Study Notes on Principles of Biochemistry

Function of Globular Proteins

Binding

• Interaction Strength Expressions:

  • Association (binding) constant, $K_a$, units: $M^{-1}$
  • Dissociation constant, $K_d$, units: $M$
  • Relationship: $K<em>d = \frac{1}{K</em>a}$
  • Formulas:
  • $K_a = \frac{[PL]}{[P][L]}$
  • $K_d = \frac{[P][L]}{[PL]}$

• Magnitude of Binding Strength:

  • Strong binding: $K_d < 10 ext{ nM}$
  • Weak binding: K_d > 10 ext{ }M

Examples of Binding Strength

• Table 5-1: Some Protein Dissociation Constants

  Protein	Ligand	$K_d$ (M)
  Avidin (egg white)	Biotin	$1 imes 10^{-15}$
  Insulin receptor (human)	Insulin	$1 imes 10^{-10}$
  Anti-HIV immunoglobulin (human)	gp41 (HIV-1 surface protein)	$4 imes 10^{-10}$
  Nickel-binding protein (E. coli)	Ni²+	$1 imes 10^{-7}$
  Calmodulin (rat)	Ca2+	$3 imes 10^{-6}$ to $2 imes 10^{-5}$

  • Typical receptor-ligand interactions include:
  • Biotin-avidin: $10^{-16}$ (high affinity)
  • Sequence-specific protein-DNA: $10^{-14}$
  • Antibody-antigen: $10^{-12}$
  • Enzyme-substrate: $10^{-10}$ to $10^{-6}$
  • Certain interactions (like avidin-biotin) may be irreversible due to their tight binding.
  • Binding constants can vary significantly due to solution conditions (e.g., salt concentration, pH).

Specificity: Lock-and-Key Model

• High Specificity of Proteins:
  • Proteins typically only bind certain ligands due to specificity explained by compatibility factors:
  • Size
  • Shape
  • Charge
  • Hydrophobic/hydrophilic character
• Lock and Key Model (Emil Fischer, 1894):
  • Assumes complementary surfaces of binding sites and ligands are preformed, leading to high specificity.

Specificity: Induced Fit

• Conformational Changes:
  • Upon ligand binding, conformational changes in the protein can occur (Daniel Koshland, 1958), a phenomenon termed "induced fit".
  • Induced fit allows:
  • Tighter binding of the ligand
  • High affinity for various ligands
  • Both ligand and protein can alter their conformations.

Heme Binding to Protein

• Binding of O2 to heme affects the binding properties of CO vs. O2 due to interactions with distal histidine (His E7) increasing O2 binding affinity.

Cooperativity and Allosteric Regulation

• Allosteric Protein:
  • Binding of one ligand affects binding properties at a different site on the same protein, can be positive or negative.
  • Types of regulation:
  • Homotropic Regulation: Normal ligand acts as allosteric regulator
  • Heterotropic Regulation: Different ligand affects normal ligand binding
• Cooperativity: Positive homotropic regulation demonstrated in hemoglobin binding O2 cooperatively.

Hemoglobin Structure and Function

• Hemoglobin (Hb):
  • A tetramer consisting of two alpha and two beta subunits (α2β2), each structurally similar to myoglobin.
• Sequence Similarity:
  • Residues conserved across all known globins (e.g., distal His E7 common to all structures, with corresponding positions differing in sequence across globins).

Subunit Interactions

• Example interactions detailed for deoxyhemoglobin in the T state highlighting ion pairs between His HC3 and Asp FG1.

R and T States of Hemoglobin

• T = Tense State:
  • More interactions; stable with lower affinity for O2
• R = Relaxed State:
  • Fewer interactions; flexible with higher affinity for O2
• O2 binding transitions Hb from T to R state, disrupting ion pair interactions.

pH Effect on O2 Binding to Hemoglobin

• Bohr Effect:
  • Active tissues produce H+, lowering blood pH near tissues compared to lungs.
  • Decreased pH stabilizes the T state of hemoglobin:
  • H+ binds to hemoglobin, protonates His146, and forms a salt bridge with Asp94, facilitating O2 release in tissues.
• Blood pH in lungs: 7.6, in tissues: 7.2.

2,3-Bisphosphoglycerate Regulation of O2 Binding

• Binds to the positively charged cavity of hemoglobin, stabilizing the T state; serves as a negative heterotropic regulator, affecting O2 affinity.
• BPG levels adjust to adaptations in altitude; facilitates O2 release where affinity is reduced, ensuring sufficient delivery to tissues during altitude changes.

Sickle-Cell Anemia

• Resulting from mutation in hemoglobin (E6V in β chain), causing strands to form and sickling of red blood cells, leading to anemia and resistance to malaria in heterozygotes.

What are Enzymes?

• Enzymes:
  • Biochemical catalysts accelerating reactions without undergoing changes in composition.
  • Most enzymes are globular proteins.
  • Enzymatic study dates back to the late 1700s, gaining prominence in biochemistry.
  • Types:
  • Apoenzyme: enzymatic protein part
  • Holoenzyme: complete form including coenzymes and metal ions.

Six Classes of Enzymes

• Based on reactions they catalyze, including lyases creating new double bonds or ring structures.

Energy Coordinate Diagram

• Enzyme-catalyzed reactions present lower activation energies ($ riangle G^
  eq$) than uncatalyzed, improving reaction rates ($k$).

Enzyme-Substrate Complex

• Enzymes form noncovalent complexes known as the Michaelis complex when binding substrates.
• Enzyme kinetics modeled by equations:
  • $v = \frac{v<em>{max}[S]}{K</em>m + [S]}$

Enzymatic Catalysis

• Enzymes do not modify equilibrium ($ riangle G$) but reduce activation energy ($ riangle G^
  eq$).
• Reaction equation:
  • $k = rac{k_B T}{h} e^{-rac{ riangle G^
    eq}{RT}}$

Saturation Kinetics

• At high substrate concentrations ($[S]$), reaction velocity becomes independent of substrate concentration.

Kinetic Parameters Determination

• Nonlinear Michaelis-Menten plots for parameter calculations, with linearized double-reciprocal plot aiding analysis of two-substrate reactions.

Michaelis-Menten Kinetics

• Under steady-state assumption, mass balance equations apply:
  • $E_{tot} = [E] + [ES]$
  • $S_{tot} = [S] + [ES] \approx [S]$
  • The rate of product formation modeled as:
  • $v_{net} = \frac{dP}{dt} = k[ES]$.

Enzyme Inhibition

• Inhibitors decrease enzyme activity; classified into:
  • Irreversible Inhibitors: Permanently inactive an enzyme, often toxins or drugs.
  • Reversible Inhibitors: Bind and dissociate, typically as structural analogs to substrates or products, used to regulate enzyme activity.

Types of Reversible Inhibition

• Competitive Inhibition:
  • Inhibitor competes with substrate for the active site, $V<em>{max}$ unchanged but $K</em>m$ apparent increases, analyzed via Lineweaver-Burk plots.
• Uncompetitive Inhibition:
  • Inhibitor binds only to the enzyme-substrate complex, altering $V<em>{max}$ and $K</em>m$ proportionally.
• Mixed Inhibition:
  • Inhibitor can bind to free enzyme or the substrate complex, both $V<em>{max}$ and $K</em>m$ may change.

General Principles of Catalysis

• Induced Fit: Enzymes often undergo conformational changes upon substrate binding to optimize fit.
• General Acid-Base Catalysis: Protons transferred to/from substrates stabilize charged intermediates to accelerate decomposition.
• Covalent Catalysis: Enzyme-substrate transient covalent bonds reshape reaction pathways, often requiring nucleophiles on enzymes.

Peptidoglycan Cleavage by Lysozyme Model

• Action of lysozyme involves successive SN2 steps with Asp52 as nucleophile for glycosidic bond cleavage via general acid catalysis by Glu35.
• Sequence of events includes hydrolysis of the covalent glycosyl-enzyme intermediate leading to product formation.

Multiple Types of Regulation in Enzymes

• Example: Role of Glucagon and Insulin in regulating pathways through phosphorylation affecting enzyme states through signaling cascades.