1. Chapter Three: Part Two

2. Uses of Enzymes Food Production Cheese Beverage brewing
Meat tenderizers
Tofu production
Wine-making
Lactose removal in milk

3. Uses of Enzymes Chemical Industries Detergents
Fructose production from glucose
Amino acid production
Vitamin production
Glucose production from starch
Aspartic acid production
Urocanic acid production
Ethanol production

4. Medical Uses Medical Applications Antibiotic production
Blood purification
Treatment of metabolic disorders
Wound healing and antibacterial agents
Treatment of stomach problems
Blood clot removal
Anticancer medicines

5. Michaelis-Menten Kinetics

6. Conservation of enzyme
Enzyme Kinetics
Enzymatic reaction
E + S ES E + P k1
k-1 k2
Rate expression for product formation
v = dP/dt = k2(ES)
d(ES)/dt = k1(E)(S)-k-1(ES)-k2(ES)
Conservation of enzyme
(E) = (E0) – (ES)

7. K’m = k-1/k1 = [E][S]/[ES]
Two Methods to Proceed
Rapid equilibrium assumption: define equilibrium coefficient
K’m = k-1/k1 = [E][S]/[ES]
[ES]= [E][S]/ K’m
Quasi-steady state assumption
[ES] = k1[E][S]/(k-1+k2)
[ES] = [E][S]/ Km
Km = (k-1+k2)/k1

8. Michaelis-Menten Kinetics
When v= 1/2 Vm, [S]= Km
so Km is sometimes called the
“half-saturation constant” and
sometimes the “Michaelis constant”

9. Michaelis-Menten Kinetics
unit on k2 is the inverse of time unit (k2 is also called the “turnover number”). Units on E0 are amount of enzyme (moles, grams, units, etc.) per unit volume
Km has the same units as [S] (mole/liter, etc.)

10. Experimentally Determining Rate Parameters for Michaelis-Menten Kinetics Lineweaver-Burk Eadie-Hofstee Hanes- Woolf Batch Kinetics

11. Determining Parameters
Rearrange the equation into a linear form.
Plot the data.
What kind of data do we have for an experiment examining enzyme kinetics (i.e., v, 1/v, [S], 1/[S], units)?
The intercept and slope are related to the parameter values.

12. Enzyme Kinetics Experiment
Place enzyme and substrate (reactants) in a constant temperature, well stirred vessel. Measure disappearance of reactant or formation of product with time.
Why constant temperature?
Why well stirred?
What about the medium? Buffer?

13. Lineweaver-Burk Plot (double reciprocal plot)
Rewrite Michaelis-Menten rate expression
Plot 1/v versus 1/[S]. Slope is Km/Vm, intercept is 1/Vm

14. Graphical Solution y-intercept Slope 1/ V Slope = Km/ Vm 1/ Vm -1/ Km

15. Eadie-Hofstee Plot
Rearrangement of Eq. 3.12b yields; V 15

16. Hanes-Woolf Plot
Rearrangement of Eq. 3.12b yields; 16

17. Example Find Vm and Km using Lineweaver-Burk plot Eadie-Hofstee plot
V(M/s)
[S], (M)
Find Vm and Km using
Lineweaver-Burk plot
Eadie-Hofstee plot
Hanes-Woolf plot 17

18. Lineweaver-Burk Slope=Km/Vm= 0.5686 y-intercept=1/Vm= 28687 Vm(M/s)=
V(M/s)
[S], (M)
1/V
1/S
100000
50000
40000
25000
20000
Slope=Km/Vm=
0.5686
y-intercept=1/Vm=
28687
Vm(M/s)=
3.4859E-05
Km (M)=Slope*Vm=
E-05

19. Eadie-Hofstee Plot Slope=-Km= -0.00002 y-intercept=Vm= 0.000035
V(M/s)
[S], (M)
V/S
1.17 1
0.875
0.776
0.7
0.5825
0.5
Slope=-Km=
y-intercept=Vm=
Vm(M/s)=
Km (M)=

20. Hanes-Woolf Plot Slope=1/Vm= 28628 y-intercept=Km/Vm= 0.5701 Vm(M/s)=
V(M/s)
[S], (M)
S/V 1 2
Slope=1/Vm=
28628
y-intercept=Km/Vm=
0.5701
Vm(M/s)=
E-05
Km (M)=
E-05

21. Comparison of Methods
Lineweaver-Burk
Eadie-Hofstee
Hanes-Woolf Km
E-05
2.0E-5
E-05 Vm
3.4859E-05
3.5E-5
E-05
Lineweaver-Burk: supposedly gives good estimate for Vm, error is not symmetric about data points, low [S] values get more weight
Eadie-Hofstee: less bias at low [S]
Hanes-Woolf: more accurate for Vm.

22. Assignment # One Problem 3.1 (Textbook) Problem 3.2 (Textbook)
Due date: Sunday, 16/10/2011 (during lecture). Late submission will not be marked and student will get zero.

23. Batch Kinetics
The time course of variation of [S] in a batch enzymatic reaction can be determined from;
By integration yield;
Km and Vm from plotting (on y-axis) vs (on x-axis) using
the following equation:
Slope=Km
Y-intercept=-Vm
Or by plotting (on y-axis) vs (on x-axis) using the following equation:
Slope=
Y-intercept= 23

24. General Form E + S ES E + P k1 k2 k-1
The following set of ordinary differential equations (ODEs) must be
solved simultaneously in order to obtain more general and more
accurate parameter values
(1)
(2)
(3)
(4)

25. Allosteric Enzyme Kinetics
In an enzyme with more than one substrate binding site, binding of one substrate molecule affects the binding of another.
The cooperativity coefficient (n) can be determined from:
n>1, cooperation; n<1, interference

26. Allosteric Enzymes Shape of rate curve is sigmoidal Michaelis-Menten