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Forces

Forces. inter-atomic interactions 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)

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Forces

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  1. Forces • inter-atomic interactions • 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

  2. 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

  3. 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

  4. 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...

  5. Hydrogen Bonding • 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%) distD-A

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

  7. 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).

  8. 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

  9. 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

  10. 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

  11. 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

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