Forces inter-atomic interactions hydrophobic effect – driving force electrostatic - Coulomb's law, dielectric constant hydrogen-bonds charge-dipole, dipole-dipole, dipole-quadrapole polarizability van der Waals, London dispersion (stickiness) cation-pi (Arg/Lys to aromatic) aromatic ring-stacking (Phe, Tyr, Trp, His) hydrophobic effect – driving force enthalpy balanced against entropy DG=DH-TDS DH adds contributions from 100s of interactions at ~1kcal/mol each yet net stability of proteins is often DG ~ 15 kcal/mol

Electrostatic Interactions formal charges Arg, Lys: +1 Asp, Glu: -1 His=0 or +1? Coulomb’s law, range dielectric constant water:  = 80 vacuum:  = 1 protein interior:  = 2-4? (due to dipoles) solvent screening, ionic strength salt bridges in proteins strength: ~1kcal/mol (Horowitz et al., 1990) (desolvation effects) (later: potential surface calculation, Poisson-Boltzmann equation) Warshel, Russell, and Churg (1984) - without solvation effects, lone ionized groups would be highly unfavorable to bury in non-polar environments, and salt bridges would predominate folding with DG=~-30kcal/mol with “self-energy”, DG=~1-4kcal/mol

pKa estimation (protonation state) ionizable residues: Arg, Lys, Asp, Glu, His, Nterm, Cterm Cys, Tyr can also get deprotonated H++: solve Poisson-Boltzmann equation protonation state depends on energy of charge presence in local electrostatic potential field reflects neighboring charges, solvent accessibility self-energy (Warshel et al., 1984) Henderson-Hasselbach equation interactions between sites Monte Carlo search (Beroza et al 1991) Onufriev, Case & Ullman (2001) – can do orthogontal transform to identify independently titrating pseudo-sites conformational changes (Marilyn Gunner) – it helps if side-chains can re-orient two interacting sites with intrinsic pKa’s of 7.0 and 7.1

PROPKA empirical rules (Li, Robertson, Jensen, 2005) pKa = model + adjustments 1. hydrogen-bonds 2. solvent exposure 3. nearby charges iterative search: deprotonate side-chain with lowest pKa first, then determine effect on rest...

Hydrogen Bonding dipole-dipole interactions donors and acceptors distD-A dipole-dipole interactions donors and acceptors Stickle et al. (1992), Baker and Hubbard (1994) ~1-5 kcal/mol (Pace) distance, geometric dependence of strength avg. distD-A = 2.9±0.1 Å think of tetrahedral lone-pair orbitals on O distribution in proteins: backbone >C=O..H-N< (68.1%) >C==O..side chain (10.9%) >N-H..side chain (10.4%) side chain--side chain hydrogen bonds (10.6%)

parameters for H-bond energy term in crystallographic refinement (Michael Chapman)

Can the lone-pair on sulfur in Met and Cys act as an H-bond acceptor? Cys often acts as a donor in H-bonds Cys, Met rarely participate in H-bonds as acceptor more often involved in VDW interactions (hydrophobic) “Hydrogen bonds involving sulfur atoms in proteins”, Gregoret..(2004). Met as acceptor, <25% free Cys: donor ~72%, acceptor ~36% Non-hydrogen bond interactions involving the methionine sulfur atom. Pal D, Chakrabarti P. (1998) Out of a total of 1276 Met residues, 22% exhibit S⋅⋅⋅O interaction (with an average distance 3.6A), 8% interact with an aromatic face (S-aromatic-atom dist. being 3.6A) 9% are in contact with an aromatic atom at the edge (3.7A).

p-p interactions Misura, Morozov, Baker (2004) anisotropy of side-chain interactions geometry: preference for planar (face-on) interactions strength? FireDock uses: Ep-p=-1.5..-0.5 kcal/mol for contact dist 5.5-7.5Å q=0-30 q=30-60 q=60-90

Cation-p interactions Gallivan and Dougherty (1999) 3.6-3.8Å, face-on vs. edge-on frequency: ~1 per 77 residues (1/2 as common as salt bridges) strength: 0-6 kcal/mol? nicotinic acetylocholine receptor quadrupole moment

VDW interactions van der Waals forces: stickiness ~0.1kcal/mol per contact induced polarization, London dispersion forces typically modeled with 12-6 Lennard-Jones potential 1/r6 attractive, 1/r12 repulsive minimum at around sum of VDW radii

Hydrophobic Effect Tanford, Kauzmann (1950s) burial of hydrophobic residues to avoid disruption of solvent H-bond networks collapse of hydrophobic core similar to oil-water phase separation; micelle formation; cause of surface tension solvent layer around crambin (0.88Å): clathrate cages (pentagonal rings) balance with other forces desolvation of backbone/side-chains reduction in entropy dependence on temperature, solvent