Lab-rapport 1 - Enzyme kinetics with β-galactosidase PDF

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Summary

Investigation of the kinetics of an enzyme catalysed reaction to determine if it meets the Michaelis-Menten equation.
Measuring the enzyme's Vmax and KM using spectrophotometry....

Description

BMB530: Laboratory Exercise 1

Enzyme kinetics with β-galactosidase Investigation of the kinetics of an enzyme catalysed reaction to determine if it meets the Michaelis-Menten equation. Measuring the enzyme's Vmax and KM using spectrophotometry.

Group: 2

Instructor: Date: 21/10-2020

Indhold

Indhold.......................................................................................................................................2 Purpose.......................................................................................................................................2 Theory........................................................................................................................................3 Method.......................................................................................................................................5 Results........................................................................................................................................6 Discussion..................................................................................................................................9 Conclusion................................................................................................................................10 References................................................................................................................................11

Purpose The purpose of this exercise is to examine the kinetics of an enzyme catalyzed reaction. By inserting data from an enzymatic reaction, of o-nitrophenyl β-D-galactopyranoside hydrolyzing lactose, into the Michaeles-Menten ecuation, it will be possible to examine whether the data behaves as is expected. As to whether it follows the relationship between available substrate and the rate of the reaction.

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Theory The reaction being examined in this experiment, comes from a naturally occurring catalyzation, happening in the bacteria Escherichia coli. Here the enzyme β-galactosidase helps the bacteria by hydrolyzing lactose, a disaccharide, into galactose and glucose, two monosaccharides.

Picture 1: Illustration of the hydrolysis of lactose to galactose and glucose

Picture 2: Illustration the of hydrolysis of ONPG to galactose and o-nitrophenol

The substrate this exercise will use will however be the artificially manufactured o-nitrophenyl β-Dgalactopyranoside, or ONPG for short. The enzyme can by the same type of reaction, a hydrolyze, convert the ONPG substrate into galactose and the yellow fluorescent o-nitrophenol. As more products are produced, the mixture appears more yellow fluorescents, which makes the absorbance rise. Picture 3: Illustration of the Micheales-Menten relation between substrate and rate of the reaction

The interaction between the enzyme and the substrate in the reaction go back and forth in equilibrium until all the substrate have gone to the product side of the equation. This transaction can be illustrated using a Michaelis-Menten equation.

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v0 =

V max [ S] K m+[ S ]

The illustration shows the relationship between the available substrate and the rate of the enzymatic reaction. As the concentration of the substrate is at its lowest, the rate will be slow, as many of the enzymes will be absent substrate to progress. But if there is an abundance of substrate available, more enzymes will be working, and the rate of the reaction will be at its highest, which will be Vmax [ CITATION Lau14 \l 1030 ]. The maximum velocity and Km are hard to determine with the use of Michalis-Menten equation. Therefor Lineweaver-Burk plot is widely used to determine both the Vmax and Km values. To achieve the values needed for the Lineweaver-Burk plot 1 is divided by both the substrate concentration and initial velocity. The y-intersection of the graph is equivalent to 1/Vmax (min/mM) and the x-intersection is the equivalent to 1/Km(mM^-1). By inverting the intersection values, the true values of both Vmax and Km can be determined.

Picture 4: Illustration of the lineweaver burk plot

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Inhibitors can drastically alter the function of certain enzymes. They are used in all sorts of prescription drugs to treat a variety of diseases. One category of inhibitors is called competitive inhibitors. These inhibitors compete with the substrates over the enzymes. When a competitive inhibition occurs, Vmax stays the same and Km increases in value. Another inhibitor is known as uncompetitive inhibitors. These inhibitors bind to the enzymesubstrate complex and inhibits conversion from substrate to product. Therefore, both the Vmax and Km values decreases. The last inhibitor is known as a noncompetitive inhibitor. The inhibitor can bind to both the enzyme-substrate complex and enzyme. When the inhibitor binds to the enzymes it renders the enzyme inactive. Whereas binding to the enzymesubstrate complex, it binds in another site than the substrate does. Therefor the substrate can still bind to the complex, but the conversion to product will not happen. When this kind of inhibition happens, Vmax decreases, and the Km stays the same.

Picture 5: Illustration of types of inhibitors

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Method The method used in this exercise consisted of a measurement of an enzymatic catalyzation by measuring the enzymatic rate. By making a series of mixtures with different volumes of buffer, ONPG substrate and lactose, the sole impact on the enzyme's catalytic effect can be measured. These volumes are as follows: Table 1: Listing of volumes added to each mixture

No.

Buffer (ml)

ONPG 30mM (µl)

Lactose 80nM (µl)

1

2,88

100

15

2 3 4

2,93 2,96 2,97

50 20 10

15 15 15

5 6 7 8 9 10

2,98 2,73 2,78 2,81 2,82 2,83

5 100 50 20 10 5

150 150 150 150 150

Enzyme 250 µg/ml (µl)

15 15 15 15 15 15

These reagents were inserted into a spectrophotometer, one by one, to determent the absorption as a function of time for the specific reagents with specific volumes of buffer, ONPG substrate and lactose. By using the enzyme β-galactosidase to catalyze o-nitrophenyl β-D-galactopyranoside into the fluorescent o-nitrophenol, the rate could spectrophotometrically be measured as the mixture would turn more and more yellow, as more and more product are produced, thereby giving an indication as to the rate of the reaction, as mentioned in the theory section. The value given from the spectrophotometric analysis was the absorption per minute. By having this value, the V0 can be calculated by the use of Lambert Beer’s law. V 0=(Δ A 412 /min)/(ɛ∗l ) ∆A412 is the absorption per minute of the solvent inside the spectrophotometer. is the absorption coefficient of ONPG given at 3 and l being the path length through the cuvette which is 1 cm. Comparing the actual enzymatic rate with the theoretic Lineweaver-Burk plot can thereby be helpful to examine whether the experiment follows the rate proposed by the MichaelisMenten equation or another path. [ CITATION Syd20 \l 1030 ].

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Results Table 1 below shows the different volumes of different substances in which were added to the mixture. Furthermore, these values were used to determine the exact concentration inside the mixture, and this was further used to calculate 1/[S]. The results from spectrophotometry were given in absorption per minute (Δ A 412 /min) , by using Lambert Beer’s law, the initial rate(v0) was calculated from the results. At last 1/V0 was determined from the initial rate. Table 2: Results from the experiment with enzymatic reaction rate

The concentration of ONPG was calculated by the use of the equation: C1 ・V1 = C2 ・V2 C1 is the initial concentration of ONPG, which is valued at 30mM. V1 is the initial volume of ONPG when added to the cuvette and V2 is the accumulated volume of all substances, including the buffer, ONPG, the enzyme and lactose if added. C2 was then isolated resulting in the equation C2 =(C 1∗V 1 )/ V 2 Example from trial 1 (30mM*0.1mL)/(0.1mL+0.0015mL.2,88mL) = 1.002 mM The values were then added to the equation for the following ten experiments The initial rate was determined by using Lambert beer's law: V0 = (∆A412(/min) / ( ・l) Example from trial 1 0.456 ∆A412 /min / (3mM^-1cm^-1・1cm) = 0.152 mM/min

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Graph 1: Michaeles Menten plot of the reaction with and without Lactose

Graph 1 includes two curves derived from data of both experiments. One with lactose and one without. The graph is called a Michaelis-Menten plot. It depicts the OPNG concentration in mM against the initial rate in mM/min. The two curves are distinguishable, as the mixture without lactose generally is faster than the one with lactose.

Graph 2: Lineweaver Burk plot of the reaction with and without Lactose

Graph 2 uses the same data from above, although 1 is divided by the ONPG concentration and initial rate, to achieve the Lineweaver Burk plot. Which makes it easier to establish a Vmax and Km. It depicts 1/S in mM^-1 against 1/V0 in min/mM. 1/Vmax is the intersection at Y and 1/Km is the intersection at X. The two 1/Vmax values 6,446 min/mM and 7,271 min/mM are approximately the same, whereas 1/Km increases from 1,927 mM^-1 to 8,180 mM^-1 as the lactose is added. Table 2 below depicts the 1/Vmax and 1/km achieved from the Lineweaver-Burk plot. These were then converted to Vmax and Km values, by using the inverse function of both 1/Vmax and 1/Km. Both Vmax values are approximately the same, at 0,155 mM/min and 0,138 mM/min. In contrast Km increased from 0,122 mM to 0,519 mM

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Table 3: Results from calculation of Vmax and Km

1/Vmax (min/mM)

Vmax (mM/min)

1/Km (mM^-1)

Km (mM)

With Lactose

6,446

0,155

8,180

0,519

Without Lactose

7,271

0,138

1,927

0,122

Value of 1/Vmax is given by the intersection of Y, which can be found in the equation given by the graph. To determine 1/Km, 1/Vmax can be divided by the slope of said graph. Afterwards to achieve the true values of Vmax and Km the inverse function of the two values can be taken. Example: 1/Vmax = 6,446 (min/mM) 1/Km = 6,446 min/mM / 0,3289 min= 1,927 mM^-1 Vmax = 1/6,446 (min/mM) = 0,155 mM/min Km = 1/1,927 mM^-1 = 0,519 mM

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Discussion The results of the experiment correlated in general with the anticipated tendencies that would be expected for an enzymatic reaction. By adding different measures of substrate, and later lactose, the enzyme reacted in the ways it was expected to, when comparing it to the Michaelis Mendes equation, and the theory of competitive inhibitors. When there was less substrate available the rate of the reaction would slow down and with an increase of substrate the rate would also increase. And by inserting this data into the Michaelis-Menten equation, this also showed to follow the expected curve, with similar point of reaching Vmax/2 and Vmax. Most of the points from the trials show a good alignment with the curve in graph 1. Some of the trials were however remeasured several times, as the measurement was a bit off. This was also done with trial 9, though a perfect measurement was never achieved. Looking at Table 1 an example such as test 9 shows a 0.0577 Δ A 412 /min . This thereby causes the data in the Michaelis-Menten plot to differ from the curve. Had the value instead been 0.13 Δ A 412/min , this plot would have had a much greater fit. And had more retakes been made, this value probably would have been found. Although several retakes of the different trials had to be made, in order to make the data correlate with the theory, this was an expected process as many human errors can occur. Both mixing and stirring of the substrate as well as use of the spectrophotometer, were all factors that could give an incorrect result, if not handled properly. This was limited by having the same person doing the same task throughout the exercise. Both Lineweaver-Burk and Michael-Mentes plot shows what effect adding lactose to the mixture has on the production of products. When a second organic substrate was introduced to the mixture, where a synthetic substrate counterpart already preexisted, the two substrates would compete over the restricted number of enzymes in the mixture, as they resemble each other in chemical structure. This would inhibit both substrates in the process of producing products, causing the initial rate of the conversion, from ONPG to product, to drop. This is due to that ONPG is the synthetic counterpart to lactose. Furthermore, the calculated Vmax from both experiments were approximately the same, whereas the Km value increased. Vmax and Km from the experiment without lactose in the mixture was estimated at 0,138 mM/min and 0,122 mM. In contrast the experiment with lactose in the mixture Vmax was estimated at 0,155 mM/min and Km at 0,519 mM. This would indicate that introducing a second substrate resulted in a competitive inhibition

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Conclusion The enzyme catalyzed reaction created in the laboratory for this exercise did align with the theoretical Michaelis-Menten plot and Lineweaver-Burk plot, although several retakes had to be made. Furthermore, the experiment shows that lactose acts as a competitive inhibitor, when introduced to the enzymatic reaction with β-galactosidase. The Vmax values of both experiments stayed approximately the same, whereas the Km value increased when lactose was introduced to the reaction, indicating that lactose is a competitive inhibitor.

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References Laurence A. Moran, R. A. H. G. S. M. P., 2014. Principles of biochemistry. 5. red. Harlow: Pearson Education Limited. Syddansk Universitet, 2020. Enzyme kinetics with B-galactosidase. s.l.:s.n.

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