1. 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

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
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%)

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= kcal/mol
for contact dist Å
q=0-30
q=30-60
q=60-90

9. Cation-p interactions
Gallivan and Dougherty (1999)
Å, 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