🧬 Proteins Are Built from Amino Acids

Proteins are polymers built from amino acids, and in biological proteins these are always L-amino acids. Each amino acid has:

• an amino group (–NH₂)
• a carboxyl group (–COOH)
• a Cα (alpha carbon) with a side chain (R-group)

🔗 Formation of the Peptide Bond

• The carboxyl group of one amino acid reacts with the amino group of another.
• This is a condensation reaction, releasing one molecule of water (H₂O).
• The resulting linkage is an amide bond, called a peptide bond.

📌 A chain of amino acids linked this way is called a peptide (or polypeptide for longer chains).

🔁 Directionality of Peptides: N → C

Peptides have directionality:

• N-terminus: free amino group
• C-terminus: free carboxyl group

➡️ Amino acid sequences are always written and read from N-terminus to C-terminus.

🧱 The Protein Backbone

The backbone is the repeating, invariant structure:

N - Cα - C

Side chains (R-groups) are attached to the Cα, but do not define the backbone geometry.

🔄 Conformation Depends on Rotation

Protein shape is controlled by rotations around backbone bonds. These rotations are described by dihedral angles, measured in degrees (°).

📐 What Is a Dihedral Angle?

A dihedral angle:

• Is defined by four atoms
• Describes rotation around the bond between the two middle atoms
• Requires viewing the molecule along that bond

🟦 Φ (Phi) Angle — Rotation Around N–Cα

• Bond rotated: Nᵢ – Cαᵢ
• Defined by atoms:
  • C(i−1) → N(i) → Cα(i) → C(i)

How to visualize Φ:

1. Look down the N–Cα bond
2. N is in front, Cα hidden behind
3. Measure the angle between:
   • Cα → C(i)
   • N → C(i−1)

🟨 Ψ (Psi) Angle — Rotation Around Cα–C

• Bond rotated: Cαᵢ – Cᵢ
• Defined by atoms:
  • N(i) → Cα(i) → C(i) → N(i+1)

Same principle: look down the bond and measure relative atom positions.

📊 Common Dihedral Angle Values

In idealized staggered conformations, dihedral angles cluster around:

• −60° → gauche⁻ (G⁻)
• +60° → gauche⁺ (G⁺)
• 180° → trans (T)

📌 In real proteins, angles can vary—but are usually close to these values.

🔒 Ω (Omega) Angle — The Peptide Bond

Ω describes rotation around the peptide bond (C–N).

Why Omega Is Special

• The peptide bond has partial double-bond character
• This makes it planar
• Rotation is highly restricted

✅ Only two values are allowed:

• 180° → trans
• 0° → cis

⚖️ Cis vs Trans Peptide Bonds

• Trans (ω = 180°)
  • Vast majority of peptide bonds
  • Minimizes steric clashes (atoms bumping into each other)
• Cis (ω = 0°)
  • Rare
  • Causes strong steric hindrance

📌 Exception: Proline

• Proline sometimes appears in cis
• Its cyclic side chain reduces the energetic penalty

🚫 Steric Hindrance (Why Cis Is Rare)

Steric hindrance means:

• Atoms occupy physical space
• Certain conformations cause atoms to overlap
• This raises energy and destabilizes the structure

➡️ Trans peptide bonds avoid these clashes, making them strongly favored.

🧠 Big Picture Summary

• Proteins are chains of L-amino acids linked by peptide bonds
• The backbone is N–Cα–C
• Conformation is controlled by three dihedral angles:
  • Φ (phi): N–Cα
  • Ψ (psi): Cα–C
  • Ω (omega): peptide bond
• Φ and Ψ are flexible → determine secondary structure
• Ω is planar → almost always trans
• Proline is the notable cis exception