enzyme kinetics and michael menten’s constant

this will give you a brief idea of how the enzyme works, how enzyme kinetics work, Michaelis constant (Km)
, Michaelis-Menten’s equation derivation, rate of reaction, Significance of Michaelis-Menten, Constant Km,
enzyme efficiently etc

1. enzyme kinetics and michael menten’s constant Manisha Roll no. 201636 Msc biotechnology 2 nd year Department of biotechnology Central university of Haryana 2021

2. ENZYME Enzymes   are   proteins or rna that act as  biological catalysts. Catalysts are substances that increases the rate of a reaction without itself being consumed . ENZYME substrates ENZYME substrate complex Free ENZYME product increases the rate of formation of product

3. A + B = P Rate of reaction Rate of reaction = rate of disappearance of reactant or rate of formation of products \ velocity \V Rate = - Δ A\ dt or - Δ B\ dt or Δ P\ dt Rate of a reaction ∝ concentration of substrate \ reactant Rate of rxn ∝ [A] [B] Rate of rxn or V = K [A] [B ] K rate constant , can be calculated expermantly for specific reactions. T=0 T=t A large value of the rate constant means  that the reaction is relatively fast , while a small value of the rate constant means that the reaction is relatively slow.

4. Vmax When Enzyme concentration is taken constant. At low concentrations of substrate , V0 increases with an increase in [S]. Linear curve After a certain concentration of substrate, Vo stop increasing with substrate concentration . When all enzymes are occupies . Vo = v max . All enzymes are occupied by substrate . Under these conditions, the enzyme is “saturated” with its substrate, so that further increases in [S] have no effect on rate. S + E = ES = E +P Source - Lehninger principal of biochemistry.pdf

5. relatively fast reversible step. The ES complex then breaks down in a slower second step to yield the free enzyme and the reaction product P Early in the reaction, the concentration of the product, [P], is negligible, that the reverse reaction, can be ignored. Assumptions in Michaelis-Menten’s equation derivation 1 st Assumption

6. Rate of ES formation = k1 [E] [S ] Rate of ES breakdown = k2 [ES ] + k-1 [ES ] [ES] remain constant over time i.e d[ES] = 0 steady-state assumption. Rate of ES formation = Rate of ES breakdown k1 [E] [S] = k2 [ES] + k-1 [ES] k1 [E] [S] = [ES] ( k2 + k-1 ) [E] [S] [ES] k2 + k-1 k1 = dt = km Michaelis constant 1 2 nd assumption

7. 3rd assumption   Total enzyme concentration does not change over time. [Et] = [E] + [ ES]. total enzyme concentration = [E] = [ Et] - [ES]. Source - Lehninger principal of biochemistry.pdf free enzyme +substrate bound enzyme [Et] [Et] = [E] + [ ES]. [Et] = [ ES]. 2

8. Because the slower second reaction limit the rate of the overall reaction, the overall rate must be proportional to the concentration of the species that reacts in the second step, that is, ES. The ES complex breaks down in a slower second step to yield the free enzyme and the reaction product P V0 ∝ [ES] V0 = K [ES] At saturation [Et] = [ES] vo = vmax Vmax = k2 [Et] Vmax k2 = [Et] 4 3

9. Michaelis-Menten equation derivation [E] [S] [ES] = km from eq. 1 Substitute value of E from eq. 2 ([Et ] - [ES ]) [S] [ES] = km [E] = [Et] - [ES ] ………2 [Et ] [S] - [ES ] [S] [ES] = km [Et ] [S] - [ES ] [S] [ES] = km [ES] [Et ] [S] - [ S] [ES] = km Rearrangment

10. Michaelis-Menten equation derivation [Et ] [S] - [ S] [ES] = km Substitute value of Et from eq 4 Vmax [S ] - [ S] [ES] = km k2 Vmax k2 = [Et ] ….4 Substitute value of K2[ES] from eq 3 V0 = K [ES ] …..3 Vmax [S ] - [ S] = km V0 Rearrangment Vmax [S ] = V0 km + [S] Lehninger principal of biochemistry.pdf

11. Vmax [S ] = V0 km + [S] Michaelis-Menten equation , the rate equation for a one-substrate enzyme-catalyzed reaction. The initial reaction velocity Vo of an enzyme catalyzed reaction is determined by km , vmax and initial concentration of substrate S . V  is the initial velocity of the reaction. V max  is the maximal rate of the reaction or rate of rxn when all enzymes are saturated with substrate . [ S]  is the concentration of the substrate . Km Michaelis constant Michaelis-Menten equation

12. That concentration of the substrate when the reaction velocity is equal to one half of the maximal velocity for the reaction. Units - M or mM Michaelis constant (Km) k2 + k-1 k1 = km https:// en.wikibooks.org/wiki/Structural_Biochemistry/Enzyme/Michaelis_and_Menten_Equation

13. Significance of Michaelis-Menten Constant Km k2 + k-1 k1 = km Rate constant for breakdown of ES Rate constant for formation of ES Km = Low value of Km High affinity of enzyme with substrate High value of Km Low affinity of enzyme with substrate Lehninger principal of biochemistry.pdf Tells affinity of an enzyme for a substrate

14. Significance of Michaelis-Menten Constant Tells affinity of an enzyme for a substrate  An equation with a low K m  value indicates a large binding affinity, as the reaction will approach V max  more rapidly . V max  will reached at lower substrate concentration .   An equation with a high K m  indicates that the enzyme have low binding efficiently with the substrate , V max  will only be reached at higher substrate concentration. Significance of Michaelis-Menten Constant Km HOW?

15. Lehninger principal of biochemistry.pdf https :// en.wikibooks.org/wiki/Structural_Biochemistry/Enzyme/Michaelis_and_Menten_Equation https:// www.researchgate.net/figure/Rectangular-hyperbola-plot-of-the-Michaelis-Menten-equation-relating-catalytic-rate-and_fig1_225038972 Refrences