Jeffrey A. Hurlbut, Thomas N. Ball, Harold C. Pound, and James L. Graves
Metropoliton Stote College Denver, Colorado 80204
I
Two Convenient Spedrophotometric Enzyme Assays A biochemistry experiment in kinetics
Virtually all biochemistry texts devote one or more chapters to enzymes, and in these chapters there is usually a discussion of enzyme kinetics centered around the Michaelis-Menton equation (1, 2). Biochemistry lahoratory texts and courses, however, frequently ignore enzyme kinetic experiments because they are either too detailed or non-existent. Since enzyme kinetics are important and since this aspect of enzyme chemistry is frequently left out of the undergraduate laboratory, we have developed two spectrophotometric assays of the enzyme, alpha-chymotrypsin (CT) that can easily he performed in the laboratory. The enzyme, CT, was chosen since a great deal is known about it (3-6), since it is easy to purchase in a pure, crystalline state, and since it obeys Michaelis-Menton kinetics (6,7). It is a proteolytic enzyme that is found in the pancreas, it has a molecular weight of 25,000 ( 6 ) , and it catalytically cleaves an amide bond in N-glutarylL-phenylalanine-p-nitroanilide (GPNA) releasing the highly colored p-nitroaniline (NA) (8). This situation is defined by eqn. (1) where
E is the free enzyme (CT), S is the substrate (GPNA), kl, k-I, and kz are rate constants, P represents the products (NA and N-glutaryl-L-phenylalanine),and ES is the enzyme-substrate complex. If we assume that kp (turnover number) is small compared to k-I, then the Michaelis-Menton eqn. (2) is easily derived (7, 9)
v,,, =
K,/[S]
+1
(2)
where u is the rate of the catalyzed reaction under the given conditions, V,,, is the maximum velocity possible, and K , is the Michaelis hinding constant and is approximately equal to k-l/kl. If kz is not small, then using the steady-state approximation we obtain the same equation in which K , now equals (k-1 + kz)/kl (7); so, it is seen that K , is only a hinding constant when kz is small compared t o k l . An enzyme assay should provide us with a way to obtain the three Michaelis-Menton parameters, K,, V,,,, and k2. Why do we want to obtain these constants, and how do we obtain them? First of all, K,, V,,,, and kz are useful. They characterize an enzyme-substrate system; they are necessary for interpreting the effect that changes of conditions have on the rate; and they are useful in enzyme inhibition studies. In short, these values are required by anyone that is investigating a particular enzyme, whether that person is a biochemist, an enzymologist, a physical bio-organic chemist, or a medicinal chemist. Now, how do we obtain these constants? We must have
Figure 1 . The chymotrypsin catalyzed cleavage of GPNA in which Nglutaryi-L-phenylalanine and NA are produced.
a way of determining the rate of the enzyme catalyzed reaction under different substrate concentrations while keeping all other variables constant, and the purpose of this paper is to present two different methods. Method I is a modification of Erlanger's GPNA procedure (a), and Method I1 is based on a modification of the Bratton-Marshall test for primary aromatic amines (10-13). Method I makes use of the reaction between CT and GPNA in which NA is released (see Fig. 1): NA absorbs strongly a t 410 mp, but GPNA, CT, and N-glutaryl-Lphenylalanine do not: so, the rate of appearance of NA can he followed using a recording spectrophotometer. If the molar ahsorptivity for NA is known at 410 mp under the conditions of the assav. then the rate can he exnressed in moles per liter per minuik. Method I1 is also hased on the reaction between CT and GPNA. The enzyme catalyzed reaction is allowed to proceed under known conditions, and aliquots are taken out every 3 min. The reaction in the aliquots is quenched with glacial acetic acid, and the NA is converted to a colored diazo dye which absorhs strongly at 542 mp (see Fig. 2). Using the molar absorptivity for the dye and by plotting out moles per liter of dye produced versus time, the rate of the reaction can be determined. Once we have the rate data, then any of a number of plots can yield the kinetic parameters (7). A plot of u versus [S] (Michaelis-Menton plot) gives a curved line, and plots of l / u versus 1/[S] (Lineweaver-Burk plot), u versus u/[Sl (Hofstee plot) and [S]/u versus [S] (Woolf plot) all yield straight lines. Since V,,, is equal to k2 times the
Figure 2.
Conversion of pnitraaniline to the diazo dye
Volume 50. Number 2, February 1973 / 149
total enzyme concentration, then k2 can easily b e determined if the total enzyme concentration and V,., are known (7). It should be pointed out that k2 is a combination of several constants (6), but it does tell us how many moles of substrate per mole of enzyme are converted to product per minute. Solutions and Equipment
Method I. The buffer, 2-amino-2-(hydroxymethyl). 1,3-propanediol, tris, was an Eastman chemical, ~4833. The buffer solution was 0.060 M in tris and 0.030 M in CaC12, and it was brought to a p H of 7.60 with concentrated HC1. The substrate, GPNA, was purchased from the Nutritional Biochemical Company, and 0.0300 g was dissolved in 5.00 ml of dimethylsulfoxide (DMSO). This made a 1.50 x M stock solution. The enzyme, CT, was purchased from Worthington Biochemical Corporation, =CDS 1475, and a solution was prepared by dissolvg of CT in 5.00 ml of M HC1. When ing 75 x 0.200 ml of this solution was diluted to 3.00 ml in the cuvet, then the CT concentration was 4.0 X M. All of the'above solutions are stable for weeks at 4°C. A Coleman 124 spectrophotometer, a Sargent recorder, a standard water bath, lambda pipets, and normal glassware were used. Method II. The buffer was the same as in Method I. The CT solution was prepared by dissolving 0.0125 g of CT in 5.00 ml of M HCI, and when 0.200 ml of th;s solution was diluted to 5.00 ml in the reaction tube, then the CT concentration was 4.0 X M. The GPNA solution was prepared by dissolving 0.0800 g of GPNA in 10.0 ml of D-MSO.This made a 2.00 X 10-2M stock solution. The ammonium sulfamate, NH4S03NHz (Mallinckrodt z1866), was used to decompose the excess NaN02, and an aqueous 0.50% (W/V) solution was prepared. The N-lnapthylethylenediamine dihydrochloride (NED) was purchased from the Matheson Coleman and Bell Company, and a 0.050% (W/V) solution of NED in 95% ethyl alcohol was prepared. An aqueous 0.10% (W/V), solution of NaN02 was also required. All of the above solutions are stable if stored a t 4°C. A Coleman 124 spectrophotometer was used, but any visual spectrophotometer could be used. A stopwatch, sixteen 10.0 ml volumetric flasks, a water bath and normal glassware were required. Method I.
Determination of K,,
V,,,
and k2
Introduction A wavelength of 410 mp is used since NA absorbs at this wavelength, but GPNA does not (8). Since this wavelength is on the side of an absorption curve, the spectrophotometer has to be carefully set. Beer's law is observed for NA concentrations ranging from about 1 x M to M, and the molar absorptivity for NA a t 410 12 x mp under the conditions of the assay (10% DMSO, 67% buffer solution, p H = 7.60) is 8,200 M - I cm-'. Finally, the substrate does not undergo noticeable acid or base catalyzed hydrolysis under assay conditions in the absence of CT. Procedure There are several things which one should keep in mind before beginning the assay. First of all, the final volume in the cuvet must be 3.00 ml. The GPNA is in DMSO, and the final solution must be 10% (VIV) in DMSO. Thirdlv. the temperature of the final soiutions should be known; and thev all should be eaual 30°C). The temoera. (around . ture of the final solutions can be approximately controlled (&Z°C) by storing the buffer a t 30°C. Finally, the spectrophotometer and the recorder should be zeroed, and one can use water for the blanks and for the reference cell 150
/ Journal of Chemical Education
since one is only interested in changes in. optical density per minute and since general hydrolysis does not occur appreciably. The following procedure can be used. (1) Into each of four 3-ml cuvets place 2.00 ml of tris buffer at 30"C, 0.50 ml of water, and 0.20 ml of CT (4.0 X 10-8 M in euvet). (2) Place into euvet 1: ( a ) 0.25 ml of DMSO and (b) 0.050 ml of GPNA (2.5 X 10-'M in cuvet). (3) Immediately shake the euvet twice and place it in the recording spectraphotometer. Follow the change in absorbance at 410 mp for at least 5 min. The recording of absorbance versus time is linear for at least 15 min. and the rate of change of absorbance per minute can he obtained from the slope. (4) Go through steps 2 and 3 with the other three cuvets using the following amounts: Cwet 2: ( a ) 0.20 ml DMSO and (b) 0.10 ml GPNA (5.0 x M in euvet); Cuvet 3: ( a ) 0.10 ml DMSO and ( b ) 0.20 ml GPNA (10.0 x 10-4 M in euvet); and Cuvet 4: 0.30 ml GPNA (15.0 X lo-* Min cuvet). (5) Using both the molar absorptivity and the cuvet path length in centimeters convert the rate to moles per liter per minute. Any of a number of plots will directly or indirectly yield the values for K , , V,,,, and k z . (See Table 1, Figure 3, and Table 2 far typical data, an example of a Wmlf plat, and the results of the Woolf plot, respectively.)
Determination of K,, V,,, and k2 Introduction NA can be diazotized and quantitatively converted to the diazo dye which has a A max a t 542 mu and a molar absorptivit; of 52,000 M - I cm-I under the conditions of the assay. Neither the CT nor the GPNA produce any ab-
Method II.
Table 1. Typical Data Obtained from Method I. The Molar Absorptivity was 8,200 M - ' cm-' at 410 mp, and the Path Length was 1.00 cm
[SI (M X 10')
Cuvet
-
1
(A
2.5 5.0 10.0 15.0
2
3
4.
U
U
0.018 0.031 0.048 0.058
2.2 3.8
OD/min) [(Mlmin)X 10"
[S]/u
--
110 130 170 210
5.9
7.1
Table 2. Woolf Plot Values Obtained for K,,V,,,, and k 2 Using Data Obtained from Method I and Method I I .- - - - -
Km
Method
-15.0
(M x 103)
-10.0
0.0
-5.0
[s] Figure 3.
Vmaz
[(M/rnin) x 1051
M X I O ~
Woolf plot data from Table 1.
5.0
10.0
kz
(min-'1
15.0
sorption a t 542 mfi with this treatment, and GPNA does not undergo any noticeable acid catalyzed hydrolysis under the assay conditions; however, if a stronger acid such as HCI is used to quench the reaction in place of glacial acetic acid, then hydrolysis does occur. Also, changes in the acid strength or amount cause small changes in the molar absorptivity. Beer's law is observed for NA concentrations ranging from about 1 x 10-6 M to 18 X lo-@ M when glacial acetic acid is used. Procedure Again there are several things to keep in mind. First of all, the final volume of the assay solution is 5.00 ml, and the solution is 10.0% (V/V) in DMSO. Second, 1.00 ml of this assay solution is diluted to 10.0 ml before obtaining the absorbance readings; so, this factor of 10.0 must be taken into account in the calculations. Third, all reagents must be checked for trace amounts of primary, aromatic amines, and this can be accomplished by employing a blank. Finally, much time can be saved if the necessary solutions are delivered from burets. The following procedure can be used. (1) Into each of four test tubes in a water bath at 30'C place 4.00 ml of tris buffer, 0.30 mlof H20 and a 1.00-mlpipet. (2) Into each of the above four test tubes place the following: 1: M in tube); 2: ( a ) 0.40 ml GPNA (1.6 0.50 ml GPNA (2.0 x x 1W3M in tube) and (b) 0.10 ml DMSO; 3: ( a ) 0.30 ml GPNA (1.2 X lW3 M in tube) and ( b ) 0.20 ml DMSO; and 4: (a) 0.20 ml M in tube) and (b)0.30 mlDMSO. GPNA (0.80 X (3) ( a ) Add 0.20 ml of CT to tube 1, begin to time the reaction and stir at least twice. ( b ) Every 3.00 min for 12 min transfer a 1.00-ml aliquot to a 10.0-ml volumetric flask which contains 1.00 ml of glacial acetic acid, and shake. (4) Continue with step 3 with each of the three remaining tuhes. (5) To each of the four volumetric flasks from test tube 1 add the following: ( a ) 1.0 ml of 0.10% NaN02, shake and wait for 3 min; (b) 1.0 ml of 0.50% NH&OsNH2, shake and wait for 2 min; and ( e ) 2.0 ml of 0.050% NED, shake and dilute to 10.0 ml with water. Wait for at least 5 min before measuring the absorbance. The diazo dye is stable for at least 1hr. (6) Continue with step 5 for each set of four flasks. (7) Record the absorbance at 542 rnp for each flask and make a plot of time versus absorbance for each of the four runs (see Fig. 4). Using the molar absorptivity, the cuvet path length, and the dilution factor, convert the rate to moles per liter per minute. Make a table of the data similar to Table 1. The values for K,, V,,,, and k a can he obtained as before. (See Table 2 for the values of the constants obtained by this method.) One can expect rates which vary from about 0.02 to about 0.06 absorbance units per min in the 10.0ml volumetric flasks. Discussion As seen in Table 2, the values obtained by Methods I and I1 are in good agreement; however, since there are so many variables great care must be used in order to obtain both consistent results in either of the methods and agreement between the two methods. Small changes in either temperature, pH, ionic strength, or wavelength can contribute to erroneous results, and inaccurate pipetting will yield large resultant errors. If one uses care, then better than i2& accuracy and agreement can be obtained. Method I is easier and faster than Method Jl, and either method can be completed in one 3-hr period if all solutions and materials are prepared beforehand. A good recording spectrophotometer is required for Method I since the changes in optical density per minute are small, whereas a Spectronic 20 can be used for Method II. The temperature is much easier to control with Method II; so, this method is quite useful if one wants to alter the temperature and ohtain energy of activation values (14). Both methods demonstrate many useful principles and both are good assays for inhibitory studies. It should be pointed out that eqn. (1) is a simplified
equation and that eqn. (3) is a better representation of the CT catalyzed cleavage of amides and esters where kt
kz
Y E P --' E + Pz (3) k., Pl EP represents the acyl-enzyme intermediate, PI an alcohol or an amine, Pz a free acid, kz a rate constant for acylation, and k3 a rate constant for deacylation (6, 15-19). For amides acylation is the rate limiting step, and for esters k3 is the rate limiting step (6, 15-19). Two other commonly used substrates for CT are p-nitrophenyl acetate (20) and p-nitrophenyl trimethylacetate (6); however, these and many other similar substrates are not as desirable as GPNA. An ideal chromogenic substrate should be moderately soluble in the test solution, stable in the absence of the enzyme, sensitive to and specific for the enzyme under consideration, and capable of releasing a colored product upon hydrolysis (8).GPNA is soluble, is quite stable in the absence of CT, and is specific for "chymotryptic" enzymes. Both p-nitrophenyl acetate and p nitrophenyl trimethylacetate are somewhat soluble (6), but they more readily undergo hydrolysis and are not specific for "chymotryptic" enzymes (19, 21, 22). Also, there is some doubt as to whether or not p-nitrophenyl acetate forms an ES complex (16, 17). Because of these drawbacks p-nitrophenyl acetate and related compounds are not good substrates (191, and are not satisfactory for reversible and irreversible inhihition studies. E + S
ES
Literature Cited (11 Conn. E. E., and Stumpf, P. K.. "Outlines of Biaehemiefry" (3rd 4.1. John Wilay &Sons, NcwYark. 1972.p~.171-195 (21 Sturtevant. J. M.. JCHEM. EDUC. I4. l84(19671. (31 Baker. B. R.."Design of Active-sito-Dirretd Irreversible Enzyme Inhibitor8,"Joho Wiiey & Sana, New York. 1967, p. 43 (4) &,"hard. S. A . "The strveture and Function o f E n r y m d ' W. A. Benjamin. New York. 1 9 M . p ~23-255. . (51 Neurath. H.. Seipnfllic Ameriricon. 211.68 (1%). (6) Bender, M.L.,K&rdy,F. J., and Wadbr. F.C.,J.CHEM.EDUC.,44,84(1967l. (71 . . Christensen. H. N.. and Palmer. G. A.. "Eozvme Kinetics." W. B. Saundcr3. Philade~phia.i w . 181 Edsnmr. 9. F.. Edel. F.. and Coowr, A. G., Arch. Bioehem. Biophys.. 115, 206 (19661. (9) Ndands, J. B.. and Stumpf. P. K.. "Outlines of Enzyme Chemistry." John Wilw & Sona, NewYork. 1968. pp. 94-109 (10) Brstlon.A.C..andMarjhall. E.K.. J Biol Chem.. 128.537(1939l. (11) Goldbarg. J.A.. andRuienhurg.A. M., Concw 11.283~19581. (12) Blackwoad. C.,andMandi.l..AmI.Bbeham.. 2.370(19611. I131 Biaekuood,C.E..Edanger,B. F.,sndMandl.1,Anol.Blochem., 12,128(1965l.
(I41 Miller. J.F..andCory.J.G., J.CHEM.EDUC.,4R.475(19711. (15) Himoe.A.. Park. P. C.. andHess, G. P.,J B i d Chem.. 242.919l1967l. (16) Himoe,A.. Brsndf. K.G.,andHlss.G.P..J B i d Chem., 242.3963(1%71. (17) Brandt.K.G.,Himoe.A.. andHes%GP., J. B i d Chem.. 242.3973 (1967). 1181 1negami.T.. Pafchornik,A.,sndYork, S. S.. J. Bioehem., 65,80911969l. (19) Jencks. W. P.. "Catalysis in Chemistry and Enzymolow." MeCrsw-Hill. New York, 1969. Chapter 2. (MI Hartley, B.S. andKi1by.B.A.. Biorhem. J., S0.672l1952l. (211 Martin. C. J.. Goiubow. J.,and*xelrod.A.E.. J Bbl. Chsm.. 234. W4(19591. (221 Martin.C.J..Goluhov. andAxclmd.A.E.,J Bbl. Chm.. 284. 1718(L9591.
M h
F +re 4 Plot 01 absaroance ver9.r tome for one set ot oala oota neo by Melhod I The GPhA Concentrmon war l 6 X 10 M Tne rate s
(0033X1011OD m n o r 6 P
~ 1 0 - m6n ~
'
Volume 50. Number 2,February 1973 / 151
