Enzymes: Catalysis, Specificity, and Regulation for Life

Enzymes: Function, Catalysis, and Regulation

Introduction to Enzymes

• At any given moment, thousands of chemical reactions are occurring within every living cell.

• Enzymes are crucial for these reactions and their pathways to proceed at rates rapid enough to sustain life.

Characteristics of Enzymes

• Differences from Ordinary Chemical Catalysts: Enzymes distinguish themselves from ordinary chemical catalysts in four key aspects:

  1. Reaction Rate: Enzymes dramatically accelerate reaction rates.

  2. Reaction Conditions: Enzymes function optimally under mild physiological conditions (temperature, pH).

  3. Reaction Specificity: Enzymes exhibit high specificity for their substrates and the reactions they catalyze.

  4. Regulation: Enzyme activity is tightly regulated within cells.

• Active Site Properties: The unique physical and chemical properties of an enzyme's active site are responsible for limiting its activity to specific substrates and reactions.

• Cofactor Requirements: Some enzymes necessitate the presence of metal ions or organic cofactors for their activity.

• Thermodynamics and Kinetics: Enzymes catalyze thermodynamically favorable reactions and cause them to proceed at extraordinarily rapid rates.

  • Therefore, enzymes enable cells to exert kinetic control over thermodynamic potentiality.

  • Example: The stability of glucose versus its breakdown via glycolysis. Although glucose is thermodynamically unstable, it remains stable for centuries without enzymes.

• Kinetic Control: The term "kinetic" specifically describes reaction rates, not thermodynamic properties like free energy.

• Living systems employ enzymes to accelerate and control the rates of vital biochemical reactions, such as those involved in metabolism.

Protein Motions and Enzyme Catalysis

• Dynamic Nature of Proteins: Proteins are not static; they are in constant motion. This includes:

  • Bonds vibrating.

  • Side chains bending and rotating.

  • Backbone loops wiggling and swaying.

  • Whole domains moving as a unit.

• Role of Motions in Catalysis: Enzymes rely on these intrinsic protein motions to initiate and direct catalytic events.

• Support for Catalysis: Protein motions contribute to catalysis in several ways, often involving active site conformational changes:

  1. Assist Substrate Binding: Conformational changes can facilitate and optimize the binding of the substrate.

  2. Bring Catalytic Groups into Position: Movements ensure that the correct catalytic amino acid residues or cofactors are precisely positioned for the reaction.

  3. Assist in Bond Making and Bond Breaking: Dynamic changes can physically aid in the formation or cleavage of chemical bonds.

  4. Facilitate Conversion of Substrate to Product: Motions help guide the substrate through the transition state and release the product.

Enzymes as Agents of Metabolic Function

• Glycolysis Example: The 10-step enzymatic pathway for glucose breakdown, known as glycolysis, serves as a prime illustration of the indispensable role of enzymes in metabolic pathways.

• Importance: Without these enzymes, glucose would remain unchanged indefinitely, demonstrating their critical role in driving metabolic processes.

Catalytic Power of Enzymes

• Magnitude of Acceleration: Enzymes can accelerate reaction rates by as much as $10^{21}$ times compared to uncatalyzed reactions.

• Urease Example: Urease provides a striking example of catalytic power:

  • Catalyzed Rate: $3 imes 10^4 ext{ sec}^{-1}$

  • Uncatalyzed Rate: $3 imes 10^{-10} ext{ sec}^{-1}$

  • Catalytic Power Ratio: $(3 imes 10^4) / (3 imes 10^{-10}) = 1 imes 10^{14}$

• Table 11-1: Catalytic Power of Some Enzymes:

  • Enzyme: Carbonic anhydrase

    • Nonenzymatic Reaction Rate ($ext{s}^{-1}$): $1.3 imes 10^{-1}$

    • Enzymatic Reaction Rate ($ext{s}^{-1}$): $1 imes 10^6$

    • Rate Enhancement: $7.7 imes 10^6$

  • Enzyme: Chorismate mutase

    • Nonenzymatic Reaction Rate ($ext{s}^{-1}$): $2.6 imes 10^{-5}$

    • Enzymatic Reaction Rate ($ext{s}^{-1}$): $50$

    • Rate Enhancement: $1.9 imes 10^6$

  • Enzyme: Triose phosphate isomerase

    • Nonenzymatic Reaction Rate ($ext{s}^{-1}$): $4.3 imes 10^{-6}$

    • Enzymatic Reaction Rate ($ext{s}^{-1}$): $4300$

    • Rate Enhancement: $1.0 imes 10^9$

  • Enzyme: Carboxypeptidase A

    • Nonenzymatic Reaction Rate ($ext{s}^{-1}$): $3.0 imes 10^{-9}$

    • Enzymatic Reaction Rate ($ext{s}^{-1}$): $578$

    • Rate Enhancement: $1.9 imes 10^{11}$

  • Enzyme: AMP nucleosidase

    • Nonenzymatic Reaction Rate ($ext{s}^{-1}$): $1.0 imes 10^{-11}$

    • Enzymatic Reaction Rate ($ext{s}^{-1}$): $60$

    • Rate Enhancement: $6.0 imes 10^{12}$

  • Enzyme: Staphylococcal nuclease

    • Nonenzymatic Reaction Rate ($ext{s}^{-1}$): $1.7 imes 10^{-13}$

    • Enzymatic Reaction Rate ($ext{s}^{-1}$): $95$

    • Rate Enhancement: $5.6 imes 10^{14}$

Enzyme Classifications (Know 1-6)

1. Oxidation-reduction (Redox) Reactions: Enzymes in this class catalyze reactions where the oxidation numbers (oxidation states) of atoms are changed. These involve the transfer of electrons.

2. Transfer of Functional Groups: These enzymes facilitate the transfer of a functional group (e.g., a methyl or phosphate group) from one molecule (the donor) to another (the acceptor).

3. Hydrolysis: Hydrolases catalyze the decomposition of a chemical compound by reaction with water. Hydrolysis reactions break down various polymers, including proteins, carbohydrates, fats, and nucleic acids.

4. Lyases: Lyases catalyze the breaking of various chemical bonds by means other than hydrolysis and oxidation, often resulting in the formation of a new double bond.

5. Isomerization: Isomerases catalyze the structural rearrangement of isomers (molecules with the same molecular weight but different structural formulas).

6. Ligases: Ligases catalyze the joining of two large molecules by forming a new chemical bond, typically coupled with ATP hydrolysis.

Enzyme Specificity

• Substrate Specificity: Enzymes act on specific substrates, and this specificity is primarily determined by precise interactions at the active site.

• Induced Fit Model (Hexokinase Example): The binding of a substrate, like glucose, in the active site of an enzyme, such as hexokinase, induces a conformational change. This change causes the enzyme's domains to close around the substrate, effectively creating the catalytic site and ensuring specificity and efficiency.

• Stereospecificity: Many enzymes exhibit exquisite stereospecificity, meaning they can distinguish between stereoisomers and act only on a specific one.

• Aconitase Example: Aconitase catalyzes the highly stereospecific conversion of citrate to isocitrate, transforming a prochiral molecule at a specific carbon.

  • $ext{Citrate (COO}^- ext{| CH}_2 ext{COO}^- ext{| HO-C-COO}^- ) <br>ightarrow ext{Isocitrate (COO}^- ext{| CH-COO}^- | ext{ HO-C-H | COO}^- )$

Cofactors: Essential Non-protein Components

• Definition: Cofactors are non-protein chemical components essential for enzyme activity.

• Functional Groups in Proteins: While protein functional groups themselves facilitate many catalytic mechanisms (acid-base reactions, transient covalent bonds, charge-charge interactions), many enzymes require additional components.

• Types of Cofactors:

  1. Metal Ions: Inorganic ions that often participate in redox reactions, stabilize transient structures, or play structural roles.

  2. Coenzymes: Organic molecules that typically serve as transient carriers of specific atoms or functional groups.

     • Transiently Associated: Some coenzymes transiently associate with the enzyme, functioning almost like a second substrate.

     • Permanently Attached (Prosthetic Group): Others are permanently (often covalently) attached to the enzyme.

• Table 13.2: Enzyme Cofactors Examples:

  • Metal Ions and Enzymes that Require Them:

    • $ext{Fe}^{2+}$ or $ext{Fe}^{3+}$: Cytochrome oxidase, Catalase, Peroxidase

    • $ext{Cu}^{2+}$: Cytochrome oxidase

    • $ext{Zn}^{2+}$: DNA polymerase, Carbonic anhydrase, Alcohol dehydrogenase

    • $ext{Mg}^{2+}$: Hexokinase, Glucose-6-phosphatase, Pyruvate kinase (also requires $ext{Mg}^{2+}$)

    • $ext{Mn}^{2+}$: Arginase

    • $ext{K}^{+}$: Pyruvate kinase

    • $ext{Ni}^{2+}$: Urease

    • Mo: Nitrate reductase

    • Se: Glutathione peroxidase

  • Coenzymes Serving as Transient Carriers of Specific Atoms or Functional Groups:

    • Coenzyme: Thiamine pyrophosphate (TPP)

      • Entity Transferred: Aldehydes

      • Representative Enzyme: Pyruvate dehydrogenase

    • Coenzyme: Flavin adenine dinucleotide (FAD)

      • Entity Transferred: Hydrogen atoms

      • Representative Enzyme: Succinate dehydrogenase

    • Coenzyme: Nicotinamide adenine dinucleotide ($ext{NAD}^{+}$)

      • Entity Transferred: Hydride ion ($ext{:H}^-$)

      • Representative Enzyme: Alcohol dehydrogenase

    • Coenzyme: Coenzyme A (CoA)

      • Entity Transferred: Acyl groups

      • Representative Enzyme: Acetyl-CoA carboxylase

    • Coenzyme: Pyridoxal phosphate (PLP)

      • Entity Transferred: Amino groups

      • Representative Enzyme: Aspartate aminotransferase

    • Coenzyme: 5'-Deoxyadenosylcobalamin (vitamin $ext{B}_{12}$)

      • Entity Transferred: H atoms and alkyl groups

      • Representative Enzyme: Methylmalonyl-CoA mutase

    • Coenzyme: Biotin (biocytin)

      • Entity Transferred: $ext{CO}_2$

      • Representative Enzyme: Propionyl-CoA carboxylase

    • Coenzyme: Tetrahydrofolate (THF)

      • Entity Transferred: Other one-carbon groups (e.g., formyl, methyl)

      • Representative Enzyme: Thymidylate synthase

More Nomenclature: Apoenzymes and Holoenzymes

• Holoenzyme: A complete, catalytically active enzyme consisting of both the protein part and its essential cofactor complex.

• Apoenzyme: The inactive protein component of an enzyme, lacking its necessary cofactor.

• Coenzyme Regeneration: Coenzymes must be regenerated for the completion of a catalytic cycle.

  • Cosubstrates: Coenzymes that transiently bind to the enzyme (like $ext{NAD}^+$). Their regeneration may be catalyzed by a different enzyme in the overall metabolic pathway.

  • Prosthetic Groups: Coenzymes that are permanently bound to the enzyme. Their regeneration typically occurs as an integral part of the enzyme's own reaction sequence.

Cofactors in Oxidation-Reduction Reactions (Example: ADH)

• Alcohol Dehydrogenase (ADH): This enzyme uses $ext{NAD}^+$ as a cofactor in the oxidation of ethanol to acetaldehyde.

  • $ext{CH}<em>3 ext{CH}</em>2 ext{OH} ext{ (Ethanol)} + ext{NAD}^+ <br>ightarrow ext{CH}_3 ext{CHO} ext{ (Acetaldehyde)} + ext{NADH} + ext{H}^+$

• Structure & Reaction of NAD(P)$^+$: Nicotinamide adenine dinucleotide ($ext{NAD}^+$) and its phosphorylated form, nicotinamide adenine dinucleotide phosphate ($ext{NADP}^+$), are critical cofactors used by oxidoreductases in metabolism. They undergo reversible oxidation-reduction, typically accepting or donating a hydride ion ($ext{:H}^-$).

  • The nicotinamide ring is the redox-active part.

  • Oxidized form includes $ext{NAD}^+$ with a positive charge.

  • Reduced form includes $ext{NADH}$ (or $ext{NADPH}$) with an additional proton ($ext{H}^+$) released into the solution.

Activation of Enzymatic Activity by Proteolysis

• Zymogens (Proenzymes): These are inactive precursor forms of enzymes.

• Proteolytic Cleavage: Activation of zymogens typically occurs through specific proteolytic cleavage (hydrolysis of a peptide bond), converting the inactive precursor into the active enzyme.

• Chymotrypsinogen Example: The digestive enzyme chymotrypsin is synthesized as the inactive zymogen chymotrypsinogen, which is then activated by cleavage.

Review of Characteristic Features that Define Enzymes

1. Enzyme Catalytic Power: Defined as the ratio of the enzyme-catalyzed rate of a reaction to the uncatalyzed rate, demonstrating their profound ability to speed up reactions.

2. Enzyme Specificity: The term used to define the selectivity of enzymes for their substrates, ensuring that specific reactions occur without unwanted side reactions.

3. Enzyme Regulation: The control mechanisms that ensure the rate of metabolic reactions is appropriate to cellular requirements (e.g., activation of inactive zymogens by proteolytic cleavage).

4. Enzyme Classification: A systematic nomenclature system that provides a standardized way of naming and categorizing metabolic reactions (e.g., Oxidoreductases, Transferases).

5. Enzyme Coenzymes and Cofactors: Nonprotein components that are essential to enzyme activity, including metal ions and organic molecules.

Activation Energy and Reaction Coordinate

• Lowering Activation Energy ($oldsymbol{oldsymbol{ ext{ ext{ ext{ ext{∆G}^ ext{ ext{#$}} }}}$): An enzyme provides a lower-energy pathway from substrate to product. It reduces the activation energy barrier for the reaction.

• No Effect on Overall Free Energy Change ($oldsymbol{oldsymbol{ ext{ ext{$ext{ ext{∆G}}$}}$): Enzymes do NOT affect the overall free energy change for the reaction, $ext{∆G}$. This is because $ext{∆G}$ describes only the difference in free energy between the products and reactants, which is a state function and path-independent.

  • $ext{∆G} = ext{G}<em>{ ext{products}} - ext{G}</em>{ ext{reactants}}$

Mechanisms of Enzyme-Induced Rate Accelerations

• Superior Catalysts: Enzymes are significantly more powerful catalysts than chemical catalysts, achieving rate accelerations of $10^7$ to $10^{15}$.

• Free Energy of Activation: These large rate accelerations correspond to large changes in the free energy of activation for the reaction, ext{∆G}^ ext{ ext{#}} (which is not a state function).

• Transition State: All reactions proceed through a transition state ( ext{X}^ ext{ ext{#}}) on the reaction pathway.

• Preferential Transition State Binding: The active sites of enzymes bind the transition state of the reaction more tightly than they bind the initial substrate.

• Stabilization: By binding the transition state more tightly, the enzyme stabilizes the transition state and effectively lowers the activation energy of the reaction.

• Binding Enhancement: This enhanced binding is achieved through the optimization of weak, non-covalent interactions (e.g., hydrogen bonds, van der Waals forces, ionic interactions), and sometimes through transient covalent interactions.

Transition State and the Reaction Coordinate

• Activation Energy ($oldsymbol{oldsymbol{ ext{ ext{ ext{ ext{∆G}^ ext{ ext{#$}} }}}$): In a reaction coordinate diagram, ext{∆G}^ ext{ ext{#}} represents the activation energy.

• Transition State ($oldsymbol{oldsymbol{ ext{ ext{X}^ ext{ ext{#}}}}}}$): ext{X}^ ext{ ext{#}} denotes the transition state, the highest energy point on the reaction pathway between reactants and products.

• Reaction Profile: The diagram illustrates reactants $ext{A + B}$ progressing to products $ext{P + Q}$ via the transition state ext{X}^ ext{ ext{#}}, with ext{∆G}^ ext{ ext{#}} being the energy barrier and $ext{∆G}_{ ext{reaction}}$ the overall free energy change.

Transition-State Theory

• Energy Profile: A typical enzyme-catalyzed reaction must pass through a transition state, which sits at the apex (top of the hill) of the energy profile in the energy diagram.

• Reaction Rate Proportionality: The reaction rate is directly proportional to the concentration of reactant molecules that have sufficient energy to reach the transition-state energy.

• Free Energy of Activation ($oldsymbol{oldsymbol{ ext{ ext{ ext{ ext{∆G}^ ext{ ext{#$}} }}}$): This energy barrier is formally known as the free energy of activation.

• Rate-Limiting Factor: A higher ext{∆G}^ ext{ ext{#}} signifies a slower reaction; conversely, decreasing ext{∆G}^ ext{ ext{#}} increases the reaction rate, speeding up the reaction.

• Relationship to Rate Constant: The activation energy ext{∆G}^ ext{ ext{#}} is related to the rate constant (k) by the Arrhenius equation (or Eyring equation derivation, which specifically relates to ext{∆G}^ ext{ ext{#}}):

  • k = ( rac{k_{ ext{B}}T}{h})e^{- ext{∆G}^ ext{ ext{#}}/RT}

  • Where $k_{ ext{B}}$ is the Boltzmann constant, $T$ is temperature, $h$ is Planck's constant, and $R$ is the gas constant.

Transition State Free Energy: Comparison of $ext{∆G}$ and ext{∆G}^ ext{ ext{#}}

• Thermodynamics ($oldsymbol{oldsymbol{ ext{ ext{$ext{ ext{∆G}}$}}$): The overall free energy change for a reaction, $ext{∆G}$, is a state function. It is related to the equilibrium constant, $ext{K}<em>{ ext{eq}}$ ($ext{∆G} = -RT ext{ln K}</em>{ ext{eq}}$).

• Kinetics ($oldsymbol{oldsymbol{ ext{ ext{ ext{ ext{∆G}^ ext{ ext{#$}} }}}$): The free energy of activation for a reaction, ext{∆G}^ ext{ ext{#}}, is related to the rate constant, k. It is NOT a state function; it describes the energy barrier to reaction.

• Crucial Distinction: It is essential to appreciate this fundamental difference between $ext{∆G}$ and ext{∆G}^ ext{ ext{#}}.

Transition State Diagram: Effect of an Enzyme

• Enzyme's Role: Enzymes lower the ext{∆G}^ ext{ ext{#}}, thereby accelerating the reaction rate.

• Graphical Representation: A reaction profile diagram for an uncatalyzed reaction shows a large free energy of activation ($ ext{∆G}^ ext{ ext{#}}$). The presence of an enzyme creates a new, lower-energy pathway, significantly reducing this activation barrier.</p></li></ul><h4 id="c05aa042-9d7c-478b-95f1-a2684a653542" data-toc-id="c05aa042-9d7c-478b-95f1-a2684a653542" collapsed="false" seolevelmigrated="true">Transition-State Stabilization in Enzyme Catalysis</h4><ul><li><p><strong>Catalytic Role</strong>: The primary catalytic role of an enzyme is to reduce the energy barrier between the substrate (<strong>S</strong>) and the transition state ($ ext{X}^ ext{ ext{#}}).

• Rate Acceleration Mechanism: For an enzyme to accelerate a reaction, the energy barrier between the enzyme-substrate complex ($ ext{ES}$) and the enzyme-transition state complex( ext{EX}^ ext{ ext{#}}) must be smaller than the barrier between the unbound substrate ($ ext{S}$) and the unbound transition state ($ ext{X}^ ext{ ext{#}}).

• Differential Stabilization: This implies that the enzyme must stabilize the ext{EX}^ ext{ ext{#}} transition state more significantly than it stabilizes the initial $ext{ES}$ complex.

Competing Effects Determine the Position of ES on the Energy Scale

• Favorable Substrate Binding: The binding of the substrate (S) to the enzyme (E) to form the $ext{ES}$ complex must be favorable (e.g., negative $ext{∆G}_{ ext{binding}}$).

• Avoid Too-Tight Binding: However, binding cannot be "too tight." If the $ext{ES}$ complex is excessively stable, it would increase the energy required to reach the transition state relative to the $ext{ES}$ complex, making the energy barrier between $ext{ES}$ and ext{EX}^ ext{ ext{#}} larger. The goal is to make this barrier small.

Raising the Energy of ES Speeds the Rate

• Principle: For a given energy level of the enzyme-transition state complex ($ ext{EX}^ ext{ ext{#}}), raising the starting energy of the enzyme-substrate complex ($ ext{ES}$) to a more positive ext{∆G}$will effectively increase the catalyzed reaction rate (by making the$ ext{ES}
  ightarrow ext{EX}^ ext{ ext{#}}$energy gap smaller).</p></li><li><p><strong>Mechanisms for Destabilizing ES</strong>: This destabilization of the$ ext{ES}$complex is accomplished by:</p><ul><li><p><strong>Loss of Entropy</strong>: The formation of the$ ext{ES}$complex results in a loss of entropy. The$ ext{ES}$complex is a more highly ordered, low-entropy state for the substrate compared to a free, solvated substrate. This entropic penalty diminishes the favorability of initial binding slightly.</p></li><li><p><strong>Destabilization of ES Complex</strong>: This can occur through:</p><ul><li><p><strong>Desolvation</strong>: Substrates typically lose favorable interactions with water molecules (waters of hydration) upon binding to the enzyme's active site. This desolvation raises the energy of the$ ext{ES}$complex, making it more reactive.</p></li><li><p><strong>Strain/Distortion</strong>: The enzyme can induce physical strain or distortion in the substrate upon binding, pushing it towards a conformation resembling the transition state. This effectively raises the energy of the$ ext{ES}$complex.</p></li><li><p><strong>Electrostatic Destabilization</strong>: The juxtaposition of like charges in the active site can electrostatically destabilize the$ ext{ES}$complex. If this charge repulsion is relieved in the transition state (e.g., by charge neutralization), then electrostatic destabilization can result in a significant rate increase.</p></li></ul></li></ul></li></ul><h4 id="d93a602d-215a-4b0b-8505-fdea5e351479" data-toc-id="d93a602d-215a-4b0b-8505-fdea5e351479" collapsed="false" seolevelmigrated="true">Transition-State Analogs: Impact on Drug Design</h4><ul><li><p><strong>Enzymes as Drug Targets</strong>: Enzymes are frequently targeted by pharmaceutical drugs and other beneficial chemical agents due to their central roles in biological processes.</p></li><li><p><strong>Ideal Enzyme Inhibitors</strong>: Transition-state analogs are often ideal enzyme inhibitors because they bind very tightly to the active site, mimicking the high-energy transition state complex, which the enzyme is designed to stabilize.</p></li><li><p><strong>Examples of Transition-State Analogs as Drugs</strong>:</p><ul><li><p><strong>Enalapril and Aliskiren</strong>: These drugs are designed to lower blood pressure by inhibiting enzymes involved in the renin-angiotensin system.</p></li><li><p><strong>Statins</strong>: A class of drugs that lower serum cholesterol by inhibiting HMG-CoA reductase, a key enzyme in cholesterol biosynthesis.</p></li><li><p><strong>Protease Inhibitors</strong>: Crucial AIDS drugs that inhibit proteases essential for viral replication.</p></li><li><p><strong>Juvenile (insect) Hormone Esterase Inhibitors</strong>: A target for developing new pesticides.</p></li><li><p><strong>Tamiflu</strong>: An antiviral drug that acts as a viral neuraminidase inhibitor, preventing the release of new influenza virions from host cells.</p></li></ul></li><li><p><strong>Genomic Context</strong>: The human genome contains approximately$20,000$genes, many of which encode enzymes. A significant number of these enzymes represent potential targets for drug therapy.</p></li><li><p><strong>Future of Drug Discovery</strong>: More than$3,000$$ experimental drugs are currently under study and testing. Many future drugs will likely be designed as transition-state analog inhibitors, leveraging the principle of transition state stabilization for therapeutic benefit (e.g., through resources like DrugBank).