The objective of this experiment was to explore how enzyme-catalyzed reaction rates are affected by the concentration of the enzyme, substrates, and any activators or inhibitors. The experiment was divided into two categories. The first category was enzyme kinetics (kinetics of β-gal) in which β-gal was used to design and perform enzyme assays to define the key kinetic parameters of Vma and Km). The second category was to study the inhibition of Acetylcholinesterase (AChE).

The enzyme kinetics was determined by using β-Gal to determine initial velocity of the reaction, a suitable enzyme concentration and also performed three different methods to calculate enzyme kinetic parameter (Vmax and Km). Absorbance versus time plot was used to calculate the timeframe, which was seven minutes and velocity and concentration was used to find enzyme concentration and that was 0.04U/mL. Same time frame and enzymatic concentration was used in the experiment. The experiment was performed with different ONPG concentration and it was found that increasing ONPG concentration was increasing the initial velocity of the reaction as well. In the experiment His-tag β-Gal and un-tagged β-Gal was used to run the reaction, the untagged β-Gal activity was lower (Vmax 0.23 µmol/min and Km=400) than His-tagged β-Gal activity (Vmax 0.27 µmol/min and Km= 600). The second part of the experiment was done was using acetylcholinesterase to study enzyme inhibitions. TPA was chosen as an inhibitor, which was a non-progressive and non-competitive inhibtor.

Materials and methods

The stock solution of 1.2 U/mL was used instead of β-Gal to find the initial velocity. TPA was used as an inhibitor and the following calculations were used for the protocol 1.

The inhibitor screening was not done for this experiment.

Solution Volume (in ml)

Z buffer 9.5 ml

1.2 Units/mL enzyme stock 0.5 ml

4 mg/mL ONPG stock 2 ml

Total 12 ml

KINETICS OF B-GAL AND INHIBITION OF ACHE

SURAYYA SANA

Results

For Enzyme Kinetics of β-gal:

1) Determination of initial velocity timeframe (Protocol 1)

Table 1: Absorbance of β-Gal at various Time Points

Graph 1: Absorbance (A412) versus Time of Reaction

#

Min 2 4 6 8 10 12 14 16 18 20

A420 0.181 0.430 0.612 0.703 0.775 0.779 0.801 0.803 0.838 0.840

Absorbance of Product at Different Time Points

Ab

sorb

an

ce(4

20

nm

)

0

0.225

0.45

0.675

0.9

Time (minutes)

0 5 10 15 20

# 2

According to table and graph number 1, we can see that the data between 4-6 minutes

was increasing by 0.2 points in their absorbances and are shown linear to each other on

the graph. However the data between 6-20 minutes was not increasing by 0.2 points and

therefore went off from the linear range on the graph. The initial velocity exists within

the linear range. Therefore it can be concluded that initial velocity is between 6-8

minutes. At point 8 minutes the data started to get off from the linear range so the data for

the linear range is within 7 minutes, therefore the initial velocity is 7 minutes.

2) Determination of suitable enzyme concentration (Protocol 2)

Table 2: Determining a Suitable [E] in linear range of assay

The velocity was calculated using the given formula:

P(mol/L)= A420/(4500M-1 cm-1 )(1 cm)= A420/(4500M-1)

P(µmol)= P(mol/L) × VRXN × 106(µmol/mol)

In this part of the experiment VRXN is a constant, which is shown in data table 2 and the designed time frame was 7 minutes, which was determined from the protocol 1. So, the velocity for the given case At [E] = 0.01, A420 = 0.432, VRXN = 1200 µL, t = 7 minutes was calculated using the below equation.

P(µmol) = A420 × VRXN/4500 and, v(µmol/min) = P(µmol)/t(mins)

Final

[Enzyme]

(Units/mL)

Vol. 1.2U/

mL enzyme

stock (µL)

Vol. Z

buffer

(µL)

Vol. 4mg/

mL ONPG

stock (µL)

Total

Vol.

(µL)

A420 v (µmol/

min)

0.01 10 990 200 1200 0.432 0.0165

0.02 20 980 200 1200 0.695 0.0265

0.04 40 960 200 1200 1.636 0.0623

0.06 60 940 200 1200 1.86 0.0709

0.08 80 920 200 1200 2.193 0.0835

0.10 100 900 200 1200 2.364 0.090

# 3

P(µmol) = 0.432 ×1200/4500 = 0.1152 and v= 0.1152µmol/7min = 0.0165 (µmol/min)

Graph 2: Reaction Velocity versus Enzyme Concentrations

# The suitable enzyme concentration is found at the linear range, which are the first three

points (0.01, 0.0165). (0.02, 0.0265) and (0.04, 0.0623) on graph 2. The point (0.04,

0.0623) seems a little off from the linear range however it was satisfactory for this

experiment; therefore we can conclude that the suitable enzyme concentration is 0.04 U/

mL.

3)

Reaction Velocity versus Enzyme Concentration

React

ion

velo

city

(µ

mo

l/m

in)

0

0.023

0.045

0.068

0.09

Enzyme Concentration (U/mL)

0 0.03 0.05 0.08 0.1

# 4

Table 3: Summary Data of Kinetic Experiment on His-tag β-Gal.

4)

Table 4: Calculation of Vo Using Curve-Fitting Method

[ONPG]

(µM)

v (µmol/min) 1/v 1/[ONPG] v/[ONPG](mL/

min)

10 0.0045 222.2 0.1 0.45

25 0.004 250 0.04 0.16

50 0.0136 73.5 0.02 0.272

75 0.0197 50.8 0.0133 0.263

100 0.0251 39.8 0.010 0.251

200 0.053 18.9 0.005 0.265

400 0.1027 9.7 0.0025 0.258

600 0.1384 7.2 0.00167 0.231

800 0.1877 5.3 0.00125 0.234

1000 0.1741 5.7 0.001 0.174

[ONPG](µM) Vo= vmax[ONPG]/([ONPG] + Km)

10 0.173

25 0.177

50 0.1789

75 0.1790

100 0.1792

200 0.1796

400 0.1798

600 0.1798

800 0.1799

1000 0.1799

# 5

Graph 3: Michaelis-Menten: Initial Velocity versus Substrate Concentration

#

■ Curve is derived from table 3 (experimental data)

▲Curve derived from table 4 (theoretical data)

The estimated Vmax ~ 0.18 µmol/min is shown in graph 3 which was derived from table 3

and the actual Km is 400 which was converted from mM into µM.

Michaelis-Menten Equation and Curve Fitting Method

Vo

(µm

ol/

min

)

0

0.045

0.09

0.135

0.18

[ONPG](mM)

0 0.25 0.5 0.75 1

# 6

5)

Graph 4: Lineweaver-Burk Format

#

The lineweaver-Brulk linear regression equation is y= 2168.1x + 10.85

Where if x = 0, y = 10.85 = 1/Vmax. Therefore calculated Vmax = 1/10.85 = 0.092µmol/

min.

The slope of equation = Km/Vmax = 2168.1. Therefore, the calculated Km = 2168.1×0.092

= 199.8.

Lineweaver-Burk

1/

Vo

(min

/µ

mo

l)

0

75

150

225

300

1/[ONPG](1/µL)

0 0.025 0.05 0.075 0.1

y = 2168.1x + 10.85

R² = 0.9792

# 7

Graph 5: The Eadie-Hofstee Format

#

The Eadie-Hofstee linear regression equation is y = -0.3688x + 0.1666.

Where if x = 0, y = Vmax = 0.1666 (µl/min) and Km = 0.3688 mL/min

6)

Table 5: Vmax and Km Values determined by Using Three Graphing Methods

Eadie -Hofstee Plot

Vo

(µm

ol/

min

)

0

0.05

0.1

0.15

0.2

Vo/[ONPG](mL/min)

0 0.125 0.25 0.375 0.5

y = -0.3688x + 0.1666

R² = 0.1593

Michael-Menten Lineweaver-Burk Eadie-Hofstee

Vmax(µmol/min) 0.18 0.092 0.1666

Km 400 200 368.8

# 8

Based on table 5 we can draw the conclusion that three different graphing method gave us

Vmax between [0.092-0.18] (µmol/min) and Km between [200-400] (µM).

7)

Table 6: His- Tagged β-Gal vs unTagged β-Gal Using LineWeaver-Burk Equation

Graph 6: Michaelis-Menten for Tagged vs untagged β-Gal

[ONPG](µM) V(µmol/min)

V (µmol/min)

His- Tagged β-Gal Untagged β-Gal

10 0 0

25 0.00187 0.0027

50 0.0072 0.0117

75 0.0149 0.0163

100 0.0195 0.0227

200 0.0547 0.0461

400 0.0981 0.1016

600 0.1512 0.1429

800 0.1973 0.1741

1000 0.264 0.223

# 9

#

#

Based on the Michaelis-Menten method, Vmax = 0.27 µmol/min and Km= 600 for tagged

β-Gal and Vmax = 0.23 µmol/min and Km= 400 for untagged untagged β-Gal.

Enzyme Inhibition of Acetylcholinesterase

1)

Table 7: Progressive vs. Nonprogressive Inhibitors (Malaoxon and TPA)

Michaelis-Menten Equation of Tagged β-Gal vs. Non-tagged β-Gal

Vo

(µm

ol/

min

)

-0.075

0

0.075

0.15

0.225

0.3

[ONPG] (µM)

0 250 500 750 1000

y = 0.0003x - 0.0044

R² = 0.9979

Tagged B-GalNon-tagged B-Gal

Time TPA Malaoxon

A412 % Inhibition A412(undiluted) % Inhibition

0 2.97 19.07 0.303 22.9

10 1.57 57.22 0.147 62.5

20 1.86 49.31 0.076 80.7

30 2.20 40.05 0.059 85.0

# 10

Graph 8: Progressive vs. Nonprogressive Inhibitiors

#

Based on Graph 8, Malaxon is the progressive inhibitor because its percent inhibition

increased when pre incubation time increased. However TPA was a non-progressive

inhibitor because its activity did not depend on the pre incubation time.

2)

Table 8: Data Summary Table without Inhibitor

100% Activity 3.67 0 0.393 0

Progressive vs. Nonprogressive Inhibitors

Inh

ibit

ion

(%

)

0

22.5

45

67.5

90

Time (Minutes)

0 8 15 23 30

TPAMalaoxon

Tube # [ONPG] (mM) Vo (µmol/min) 1/ Vo(min/

µmol)

1/[ONPG] (1/

mM)

2 0.05 0 N/A 20

5 0.1 0.0285 35.088 10

8 0.2 0.0659 15.175 5

11 0.5 0.1272 7.862 2

14 1.0 0.240 4.167 1

17 2.0 0.163 6.135 0.5

# 11

Table 9: Data Summary Table with Inhibitor

Graph 9: Lineweaver-Burk for Reactions with Inhibitor vs. without Inhibitor

Tube # [ONPG] (mM) Vo (µmol/min) 1/ Vo(min/

µmol)

1/[ONPG] (1/

mM)

3 0.050 0.0119 84.034 20

6 0.1 0.0230 43.48 10

9 0.2 0.043 23.256 5

12 0.5 0.08556 11.688 2

15 1.0 0.1060 9.434 1

18 2.0 0.1164 8.591 0.5

# 12

#

#

The linear regression equation for the reactions without inhibitor is y= 3.1802x+1.9188.

Where calculated Vmax is 1/1.9188=0.521 (µmol/min) and when [ONPG] is in mM, Km is

3.1802 × 0.521 = 1.65

The linear regression equation for the reaction with inhibitor is y= 3.7431x+5.4403.

Where Vmax is 1/5.4403=0.1838 (µmol/min) and when [ONPG] is in mM. Km is 3.7431 ×

0.1838 = 0.7

Graph 8 showed that TPA was a non-progressive inhibitor therefore; TPA was used to test

if it was a competitive or noncompetitive inhibitor. TPA was found to be a

noncompetitive inhibitor because at the presence of the inhibitor Vmax and Km of TPA

were decreased. Vmax decreased 0.521 to 0.1838 (µmol/min) and Km also decreased

from1.65 to 0.7).

Lineweaver-Burk for Reactions With Inhibitor vs. Without Inhibitor

1/

Vo

(min

/µ

mo

l)

0

12.5

25

37.5

50

1/[ONPG](1/µmol)

0 3 5 8 10

y = 3.7431x + 5.4403

R² = 0.9949

With InhibitorWithout Inhibitor

# 13

Discussion The objective of this experiment was to explore how enzyme-catalyzed reaction rates are

affected by the concentration of the enzyme, substrates, and any activators or inhibitors.

The experiment was divided into two categories. The first category was enzyme kinetics

(kinetics of β-gal) in which β-gal was used to design and perform enzyme assays to

define the key kinetic parameters of Vma and Km). The second category was to study the

inhibition of Acetylcholinesterase (AChE). Two variables timeframe (seven minutes) and

enzyme concentration (0.4 U/mL) were calculated before the experiment and were used

in determining the kinetic parameters (Vmax and Km). The experiment seemed to be

successful and we were able to find that TPA was non-progressive and non-competitive

inhibitor while Malaoxon was a progressive inhibitor.

Three different graphing methods, Michaelis-Menten, Lineweaver-Burk and

Eadie-Hofstee were used to calculate Vmax and Km. All three methods gave us different

values of Vmax and Km. The values for Vmax were between 0.092-1.8(µmol/min) and the

values for Kmwere between 200- 400. The experimental value for Vmax in Michaelis-

Menten method (graph 3) was lower than the theroretical value. The expected for

Vmaxwas a curve however it gave us a linear graph instead of a curve and the theoretical

data gave us the curve graph. Since the Vmax for experimental data was based on an eye

observation it might have cause the data to be liner instead of a curve. The lineweaver-

burk method (graph 4) gave us the best results, because of its data fit into the linear range

except two points (0.02, 73.5) and (0.0133, 50.8). The Eadie-Hofstee method (graph 5)

gave us very poor results, almost none of its data fit into the linear range. Based on the

observation we can say lineweaver-burk was the best and Eadie-Hofstee was the worst

# 14

method and also if we had a small range of Vmax and Km we might have end up with

better results.

I used the Michaelis-Menten to calculate the kinetic parameters to compare the

activities of tagged and un tagged β-Gal. The Vmax of the tagged β-Gal was 0.27 µmol/

min, which was greater than the Vmax value of untagged β-Ga0.23 µmol/min. The Km for

tagged β-Gal was 600, which was greater than the value of Km for untagged β-Gal (400).

This calculations and result proves that his-Tag Changes the activity of β-Gal by

decreasing its enzymatic activity.

Based on the observation from Graph 8, Malaxon is the progressive inhibitor

because its percent inhibition increased when pre incubation time increased. However

TPA was a non-progressive inhibitor because its activity did not depend on the pre

incubation time. After knowing that TPA was a non-progressive inhibitor it was tested to

see if it was competitive or noncompetitive. TPA was found to be a noncompetitive

inhibitor because at the presence of the inhibitor Vmax and Km of TPA were decreased.

Vmax decreased 0.521 to 0.1838 (µmol/min) and Km also decreased from1.65 to 0.7).

# 15