W. G. Nigh University of Puget Sound Tacoma. Washington 98416
I I I
A Kinetic Investigation of an Enzyme Catalyzed Reaction A biochemistry or physical chemistry laboratory
Although the subject of enzyme catalysis has generally been reserved for consideration in biochemistry courses, there are several advantages to be gained by introducing the topic in other areas of the chemistry curriculum. Besides the obvious student interest generated by these hiological catalysts, the subject provides a link between several different subject areas and therefore illustrates the general nature of chemical techniques. For example, the laboratory investigation of enzymes (biochemistry) involves the application of steady-state kinetics and thermodynamic equilibrium (physical chemistry) to spectrophotornetric data (instrumental analysis) obtained by careful analytical technique. Alternately the stereospecificity of enzyme reactions may be used t o demonstrate the concept of asymmetric syntheses in the beginning organic chemistry or chemical synthesis laboratories. Several enzyme experiments ( 1 4 ) have been developed for use in the undergraduate laboratory but none of these offer as many advantages as fumarate hydratase (EC 4.2.1.2.). Commonly called fumarase, this enzyme catalyzes the interconversion of fumaric acid and L-malic acid under neutral conditions and without the need of any cofacton (9).
Fumarase is directly involved in the citric acid cycle which is the primary hiological pathway in plants and animals for the conversion of pyruvic acid to carbon dioxide and water (10). The cvcle onerates within the mitochondria and olavs mijor rolein the oxidative metabolism of carbohydratds &d lioids. Under these conditions fumarate is hvdrated to form the thermodynamically favored L-malate ( l i ) . When the reaction is carried out in deuterium oxide the addition occurs only with an anti-stereochemistry (12-15).
a
The stringent steric requirements of the enzyme are further emphasized by the fact that only fumarate, L-malate, and a few of their derivatives (cf. Table 2) are known to undergo chemical reaction in the presence of fumarase (16). The available evidence suggests that the enzymatic reaction proceeds through the following reaction E+F=EF+EXf
+EM*E+M
where E is the enzyme, M is L-malate, F is fumarate, EM and EF are enzyme-substrate complexes, and EX+ is an enzyme-carbonium ion complex (17). Experimental Procedure Therefore the reaction may be studied kinetically in both directions and the results compared with the readily obtained thermodynamic equilibrium constant. T h e progress of the reaction is easily monitored spectrophotometrically since fumaric acid nossesses a coniueated double bond which ab. .. sorbs strongly in the near ultra\,iolet region ofthe spectrum. The molar absororivitie.i of disdium fumarafe are pre~enred in Table 1. Table 1. Molar Absorptivities of Diradium Fumarate a t 25°C (10)
220 230 240 250 260
manium sulfate solution. A stack fumarase solution, F1, is prepared for class use by shaking the suspension to disperse any enzyme which has farmed a cake on the bottom of the container and transferringthe entire contents to asmall centrifuge tube. The tube is spun until the liquid phase is clear, the supernatant liquid carefully removed with n tinet. and the solid dissolved in 50 ml of a 0.015 M sodium ohas-
to dialyze the solution or to accurately determine the concentration of the enzyme. Keep the fumarase solution refricerated when not in use. Each student should prepare a stock 0.015 M sodium phosphate buffer solution bv dissolvine 2.07 e (0.015mole) of sodium dihvdroeen
270 280 290
Table 2. Fumarase Substrates IPH 7.3.25"CI Substrate
Furnayate
frigerated when not in use. In addition, stock solutions of the substrates are prepared by dissolving 0.3218 g (2.40 mmale) of L-malie acid and 0.0696 g (0.600 mmole) of fumaric acid in 60-mi portions of the buffer and titrating each solution to p H 7.0 with 2Wb aqueous sodium hydroxide. The solutions are quantitatively transferred to volumetric flasks and diluted to exactly 100ml with additional buffer solution. A 25-ml pipet and 50-ml volumetric flasks are used to prepare 0.012,0.006,0.003,and 0.0015 Mdilutions of L-malate and 0.003, 0.0015.0.00075. and 0.000375 M dilutions of fumarate. The exoerimentr are made bv. hrineine the fumarase and - - ~ kinetic e substrate solutions to 25°C in a constant temperature bath. Two milliliters of a subatrate solution are placed in a stoppered silica euvet with l-em path-length. The euvet isinserted in the thermostated cell compartment of a recording spectrophatameter and allowed to ~~~~~~~
668 / Journal of Chemical Education
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Table 3. O b s e r v a t i o n a l W a v e l e n g t h s to Be Used W i t h Various Reaction Mixtures
thermally equilibrate with the instrument. One milliliter of Fzis added ( t h e recorder is started when half of the fumarase solution has been added) and the solutions mixed by inverting the stoppered cell several t i m e s . The c u v e t is quickly returned to the cell compartment and the shutter opened to record the absorbance as a f u n c t i o n of time. At least one satisfactory run should he obtained for each of the ten substrate concentrations prepared. Due ta the i n i t i a l absorbance ofthe fumarate s o l u t i o n s , it is necessary to use different ahservational wavelengths to o h t a i n c o n v e n i e n t s h e s f o r the absorbance v e r s u s time curves. S y g r r ~ e d , + e r w t i o n : d w n v r l r n g t h a f u r the ten s u t , s t r a t e vonrcnt r a t i u n a a r e g i v c n i n ' l ' a b l s R . N U I P r h n r t h e f i n a l rearrim c u n c e n t r a t i o n e a r p tsvo-rh~rdsoftheoriginald u e t o d i l u t i u n by t h e a d d i t i o n o f the enzyme solution. The equilibrium experiment is carried out hy adding 1rnl of FIto 2 ml of 0.003 M L-malate and allowing the resulting solution to eouilihrate at 25°C ( u s u a l l v a h o u t 1hr is sufficient). Theexneriment i s ' r e p e a t e d using a" equafconcentration of f u m a r a t e . ~he'finalahsorhanee of each s o l u t i o n is measured at 250 mm. ~
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Calculations The initial rates of reaction at the various suhstrate concentrations are obtained from the absorbance versus time data by drawing a tangent to the curve at the earliest possible reaction time. The slooe of this taneent is the initial rate of change in the absorbance at the corresponding initial concentration of substrate. This mav he converted to the initial rate uf change in the substrate concentration using the molar absurotivities rivrn i n Table I . The r e s u l t i n r ! data is treated by cithrr t h ~Eadie . or 1 . i n e a e a v e r - H u r k methods in order t o CHI( ulnte the muximum veluciries. 1'. and Mirhaelis ronstants. K,,, inr borh I.-malate and fumarate (18).The experimental results should he w m r ) a r e d u.ith thedvra reported in the lit-
The thermodynamic equilibrium constant, K,,, is calculated from the absorption at equilibrium and the molar ah-
sorptivity at 250 nm and the result compared with that ohtained by means of the Haldane relationship (18)
where Vf and Vr are the maximum velocities for the foreward and reverse reactions and K m f and Kmr are the Michaelis constants for the same reactions. The turnover number is another quantity which is commonly used to characterize enzyme systems. It is defined as the number of substrate molecules converted to product by one molecule of enzyme in a unit of time (18).The turnover number for fumarase has been calculated to be 2000 molecule-Is-' using a value of 200,000 for the molecular weight of the enzyme. The experiment may he readily expanded or modified to include an investigation of the competitive inhibition by trans-aconitate (191,the activation by phosphate ( l l ) or , the effect of pH on the maximum initial rate (11).
Literature Cited (11 (21 (3) (41
Bende1.M. L.,Ka&,F. L a n d Wed1er.F.C.. J.CHEM. EOUC.,44.M (19671. F.,andCory, Miller, J. F . , a n d C o j , J. G., J. CHEM. EDUC.,48,4iS (19711. Carper, M.A.,andCarper, R. W., J.CHEM. EDUC.,50.599(19731. Daniel, L. J..and Neal. A. L.,"Lsboratory Experiment. in Biochemistry," Academic Press,Now York, 1967, pp. 195-226. (51 Wharton. D. C.. and McCarty, R. E.,"ExperimenUand Methods in Biochemistri." MacMillan. Nerv York, 1972, pp. 2%2-41. 161 Rendine. G.. '"Emerimontal Methods in Modern Biochemistry," W. B. Saunders, Philadelphia. pa.. 1971, pp. 200-210. (7) Litwark, G., "Experimental Biachemistry: John Wiley and Sons, New Ynrk. 1960. Chap. IV. (8) Clark, J. W.. Jr,"Experimental Biochemistry: W. H. Freeman, San Francism, Calif.. 1984.p~.101-118. (91 Alberty, R. A. in"Enzymes: 2nd E d (Editors: Boyer, P. D.. Lardy, H., and Myrbaek, K.).AcademicPrcs.NewYork,1961.Vol. 5, p. 531. (10) Mahler. H. R.. and Cordea. E. H.. "Biolugical Chemistry: 2nd Ed.. Harper and Row. NeuYork, 1971.pp.605-630. (111 Alberfy, R. A,, Mas~cy,V.. F ~ i d e nC., , and Fuhlbrigge. A. R.. il Amei Chem. S o r , 76.2485 (19541. I121 Fisher,H.,Frieden,C.,MeKec, J. S. M.,andAlberty,R. A,. J. Arne,. Cham. Soe., 77, 4436 (19551. (13) A1brty.R. A..andBender,P.. J.Amsr Chem Sor., 81,542 119591. (14) Gawron,O..snd Fondy, R. P.,J Amer Chern. Soc.. 81,6333 (19591. (15) Anet, F. A. L.,J Amer Chem Sac.. 82,994 (1960). (161 Hill. R. L., andTeipel. J. W., "The Enzymes: (Edrtor: Boyer. P. D.I. 3rd Ed.. Academic Pmrs, New York. 1971, pp. 605.830. 1171 . . SchmidLD. E..Jr..Nieh. . . W.G..Tanzer.C..andRicharda.d.H.. J A m e r . Chem.Soc.. 91.5849 (19691. (I81 Mshler. H. R.,and Cordes. E. H.. "Biologicel Chemistry," 2nd Ed.. Hsrper and Row, New York, 1971. pp. 267-324. . 55,172 (19531. 1191 Massey, V . , R i o r h ~ mJ.. 1 Sigma Chemical Co., P.O. Box 14508, Saint Louis, Missouri 63178.
Volume 53, Number 10, October 1976 / 669
