Chemical Kinetics.pdf. huytibkvjhgfydy

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1. Reaction Kinetics
Adebanjo Adegbola, PhD
PHC 201

2. Chemical Kinetics- applications in pharmacy
Reaction Rates How we measure rates.
Rate Laws How the rate depends on amounts of
reactants, orders of reaction
Integrated rate laws How to calculate amount left or time to
reach a given amount; Half live, shelf-life,
expiry dating.
Factors affecting the rate of reaction How rate constant changes with
temperature. Arrhenius Equation
Stability study Stability testing and mechanisms of drug
degradation. ICH guidelines
Enzyme Kinetics- applications
Kinetic parameters
Enzyme inhibition and induction
Outline:Kinetics

3. •
•
Thermodynamics – does a reaction take place?
Kinetics – how fast does a reaction proceed?
Kinetics- Reaction rate
A B
•How long it takes it to get there

4. •
•
Reaction rate:The rate of reactions is defined as
the change in concentration of any of reactant or
product per unit time.

The rate of a chemical reaction is a measure of
how fast the concentration changes.
•Rate of reaction = rate of disappearance of A
= rate of appearance of B
•Can be determined by monitoring the change in
concentration of either reactants or products as a
function of time t.

6. •Instantaneous rate = rate for specific instance in time

7. RATE LAWS
•Rate Law or Rate equation is an expression which
shows how the reaction rate is related to
concentrations
•The rate of a reaction is directly proportional to
the reactant concentrations, each concentration
being raised to some power.

8. ORDER OF A REACTION
•The order of a reaction is defined as the sum of
the powers of concentrations in the rate law.
•The order of such a reaction is ( m + n)
.
•Usually the powers of concentration in the rate
law are different from coefficients.
•The order of a reactant is not related to the
stoichiometric coefficient of the reactant in the
balanced chemical equation.

9. •
•
•
Reaction is mth order in A
Reaction is nth order in B
Reaction is (m+n)th order overall

10. •The order of a chemical reaction cannot be
determined by inspection, it must be determined
experimentally

11. Zero order Kinetics
Attributes of zero-order kinetics
•Rate is independent of the concentration of the
reactions
•
•
The time required for the concentration of a reactant
to decrease to half its initial value DEPENDS on its
initial concentration



Half-life is the time required for one-half of the rxn to
be completed.

12. •The units of k = mol/ L/ time
Attributes of zero-order kinetics

14. First order reaction

15. First-order
kinetics
•The time taken for the reactant concentration to fall from 1 M to
0.5 M will be the same as the time taken to fall from 0.5 M to
0.25 M.

16. •At the beginning of the reaction, ( t = 0),
•After time t, x moles of A have changed, the concentration of A
is a – x.
The rate of reaction, dx/ dt, is directly proportional to
the concentration of the reactant.
or
•The concentration of A is a moles/
litre
or 2
1

17. or 3

18. First-order kinetics
If a reaction is first-order, a plot of ln [A] t vs. t will yield a straight line with a
slope of -k.

19. •
Half-life for a first-order Kinetics
•Half-life for a first order reaction is independent of
the initial concentration
•It is inversely proportional to k, the rate-constant

20. Let’s combine (a) and (b)
Parameters to characterize first-order kinetics
•Relaxation time

21. Relaxation time
•
•
The half-life, the relaxation time, and rate coefficient
depend only on ratios of concentrations.

We do not need to know actual concentrations to
characterize the kinetics of first-order reactions

22. Second order reaction

23. Second order
reaction
2A products
A second-order reaction corresponds to the rate law v = kc²

24. Thus,

26. •So if a process is second-order, a plot of 1/[A] versus t
will yield a straight line with a slope of k
•So a plot of l/[A]t vs. t is a straight line with slope ( k)
and intercept of 1/[A]0.

•This equation has the general
form for a straight line,

y=mx+b

28. The Characteristics of Simple-Order Reactions

29. Examples

30. HOW TO DETERMINE THE ORDER OF A REACTION
(1)Substitution method using integrated rate
equations
The data accumulated in a kinetic study can be
substituted in the integrated form of the equations that
describe the various orders.

31. When the equation is found in which the
calculated k values remain constant within the
limits of experimental variation, the reaction is
considered to be of that order

32. From the following data for the decomposition of N2O5 in CCl4 solution at
48°C, show that the reaction is of the first order

33. •
•
•
A plot of the data in the form of a graph can also be
used to ascertain the order.

If a straight line results when concentration is
plotted against t, the reaction is zero order.

The reaction is first order if log ( a - x) versus t
yields a straight line

It is second order if 1/( a - x) versus t gives a
straight line.
(2)Graphical method

34. In case of First order
By rearranging the integrated equation;
The equation becomes;

35.  A pharmacist dissolved a few milligrams of cefuroxime (an
antibiotic) into exactly 100 ml of distilled water and placed the
solution in a refrigerator (4°C). At various time intervals the
pharmacist removed a 2-mL aliquot from the solution and
measured the amount of drug contained in each aliquot. The
following data were obtained:
Time (hr) Cefuroxime (µg/mL)
0.5 84.5
1.0 81.2
2.0 74.5
4.0 61.0
6.0 48.0
8.0 35.0
12.0 8.7
Illustration

36. •
•
•
•
•
Is the decomposition of this antibiotic a first-order or
zero-order process?

Why would the stability of cefuroxime be in doubt in
this medium?

What is the rate of decomposition of this antibiotic?

How many milligrams of antibiotics were in the
original solution prepared by the pharmacist?

Give the equation for the line that best fits the
experimental data

37. Time
(hr)
Cefuroxime
(µg/mL) lnconcn log concn 1/concn
0.5 84.50.54.4367520.51.9268570.50.011834
1 81.2 14.396915 11.909556 10.012315
2 74.5 24.310799 21.872156 20.013423
4 61 44.110874 41.78533 40.016393
6 48 63.871201 61.681241 60.020833
8 35 83.555348 81.544068 80.028571
12 8.7122.163323120.939519120.114943

38. y = - 6.5898x + 87.6654
R
2
= 1.
0 2 4 6 8 10 12 14
0
10
20
30
40
50
60
70
80
90
Concn vs Time

39. 0 2 4 6 8 10 12 14
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
log concn vs Time

40. 0 2 4 6 8 10 12 14
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
ln transform

41. 0 2 4 6 8 10 12 14
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
1/A vs Time

42. (3)Using half-life period
•
•
•
•
Two separate experiments are performed by
taking different initial concentrations of a reactant.

The progress of the reaction in each case is
recorded by analysis.

When the initial concentration is reduced to one-
half, the time is noted.

Let the initial concentrations in the two
experiments be [A1] and [A2].



Expt 1

44. •A plot of logarithms of ratio of half-life periods
versus ratio of initial concentrations will be linear
passing through the origin with a slope equal to ( n –
1) and thus the order can be determined from its
slope

45. •This method is called Van’t Hoff’s differential
method
(4)Differential method
•The rate of reaction at two different
concentrations c1 and c2 can be given as;
•
•
The reaction is carried out with different initial
concns of the reactant.

The concn versus time plots for both the
experiments are obtained.

46. From either (1) or (2)

47. •
•
•
Let’s consider the stability
of the antibiotic penicillin as
a practical example.

Assume that our job is to
learn how long penicillin
remains active when it is
stored at room temperature

We want to determine its
activity versus time

48. Time (min) 255075100125150200
evolved ( 0.641.101.451.701.902.052.232.45
•An organic acid decarboxylates spontaneously at 298K
and at pH = 6. The solution was measured at various
times as follows:
Determine the order and rate constant for this
reaction.

49. Examples
•

52. Factors affecting the reaction
rate

53. Factors affecting the reaction
rate
•
•
•
•
•
•

Concentration
pH
Solvent effect
Light/Oxygen
Catalysis
Temperature

According to collision theory, a chemical
reaction takes place only by collisions between
the reacting molecules.

But not all collisions are effective. Only a small
fraction of the collisions produce a reaction

55. •
•
•
Concentration:
Collision frequency, the rate of collisions between
species A and B, is proportional to both their
concentrations:

Collision frequency ∝ [A][B]

If the concentration of B is doubled, then the rate at
which A molecules collide with B molecules is
doubled and;

If the concentration of A is doubled, then the rate at
which B molecules collide with A molecules is also
doubled.

56. •
•
•
•
For each reaction a certain energy barrier must be
surmounted that is the reactant molecules must possess
the activation energy, Ea, for the reaction to occur.

The catalyst functions by providing another pathway with
lower activation energy, Ecat.

Thus a much large number of collisions becomes
effective at a given temperature.

Since the rate of reaction is proportional to effective
collisions, the presence of a catalyst makes the reaction
go faster, other conditions remaining the same.
Catalysis

57. ACTIVATION ENERGY AND CATALYSIS

58. EFFECT OF INCREASE OF TEMPERATURE ON REACTION RATE
Generally, an increase of temperature
increases the rate of reaction

As a rule the rate of reaction doubles by
an increase of 10°C

The ratio of rate constants of a reaction
at two different temperatures differing by
10 degree is known as Temperature
Coefficient
The kinetic energy of a gas is directly proportional to its
temperature

60. •Taking natural logs of each side of the Arrhenius
equation
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�����������

61. Example
Time (hr)
Concn (mol/
dm³)
0 57.9
6 50.4
12 43.9
24 29.1
48 16.7
72 9.6
96 5.4
120 3.1

62. 0 20 40 60 80 100 120 140
0
10
20
30
40
50
60
70
Concn vs Time
y = - 0.0245x + 4.0344
R
2
= 0.9985
0 20 40 60 80 100 120 140
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
Lnconcn vs Time
Time
(minutes) Concn (mol/dm³) LnConcn
0 57.9 0 4.058717
6 50.4 6 3.919991
12 43.9 12 3.781914
24 29.1 24 3.370738
48 16.7 48 2.815409
72 9.6 72 2.261763
96 5.4 96 1.686399
120 3.1 120 1.131402

64. Application of AE in pharmaceutical sciences
•

65. Stability Studies.
•
•
The experimental protocols commonly used
for data collection that serve as the basis for
estimation of shelf life are called stability tests.

To provide reasonable assurance that;
The products will remain at an acceptable level
of fitness/quality when the medicinal products
or APIs are in circulation under different
climatic conditions or a variety of
environmental factors such as temp, light, or
Humidity .

66. (1)Analytical methods development-It provides a re-
test period for the API

(2)Formulation and packaging development- The
stability of drug products needs to be evaluated over
time in the same container-closure system in which
the drug product is marketed

(3)Appropriate storage conditions and shelf-life
determination- To recommend appropriate storage
conditions.

(4)Safety/toxicological concerns- To ensure that the
quality, safety and efficacy are maintained throughout
the shelf life.
Stability-related issues can affect many areas,
including the following

67. (5)
(6)
(7)
Salt selection/polymorph screening

Manufacturing/processing parameters -This is
considered as pre-requisite for the acceptance and
approval of any pharmaceutical product

Absorption, distribution, metabolism, and
excretion (ADME) studies

(8)Environmental assessment

68. •Stability of new formulation
•Stability of drugs after short-term
excursions
Case studies

70. Types of Stability Studies
•

71. Accelerated stability testing (ASS)
:
•A product is stored at elevated stress conditions (such
as temperature, humidity, light, agitation and pH)
which causes increase in the rate of chemical
degradation or physical change of a drug substance or
drug product
•
•
We can now predict degradation at the recommended
storage conditions using known relationships between
the acceleration factor and the degradation rate.
Temperature is the most common acceleration factor
used for chemicals, pharmaceuticals, and biological
products because its relationship with the degradation
rate is characterized by the Arrhenius equation.

72. •“The validated method or methods by which
product stability may be predicted by storage of
the product under conditions, which accelerate
change in a defined and predictable manner
Accelerated stability testing
•The ICH defined “accelerated testing” as: Studies
designed to increase the rate of chemical
degradation or physical change of an active drug
substance or drug product using exaggerated
storage conditions as part of the formal,
definitive, storage program
•Accelerated testing is the main tool that is used to
predict stability-related problems

73. 1Provides an early indication of the product shelf
life and thus shortening the development schedule

2To assess or predict longer-term chemical effect
at non-accelerated conditions.

3To evaluate the effect of short-term excursions
outside the label storage conditions

4It can help identify the likely degradation products
and degradation pathways
USES OF ASS Cont’d

74. •
•
Advantages over RTSS

Because the duration of the analysis is
short, the likelihood of instability in the
measurement system is reduced in
comparison to the real-time stability testing

Comparison of the unstressed product with
stressed material is made within the same
assay and the stressed sample recovery is
expressed as percent of unstressed sample
recovery.

75. •
•
•
•
•
Limitation of AST

It is considered when the breakdown depends on
temperature

Not useful when degradation is due to microbial
contamination, photochemical reactions, excessive
agitation etc

The Ea obtained in the stability should be between 10-30
kcal/mole

When the order of reaction changes at elevated
temperature

When the product looses its physical integrity at higher
temperature, for instance, coagulation of suspending
agent, denaturation of protein

76. Procedure for ASS
•
•
•
ASS of Pharmaceutical products are based on the principles
of chemical kinetics.

The concept of accelerated stability testing is based upon the
Arrhenius equation and modified Arrhenius equation.
These describe the relationship between storage temperatures and
degradation rate thus it is considered for stressed temperatures




•The temperatures range typically from 50°C to 80°C and
the humidity can be as low as 10% to as high as 75%. The
exposure time can range from less than 7 days to 3
months; however, most protocols last 14 to 21 days

77. •
•
•
•
Accelerated Stability protocols consist of exposing
drug substance and drug product to different
combinations of high temperatures and humidity
levels.

The samples are subjected to stress,

For statistical reasons, the treatment in accelerated
stability projections is recommended to be
conducted at four different stress temperatures

Refrigerated after stressing and then assayed
simultaneously

78. •k values for the decomposition of a drug at various
elevated temperatures are obtained by plotting some
functions of concentration (log C) vs time

Log C vs time
profile

79. •
•
•
The log of the specific rates of decomposition are
then plotted vs the reciprocals of the absolute
temperature

The resulting line is extrapolated to room
temperature.

The k25 is used to obtain a measure of the stability
of the drug under ordinary shelf conditions

80. Fig 2: Arrhenius plot for predicting drug stability at
room temperature.

81. •
•
Learning goals

Will be able to understand and describe physical
and chemical instability

will be able to predict degradative pathways and
products in general terms

Drug Degradation

82. •Pharmaceutical products in storage change as they
age, but they are considered to be stable as long as
their characteristics remain within the manufacturer's
specifications.

Degradation pattern can follow either zero-, first- or
second-order reaction mechanism.
Predicting Drug Degradation

83. DRUG SUBSTANCE
AGGREGATION
CHEMICAL
PHYSICAL
DECOMPOSITION
CHEMICAL
PHYSICAL
Protein

84. Common Degradation
Physical instability Chemical instability
Denaturation
Cold, thermal(Freeze-
thaw), pressure-induced
(agitation),chemical
Hydrolysis
Oxidation
Deamidation

Cavitation Polymerization
Organic solvents Isomerization
Surface Adsorption Photolysis
Precipitation Disulfide shuffling
Fragmentation

85. Factors affecting protein stability

88. •Esters and Lactones
Base-catalyzed hydrolysis of an ester

89. •The ring strain inherent in lactones tends to affect a larger
degree of liability resulting in more faster hydrolysis
•The smaller the lactone ring the higher the ring strain, and
therefore the more susceptible to hydrolysis (rate of
hydrolysis of (β-lactone > γ-lactone > δ-lactone)

90. Amides and Lactams

91. ASPIRI
N

94. Example
s

95. •The strained four-member ring is easily hydrolyzed to give
an inactive compound. The stoichiometric reaction is

97. •
•
•
•
Penicillin and cephalosporin antibiotics are insufficiently
stable to be supplied dissolved in aqueous solutions.
Instead, they are supplied as a dry powder, which is
reconstituted immediately prior to dispensing.
The solution dispensed must be stored in a refrigerator and
discarded after 7 days.
The ring-opened product (penicilloic acid) is inactive as an
antibiotic.

99. •Chloramphenicol possesses an amide bond that
can undergo hydrolysis to 2-amino-1-(4-
nitrophenyl)propane-1,3-diol, which is inactive as an
antibiotic

100. OXIDATION
•
•
•
Oxidation involves the removal of an
electropositive atom or electron, or the addition of
an electronegative atom

Oxidative degradation can occur by auto-oxidation,
in which reaction is uncatalyzed and proceeds
quite slowly under the influence of molecular
oxygen

Examples of drugs that are susceptible to
oxidation include steroids and sterols,
polyunsaturated fatty acids, phenothiazines, and
drugs with conjugated double bonds such as
simvastatin and polyene antibiotics

101. Examples
•All of these compounds are white crystalline solids
that darken on exposure to air. Adrenaline forms the
red colored compound adrenochrome on oxidation

103. Isomerisation
•
•
Isomerisation is the process of conversion of a drug
into its optical or geometric isomers, which are
often of lower therapeutic activity.
Examples of drugs that undergo isomerisation
include adrenaline (epinephrine: racemisation in
acidic solution), tetracyclines (epimerisation in acid
solution), cephalosporins (base-catalysed
isomerisation) and vitamin A ( cis–trans
isomerization)

104. •
•
Polymerisation
Polymerisation is the process by which two or
more identical drug molecules combine
together to form a complex molecule.

Examples of drugs that polymerise include
amino-penicillins, such as ampicillin sodium in
aqueous solution, and also formaldehyde.

105. Photolytic degradation
•
•
•
Examples of drugs that degrade when exposed to
light include phenothiazines, hydrocortisone,
prednisolone, riboflavin, ascorbic acid and folic acid.

Photodecomposition may occur not only during
storage, but also during use of the product.

For example, sunlight is able to penetrate the skin to
a depth sufficient to cause photodegradation of
drugs circulating in the surface capillaries or in the
eyes of patients receiving the drug.

106. •
•
•
•
•
Various precautions should be taken during
manufacture to prevent degradation;

Use of amber or colored glassware

The oxygen in pharmaceutical containers should
be replaced with nitrogen or carbon dioxide.

Contact of the drug with heavy-metal ions such as
iron, cobalt or nickel, which catalyse oxidation,
should be avoided or use of chelator

Storage should be at reduced temperatures.

Antioxidants should be included in the formulation.
Butylated hydroxytoluene (BHT), Ascorbic acids

107. •
•
Pharmaceutical products can be adequately
protected from photo-induced decomposition by
the use of colored glass containers (amber glass
excludes light of wavelength < 470 nm) and
storage in the dark.

Coating tablets with a polymer film containing
ultraviolet absorbers has been suggested as an
additional method for protection from light

108. MECHANISM OF ENZYME
CATALYSIS
•
•
•
•
The long chains of the enzyme (protein) molecules are
coiled on each other to make a rigid colloidal particle with
cavities on its surface. These cavities which are of
characteristic shape and abound in active groups (NH2,
COOH, SH, OH)] are termed Active centres.
The molecules of substrate which have complementary
shape, fit into these cavities just as key fits into a lock (Lock-
and-Key theory)
By virtue of the presence of active groups, the enzyme forms
an activated complex with the substrate which at once
decomposes to yield the products.
Thus the substrate molecules enters the cavities, forms
complex and reacts, and at once the products get out of the
cavities

109. ENZYME KINETICS
Dr. A.J. Adegbola
Applications of Kinetics to Biological Systems

110. Enzymes
•
•
•
•
•
•
An enzyme—a biological catalyst
Can increase the rate of a reaction by many orders of
magnitude.

However, it is left unchanged at the end of the reaction

Enzyme Kinetic: Is the field in biochemistry
concerned with;
Quantitative measurements of the rates of the enzyme
catalyzed reaction

Factors that affect these rates

111. Relevance
•
•
•
Enzyme deficiencies are the source of many
diseases.

Enzymes are also a target for medical research

Modern therapeutics
Are protein molecules
acting as biocatalysts
to speed up organic
reactions in living cells

112. Enzyme kinetics studies the reaction rates of
enzyme-catalyzed reactions and how the rates are
affected by changes in experimental
conditions

113. In vitro CL
int
CL
int
x gram of liver
CL
int
x whole
liver
LIVER
WEIGHT
AMOUNT OF ENZYME x
GRAM OF LIVER
AGE
GENETIC
S
GENDERWEIGH
TETHNICIT
Y
DISEASE
S

114. 1
2
3
4
Characteristics of Enzymes Catalysis

Enzyme catalysis is marked by absolute
specificity

Enzymes are the most efficient catalysts known-
High rate, minute amount

The rate of enzyme-catalyzed reactions is
maximum at the optimum temperature

Rate of enzyme-catalyzed reactions is maximum
at the optimum pH

115. 5Enzymes can be inhibited or poisoned

6Catalytic activity of enzymes is greatly enhanced by
the presence of Activators or Coenzymes

7Enzyme/Substrate concentrations
Characteristics of Enzymes Catalysis

116. •
•
•
•
Enzymes are the most efficient catalysts known
High rate, one molecule of an enzyme may transform one
million molecules of the substrate (reactant) per minute.
Like inorganic catalysts, enzymes function by lowering the
activation energy of a reaction.
For example, the activation energy of the decomposition of
hydrogen peroxide; without a catalyst is 18 kcal/mole
With colloidal platinum (inorganic catalyst) is lowered to
11.7 kcal/mole.

117. •The enzyme catalase lowers the activation
energy of the same reaction to less than 2 kcal/
mole

118. The rate of enzyme catalysed reactions is
maximum at the optimum temperature
•
•
•
•
•
The rate of an enzyme-catalysed reaction is increased
with the rise of temperature but up to a certain point.

Thereafter the enzyme is denatured as its protein
structure is gradually destroyed.

For example, the optimum temperatures, of enzyme
reactions occurring in human body is 37°C (98.6°F).

At much higher temperatures, all physiological reactions
will cease due to loss of enzymatic activity.

This is one reason why high body temperature (fever) is
very dangerous.

119. The rate of an enzyme reaction with raising of temperature
gives a bell-shaped curve. The temperature at which the
reaction rate is maximum is called the optimum temperature.

120. Rate of enzyme-catalysed reactions is maximum
at the optimum pH
•
•
•
The rate of an enzyme catalysed reaction varies with pH
of the system.
The rate passes through a maximum at a particular pH,
known as the optimum pH.
The enzyme activity is lower at other values of pH. Thus
many enzymes of the body function best at pH of about
7.4, the pH of the blood and body fluids

121. Enzymes can be inhibited or
poisoned
•
•
•
The catalytic activity of an enzyme is often reduced
(inhibited) or completely destroyed (poisoned) by
addition of other substances.

These inhibitors or poisons interact with the active
functional groups on the enzyme surface. For
example, heavy metal ions (Ag+, Hg2+) react with the
–SH groups of the enzyme and poison it.


Mechanisms of action of many drugs are related to
enzyme inhibitors.

123. Some Inorganic Elements That Serve as
Cofactors for Enzymes

124. Some Coenzymes That Serve as Transient
Carriers of Specific Atoms or Functional Groups

125. Enzyme/Substrate concentrations
•
•
•
•
Enzyme concentration affects the initial rate of the
reaction up to the point where all substrate is
consumed after which there is no more increase in
the velocity
Reaction Velocity: the rate or the velocity of a
reaction (V) is the number of substrate molecules
converted to product per unit time. Velocity is
usually expressed in µmol of product formed per
minute.
Substrate Concentration Affects the Rate of
Enzyme-Catalyzed Reactions
The rate of the enzyme-catalyzed reaction increases
with the increased substrate concentration until a
maximal velocity (Vmax) is reached.

126. Enzyme Kinetics as an Approach to
Understanding Mechanism
where E = Enzyme;
S = Substrate (reactant);
ES = Activated complex;
P = Products.
Illustration of the lock-and-key model of enzyme
catalysis

127. A plot of the initial velocity, v, versus the substrate
concentration, [S]
Enzymatic reaction that can be described by the
Michaelis–Menten mechanism

128. •
•
The reaction at high substrate concentrations reflects
the saturation with substrate of all available binding
sites on the enzyme molecule (Vmax).










At low [S], most of the enzyme is in the uncombined
form E.

129. •
•
•
•
•
•
Here, the rate is proportional to [S] because the
equilibrium of Equation is pushed toward
formation of more ES

As [S] increases, (Vmax) is observed;
when virtually all the enzyme is present as
the ES complex and
[E] is small.

Under these conditions, the enzyme is “saturated”
with its substrate

So that further increases in [S] have no effect on
the rate of reaction.

130. Leonor Michaelis,
1875–1949
Maud Menten,
1879–1960
The quantitative relationship between the initial velocity
V0, the maximum velocity Vmax, and the initial
substrate concentration[S], all related through the
Michaelis constant Km.
It shows the effect of [S] on reaction
velocity.

131. •
•
•
•
•
The equation describes how reaction velocity
varies with substrate concentration.

Vo = Vmax [S]
K
M
+ [S]

The Vo is the initial velocity

The V
max
is the maximum velocity

K
M
is the Michaelis constant

[S] is the substrate concentration.

133. •
Michaelis–Menten kinetics

134. The characters of the K
m
:
•
•
•
•

K
m
is characteristic of an enzyme and its
particular substrate, and reflects the
affinity of the enzyme to the substrate.

K
m
is numerically equal to the (S) at which
the reaction velocity is equal to ½ V
max
.

Small K
m
: reflects high affinity of the enzyme
for substrate, because a low concentration of the substrate is needed
to half saturate the enzyme, that is to reach the ½ V
max
.

Large Km: reflects a low affinity of enzyme for substrate, because
high
concentration of the substrate is needed to ½ saturate the enzyme.

135. •
•
•
•
The maximal rate, Vmax, reveals the turnover
number of an enzyme.

TON is the number of substrate molecules
converted into product by an enzyme molecule in
a unit time when the enzyme is fully saturated
with substrate.

It is equal to the rate constant k2, which is also
called kcat.

The maximal rate, Vmax, reveals the turnover
number of an enzyme if the concentration of
active sites [E]T is known
Vmax

136. •
•
An estimate of "how perfect" the enzyme is.
It measures how the enzyme performs when S is
low.
A measure of catalytic activity

138. •The most common kind of enzyme kinetics
experiment is to vary the concentration of substrate
and measure enzyme velocity
Kinetic Data Analysis
Vo = Vmax [S]
K
M
+ [S]

139. •For quantitative purposes it is useful to rewrite the
saturable equation in a form that suggests a
straight-line plot of the data or linearization
methods
•
•
•
Lineweaver-Burk plot

Dixon plot

Eadie–Hofstee plot
•When the Vo is plotted against the (S), it is not
always possible to determine when the V
max
is
reached
•The goal is to determine the enzyme's Km (substrate
concentration that yield a half-maximal velocity) and
Vmax (maximum velocity)

140. •
•
•
•
•
•
Hans Lineweaver and Dean Burk (1934)

If the 1/Vo is plotted verses 1/(S), a straight line (a
linear form) is obtained.

This plot is also called double reciprocal plot and
can be used to calculate
K
m
V
max
and the mechanism of action of enzyme inhibitors.


Lineweaver-Burk plot

141. In the equation for a straight line, y = 1/vi and x =
1/[S].

A plot of 1/vi as y as a function of 1/[S] as x,
therefore gives a straight line whose y intercept is
1/V
max
and whose slope is K
m
/ V
max

143. Eadie-Hofstee
•

146. The Hanes-Woolf Plot or Dixon Plot
•

149. 0 2 4 6 8 10 12 14 16 18
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
V µmol/sec
1 0.667 1.001.49925 0.667 0.667 11.49925
2 0.8 0.50 1.25 0.4 0.8 2 2.5
4 0.889 0.25
1.12485
90.22225 0.889 4
4.49943
8
8 0.937 0.13
1.06723
6
0.11712
5 0.937 8
8.53788
7
16 0.958 0.06
1.04384
1
0.05987
5 0.958 16
16.7014
6

150. y = 0.4901x + 1.0071
R
2
= 0.9995
-1.00 -0.50 0.00 0.50 1.00 1.50
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
Axis Title
Axis Title
1/v vs 1/[s]
Series1
Linear(Series1)
0.990099, 0.485248

151. y = - 0.4844x + 0.9922
R
2
= 0.999
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
v/[s]
v vs v/[s]
Series1
Linear(Series1)

152. y = 1.0138x + 0.4623
R
2
= 1.
0 2 4 6 8 10 12 14 16 18
0
2
4
6
8
10
12
14
16
18
Axis Title
Series1
Linear(Series1)

153. •
•
Irreversible Inhibition
The irreversible inhibitors are those that bind covalently with or
destroy a functional group on an enzyme that is essential for the
enzyme’s activity, or those that form a particularly stable
noncovalent association.

Examples;
Suicide inactivators also called mechanism-based inactivators,
b’cos they hijack the normal enzyme reaction mechanism to
inactivate the enzyme


ENZYME INHIBITION:

There are broadly two types of inhibitors namely

(1) Reversible inhibitor (2) Irreversible inhibitor

154. Reversible Inhibition
•
•
•
•
Reversible inhibitors tend to bind to E by;
H-bonding,
Electrostatic bond
van der Waal forces.



site of action on the enzyme,
on whether they chemically modify the enzyme
on the kinetic parameters they influence

•Reversible inhibitors are of three types and can be
classified on the basis of their;

155. •
•
•
Competitive Inhibition

Inhibitor binds to the same site on the enzyme as
the substrate.
Inhibitor binds ONLY the free enzyme.
Inhibitor is usually structurally very similar to the
substrate or resemble the substrate.

156. •

157. •Methanol and ethanol compete for the same binding site in
alcohol dehydrogenase

158. •Succinate is the normal substrate for the enzyme succinate
dehydrogenase. Malonate is an effective competitive
inhibitor of this enzyme.
•p-aminobenzoate (PABA) is the normal substrate for the
bacterial enzyme dihydrofolate synthetase. The sulfa drug
sulfanilamide is an effective competitive inhibitor of this
enzyme.

159. Methotrexate and Trimethoprim.

Are potent competitive inhibitors of the enzyme dihydrofolate
reductase. Both are structural analogs of dihydrofolate, a substrate
for dihydrofolate reductase.
•
•
Ibuprofen (NSAIDs)

Statin- Inhibits 3-hydroxyl-3-methylglutaryl coenzyme A
(HMG-CoA) reductase

160. •
•
•
A competitive inhibitor reduces the amount of [E] by the
formation of an [EI] complex.

The inhibitor cannot affect the [ES] complex after it has
formed since the inhibitor can no longer bind.

There are two anticipated consequences of this binding
mode on the steady-state kinetics.
•Vmax is unchanged: At high levels of substrate all of the
inhibitor can be displaced by substrate.
•The apparent Km is increased: It requires more substrate to
reach ½ maximal velocity because some of the enzyme is
complexed with inhibitor.

162. Uncompetitive Inhibition
•
•
•
In an uncompetitive inhibition, the inhibitor is not in
competition with the substrate for the active site of the
enzyme.

It binds only the substrate-enzyme complex and ESI does not
go on to form any product.

The substrate facilitates the binding of the inhibitor to the
enzyme.

163. •

164. Consequently, the lines in double reciprocal plots will
be parallel.

165. Non-Competitive Inhibition
•
•
•
In a non-competitive inhibition both types of
inhibition are present: the inhibitor can bind either
the free enzyme or the enzyme-substrate complex.

In essence, the inhibitor simply lowers the
concentration of functional enzyme. The resulting
solution behaves as a more dilute solution of
enzyme does.

Noncompetitive inhibition cannot be overcome by
increasing the substrate concentration.

167. •

168. •
•
Deoxycycline, an antibiotic, functions at low concentrations
as a noncompetitive inhibitor of a proteolytic enzyme
(collagenase). It is used to treat periodontal disease.

Some of the toxic effects of lead poisoning may be due to
lead’s ability to act as a noncompetitive inhibitor of a host of
enzymes. Lead reacts with crucial sulfhydryl groups in these
enzymes

169. The fact that in non-competitive inhibition the inhibitor does
not bind to the active site of the enzyme means that the
structure of the substrate cannot be used as the basis for
designing new drugs that act in this manner to inhibit enzyme
action.

Non-competitive inhibitors have been used Antiretroviral drugs

170. LIVER
WEIGHT
MINCED
Teflon pestle/glass
homogenizer
•
•
•
•
Homogenisation buffer: sucrose 250 mM, HEPES 50 mM, KCl 25
mM, MgCl2 5 mM, EDTA 0.1 mM, adjust pH to 7.4
4-(2-hydroxyethyl)-1-piperazineethanesulfonic acid 
phosphate solutions buffered at a pH of 7.4.
Solutions of magnesium chloride
NADH.

171. 10,000 g
for 10 min
15,000 g for
20 minutes
105,000 g for
60 minutes

172. In vitro CL
int
CL
int
x gram of liver
CL
int
x whole
liver
LIVER
WEIGHT
AMOUNT OF ENZYME x
GRAM OF LIVER
AGE
GENETIC
S
GENDERWEIGH
TETHNICIT
Y
DISEASE
S

173. Microsome Incubation
Microsome incubations were performed using 50 µL
microsome extract,
50 µL cofactor solution, the analyte,
phosphate buffer added to bring volume to 500 µL.

174. Exercise 1

The following experimental data were collected during a
study of the catalytic activity of an intestinal peptidase with
the substrate glycylglycine:
[S] (mM) (µmol/min)
1.5 0.21
2 0.24
3 0.28
4 0.33
8 0.4
16 0.45

175. y = 4.2663x + 1.9978
R
2
= 0.9928
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
1/[S]
1/V
1/V vs 1/[S]
Series1
Linear(Series1)
0.666667 4.761905
0.5 4.166667
0.333333 3.571429
0.25 3.030303
0.125 2.5
0.0625 2.222222

176. 1 3.8 2.2 1 0.26315
8
0.454545
2 7.3 4.3 0.5 0.13698
6
0.232558
1.5 4 13.3 8.2 0.25 0.07518
8
0.121951
8 22.9 14.9 0.125 0.04366
8
0.067114
12 30 20.4 0.083333 0.03333
3
0.04902