ANALYTICAL CHEMISTRY, VOL. 51, NO. 9, AUGUST 1979
degree of precision, although considerably less than that which can be achieved under the best conditions using isotope ratio mass spectrometry, should be sufficient to measure KIEs due to 13C and 15N as well as l80.When used in concert with the direct rate method described in the accompanying paper, this technique should continue to prove versatile in helping to probe both organic and enzyme reaction mechanisms.
ACKNOWLEDGMENT We thank Clinton E. Ballou for t h e use of the mass spectrometer, Chris Reading for designing t h e automatic repetitive scan attachment, and Charles B. Sawyer for assistance with computer programming.
1379
(8) M. H.O'Leary and J. F. Marlier, J. Am. Chem. Soc., 100, 2582 (1978). (9) M. I. Schimerlik, J. E.Rife, and W. W. Cleland, Biochemistry, 14, 5347 (1975). (10) S.Rosenbergand J. F. Kirsch, Anal. Chem., following paper in this issue. (11) F. Balhrdie, B. Capon, J. D. G. Sutherland, D. Cocker, and M. L. Sinnott, J . Chem. Soc., Perkin Trans. 1 , 2418 (1973). (12) M. L. Sinnott and 0. M. Viratelle, Biochem. J., 133, 81 (1973). (13) A . A. Clifford, "Multivariate Error Analysis", Halstead, New York, 1973. (14) A. C. SatterthwaitandW. P. Jencks, J. Am. Chem. Soc., 96, 7018 (1974). (15) A. C. Satterihwait and W. P. Jencks, J. Am. Chem. Soc., 96, 7031 (1974). (16) M.Gresser and W. P. Jencks, J . Am. Chem. Soc., 99, 6963 (1977). (17) M. Gresser and W. P. Jencks. J . Am. Chem. Soc., 99, 6970 (1977). (18) "CRC Handbook of Biochemistry", H. A. Sober, Ed., Chemical Rubber Co., Cleveland, Ohio, 1968, J151-190. (19) M. L. Sinnott, FEBS Lett., 94, 1 (1979). (20) M. L. Sinnott and 1. J. L. Souchard, Biochem. J . , 133, 89 (1973). (21) M. L. Sinnott, S.G. Withers, and 0. M. Viratelle, Biochem. J . , 175, 539 1197RI - -/. I
LITERATURE CITED (1) C. B. Sawyer and J. F. Kirsch, J . Am. Chem. Soc., 95, 7375 (1973). (2) M. H. O'Leary in "Transition States in Biochemical Processes", R . D. Gandour and R. L. Schowen, Eds., Plenum Press, New York, 1978, pp 285-316. (3) J. Bigeleisen and M. Wolfsberg, Adv. Chem. Phys., 1, 15 (1958). (4) H. Kwart and J. Stanulonis, J . Am. Chem. Soc.. 98. 4009 (1976). (5) C. B. Mitton and R. L. Schowen, Tetrahedron Lett., 55, 5803 (1968). (6) D. G. Gorenstein, J . Am. Chem. Soc.. 94, 2523 (1972). (7) D. G. Gorenstein, Y. Lee, and D. Kar, J , Am. Chem. Soc., 99, 2264 (1977).
(22) S. Rosenberg and J. F. Kirsch, Fed. Proc., Fed. Am. SOC.E x p . Bid., 37, Abst. 151 (1978).
RECEIVED for review February 23,1979. Accepted May 2,1979. We are grateful to t h e National Science Foundation (grant P C M 74-17643AO2) for financial support, t h e U S . Public Health Service (grant 5T01 GM00031-20) for support of one of us (S.R.), and the Computer Center of the University of California, Berkeley.
Direct Spectrophotometric Measurement of Small Kinetic Isotope Effects Steven Rosenberg
and Jack F. Kirsch*
Department of Biochemistry, University of California, Berkeley, California 94720
A method is described for the measurement of heavy atom kinetic isotope effects by directly determining the rate differences due to isotopic substitution. This is accomplished by measuring the rates of reaction of highly enriched reactants compared with compounds of natural abundance using a high precision spectrophotometer interfaced to a teletype via a microprocessor for automated digital readout. The spectrophotometric data are fit directly to the relevant rate expression by nonlinear least squares regression analysis. Applications of this method to the measurement of oxygen-18 leaving group kinetic isotope effects on the reaction of nicotinamide with 2,4-dinitrophenyl acetate and on the pgalactosidase catalyzed hydrolysis of p-nitrophenyl-@-Dgalactoside are given.
Heavy atom kinetic isotope effects (KIEs) have usually been measured by a competitive technique involving the determination of the isotopic composition of reactants or products as a function of t h e extent of reaction. This has been done in most cases by isotope ratio mass spectrometry following chemical conversion of t h e products or starting materials to a gas. A few workers have succeeded in measuring heavy atom KIEs by determining directly the rate differences engendered by isotopic substitution. Mitton and Schowen were the first to show the feasibility of this technique. They determined the carbonyl oxygen, l8O KIE for the methanolysis of phenyl benzoate ( I ) . Subsequently, Gorenstein and co-workers ( 2 . 3 ) utilized a similar approach to analyze t h e detailed mechanism of phosphate ester hydrolysis. The measurement of heavy atom KIEs by this method for enzyme-catalyzed 0003-2700/79/0351-1379$01 0010
reactions has been questioned ( 4 ) . I t is important to develop the direct method to as high a degree of accuracy and precision as possible because of the ease of application compared to mass spectrometric procedures which require larger amounts of isotopically enriched materials and are more time consuming; and because this method offers the only apparent possibility to obtain isotope effects on V, (the rate a t saturating substrate concentration) for enzyme-catalyzed reactions. T h e recent development of high precision spectrophotometers such as t h e Cary 118 and the interfacing of these instruments via microprocessors to yield data in digital form without intervention of the experimenter led us to explore this system for the direct measurement of heavy atom KIEs. T h e photometric accuracy of such a spectrophotometer is better than 0.01absorbance unit, representing an error of only 0.1% for a change in absorbance of 1.0. We have found t h a t this degree of precision allows KIEs t o be determined to f0.1% . Although considerably less than t h a t obtainable by isotope ratio mass spectrometry, this precision is sufficient for all but the most exacting studies using heavy atom KIEs.
EXPERIMENTAL Apparatus. All spectrophotometric measurements of reaction kinetics were made on a Cary 118C Spectrophotometer interfaced via a microprocessor (Claremont Research) to an ASR 33 teletype
and tape-punch. The microprocessor can be set to sample the absorbance data at intervals from 1-999 s. Both the cell holder and cell compartment were maintained at constant temperature with a Lauda Model K2 circulating water bath. A cell holder capable of holding up to 5 cuvettes was used for all isotope effect experiments. The original design of the microprocessor was modified so that up to 5 reactions could be monitored simultaneously. A Radiometer Model PHM4c pH meter equipped with 'C 1979 American Chemical Society
1380
ANALYTICAL CHEMISTRY, VOL. 51, NO. 9, AUGUST 1979
a B type electrode was used for all pH measurements. The isotopic enrichment of the oxygen-18 labeled reactants was measured using a n u Pont Model 21-491 mass spectrometer equipped with a Columbia Scientific Model 260/722 data system and digital printer, as described in the preceding paper ( 5 ) . Reagents. 2,4-Dinitrophenyl acetate (DNPA) substituted with "0 in the ether oxygen was synthesized by condensing the potassium salt of "0 labeled 2,4-dinitrophenol with acetyl chloride in N,N-dimethyl formamide. This reaction is complete within 1 min. The addition of an excess of 0.1 M sodium acetate, pH 6, followed by seeding with a crystal of the product and placing the solution at 4 "C overnight led to the crystallization of the product. Recrystallization from cyclohexane yielded DNPA, mp 70.5-71.5 "C, lit. 71-72 "C (6). Mass spectrometric analysis of the ester or the 2,4-dinitrophenol obtained by alkaline hydrolysis of the ester showed no loss of "0 as compared with the starting material. p-Nitrophenol-'80 was synthesized by a two-step procedure involving the condensation of methanol-"O prepared by the method of Sawyer (7) with p-nitrofluorobenzene in hexamethylphosphoric triamide in the presence of lithium hydride. The resulting p-nitroanisole-"O was reacted with pyridine hydrochloride to yield p-nitrophenol-'@0(8). The product was identical to authentic p-nitrophenol by melting point, 112.5-113.5 "C, lit. 113-114 "C (9),NMR and UV-visible spectrophotometry. A synthesis begun with H2180 containing 95% l8O (BioRad) yielded p-nitrophenol-180 with 89.9% "0 as measured by direct mass spectrometry. p-Nitrophenyl-0-D-galactoside, l60or "0 was synthesized from the labeled or unlabeled p-nitrophenol and acetobromogalactose (Sigma) by standard methods (10,11). All other materials were reagent grade and were used without further purification. 3Galactosidase from E. coli was obtained from Worthington as a chromatographically purified suspension in ammonium sulfate. Glass distilled water was used for all isotope effect measurements. Small impurities which could affect the rate of reaction by even a few percent clearly would invalidate the measurement of heavy atom KIEs by the direct rate method, as the latter are of a similar magnitude. For this reason both the isotopically enriched and unlabeled reactants were synthesized and purified by the same method. The chemical purities were monitored by several criteria including melting point, NMR, IR, and UV-visible spectrophotometry. These combined methods may still be inadequate to rule out completely impurities of less than a few percent. In order to check further that no impurities which affect the rate of reaction were present, isotope effects were sometimes additionally determined by the method reported in the preceding paper ( 5 ) . The competitive technique should not be sensitive to such impurities, unless they produce the same parent molecular ion in the mass spectrometer. In addition, if a reaction could be found which should yield a KIE of 1.000, it was monitored as a control on substrate purity. The determination of a KIE by two independent methods and the observation of a KIE = 1.000 in one reaction while a second reaction yields a measurable KIE greatly reduces the possibility of an artifact due to a small contaminant in either the enriched or unenriched reactant. Kinetics. All reactions were monitored spectrophotometrically on a Cary 118c spectrophotometer interfaced to a microprocessor as described to yield direct digital output. Two variables require particular attention-the rates of the reactions of interest are dependent upon both temperature and the concentrations of some of these reactants. The first of these parameters was controlled by monitoring the kinetics of 4 or 5 reactions simultaneously in the cell compartment. Typically, two of the cuvettes contained enriched reactant and the others unenriched material. Several such sets of kinetic runs were measured in a given experiment. In order to ensure that there was no temperature variation between the cuvettes in the cell holder, the positions of enriched and unenriched reactants were alternated between sets of kinetic runs. In addition, the order in which the reactions were initiated with respect to the labeled and unlabeled reactants was varied. Finally, in alternate sets the same cuvette was used for kinetic runs of enriched and unenriched reactants to eliminate any deterministic error due to slight differences in pathlength between cuvettes. These procedures should minimize any systematic differences due to temperature, cell position, and pathlength.
As the reactions of interest here are all linearly dependent on the concentration of catalyst, this variable must be controlled with an accuracy of ca. 0.1%. This was accomplished by preparing a large stock solution which contained all the reaction components except the substrate containing the isotopic label. Typically, 3.00 mL of this mixture was transferred to the cuvettes in the cell holder with a single calibrated volumetric pipet. This transfer could be accomplished in an extremely reproducible manner if care was taken to use exactly the same technique each time. These solutions were equilibrated in the cell compartment of the spectrophotometer for 5-10 min. Glass distilled water or the stock solution was used in the reference position. The microprocessor was set at the appropriate time interval and the reactions were initiated by the addition of less than 100 pL of a concentrated solution of the labeled or unlabeled reactant. The order of addition of the two solutions was alternated from set to set. After the solutions were mixed without removing the cuvettes from the cell holder, the microprocessor was activated and data acquisition initiated. Data for each of the five reactions were sampled sequentially, and between 20 and 50 data points were acquired for each kinetic run. End points were determined after ca. 10 half-lives for reactions run under pseudo-first-order conditions, and after the absorbance was constant for several minutes for enzyme-catalyzed reactions. The time at which each reaction was started and the time of the first absorbance reading for each reaction were recorded. These are important only for the enzyme-catalyzed reactions. Pseudo-first-order reactions were followed for three to six half-lives. The entire progress curves for the enzymecatalyzed reactions were monitored. After the reactions were complete, the pH of each solution was measured. This procedure was repeated for each set of kinetic runs-typically, 4-6 times for a single experiment. Thus, each experiment consisted of about 10 kinetic runs of the labeled and unlabeled reactants. As an additional control against subconscious deterministic prejudice on the part of the experimenter, some of the KIE determinations were carried out in a "double-blind" mode; Le., the solutions of the two isotopic reactants were prepared by a disinterested third party and supplied to the experimenter as coded samples whose identity was not disclosed until completion of the experiment. The oxygen-18 enriched sample was observed to react more slowly in all such cases. Computer Analysis of Kinetic Data. The progress curves of the reactions, consisting of the absorbances and times for each point, were fit directly to the appropriate function by nonlinear least squares regression analysis. Reactions run under pseudo-first-order conditions were fit to Equation 1: Aobsd =
A,
-
(A, -
(1)
where Aobsd is the observed absorbance at time t , A , is the absorbance at the end point of the reaction, A,, is the initial absorbance, and k is the pseudo-first-order rate constant for the reaction. The observed data were fit with the end point and the rate constant as variable parameters. Enzyme-catalyzed reactions were fit to the integrated form of the Michaelis-Menten equation shown in Equation 2 using a computer program written by C. B. Sawyer: -V,,.t = K,.ln ( S / S o )- S - So (2) The variable parameters were V,,,, K,, the initial substrate concentration, So,and the end point. An accurate value for the extinction coefficient is required for this analysis and the same figure was used for both enriched and unenriched substrates. The validity of this assumption was checked in independent experiments. The computer analyses yielded the best values of the parameters of interest which are the pseudo-first-order rate constants and values of V,, as well as their estimated standard errors. Kinetic runs were included for further calculation of the isotope effect if they fulfilled three criteria: (1) A plot of the residuals (the observed absorbance less the calculated value at each data point) was relatively random, as determined visually, when the end point was included as an adjustable parameter. This indicated that the kinetics did fit the appropriate function within the precision of the data. (2) The measured pH of the solution did not differ by more than 0.02 pH unit from the other kinetic runs
ANALYTICAL CHEMISTRY, VOL. 51, NO. 9, AUGUST 1979
I
0.004
0.003
a a
I
1
I
I half-time half-times
c
0
0
3 half-times 0
1
4 halftimes
1 I
0
0
Y
0
I3
I
1381
Complete enrichment is rarely feasible, because of difficulties in synthetic methods and the expense of 100% enriched starting materials. T h e kinetics of a mixture of l60and "0 containing reactants are rigorously described by the weighted sum of two exponentials as shown in Equation 7:
if the rate law for each component is first order. Absorbances are as defined above, f l s and f 1 8 are the fraction of unlabeled and labeled reactants in the reaction mixture, and k16and k l 8 are the rate constants for the isotopically homogeneous species. In practice, one cannot distinguish the sum of two exponentials with rate constants which differ by a few percent from a single exponential with a rate constant which is the weighted average of the rate constants of the two exponentials shown in Equation 7 (13). Thus, Equation 8 is a very good approximation t o Equation 7:
1 OI
I
I
I
I
where f is the fraction of labeled reactant and R = 1- k18/kle This expression has the advantage that it can be evaluated Time to yield a single observed rate constant whereas the two rate (arbitrary units) constants in Equation 7 are usually impossible to determine independently. The rate constant for the unenriched reactant, Figure 1. Absorbance differences expected between two reactions h16, can be measured independently in separate experiments. which follow pseudo-first-order kinetics with rate constants which differ Computer modeling of the difference between Equations 1 by 1% ( 0 )and 0.3% (0). The total absorbance change is 1.O for the complete reaction and 8, assuming 50% enrichment, an isotope effect of 1.07, and a total absorbance change of 1 shows t h a t under these in that set. (3) The calculated rate constant did not differ from conditions the theoretical progress curves differ by less than the others in the set by more than 5 standard errors. Kinetic runs 0.0001 absorbance unit at any point. Thus, in all cases the which were clearly anomalous could usually be traced t o a dirty pseudo-first-order reaction kinetics can be fit by a single cuvette or pipet. These three conditions were fulfilled by at least exponential, since a difference of O.ooO1 is considerably smaller 80% of the kinetic runs in a given experiment and often by all than the precision of the data. of the runs. The weighted average of the rate constants for the enriched Application to Ester Aminolysis. The reaction of DNPA and unenriched reactants were then calculated for each set of four with amines is of mechanistic interest because of the evidence or five kinetic runs. The observed isotope effects for each set and for a change in the rate-determining step for this reaction as their associated propagated standard errors were calculated using a function of amine basicity which is described in the preEquations 3 and 4: ceding paper. The determination of an oxygen-18 KIE for KIE(each set) = k16(mean)/ k18(mean) (3) DNPA lends itself to ready analysis by the direct method of the large absorbance change accompanying the Standard Error of KIE = [(SE16/k18)2+ ( ( k l ~ / k ~ ~ 2 ) S E ~ ~ ) 2 1 1because '2 release of 2,4-dinitrophenol, e.g., Equation 3 of the preceding (4) paper ( 5 ) . The isotope effect for the reaction of nicotinamide The KIE for an entire experiment was calculated by weighted with DNPA was measured directly and also by mass specaveraging of the KIEs for each set. Since the labeled reactant trometry as described in the previous paper; thus a direct usually was not 100% enriched, the observed KIE was corrected comparison of the results and precision of the two methods finally for incomplete labeling using Equation 5 (12): is possible. Although both procedures are subject to possible KIEcorr = (KIEobsd -!- f ) / f (5) artifacts, these would almost certainly be different. where f is the fraction of isotopic enrichment, KIEobadis the The observed reaction kinetics for a typical run monitored observed isotope effect, and KIE,, is the isotope effect corrected by the release of 2,4-dinitrophenoxide are shown in Figure 2. for incomplete enrichment. The reaction was followed for 3 half-lives and the maximum deviation of the observed data from the theoretical progress RESULTS AND DISCUSSION curve was 0.0003 absorbance unit (Figure 2 insert). Before initiating experimental work, the magnitude of the The rate constants for a series of reactions of nicotinamide smallest KIE that can be determined given the photometric with DNPA containing natural abundance, 38%, and 76.7% reproducibility of the available spectrophotometer was asoxygen-18 in the ether oxygen are shown in Figure 3. These sessed by computer modeling. The results of this modeling data were acquired in sets of five kinetic runs monitored of some theoretical data are shown in Figure 1, which is a simultaneously, and the computer analysis of the data was graphical representation of Equation 6: done by two methods. First, the progress curves were fit to AA = A, - ( A , - Ao)(e-kt- e-A.kt) (6) a single exponential to yield pseudo-first-order rate constants. The apparent oxygen-18 KIEs for the entire experiment were where I A is the absorbance difference a t time t , A, is the k16/k18 = 1.0152 f 0.0024 for the 38% labeled ester and 1.0309 end-point absorbance, A , - A , is the total absorbance change during the reaction, h is the rate constant for the reaction, f 0.0023 for the 76.7 % labeled ester. These KIEs were then and A is the value of the isotope effect. A difference of 1% corrected for incomplete labeling using Equation 5 . T h e in the rate constants gives a maximum absorbance difference second method of data analysis involved fitting the progress of 0.004 from a total (A, - Aol = 1.0. This is well within the curves for the partially labeled esters to the rigorous solution resolving power of the Cary 118C. A rate constant difference of the kinetics given by Equation 7. This was done using the of 0.3% is at the borderline of detection for a single set of runs. independently measured rate constant for reaction of the unlabeled ester for each set and the known fraction of label A second problem addressed by theoretical simulations is for each sample which was determined by mass spectrometry. t h a t of incomplete enrichment of the labeled substrate. Od
1.0
2 .o
3.0
1382
ANALYTICAL CHEMISTRY, VOL. 51, NO. 9, AUGUST 1979
__
'
--__
Table I. Computer Analysis of t h e Kinetic Data for the Isotope Effect o n t h e Reaction of Nicotinamide with DNPA by Two Different Methods
c
DNPA Sample --___
0
method seta 1
48
2
a
I
i
3
4 1
I
\
,
2
l
3
weighted mean S.E.
Time (sec x Figure 2. Kinetics of the reaction of 2,4-dinitrophenyl acetate 3 8 % labeled with oxygen-18 in the ether oxygen with nicotinamide monitored at 360 nm. The reaction was run at pH 4.33, I , = 1.0 and initial concentrations of ester and nicotinamide of 65 pM and 0.010 M, respectively. The psewbfirstarder rate constant calculated from these s-', The inset data as described in the text is 8.447 f 0,008 X is a plot of the residuals at each data point
fi
NO2
N i co t i nom i de + C H,-C-*O&N 8.71
I
I
0,
I
method 2c
DNPA Sample 2b .___ method method 1 2
1.0353 1.0361 1.0421 1.0423 (0.0011)d (0.0028) (0.0013) (0.0016) 1.0480 1.0499 1.0373 1.0376 (0.0016) (0.0042) (0.0017) (0.0021) 1.0430 1.0445 (0.0015) (0.0039) 1.0354 1.0363 1.0415 1.0421 (0.0013) (0.0035) (0.0015) (0.0020) 1.0466 1.0473 (0.0020) (0.0027) 1.0389 1.0399 1.0331 1.0335 (0.0027) (0.0046) (0.0027) (0.0030) 1.0390 0.0025
1.0401
1.0410
0.0026
0.0018
1.0410 0.0019 A set consists of the five kinetic runs which were monitored simultaneously. Sample 1 contained 38% oxygen-18 labeled dinitrophenyl acetate. Sample 2 contained 76.7% oxygen-18. Method 1 involved fitting all of the kinetic runs t o Equation 8, and then correcting for incomplete labeling. Method 2 used the independently determined values of the rate constant for unlabeled ester for each set and fit the observed kinetics of the partially labeled material t o the sum of two exponentials (Equation 7). Values in parentheses are the propagated standard errors of the observed KIEs.
T
f l
8.61
4 , 0
- '60
3 - 38% '80
4
1C
lb
( 5 ) . The agreement of the results from the two disparate methods supports the contention t h a t these simplified procedures can yield accurate values of KIEs. The observation of a large oxygen-18 leaving group KIE for the reaction of nicotinamide with DNPA by two independent methods strongly supports the idea t h a t cleavage of the bond to t h e dinitrophenyl group is well advanced in the transition state for this reaction. If a tetrahedral intermediate exists along the reaction pathway, then its decomposition must be rate determining. Application t o an E n z y m e C a t a l y z e d Reaction. The oxygen-18 leaving group KIE for the hydrolysis of p-nitrophenyl-3-D-galactoside was also measured by the direct rate method (Equation 10).
4 , i
2
3
4
Set Number Figure 3. Calculated pseudo-first-order rate constants for a series of reactions of nicotinamide with 2,4-dinitrophenyl acetate at pH 4.33, I , = 1.0. Each reaction contained 0.010 M nicotinamide and either oxygen-16 ester (O), 3 8 % oxygen-18 enriched ester (0),or 7 7 % oxygen-18 enriched ester (A) initially at 65 p M concentration. The reactions were run in sets of 5 which were monitored simultaneously. The error bars represent the estimated standard errors of the pseudo-first-order rate constants for each kinetic run. These data were analyzed as described in the text and are presented in Table I. The obsewedKIEs unadjusted for the fraction enriched are k,,lk,, = 1.0152 f 0.0024 for the 38% labeled ester and 1.0309 f 0.0023 for the 7 7 YO labeled ester
T h e results of these analyses are summarized in Table I. I t is clear t h a t the two methods yield equivalent results within t h e accuracy of the measurements. This confirms the theoretical simulations described earlier. In addition, the measured isotope effect of k16/k18 = 1.040 f 0.002 from this experiment is the same as that measured by mass spectrometry, which yielded a value of the KIE of 1.043 f 0.007
(10)
These reactions were run a t saturating substrate concentrations so the resulting KIE is on Vmm. Thus, if a substantial KIE is observed, cleavage of the bond to the isotopically labeled atom must occur in the overall rate-determining step in the reaction sequence a t substrate saturation. A typical complete progress curve for this reaction is shown in Figure 4, where the maximum deviation of the observed data from the theoretical curve is 0.0003 absorbance unit. A series of sets of five kinetic runs were measured, each of which consisted of two or three unlabeled and two or three oxygen-18 (74% atom excess) labeled samples. A typical experiment is shown in Figure 5 . .4 minor correction amounting to ca. 10% of the KIE must be applied to account for the oxygen-18 equilibrium isotope effect on the ionization constant of p-nitrophenol. This reduces t h e KIE from 1.0200 to 1.0181 ( 2 4 ) . This value is finally corrected for the effect of incomplete labeling of the oxygen-18 enriched substrate on the kinetic isotope effect using Equation 5. The final value of the isotope effect on V,, for this substrate in this experiment is 1.0243. The two
ANALYTICAL CHEMISTRY, VOL. 51, NO. 9, AUGUST 1979
LOO(
I
I
C
0
0 0
0
0
IO 20 30 U Data Point Number 0 0 r .
0
U
0 0
0
l
i
o 0
oo
i 3 I
I
I
2
Time (sec x Flgure 4. Kinetics of the reaction of @-galactosidasewith unlabeled p-nitrophenyl-fl+galactoside
at pH 7.82 as monitored at 450 nm. The reaction was run in 0.1 M sodium phosphate buffer containing 1 mM MgCI,. The initial substrate concentration was 423 pM. The calculated value of the maximum velocity from these data is 0.1305 f 0.0004 ~ M l s .The inset is a plot of the residuals
1
1
1383
precision has been obtained for both organic and enzymecatalyzed reactions. I t is doubtful that more precise data can be obtained with the presently available technology. The maximum deviations from the theoretical progress curves for a given kinetic run were typically less than 0.001 absorbance unit, approximately the limits of precision of the spectrophotometer. As previously described, each experiment was comprised of approximately 10 kinetic runs of the enriched and unenriched reactants. Increasing the number of runs might decrease the standard error, although a precision of 0.1 % is certainly sufficient for the interpretation of most heavy atom KIEs. In addition, the reproducibility of this method is not as good as its precision; typically, duplicate experiments agreed to within 0.5%. The applicability of this method is limited primarily to two factors; the rate of the reaction of interest and the change in absorbance which occurs during the reaction. Since it is critical to monitor several reactions simultaneously and to obtain sufficient numbers of data points to define the rate constants extremely accurately, reactions with half-lives of less than 5 min are not amenable to investigation by this technique. The determination of V, must be optimized for measurements of isotope effects on enzyme-catalyzed reactions. This involves using a substrate concentration which is as high as possible (at least eight times K,) to minimize the extrapolation to V,,,. The slowest reactions investigated by this method had half-times of about 4 h. This required the maintenance of essentially invariant reaction conditions for a t least 1 2 h. Possible problems which may develop over this period of time include photoreactivity of the substrate, insufficient temperature control, spectrophotometer drift, and side reactions. As discussed above, the maximum absorbance difference between two first-order reactions with rate constants differing by 1% is about 0.004 absorbance unit, for a total change in absorbance of 1. This difference is directly proportional to the total absorbance change which occurs during the reaction; therefore the magnitude of the isotope effect that can be measured decreases for smaller values of /A, - Ao(. As the highest value of signal-to-noise in absorption spectrophotometry is obtained for a U = 0.868 ( I $ , larger values of this parameter do not necessarily lead to more precise determination of KIEs.
'
LITERATURE CITED
09 9 0 L L . - I
~~~~
2
-~
3
. 4
~
~__ 5
Set Number
Figure 5. A complete set of data for the measurement of the oxygen-18 KIE on Vmx for &galactosidase with p-nitrophenyl-P-c-galactoside as substrate at pH 7.82. These data were obtained in sets of 5 kinetic runs monitored simultaneously. The lower dashed line represents the average value of V, for the two or three ("Oenriched) samples which is defined as 1.000. The points (0)represent the ratio of the individual contributions to this average. The filled circles ( 0 )represent the ratios of V,,, (unenriched) to the value indicated by the lower dashed line. The upper dashed line represents the weighted average of the KIE for the complete experiment which is 1.0200 k 0.007
corrections of the KIE effect only a small change in the total value and do not alter the interpretation of this result. The substantial isotope effect observed on V,,, requires t h a t cleavage of the bond to the isotopically labeled oxygen must occur during the overall rate-determining step in the reaction sequence at substrate saturation. Thus, a conformation change of the Michaelis complex cannot be rate determining for this substrate. Limits of Precision and Applicability. The most precise experiments we have done using this method have yielded KIEs with propagated standard errors of about 0.1 7% for an experiment comprised of ca. 20 kinetic runs. This degree of
(1) C. B. Mitton and R. L. Schowen, Tetrahedron Lett., 55, 5803 (1968). (2) D. G . Gorenstein, J . Am. Chem. Soc., 94, 2523 (1972). (3) D. G. Gorenstein, Y . Lee, and D. Kar, J . Am. Chem. Soc., 99, 2264 (1977). (4) W. W. Cleiand in "Isotope Effects on Enzyme Catalyzed Reactions", W. W. Clebnd, D. B. Northrop, and M. H.O'Leary, Eds., University Park Press, Baltimore, Md., 1977, pp 122-153. (5) S. Rosenberg and J. F.Kirsch, Anal. Chem., preceding paper in this issue. 86, 837 (1964). (6) J. F. Kirsch and W . P. Jencks, J . Am. Chem. SOC., (7) C.B. Sawyer, J . Org. Chem., 37, 4225 (1972). (8) V. Prey, Ber., 74, 1219 (1941). (9) "The Merck Index", P. G. Stecher, Ed., Merck and Co., Inc., Rahway. N.J., 1968, p 741. (10) J. Conchie and G. A . Levy, Methods Carbohydr. Chem., 2, 335 (1963). (11) D. H. Leaback. J . Chem. Soc., 3166 (1960). (12) F. W. Dahlquist, T. Rand-Meir, and M. A. Raftery, Biochemistry, 8, 4214 (1969). (13) C. Lanczos, "Applied Anaiysis", Prentice Hall, Engkwood Cliffs, N.J., 1964, p 272 f f . (14) S. Rosenberg and J. F. Kirsch, unpublished. (15) M. Eigen and L. de Maeyer in "Technique of Organic Chemistry", Vol. 8, Part 2, 2nd ed., A. Weissberger, Ed., Interscience, New York, 1963, p 975.
for review February 23,1979. Accepted May 2,1979. We are grateful to the National Science Foundation (grant PCM 74-17643AO2) for financial support, the US.Public Health Service (grant 5-TO1 GM00031-20) for support of one of us (S.R.), and the Computer Center of the University of California, Berkeley. RECEnTD
