Comprehensive Study Notes on General Properties of Enzymes, Catalytic Mechanisms, and Kinetics

Fundamental Properties of Enzymes

• Definition: Enzymes are biological catalysts, which are primarily proteins (the majority) or RNA molecules (some, such as ribozymes) that catalyze specific chemical transformations and reactions.
• Etymology: The term originates from the Greek "en" "zyme," meaning "in yeast."
• Enzymology: This is the study of enzymes and represents the oldest subfield of biochemistry.
• Historical Discovery: The first protein enzyme discovered was Urease, isolated by James Sunner at Cornell University in 1926.
• Scope of Study: Enzymology focuses on mechanisms of action, kinetics (catalytic rates), and inhibition.
• Distinctions from Chemical Catalysts:     * Higher Reaction Rates: Enzymes can enhance reaction rates by factors of up to $10^{12}$.     * Milder Reaction Conditions: They operate at neutral pH, atmospheric pressure, and room temperature.     * Greater Reaction Specificity: They produce no unwanted byproducts.     * Capacity for Regulation: Activity is controlled through allosteric control, covalent modification, and regulation of enzyme expression levels.
• Catalytic Power Examples (Table 11-1):     * Carbonic Anhydrase: Nonenzymatic rate = $1.3 \times 10^{-1}\,s^{-1}$; Enzymatic rate = $1 \times 10^{6}\,s^{-1}$; Rate enhancement = $7.7 \times 10^{6}$.     * Chorismate Mutase: Nonenzymatic rate = $2.6 \times 10^{-5}\,s^{-1}$; Enzymatic rate = $50\,s^{-1}$; Rate enhancement = $1.9 \times 10^{6}$.     * Triose Phosphate Isomerase: Nonenzymatic rate = $4.3 \times 10^{-6}\,s^{-1}$; Enzymatic rate = $4300\,s^{-1}$; Rate enhancement = $1.0 \times 10^{9}$.     * Carboxypeptidase A: Nonenzymatic rate = $3.0 \times 10^{-9}\,s^{-1}$; Enzymatic rate = $578\,s^{-1}$; Rate enhancement = $1.9 \times 10^{11}$.     * AMP Nucleosidase: Nonenzymatic rate = $1.0 \times 10^{-11}\,s^{-1}$; Enzymatic rate = $60\,s^{-1}$; Rate enhancement = $6.0 \times 10^{12}$.     * Staphylococcal Nuclease: Nonenzymatic rate = $1.7 \times 10^{-13}\,s^{-1}$; Enzymatic rate = $95\,s^{-1}$; Rate enhancement = $5.6 \times 10^{14}$.     * Note on Spontaneous Rates: Without enzymes, C-O bond cleavage can take 320,000 years, and P-O bond cleavage can take 30 million years. Rate enhancement is calculated as: $\text{Enzyme Rate} \div \text{Non-enzyme Rate}$.

Enzyme Classification and Nomenclature

• General Classification (Table 11-2):     1. Oxidoreductases: Catalyze oxidation-reduction reactions; involve the transfer of electrons (often as hydride ions or H atoms) from a reductant to an oxidant.     2. Transferases: Catalyze the transfer of functional groups (e.g., methyl, phosphate, or amino groups) from a donor to an acceptor.     3. Hydrolases: Catalyze hydrolysis reactions; breaking bonds (C-O, C-N, C-S) via the addition of a water molecule.     4. Lyases: Catalyze nonhydrolytic bond cleavage (group elimination) to form double bonds.     5. Isomerases: Catalyze isomerization; rearranging atoms within a molecule to change structure without changing the empirical formula.     6. Ligases: Catalyze bond formation (joining two large molecules) coupled with ATP consumption.
• Enzyme Commission (EC) Numbers: A numerical classification system based on the format: EC class.subclass.subsubclass.serial_number.     * Example: EC 3.1.4.11:         * EC 3: Hydrolases         * EC 3.1: Acting on ester bonds         * EC 3.1.4: Phosphoric diester hydrolases         * EC 3.1.4.11: Phosphoinositide phospholipase C
• Hydrolase Subclasses (EC 3.x.x.x):     * EC 3.1: Ester bonds (phosphatases, nucleases).     * EC 3.2: Glycosylases (glycosidic bonds in carbohydrates).     * EC 3.3: Ether bonds.     * EC 3.4: Peptide (amide) bonds (peptidases).     * EC 3.5: Non-peptide carbon-nitrogen bonds.     * EC 3.6: Acid anhydrides (ATPases).     * EC 3.7: Carbon-carbon bonds.     * EC 3.8: Halide bonds.     * EC 3.9: Phosphorus-nitrogen bonds.     * EC 3.10: Sulfur-nitrogen bonds.     * EC 3.11: Carbon-phosphorus bonds.
• Information Systems: BRENDA (Comprehensive Enzyme Information System) and IUBMB provide rules and definitions for EC numbers.

Substrate Specificity and Enzyme Binding

• Active Site: The specific region or pocket in the enzyme molecule where substrate binding and catalysis occur.
• Specificity Determinants: Enzyme specificity is driven by geometric compatibility (shape) and electrostatic compatibility (charge).
• Binding Models:     * Lock-and-Key Model: Describes pre-formed active sites perfectly matched to the substrate.     * Induced Fit: Substrate binding induces a conformational change in the enzyme, leading to a better fit at the transition state.
• Stereospecificity: Interactions are often absolutely stereospecific for chiral reactions. Highly specific binding is guaranteed by multi-point (at least three) contact.     * Aconitase: Catalyzes the interconversion of citrate and isocitrate; it is stereospecific for a particular orientation of citrate.

Cofactors, Coenzymes, and Holoenzymes

• Role of Cofactors: Enzymes (proteins) alone are insufficient for redox, isomerization, or complex group transfers. Cofactors act as "helpers" to expand the range of enzymatic reactions. They are often chemically changed and must be regenerated.
• Categories of Cofactors:     * Inorganic Metal Ions: Such as $Zn^{2+}$, $Cu^{2+}$, $Mn^{2+}$, and $Fe^{3+}$.     * Organic Coenzymes:         * Cosubstrates: Transiently associated, they dissociate from the enzyme (e.g., $NAD^{+}$, $NADP^{+}$).         * Prosthetic Groups: Permanently associated with the enzyme (e.g., Heme).
• Electron Carriers: $NAD^{+}$ (oxidized) and $NADH$ (reduced) are intracellular carriers. They facilitate the transfer of a hydride ion and a proton. Example: Alcohol dehydrogenase (ADH) uses $NAD^{+}$ to oxidize ethanol to acetaldehyde.
• Enzyme States:     * Apoenzyme: The inactive protein portion without the cofactor.     * Holoenzyme: The active complex consisting of the apoenzyme plus the required cofactor.

Transition State Theory and Reaction Energetics

• Basics: Reactants and products exist at states of minimum free energy. As they react along the "reaction coordinate," they reach a maximum free energy state known as the Transition State ($X^{\ddagger}$).
• Transition State Properties: Passages are extremely fast ($10^{-13}\,s$) and concentrations are low. The highest point on a free energy diagram represents this state.
• Thermodynamics vs. Kinetics:     * Free Energy Charge ($\Delta G$): $\Delta G = \text{Free energy of products} - \text{Free energy of reactants}$. This determines spontaneity ($\Delta G < 0$ is spontaneous).     * Free Energy of Activation ($\Delta G^{\ddagger}$): $\Delta G^{\ddagger} = \text{Free energy of transition state} - \text{Free energy of reactants}$. This determines the reaction rate; larger values mean a slower reaction.
• Role of a Catalyst: An enzyme lowers $\Delta G^{\ddagger}$ by providing a different pathway with a lower-energy transition state. It does NOT alter the overall $\Delta G$ or the equilibrium of a reaction.
• Rate Enhancement Factor: An enzyme increases the rate by a factor of $e^{(\Delta \Delta G^{\ddagger})/RT}$, where $\Delta \Delta G^{\ddagger}$ is the reduction in activation energy.
• Multistep Reactions: In a reaction involving two or more steps, the step with the highest-energy transition state (tallest barrier) is the "rate-determining" or "rate-limiting" step.
• Intermediates vs. Transition States: Intermediates are local minima between transition states; transition states are local maxima.

Enzymatic Catalytic Mechanisms

• Mechanism Elucidation Techniques: Kinetic measurements and X-ray crystallography.
• The Five Mechanisms:     1. Acid-Base Catalysis: Protons are transferred from an acid on the enzyme to the substrate (general acid catalysis) or abstracted from the substrate by a base on the enzyme (general base catalysis). Common residues: Asp, Glu, His, Cys, Tyr, Lys (pKa values near physiological pH).         * Example: RNase A: A digestive enzyme hydrolyzing RNA. His12 acts as a general base to promote nucleophilic attack; His119 acts as a general acid to promote bond cleavage. Later, roles reverse to promote hydrolysis of the 2\',3\'-cyclic nucleotide intermediate.     2. Covalent Catalysis: Involves the transient formation of a covalent bond between the enzyme (nucleophile) and substrate (electrophile). Example: Formation of a Schiff Base (imine) by a deprotonated Lys side chain.     3. Metal Ion Catalysis: Used by 1/3 of enzymes (metalloenzymes). Metals orient substrates, mediate redox via oxidation state changes, shield negative charges, or make nucleophiles by kicking off protons.         * Example: Carbonic Anhydrase: Uses $Zn^{2+}$ to polarize water and facilitate the reaction $CO_2 + H_2O \rightleftharpoons HCO_3^{-} + H^{+}$.     4. Proximity and Orientation Effects: Enzymes bring reacting groups together and freeze rotational/translational motions to ensure proper alignment for catalysis.     5. Preferential Binding of the Transition State: The active site has a higher affinity for the transition state than the substrate, often involving additional hydrogen bonds or "straining" the substrate to fit. This significantly lowers activation energy.

Serine Proteases: Mechanism and Specificity

• Overview: Enzymes like chymotrypsin, trypsin, and elastase share ~40% sequence identity and a similar tertiary structure. They catalyze peptide bond hydrolysis.
• The Catalytic Triad: Consists of three critical residues: Asp102, His57, and Ser195.
• Specificity Pockets:     * Chymotrypsin: Cleaves after bulky, hydrophobic side chains (e.g., Phe). The pocket is wide and deep.     * Trypsin: Cleaves after positively charged side chains (Lys, Arg). Contains an Asp189 at the bottom to stabilize the charge.     * Elastase: Cleaves after small, neutral side chains (Ala, Val). The pocket is shallow due to bulky Val226 and Thr216 residues.
• Seven-Step Mechanism Summary:     1. Substrate binding.     2. General base catalysis (His side chain) and nucleophilic attack (Ser side chain) to form a tetrahedral intermediate.     3. General acid catalysis (His) aids breakdown of the tetrahedral intermediate into an acyl-enzyme intermediate and releases the amine product.     4. Amine product is replaced by water.     5. General base catalysis (His) and nucleophilic attack by water to form a second tetrahedral intermediate.     6. General acid catalysis (His) aids breakdown of the tetrahedral intermediate into the carboxyl product and active enzyme.     7. Release of carboxyl product.

Zymogens and the Coagulation Cascade

• Zymogens (Proenzymes): Inactive precursors of enzymes that must be cleaved to become active. This prevents self-digestion (proteolysis) in inappropriate locations.
• Pancreatic Zymogens: Trypsinogen is made in the pancreas and activated to Trypsin by enteropeptidase only in the small intestine.
• Blood Coagulation Cascade: A series of zymogen activations involving an intrinsic and extrinsic pathway to ensure rapid clotting and amplification. Major factors include Factor XIa, IXa, Xa, and Thrombin, which eventually converts Fibrinogen to cross-linked Fibrin.

Enzyme Kinetics: Michaelis-Menten and Reaction Orders

• Chemical Kinetics Definitions:     * Rate constant (k): Proportionality constant for reaction speed.     * Reaction velocity (v): Rate of appearance of product or disappearance of substrate.     * Reaction order: Molecularity (number of colliding molecules).
• First-Order Reaction: $v = k[A]$. Linear plot: $\ln[A] = \ln[A]<em>0 - kt$. Half-life ($t</em>{1/2}$) is constant: $t_{1/2} = \frac{0.693}{k}$.
• Second-Order Reaction: $v = k[A]^2$ or $v = k[A][B]$. Half-life depends on initial concentration: $t_{1/2} = \frac{1}{k[A]_0}$.
• Michaelis-Menten Equation:     * $E + S \rightleftharpoons ES \rightarrow E + P$     * $v_0 = \frac{V_{max} [S]}{K_M + [S]}$     * $V_{max}$: Maximum initial velocity when enzyme is saturated with substrate.     * $K_M$ (Michaelis Constant): Substrate concentration at which $v_0 = \frac{1}{2} V_{max}$. It measures enzyme affinity for substrate if $k_2 \ll k_1$.     * $k_{cat}$ (Turnover Number): Catalytic constant ($V_{max} / [E]<em>T$).     * Catalytic Efficiency: Defined as $k</em>{cat} / K_M$ ($M^{-1}s^{-1}$).
• Lineweaver-Burk Plot: A double-reciprocal plot ($1/v_0$ vs. $1/[S]$) used to linearize kinetic data and calculate $K_M$ and $V_{max}$.
• Bisubstrate Reactions: 60% of biochemical reactions (mostly group-transfer).     * Ordered Sequential: Substrate order matters.     * Random Sequential: Substrate order does not matter.     * Ping-Pong: One product is released before all substrates have bound; the two substrates never meet on the enzyme surface.

Enzyme Inhibition

• Inhibitors vs. Inactivators: Inhibitors reduce activity reversibly; Inactivators (irreversible inhibitors) bind covalently and permanently.
• Reversible Inhibition Types:     1. Competitive: Binds at the active site; competes with substrate. Increases apparent $K_M$; $V_{max}$ remains unchanged.     2. Uncompetitive: Binds only to the ES complex, distorting the active site. Decreases both apparent $K_M$ and $V_{max}$.     3. Mixed (Noncompetitive): Binds to both free E and ES complex.
• Inhibition Examples:     * Substrate Analogs: Methanol poisoning treatment using ethanol to compete for alcohol dehydrogenase.     * Transition-State Analogs: Highly potent because enzymes have highest affinity for the TS. Examples: adenosine deaminase inhibitor used for leukemia; Saquinavir and Ritonavir for HIV protease.

Drug Discovery and Development

• Methods:     * Combinatorial Chemistry: Rapid synthesis of large libraries and high-throughput screening to find a "hit."     * Structure-Based Design: Uses X-ray crystallography and modeling to optimize drug candidates for potency and bioavailability.
• Drug Pipeline:     * In Vitro/Animal/Organoid Models: Initial testing.     * Clinical Trials:         * Phase I: 20-100 healthy volunteers; tests safety and dosage.         * Phase II: 100-500 patients; single-blind tests for efficacy.         * Phase III: 1000-5000 patients; double-blind tests (neither patient nor investigator knows who gets the placebo) to reduce bias.
• Cytochrome P450: A family of >50 variants that metabolize 90% of medications, primarily in the liver. They often modify drugs to increase water solubility for excretion.     * Acetaminophen Toxicity: Metabolized to reactive acetimidoquinone. Usually quenched by glutathione, but high doses lead to protein conjugation and fatal hepatotoxicity.     * Pharmacogenomics: The study of how genetic variations in Cytochrome P450 affect individual drug responses; essential for personalized medicine.

Questions & Discussion

• Question: How long would it take to digest a fried breakfast without enzymes?     * Answer: Approximately 50 years.
• Question: Which amino acid is least likely to be a nucleophile in covalent catalysis?     * Answer: Phenylalanine (F), as it lacks available lone pairs or reactive hydroxyl/thiol/amine groups.
• Question: What is the factor for rate enhancement in enzymic reactions?     * Calculation: Enzyme rate divided by nonenzymatic rate.
• Quiz: A compound that distorts the substrate-occupied active site, rendering the enzyme catalytically inactive is an uncompetitive inhibitor.
• Quiz: Irreversible enzyme inhibitors inactivate the enzyme.