogues.6. Dissociation constants of complexes between enzyme-co-enzyme complex and inhibitory substrate analogues derived

kinetically are in close agreement with the constants derived byspectrophotometric equilibrium titration.7. Substrate analogues that cannot engage in transamination

inhibit by occupying the substrate binding site on the enzyme-coenzyme complex and form complexes with the same dissocia-tion constant whether the bound coenzyme is in the amino oraldimine form.

and

In both cases, the rate constants within the brackets occur inratios, and each ratio involves a pair of constants that apply tothe same intermediate. A derivation of the pH dependence ofK,/Vf involves multiplying each rate constant by its own pHfunction, which is determined by the pK values of the inter-mediate. These pH functions cancel out in pairs, leaving only thepH function of the unpaired rate constant outside the brackets.This argument also applies to expanded cases with any additionalnumber of explicit intermediates. Thus a plot of Vf/Ka againstpH describes the pH dependence of kl, and a plot of Vr/K,describes the pH dependence of kl. The corresponding plotsare shown in Fig. 20.

The curve, Vi/K* against pH, exhibits two inflections, oneat pH 6.3 and the second at pH 9. The pK of 6.3 is close to thepK o f the ionizing group, which aff ect s the spectrum of the boundcoenzyme in the absence of substrate and could, for example,correspond to the ionization of the phenolic hydroxyl or ringnitrogen of the bound coenzyme. This is in accord with thetheory outlined above that such a plot should reveal the pK of agroup in the enzyme or enzyme-coenzyme complex and not inthe enzyme-substrate complex. Since the pK of the spectral ly

8. The theory has been developed and established experi-mentally for the case of a competit ive inhibitor that interactsexclus ively with one form of the bound coenzyme. Hydroxyl-amine reacts revers ibly only with the bound pyridoxal phosphateand not with the pyridoxamine, and it competes only with theamino acid forms of the substrate.

9. By the appropriate combination of kinetic and equilibriummeasurements, it is possible, for the mechanism derived, toseparate the rate constants for the formation and dissociationof the enzyme-substrate complexes from those that occur intra-molecularly on the enzyme and invo lve the formation, isomeriza-tion, and cleavage of the Schif fs base intermediates.

10. Dissociation constants of the enzyme-substrate complexesare derived kinetica lly.

11. The bimolecular association reactions between enzyme andsubstrate are not rate-limiting. The possibili ty that they ap-proach dif fusion controlled rates is indicated.

12. Macroscopic rate constants for the four intramolecularreaction sequences, two in each reaction direction, are derivedalgebraically and are evaluated numerically from the experi-


14/14

2122 Glutamic Oxaloacetate Transaminase Mechanism Vol. 237, No. 7mental data fo r the favored case, that in which the bimolecularsteps are very rapid compared with the intramolecular steps.13. The constants so obtained may be used to compute therates of isotopic equilibration in isolated half-reactions and arein accord with data in the literature.

15. The pH dependence of the maximal velocity has beeninvestigated in both reaction direct ions. There is no dependencein the region pH 6 to 9.

14. The rate-limiting step in the transamination of ketoglu-tarate b y aspartate is intramolecular and occurs in the half-reaction in which phosphopyridoxal enzyme and aspartate areconverted to phosphopyridoxamine enzyme and oxaloacetate.The rate-limiting step in the reverse reaction is also intramolecu-lar and occurs in the half-reaction in which glutamate is con-verted to ketoglutarate.

16. In the aspartate ketoglutarate reaction, there is a rate-controlling hydrogen ion dissociation with a pK of 5.1. ThispK corresponds to an ionization in the reactive intermediateformed by enzyme-coenzyme with the 4-carbon substrate.

17. The rate of the bimolecular association reaction betweenaspartate and enzyme is controlled by a hydrogen ion dissocia-tion of pH 6.3. This pK coincides with the spectrally linked pKof the bound pyridoxal phosphate. It does not af fec t the max-imal velocity and is involved in the reaction rate at submaximalsubstrate concentrations only through its influence on Michaelisconstants.

18. The rate equations for the mechanisms described abovewere derived on the assumption that the enzyme species are in a

steady state during initial velocity measurements. Conditionsare defined for obtaining the kinetic and equilibrium parametersfrom primary and secondary plots of the experimental data.

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Sot., 78, 648 h954). 3. MEISTER, A., SOBER, H., AND PETERSON, E. A., J. Biol. Chem.,

206, 89 (1954).4. JENKINS, W. T.. YPHANTIS, D. A., AND SIZER, I. W., J. Biol.

Chem.,234, 5i (1958).5. NISONOFF. A.. BARNES. F. W.. JR.. ENNS. T.. AND VON SUCH-

ING, S.,Buk John s Hopkins Hdsp., 94, ll? (1954).6. JENKINS, W. T., AND SIZER, I. W., J. Biol. Chem., 234,1179(1959).7. KING. E. L.. AND ALTMAN . C., J. Phys. Chem., 60, 1375 (1956).8. KR&, H. k., Bioche m. j., 54, 82 (1953).9. NISONOFF. A.. BARNES. F. W.. JR.. AND ENNS. T.. J. Biol.

I / , IChem., 204, 957 (1953).10. HALDANE, J. B. S., Enzymes, Longmans, Green and Company,Ltd., London, 1930.11. ALBERTY, R. A., J. Am. Chem. Sot., 75, 1928 (1953).12. FISCHER, E. H., AND KREBS, E. G., Abstra cts of the 136thMeeting of the America n Chemical Society, Atlantic City,September 1959, p. 24~.13. ALBERTY, R. A., AND PIERCE, W. H., J. Am. Chem. Sot., 79,1526 (1957).14. WAHL, A. H., AND BONNER, N. A., Radioactivity applied tochemistry, John Wiley and Sons, Inc., New York, 1951.15. FRIEDEN, C., AND ALBERTY, R. A., J. Biol. Chem., 212, 859(1955).

velick vavra 1962l

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