JBB2026 Fall 2020 Simon Sharpe Protein Structure • peptide conformations and residue preferences • elements of secondary structure • supersecondary structure and motifs • packing of helices and sheets • chain topologies • internal packing • protein interfaces • membrane proteins • multimeric proteins • domain motions Folded Disordered Tyr Thr Gly Cys Ile Ile Ala Gly The structure (conformer) defined by the dihedral angles main chain (φ,ψ) side chains (�1, �2, …) φ =180 ; ψ=180 φ =-60 ; ψ=-45 The structure (conformer) defined by the dihedral angles main chain (φ,ψ) side chains (�1, �2, …) The minimum energy conformer of the polymer is determined largely by the non-local interactions between the side chains. D. Goodsell One way of categorizing the 20 amino acids - each amino acid has particular characteristics Amino acid hydrophobicity Protein conformations The conformation is the arrangement of the atoms in 3D space. The most stable conformation is at a potential energy minimum Proper treatment is quantum mechanical - but this is intractable with proteins (too many atoms). We use Newtonian mechanics and describe the system as a set of potential energy terms, each with a particular form. The overall potential energy can be broken down into a set of energy functions: LOCAL bond length (1,2) (strong) bond angle (1,3) (strong) dihedral angle (1,4) (medium) NON-LOCAL solvation / hydrophobic effect van der Waals (packing, steric clashes) electrostatics (incl. hydrogen bonds) conformational entropy These are additive: calculate the overall potential energy as the sum of these individual functions Non-local molecular interactions attractive or distance Type repulsive? dependance Basis for van der Short Range Pauli exclusion Repulsive 1/r12 Waals radii of atoms * Electrostatic either; depends on Coulomb’s law 1/r (charge-charge) q1q2 either; depends of the involves polar Dipole-dipole Keesom interactions directions of the dipole 1/r3 molecules/groups moments polarization: Dipole-induced dipole Debye interactions attractive 1/r4 change in a dipole due to an external electronic field. Charge-dipole attractive London dispersive resonant induced Fluctuating dipoles attractive 1/r6 interactions dipoles * often treated as Hydrogen bond attractive electrostatic similar to charge- Cation-pi attractive induced dipole Hydrophobic effect Loren Williams website! http://ww2.chemistry.gatech.edu/~lw26/structure/molecular_interactions/mol_int.html! *Lennard-Jones “6-12” potential! The peptide bond Delocalized electrons over peptide bond: (1) Increased polarity - gives rise to dipole moment represented by arrow (2) Partial double bond - O-C-N bonds coplanar and rotation is limited Conformational energy of butane as a function of the central torsion angle Boltzman distribution: Populate according to energies 4 0 3 9 3 8 3 7 3 6 potential energy (kcal/mol) 35 0 90 180 270 360 e g+ t g- e Torsion angle (°) Population: 0% 15% 70% 15% 0% ω ισ φ ψ ω φ ψ Note: unsaturated C-N bond length is 1.45 Å - Peptide bond has ~40% double bond character - dihedral is constrained. ω is constrained to ~180° Bond lengths Bond angles Dihedrals sp2-hybridized atoms Shorter 120° (flat) More restrained (trans) sp3-hybridized atoms longer 109° (tetrahedral, Less restrained often chiral) (gauche-, gauche+, trans) Geometry of the peptide bond Potential energy curve for the peptide omega dihedral angle : Barriers for dihedral angle rotation can be attributed to: -the exchange interaction of electrons in adjacent bonds -repulsive interactions between overlapping bond orbitals -- steric clashes between atoms (Clash between groups 1 and 4 in the 1,4 bond disfavors cis). Note : only two minima here Occurrence of omega in cis: (Stewart et al 1990) X-X 0.36% (116/32,539) X-Pro 6.5% Ser-Pro 11% Tyr-Pro 25% Xaa-Pro is an exception (peptide bond preceding a proline) - lower barrier to interconversion - only ~2 kcal/mol energy difference between cis and trans omega bond - but slow interconversion (usu. needs to be catalyzed to equilibrate) - ~6% of Xaa-Pro have cis omega angles, otherwise v. rare (<0.5%) Ramachandran plot of φ, ψ angles in proteins Main Chain Calculated energy surface “Classic” Ramachandran Plot (theoretical) Based on hard sphere potentials (sum off vdw radii; simple form of the L-J potential) Ramachandran plot of φ, ψ angles in proteins Calculated energy surface Observed distribution of (phi,psi) (theoretical) in protein structures from the PDB (experimental) Conformationally unusual residues O Cysteine Cys or C Cys-Cys Ramachandran plot for Xaa – Pro any residue preceding Pro Proline Pre-Pro - φ is relatively normal Proline φ “fixed” at -60° ψ is restricted to 90 - 180° ψ = -55° or 145° Residue-specific Ramachandran plots Amino acid side chain torsion angles (χn) Torsion angle definition - shown here for arginine Amino acid side chain torsion angles (χn) The different conformations of the side chain as a function of χ1 are referred to as gauche(+), trans and gauche(-). These are indicated in the diagrams below in which the amino acid is viewed along the Cβ-Cα bond. Most common least common χ1=-60° χ1=180° χ1=+60° Amino acid side chain torsion angles (χn) χ1= -60° χ1= 180° χ1=+60° Cγ1 Cγ2 β- branched residues eg. Val Potential surfaces for side chain dihedral angles This defines the major rotamers for each amino acid. Ε.γ. χ 1 χ 2 plot for Phenylalanine gauche- χ 2 χ2 χ1 gauche+ φ ψ χ 1 Why can’t Phe χ 2 be trans? gauche- gauche+ trans Potential surfaces for side chain dihedral angles gauche+ χ2 Chi-2 χ1 gauche- Cα Chi-1 Cδ1 Cδ2 gauche- gauche+ trans Cγ is sp2 hybridized Ch1 - Chi2 plots Three rules for secondary structure 1) Local “bonded” potentials must be minimized - bond lengths (1,2) - bond angles (1,3) - dihedrals (1,4) (Ramachandran) regular: all (phi,psi) the same 2) Satisfy main chain hydrogen bonding - Typically, >90% of the potential backbone hydrogen bond donors and acceptors are involved in hydrogen bonds 3) No unfavourable steric interactions - Ramachandran Types of Secondary Structure: Helices α, 310, Pi, poly-proline II β- Sheets parallel antiparallel Beta Bulges Turns / hairpins Specific residue preferences φ,ψ,χ for particular amino acids i.e. how side chains affect the above ‘allowed’ regions of the Ramachandran plot Π helix Name Frequency* φ (°) ψ (°) n d (Å) H-bonding 310 helix ~4% -74 -4 +3.0 2 i,i+3 α helix ~35% -57 -47 +3.6 1.5 i,i+4 αL helix - +57 +47 -3.6 1.5 i,i+4 Π helix - -57 -70 +4.3 1.1 i,i+5 Collagen (PP type II) Fibres -78 +149 -3.3 2.9 planar β-sheet (para) - -115 +115 2 3.2 twisted β- sheet parallel ~25% -120 +135 -2.3 3.3 interstrand twisted β- sheet antiparallel ~8 -139 +135 -2.3 3.3 interstrand B-DNA - - 10 3.4 interchain *Crude estimate in globular proteins Helical Structures _ Translation per residue (in Å) = rise per residue (d) Helical wheel representation - every 4th residue clusters (1,5,8 etc) Allow definition of amphipathic helix - i.e. one face polar the other non-polar C Alpha helix Hydrogen bond between carbonyl of residue i with amide-H of residue i + 4 i i+1 i+2 i+3 i+4 i+5 i+6 i+7 N i,i+3 i,i+4 i,i+5 n: residues per turn 3 α 10 R π d: rise per residue (n,d): (3.0, 2.0 Å) (3.6, 1.5 Å) (4.3, 1.1 Å) Amphipathic helices 100° /residue Long helices - rarely straight. smooth bends (e.g. tropomyosin - coiled coiled dimers) kinks waters often bridge i,i+4 H-bond. membrane proteins often amphipapthic - one face interacting with bulk solvent, one with protein core. lots of strains due to longer-range contacts the proteins (non-local effects). Transmembrane helices 60 Å radius of curvature: bending is not energetically expensive (< 2 kcal/mol for a 5-turn helix) Saposin A kink in alpha3 closed form open form (ligand bound) (apo) Ahn et al. , PNAS (2003) Y54 (n) Ahn et al. , Protein Science (2006) Polyproline II helix The PPII helix is defined by (φ,ψ) backbone dihedral angles of roughly (-75°, 150°) and TRANS isomers of the peptide bonds. Top view of a twenty- residue poly-Pro II helix, showing the three-fold symmetry. Left handed helix 3 residues /turn, 3.1Å rise/residue No internal hydrogen bonds - no H-bond donor in proline poly-Pro II helix, showing its openness and lack of internal important in binding of peptides to SH3 domains hydrogen bonding. Polyproline II helix PPII structures are binding targets for SH3 signalling domains Polyproline I helix The PPI helix is defined by (φ,ψ) backbone dihedral angles of roughly (-75°, 160°) and CIS isomers of the peptide bonds. Rarely found because the cis isomer is higher in energy than the trans. Right handed helix 3.3 residues /turn, 1.9Å rise/residue Beta-sheets R1 R3 Parallel R R 2 4 • Generally buried • Less twisted Antiparallel • Generally, one side exposed, other side buried. • Can withstand greater distortions (twisting and beta- bulges) Pitch = 7.0 Å MORE STABLE Antiparallel beta sheet Parallel beta sheet Twist of a mixed β -sheet Thioredoxin (1TRX) The β - bulge A motif of three residues within a beta-sheet in which the main chains of two consecutive residues are H-bonded to that of the third, and in which the dihedral angles are as follows: Disrupts normal alternation of side chain direction Accentuates the twist of the sheet. Chain Topologies (tertiary structure) Huge variety some are regular (e.g. TIM barrel; β-barrel), some are not. Proteins often assembled from “domains” “Never” see knots Minimum size for stability ~60 amino acids if small - often stabilized by disulfides, co-factors, etc e.g.