Enzyme Structure, Function, and Kinetics: Study Notes for Biochemistry

Enzyme Structure and Function

Basic Definitions

• Enzyme: A biological catalyst that accelerates chemical reactions in living organisms by lowering the activation energy required for the reaction.

• Apoenzyme: The protein portion of an enzyme, which is inactive until combined with a cofactor.

• Holoenzyme: The complete, active enzyme consisting of the apoenzyme plus its cofactor(s).

DNA Polymerase I

• Function: Catalyzes nucleotide addition to the 3' end of a DNA strand during replication in prokaryotes.

• Active Site: Contains two Mg2+ ions that stabilize incoming dNTPs.

• Role of Mg2+: Essential for catalysis and stabilization of negative charges during nucleotide addition.

Ribosomes

• Function: Facilitate synthesis of polypeptides from mRNA templates.

• Mechanism: Enzymes in ribosomes transfer amino acids from tRNA to the growing polypeptide chain.

• Structure: Small subunit binds mRNA; large subunit catalyzes peptide bond formation.

Enzyme Classification

Main Classes of Enzymes

Class Name	Type of Reaction Catalyzed
Oxidoreductases	Transfer of electrons (oxidation-reduction)
Transferases	Transfer of functional groups
Hydrolases	Hydrolysis (transfer of functional groups to water)
Lyases	Cleavage of C-C, C-O, C-N bonds by elimination, leaving double bonds or rings
Isomerases	Transfer of groups within molecules to yield isomeric forms
Ligases	Formation of C-C, C-S, C-O, C-N bonds by condensation reactions coupled to ATP cleavage
Translocases	Movement of molecules or ions across membranes

Enzyme Reaction Mechanisms

General Reaction Scheme

• Equation: $E + S \rightleftharpoons ES \rightarrow EP \rightarrow E + P$

• Explanation: Enzyme (E) binds substrate (S) to form an enzyme-substrate complex (ES), which is converted to enzyme-product complex (EP), and finally releases product (P).

Thermodynamics of Enzyme Reactions

• Spontaneity: A reaction with positive $\Delta G$ is non-spontaneous; enzymes do not change $\Delta G$ but lower activation energy.

• Reverse Reaction: Adding an enzyme for the reverse reaction in high concentration can shift equilibrium, affecting product and reactant amounts.

Free Energy Diagrams

• Uncatalyzed vs. Catalyzed: Catalyzed reactions have lower activation energy ($\Delta G^{\ddagger}$) than uncatalyzed reactions.

• Diagram Labels: $\Delta G^{\ddagger}$ (activation energy), transition state, $\Delta G_{uncat}$, $\Delta G_{cat}$, ES, EP.

Enzyme-Substrate Interactions

Lock and Key vs. Induced Fit Hypotheses

• Lock and Key: Enzyme active site is a rigid structure complementary to the substrate.

• Induced Fit: Enzyme active site is flexible and molds itself around the substrate upon binding.

• Preferred Hypothesis: Induced fit is generally favored as it explains enzyme flexibility and specificity.

Specificity

• Definition: The ability of an enzyme to select and bind a particular substrate among many possible molecules.

Entropy and Substrate Binding

• Effect: Binding of substrate decreases entropy (increases order), which can increase $\Delta G$.

• Compensation: Enzymes compensate by forming multiple weak interactions, releasing energy and stabilizing the transition state.

Hexokinase Reaction

• General Steps: Hexokinase catalyzes the phosphorylation of glucose to glucose-6-phosphate using ATP.

• Mechanism: Substrate binding induces conformational change, facilitating transfer of phosphate group.

Enzyme Kinetics

Michaelis-Menten Theory

• General Reaction: $E + S \rightleftharpoons ES \rightarrow E + P$

• Steady-State Assumption: The concentration of ES remains constant during the initial phase of the reaction.

Michaelis-Menten Equation

• Equation: $v = \frac{V_{max}[S]}{K_m + [S]}$

• Parameters: $V_{max}$ is the maximum velocity; $K_m$ is the substrate concentration at half-maximal velocity.

Lineweaver-Burk Equation

• Equation: $\frac{1}{v} = \frac{K_m}{V_{max}} \cdot \frac{1}{[S]} + \frac{1}{V_{max}}$

• Purpose: Linearizes the Michaelis-Menten equation for easier determination of $K_m$ and $V_{max}$.

Enzyme Efficiency

• Turnover Number ($k_{cat}$): Number of substrate molecules converted to product per enzyme per second.

• Comparison: Higher $k_{cat}$ indicates greater efficiency.

Enzyme Preference (Km)

• Lower $K_m$: Indicates higher affinity for substrate; enzyme is more effective at low substrate concentrations.

• Example: Hexokinase ($K_m = 0.1$ mM) is preferable to glucokinase ($K_m = 10$ mM) for glucose phosphorylation at low glucose concentrations.

Types of Enzyme Reactions

• Ternary Complex: Both substrates bind to the enzyme simultaneously.

• Ping-Pong (Double Displacement): One substrate binds and releases product before the second substrate binds.

Enzyme Inhibition

Classes of Inhibitors

• Reversible Inhibitors: Bind non-covalently and can be removed.

• Irreversible Inhibitors: Bind covalently, permanently inactivating the enzyme.

Types of Reversible Inhibition

Type	Binding Site	Effect on Kinetics
Competitive	Active site	Increases $K_m$, no change in $V_{max}$
Noncompetitive	Allosteric site	No change in $K_m$, decreases $V_{max}$
Uncompetitive	Enzyme-substrate complex	Decreases both $K_m$ and $V_{max}$
Mixed	Active or allosteric site	Changes both $K_m$ and $V_{max}$

Types of Irreversible Inhibition

• Group-specific reagents: React with specific amino acid side chains.

• Affinity labels: Structurally similar to substrate, covalently modify active site residues.

• Example: DIPF irreversibly inhibits chymotrypsin by covalently binding to serine in the active site.

Enzyme Regulation

Types of Regulation

• Allosteric Regulation: Effector molecules bind at sites other than the active site, altering enzyme activity.

• Covalent Modification: Addition or removal of chemical groups (e.g., phosphorylation) changes enzyme activity.

• Proteolytic Activation: Enzymes activated by cleavage of peptide bonds.

• Genetic Regulation: Control of enzyme synthesis at the transcriptional or translational level.

Application and Analysis

Graphical Analysis

• Michaelis-Menten Plot: Shows hyperbolic relationship between velocity and substrate concentration.

• Lineweaver-Burk Plot: Double reciprocal plot used to determine $K_m$ and $V_{max}$; inhibition types can be visualized by changes in slope and intercept.

Experimental Data Interpretation

• Determining $V_{max}$, $K_m$, and $k_{cat}$: Use initial velocity data and plots to extract kinetic parameters.

Summary Table: Enzyme Inhibition Effects

Inhibitor Type	Effect on $K_m$	Effect on $V_{max}$
Competitive	Increases	No change
Noncompetitive	No change	Decreases
Uncompetitive	Decreases	Decreases
Mixed	Increases or decreases	Decreases

Key Equations

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

• Lineweaver-Burk: $\frac{1}{v} = \frac{K_m}{V_{max}} \cdot \frac{1}{[S]} + \frac{1}{V_{max}}$

• Turnover Number: $k_{cat} = \frac{V_{max}}{[E]_T}$

Example Applications

• Hexokinase vs. Glucokinase: Hexokinase is more efficient at low glucose concentrations due to lower $K_m$.

• Beta-lactamase vs. Carbonic Anhydrase: Carbonic anhydrase ($k_{cat} = 400,000$ s-1) is more efficient than beta-lactamase ($k_{cat} = 800$ s-1).

Additional info: These notes expand on the provided questions and prompts, supplying definitions, explanations, and context for a comprehensive review of enzyme structure, function, kinetics, inhibition, and regulation as covered in a college-level Biochemistry course.