Enzyme kinetics

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.