Lab #9 Enzyme Kinetics PDF

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Complete Lab Report for Biochemistry on Enzyme Kineteics...

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Enzyme Kinetics Michael J. Blanco November 21, 2016

Abstract The purpose of the lab was to determine the Km and Vmax of alkaline phosphatase. The absorbance was measured at 410 nm per sample. Each sample obtains different volumetric measure of PNPP and Tris-HCl. The initial velocity was obtained from the slope of absorbance over time graph. The concentration then was obtained through the Beer-Lambert’s equation and plot against the initial velocity. Lastly, the LineWeaver Burt Plot was graphed to find the Km and Vmax, .15552 and .288, respectively. Introduction Enzymes are proteins that act as a catalyst to speed up the reactions by lowering the activation energy. Enzymes contain active sites that allow substrates to bind. Two concepts can be derived from the concentration of the substrate and the amount of enzyme; Vmax and Km. If the concentration of the substrate is gradually increased and the amount of enzyme is kept constant, then the velocity of reaction will increase until it reaches Vmax (Introduction to Enzymes). Increasing the concentration of the substrate will not affect the velocity after it reaches the hypothetical value of V max. In theory, when Vmax is reached, the available enzyme has been converted to the enzyme-substrate complex (Introduction to Enzymes). The second important enzyme kinetics concept is the Michaelis constant (Km). The Km is the substrate concentration that half of the maximum velocity is reached. A small Km means that only a small amount of substrate is needed to saturate the enzyme, on the contrary a large Km indicates that high amount of

substrate is needed to achieve the maximum velocity (Introduction to Enzymes). The Km also measures the affinity of the binding of the enzyme and its substrate. The smaller the Km is the greater the affinity (Introduction to Enzymes). The graph of ‘Initial Velocity vs. Substrate Concentration’ and the ‘LineWeaver Burk Plot’ are two visual techniques to determine the value of Vmax and Km. The ‘Initial Velocity vs. Substrate Concentration’ graph is useful when applying: Km=

1 V 2 max

The Vmax is the asymptote represented in the following graph (Enzyme Kinetics):

The Km is the half of the maximum velocity. The LineWeaver Burk Plot is also commonly used to determine Vmax and

Km. The slope of the following graph is

Km ( Enzyme Kinetics ) : V max

The Vmax and Km can be easily determined by taking the reciprocal of the y and x-intercept, respectively.

Procedure Five solutions were prepared with different volume of .2mM PNPP and . 2M Tris HCl. The following are the corresponding volume per sample: Sample #1 .2 mM PNPP 0.1 mL .2 M Tris-HCl 2.7 mL

Sample

Sample

Sample

Sample

#2 0.3 L 2.5 mL

#3 0.5 mL 2.3 mL

#4 0.8 mL 2.0 mL

#5 1.3 mL 1.5 mL

The absorbance value was measured for each sample at 20s intervals for 120 seconds at 410 nm. The first sample was used as a blank. In order to measure the absorbance, .2 mL of the enzyme were added and mixed quickly per sample. The graph absorbance vs. time was obtained per sample. The initial velocity is the slope of the graph ‘Absorbance Vs. Time’. With the initial velocity at hand, the Beer-Lambert law can be used to find the concentration of the substrate. Finally, the graph of ‘Velocity vs. Substrate

Concentration’ was obtained and the Km and the Vmax was calculated by graphing a LineWeaver- Burk Plot. Results

20 seconds 40 seconds 60 seconds 80 seconds 100

Sample #1 .060 .062 .062 .062 .062

Sample #2 .158 .184 .189 .190 .191

Sample #3 .226 .287 .305 .317 .321

Sample #4 .260 .377 .436 .470 .486

Sample #5 .341 .556 .611 .686 .731

seconds 120

.062

.191

.322

.495

.704

seconds

Absorbance Vs. Time Absorbance

0.06 f(x) = 0 x + 0.06 R² = 0.43

0.06 0.06 0.06 0.06 0

20

40

60

80

100

120

140

120

140

Time (s)

Figure 1-.1mL of 2mM PNPP

Absorbance Vs. Time Absorbance

0.25 0.2

f(x) = 0 x + 0.17 R² = 0.6

0.15 0.1 0.05 0 0

20

40

60 Time (s)

80

100

Figure 2- .3 mL of 2mM PNPP

Absorbance

Absorbance Vs. Time 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0

f(x) = 0 x + 0.24 R² = 0.77

0

20

40

60

80

100

120

140

120

140

120

140

Time (s)

Figure 3-.5mL of .2 mM PNPP

Absorbance

Absorbance Vs. Time 0.6 0.5 0.4 0.3 0.2 0.1 0

f(x) = 0 x + 0.27 R² = 0.84

0

20

40

60

80

100

Time (s)

Figure 4- .8mL of .2mM PNPP

Absorbance Vs. Time Absorbance

1 0.8

f(x) = 0 x + 0.34 R² = 0.88

0.6 0.4 0.2 0 0

20

40

60 Time (s)

Figure 5- 1.3 mL of .2mM PNPP

80

100

The initial velocity of the graph is the slope before the point of inflection, thus the latter points are removed to obtain the initial linear rate. Sample

Initial Velocity

Equation of the slope

.1 mL of .2mM PNPP .3 mL of .2mM PNPP

1 x 10-4 s-1 5 x 10-4 s-1

* y = 1 x 10-4x + 0.058 y = 5x10-4 x + 0.155

.5 mL of .2mM PNPP

2 x 10-3 s-1

y= 0.002x + 0.1937

.8 mL of .2mM PNPP

4.4 x 10-3 s-1

y = 0.0044x + 0.1817

1.3 mL of .2mM PNPP

6.8 x 10-3 s-1

y = 0.0068x + 0.2327

*The latter three points for each sample were removed to obtain the initial linear rate Use Beer-Lambert law: A=εLc

Rearrange: c=

A εL

Find the Concentration: Sample 1: c=

1 x 10−4 s−1 (18.5 mM −1 cm−1)(1 cm) c = 5.4 x 10-6 mM/s

Sample 2: c=

5 x 10− 4 s−1 (18.5 mM −1 cm−1)(1 cm) c = 2.7 x 10-5 mM/s

Sample 3:

c=

2 x 10−3 s−1 (18.5 mM −1 cm−1)(1 cm) c = 1.1 x 10-4 mM/s

Sample 4: c=

4.4 x 10−3 s−1 (18.5 mM −1 cm−1)(1 cm) c = 2.4 x 10-4 mM/s

Sample 5: c=

6.8 x 10−3 s−1 (18.5 mM −1 cm−1)(1 cm) c = 3.7 x 10-4 mM/s

Velocity Vs. Substrate Concentration 12000 Initial Velocity (Vo)

10000

f(x) = 0.05 x + 3.47 R² = 1

8000 6000 4000 2000 0 0

0 0 0 0 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 4 0 0 2 6 8 20 40 60 80 1 1 1 1 1 2

Substrate Concentration

made to find Km and Vmax.

A LineWeaver Plot was

LineWeaver-Burk Plot 12000 10000

f(x) = 0.05 x + 3.47 R² = 1

8000 1/V

6000 4000 2000 0 0

0 0 0 0 00 00 00 00 00 00 00 00 00 00 0 0 0 0 00 00 00 00 00 00 2 4 6 8 4 0 0 2 6 8 1 1 1 1 1 2

1/[S]

y = 0.054x + 3.4689 where the slope is .054 and the y-intercept is 3.4689 1 =.288 . Thus, the Vmax is 3.4689 Km , thus multiply the slope by Vmax to get Km. V max Km = (.288)(.054) Km = .015552 The slope is

Discussion The purpose of the experiment was to determine the Km and Vmax of alkaline phosphatase. The following was achieved by measuring the absorbance of the solution with p-nitrophenylphosphate (.2mM) in .2 M Tris-HCl. The volume was changed per sample. The absorbance was measured every 20s for 120s. The absorbance over time was measured per sample and the liner slope is the initial velocity of the sample. The Beer-Lambert’s Law was used to find the

substrate concentration and plot that against the initial velocity, with an R 2 value of 1. The linearity of the graph explains the relationship between the rate of formation of the product and the concentration of the substrate. Since the reaction was not catalyzed there is no hyperbolic relationship that is commonly witnessed in a Michaelis-Menten function. Thus, the following reaction is not applicable to Michaelis-Menten. The LineWeaver Plot was obtained by taking the inverse of the velocity and substrate concentration and plotting it against the x and y-axis, respectively. The Vmax is the y-intercept and Km can be determined by multiplying the slope by Vmax. The Km obtained is .015552 and the Vmax is .288.

References Enzyme Kinetics. (n.d.). Retrieved November 21, 2016, from http://users.rcn.com/jkimball.ma.ultranet/BiologyPages/E/EnzymeKinetics.ht ml Introduction to Enzymes. (n.d.). Retrieved November 21, 2016, from http://www.worthington-biochem.com/introbiochem/substrateconc.html...