8.2 Zwitterions, Titration Curves, Isoelectric Points & the Peptide Bond

8.2 Zwitterions, Titration Curves, Isoelectric Points & the Peptide Bond

Acid-Base Chemistry, Titration Dynamics & Zwitterions

Amino acids are polyprotic amphoteric molecules capable of acting as both Brønsted-Lowry acids (proton donors) and Brønsted-Lowry bases (proton acceptors).

The Zwitterionic State

At physiological pH (~7.4):

• The alpha-carboxylic acid group (pKa1 ≈ 2.0) experiences a solution pH substantially greater than its pKa (pH > pKa1), causing it to lose its proton to exist as a carboxylate anion (–COO–).
• The alpha-amino group (pKa2 ≈ 9.0–10.0) experiences a solution pH lower than its pKa (pH < pKa2), causing it to remain protonated as an ammonium cation (–NH3+).
• This dipolar species carrying simultaneous positive and negative formal charges with a net charge of zero is termed a zwitterion (from the German zwitter, hermaphrodite).

The Henderson-Hasselbalch Relationship

Protonation states are governed by the Henderson-Hasselbalch equation:

pH = pKa + log([Conjugate Base] / [Conjugate Acid])

• When pH < pKa: The protonated form dominates ([HA] > [A-]).
• When pH = pKa: Exactly 50% of the ionizable group is protonated and 50% is deprotonated ([HA] = [A-]); this point defines the buffer midpoint on a titration curve where buffering capacity is maximal.
• When pH > pKa: The deprotonated conjugate base dominates ([A-] > [HA]).

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Calculating Isoelectric Points (pI)

The isoelectric point (pI) is the exact pH at which an amino acid or peptide carries a net electric charge of zero. At its pI, a molecule will not migrate in an electric field during isoelectric focusing gel electrophoresis.

Mathematical Principles for Calculating pI

1. Neutral Amino Acids (No Ionizable Side Chain): For residues with two ionizable groups (Gly, Ala, Val, Leu, Ile, Met, Pro, Phe, Trp, Ser, Thr, Asn, Gln): pI = (pKa1 + pKa2) / 2 Worked Example (Alanine): With pKa1 = 2.34 and pKa2 = 9.69: pI = (2.34 + 9.69) / 2 = 6.02

2. Acidic Amino Acids (Aspartate, Glutamate): Contain two carboxylic acid groups. At very low pH, the net charge is +1. Deprotonating the alpha-COOH (pKa1) yields the neutral zwitterion (0). Deprotonating the side-chain carboxyl (pKaR) produces a –1 charge. Thus, the neutral species is flanked by pKa1 and pKaR: pI = (pKa1 + pKaR) / 2 Worked Example (Glutamate): With pKa1 = 2.19, pKaR = 4.25, and pKa2 = 9.67: pI = (2.19 + 4.25) / 2 = 3.22

3. Basic Amino Acids (Histidine, Lysine, Arginine): Contain two basic nitrogen groups. At very low pH, the molecule carries a +2 charge. Deprotonating the alpha-COOH (pKa1) reduces the charge to +1. Deprotonating the lower-pKa basic group yields the neutral species (0). Deprotonating the second basic group produces a –1 charge. Thus, the neutral species is flanked by pKaR and pKa2: pI = (pKaR + pKa2) / 2 Worked Example (Histidine): With pKa1 = 1.82, pKaR = 6.00, and pKa2 = 9.17: pI = (6.00 + 9.17) / 2 = 7.59 Worked Example (Lysine): With pKa1 = 2.18, pKa2 = 8.95, and pKaR = 10.53: pI = (8.95 + 10.53) / 2 = 9.74

Universal pI Calculation Algorithm: Identify the ionic charge of the molecule at pH = 0 when fully protonated. Write out each deprotonation step in order of ascending pKa values, calculating the net charge at each plateau. Average the two pKa values that border the state where net charge equals 0.

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Peptide Bond Formation, Resonance Stabilization & Spatial Constraints

Peptides are linear polymers formed by linking the alpha-carboxyl group of one amino acid to the alpha-amino group of an adjacent amino acid via a peptide (amide) bond.

Condensation / Dehydration Reaction Mechanism

1. Nucleophilic Attack: The unshared lone pair of electrons on the alpha-amino nitrogen of the incoming amino acid acts as a nucleophile, attacking the electrophilic carbonyl carbon of the growing peptide chain.
2. Tetrahedral Intermediate: Attack generates a tetrahedral alkoxide intermediate.
3. Elimination of Water: The carbonyl pi bond reforms, eliminating a hydroxyl group that combines with a proton from the amino group to release a molecule of water (H2O).
4. Thermodynamics and Kinetics: Peptide bond condensation has a positive standard free energy change (ΔG°' ≈ +10 to +15 kJ/mol) and is non-spontaneous. In vivo, peptide synthesis is driven by coupling to high-energy phosphoanhydride bonds via ATP-dependent aminoacyl-tRNA synthetases during ribosomal translation. Hydrolysis of peptide bonds is exergonic (ΔG°' ≈ –10 kJ/mol), but uncatalyzed hydrolysis exhibits an immense activation barrier, rendering peptide bonds kinetically stable under physiological conditions (half-life > 1,000 years).

Resonance Delocalization and Double-Bond Character

The peptide bond can be represented as a resonance hybrid between two principal canonical structures:

• Structure 1 (Major): Neutral structure with a carbon-oxygen double bond (C=O) and a carbon-nitrogen single bond (C–N).
• Structure 2 (Minor): Dipolar zwitterionic structure with a carbon-oxygen single bond carrying a negative formal charge (C–O–) and a carbon-nitrogen double bond carrying a positive formal charge (C=N+).

Geometric Consequences for Protein Architecture

• Planarity: The C–N bond exhibits approximately 40% double-bond character. As a consequence, the C–N bond length is 1.32 Å, significantly shorter than a standard aliphatic C–N single bond (1.47 Å) and approaching a C=N double bond (1.28 Å).
• Restricted Rotation: Free rotation around the peptide C–N bond (the omega, ω, dihedral angle) is prevented by an energy barrier of ~80 kJ/mol. The six atoms of the peptide group (Cα1, C, O, N, H, Cα2) lie rigidly within a single plane.
• Trans vs. Cis Conformation: Steric clash between bulky R groups on adjacent Cα atoms strongly favors the trans configuration (ω = 180°), which is ~1,000 times more stable than the cis configuration (ω = 0°). The sole exception occurs with proline, where the cyclic pyrrolidine ring causes similar steric hindrance in both cis and trans forms; approximately 10–30% of X-Pro peptide bonds adopt the cis conformation in native proteins.