1) Chemical kinetics describes relationships between reaction rates and concentrations of reactants and products. Enzyme kinetics follows Michaelis-Menten kinetics which describes reaction rates at varying substrate concentrations. 2) The Michaelis-Menten equation models reaction rates as substrate concentration increases, with an initial linear increase until reaching the maximum reaction rate (Vmax) at substrate saturation. 3) The Michaelis constant KM represents the substrate concentration at half Vmax and indicates an enzyme's affinity for its substrate. Lower KM means higher affinity.

1. Chemical kinetics
 Relationships between product (P) formed in a unit of time (ΔP/ Δt)
 Velocity (v) of the reaction
 Rate of equation
ΔP
Δt
= V = k[S]
S P
k1
k-1

2. Single-substrate mechanism for an enzyme reaction.
k1, k-1 and k2 are the rate constants for the individual steps.
Enzyme kinetics
Enzyme binds supstrate in enzyme-substrate form.

3. Progress curve for an enzyme-catalyzed reaction
Initial slope = v0 =
Δt
Δ[P]
Δ[P]
Δ[P]
Δt ΔtProgress curve at two different
enzyme concentration in the
presence of the high initial
concentrations of substrate:
[S] >> [E]
In this case = the rate product
formation depends on enzyme
concentration and not on the
substrate concentration.

4. The Michaelis –Menten Equation
 Michaelis-Menten kinetics describes the kinetics of many enzymes.
It is named after Leonor Michaelis and Maud Menten.
 This kinetic model is relevant to situations where the concentration of
enzyme is much lower than the concentration of substrate (i.e. where
enzyme concentration is the limiting factor), and when the enzyme is
not allosteric.

5. Determination of constants
Saturation curve for an enzyme showing
the relation between the concentration
of substrate and rate.

6.  To determine the maximum rate of an enzyme mediated
reaction, the substrate concentration ([S]) is increased until
a constant rate of product formation is achieved.
 This is the maximum velocity (Vmax) of the enzyme.
 In this state enzyme active sites are saturated with
substrate.
 Note that at the maximum velocity, the other factors that
affect the rate of reaction (ie. pH, temperature, etc) are at
optimal values.

7. Reaction rate/velocity V
 The speed V means the number of
reactions per second that are catalyzed by
an enzyme.
 With increasing substrate concentration
[S], the enzyme is asymptotically
approaching its maximum speed Vmax,
but never actually reaching it.
 Because of that, no [S] for Vmax can be
given.
 Instead, the characteristic value for the
enzyme is defined by the substrate
concentration at its half-maximum speed
(Vmax/2).
This KM value is also called
the
Michaelis-Menten constant.

8. Rate (or kinetic assay):
 Measure concentration of analyte or product in initial stages only
of the reaction (usually < 5 mins.)
 Determine INITIAL RATE (= SLOPE of the line as close as
possible to start of reaction).
 Measurement and Interpretation of Rate
 Automated instrument may make readings at two set times, say 1
min and 5 mins after initiating reaction.
 Computes the rate between these two times
C5 - C1
5 - 1
(but must be sure the concentration - time
graph is close to linear over this time)i e

9. Michaelis-Menten constant 'KM'
 Since Vmax cannot be reached at any substrate concentration
(because of its asymptotic behaviour, V keeps growing at any [S],
albeit ever more slowly), enzymes are usually characterized by the
substrate concentration at which the rate of reaction is half its
maximum.
 This substrate concentration is called the Michaelis-Menten constant
(KM).
 This represents (for enzyme reactions exhibiting simple Michaelis-
Menten kinetics) the dissociation constant (affinity for substrate) of
the enzyme-substrate (ES) complex.

10.  Low values indicate that the ES complex is held together very tightly
and rarely dissociates without the substrate first reacting to form
product.
 KM can only be used to describe an enzyme's affinity for substrate when
product formation is rate-limiting, i.e., when k2 << k-1 and KM becomes
k-1/k1.
 Often, k2 >> k-1, or k2 and k-1 are comparable.

11. Derivation of the Michaelis-Menten Equation
This derivation of "Michaelis-Menten" was actually described by Briggs
and Haldane.
It is obtained as follows:
The enzymatic reaction is supposed to be irreversible, and the product
does not rebind the enzyme.

12. Because we follow the steady state approximation,
The concentrations of the intermediates are assumed to equillibrate much
faster than those of the product and substrate, i.e. their time derivatives are
zero:
Let's define the Michaelis constant:

13. This simplifies the form of the equation:
The total (added) concentration of enzyme is a sum of that which is free in
the solution and that which is bound to the substrate, and the free enzyme
concentration is derived from this:
[E0] = [E] + [ES]
[E] = [E0] − [ES] (2)
Using this concentration (2), the bound enzyme concentration (1) can now
be written:
(1)

14. (3)
(4)
The rate (or velocity) of the reaction is:
Rearranging gives:

15. Substituting (3) in (4) and multiplying numerator and denominator by [S]:
This equation may be analyzed experimentally with a Lineweaver-Burk
diagram or a Hanes-Woolf Plot.

16. This equation may be analyzed experimentally with a Lineweaver-Burk
diagram or a Hanes-Woolf Plot.
The plot provides a useful graphical
method for analysis of the Michaelis-
Menten equation:
Taking the reciprocal gives:
V = reaction velocity (the reaction rate),
Km = Michaelis-Menten constant,
Vmax = maximum reaction velocity
[S] is the substrate concentration.

17. Effect of enzyme concentration on reaction rate

18. Effect of substrate concentration on reaction rate (hyperbolic)

19.  An increase substrate concentration initially leads to a linear
increase in reaction rate
 This trend continues as long as the initial substrate
concentration does not saturate or occupy all available active
sites.
 As the concentration of substrate reaches levels where the active
sites are saturated, the initial reaction rate starts to decrease
 Eventually the substrate concentration is so high that it
continuously keeps the active sites occupied and saturated,
reaching a maximum initial velocity
 Km on the graph indicates where half Vmax is reached.
 This type of kinetics is termed hyperbolic and is usually shown
by simple, monomeric enzymes.

20. Units for expressing enzyme activity
 Reaction rate implies substrate utilised per unit time or product
formed per unit time.
 The katal is the SI unit but is not often used in ordinary
conversation. It is defined as the transformation of mole of substrate
per second.
 Enzyme activity is defined as the amount of enzyme converting 1 μm
of substrate per second.
 Turnover number is another common term i.e. the number of
substrate molecules converted by one enzyme molecule under
specified conditions.
 Specific activity refers to enzyme activity per mass of protein i.e. all
the protein in a sample may not be enzyme.
This unit also gives an indication of enzyme purity i.e. an impure
enzyme will give low activity per unit mass.

21. Meaninig of Km
 Michaelis constants have been determined for many of the
commonly used enzymes. The size of Km tells us several things
about a particular enzyme:
1. A small Km indicates that the enzyme requires only a small
amount of substrate to become saturated. Hence, the maximum
velocity is reached at relatively low substrate concentrations.
2. A large Km indicates the need for high substrate concentrations to
achieve maximum reaction velocity.
 The substrate with the lowest Km upon which the enzyme acts as a
catalyst is frequently assumed to be enzyme's natural substrate,
though this is not true for all enzymes.
 A Km of 10-7 M indicates that the substrate has a greater affinity
for the enzyme than if the Km is 10-5 M.

22. The Catalytic Constant kcat
 At high substrate concentration the overall velocity of the reaction is
Vmax and the rate is determined by the enzyme concentration.
 The rate constant observed under these conditions is called the
catalytic constant, kcat, defined as:
 kcat indicates the maximum number of substrate molecules
converted to product each second by each active site. This is called
turnover number.
 The catalytic constant measures how fast a given enzyme can
catalyze a specific reaction (describing the effectiveness of an
enzyme)
 The unit for kcat is s-1 (for the most enzymes, kcat is 102 to 103 s-1)