Chapter 2 - Enzymes and Kinetics

Enzymes as Biological Catalysts

• Definition of Enzymes: Enzymes are specialized proteins that function as biological catalysts, accelerating chemical reactions within the body.

• Role of Catalysts: Catalysts increase the rate of chemical reactions without being consumed or permanently altered in the process. This means enzymes are reusable and remain unchanged by the reactions they catalyze.

• Kinetics vs. Thermodynamics:

  • Enzymes affect the kinetics of a reaction, meaning they increase the speed at which equilibrium is reached.

  • Enzymes do not alter the thermodynamics of a reaction. They do not change whether a reaction is spontaneous or non-spontaneous (favorable or unfavorable) and do not alter the overall free energy ($\Delta G$) or the equilibrium constant ($K_{eq}$).

• Essential Concept Summary:

  • Enzymes lower the activation energy ($E_a$) required for a reaction to proceed.

  • By lowering $E_a$, molecules can reach the transition state much more quickly.

  • The amount of product formed at equilibrium remains the same; only the rate of reaching that equilibrium is altered.

  • Enzymes are sensitive to the local environment, specifically pH and temperature. Deviation from optimal ranges results in denaturation (loss of structural integrity).

Classifications of Enzymes

Enzymes are classified into six major categories based on their function or mechanism of action. These can be remembered using the mnemonic LIL HOT:

• Oxidoreductases: These catalyze oxidation-reduction reactions, which involve the transfer of electrons between biological molecules. They often utilize electron carriers like $NADH$ or $FADH_2$.

  • Examples: Dehydrogenase, reductase, and oxidase.

• Transferases: These enzymes catalyze the movement of a functional group from one molecule to another.

  • Examples: Kinase (specifically transfers phosphate groups, usually from $ATP$) and aminotransferase (involved in amino acid metabolism).

• Hydrolases: These catalyze the cleavage of a molecule into two products by adding a water molecule across the bond (hydrolysis).

  • Examples: Phosphatase, peptidase, nuclease, and lipase.

• Lyases: These catalyze the cleavage of a single molecule into two products without using water and without performing redox chemistry. They break bonds specifically through other mechanisms.

  • Example: Synthase (when acting in the reverse of a cleavage reaction).

• Isomerases: These catalyze the rearrangement of bonds within a single molecule to transform it into an isomer.

  • Example: Phosphohexoisomerase.

• Ligases: These catalyze addition or synthesis reactions, typically between large, similar molecules. These reactions often require an energy input from $ATP$.

  • Application: Essential in DNA replication and repair when joining segments of nucleotides together.

Impact on Activation Energy and Reaction Energetics

• Free Energy ($\Delta G$): This represents the usable energy available to perform work in a cell. The symbol $\Delta G$ denotes the change in free energy during a reaction.

• Classification of Reactions Based on Free Energy:

  • Endergonic Reactions: Require an input of energy. Here, \Delta G > 0 (positive).

  • Exergonic Reactions: Release energy into the environment. Here, \Delta G < 0 (negative).

• The Activation Barrier: Regardless of whether a reaction is endergonic or exergonic, an activation barrier must be overcome to reach the transition state. Catalysts exert their effect by lowering this barrier, making it easier for the substrate to reach the transition state.

Mechanisms of Enzyme Activity

Enzymes facilitate reactions through several critical strategies, all of which depend on the binding of a substrate to the enzyme's active site.

• Binding and Synthesis:

  • Substrate: The specific molecule upon which an enzyme acts.

  • Enzyme-Substrate Complex: The physical interaction and temporary association between the enzyme and the substrate.

  • Active Site: A specialized pocket within the enzyme with a specific shape and charge distribution tailored to recognize and hold the substrate. This is where the catalytic function occurs.

• Methods of Acceleration:

  • Providing a favorable microenvironment (specific pH or charge distribution).

  • Stabilizing the transition state to lower required energy.

  • Bringing reactive groups closer together in the correct spatial orientation for the reaction to occur.

• Models of Binding Interaction:

  1. Lock and Key Theory: Suggests the active site (the lock) is already in the perfect conformation to fit the substrate (the key) without any changes.

  2. Induced Fit Model: A more scientifically accepted model suggesting the enzyme changes its shape slightly upon binding to the substrate to create a more precise, high-affinity fit that facilitates catalysis.

Cofactors and Coenzymes

Many enzymes require non-protein helper molecules to be effective. These are classified into two groups:

• Cofactors: Generally inorganic molecules or metal ions. These are often dietary minerals.

  • Examples: $Mg^{2+}$, $Zn^{2+}$, $Fe^{2+}$.

• Coenzymes: Small organic molecules, most of which are derived from vitamins.

  • Examples: $NAD^+$ (Vitamin $B_3$), $FAD$ (Vitamin $B_2$), $TPP$ (Vitamin $B_1$), $PLP$ (Vitamin $B_6$), and Coenzyme A.

• Enzyme States:

  • Apoenzymes: Enzymes that are currently lacking their necessary cofactors or coenzymes and are therefore inactive.

  • Holoenzymes: The functional, active form of an enzyme containing all its necessary cofactors or coenzymes.

Enzyme Kinetics and the Michaelis-Menten Equation

• Kinetics Fundamentals: The study of reaction rates and the factors influencing them, such as enzyme concentration, substrate concentration, and environmental conditions.

• Saturation and Maximum Velocity ($V_{max}$):

  • Initially, increasing substrate concentration ($[S]$) leads to an increased reaction rate ($V$).

  • As more substrate is added, all available active sites become occupied. This state is known as saturation.

  • Once saturated, the enzyme reaches its maximum possible rate, $V_{max}$. Adding further substrate beyond this point does not increase the rate.

• The Michaelis-Menten Equation:     $V = \frac{V_{max} [S]}{K_m + [S]}$

• Michaelis Constant ($K_m$):

  • $K_m$ is defined as the substrate concentration at which the reaction rate is exactly half of $V_{max}$ ($V = \frac{1}{2} V_{max}$).

  • $K_m$ is used to measure the affinity of the enzyme for its substrate.

  • Low $K_m$: Indicates high affinity; the enzyme reaches half-saturation with very little substrate.

  • High $K_m$: Indicates low affinity; a large amount of substrate is needed for the enzyme to work efficiently.

• Turnover Number ($K_{cat}$):

  • $K_{cat}$ represents the number of substrate molecules one enzyme molecule converts to product per second when fully saturated.

  • Relationship to $V_{max}$: $V_{max} = [E] K_{cat}$.

  • The complete rate equation can be written as: $V = \frac{K_{cat} [E] [S]}{K_m + [S]}$.

  • At very low substrate concentrations ($K_m \gg [S]$), the equation simplifies to: $V = \frac{K_{cat}}{K_m} [E] [S]$.

Lineweaver-Burk Plots

• Definition: A graphical representation produced by taking the reciprocal of the Michaelis-Menten equation ($\frac{1}{V}$ vs. $\frac{1}{[S]}$).

• Utility: It transforms the hyperbolic Michaelis-Menten curve into a straight line, making it easier to identify kinetic constants.

• Key Intercepts:

  • Y-intercept: $\frac{1}{V_{max}}$

  • X-intercept: $-\frac{1}{K_m}$

  • Slope: $\frac{K_m}{V_{max}}$

Cooperativity

• Sigmoidal Kinetics: Some enzymes (typically those with multiple subunits and active sites) do not follow the standard hyperbolic curve. Instead, they produce an S-shaped (sigmoidal) curve.

• Mechanism: Binding of a substrate to one subunit induces a conformational change in the other subunits.

  • T-state (Tense): Low-affinity state.

  • R-state (Relaxed): High-affinity state.

  • Substrate binding triggers a transition from the T-state to the R-state.

• Hill's Coefficient ($n$): A numerical value quantifying cooperativity.

  • n > 1: Positive cooperativity (binding increases affinity for further substrates).

  • n < 1: Negative cooperativity (binding decreases affinity for further substrates).

  • $n = 1$: No cooperativity (follows standard Michaelis-Menten kinetics).

Effects of Local Conditions on Enzyme Activity

• Temperature:

  • Reaction velocity typically doubles for every $10^\circ C$ increase until the optimal temperature is reached.

  • Increased heat leads to faster molecular collisions, aiding the crossing of the activation barrier.

  • Past the optimal temperature, thermal energy disrupts the protein structure, leading to denaturation and a sharp drop in activity.

• pH:

  • Changes in pH affect the ionization of amino acids in the active site, which can disrupt substrate binding or catalysis.

  • Extreme pH levels lead to denaturation.

  • Examples of Optimal pH:

    • Pepsin: Works best in the acidic environment of the stomach (low pH).

    • Trypsin: Works best in the basic environment of the small intestine.

• Salinity:

  • Observed primarily in vitro (in laboratory settings).

  • High salt concentrations can disrupt the hydrogen and ionic bonds that maintain enzyme structure.

Regulation of Enzyme Activity

Feedback Regulation

• Feedback Inhibition (Negative Feedback): The most common regulatory mechanism where the final product of a metabolic pathway inhibits an enzyme that acts earlier in the pathway. This prevents energy waste and overproduction.

• Feed-forward Regulation: A mechanism where an early intermediate in a pathway activates an enzyme that functions later in the pathway.

Reversible Inhibition

There are four distinct types of reversible inhibition, categorized by where they bind and their effects on kinetics:

1. Competitive Inhibition:

   • Binding Site: Active Site.

   • Mechanism: Inhibitor competes with the substrate for the same spot.

   • Impact on $K_m$: Increases (affinity appears lower).

   • Impact on $V_{max}$: Unchanged (can be overcome by adding more substrate).

2. Noncompetitive Inhibition:

   • Binding Site: Allosteric Site (a different site than the active site).

   • Mechanism: Binding induces a shape change that reduces catalytic function regardless of substrate binding.

   • Impact on $K_m$: Unchanged (substrate affinity is not affected).

   • Impact on $V_{max}$: Decreases (fewer functional enzymes available).

3. Uncompetitive Inhibition:

   • Binding Site: Allosteric Site of the Enzyme-Substrate (ES) complex.

   • Mechanism: The inhibitor binds only after the substrate has already bound, locking the substrate in place and preventing product release.

   • Impact on $K_m$: Decreases (affinity appears higher because the substrate is trapped).

   • Impact on $V_{max}$: Decreases.

4. Mixed Inhibition:

   • Binding Site: Allosteric Site.

   • Mechanism: Inhibitor can bind to the free enzyme or the ES complex, but has a different affinity for each.

   • Impact on $K_m$: Increases (if binding to free enzyme) or decreases (if binding to ES complex).

   • Impact on $V_{max}$: Always decreases.

Irreversible Inhibition

• Mechanism: The inhibitor permanently deactivates the enzyme, usually through the formation of a covalent bond at the active site or by causing irreparable structural damage.

• Recovery: The cell must synthesize brand-new enzyme molecules to recover the lost activity.

Regulated Enzyme Mechanisms

• Allosteric Regulation: Activators or inhibitors bind to allosteric sites to increase or decrease enzymatic turnover/affinity.

• Covalent Modification: Enzyme activity can be altered through phosphorylation (adding a phosphate) or glycosylation (adding a sugar).

• Zymogens: Enzymes that are secreted in an inactive form and must be activated by specific proteolytic cleavage (e.g., digestive enzymes).