Comprehensive Study Guide to Enzyme Kinetics and Biochemistry

Fundamentals of Enzymes and Ribozymes

• Definition of Enzymes:

  • Enzymes are macromolecular biological components composed of proteins.
  • They serve as biological catalysts responsible for supporting almost all of the chemical reactions that maintain life processes.

• Specificity and Stereospecificity:

  • Enzymes exhibit a high degree of specificity for the specific types of reactions catalyzed as well as for their specific substrates.
  • They function as stereospecific catalysts, acting on specific stereoisomers (such as $\text{L}$ and $\text{D}$ forms).

• Ribozymes:

  • While almost all enzymes are proteins, ribozymes represent a major exception where specific $\text{RNA}$ molecules function as catalysts.
  • Ribozymes catalyze the cleavage and synthesis of phosphodiester bonds in $\text{RNA}$ at specific sequence sites.

Classification, Composition, and Cofactors of Enzymes

• Structural Categories:

  • Simple Enzymes: Composed completely of protein.
  • Complex Enzymes (Holoenzymes): Composed of a protein component plus a relatively small non-protein organic or inorganic molecule.

• Components of Holoenzymes:

  • Apoenzyme: The protein component of a complex enzyme, which is catalytically inactive on its own.
  • Cofactor: A non-protein component required to convert an apoenzyme into an active holoenzyme.
  • Assembly Equilibrium:     $\text{Apoenzyme} + \text{Cofactor} \rightarrow \text{Holoenzyme}$

• Types of Cofactors:
  • Inorganic Cofactors (Metal Ions):
  • Include inorganic metal ions such as $\text{Mg}^{2+}$, $\text{Zn}^{2+}$, $\text{Cu}^{2+}$, $\text{Mn}^{2+}$, and $\text{Fe}^{2+}$ or $\text{Fe}^{3+}$.
  • Function by bridging the enzyme and substrate together or combining directly with the protein structure to serve as a catalyst.
  • Organic Cofactors:
  • Prosthetic Groups: Organic cofactors that are tightly or covalently bound to an enzyme (e.g., flavin and heme).
  • Coenzymes: Non-protein organic complexes bound non-covalently to the apoenzyme. They bind apoenzyme protein molecules to produce active holoenzymes and are released from the enzyme's active site during the chemical reaction.

Enzyme Nomenclature and Functional Classes (I.U.B. System)

Enzymes are organized into six primary functional classes established by the International Union of Biochemists (I.U.B.):

• Class 1: Oxidoreductases:

  • Catalyze all oxidoreduction reactions.
  • The substrate undergoing oxidation is regarded as the hydrogen donor.
  • Act on various chemical groupings to add or remove hydrogen atoms.
  • Common names include dehydrogenase and reductase. The term oxidase is exclusively used in cases where oxygen ($\text{O}_2$) serves as the acceptor.

• Class 2: Transferases:

  • Transfer chemical groups from one molecule to another, or to another region of the same molecule.
  • Specialized transferases known as kinases regulate metabolic pathways by transferring phosphate groups from $\text{ATP}$ to target molecules.

• Class 3: Hydrolases:

  • Catalyze hydrolytic cleavage of $\text{C-O}$, $\text{C-N}$, $\text{C-C}$, and other bonds by adding water across a bond.
  • Systematic names always include the term hydrolase (e.g., digestive enzymes).

• Class 4: Lyases:

  • Remove functional groups from double bonds or add groups across double bonds without hydrolysis.
  • Add water, ammonia ($\text{NH}_3$), or carbon dioxide ($\text{CO}_2$) across double bonds, or eliminate these elements to form double bonds.
  • Common names include expressions such as decarboxylase, aldolase, and dehydratase (used during elimination of $\text{CO}_2$, aldehydes, or water, respectively).

• Class 5: Isomerases:

  • Catalyze geometric or structural changes within a single molecule, interconverting isomeric structures by molecular rearrangements.
  • Classified based on the specific type of isomerism catalyzed, including cis-trans-isomerases, isomerases, tautomerases, mutases, and $\text{L}$ to $\text{D}$ isomerases.

• Class 6: Ligases:

  • Catalyze reactions in which two chemical groups or distinct molecules are joined (ligated) together.
  • Catalytic activity is directly coupled with energy released from the hydrolysis of a diphosphate bond in $\text{ATP}$ or a similar nucleoside triphosphate.

Catalytic Properties and Energetics of Enzymatic Reactions

• Fundamental Properties of Enzymes:

  1. Increase the rate of chemical reactions without being consumed or permanently altered by the reaction.
  2. Increase reaction rates without altering the chemical equilibrium between reactants (substrates, $[S]$) and products ($[P]$).

• Determinants of Functional Catalytic Activity:

  • Dependent on the protein portion of the enzyme as well as any associated non-protein prosthetic groups or coenzymes.
  • Enzyme activity within a biological system is affected by:
  1. Negative modifiers.
  2. Changes in $\text{pH}$.
  3. Changes in enzyme concentration.

• Energy Changes and Activation Energy:

  • All chemical reactions possess an energy barrier separating the substrate ($[S]$) and the product ($[P]$).
  • Free Energy of Activation ($E_a$): The energy difference between the energy level of the reactant and high-energy intermediates formed during product synthesis.
  • Gibbs Free Energy Change ($\Delta G$): The net change in free energy occurring during a reaction, which remains unchanged by the presence of an enzyme.

• Theories of Reaction Mechanisms:
  • Collision Theory:
  • Chemical reactions occur because molecules collide; faster collision frequencies lead to faster reaction rates.
  • Activation energy ($E_a$) is the threshold energy level required for colliding molecules to undergo a reaction.
  • Enzymes lower activation energies so that reactions proceed rapidly.

• Transition State Theory:
  • Substrates sequentially form and break bonds until product structures are achieved.
  • During bond rearrangement, free energy increases until reaching a peak known as the transition state (activated complex), representing the midpoint between reactants and products.
  • Reactions proceed faster when a higher concentration of activated complex is maintained.
  • If $\text{E}_a$ is high, transition state formation is low and reaction rate is slow; if $\text{E}_a$ is lowered, more transition state complexes form, accelerating reaction velocity.

Active Sites and Substrate Binding Models

• Active Site Dynamics:
  • Catalytic activity involves binding of substrate to a specific region on the enzyme called the active site, forming an enzyme-substrate complex ($ES$).
  • Bound substrate is converted into product ($[P]$) and released, freeing the enzyme active site.
  • Active sites lower $E_a$ and speed chemical reactions by:
  1. Orienting substrates correctly.
  2. Straining substrate bonds.
  3. Providing a favorable micro-environment.
  4. Covalently bonding directly to the substrate.
  • Provides a physical template upon which multiple substrates are brought together in the proper position and alignment to react.

• Models of Substrate Binding:
  • Lock and Key Model:
  • Proposes that the substrate and active site possess rigid, exact complementary shapes, allowing the substrate to fit precisely into the active site.

• Induced Fit Model:
  • Proposes that initial binding interactions between enzyme and substrate are relatively weak, but these interactions rapidly induce structural conformational changes in the enzyme that strengthen binding and strain bonds.

Enzyme Kinetics and Mathematical Relationships

• Key Kinetic Parameters:
  • Initial Velocity ($V_i$ or $V_0$): The rate of reaction measured immediately after mixing enzyme and substrate, expressed in $\text{moles/time}$.
  • Substrate Concentration ($[S]$): The molar concentration of substrate, expressed as $\text{molar}$.
  • Maximum Velocity ($V_{\max}$): The plateau rate achieved when all available enzyme active sites are saturated with substrate.
  • Michaelis-Menten Constant ($K_m$): The substrate concentration at which the initial velocity $V_i$ reaches exactly one-half of maximum velocity ($\frac{1}{2}V_{\max}$).

• Reaction Orders and Velocity Kinetics:

  • First-Order Kinetics:
  • Occurs at low substrate concentrations ($[S]$).
  • Initial velocity ($V_i$) increases linearly in direct proportion to increases in $[S]$.
  • Zero-Order Kinetics:
  • Occurs at high substrate concentrations ($[S]$).
  • Increases in $V_i$ become minimal as the reaction reaches $\text{V}_{\max}$.
  • At substrate saturation, higher concentrations of substrate cannot increase reaction velocity further because all active sites are filled.

• Factors Affecting Enzyme Reaction Rates:

  1. Substrate concentration ($[S]$).
  2. Enzyme concentration.
  3. $\text{pH}$ (hydrogen ion concentration).
  4. Temperature.
  5. Product concentration.
  6. Inhibitors.

Enzyme Inhibition Mechanisms

• Reversible Inhibition Dynamics:

  • Reversible inhibitors bind to enzymes via non-covalent forces and maintain a dynamic, reversible equilibrium with the enzyme.
  • When inhibitor concentration drops, full enzyme catalytic activity is regenerated.
  • Dissociation constant for enzyme-inhibitor complexes is designated as $K_i$.

• Competitive Inhibitors:

  • Bind directly to the catalytic active site, competing with the substrate for binding in a dynamic equilibrium.
  • Inhibition is completely reversible by increasing substrate concentration ($[S]$).
  • Kinetic Effect:
  • Maximum velocity ($V_{\max}$) is unchanged.
  • Michaelis-Menten constant ($K_m$) is increased (a higher $[S]$ is required to achieve $\frac{1}{2}V_{\max}$).

• Non-competitive Inhibitors:
  • Bind to the enzyme ($E$) or enzyme-substrate complex ($ES$) at a site distinct from the catalytic active site.
  • Substrate binding affinity remains unaltered, but the resulting $ES$ complex cannot catalyze product formation. Inhibition cannot be reversed by adding more substrate.
  • Kinetic Effect:
  • Michaelis-Menten constant ($K_m$) remains unaltered.
  • Maximum velocity ($V_{\max}$) is decreased proportionately to inhibitor concentration.

Regulatory and Allosteric Enzymes

• Rate-Limiting Enzymes:

  • Within sequential enzyme pathways, at least one enzyme sets the rate of the overall reaction sequence because it catalyzes the slowest (rate-limiting) reaction step.
  • These regulatory enzymes increase or decrease catalytic activity in direct response to physiological metabolic signals.

• Allosteric Regulation:

  • The regulation of an enzyme or protein caused by binding an effector molecule at an allosteric site (a site distinct from the active site).
  • Allosteric Activators (Positive Effectors): Effectors that bind positive allosteric sites and enhance catalytic activity.
  • Allosteric Inhibitors (Negative Effectors): Effectors that bind negative allosteric sites and decrease catalytic activity.