1. Chapter 13 Enzyme Kinetics

2. Outline What characteristic features define enzymes?
Can the rate of an enzyme-catalyzed reaction be defined in a mathematical way?
What equations define the kinetics of enzyme-catalyzed reactions?
What can be learned from the inhibition of enzyme activity?
What is the kinetic behavior of enzymes catalyzing bimolecular reactions?
How can enzymes be so specific?
Are all enzymes proteins?
Is it possible to design an enzyme to catalyze any desired reaction?

3. Virtually All Reactions in Cells Are Mediated by Enzymes
Enzymes catalyze thermodynamically favorable reactions, causing them to proceed at extraordinarily rapid rates
Enzymes provide cells with the ability to exert kinetic control over thermodynamic potentiality
Living systems use enzymes to accelerate and control the rates of vitally important biochemical reactions
Enzymes are the agents of metabolic function

4. 13.1 What Characteristic Features Define Enzymes?
Catalytic power is defined as the ratio of the enzyme-catalyzed rate of a reaction to the uncatalyzed rate
Specificity is the term used to define the selectivity of enzymes for their substrates
Regulation of enzyme activity ensures that the rate of metabolic reactions is appropriate to cellular requirements
Enzyme nomenclature provides a systematic way of naming metabolic reactions
Coenzymes and cofactors are nonprotein components essential to enzyme activity.

5. 13.1 What Characteristic Features Define Enzymes?
Enzymes can accelerate reactions as much as 1021 over uncatalyzed rates
Urease is a good example:
Catalyzed rate: 3x104/sec
Uncatalyzed rate: 3x10 -10/sec
Ratio (catalytic power) is 1x1014

6. Specificity
Enzymes selectively recognize proper substrates over other molecules
Enzymes produce products in very high yields - often much greater than 95%
Specificity is controlled by structure - the unique fit of substrate with enzyme controls the selectivity for substrate and the product that’s formed.

7. 90% yield in each step; 35% over 10 steps

8. Enzyme Nomenclature Provides a Systematic Way of Naming Metabolic Reactions

9. 13.2 Can the Rate of an Enzyme-Catalyzed Reaction Be Defined in a Mathematical Way?
Kinetics is the branch of science concerned with the rates of reactions
Enzyme kinetics seeks to determine the maximum reaction velocity that enzymes can attain and the binding affinities for substrates and inhibitors
Analysis of enzyme rates yields insights into enzyme mechanisms and metabolic pathways
This information can be exploited to control and manipulate the course of metabolic events

10. Several Kinetics Terms to Understand
rate or velocity
rate constant
rate law
order of a reaction
molecularity of a reaction

11. Chemical Kinetics Provides a Foundation for Exploring Enzyme Kinetics
Consider a reaction of overall stoichiometry as shown:
The rate is proportional to the concentration of A

12. Chemical Kinetics Provides a Foundation for Exploring Enzyme Kinetics
The simple elementary reaction of A→P is a first-order reaction
Figure 13.4 shows the course of a first-order reaction as a function of time
This is a unimolecular reaction
For a bimolecular reaction, the rate law is:
v = k[A][B]
Kinetics cannot prove a reaction mechanism
Kinetics can only rule out various alternative hypotheses because they don’t fit the data

13. The Time-Course of a First-Order Reaction
Figure 13.4 Plot of the course of a first-order reaction. The half-time, t1/2 is the time for one-half of the starting amount of A to disappear.

14. Catalysts Lower the Free Energy of Activation for a Reaction
A typical enzyme-catalyzed reaction must pass through a transition state
The transition state sits at the apex of the energy profile in the energy diagram
The reaction rate is proportional to the concentration of reactant molecules with the transition-state energy
This energy barrier is known as the free energy of activation
Decreasing ΔG‡ increases the reaction rate
The activation energy is related to the rate constant by:

15. Catalysts Lower the Free Energy of Activation for a Reaction
Energy diagram for a chemical reaction (A→P) and the effects of (a) raising the temperature from T1 to T2, or (b) adding a catalyst.

16. Understand the difference between DG and DG‡
The Transition State
Understand the difference between DG and DG‡
The overall free energy change for a reaction, DG, is related to the equilibrium constant
The free energy of activation for a reaction, DG‡, is related to the rate constant
It is extremely important to appreciate this distinction

17. 13.3 What Equations Define the Kinetics of Enzyme-Catalyzed Reactions?
Simple first-order reactions display a plot of the reaction rate as a function of reactant concentration that is a straight line
Enzyme-catalyzed reactions are more complicated
At low concentrations of the enzyme substrate, the rate is proportional to S, as in a first-order reaction
At higher concentrations of substrate, the enzyme reaction approaches zero-order kinetics
This behavior is a saturation effect

18. As [S] increases, kinetic behavior changes from 1st order to zero-order kinetics
Figure 13.7 Substrate saturation curve for an enzyme-catalyzed reaction.

19. Louis Michaelis and Maud Menten's theory
The Michaelis-Menten Equation is the Fundamental Equation of Enzyme Kinetics
Louis Michaelis and Maud Menten's theory
assumes the formation of an enzyme-substrate complex
assumes that the ES complex is in rapid equilibrium with free enzyme
assumes that the breakdown of ES to form products is slower than
1) formation of ES and
2) breakdown of ES to re-form E and S

20. Michaelis-Menten Equation
Derive Michaelis-Menten Equation

21. The Michaelis-Menten equation
where
and

22. The "kinetic activator constant"
Understanding Km
The "kinetic activator constant"
Km is a constant
Km is a constant derived from rate constants
Km is, under true Michaelis-Menten conditions, an estimate of the dissociation constant of E from S
Small Km means tight binding; high Km means weak binding

23. The theoretical maximal velocity
Understanding Vmax
The theoretical maximal velocity
Vmax is a constant
Vmax is the theoretical maximal rate of the reaction - but it is NEVER achieved in reality
To reach Vmax would require that ALL enzyme molecules are tightly bound with substrate
Vmax is asymptotically approached as substrate is increased

24. The dual nature of the Michaelis-Menten equation
Combination of 0-order and 1st-order kinetics
When S is low, the equation for rate is 1st order in S
When S is high, the equation for rate is 0-order in S
The Michaelis-Menten equation describes a rectangular hyperbolic dependence of v on S

25. Table 13.3 gives the Km values for some enzymes and their substrates

26. The Turnover Number Defines the Activity of One Enzyme Molecule
A measure of catalytic activity
kcat, the turnover number, is the number of substrate molecules converted to product per enzyme molecule per unit of time, when E is saturated with substrate.
If the M-M model fits, k2 = kcat = Vmax/Et
Values of kcat range from less than 1/sec to many millions per sec

27. The Turnover Number Defines the Activity of One Enzyme Molecule

28. The Ratio kcat/Km Defines the Catalytic Efficiency of an Enzyme
The catalytic efficiency: kcat/Km An estimate of "how perfect" the enzyme is
kcat/Km is an apparent second-order rate constant
It measures how well the enzyme performs when S is low
The upper limit for kcat/Km is the diffusion limit - the rate at which E and S diffuse together

29. The Ratio kcat/Km Defines the Catalytic Efficiency of an Enzyme

30. Linear Plots Can Be Derived from the Michaelis-Menten Equation
Be able to derive these equations
Lineweaver-Burk:
Begin with v = Vmax[S]/(Km + [S]) and take the reciprocal of both sides
Rearrange to obtain the Lineweaver-Burk equation:
A plot of 1/v versus 1/[S] should yield a straight line

31. Linear Plots Can Be Derived from the Michaelis-Menten Equation

32. Linear Plots Can Be Derived from the Michaelis-Menten Equation
Hanes-Woolf:
Begin with Lineweaver-Burk and multiply both sides by [S] to obtain:
Hanes-Woolf is best - why?
Because Hanes-Woolf has smaller and more consistent errors across the plot

33. Linear Plots Can Be Derived from the Michaelis-Menten Equation

34. Enzymatic Activity is Strongly Influenced by pH
Enzyme-substrate recognition and catalysis are greatly dependent on pH
Enzymes have a variety of ionizable side chains that determine its secondary and tertiary structure and also affect events in the active site
The substrate may also have ionizable groups
Enzymes are usually active only over a limited range of pH
The effects of pH may be due to effects on Km or Vmax or both

35. Enzymatic Activity is Strongly Influenced by pH
The pH activity profiles of four different enzymes.

36. The Response of Enzymatic Activity to Temperature is Complex
Rates of enzyme-catalyzed reactions generally increase with increasing temperature
However, at temperatures above 50°to 60°C, enzymes typically show a decline in activity
Two effects here:
Enzyme rate typically doubles in rate for ever 10º C as long as the enzyme is stable and active
At higher temperatures, the protein becomes unstable and denaturation occurs

37. The Response of Enzymatic Activity to Temperature is Complex
The effect of temperature on enzyme activity.

38. 13.4 What Can Be Learned from the Inhibition of Enzyme Activity?
Enzymes may be inhibited reversibly or irreversibly
Reversible inhibitors may bind at the active site or at some other site
Enzymes may also be inhibited in an irreversible manner
Penicillin is an irreversible suicide inhibitor

39. Reversible Inhibitors May Bind at the Active Site or at Some Other Site

40. Competitive Inhibitors Compete With Substrate for the Same Site on the Enzyme
Lineweaver-Burk plot of competitive inhibition, showing lines for no I, [I], and 2[I].

41. Pure Noncompetitive Inhibition – where S and I bind to different sites on the enzyme
Lineweaver-Burk plot of pure noncompetitive inhibition. Note that I does not alter Km but that it decreases Vmax.

42. Mixed Noncompetitive Inhibition: binding of I by E influences binding of S by E
Lineweaver-Burk plot of mixed noncompetitive inhibition. Note that both intercepts and the slope change in the presence of I.

43. Uncompetitive Inhibition, where I combines only with E, but not with ES
Lineweaver-Burk plot of uncompetitive inhibition. Note that both intercepts change but the slope (Km/Vmax) remains constant in the presence of I.

44. Enzymes Can Be Inhibited Irreversibly
Penicillin is an irreversible inhibitor of the enzyme glycoprotein peptidease, which catalyzes an essential step in bacterial cell all synthesis.

45. Enzymes often catalyze reactions involving two (or more) substrates
What Is the Kinetic Behavior of Enzymes Catalyzing Bimolecular Reactions?
Enzymes often catalyze reactions involving two (or more) substrates
Bisubstrate reactions may be sequential or single-displacement reactions or double-displacement (ping-pong) reactions
Single-displacement reactions can be of two distinct classes:
1. Random, where either substrate may bind first, followed by the other substrate
2. Ordered, where a leading substrate binds first, followed by the other substrate

46. Conversion of AEB to PEQ is the Rate-Limiting Step in Random, Single-Displacement Reactions
In this type of sequential reaction, all possible binary enzyme-substrate and enzyme-product complexes are formed rapidly and reversibly when enzyme is added to a reaction mixture containing A, B, P, and Q.

47. In an Ordered, Single-Displacement Reaction, the Leading Substrate Must Bind First
The leading substrate (A) binds first, followed by B. Reaction between A and B occurs in the ternary complex and is usually followed by an ordered release of the products, P and Q.

48. An Alternative way of Portraying the Ordered, Single-Displacement Reaction

49. 13.5 - What Is the Kinetic Behavior of Enzymes Catalyzing Bimolecular Reactions?
Single-deplacement bisubstrate mechanism.

50. The Double Displacement (Ping-Pong) Reaction
Double-Displacement (Ping-Pong) reactions proceed via formation of a covalently modified enzyme intermediate. Reactions conforming to this kinetic pattern are characterized by the fact that the product of the enzyme’s reaction with A (called P in the above scheme) is released prior to reaction of the enzyme with the second substrate, B.

51. An Alternative Presentation of the Double-Displacement (Ping-Pong) Reaction

52. The Double Displacement (Ping-Pong) Reaction
Double-displacement (ping-pong) bisubstrate mechanisms are characterized by parallel lines.

53. 13.7 – How Can Enzymes Be So Specific?
The “Lock and key” hypothesis was the first explanation for specificity
The “Induced fit” hypothesis provides a more accurate description of specificity
Induced fit favors formation of the transition state
Specificity and reactivity are often linked. In the hexokinase reaction, binding of glucose in the active site induces a conformational change in the enzyme that causes the two domains of hexokinase to close around the substrate, creating the catalytic site

54. 13.7 – Are All Enzymes Proteins?
Ribozymes - segments of RNA that display enzyme activity in the absence of protein
Examples: RNase P and peptidyl transferase
Abzymes - antibodies raised to bind the transition state of a reaction of interest

55. 13.8 Is It Possible to Design An Enzyme to Catalyze Any Desired Reaction?
A known enzyme can be “engineered” by in vitro mutagenesis, replacing active site residues with new ones that might catalyze a desired reaction
Another approach attempts to design a totally new protein with the desired structure and activity
This latter approach often begins with studies “in silico” – i.e., computer modeling
Protein folding and stability issues make this approach more difficult
Further, the cellular environment may provide complications not apparent in the computer modeling

56. 13.8 Is It Possible to Design An Enzyme to Catalyze Any Desired Reaction?
cis-1,2-Dichloroethylene (DCE) is an industrial solvent that poses hazards to human health.
Site-directed mutations have enabled the conversion of a bacterial epoxide hydrolase to catalyze the chlorinated epoxide hydrolase reaction.