Enzyme Kinetics and Inhibition Notes

Enzyme Kinetics and Inhibition

Learning Objectives

• Identify the properties of enzymes, their classification, regulation, and kinetics using equations, models, and graphs.

What is an Enzyme?

• Biological catalysts.
• Usually proteins, sometimes RNA (ribozymes).
• Essential for metabolism and DNA replication.
• Speed up reactions without being consumed.

Factors Influencing Reaction Rate

• Increasing temperature: Up to 42°C (onset of protein denaturation).
• Increasing concentration of reactants.
• Adding a catalyst.
• pH:
  • Pepsin in the stomach (acidic).
  • Lipase in the pancreas (basic).

Definition of Terms

• Substrate: Specific molecule that an enzyme acts on.
• Active Site: Special region on the enzyme where the substrate binds.
• Activation Energy (\Delta G^{\ddagger}): Minimum amount of energy needed for a chemical reaction to begin.
• Specificity: Enzyme’s ability to choose a specific substrate.

Enzymes and Reaction Speed

• Enzymes speed up chemical reactions by lowering the activation energy.
• Enzymes make reactions happen fast enough at body temperature and pH.
• Most biological reactions are too slow without enzymes.

Enzyme Classes and Reactions

1. Oxidoreductases: Oxidation-reduction reactions.
2. Transferases: Transfer of functional groups.
3. Hydrolases: Hydrolysis reactions.
4. Lyases: Group elimination to form double bonds.
5. Isomerases: Isomerization reactions.
6. Ligases: Bond formation coupled with ATP hydrolysis.
7. Translocases: Solute transport through membranes.

Example Reaction

• Alanine + α-Ketoglutarate catalyzed by alanine aminotransferase forms Pyruvate + Glutamate.

Catalytic Mechanisms

• Idealized Transfer Reaction: (AB) + (C) \rightarrow (A) + (BC)
• Involves a progress of reaction coordinate and free energy changes.

Definition of Terms (cont.)

• Reaction Coordinate: Progress of the reaction.
• Transition State: Point of highest free energy; midway between reactants and products.
• Enzyme-Substrate Complex: Temporary molecule formed when the enzyme binds the substrate.
• Activation Energy (\Delta G^{\ddagger}): Energy-requiring step or energy barrier. Height of \Delta G^{\ddagger} determines the rate of a reaction; higher \Delta G^{\ddagger} = less likely rxn will occur = slower.

Catalytic Mechanisms in Nature

• Involves reactants, products, and the reaction coordinate, showing the free energy change during the reaction.

Catalyst and Activation Energy

• Catalyst (enzyme) provides a reaction pathway with a lower \Delta G^{\ddagger}.
• Uncatalyzed reaction has a higher \Delta G^{\ddagger}_{uncat}.
• Catalyzed reaction has a lower \Delta G^{\ddagger}_{cat}.

Enzyme Catalysts and Free Energy Change

• Enzyme catalysts do not alter \Delta G of a reaction.
• It merely provides a pathway from reactants to products through a transition state.
• Enzymes lower the height of \Delta G^{\ddagger} by lowering the energy of the transition state.

Lock-and-Key Model

• The enzyme and substrate fit together like a key to a lock.
• Fails to explain the dynamic changes that accompany catalysis.
• Less accepted model.

Induced Fit Model

• Binding of substrate induces conformational changes in the active site of the enzyme.
• Explains dynamic changes.
• More accepted model.

Enzyme Kinetics

• Kinetics = how fast enzymes work.
• Helps understand enzymatic reactions and regulation.

Reaction Velocity

• Progress of reaction can be expressed as velocity (v).
• Rate of disappearance of substrate (S) or rate of appearance of the product (P).

Enzyme Kinetics and Substrate Concentration

• When enzyme concentration is held constant, the reaction velocity varies with [S] in a nonlinear (hyperbolic) fashion.
• Suggests that an enzyme physically combines with its substrate to form an ES complex.

Enzyme Kinetics: Reaction Scheme

• E + S \rightleftharpoons ES \rightarrow E + P

Enzyme Kinetics: Saturation

• As substrate concentration increases, the reaction velocity reaches a saturation point.

Enzyme Kinetics: Unimolecular Reactions

• Unimolecular (first-order) reaction: involves a single reactant.
• k = rate constant in s-1
• v is directly proportional to [A].

Enzyme Kinetics: Bimolecular Reactions

• Bimolecular (second-order) reaction: involves 2 reactants.
• k = rate constant in M-1 s-1
• v is directly proportional to [A] x [B].

Problem: Determining Reaction Velocity

• Determine the velocity of the reaction X + Y \rightarrow Z when the sample contains 3 μM X and 5 μM Y and k for the reaction is 400 M-1 s-1.
• Is the reaction uni- or bimolecular?
• Express the answer in M/s.

Solution

• The reaction is bimolecular.
• v = 6 \times 10^{-9} M/s

Michaelis-Menten Equation

• Rate equation for an enzyme-catalyzed reaction.
• E binds its S (in an ES complex) before converting it to product.
• Overall reaction has first- & second-order reactions.
• Each with a characteristic rate constant.

Michaelis-Menten Equation: Historical Context

• Derived by Leonor Michaelis and Maude Menten.
• Mathematical description of the hyperbolic curve.

Michaelis-Menten Equation: Terms

• v_0 = initial velocity (velocity at the start of the reaction at time 0).
• V_{max} = maximum reaction velocity; proportional to [E].
• K_m = Michaelis constant.

Michaelis-Menten Equation: Formula

• v0 = \frac{V{max}[S]}{K_m + [S]}

Michaelis-Menten Equation: Problem

• An enzyme-catalyzed reaction has a KM of 1 mM and a V{max} of 5 nM⋅s-1. What is the reaction velocity when the substrate concentration is 0.25 mM?

Michaelis-Menten Equation: Answer

• Answer: 1 \times 10^{-9} M/s or 1 nM/s

Michaelis Constant (K_m)

• [S] at which v0 is half-maximal (i.e., v0 = \frac{V{max}}{2} when [S] = Km).
• Indicates how efficiently an enzyme selects its substrate and converts it to product.
• Lower K_m = enzyme is more effective at low [S].
• Higher K_M = the less effective the enzyme is.
• Inversely proportional to the affinity of the enzyme for its substrate.

Michaelis-Menten Equation: Kinetics

• First-order kinetics: Rate of reaction is dependent on [S].
• Zero-order kinetics: Rate of reaction is independent of [S].

Lineweaver-Burk Plot

• In practice, hyperbolic curves are prone to misinterpretation; difficult to estimate the upper limit of the curve (V_{max}).
• Linear transformation = Lineweaver–Burk plot.

Lineweaver-Burk Plot: Equation

• Reciprocal of the Michaelis-Menten equation:
• \frac{1}{v0} = (\frac{KM}{V{max}}) \frac{1}{[S]} + \frac{1}{V{max}}

Lineweaver-Burk Plot: Slope-Intercept Form

• Recall: Slope-intercept form: y = mx + b
  • x is the independent variable.
  • m is the slope of the line.
  • y is the dependent variable.
  • b is the y-intercept of the line.

Lineweaver-Burk Plot: Equation (cont.)

• \frac{1}{v0} = (\frac{KM}{V{max}}) \frac{1}{[S]} + \frac{1}{V{max}}
• y = mx + b

Lineweaver-Burk Plot: Interpretation

• Plot of 1/v versus 1/[S] gives a straight line whose slope is Km /V{max} and whose intercept on the 1/v axis is 1/V_{max}.

Lineweaver-Burk Plot: Graph

• The extrapolated intercept on the 1/[S] axis is -1/K_m.
• Slope = \frac{KM}{V{max}}

Lineweaver-Burk Plot: Velocity Problem

• The velocity of an enzyme-catalyzed reaction was measured at several substrate concentrations. Calculate KM and V{max} for the reaction.
• Solution: Calculate the reciprocals of the substrate concentration and velocity, and then make a plot of 1/vo versus 1/[S] (a Lineweaver-Burk plot).

Lineweaver-Burk Plot: Calculations

• Recall: \frac{1}{v0} = (\frac{KM}{V{max}}) \frac{1}{[S]} + \frac{1}{V{max}}
• Slope = \frac{KM}{V{max}}

Lineweaver-Burk Plot: Solution

• The intercept on the 1/[S] axis (which is equal to -1/K_M) is -1.33 μM-1. Therefore,
• K_M = -\frac{1}{-1.33 \mu M^{-1}} = 0.75 \mu M
• The intercept on the 1/v axis (which is equal to 1/V_{max}) is 0.33 mM-1⋅s. Therefore,
• V_{max} = \frac{1}{0.33 mM^{-1} \cdot s} = 3.0 mM \cdot s^{-1}

Enzyme Inhibition

• Enzyme inhibitor: Any substance that can diminish the velocity of an enzyme-catalyzed reaction.
• Many naturally occurring substances inhibit the activity of essential enzymes.
• Examples: antibiotics, pesticides, and other poisons.

Enzyme Inhibition: Reversible

• The inhibitor binds temporarily to the enzyme (e.g., to the active site or elsewhere).
• The enzyme can regain activity if the inhibitor is removed.
• Examples: Ibuprofen, mefenamic acid.

Enzyme Inhibition: Irreversible

• Permanently disables the enzyme molecule.
• The only way to restore function is to make new enzyme.
• Example: Aspirin.

Competitive Inhibition

• Inhibitor binds to the active site, competing with substrate.
• Increases K_m due to low affinity.
• No change in V_{max} due to unchanged [E].
• May be reversed by increasing [S]; outcompetes the inhibitor.

Competitive Inhibition: Alpha Factor

• \alpha = factor that makes K_m appear larger.
• Recall: High K_m, lower affinity.

Uncompetitive Inhibition

• Inhibitor binds only to the ES complex which is rare.
• Decreases K_m. Inhibitor stabilizes the ES complex. Enzyme