Enzyme kinetics is the study of enzyme-catalyzed reaction rates. The Michaelis-Menten equation relates reaction velocity to substrate concentration and kinetic parameters. It describes the hyperbolic relationship between velocity and substrate concentration. The equation can be linearized into the Lineweaver-Burk plot for easier analysis. Enzyme inhibition studies help understand reaction mechanisms and are important for drug development, as most drugs function by inhibiting specific enzymes.

1. Enzyme Kinetics
by Mahwish Kazmi

2. • Enzyme kinetics is the study of the mechanism of an
enzyme catalysed reation to determine the rate of the
reaction.
Study of enzyme kinetics is useful for measuring
• concentration of an enzyme in a mixture (by its catalytic
activity),
• its purity (specific activity),
• its catalytic efficiency and/or specificity for different
substrates
• comparison of different forms of the same enzyme in
different tissues or organisms,
• effects of inhibitors (which can give information about
catalytic mechanism, structure of active site, potential
therapeutic agents...)

3. Michaelis and Menton Equation
• A model for enzyme kinetics was propsed by Michaelis
and Menton in 1913.
• MM equation relates the initial rate of an enzyme
catalysed reaction to the substrate concentration and a
ratio of rate constants.
• It co-relates velocity with enzyme and substrate
concentration.
• It has been derived for a single substrate-enzyme-
catalysed reaction.

4. Michaelis and Menton Equation
• In MM expression
Total enzyme concentration= [ET] = [E] + [ES]
Free enzyme conc [E] = [ET] - [ES]
Substrate concentration = [S]
Initial velocity = Vo, Velocity measured immediately after
mixing E + S, at beginning of reaction (initial velocity), is
called Vo.
Maximum velocity = Vmax
Half Vmax = Km (substrate concentration)
Km = substrate concentration that gives Vo = 1/2 Vmax.

5. At very low [S]:
• Vo is proportional to [S];
doubling [S] → double Vo.
2. In mid-range of [S], Vo is
increasing less as [S]
increases (where Vo is
around 1/2 Vmax).
Km = [S] that gives Vo = 1/2
Vmax.
3. At very high [S], Vo is
independent of [S]:
Vo = Vmax.
Enzyme-catalyzed reactions show a hyperbolic
dependence of Vo on [S]

6. Derivation
• Initial velocity Vo= k2[ES]
• Rate of formation of [ES] = k1 [E][S]
= k1([ET]-[ES]).[S]
= k1[ET][S] - [ES][S]
• Rate of breakdown of [ES] =k-1[ES] + k2[ES]
= (k-1+k2)[ES]
• Steady state:
Rate of formation = Rate of breakdown
k1[ET][S] - [ES][S] = (k-1+k2)[ES]

7. • separation of rate constants
k1[ET][S] - [ES][S] = (k-1+k2)[ES]
k1[ET][S] = [ES][S] + (k-1+k2)[ES]
k1[ET][S] = {[S] + (k-1+k2)} [ES]
[ES] = k1[ET][S]
[S] + (k-1+k2)
[ES] = [ET][S]
[S] + k-1+k2
k1
k-1+k2 = Km [ES] = [ET][S] ......... (i)
k1 [S] + Km

8. • Expressing Vo in term of [ES]:
multiply k2 on both side of eq (i)
k2. [ES] = k2 [ET][S] ...... (ii)
[S] + Km
As we know Vo= k2[ES]
So, eq (ii) becomes
Vo = k2 [ET][S] .....(iii)
[S] + Km
When [S] is greater, then Vo becomes Vmax and
Vmax= k2 [ET]
So, eq (iii) becomes
Vo = Vmax [S]
[S] + Km

9. Michaelis-Menten equation
explains hyperbolic Vo vs. [S]
curve:
1. At very low [S] ([S] << Km), Vo
approaches (Vmax/Km)[S]. Vmax and
Km are constants, so linear
relationship between Vo and [S]
at low [S].
2. When [S] = Km, Vo = 1/2 Vmax
3. At very high [S], ([S] >> Km), Vo
approaches Vmax (velocity
independent of [S])
Explaination of hyperbolic curve

10. Significance of MM equation
It describes
• kinetic behaviour of enzymes
• hyperbolic dependence of Vo on [S]
• independance of number of steps involved
• different enzymes have different Km and Vmax.
• Km and Vmaxmay be influenced by pH, temperature.
• Km can be used as a relative measure of the affinity of the
enzyme for each substrate (smaller Km means higher
affinity)
• in a metabolic pathways, Km values may indicate the rate-
limiting step (highest Km means slowest step).
• Vmax is independent of [S] at saturation.

11. • Turnover number (kcat)
Number of substrate molecules converted into product
by one molecule of enzyme active site per unit time,
when enzyme is fully saturated with substrate.
• units of kcat is s–1
Lysozyme: kcat = 0.5 s–1
Catalase: kcat = 4 x 107
s–1
• kcat/Km is the criterion of substrate specificity, catalytic
efficiency and "kinetic perfection”.
• units of kcat/Km = conc–1
time–1
.
• max. possible kcat/Km for an enzyme = ~ 108
–109
M–1
sec–1
.

12. Lineweaver-Burk plot
• A more convenient graphical representation of MM
equation
• It is a straight line plot, easier to evaluate than curves.
• Lineweaver-Burk plot is a double reciprocal plot obtained
by taking reciprocal of both sides of MM equation and
rearranging
1 = Km + [S]
V [S] Vmax
1 = Km 1 + 1
V Vmax [S] Vmax

13. • A plot of 1/V versus 1/[S] is a straight line having a slope
of Kmax/Vmaxand an intercept of 1/Vmax on the y-axis

14. Inhibition
• Enzyme inhibition is one of the ways in which enzyme
activity is regulated experimentally and naturally.
• Most therapeutic drugs function by inhibition of a specific
enzyme.
• In body, some of the processes controlled by enzyme
inhibition are blood coagulation, blood clot dissolution,
complement activation, conective tissue turnover and
inflammatory reactions.
• It may be reversible or irreversible.

15. Reversible Inhibition
• It is further subdivided into competitive, noncompetitive
and uncompetitive types.
• In reversible inhibition, equilibrium exists between
inhibitor I and enzyme E as
E+I EI
• The eq. constant for the dissociation of EI complex,
called Ki is given by equation
Ki = [E][I]
[EI]
• Ki is the measure of affinity of the inhibitor for enzyme
simliar to Km.

16. Competitive inhibition
• The inhibitor is a structural analogue that competes with
the substrate for binding at active site.
• Because the inhibitor binds reversibly to the enzyme,so
when [S] far exceeds [I], the probability that an inhibitor
molecule will bind to the enzyme is minimized and the
reaction exhibits a normal Vmax.

17. Noncompetitive inhibition
• Inhibitor does not usually bear any structural
resemblance to the subatrate and it binds to the enzyme
at a site distinct from the substrate binding site.
• No competition exists between inhibitor and substrate,
so inhibition cannot be overcome by increase of [S].
• Vmax is reduced by inhibitor but Km is unaffected
because the affinity of S for E is unchanged.

18. Uncompetitive Inhibition
• Inhibitor I combines with ES to form ESI complex
• It yields parallel line on double reciprocal plot and
intercepts on both x and y axes are altered by presence
of inhibitor.