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

– G=H-TS– H adds contributions from 100s of interactions at ~1kcal/mol

each– yet net stability of proteins is often G ~ 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 G=~-30kcal/mol• with “self-energy”, G=~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...

• 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%)

Hydrogen BondingdistD-A

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

• 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).

Can the lone-pair on sulfur in Met and Cys act as an H-bond acceptor?

interactions

• Misura, Morozov, Baker (2004)• anisotropy of side-chain interactions• geometry: preference for planar (face-on) interactions• strength?

– FireDock uses:

E=-1.5..-0.5 kcal/mol

for contact dist 5.5-7.5Å

Cation- 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