1. بسم الله الرحمن الرحيم

2. Enzyme Kinetics S.M.K 10/2010

3. Content Enzymes background Definition Important prosperities
Enzyme Kinetics
Michaelis-Menten equation
Line weaver-Burk plot
Practical exercise

4. Enzymes background Enzyme definition
Enzymes are the catalysts of biological systems and are extremely efficient and specific as catalysts.
Prosperities of Enzymes
Accelerates the rate of the reaction
Lower the activation energy of the reaction
Highly specific

5. Enzyme accelerates the of a reaction
Enzyme accelerates the rate of a reaction by factors of at least a million compared to the rate of the same reaction in the absence of the enzyme without affecting the equilibrium.
Enzymes do not alter the equilibrium point of the reaction. This means that the enzyme accelerates the forward and reverse reaction by precisely the same factor.
For example, consider the interconversion of A and B.
A↔B
Suppose that in the absence of the enzyme the forward rate constant (kf) is s-1 and the reverse rate constant (kr) is 10-6 s-1. The equilibrium constant (Keq) is given by the ratio of the two rate constants.
The equilibrium concentration of B is 100 times that of A whether or not an enzyme is present. However, in the absence of an enzyme the reaction could take more than an hour to approach this equilibrium, whereas in the presence of an enzyme, equilibrium could be attained within a 2 second.

6. Enzyme lowers the activation energy of reaction
The enzyme lowers the height of the energy barrier to the reaction thereby increasing the rate of the reaction, but since the rate of both the forward and reverse reaction are affected by the same amount, the equilibrium constant is not affected by the presence of the enzyme.
EAf is the activation energy for the forward reaction in the absence of a catalyst and E’Af is the activation
energy forthe forward reaction
in the presence of a catalyst,
ΔGo is the change in free
energy for the reaction.Since
ΔGo is the same for the catalyzed
and uncatalyzed reaction, Keq is the same for both reactions.

7. Enzymes are highly specific
Enzymes are highly specific. Typically a particular enzyme catalyzes only a single chemical reaction or a set of closely related chemical reactions.
There are two proposed models to explain the specificity of the interaction between the substrate molecule and the active site of an enzyme.
(a) The “lock and key” model – in this model the substrate has a shape matching the enzyme’s active site

8. (b) The “induced fit model” – the active site has a shape complementary to that of the substrate after the substrate is bound

9. Enzyme kinetics Definition
It is the branch of enzymology that deals with the factors affecting the rates of enzyme-catalyzed reactions.
Factors affecting enzyme reaction
Enzyme concentration
Ligand concentration (substrate, products, inhibitors and activators)
Temperature pH
Ionic strength

10. Effect of enzyme concentration
Rate of the enzyme catalyzed reaction depends directly on the concentration of the enzyme [E]
in the presence of an excess of the compound which is being transformed (substrate)
Velocity (V)= d[p]/d[t]

11. Effect of substrate concentration
At fixed concentration of enzyme
an increase of substrate will result in
At first : a very rapid rise of velocity or reaction rate
Then the increase in the rate of the reaction begins to slow down until at a large substrate concentration no further increase in the velocity
By plotting the velocity (rate of reaction ) against substrate concentration a section of rectangular hyperbola is obtained
Vedio (1) (2)

12. This curve is biphasic
Phase 1: (1st order kinetics)
Phase 2: (zero order kinetics)
Phase 1: there is low substrate concentrations  the active site on the enzyme molecules are not saturated by the substrate = Reaction rate is depending on substrate concentration
( 1st order kinetics)

13. Phase 2 : the number of substrate molecules increases,  the sites are covered to a greater extended until reach saturation no more sites are available  The Enzyme is working at full capacity
=Reaction rate is independent of substrate concentration
( zero order kinetics)

14. Michaelis-menten equation
The mathematical equation the define the quantitative relationship between the rate of the reaction and substrate concentration
V is the observed velocity at given substrate concentration [s]; Km represent the amount of substrate required to bind with half of the available enzyme and produce half of maximal velocity V max video

15. Notes
if [s] is very large ([s]>100 km) , Km become insignificant and V= V max
If V=1/2 Vmax , Km=[s]
If [s] is very small ([s]<0.01 Km) , equation will be
V =( Vmax [s])/Km

16. Graphical determination of Vmax and Km
Because the graphical drawing of V versus [s] is hyperbola it is difficult to determine Km and Vmax
So we use line weaver-burk plot, where 1/[v] versus 1/[s] derived from michaelis- menten equation

17. Notes
The substrate concentration chosen to generate the plot should be in the neighborhood of Km ([s] in the range from 0.33 to 2 Km)
If [s]=3.3 to 20Km the obtained curve will be horizontal
Also if [s] is very small ([s]= Km)
curve will intercept both axis too close to the origin Km or Vmax cannot be determine accurately