Protein Secondary Structure: Alpha Helices and Beta Strands

Levels of Protein Organization

• Primary Structure:

  • Definition: The linear covalent sequence of amino acid residues linked by peptide bonds, ordered from the N-terminal end ($NH_3^+$) to the C-terminal end ($COO^-$).

  • Example sequence: $NH_3^+ \text{ - Gln - Ala - Thr - Met - Lys - Arg - Leu - Ile - Glu - Ala - Thr - Gln - Phe - Ser - } COO^-$

• Secondary Structure:

  • Definition: The local spatial arrangement of the polypeptide backbone atoms without regard to side chain conformations or long-range tertiary folding.

  • Key regular secondary structures include the $\alpha$-helix and the $\beta$-strand / $\beta$-pleated sheet.

• Tertiary Structure:

  • Definition: The complete three-dimensional, folded spatial architecture of a single polypeptide chain, incorporating all secondary structural motifs and side chain arrangements.

• Quaternary Structure:

  • Definition: The spatial arrangement and assembly of multiple folded polypeptide chains (subunits) into a multi-subunit functional complex.

Forces Governing Protein Structure

• Non-Covalent Interactions:

  • Hydrogen Bonds (H Bonds): Electrostatic attractions between a hydrogen atom covalently bonded to an electronegative atom (hydrogen bond donor, such as backbone amide $-N-H$) and another electronegative atom (hydrogen bond acceptor, such as carbonyl oxygen $-C=O$).

  • Ionic Bonds (Salt Bridges): Electrostatic attractions between oppositely charged amino acid side chains (e.g., negatively charged Asp/Glu carboxyl groups and positively charged Lys/Arg/His groups).

  • Van der Waals Interactions: Weak, transient dipole-dipole forces between nonpolar atomic groups in close proximity.

  • Hydrophobic Clusters: The thermodynamic tendency of nonpolar side chains to aggregate together in the interior of the protein structure, minimizing unfavored entropic ordering of water molecules.

  • Stacked Rings: Aromatic interactions ($\pi-\pi$ stacking) between aromatic side chains (e.g., Phenylalanine, Tyrosine, Tryptophan).

• Covalent Interactions:

  • Disulfide Bonds: Strong covalent linkages ($-S-S-$) formed between the sulfhydryl (thiol) groups of two cysteine residues, stabilizing folded tertiary or quaternary conformations.

Peptide Bond Conformational Flexibility

• Peptide Bond Rotation and Dihedral Angles:

  • The peptide bond itself has partial double-bond character due to resonance and is rigid and planar.

  • Free rotation occurs around the single bonds connected to the central $\alpha$-carbon ($C_\alpha$):

  • Phi angle ($\phi$): Angle of rotation around the $N-C_\alpha$ bond.

  • Psi angle ($\psi$): Angle of rotation around the $C_\alpha-C$ (carbonyl carbon) bond.

• Steric Hindrance Constraints:

  • Many potential combinations of $\phi$ and $\psi$ angles are energetically unfavorable due to steric clashes (overlapping van der Waals spheres between backbone atoms, carbonyl oxygens, or side chain groups).

  • Stable secondary structures correspond to specific permissible ranges of $\phi$ and $\psi$ angles.

Molecular Basis of Secondary Structure

• Definition of an Amino Acid Residue:

  • An amino acid integrated within a polypeptide chain is called a residue because it loses a molecule of water ($H_2O$) during peptide bond formation and is no longer a free amino acid.

• Backbone Hydrogen Bonding Scheme:

  • Secondary structures are stabilized exclusively by hydrogen bonding between peptide backbone atoms rather than side chain interactions.

  • The carbonyl oxygen ($-C=O$) acts as the hydrogen bond acceptor.

  • The amide nitrogen-bound hydrogen ($-N-H$) acts as the hydrogen bond donor.

Detailed Structure and Properties of the Alpha Helix

• Geometric Parameters of the $\alpha$-Helix:

  • Handedness: Right-handed helix.

  • Residues per Turn: Exactly $3.6$ amino acid residues per turn.

  • Pitch (Rise per Turn): $5.4\,\text{\AA}$ ($0.54\,\text{nm}$) along the helical axis.

  • Helix Diameter / Width: Approximately $12\,\text{\AA}$ ($1.2\,\text{nm}$), including the backbone and average side chain projections.

  • Hydrogen Bonding Pattern: A hydrogen bond forms between the backbone carbonyl oxygen ($C=O$) of residue $n$ and the backbone amide nitrogen ($N-H$) of residue $n + 4$

  • Consequence: All backbone hydrogen bond donors ($N-H$) and acceptors ($C=O$) are satisfied within the helix, except for the first $4$ amide $N-H$ groups at the N-terminus and the last $4$ carbonyl $C=O$ groups at the C-terminus.

  • Side Chain Orientation: All side chains (R groups) project outwards and slightly backwards (towards the N-terminus) relative to the central helical axis.

  • Periodicity: Structural periodicity is $7$ residues, spanning approximately two turns ($2 \times 3.6 = 7.2$ residues), causing side chains at every 7th position to line up along the same side of the helix.

• Amphipathic Helices:

  • An amphipathic helix has hydrophobic side chains concentrated on one face of the cylinder and polar/charged side chains on the opposite face.

  • This arrangement occurs when nonpolar amino acids repeat every $\approx 3.5$ residues.

  • Allows the helix to interact simultaneously with hydrophobic environments (e.g., lipid membranes or protein cores) and hydrophilic environments.

• Coiled-Coil Structural Motif:

  • Formed when two or more $\alpha$-helices wrap around each other to build a stable superhelical structure.

  • Driven by a heptad repeat sequence pattern labeled $a-b-c-d-e-f-g$

  • Positions $a$ and $d$ are occupied by hydrophobic amino acid residues (such as Leucine or Isoleucine) that interlock at the helical interface to hide nonpolar surfaces.

• Amino Acid Propensities for $\alpha$-Helix Formation:

  • Amino acid choices represent statistical tendencies rather than absolute restrictions.

  • Favored Residues ("MALEK"): Methionine (M), Alanine (A), Leucine (L), Glutamate (E), and Lysine (K) strongly favor $\alpha$-helix formation.

  • Helix Breakers and Disfavored Residues:

  • Proline (P): Functions as a helix breaker because its cyclic side chain fixes the $N-C_\alpha$ ($\phi$) bond angle and eliminates the backbone amide hydrogen needed for hydrogen bonding.

  • Glycine (G): Disfavored in $\alpha$-helices because its lack of a side chain gives it high conformational flexibility (entropy), leading to a high entropic cost when constrained into a rigid helix.

Detailed Structure and Properties of Beta Strands and Beta Sheets

• Properties of $\beta$-Strands and $\beta$-Sheets:

  • A $\beta$-strand is a polypeptide chain segment extended in a pleated, zigzag conformation.

  • Multiple $\beta$-strands align laterally to form a $\beta$-pleated sheet, stabilized by inter-strand backbone hydrogen bonds.

  • Repeat Distance: A distance of $\approx 7\,\text{\AA}$ ($0.7\,\text{nm}$) corresponds to $2$ amino acid residues along the strand.

  • Side Chain Alternation: R groups alternate sequentially, projecting above and below the median plane of the sheet.

• Strand Orientation and Hydrogen Bonding Geometry:

  • Directionality convention: Arrows representing $\beta$ strands point from the N-terminus to the C-terminus.

  • Antiparallel $\beta$-Sheet:

  • Adjacent strands run in opposite directions (N-to-C alongside C-to-N).

  • Inter-strand hydrogen bonds between backbone $C=O$ and $N-H$ groups are linear and perpendicular to the strands, yielding high structural stability.

  • Parallel $\beta$-Sheet:

  • Adjacent strands run in the same direction (N-to-C alongside N-to-C).

  • Inter-strand hydrogen bonds are angled / slanted relative to the strand axis, making individual hydrogen bonds slightly weaker than in antiparallel sheets.

• Connecting Loops and Turns:

  • Regular secondary structure elements ($\alpha$-helices and $\beta$-strands) are connected by loop or turn regions.

  • Hairpin Loops (Reverse Turns): Compact turns (often consisting of as few as $2$ amino acid residues) that reverse polypeptide direction, commonly connecting antiparallel $\beta$-strands.

  • Loops can also be large and flexible, forming prominent surface features of proteins.

General Properties and Structural Implications of Secondary Elements

• Stability and Packing Density:

  • Both $\alpha$-helices and $\beta$-sheets are highly compact, thermodynamically stable conformations.

  • Their regular geometry allows close packing within protein structures.

• Complete Backbone Hydrogen Bonding:

  • All internal backbone hydrogen bond donors ($N-H$) and acceptors ($C=O$) are fully satisfied within the secondary structure.

  • Consequence: If all side chains (R groups) on an $\alpha$-helix or $\beta$-strand are nonpolar, the entire surface of that segment becomes completely hydrophobic.

• Biological Applications:

  • Hydrophobic helices or strands can be packed into the interior hydrophobic core of globular proteins.

  • Hydrophobic or amphipathic secondary elements can span or insert into phospholipid bilayers of cellular membranes.