Enzyme Kinetics Lab Report

Enzyme Kinetics Abstract: Enzymes are biological catalysts of the many reactions that take place in the human body, as well as all other living things. These catalysts can increase the rate at which the reaction takes place, allowing more product to be created in an efficient manner. In order to understand the functions of enzymes the kinetics, or the rate of reaction, can be analyzed. In this experiment Michaelis-Menten kinetics were used to analyze the enzyme tyrosinase acting on the substrate DOPAC. In order to analyze this enzyme, the following values were determined: maximum velocity, KM, and turnover rate. The concentrations of the substrate were varied as the reaction was measured by absorbance for 100 seconds. The Vmax was calculated to be 6.22x10-4 mM/s the KM was calculated to be 1.434 mM and the Kcat was calculated to be 3.11x10-3 s-1. Introduction A major function of some proteins is that they can act increase the rate at which a biological reaction can occur (1). The study of enzyme kinetics explains the effects that each piece of a certain reaction will have on the overall rate of the reaction. The factors that are the focus of the study include substrate concentration as well as velocity of the reaction (2). The relationship between the rate at which the reaction proceeds and the concentration of the substrate can be demonstrated using Michaelis-Menten kinetics (3). Figure 1 shows the equation that is the basis of Michaelis-Menten kinetics, where V is the reaction velocity and [s] is the substrate concentration. V= V max [ S ] [ S ]+ K M Figure 1. Michaelis-Menten Equation. The equation in Figure 1 is a tool used to determine the maximum rate at which a reaction can take place, which is noted as Vmax. The given equation is also used to determine the concentration of the substrate when the velocity of the reaction is at half of its max, denoted Km. Figure 2 demonstrates a typical Michaelis-Menten plot, which starts off with a dramatic increase and slowly levels off as Vmax is reached. Figure 3 demonstrates a typical Lineweaver-Burk plot which is created by taking the inverse of the reaction rate versus the inverse of the substrate concentration. The slope of this line is equal to Km over Vmax and has a yintercept equal to the inverse of Vmax. Enzyme activity can be measured by the amount of product that is created from the substrate that was added to the reaction. In order to do this successfully, the substrate and the product need to be distinguished from one another. The two can be distinguished in a number of ways, by having a colored product from an uncolored substrate, or a non-UV absorbent substrate forming a UV absorbent substrate (4). In this experiment a spectrophotometer was used to measure the enzyme activity, and this is one of the most common ways this experiment is performed. The change in absorbance over a period of time can be used to determine the velocity of the occurring reaction by dividing the change in concentration over a given time interval. The graph shown in Figure 2 can be used to determine Km and Vmax, but it can be difficult, so the graph in Figure 3 is used to make calculations easier. Figure 4 shows the equation that is used to determine the line of best fit of a graph like in Figure 3. ( ) KM 1 1 = + V V max [ S ] V max Data Collection: A LabQuest SpectroVis Plus was used in order to collect the data of the ongoing biological reaction. This device was allowed to warm up and then was calibrated with 3 mL of phosphate buffer in a clean cuvette. There were 6 trials ran, each in a new cuvette. Table 1 shows the amount of the substrate, enzyme, and buffer that was used in each run. After calibrating the spectrophotometer, the substrate and the buffer for each run were mixed in test tubes in order to do each trial efficiently. A new cuvette was obtained and the mixture from test tube 1 was poured in. The cuvette was placed into the spectrophotometer, one person pipetted the enzyme into the cuvette as another person pressed start on the data collection as soon as possible. This process was repeated with test tubes 2-6, with the people involved keeping the same roles for accuracy. The spectrophotometer recorded the absorbance of the mixture in the cuvette for 100 seconds. Table 1: Amount of Enzyme, Substrate, and Enzyme Substrate Buffer Buffer addedVolume to each trialVolume in experiment. Volume (ul) Test Tube (ul) Figure 4. Lineweaver-Burk plot best of fit line equation. In this experiment the enzyme used was tyrosinase and the original substrate LDOPA poses a health hazard, so we used an alternative substrate DOPAC (1). When tyrosinase is introduced into a solution with DOPAC present the oxidation reaction shown in Figure 5 takes place and DOPAC quinone is produced. Materials and Methods 1 2 3 4 5 6 150 150 150 150 150 150 (ul) 50 100 200 400 800 1000 2800 2750 2650 2450 2050 1850 Data Analysis: In order to interpet the data that was collected by the spectrophotometer, it was graphed as time versus absorbance for each of the six trials. A time interval of ten seconds lasting from t = 70 seconds to t = 80 seconds was selected. The change in absorbance over this time period was then divided by the extinction coefficient (0.8 mM-1cm-1) and the change in time to determine the velocity of the reaction. This velocity was graphed versus the substrate concentration to create the MichaelisMenten plot. When the reciprocal of velocity is graphed against the reciprocal of substrate concentration, a LineweaverBurk plot is created. The Lineweaver-Burk plot helped determine the Vmax and the Michaelis-Menten constant (Km). Results In Figure 8. Graph of Absorbance at 399.2 nm vs. Time (s) for [S] of 1 mM. For each of the 6 trials that were run, the LabQuest equipment produced a graph of time versus absorbance. Each trial had data collected for 100 seconds. The six trials are shown in Figures 6-11. Figure 9: Graph of Absorbance at 399.2 nm vs. Time (s) for [S] of 2 mM. Figure 6: Graph of Absorbance at 399.2 nm vs. Time (s) for [S] of 0.25 mM. Figure 6: Graph of Absorbance at 399.2 nm vs. Time (s) for [S] of 0.25 mM. Figure 10: Graph of Absorbance at 399.2 nm vs. Time (s) for [S] of 4 mM. Figure 7: Graph of Absorbance at 399.2 nm vs. Time (s) for [S] of 0.5 mM. order to create the Michaelis-Menten and the Lineweaver-Burk plots velocity needed to be determined. The reaction velocity was based on the change in absorbance over a specific time interval. The reciprocal of the velocity graphed against the reciprocal of the substrate concentration is used to create the Lineweaver-Burk plot. Figure 11: Graph of Absorbance at 399.2 nm vs. Time (s) for [S] of 5 mM. Lineweaver-Burk Plot t=10 to t=20 12000 f(x) = 2453.44 x + 1122.83 R² = 0.92 1/V (1/mM/s) 10000 8000 6000 4000 2000 Michaelis-Menten Graph t=70 to t=80 4.50E-04 4.00E-04 Velocity (mM/s) 3.50E-04 3.00E-04 2.50E-04 2.00E-04 1.50E-04 1.00E-04 5.00E-05 0.00E+00 0 1 2 3 4 5 6 Substrate Concentration (mM) Figure 13: Michaelis-Menten plot if reaction rate (mM.s) vs. substrate concentration (mM) at the interval of t=70 to t=80 seconds Figure 14. Lineweaver-Burk plot for the reciprocals of both the reaction velocities and substrate concentrations of the time interval from t=10 sec to t=20 sec. Lineweaver-Burk Plot t=70 to t=80 12 1/V (1/mM/s) 10 8 6 4 2 0 0 1 f(x) = 0 R² = 0 2 3 4 5 6 7 8 1/[S] (S-1) Figure 15 Lineweaver-Burk plot for the reciprocals of both the reaction velocities and substrate concentrations The Vmax and KM were determined from Figures 12-15. The average Vmax was calculated to be 6.22x10-4 mM/s while the KM was calculated to be 1.434 mM. The equations used to calculate both the Vmax and KM values are shown in Figure 16. Discussion The Vmax for tyrosinase was calculated to be 6.22x10-4 mM/s and KM for tyrosinase was calculated to be 1.434 mM. The turnover (Kcat) of tyrosinase was calculated to be 3.11x10-3 s-1. Figure 17 shows the equation used to determine the turnover or tyrosinase. The time interval of t = 10 to t = 20 had a Vmax of 8.91x 10-4 mM/s and the time interval of t = 70 to t = 80 had a Vmax of 3.53 x 10-4 mM/s. The turnover (Kcat) for tyrosinase was calculated using the equation shown in Figure 17. [ET] is the total enzyme concentration and Vmax was the value determined previously. The Kcat was determined to be 4.46x10-3 s-1 for the time interval of t = 10 to t = 20 and 1.77x10-3 s-1 for the time interval of t = 70 to t = 80. The average of these two Kcat values is 3.11 x 10-3 s-1. Appendix: Elementary Statistics for Biochemists Frequency Histogram Data Set 1 2500 2227 2058 Frequency 2000 1734 1449 1500 1121 Frequency 1000 732 500 340 157 0 5 15 25 35 45 55 65 75 39 85 Bin Size Mean 26.76 Median Between X_i = 15.0 and X_i = 25.0. Mode 5 Standard Deviation 18.54 Frequency Histogram Data Set 2 6000 5236 5000 frequncey 4000 3000 2864 2526 2461 2000 1577 1648 4.25 4.75 1779 1975 5.25 5.75 1045 1000 0 3.25 3.75 6.25 6.75 7.25 Bin Size Standard Deviation 1.34 # of times observed Group A Histogram 1800 1600 1400 1200 1000 800 600 400 200 0 1702 1220 1183 # of times observed 362 365 15 39 0 1 2 38 16 3 4 pH 5 6 7 8 9 10 0 Group C Histogram 2500 1976 2001 1500 Ranking of the three graphs based on visual assessment: 1000 Precision: B>C>A # of times observed 2000 450 500 44 0 0 0 1 2 Accuracy A>C>B 430 39 3 4 5 pH 6 7 08 09 10 0