Module 6: Enzymes – Structure, Function, and Kinetics

Enzymes

Introduction

Enzymes are biological catalysts essential for life, enabling chemical reactions to occur efficiently and selectively under physiological conditions. Most biomolecules are stable and would not react at a rate compatible with life without enzymatic catalysis. Enzymes provide mechanisms for acceleration, regulation, and coordination of biochemical reactions, with remarkable catalytic power and specificity. Some enzymes also serve as information sensors and catalysts, ensuring that side reactions leading to harmful products are avoided.

• Catalytic Power: Enzymes can increase reaction rates by factors of 106 or more compared to uncatalyzed reactions.

• Specificity: Enzymes are highly specific for their substrates and the reactions they catalyze.

Vitalism

Historically, biochemical reactions were believed to be inseparable from life (vitalism). Eduard Buchner's experiments with dead yeast converting sugars to alcohol demonstrated that enzymes, not 'life force,' catalyze biochemical reactions. The term 'enzyme' is derived from the Greek for 'in yeast.'

Co-Enzymes and Co-Factors

Many enzymes require additional non-protein components for activity:

• Co-factors: Inorganic ions (e.g., Mg2+, Fe2+).

• Co-enzymes: Complex organic molecules (often derived from vitamins).

• Prosthetic group: A co-enzyme or co-factor tightly associated with the enzyme.

• Holoenzyme: The active enzyme with its co-factor/co-enzyme.

• Apoenzyme: The protein component without its co-factor/co-enzyme.

Equation: Apoenzyme + Co-factor/Co-enzyme = Holoenzyme

Catalysts

General Properties

• Lower the activation energy required for a reaction to proceed.

• Speed up attainment of equilibrium but do not change the equilibrium position.

• Are unchanged by the reaction and can be reused.

The catalytic power of enzymes is demonstrated by the rate enhancements they provide compared to uncatalyzed reactions.

Enzymes vs Chemical Catalysts

• Speed: Enzymes are often much faster, sometimes approaching catalytic perfection.

• Conditions: Enzymes function under mild physiological conditions, unlike many chemical catalysts that require extreme conditions.

• Specificity: Enzymes exhibit high specificity, including stereospecificity, for their substrates and products.

• Regulation: Enzyme activity is regulated according to cellular needs, unlike most chemical catalysts.

Circe Effect

Some enzymes catalyze reactions at rates limited only by the diffusion of substrates to the enzyme. This phenomenon, where enzymes attract and bind substrates efficiently, is called the Circe effect.

Enzyme Mechanism

Equilibrium and ES Complex

Enzymes catalyze the interconversion of substrate (S) and product (P) via the enzyme-substrate (ES) complex:

$E + S \leftrightarrow ES \leftrightarrow E + P$

• Substrate (S): Molecule acted upon by the enzyme.

• Product (P): Molecule produced by the enzyme.

• Active Site: Region of the enzyme responsible for substrate binding and catalysis.

The Active Site

• 3D cleft formed from different parts of the polypeptide chain.

• Represents a small part of the enzyme but is crucial for function.

• Unique microenvironment for substrate binding via multiple weak interactions.

• Specificity depends on the arrangement of groups within the active site.

• Active sites can be flexible, allowing for induced fit or conformation selection.

Lock-and-Key vs Hand-in-Glove (Induced Fit)

• Lock-and-Key: Substrate fits exactly into the active site.

• Hand-in-Glove (Induced Fit): Active site molds around the substrate upon binding.

Thermodynamics and Kinetics

Free Energy (Rates and Equilibrium)

• Spontaneous Reaction: $\Delta G$ is negative (exergonic).

• Non-spontaneous Reaction: $\Delta G$ is positive (endergonic).

• At equilibrium, $\Delta G = 0$ and concentrations of products and reactants do not change.

• $\Delta G$ depends only on the difference in free energy between products and reactants, not on the reaction pathway.

• $\Delta G$ provides no information about reaction rate.

Activation Energy and Rate Enhancement

• Activation Energy ($\Delta G^{\ddagger}$): Energy barrier between substrate and product; determines reaction rate.

• Enzymes lower $\Delta G^{\ddagger}$, providing an alternate, lower-energy pathway.

• Enzymes do not affect the equilibrium position ($\Delta G$ for the reaction).

Modes of Enzyme Catalysis

Binding Effects

• Substrate Binding: Promotes reaction by reducing entropy, aligning reactive groups, desolvating substrate, distorting substrate, and inducing fit.

• Transition-State Stabilization: Enzyme binds the transition state more tightly than the substrate, stabilizing it and lowering activation energy.

Chemical Effects

• Acid/Base Catalysis: Catalytic transfer of protons; side chains act as acids/bases (e.g., His, Asp, Glu).

• Covalent Catalysis: Substrate forms a transient covalent bond with the enzyme, creating a reactive intermediate.

Transition-State Analogs and Competitive Inhibitors

• Transition-State Analogs (TSAs): Stable compounds resembling the transition state; act as competitive inhibitors by binding the active site with high affinity.

• Competitive Inhibitors: Molecules that compete with substrate for active site binding.

Enzyme Kinetics

General Concepts

• Kinetics is the study of reaction velocity.

• Velocity ($V$) is the change in product concentration over time: $V = \frac{\Delta [P]}{\Delta t}$

• Enzyme activity is sensitive to temperature, pH, and enzyme concentration.

Initial Velocity ($V_0$)

• Measured at the start of the reaction, before product accumulation.

• Depends on rapid, non-covalent interactions between enzyme and substrate.

• $V_0 = [ES]k_2$

Michaelis-Menten Equation and Plot

• Describes the relationship between substrate concentration and initial velocity:

$V_0 = \frac{V_{max}[S]}{K_m + [S]}$

• $K_m$: Substrate concentration at which velocity is half-maximal.

• $V_{max}$: Maximum velocity of the enzyme.

Steady State Assumption

• Assumes the rate of formation of the ES complex equals its breakdown.

• Mathematically: $[E][S]k_1 = [ES]k_{-1} + [ES]k_2$

Interpretation of $K_m$

• When $[S] < K_m$, enzyme is sensitive to substrate changes but has low activity.

• When $[S] > K_m$, enzyme has high activity but is insensitive to substrate changes.

• When $[S] = K_m$, enzyme is responsive and has significant activity.

Lineweaver-Burk Plots

• Double-reciprocal plot of $1/V_0$ vs $1/[S]$ for precise determination of $V_{max}$ and $K_m$.

$\frac{1}{V_0} = \frac{K_m}{V_{max}[S]} + \frac{1}{V_{max}}$

Enzyme Turnover Number ($k_{cat}$)

• Number of substrate molecules converted to product per enzyme molecule per unit time under saturating conditions.

• Calculated as $V_{max}/[E_t]$

Reversible Enzyme Inhibition

General

• Inhibitors bind to enzymes and interfere with activity.

• Reversible inhibitors bind non-covalently and can be classified as:

  • Competitive: Bind to free enzyme, compete with substrate.

  • Uncompetitive: Bind only to ES complex.

  • Noncompetitive: Bind to both E and ES complex.

Type	Binding	Kinetic Consequence
Competitive	E only	Increases $K_m$, $V_{max}$ unchanged
Uncompetitive	ES only	Decreases $K_m$ and $V_{max}$
Noncompetitive	E and ES	$K_m$ unchanged, $V_{max}$ decreased

Serine Proteases

General Properties

• Serine proteases are a family of enzymes that cleave peptide bonds in proteins.

• They share a conserved catalytic mechanism involving a catalytic triad (Ser, His, Asp).

Substrate Specificities

• Chymotrypsin cleaves after aromatic residues (Phe, Tyr, Trp).

• Trypsin and thrombin have different specificities based on their active site structure.

Catalytic Triad and Mechanism

• Serine acts as a nucleophile, His as a general acid/base, and Asp stabilizes His.

• The mechanism involves two phases: acylation (formation of covalent intermediate) and deacylation (hydrolysis of intermediate).

Regulation of Enzyme Activity

Overview

• Enzyme activity can be regulated by controlling enzyme amount (synthesis/degradation) or by modulating activity (covalent or non-covalent modification).

• Regulation often occurs at the first committed step of a pathway (feedback inhibition).

Allosteric Enzymes

• Allosteric enzymes are regulated by effectors binding at sites other than the active site.

• They often catalyze branch-point reactions and display sigmoidal kinetics (cooperativity).

• Allosteric modulators can be activators or inhibitors.

Enzyme Regulation by Covalent Modification

• Common modifications include phosphorylation, methylation, and glycosylation.

• Phosphorylation is reversible and regulates enzyme activity (kinases add, phosphatases remove phosphate groups).

Glycogen Metabolism Example

• Glycogen synthase (anabolic) and glycogen phosphorylase (catabolic) are regulated by phosphorylation in response to hormones (e.g., insulin, glucagon, epinephrine).

• Phosphorylation activates the catabolic enzyme and inactivates the anabolic enzyme, favoring glycogen breakdown.

• Dephosphorylation has the opposite effect, favoring glycogen synthesis.