Lecture 12: Burst Substrates and the V vs [S] Experiment

Transcription

1 Biological Chemistry Laboratory Biology 3515/Chemistry 3515 Spring 2019 Lecture 12: Burst Substrates and the V vs [S] Experiment 14 February 2019 c David P. Goldenberg University of Utah goldenberg@biology.utah.edu

2 Outline of Enzyme Kinetics Experiment This week: 1 Measure velocity as a function of enzyme concentration. 2 Determine enzyme concentration by titration with an inhibitor. Next week: 1 Determine enzyme concentration by reaction with a burst substrate. 2 Measure reaction velocity as a function of substrate concentration. Data analysis. Calculate: K m V max k cat

3 Experiment 3, Part C: Another Way to Measure the Trypsin Concentration Based on a historically important experiment: p-nitrophenyl acetate (PNPA) acetate p-nitrophenol Reaction with chymotrypsin: PNPA isn t a very good substrate! Reactions are not linear with time. Initial displacement of curves increases with enzyme concentration. What is going on? Hartley, B. S. & Kilby, B. A. (1954). The reaction of p-nitrophenyl esters with chymotrypsin and insulin. Biochem. J., 56,

4 Proposed Mechanism to Explain Burst Kinetics E-Nu fast H 3 C E-Nu O slow H 3 C O O + E-Nu Enzyme reacts rapidly with substrate to form a covalent intermediate and releases p-nitrophenol. Each molecule of enzyme produces one molecule of product in burst phase. Hydrolysis of the covalent intermediate is much slower and is required to regenerate enzyme (turnover). Steady state rate of product formation is determined by the second step. Among the first evidence for a covalent intermediate in an enzyme-catalyzed reaction.

5 A Designed Burst Substrate for Trypsin + Enzyme Enzyme Guanido group resembles arginine side chain. Hydrolysis of covalent intermediate is very slow. (half-time greater than 40 h) An (almost) irreversible inhibitor, or suicide substrate. Why is hydrolysis so slow?

6 Resonance Stabilization of the Covalent Intermediate NH 2 NH 2 H 2 N O H 2 N O HN N O O Enzyme Enzyme Resonance structures shift electrons from phenyl ring to carbonyl carbon. Electron density on carbonyl carbon disfavors nucleophilic attack by water. Why doesn t the same effect prevent formation of the intermediate?

7 Resonance Also Favors Formation of the Covalent Intermediate NH 2 H 2 N HN O O NO 2 + Enzyme Enzyme Resonance shifts electrons from carbonyl carbon to nitrophenyl ring. Makes the nitrophenyl group a better leaving group. Favors nucleophilic attack in the first step of the reaction.

8 Three-dimensional Structure of p-guanido benzoate intermediate Gly 193 As predicted, Ser 195 O γ forms ester with p-guanido benzoate. Ser 195 His 57 Asp 102 Amide groups of Ser 195 and Gly 193 form oxyanion hole that stabilizes negative charge on carbonyl oxygen in transition state. Where would the water molecule be for hydrolysis of the intermediate? Mangel, W. F., Singer, P. T., Umland, T. C., Toledo, D. L., Stroud, R. M., Pflugrath, J. W. & Sweet, R. M. (1990). Structure of an acyl-enzyme intermediate during catalysis:(guanidobenzoyl)trypsin. Biochemistry, 29,

9 Experiment 3, Part C: Measurement of Trypsin Concentration with Burst Substrate 0.2 "Burst" Spontaneous hydrolysis A Time (min) Requires high enzyme concentration, since each enzyme molecule generates only one chromophore molecule. Tris buffer is bad for this experiment, because amines are nucleophilic and react with p-npgb. Need to record both the absolute increase in absorbance and the rate of steady-state increase, in order to extrapolate initial burst phase. Ignore first data point, since it is recorded slightly after reaction starts, but probably before the burst is complete.

10 Experiment 3, Part C: Velocity as a Function of Substrate Concentration Velocity (M/min) [S] (M) To reliably estimate both K m and V max, substrate concentrations must cover range both below and above K m. We will use eleven substrate concentrations, plus a control without substrate. Two groups of six reactions. How should the reactions be grouped?

11 Two Ways to Group the Reactions Group 1 Group Group 1 Group V V [S] (µm) [S] (µm) Is one way better than the other? What if something changes between the reactions?

12 Two Ways to Group the Reactions Group 1 Group Group 1 Group V V [S] (µm) [S] (µm) 1 6 grouping: changes between reaction groups may be hard to detect. Odd even grouping: changes between reaction groups are easier to detect. Fitting data together averages effects more evenly.

13 Warning! Direction Change Data Analysis for the Michaelis-Menten Experiment

14 Analysis of Data from the V versus [S] Experiment Velocity Substrate Concentration We want to fit the experimental data to the Michaelis-Menten Equation: V = [S]V max [S] + K m From the fit, we obtain estimates of K m and V max.

15 Clicker Question #1 Estimate V max from the graph: 40 A) 30 nm/s B) 40 nm/s 20 C) 50 nm/s D) 80 nm/s close enough for credit

16 Clicker Question #2 Estimate K m from the graph: 40 A) 1 µm B) 2 µm 20 C) 5 µm D) 10 µm

17 A Classic Method for Analyzing Enzyme Kinetics Data Rearrangement of the Michaelis-Menten Equation: V = [S]V max [S] + K m 1 V = [S] + K m [S]V max = [S] [S]V max + 1 V = 1 [S] K m + 1 V max V max K m [S]V max A plot of 1/V versus 1/[S] should generate a straight line with a slope of K m /V max and an intercept of 1/V max on the 1/V axis.

18 The Lineweaver-Burk Plot 0 0 If the data are perfect, this plot gives good estimates of K m and V max. But, experimental error in V can lead to strange effects!

19 Experimental Error and Uncertainty Error bars for rate measurements are of approximately constant size (e.g., ±0.005 A/min), rather than a constant percentage of the measurement. 0.1 Rate (A/min) For 0.1 A/min, ±0.005 A/min = ±5%. For 0.01 A/min, ±0.005 A/min = ±50%. Enzyme Concentration Least-squares fitting works well if the absolute uncertainties of all data points are approximately equal.

20 What Happens When We Take Reciprocals? V = 0.1 ± = 9.52, = 10.5, 1 V = 10 ± 0.5 V = 0.01 ± = 66.7, = 200, 1 V = 100 ± 50 The values of 1/V derived from small velocities can have huge absolute errors.

21 The Effects on a Lineweaver-Burk Plot Errors in the least precise measurements (low V ) can cause large changes in the line fit to the Lineweaver-Burk plot.