-Galactosidase enzyme kinetics. Bring a diskette (PC or Mac) for saving your SC115 on-site plots.

Transcription

1 Biological Sciences 11 Spring 2000 Experiment 2: -Galactosidase enzyme kinetics. Bring a diskette (PC or Mac) for saving your SC115 on-site plots. Part To do... More information A (1) Review lecture notes and videotape for "Enzyme kinetics." [Cabot Library]. (2) Voet, D. And Voet, J.G. (1995) Biochemistry, 2th ed., John Wiley, New York, Chap 13, pp (3) Stryer, L. (1995) Biochemistry, 4th ed, Freeman, Chap 8, pp [Cabot Library]. B1 Overview of experiment by teaching fellows. Introduction. This handout. B2 Instructions for Ultrospec Instructions affixed to spectrophotometer and printed sheets near each instrument. TF demonstration. B3 C1 C2 C3 C4 Work in partners. Plan your afternoon. Alternate tasks so that each person does some pipetting and some absorbance measurements. Determine optimal dilution of stock solution of enzyme. Look for A 420 of after 2 min. Prepare set of dilutions of ONPG so that a uniform volume of each dilution can be added to appropriate cuvettes. Prepare sets of cuvettes with variable [ONPG]. Measure activity vs time for each [ONPG]. Prepare sets of cuvettes with fixed [lactose] and variable [ONPG] - same values of [ONPG] as in C3. Measure activity vs time. Pages 4-5 Pages 5-6 1

2 D1 Verify with your TF that your data from C3 and C4 show reasonable trends by plotting [ONP-] product vs time (sec) for each initial [ONPG] in your set of 7 cuvettes. Use computers in lab or in computer rooms downstairs. Instructions from teaching fellows. D2 From A 420 calculate [ONP-]. ε = 4500 M -1 cm -1 D3 D4 Beer s law: A = ε b c as in Expt 1. B (path length) is 1 cm. c is in moles/liter. Determine slope of each line, in units of [ONP-] produced per unit time. Make an overlay plot of your data on a graph with different symbols for each starting [ONPG]. Make graphs for your report. Make overlay plots (2 or more sets of data on one set of axes). Get information for figure captions. Write captions. In this series of experiments, V max and K m for β-galactosidase will be determined by varying substrate concentration and measuring V o for each [S]. S is o-nitrophenyl-β-d-galactoside, a substrate that yields a colored product, ONP. Next, the rate of ONP formation in the presence of lactose will be used to determine the K i of lactose. V o will be measured for a range of ONPG concentrations in the presence of a fixed concentration of lactose. HOCH 2 HO O O OH OH NO 2 H 2 O HOCH 2 HO OH β-galactosidase O OH OH + - O NO 2 + H + ONPG ONP 2

3 Reagents: Reagent Container Storage β-galactosidase stock solution, (1.2 mg/ml) in Z-DTT buffer; ask TF for updated information. 1.5 ml Eppendorf, blue circle on cap keep in your ice bucket Use this value for calculation of specific activity in your report. Lactose H 2 O MW High= 72 mg/ml in water; Low = 36/mg/mL o-nitrophenylgalactoside (ONPG); MW 301.3, 4 mg/ml stock solution Z-DTT buffer 100 mm Tris ph mm MgSO 4 1 mm dithiothreitol (DTT) 1.5 ml orange H yellow cap, labeled L 5 -ml white freezer tube 100 ml glass bottle with green cap Keep at room temperature because the solubility of lactose in cold water is lower than at room temperature 4mg/mL in distilled water, frozen in 4-mL aliquots; thaw and use at room temp on afternoon of experiment kept in refrigerator, but used at room temperature; please pour 20 ml into a beaker for your use Product of reaction Beer s law ONP - ε = 4500 M -1 cm -1 A 420 = ε b c cuvette path length b = 1 cm C1. Determine working -galactosidase concentration: Each pair should determine the optimal dilution of β-galactosidase to use throughout this experiment. Then prepare a larger batch of this diluted β- galactosidase -- enough for the entire experiment. Calculate how much you will need. Include a safety margin for repeats. Verify amount with TF. 3

4 Setup: Find optimal dilution of -Galactosidase (3) 100 µl water (2) 200 µl ONPG (4 mg/ml) (1) 675 µl Z-DTT buffer Mix. 20 times up & down with 200 µl (yellow tip) pipetteman. Start with plunger down, insert tip 75%, then up & down. Avoid air bubbles. (4) Take blank reading for each cuvette in this "setup" section of the experiment. set ref (5) Add enzyme. Mix up & down 20 times. run 25 µl enzyme β-galactosidase Try various dilutions of supplied b-gal in Z-DTT buffer, e.g., 1. 1 vol stock + 1 vol buffer (50 / 50 µl) 2. 1 vol stock vol buffer (40 / 60 µl) 3. 1 vol stock + 2 vol buffer (33 / 66 µl) 4. undiluted stock (25 µl; one trial) Look at list of data. Choose dilution that gives A 420 of 0.9 to 1.0 after 2 min. Make a dilution intermediate between 1-4 if necessary. 4

5 For your notes: Dilution β-galactosidase stock ( 1.2 mg/ml) Z-DTT buffer Dilution A 420 after 120 sec Space for notes yours C2. Choose the enzyme dilution (or make your own recipe and test it) which will be used for the remainder of the experiment. C3.- C4. Kinetics using the optimal -galactosidase dilution: We will now examine the effect of varying substrate concentration [ONPG] on reaction kinetics and we will repeat the experiment with fixed [lactose]. 1. Label 7 plastic tubes with screw cap S1 through S7 for substrate (ONPG) dilutions. Five ml is the total volume. Fill in this table. Tube # Vol stock ONPG Vol distilled H 2 O ONPG (mg/ml) S S S ml 4.5 ml 0.4 S S 5 1 S 6 2 S 7 5 ml 0 ml 4 5

6 2. Label 21 cuvettes near the top -- use different colored pens: 1Β through 7Β (β-galactosidase sample) 1L through 7L (β-galactosidase sample + low lactose (36 mg/ml)) 1H through 7H (β-galactosidase sample +high lactose (72 mg/ml)) 3. Add 675 µl Z-DTT buffer to each cuvette. 4. Add 200 µl of the appropriate ONPG dilution to each cuvette (i.e., add 200 µl S1 to cuvettes B1, L1 and H1, 200 µl S2 to B2. L2 and H2, etc.). 5. Add 100 µl dd H 2 0 to cuvettes B1-B st partner. Add 25 µl optimal dilution β-galactosidase. Step d below. {Save the lactose addition for later, Step 6, while the control series is running. One partner watches over the spectrometer, and the other person finishes preparing the Low Lactose and High Lactose cuvette series.} Efficient mixing is essential for obtaining consistent data. Remember that β-galactosidase (and most proteins) are more dense than water [For example, Voet and Voet, Table 5.5, d = 1/ρ; 1/0.73 = 1.37 g/ml] and that proteins will settle to the bottom of the container. Gently mix the contents of the Eppendorf tube before withdrawing your β- galactosidase. Set ref for the Pharmacia Ultrospec 2000 spectrophotometer for the first cuvette in each series. Optional: You may set ref for each cuvette because each one has a different ONPG concentration and therefore wmay have a different starting [ONP-] from photodecomposition. a. Place cuvette Β1 in the blue cell number 1, oriented so that the light beam will pass through the clear sides of the cuvette. b. Push "Set Reference" button to blank the instrument (wait for A 420 value to print out); remove the cuvette. c. Prepare a 200-µl pipetteman for service as a quick mixer. Outfit it with a clean tip for each sample and adjust the volume to 180 µl. d. Remove the cuvette from the spectrophotometer. Add 25 µl optimal dilution -galactosidase to the cuvette. Begin with the pipettman plunger depressed. Insert the tip 3/4 of the way into the solution in the cuvette. Mix immediately by drawing 180 µl of the liquid up into the pipette tip and expelling it into the cuvette. Repeat 20 times. Perform the pipettor operations carefully (rather than vigorously) -- avoid bubbles, which can alter absorbance readings. e. Quickly replace the sample in cell 1 and press the "Run" button. f. Wait for the 3 minute kinetics readings (taken at 15 sec intervals). g. Reset position of the cuvette holder by pushing "Sample" and choosing cell number 1. h. Proceed with next sample (Β2, Β3...); repeat steps a-g. 6

7 (3) 100 µl water (control) or 100 µl lactose (2) 200 µl ONPG dilution (1) 675 µl Z-DTT buffer Mix. 20 times up & down with 200 µl (yellow tip) pipetteman. Start with plunger down, insert tip 75%, then up & down. Avoid air bubbles. (4) Take blank reading for 1st cuvette in series set ref (5) Add enzyme. Mix up & down 20 times. run µl (25 µl typically) enzyme β-galactosidase (your optimal dilution) Before you start: Make enough "optimal dilution" β-gal for your entire (3) series with water (control) & 2 lactose concentrations. 7

8 7. 2nd partner -- Add 100 µl Lactose (36 mg/ml) to cuvettes L1-L7. Mix. Add 100 µl Lactose (72 mg/ml) to cuvettes H1-H7. Mix. 8. 1st partner -- plot raw data on spreadsheet. Verify with TF. Make replicate cuvettes to check any suspicious results. 9. 2nd partner -- Proceed with kinetics measurements on Low Lactose series. 10. Plot and collaborate. Plot each series of raw data. Save it to a disk. Other partner collects data. Change roles. 11. Look over the raw data plots. Make a replicate set of samples if necessary. Suggested spreadsheet layout. Time (sec) S 1 S 2 S 3 S 4 S 5 S 6 S 7 0 A Copy Time column and enter forumlas. Begin with equal sign, enter cell address, constants and math operations. Calculate rate of formation of ONP-. Look at data points critically to ascertain the initial velocity. Write comments on your choices in a text box on the spreadsheet. Time S 1 S 2 S 3 S 4 S 5 S 6 S 7 0 formula

9 Rate ƒx function SLOPE Calculate [ONP-] from the absorbance, A 420. Beer s law: A = ε b c as in Expt 1. ε = 4500 M-1 cm-1 b (path length) is 1 cm. c is in moles/liter. Suggestion: Enter a formula lower in the same column in your Excel spreadsheet. Refer back to your A 420 values by spreadsheet cell number and perform the math. 12. Make a Lineweaver-Burk double reciprocal plot of your data. All 3 sets of data are to be placed on the same graph. Calculate 1/[ONPG] from [ONPG] in cuvette. Calculate 1/rate. Make a summary. Suggested layout... Series B control Series L low lac [ONPG1]... [ONPG7] are concentrations in the cuvettes. S 1 S 2 S 3 S 4 S 5 S 6 S 7 [ONPG1] rate1b rate1l [ONPG2] rate2b rate2l [ONPG3] rate3b [ONPG4] SeriesH high lac rate1h If you elect to use software (Examples: Cricket Graph, Excel, Kaleidagraph), highlight the cells containing the 1/x and 1/y data to make your plot. Test your data to determine which points lie on a line and which (if any) should be excluded. Use functions to calculate linear regression best fit and compare the goodness of fit (r values). Extend the x axis to negative values so that you may see the x intercept (-1/Km). Summarize the results of your calculations (Km, Vmax, Ki) in a table of your own design. D. Suggestion. Complete your double reciprocal plot within a few days after collecting your data. Come to your TF s office hour or stop by the lab SC115 for assistance. 9

10 Expt 2. Report is due at 1 pm one week after lab experiment. Graphs plus one page text. Display graphs in informative overlay plots including title, labeled axes, and caption. An overlay plot shows two or more y values for each x, on one set of axes, as in Voet and Voet, Figs , 13-12, and You may find it convenient to include a legend in your graph -- a table of symbols (circles, squares, triangles) and their meaning. Display Km, Vmax, Ki in a table of your own design or in a text box inset into the graph. In your results paragraph, describe the data in your plots and refer to your plots by figure number, similar to the usage in texts Voet and Voet, Biochemistry or Alberts et al, Molecular Biology of the Cell. Include answers to these questions in your conclusions paragraph: (1) Which plot, direct or double reciprocal, do you think gives a more accurate K m and V max? Explain why. (2) Using your data, explain whether lactose is a competitive on non-competitive inhibitor. Which type of inhibition would you have predicted based on the structures of lactose and ONPG? In this kinetic experiment, lactose is an inhibitor. Are the roles of lactose and ONPG different or the same in this experiment and in vivo? (3) Calculate the k cat for β-galactosidase. The molecular weight of β-galactosidase is 532,000 g/mole and the units of k cat are per second. What is the ratio of k cat /K m? Why is there an upper limit to k cat/ K m? How close is β-galactosidase to a perfect enzyme (the upper limit for k cat /K m is approximately 5 x 109 M-1 sec-1)? Calculations in appendix. (4) Calculate the specific activity of your sample of β-galactosidase, using the activity data from this experiment (first part, setup) and using the protein concentration obtained from your TF. Units of specific activity are µmoles ONP- produced per mg enzyme per minute. Show your calculations in an Appendix. Place a header with this information on the first page of your report. Name Section TF Phone 10

11 Background for analysis of data. Enzymes enhance the rate of conversion of substrate to product in chemical reactions; they do not alter chemical equilibria. They effect this enhancement by binding substrate in a manner such that the spatial conformation of the substrate becomes favorable for conversion to product. For each enzyme-substrate complex, specific amino acid side chains participate in providing the binding pocket for substrate. Much of our present knowledge of enzyme mechanism derives from studies of kinetics -- the rate of reaction -- under controlled conditions of substrate concentration, temperature, ph, concentration of competing substrates (e.g., products), and so on. Only recently have new tools such as site-specific mutagenesis been applied to the elucidation of the role of specific amino acid residues in binding of the substrate. The analytical formalism for translation of kinetic data into mechanistic models of enzyme action derives from the theory proposed by Leonor Michaelis and Maud Menten in Discussions are available in texts such as Biochemistry (Chap. 13) by Voet and Voet, and Biochemistry (1995) by Stryer [Chapter 8],, so we describe the method of analysis in simplified format here. Michaelis and Menten proposed that the overall reaction could be written as: k 1 ( ) k 3 E + S < > E S > E + P (2.1) k 2 ( ) where E represents the enzyme, S is the substrate, ES is the enzyme-substrate complex, P is the product, and k 3 is the first order rate constant describing the conversion of ES to E and P. The Michaelis-Menten equation can be rewritten in terms of the velocity (v) of the reaction, i.e., the number of moles of substrate converted to product per unit time: v = V max [S] / {[S] + K m } (2.2) In this equation, Vmax is the maximum rate of reaction when the substrate concentration [S] is in large excess. It is defined as V max = k 3 x [E T ]. When [S] >> [E T ], k 3 is equivalent to k cat, the turnover number. E T is the total enzyme concentration (E + ES). K m is the substrate concentration at which the v = V max /2. K m represents a measure of the ability of the enzyme to bind a given substrate. K m also represents the apparent dissociation constant of all enzyme-bound species; this definition is useful for the quantitative analysis of reactions in the presence of substrate and inhibitor. Inversion of eq. (2-2) yields: 1 1 K m = ( ) ( ---- ) (2.3) V o Vmax Vmax [S] {Voet&Voet p. 357} 11

12 V o refers to initial velocity, measured at times soon after initiation of the reaction, when [S] >> [P]. A Lineweaver-Burk plot of 1/V o (y-axis) versus 1/[S] (axis) allows determination of V max from the y-intercept, -1/K m from the x-intercept and K m /V max from the slope. The study of enzyme kinetics in the presence of inhibitors has provided information on the nature of the substrate binding pocket and on the protein conformational changes in substrate binding. A practical application of such studies is the development of therapeutic procedures based on inhibition of selected enzymes. Two major classes of inhibitors are competitive and non-competitive. [Refer to Voet and Voet 13.3.A, page 356 and 13.3.C, page 359, mixed inhibition.] A competitive inhibitor binds to the same site as the substrate. One example of competitive inhibition occurs when [P] [S] and the reverse reaction proceeds concurrently with the forward reaction. Another example is the competition of two substrates of similar chemical structure for occupancy of the binding pocket. For competitive inhibition, increasing the ratio of [S]/[I] results in an increase in [ES]/[EI] and the velocity increases. The same V max can be achieved if [S]/[I] is adequately high. However, K m, the concentration of S required for half-maximal activity, is elevated in the presence of I. The Lineweaver-Burk equation for two competing substrates is modified as follows: (2.4) 1 1 K m [ I ] = { } { [ 1 + ( ---- )] ( ----) } V o V max V max K i [S] [I] is the concentration of inhibitor, K i is the inhibitor analog of K m and K m has its usual meaning. In this situation, the x-intercept is -1/{K m (1+[I]/K i )}, as shown in Voet and Voet, Fig and Stryer, Fig A simple example of non-competitive (mixed) inhibition is the binding of substrate and inhibitor to different sites on the enzyme, but the binding of inhibitor alters the binding of S. It retards catalysis of S ----> P. A non-competitive inhibitor therefore does not alter K m for S but does decrease V max. For this case, the Lineweaver-Burk equation is: (2.5) 1 1 [ I ] K m [ I ] = ( ) + { } { [ 1 + ( ----)] ( --- ) } V o V max K i V max K i [S] The y-intercept is (1+[I]/K i )/V max, as shown in Voet and Voet, Fig and Stryer, Fig