Enzyme Kinetics, Inhibition, and Control

Equilibrium and Free Energy

• Every reaction aims to achieve equilibrium, which is not always beneficial in biological systems.

• Equilibrium requires an initial state (reactants) and a final state (products).

• Standard free energy $(\Delta G)$ is calculated as the free e n erg y of products minus the free energy of reactants.

• Formula: $\Delta G = \Delta G^{\circ} + RT \ln(K_{eq})$, where:

  • $\Delta G$ is the change in Gibbs free energy.

  • $\Delta G^{\circ}$ is the standard free energy change.

  • $R$ is the gas constant.

  • $T$ is the temperature in Kelvin.

  • $K_{eq}$ is the equilibrium constant (ratio of products to reactants).

• $R$ and $T$ represent standard conditions.

• A reaction proceeds to completion if \Delta G > 2.73 , corresponding to approximately 11 kilojoules per mole at 25 degrees Celsius.

• In biochemistry, completion requires around 11.2 kilojoules per mole.

Biological Systems and Work

• Biological systems perform various types of work, including concentration, electrical work (ion movement), and synthetic work (changes in chemical bonds).

• These processes require energy, often derived from the hydrolysis of ATP to ADP.

• Some reactions are energetically unfavorable and will not occur spontaneously (positive $\Delta G$).

• Example: Glucose + Phosphate → Glucose-6-Phosphate ($\Delta G = +13.8$ kJ/mol).

Reaction Coupling

• Unfavorable reactions are made favorable by coupling them with reactions that have a large negative $\Delta G$.

• Example: Coupling glucose phosphorylation with ATP hydrolysis.

• ATP Hydrolysis: ATP → ADP + Pi ($\Delta G = -32.2$ kJ/mol).

• Overall reaction: Glucose + Phosphate + ATP → Glucose-6-Phosphate + ADP ($\Delta G = -18$ kJ/mol).

Rate of Reaction

• Uncatalyzed reactions depend on the starting substrate concentration.

• Enzyme-catalyzed reactions depend on both substrate and enzyme concentrations.

• Substrate concentration influences the reaction rate; low substrate concentrations result in slower rates.

• The relationship between substrate concentration and reaction rate is not linear; it is parabolic.

• Vmax is the maximum reaction rate achievable with sufficient substrate.

Substrate and Product Concentrations Over Time

• Substrate concentration decreases over time as the product concentration increases.

• The relationship between substrate and product concentrations over time is not linear.

• Enzyme concentration decreases as the enzyme-substrate complex concentration increases.

• Equilibrium ensures that enzyme concentration never reaches zero; there will always be some free enzyme.

Michaelis-Menten Equation

• The Michaelis-Menten equation describes the relationship between reaction rate and substrate concentration:

  • $v = \frac{V<em>{max} [S]}{[S] + K</em>m}$

  • $V_{max}$ is the maximum velocity.

  • $[S]$ is the substrate concentration.

  • $K_m$ is the Michaelis constant

Vmax and Kilometers

• $V_{max}$ is the maximum velocity at infinite substrate concentration.

• $K<em>m$ (Michaelis constant) indicates the substrate concentration at which the reaction rate is half of $V</em>{max}$.

• Kilometers reflects the affinity of an enzyme for its substrate.

• When $[S] = K<em>m$, then $v = \frac{V</em>{max}}{2}$.

Lineweaver-Burk Plot

• The Lineweaver-Burk plot is a double reciprocal plot used to linearize the Michaelis-Menten equation.

• Equation: $\frac{1}{v} = \frac{K<em>m}{V</em>{max}} \cdot \frac{1}{[S]} + \frac{1}{V_{max}}$

• The plot yields a straight line, where:

  • The y-intercept is $\frac{1}{V_{max}}$.

  • The x-intercept is $-\frac{1}{K_m}$.

  • The slope is $\frac{K<em>m}{V</em>{max}}$.

• As $v$ decreases, $\frac{1}{v}$ increases, and as substrate concentration increases, $\frac{1}{[S]}$ decreases (becomes more negative).

Significance of Kilometers

• Kilometers is the substrate concentration at which $v = \frac{V_{max}}{2}$, measured in moles per liter.

• A small Kilometers indicates high affinity: less substrate is needed to achieve a high reaction rate.

• A large Kilometers indicates low affinity: more substrate is needed for a high reaction rate.

Catalytic Constant and Enzyme Specificity

• Catalytic Constant (kcat):

  • Measures the intrinsic speed of an enzyme.

  • $k<em>{cat} = \frac{V</em>{max}}{[E]}$, where $[E]$ is the enzyme concentration.

• Enzyme Specificity Constant:

  • Measures the efficiency of an enzyme.

  • $\frac{k<em>{cat}}{K</em>m}$

  • Indicates how well an enzyme works at low substrate concentrations.

  • A high specificity constant means the enzyme is very efficient even at low substrate concentrations.

Inhibition and Control of Enzyme Activity

• Enzymes are central to biological functions, and controlling their activity is crucial.

• Dysfunctional or uncontrolled enzymes can lead to diseases, including cancer.

• Understanding enzyme inhibition is essential for biochemistry, especially in drug development.

Active Site of Enzymes

• The active site is the region on an enzyme where substrates bind and catalysis occurs.

• Enzyme inhibition can occur at the active site (competitive inhibition) or at an allosteric site (allosteric inhibition).

• Allosteric effectors bind to the enzyme, changing the shape and activity of the active site.

• Chemical modifications, such as phosphorylation, can also alter enzyme activity.

Enzyme Inhibitors and Drugs

• Many drugs act as enzyme inhibitors, blocking enzyme function.

• Inhibitors can target enzymes in metabolic pathways, providing control over biological processes.

• Feedback inhibition involves the end product of a reaction inhibiting an earlier enzyme in the pathway.

Critical Residues at the Active Site

• Active site residues are crucial for enzyme function, facilitating substrate binding.

• Mutating these residues can impair enzyme activity.

• Active site residues are located in a three-dimensional structure, complementing the transition state.

Serum Proteases

• Serum proteases, like trypsin, have a catalytic triad crucial for their function.

• The triad consists of three residues that come together to form a functional active site.

• These residues create an environment that facilitates the reaction, positioning the substrate correctly.

Induced Fit Model

• The induced fit model describes how an enzyme changes its shape upon substrate binding to better fit the transition state.

• The active site does not perfectly fit the substrate initially; it changes to better accommodate the transition state.

• The surrounding environment of the active site is different from the rest of the enzyme, excluding water and providing a hydrophobic environment.

• The active site restricts substrate orientation, lowering activation energy.

• Understanding the active site is critical for rational drug design.

Enzyme Inhibition Types

• Enzymes bind to substrates reversibly, forming an enzyme-substrate complex that leads to product formation.

• Inhibitors disrupt this process by binding to the enzyme, either preventing substrate binding or affecting the reaction indirectly.

• Enzyme inhibitors are classified as antagonists, while activators are agonists.

• Many drugs are enzyme inhibitors, and toxins can also act as inhibitors.

• Inhibitors can be reversible (non-covalently bound) or irreversible (covalently bound).

Reversible Inhibition

• There are three main types of reversible inhibition: competitive, uncompetitive, and noncompetitive.

Competitive Inhibition

• Competitive inhibition occurs when an inhibitor and substrate compete for the active site.

• The degree of inhibition depends on the relative concentrations of the inhibitor and substrate.

• In the presence of a competitive inhibitor, the Kilometers increases, while the Vmax remains unchanged.

• The Lineweaver-Burk plot shows that Vmax is constant (y-intercept does not change), but Kilometers increases (x-intercept moves closer to zero).

• Examples: Methanol poisoning treated with ethanol, melanate inhibiting succinate dehydrogenase.

• The inhibitor must have a structural similarity to the substrate.