1. the kinetic parameters of enzyme-induced reactions
CP504 – ppt_Set 03
Enzyme kinetics and associated reactor design:
Determination of
the kinetic parameters of
enzyme-induced reactions
learn about the meaning of kinetic parameters
learn to determine the kinetic parameters
learn the effects of pH, temperature and substrate concentration on enzyme activity (or reaction rates)
learn about inhibited enzyme kinetics
learn about allosteric enzymes and their kinetics
Prof. R. Shanthini Updated: 23 Nov 2012

2. Simple Enzyme Kinetics (in summary)
E + S ES
E + P k2
which is equivalent to
[E] S P
S for substrate (reactant)
E for enzyme
ES for enzyme-substrate complex
P for product
Prof. R. Shanthini Updated: 23 Nov 2012

3. Simple Enzyme Kinetics (in summary)
rmaxCS
rP =
- rS =
KM + CS
where rmax = k3CE0 = kcatCE0
and KM = f(rate constants)
rmax is proportional to the initial concentration of the enzyme
KM is a constant
Prof. R. Shanthini Updated: 23 Nov 2012

4. Simple Enzyme Kinetics (in summary)
-rs
Catalyzed reaction
Catalyzed reaction
rmax
- rS
rmaxCS =
KM + CS
rmax
uncatalyzed reaction 2 KM Cs
Prof. R. Shanthini Updated: 23 Nov 2012

5. An exercise
Consider an industrially important enzyme, which catalyzes the conversion of a protein substrate to form a much more valuable product.  The enzyme follows the Briggs-Haldane mechanism:
                              
An initial rate analysis for the reaction in solution, with E0 = 0.10 μM and various substrate concentrations S0, yields the following Michaelis-Menten parameters: Vmax = 0.60 μM/s; KM = 80 μM.
A different type of experiment indicates that the association rate constant, k1, is k1 = 2.0 x 106 M-1s-1 (2.0 μM-1s-1).
a. Estimate the values of k2 and k-1.
b. On average, what fraction of enzyme-substrate binding events result in product formation?
Prof. R. Shanthini Updated: 23 Nov 2012
Source: Jason Haugh, Department of Chemical & Biomolecular Engineering, North Carolina State University

6. Simple Enzyme Kinetics (in summary)
Catalytic step k1 k3
E + S ES
E + P k2
Substrate binding step
k3 = kcat
Prof. R. Shanthini Updated: 23 Nov 2012

7. learn about the meaning of kinetic parameters
learn to determine the kinetic parameters
learn the effects of pH, temperature and substrate concentration on enzyme activity (or reaction rates)
learn about inhibited enzyme kinetics
learn about allosteric enzymes and their kinetics
Prof. R. Shanthini Updated: 23 Nov 2012

8. t Cs - rs given 10 15 rmaxCS - rS = KM + CS
How to determine the kinetic parameters rmax and KM ?
Carry out an enzyme catalysed experiment, and measure the substrate concentration (CS) with time. t Cs
- rs
given 10 15
rmaxCS
- rS =
KM + CS
Prof. R. Shanthini Updated: 23 Nov 2012

9. How to determine the M-M kinetics rmax and KM ?
Carry out an enzyme catalysed experiment, and measure the substrate concentration (CS) with time. t Cs
- rs
given 10 15
rmaxCS
- rS =
KM + CS
Prof. R. Shanthini Updated: 23 Nov 2012

10. rmaxCS - rS = KM + CS = - rS CS rmax KM 1 + (14) = - rS 1 rmax KM + CS
We could rearrange
rmaxCS
- rS =
KM + CS
to get the following 3 linear forms: =
- rS CS
rmax KM 1 +
(14) =
- rS 1
rmax KM + CS
(15) =
- rS
rmax KM - CS
(16)
Prof. R. Shanthini Updated: 23 Nov 2012

11. The Langmuir Plot CS KM 1 CS (14) = + - rS rmax rmax - rS CS 1 rmax
Prof. R. Shanthini Updated: 23 Nov 2012

12. Determine rmax more accurately than the other plots.
The Langmuir Plot CS KM 1 CS
(14) = +
- rS
rmax
rmax
- rS CS 1
rmax
Determine rmax more accurately than the other plots.
- KM CS
Prof. R. Shanthini Updated: 23 Nov 2012

13. The Lineweaver-Burk Plot1 KM 1 1
(15) = +
- rS
rmax
rmax CS
- rS 1 KM
rmax 1
- KM CS 1
Prof. R. Shanthini Updated: 23 Nov 2012

14. The Lineweaver-Burk Plot1 KM 1 1
(15) = +
- rS
rmax
rmax CS
- rS 1
Gives good estimates of rmax, but not necessarily KM
- Data points at low substrate concentrations influence the slope and intercept more than data points at high Cs KM
rmax 1
- KM CS 1
Prof. R. Shanthini Updated: 23 Nov 2012

15. The Eadie-Hofstee Plot
- rS
- rS
rmax = - KM
(16) CS
- rS KM
rmax KM CS
-rS
Prof. R. Shanthini Updated: 23 Nov 2012

16. The Eadie-Hofstee Plot
- rS
- rS
rmax = - KM
(16) CS
- rS
Can be subjected to large errors since both coordinates contain (-rS)
- Less bias on point at low Cs than with Lineweaver-Burk plot KM
rmax KM CS
-rS
Prof. R. Shanthini Updated: 23 Nov 2012

17. Data: CS
(mmol/l) rS
(mmol/l.min) 1
0.20 2
0.22 3
0.30 5
0.45 7
0.41 10
0.50
Determine the M-M kinetic parameters for all the three methods discussed in the previous slides.
Prof. R. Shanthini Updated: 23 Nov 2012

18. rmax = 1 / slope = 1 / 1.5866 = 0.63 mmol/l.min
KM = rmax x intercept = 0.63 x = 2.93 mmol/l
Prof. R. Shanthini Updated: 23 Nov 2012

19. rmax = 1 / intercept = 1 / 1.945 = 0.51 mmol/l.min
KM = rmax x slope = 0.51 x = 1.78 mmol/l
Prof. R. Shanthini Updated: 23 Nov 2012

20. rmax = intercept = 0.54 mmol/l.min
KM = - slope = 1.89 mmol/l
Prof. R. Shanthini Updated: 23 Nov 2012

21. The Lineweaver-Burk Plot The Eadie-Hofstee Plot
Comparison of the results
The Langmuir Plot
The Lineweaver-Burk Plot
The Eadie-Hofstee Plot
rmax KM R2
Prof. R. Shanthini Updated: 23 Nov 2012

22. The Lineweaver-Burk Plot The Eadie-Hofstee Plot
Comparison of the results
The Langmuir Plot
The Lineweaver-Burk Plot
The Eadie-Hofstee Plot
rmax
0.63
0.51
0.54 KM
2.93
1.78
1.89 R2
94.9%
84.6%
66.2%
Prof. R. Shanthini Updated: 23 Nov 2012

23. The Lineweaver-Burk Plot The Eadie-Hofstee Plot
Comparison of the results
The Langmuir Plot
The Lineweaver-Burk Plot
The Eadie-Hofstee Plot
rmax
0.63
0.51
0.54 KM
2.93
1.78
1.89 R2
94.9%
84.6%
66.2%
Determine
rmax more accurately than the other plots
Gives good estimates of rmax, but not necessarily KM
Can be subjected to large errors
Prof. R. Shanthini Updated: 23 Nov 2012

24. learn about the meaning of kinetic parameters
learn to determine the kinetic parameters
learn the effects of pH, temperature and substrate concentration on enzyme activity (or reaction rates)
learn about inhibited enzyme kinetics
learn about allosteric enzymes and their kinetics
Prof. R. Shanthini Updated: 23 Nov 2012

25. Effects of temperature on enzyme activity:
Increases in the temperature of a system results from increases in the kinetic energy of the system.
Kinetic energy increase has the following effects on the rates of reactions:
More energetic collisions
Increase in the number of collisions per unit time
Denaturation of the enzyme or substrate
Prof. R. Shanthini Updated: 23 Nov 2012

26. Effects of temperature on enzyme activity:
More energetic collisions:
When molecules collide, the kinetic energy of the molecules can be converted into chemical potential energy of the molecules.
If the chemical potential energy of the molecules become great enough, the activation energy of a exergonic reaction can be achieved and a change in chemical state will result.
Thus the greater the kinetic energy of the molecules in a system, the greater is the resulting chemical potential energy when two molecules collide.
As the temperature of a system is increased it is possible that more molecules per unit time will reach the activation energy.
Thus the rate of the reaction may increase.
Prof. R. Shanthini Updated: 23 Nov 2012

27. Effects of temperature on enzyme activity:
Increase in the number of collisions per unit time:
In order to convert substrate into product, enzymes must collide with and bind to the substrate at the active site.
Increasing the temperature of a system will increase the number of collisions of enzyme and substrate per unit time.
Thus, within limits, the rate of the reaction will increase.
Prof. R. Shanthini Updated: 23 Nov 2012

28. Effects of temperature on enzyme activity:
Denaturation of the enzyme:
Enzymes are very large proteins whose three dimensional shape is vital for their activity.
When proteins are heated up too much they vibrate.
If the heat gets too intense then the enzymes literally shake themselves out of shape, and the structure breaks down.
The enzyme is said to be denatured.
A denatured enzyme does not have the correct 'lock' structure.
Therefore it cannot function efficiently by accepting the 'key' substrate molecule.
Prof. R. Shanthini Updated: 23 Nov 2012

29. Effects of temperature on enzyme activity:
Denaturation of the enzyme:
Prof. R. Shanthini Updated: 23 Nov 2012

30. Effects of temperature on enzyme activity:
Denaturation of the enzyme:
As temperature increases, enzyme activity increases until its optimum temperature is reached. At higher temperatures, the enzyme activity rapidly falls to zero.
Prof. R. Shanthini Updated: 23 Nov 2012

31. Effects of temperature on enzyme activity:
Denaturation for most human enzymes:
The optimum temperature for most human enzymes to work at is around 37ºC which is why this temperature is body temperature.
Enzymes start to denature at about 45°C.
Optimal for most human enzymes
Prof. R. Shanthini Updated: 23 Nov 2012

32. Effects of temperature on enzyme activity:
Optimal for most human enzymes
Optimal for some
thermophillic
bacterial
enzymes
Reaction rate
Temperature (deg C)
Prof. R. Shanthini Updated: 23 Nov 2012

33. Effects of pH on enzyme activity:
The structure of the protein enzyme can depends on how acid or alkaline the reaction medium is, that is, it is pH dependent.
If it is too acid or too alkaline, the structure of the protein is changed and it is 'denatured' and becomes less effective.
If the enzyme does not have the correct 'lock' structure, it cannot function efficiently by accepting the 'key' substrate molecule.
In the optimum pH range, the enzyme catalysis is at its most efficient.
Prof. R. Shanthini Updated: 23 Nov 2012

34. Effects of pH on enzyme activity:
Optimal for pepsin
(a stomach
enzyme)
Optimal for trypsin
(an intestinal
enzyme)
Reaction rate pH
Prof. R. Shanthini Updated: 23 Nov 2012

35. Effects of pH on enzyme activity:
Amylase (pancreas) enzyme
Optimum pH:
Function: A pancreatic enzyme that catalyzes the breakdown/hydrolysis of starch into soluble sugars that can readily be digested and metabolised for energy generation.
Amylase (malt) enzyme
Optimum pH:
Function: Catalyzes the breakdown/hydrolysis of starch into soluble sugars in malt carbohydrate extracts.
Prof. R. Shanthini Updated: 23 Nov 2012

36. Effects of pH on enzyme activity:
Catalase enzyme
Optimum pH: ~7.0
Function: Catalyses the breakdown of potentially harmful hydrogen peroxide to water and oxygen. Important in respiration/metabolism chemistry.
2H2O2(aq) ==> 2H2O(l) + O2(g)
Prof. R. Shanthini Updated: 23 Nov 2012

37. Effects of pH on enzyme activity:
Invertase enzyme
Optimum pH: 4.5
Function: Catalyses the breakdown/hydrolysis of sucrose into fructose + glucose, the resulting mixture is 'inverted sugar syrup'.
C12H22O11 + H2O ==> C6H12O6 + C6H12O6
Prof. R. Shanthini Updated: 23 Nov 2012

38. Effects of pH on enzyme activity:
Lipase (pancreas) enzyme
Optimum pH: ~8.0
Function: Lipases catalyse the breakdown dietary fats, oils, triglycerides etc. into digestible molecules in the human digestion system.
Lipase (stomach) enzyme
Optimum pH:
Function: As above, but note the significantly different optimum pH in the acid stomach juices, to optimum pH in the alkaline fluids of the pancreas.
Prof. R. Shanthini Updated: 23 Nov 2012

39. Effects of pH on enzyme activity:
Maltase enzyme
Optimum pH:
Function: Breaks down malt sugars.
Prof. R. Shanthini Updated: 23 Nov 2012

40. Effects of pH on enzyme activity:
Pepsin enzyme
Optimum pH:
Function: Catalyses the breakdown/hydrolysis of proteins into smaller peptide fragments.
Prof. R. Shanthini Updated: 23 Nov 2012

41. Effects of pH on enzyme activity:
Trypsin enzyme
Optimum pH:
Function: Catalyses the breakdown/hydrolysis of proteins into amino acids. Note again, the significantly different optimum pH to similarly functioning pepsin.
Prof. R. Shanthini Updated: 23 Nov 2012

42. Effects of pH on enzyme activity:
Urease enzyme
Optimum pH: ~7.0
Function: Catalyzes the breakdown of urea into ammonia and carbon dioxide.
(NH2)2(aq) + H2O(l) ==> 2NH3(aq) + CO2(aq)
Prof. R. Shanthini Updated: 23 Nov 2012

43. Effects of substrate concentration on enzyme activity:
Prof. R. Shanthini Updated: 23 Nov 2012

44. Effect of shear
Prof. R. Shanthini Updated: 23 Nov 2012

45. Complex enzyme kinetics
learn about the meaning of kinetic parameters
learn to determine the kinetic parameters
learn the effects of pH, temperature and substrate concentration on enzyme activity (or reaction rates)
learn about inhibited enzyme kinetics
learn about allosteric enzymes and their kinetics
Prof. R. Shanthini Updated: 23 Nov 2012

46. Inhibited enzyme reactions
Inhibitors are substances that slow down the rate of enzyme catalyzed reactions.
There are two distinct types of inhibitors:
- Irreversible inhibitors form a stable complex with enzymes and reduce enzyme activity (e.g. lead, cadmium, organophosphorous pesticide)
- Reversible inhibitors interact more loosely with enzymes and can be displaced.
Prof. R. Shanthini Updated: 23 Nov 2012

47. Inhibited enzyme reactions - applications
Many drugs and poisons are inhibitors of enzymes in the nervous system.
Poisons: snake bite, plant alkaloids and nerve gases
Medicines: antibiotics, sulphonamides, sedatives and stimulants
Prof. R. Shanthini Updated: 23 Nov 2012

48. Primary constituents of Snake Venom
Enzymes - Spur physiologically disruptive or destructive processes.
Proteolysins - Dissolve cells and tissue at the bite site, causing local pain and swelling.
Cardiotoxins - Variable effects, some depolarise cardiac muscles and alter heart contraction, causing heart failure.
Harmorrhagins - Destroy capillary walls, causing haemorrhages near and distant from the bite.
Coagulation - Retarding compounds prevent blood clotting.
Thromboses - Coagulate blood and foster clot formation throughout the circulatory system.
Haemolysis - Destroy red blood cells.
Cytolysins - Destroy white blood cells.
Neurotoxins - Block the transmission of nerve impulses to muscles, especially those associated with the diaphragm and breathing.
Prof. R. Shanthini Updated: 23 Nov 2012

49. Inhibited enzyme reactions
Inhibitors are also classified as competitive and non-competitive inhibitors.
Prof. R. Shanthini Updated: 23 Nov 2012

50. Competitive inhibition
- The structure of inhibitor molecule closely resembles the chemical structure and molecular geometry of the substrate.
- The inhibitor competes for the same active site as the substrate molecule.
It does not alter the structure of the enzyme.
The inhibitor may interact with the enzyme at the active site, but no reaction takes place.
Prof. R. Shanthini Updated: 23 Nov 2012

51. Competitive inhibition
The inhibitor is "stuck" on the enzyme and prevents any substrate molecules from reacting with the enzyme.
However, a competitive inhibition is usually reversible if sufficient substrate molecules are available to ultimately displace the inhibitor.
Therefore, the amount of enzyme inhibition depends upon the inhibitor concentration, substrate concentration, and the relative affinities of the inhibitor and substrate for the active site.
Prof. R. Shanthini Updated: 23 Nov 2012

52. Competitive inhibition
Competitive inhibitors (denoted by I) compete with substrate to occupy the active site of the enzyme. k1 k3
E + S ES
E + P k2 k4
E + I EI k5
where
rP = k3 CES
(17)
CE0 = CE + CES + CEI
(18)
Prof. R. Shanthini Updated: 23 Nov 2012

53. Competitive inhibition
Assuming rapid equilibrium, we get
k1 CE CS = k2 CES k2
CE CS
KM = =
(19) k1
CES
k4 CE CI = k5 CEI k5
CE CI
KI = =
(20) k4
CEI
Prof. R. Shanthini Updated: 23 Nov 2012

54. Competitive inhibition
Combining (17) to (20), we get
k3CE0CS
rmaxCS
rP = =
(21)
KM (1 + CI / KI) + CS
KM,app + CS
where
rmax = k3CE0
(5)
KM (1 + CI / KI)
(22)
KM,app =
KM = k2 / k1
(6)
KM,app > KM
Prof. R. Shanthini Updated: 23 Nov 2012

55. Competitive inhibition The Lineweaver-Burk Plot
- rS 1
CI > 0
CI = 0 (no inhibitor) 1
- KM, app 1
- KM 1
rmax CS 1
Prof. R. Shanthini Updated: 23 Nov 2012

56. Competitive inhibition
In the presence of a competitive inhibitor,
the maximal rate of the reaction (rmax) is unchanged,
but the Michaelis constant (KM) is increased.
Prof. R. Shanthini Updated: 23 Nov 2012

57. Competitive inhibition – an example
Ethanol is metabolized in the body by oxidation to acetaldehyde, which is a toxic compound and a known carcinogen.
The enzyme alcohol dehydrogenase (ADH) converts ethanol into acetaldehyde plus two hydrogen atoms.
Prof. R. Shanthini Updated: 23 Nov 2012

58. Competitive inhibition – an example
Acetaldehyde is generally short-lived; it is quickly broken down to a less toxic compound called acetate in a rapid reaction so that acetaldehyde does not accumulate in the body. .
The enzyme aldehyde dehydrogenase (ALDH) converts acetaldehyde to acetyl (acetate) radical and a hydrogen atom.
Prof. R. Shanthini Updated: 23 Nov 2012

59. Competitive inhibition – an example
A drug, disulfiram (Antabuse) inhibits the aldehyde dehydrogenase.
Such inhibition results in the accumulation of acetaldehyde in the body.
High levels of acetaldehyde act directly on the heart and blood vessels, causing flushing, a racing heartbeat and a drop in blood pressure that causes dizziness. Other unpleasant symptoms include headache, shortness of breath, palpitations, nausea and vomiting.
This drug is sometimes used to help people overcome the drinking habit.
Prof. R. Shanthini Updated: 23 Nov 2012

60. Non-competitive inhibition
- The structure of inhibitor molecule is entirely different from that of the substrate molecule.
The inhibitor forms complex at a point other than the active site (remote from or very close to the active site).
It does not complete with the substrate.
It alters the structure of the enzyme in such a way that the substrate can no longer interact with the enzyme to give a reaction.
Prof. R. Shanthini Updated: 23 Nov 2012

61. Non-competitive inhibition
Non competitive inhibitors are usually reversible,
but are not influenced by concentrations of the substrate as is the case for a reversible competitive inhibitor.  
Prof. R. Shanthini Updated: 23 Nov 2012

62. Non-competitive inhibitionk1 k3
E + S ES
E + P k2 k4
E + I EI k5 k6
EI + S ESI k7 k8
ES + I ESI k9
Prof. R. Shanthini Updated: 23 Nov 2012

63. Non-competitive inhibition
We could drive the rate equation (given on the next page) assuming the following: k2 k7
= KIM
= KM = k1 k6 k5 k9
= KMI
= KI = k4 k8
Prof. R. Shanthini Updated: 23 Nov 2012

64. Non-competitive inhibition
rmax,appCS
rP =
(23)
KM + CS
where
rmax
rmax,app =
(24)
(1 + CI / KI)
rmax = k3CE0
(5)
KM = k2 / k1
(6)
rmax,app < rmax
Prof. R. Shanthini Updated: 23 Nov 2012

65. Non-competitive inhibition The Lineweaver-Burk Plot
- rS 1
CI > 0 1
rmax,app
CI = 0 (no inhibitor) 1
- KM 1
rmax CS 1
Prof. R. Shanthini Updated: 23 Nov 2012

66. Non-competitive inhibition
In the presence of a non-competitive inhibitor,
the maximal rate of the reaction (rmax) is lower
but the Michaelis constant (KM) is unchanged.
Prof. R. Shanthini Updated: 23 Nov 2012

67. Uncompetitive inhibitionk1 k3
E + S ES
E + P k2 k4
ES + I ESI k5
Inhibitor can only bind to the enzyme-substrate complex, reversibly forming a nonproductive complex.
Prof. R. Shanthini Updated: 23 Nov 2012

68. Uncompetitive inhibition
An uncompetitive inhibitor binds only to the enzyme-substrate complex preventing the formation or release of the enzymatic products.
Unlike with competitive inhibition an uncompetitive inhibitor need not resemble the structure of the enzymes natural substrate.
An uncompetitive inhibitor is most effective at high substrate concentration as there will be more enzyme-substrate complex for it to bind.
Unlike with competitive inhibitors the effects of an uncompetitive inhibitor cannot be overcome by increasing the concentration of substrate.
Prof. R. Shanthini Updated: 23 Nov 2012

69. Non-competitive inhibition
rmax,appCS
rP =
(23)
KM + CS
where
rmax
rmax,app =
(24)
(1 + CI / KI)
rmax = k3CE0
(5)
KM = k2 / k1
(6)
rmax,app < rmax
Prof. R. Shanthini Updated: 23 Nov 2012

70. Uncompetitive inhibition
rmax,appCS
rP =
(25)
KM,app + CS
where
rmax
rmax,app =
(24)
rmax,app < rmax
(1 + CI / KI)
(26)
KM,app =
KM / (1 + CI / KI)
KM,app < KM
rmax = k3CE0
(5)
KM = k2 / k1
(6)
Prof. R. Shanthini Updated: 23 Nov 2012

71. Uncompetitive inhibition
KM is reduced
rmax is also reduced
This is because the total ‘pool’ of enzymes available to react has been reduced, effectively our enzyme concentration has reduced.
Can be explained by rmax = k3CE0 = kcatCE0
Prof. R. Shanthini Updated: 23 Nov 2012

72. Uncompetitive inhibition The Lineweaver-Burk Plot
- rS 1
CI > 0 1
rmax,app
CI = 0 (no inhibitor) 1
- KM, app 1 CS 1 1
rmax
- KM
Prof. R. Shanthini Updated: 23 Nov 2012

73. Competitive versus Uncompetitive inhibition
Prof. R. Shanthini Updated: 23 Nov 2012

74. Mixed inhibition
Prof. R. Shanthini Updated: 23 Nov 2012

75. An exercise
The kinetic properties of the ATPase enzyme, isolated from yeast, which catalyzes the hydrolysis of ATP to form ADP and Pi, are assessed by measuring initial rates in solution, with various ATP concentrations S0 and a total ATPase concentration E0 = 0.60 μM. 
From these experiments, it is determined that
Vmax = 1.20 μM/s; KM = 40 μM.
a. Calculate the values of kcat and the catalytic efficiency for ATPase under these conditions.
b. An inhibitor molecule is added at a concentration of 0.1 mM, and the experiments are repeated.  The apparent Vmax and KM are now found to be 0.6 μM/s, and 20 μM, respectively.  Speculate on how this inhibitor works (i.e., specify which species are engaged by the inhibitor).
Prof. R. Shanthini Updated: 23 Nov 2012
Source: Jason Haugh, Department of Chemical & Biomolecular Engineering, North Carolina State University

76. Substrate / Product inhibition
Either the substrate or product of an enzyme reaction inhibit the enzyme's activity.
This inhibition may follow the competitive, uncompetitive or mixed patterns.
In substrate inhibition there is a progressive decrease in activity at high substrate concentrations.
Product inhibition is often a regulatory feature in metabolism and can be a form of negative feedback.
Prof. R. Shanthini Updated: 23 Nov 2012

77. Substrate / Product inhibition
Prof. R. Shanthini Updated: 23 Nov 2012

78. Assignment Get the rate equations for substrate and product inhibition
Prof. R. Shanthini Updated: 23 Nov 2012

79. “Food for Thought” CS (mg/l) -rS (mg/l.h) 10 5 20 7.5 30 50 12.5 60
13.7 80 15 90
110
21.5
130
9.5
140
150
5.7
Problem 3.13 from Shuler & Kargi:
The following substrate reaction rate (-rS) data were obtained from enzymatic oxidation of phenol by phenol oxidase at different phenol concentrations (CS).
By plotting (-rS) versus (CS) curve, or otherwise, determine the type of inhibition described by the data provided?
Prof. R. Shanthini Updated: 23 Nov 2012

80. Sigmoid/Hill kinetics
A particular class of enzymes exhibit kinetic properties that cannot be studied using the Michaelis-Menten equation.
The rate equation of these unique enzymes is characterized by Sigmoid/Hill kinetics as follows:
rmaxCSn
The Hill equation
rP =
(27)
K + CSn
Hill constant
Hill coefficient
n = 1 gives Michaelis-Menten kinetics
n > 1 gives positive cooperativity
n < 1 gives negative cooperativity
Prof. R. Shanthini Updated: 23 Nov 2012

81. Sigmoid/Hill kinetics
Examples of the “S-shaped” sigmoidal/Hill curve, which is different from the hyberbolic curve of M-M kinetics.
n = 6
n = 4
n = 2
Prof. R. Shanthini Updated: 23 Nov 2012

82. Sigmoid kinetics rP CSn rmax K + CSn θ ln = n ln(CS) – ln (K) (28)
For an alternative formulation of Hill equation, we could rewrite (25) in a linear form as follows: rP
CSn
θ = =
rmax
K + CSn θ ln
= n ln(CS) – ln (K)
(28)
1 - θ
Prof. R. Shanthini Updated: 23 Nov 2012

83. Allosteric enzyme Find out what it is on your own
Prof. R. Shanthini Updated: 23 Nov 2012