CHEM 114A: Chapter 6 - Lecture 1

Peptide‐Bond Planarity & Backbone Constraints

• Historical insight: Pauling & Corey (X-ray diffraction)
  • Resonance between the carbonyl O and amide N gives the C–N bond ≈ $40\%$ double-bond character.
  • Consequence: every peptide group is rigid and planar, forcing the backbone to propagate as a series of linked planes.
• Bonds outside the peptide plane ( $C<em>{\alpha}-C$ and $N-C</em>{\alpha}$ ) are single-bonded and free to rotate.

Torsion (Dihedral) Angles

• $\phi$ (phi): $\angle(C<em>{i-1},\,N</em>i,\,C<em>{\alpha i},\,C</em>i)$ — rotation about the $N<em>i–C</em>{\alpha i}$ bond.
• $\psi$ (psi): $\angle(N<em>i,\,C</em>{\alpha i},\,C<em>i,\,N</em>{i+1})$ — rotation about the $C<em>{\alpha i}–C</em>i$ bond.
• $\omega$ (omega): rotation around the peptide bond itself ( $C<em>i–N</em>{i+1}$ ); planarity constrains $\omega \approx 180^{\circ}$, so it carries little conformational information.
• Steric hindrance: certain $\phi,\psi$ combinations push atoms (e.g., carbonyl O and amide H) closer than van-der-Waals limits ⇒ energetically forbidden conformations.

Ramachandran Plot

• Axes: $\phi$ (x-axis) vs. $\psi$ (y-axis).
• Color code (example figure):
  • Tan = disallowed, Green = allowed, Blue = highly favorable.
• Clusters (yellow circles) correspond to most probable secondary structures:
  • Right-handed $\alpha$-helix, left-handed $\alpha$-helix, parallel & antiparallel $\beta$-sheets, collagen/"core" region, etc.
• Practical use: knowing an amino-acid pair’s allowed $\phi/\psi$ angles enables prediction of secondary structure.

Hierarchy of Protein Structure (quick recap)

• Primary = linear amino-acid sequence.
• Secondary = local backbone patterns stabilized mainly by H-bonds.
• Tertiary = 3-D fold of a single polypeptide.
• Quaternary = assembly of multiple chains.

Major Secondary Structures

1. $\alpha$-Helix
2. $\beta$-Sheet
3. Turns & loops (especially $\beta$-turns)

1 The $\alpha$-Helix

• Handedness: predominantly right-handed; left-handed variants exist but are rare.
• Geometry:
  • $3.6$ residues/turn.
  • Rise per residue: $1.5\,\text{\AA}$ ⇒ $5.4\,\text{\AA}$ per full turn.
  • Rotation: $100^{\circ}$ per residue ⇒ tight coil.
• Orientation: N-terminus → C-terminus along helix axis.
• Stabilizing H-bonding: carbonyl O of residue $i$ H-bonds to amide H of residue $i+4$ (shown by dashed lines).
• Dipole moment: cumulative alignment of peptide dipoles ⇒ partial $+$ at N-terminus, partial $-$ at C-terminus.
• Side-chain placement:
  • Backbone atoms inside the coil; side chains & carbonyl O project outward.
  • Residues $i$ and $i!+!3$ or $i!+!4$ sit spatially adjacent, enabling side-chain interactions.
• Helix capping:
  • Charged/polar residues (e.g., Asp, Glu) at ends fold back to H-bond and “seal” the helix.
  • Example shown: Asp/Glu (positions 102/103) H-bonding with Arg to stabilize helix termination.
• Sample problem (video): peptide $\text{N‐ASGHYTRLW‐C}$ forms an $\alpha$-helix; CO of Ser ($i$) H-bonds to NH of Thr ($i+4$).
• Cartoon depictions: ribbons, coils, cylinders for clarity.

2 The $\beta$-Sheet

• Composition: 2 or more nearly extended strands stabilized by inter-strand H-bonds.
• Pleated geometry: planarity of peptide bonds ⇒ slight up/down crinkle.
• Side-chain alternation: R groups project alternately above and below the sheet; repeat distance ≈ $7\,\text{\AA}$ ⇒ too far for intra-strand side-chain contacts.
• Two topologies:
  1. Antiparallel
  • Adjacent strands run in opposite $N \rightarrow C$ directions.
  • H-bonds nearly perpendicular to strands; each residue pairs with exactly one partner.
  1. Parallel
  • Strands run in the same direction.
  • H-bonds diagonal; each residue bonds to two partners on the opposing strand.
• Mixed sheets: combinations of parallel & antiparallel strands common (e.g., barrels).
• Connectivity: strands may be contiguous segments of the same chain folded back or come from different chains; loops, turns or helices serve as connectors.
• Cartoon symbol: broad arrow pointing toward the C-terminus.
• Typical size: 4–5 strands per sheet; complex structures (e.g., $\beta$-barrels) may use 10–40 strands.

3 Turns & Loops (Focus on $\beta$-Turns)

• Function: reverse chain direction; connect secondary segments; found mainly on protein surfaces.
• Type I & Type II (differ by backbone dihedrals of residues 2 & 3).
• H-bond: CO of residue $i$ ↔ NH of residue $i+3$.
• Residue preferences:
  • Glycine (often at position $i+2$ in Type II) – tiny side chain reduces steric clashes.
  • Proline (often at $i+1$) – cyclic structure pre-bends the backbone.

Coiled-Coils & α-Keratin (Super-Secondary Structures)

• Coiled-coil motif: two right-handed $\alpha$-helices wrap to form a left-handed superhelix.
  • Heptad repeat (abcdefg) where positions a & d are hydrophobic (denoted “HP”), yielding pattern HP-X-X-HP-X-X.
  • Hydrophobic strip along each helix interlocks ⇒ stabilization; disulfide bonds may add covalent reinforcement.
• α-Keratin architecture:
  1. Single $\alpha$-helix.
  2. Two helices ⇒ coiled-coil.
  3. Coiled-coils stack ⇒ protofilament.
  4. Protofilaments bundle (4 per group) ⇒ protofibril (total 32 helices).
  5. Protofibrils pack to form hair, claws, horns, feathers, nails, etc.
  • Bulky residues at coil ends create steric “knots” preventing unwinding.

Amino-Acid Propensity for Secondary Structures

• $P<em>{\alpha} > 1$ or P{\beta} > 1 means residue appears more often than average in that structure.

Worked Example (Ramachandran Application)

• Given $\phi,\psi$ pairs: $(-100^{\circ},\;140^{\circ})$, $(-80^{\circ},\;120^{\circ})$, etc.
• All fall within the $\beta$-strand region ⇒ peptide will adopt a $\beta$-sheet conformation.

Practical / Conceptual Take-Aways

• Backbone geometry (planarity + dihedrals) limits fold space, enabling predictive tools like the Ramachandran plot.
• Hydrogen bonding is the dominant stabilizer of local secondary structure; side-chain chemistry fine-tunes stability & specificity.
• Sequence → structure → function: local propensities (e.g., Pro → turn) inform higher-order folding and ultimately biological activity.
• Understanding secondary structures underpins fields from protein engineering (designing coiled-coil biomaterials) to disease research (mis-folded $\beta$-rich aggregates in amyloidoses).