1. Michaelis-Menten Kinetics
Presented by
Avinash Kodoori
M.Pharm I semester
Dept. of Pharmaceutics,
Univ. College of Pharmaceutical Sciences,
Kakatiya University,
Warangal.

2. Contents Linear and Non linear kinetics Causes
The Michelis Menten kinetics
Introduction
Assumptions
Derivation
Important conclusions
Understanding Km and Vmax
Determination of Km and Vmax
In vitro , Lineweaver-Burk plot
In vivo
Applications

4. Effect of dose on riboflavin urinary recovery when given on an empty stomach

5. Effect of dose on ascorbic acid absorption.
April 7, 2019

6. Steady-state Vitamin C plasma concentration as a function of dose in 13 female subjects receiving doses from 30 to 2,500 mg.

8. CAUSES OF DOSE DEPENDENT KINETICS
Drug
GI absorption
Saturable transport in gut wall
Riboflavin, L-dopa
Intestinal metabolism
Propanolol
Distribution
Saturable plasma protein binding
Salicylic acid , phenytoin
Cellular uptake
Methicillin
Renal elimination
Active secretion
p-amino hippuric acid
Tubular reabsorption
Riboflavin, ascorbic acid
Metabolism
Saturable metabolism
Phenytoin, valproic acid
Metabolite inhibition
Diazepam

9. The Michaelis-Menten Kinetics
Louis Michaelis and Maude Menten's theory (1913)
Applies to – Enzymes
- Carriers
- proteins
Related terms - Dose dependent kinetics
- Saturation Kinetics
- Capacity limited kinetics

10. Saturation Kinetics/ Capacity limited kinetics

11. Assumptions It assumes the formation of an enzyme- substrate complex
It assumes that the ES complex is in rapid equilibrium with free enzyme
Breakdown of ES to form products is assumed to be slower than
1) formation of ES and
2) breakdown of ES to re-form E and S

12. Derivation k-2 For the reaction E + S ES P + E
the reverse reaction can be neglected at the beginning (initial rate with [P]=0)
k-2

13. 1) The rate of formation of the product
v = k2[ES],
2)[Enzyme]total = [E]t = [E] + [ES]
3) At steady state:
d[ES]/dt = 0
4) KM = (k-1 + k2)/k1

15. The rate of formation of ES is given as
Assume steady state: d[ES]/dt = 0
So: k1[E][S] = k-1[ES] + k2[ES]

16. [ES] = ([E][S])/KM Rearranging we get [ES] = (k1/(k-1 + k2))[E][S]
Substituting
(KM = (k-1 + k2)/k1):
[ES] = ([E][S])/KM
KM[ES] = [E][S]
Substituting ([E] = [E]t - [ES]):
KM[ES] = [E]t[S] - [ES][S]

17. Rearranging: [ES](KM + [S]) = [E]t[S]
So:
The rate of formation of the product is given as

18. the maximum rate is given as
hence

19. The Michaelis Mentens Equation

20. At [S] « Km, Vo is proportional to [S] At [S] » Km, Vo = Vmax

21. Important Conclusions of Michaels - Menten Kinetics
when [S]= KM, the equation reduces to
when [S] >> KM, the equation reduces to
when [S] << KM, the equation reduces to

22. The "kinetic activator constant"
Understanding Km
The "kinetic activator constant"
Km is a constant
Km is a constant derived from rate constants
Km is, under true Michaelis-Menten conditions, an estimate of the dissociation constant of E from S
Small Km means tight binding; high Km means weak binding

23. The theoretical maximal velocity
Understanding Vmax
The theoretical maximal velocity
Vmax is a constant
Vmax is the theoretical maximal rate of the reaction - but it is NEVER achieved in reality
To reach Vmax would require that ALL enzyme molecules are tightly bound with substrate
Vmax is asymptotically approached as substrate is increased

24. The dual nature of the Michaelis-Menten equation
Combination of 0-order and 1st-order kinetics
When S is low, the equation for rate is 1st order in S
When S is high, the equation for rate is 0-order in S
The Michaelis-Menten equation describes a rectangular hyperbolic dependence of v on S

26. a)Invitro determination Lineweaver – Burk Double Reciprocal Plots
It is difficult to determine Vmax experimentally
The equation for a hyperbola can be transformed into the equation for a straight line by taking the reciprocal of each side

28. The formula for a straight line is y = mx + b
A plot of 1/V versus 1/[S] will give a straight line with
slope of KM/Vmax and
y intercept of 1/Vmax
Such a plot is known as a Lineweaver-Burk double reciprocal plot

29. Lineweaver-Burk plot (double-reciprocal)

30. Hanes–Woolf plot
invert and multiply by [S]:
Rearrange

32. b. In Vivo Determination
Vmax Km K0
K0/Css

33. JB is an 18 year male receiving phenytoin for prophylaxis of post-traumatic head injury seizures. The following steady state concentrations were obtained at the indicated doses:
Dose (mg/d) Css (mg/L)
From this data, determine this patient’s Km and Vmax for phenytoin.

34. Dose (mg/d) Css (mg/L) Dose Rate/Css (L/d) 100 3.7 27 300 47 6.4
JB is an 18 year male receiving phenytoin for prophylaxis of post-traumatic head injury seizures. The following steady state concentrations were obtained at the indicated doses:
Dose (mg/d) Css (mg/L) Dose Rate/Css (L/d)
Vmax = 362 mg/d
K0 (mg/d)
Km = 9.7 mg/L
K0/Css (L/d)
April 7, 2019

35. Significance of Km Km is a constant
Small Km means tight binding; high Km means weak binding
Useful to compare Km for different substrates for one enzyme
Hexokinase : D-fructose – 1.5 mM
D-glucose – 0.15 mM
Useful to compare Km for a common substrate used by several enzymes
Hexokinase: D-glucose – 0.15 mM
Glucokinase: D-glucose – 20 mM

37. Other applications 1)The Catalytic Efficiency
kcat, the turnover number, is the number of substrate molecules converted to product per enzyme molecule per unit of time, when E is saturated with substrate.
kcat/Km is an apparent second-order rate constant which measures how the enzyme performs when S is low

39. Competitive inhibitor2)
Vmax unaltered, Km increased

40. Noncompetitive inhibitor3)
Km unaltered, Vmax decreased

41. References
Leon Shargel, A Text book of Applied Bio pharmaceutics and pharmacokinetics,5th edition
Milo Gibaldi , Donald Perrier, Pharmacokinetics,2nd edition
V.Venkateshwarlu, Biopharmaceutics and pharmacokinetics,(2004)
Garret & Grisham , Biochemistry, 2nd edition

42. German biochemist
and physician
Canadian medical scientist

43. Thank You