1. Lecture 8 Enzyme Kinetics
Biochemistry
Lecture 8
Enzyme Kinetics

2. Why Enzymes? Higher reaction rates Greater reaction specificity
Milder reaction conditions
Capacity for regulation
Metabolites have many potential pathways of decomposition
Enzymes make the desired one most favorable

3. Enzymatic Substrate Selectivity
No binding
Binding but no reaction
Example: Phenylalanine hydroxylase

4. Enzymes Affect Reaction Rates
Catalyst
Protein (globular) or RNA
Classified based on the reaction catalyzed
Catalyst – accelerates a reaction without being used up in the reaction

5. Chapter 8, Figure 8.4, Enzymatic rate enhancements

6. Chapter 8, Figure 8.2, Free energy diagrams for the simple reaction AB

7. H2O CO HOCO2– H+ Ea Ea '
Potential Energy
Reaction

8. Enzymes bind transition states best
How to Lower G?
Enzymes bind transition states best

9. How Do Enzymes Stabilize the Transition State and Increase Reaction Rate?
Conserved active site amino acid residues in the enzyme can help with orientation of the substrate and stabilizing transition state

10. Serine Protease Mechanism
Ser 195 nucleophilic attack on peptide carbonyl group to form tetrahedral intermediate (aided by oxyanion sink TS binding pocket in the enzyme). Proton from Serine is absorbed by neighboring His 57 (general base catalysis, aided by Asp 102)
Decomposition of tetrahedral intermediate: Donation of a proton from N3 of His 57 (general acid catalysis). Helped by polarizing effect of Asp 102 on His 57 (electrostatic catalysis).
Amine leaving group (new N-termius of cleaved peptide) is release from the enzyme and replaced by water from the solvent.
Hydrolysis of the acyl-intermediate by water to form a second tetrahedral intermediate.
Reversal of step 1: release of carboxylate product that is the new C-terminus of cleaved peptide and regenerates the active enzyme.

11. How Do Enzymes Stabilize the Transition State and Increase Reaction Rate?
Conserved active site amino acid residues, metal ions and organic molecules in the enzyme can help with orientation of the substrate and stabilizing transition state

12. How is TS Stabilization Achieved?
acid-base catalysis: give and take protons
covalent catalysis: change reaction paths
metal ion catalysis: use redox cofactors, pKa shifters
electrostatic catalysis: preferential interactions with TS
End result? Rate enhancements of 105 to 1017!

13. How is TS Stabilization Achieved?
covalent catalysis: change reaction paths

14. Enzymes organizes reactive groups into proximity
How to Lower G?
Enzymes organizes reactive groups into proximity

40. Enzyme Kinetics
Kinetics is the study of the rate at which compounds react
Rate of enzymatic reaction is affected by
Enzyme
Substrate
Effectors
Temperature

41. How to Do Kinetic Measurements

42. Steady-State Assumption

43. FIGURE 6-10 Initial velocities of enzyme-catalyzed reactions
FIGURE 6-10 Initial velocities of enzyme-catalyzed reactions. A theoretical enzyme catalyzes the reaction S ↔ P, and is present at a concentration sufficient to catalyze the reaction at a maximum velocity, Vmax, of 1 μM/min. The Michaelis constant, Km (explained in the text), is 0.5 μM. Progress curves are shown for substrate concentrations below, at, and above the Km. The rate of an enzyme-catalyzed reaction declines as substrate is converted to product. A tangent to each curve taken at time = 0 defines the initial velocity, V0, of each reaction.

44. Chapter 8, Figure 8.21, Reaction velocity as a function of substrate concentration

45. What equation models this behavior?
Michaelis-Menten Equation

46. Michaelis-Menten Kinetics
E + S  ES  E + P
k-1
Derived using a few assumptions:
steady state assumption: formation of ES = breakdown of ES (until a significant amount of S has been consumed).
consider initial velocity at early time-points, [P] = 0: rate of reaction depends exclusively on the breakdown of ES (k-2 can be ignored).
free ligand assumption: [S] is in such excess that its decrease in concentration when forming ES is negligible (total [S] = free [S] + [ES]).
MM equation is the rate equation for a one-substrate enzyme-catalyzed reaction. It is a statement of the quantitative relationship between the initial velocity V0, the maximum velocity Vmax and the initial substrate concentration [S] – all of which are related through the Km.
We assume the reverse reaction,
E + P  P doesn’t happen significantly at the beginning of the reaction when there isn’t much P formed (we omit k-2)

47. Chapter 8, Figure 8.21, Reaction velocity as a function of substrate concentration

48. Simple Enzyme Kinetics
The final form in case of a single substrate is
kcat (turnover number): how many substrate molecules can one enzyme molecule convert per second
Km (Michaelis constant): an approximate measure of substrate’s affinity for enzyme
Microscopic meaning of Km and kcat depends on the details of the mechanism

49. Calculating Vmax and Km: The Double Reciprocal Plot
Lineweaver-Burk Plot (Lineweaver-Burk equation)
Linearized double-reciprocal plot is good for analysis of two-substrate data or inhibition.
This plot allows for accurate determination of Vmax – which can only be approximated by plotting V0 versus [S] (hyperbolic curve)

50. Enzyme Inhibition
Inhibitors are compounds that decrease enzyme’s activity
Irreversible inhibitors (inactivators) react with the enzyme
one inhibitor molecule can permanently shut off one enzyme molecule
they are often powerful toxins but also may be used as drugs
Reversible inhibitors bind to, and can dissociate from the enzyme
- they are often structural analogs of substrates or products
- they are often used as drugs to slow down a specific enzyme
Reversible inhibitor can bind:
To the free enzyme and prevent the binding of the substrate
To the enzyme-substrate complex and prevent the reaction

51. FIGURE 6-15a Three types of reversible inhibition
FIGURE 6-15a Three types of reversible inhibition. (a) Competitive inhibitors bind to the enzyme's active site; KI is the equilibrium constant for inhibitor binding to E.

52. Reversible Inhibition - Competitive
No change in Vmax; apparent increase in Km
Lineweaver-Burk: lines intersect at the y-axis
No change in Vmax, thus sufficiently high concentrations of substrate will always displace the inhibitor from the enzyme’s active site.

53. FIGURE 6-15b Three types of reversible inhibition
FIGURE 6-15b Three types of reversible inhibition. (b) Uncompetitive inhibitors bind at a separate site, but bind only to the ES complex; KI′ is the equilibrium constant for inhibitor binding to ES.

54. Reversible Inhibition - Uncompetitive
Decrease in Vmax; apparent decrease in Km
No change in Km/Vmax
Lineweaver-Burk: lines are parallel
Initial velocity approaches Vmax faster (it is decreased with increased inhibitor), and thus an overall decrease in the Vmax. So, at high concentrations of inhibitor, it takes longer for the substrate and inhibitor to leave the enzyme’s active site.
Apparent Km decreases because the [S] to reach 1/2Vmax is decreased by the concentration of the inhibitor. Essentially a buildup of ES complexes tends to look like “tighter binding” or an increase in Km.

55. FIGURE 6-15c Three types of reversible inhibition
FIGURE 6-15c Three types of reversible inhibition. (c) Mixed inhibitors bind at a separate site, but may bind to either E or ES.

56. Reversible Inhibition – Mixed Inhibition
Decrease in Vmax; apparent change in Km
Lineweaver-Burk: lines intersect left from the y-axis
Noncompetitive inhibitors are mixed inhibitors such that there is no change in Km
Mixed type inhibition is similar to noncompetitive inhibition except that binding of the substrate or the inhibitor affect the enzyme’s binding affinity for the other. The change in binding affinity is included in the chemical equation by the term ki. For mixed type inhibition ki>1, which means that binding affinity for the substrate is decreased when the inhibitor is present. 
In noncompetitive inhibition, the inhibitor binds to the enzyme at a location other than the active site in such a way that the inhibitor and substrate can simultaneously be attached to the enzyme. The substrate and the inhibitor have no effect on the binding of the other and can bind and unbind the enzyme in either order. The inhibitor and the substrate are not binding to the same site.

57. Acetylcholinesterase

62. F