Table 1.

Typical physical interactions stabilizing protein structures.^a

Type	Covalent/noncovalent	Occurrence	Abundance of interactions	Stabilizing free energy, kcal/M	Specificity	Comments
Van der Waals interactionsb,c	Noncovalent	All proteins	Numerous	For methyld and NH groups, and O, N and S atoms: In water: ∼0.0 to −0.05 In vacuum: ∼−0.2 to −0.5	Nonspecific	Electrons oscillate around positively charged nucleus making atom an oscillating dipole. In two interacting atoms these oscillations are correlated and the atoms attract each other with energy proportional to r−6, r being the distance between atoms.
Hydrophobic interactionse	Noncovalent	All proteins	Numerous	For methyld groups: In water: ∼−0.3f In vacuum: –	Less specific	The origin is that water molecules are partly constrained to minimize their interaction with hydrophobic (non-polar) groups in order to save hydrogen bonds.
Hydrogen bondse	Noncovalent	All proteins	Moderate	In water: ∼−1.5 In vacuum: ∼−5	More specific	Electrostatic interactions between directed H-containing dipoles (–O−–H+ or –N−–H+ groups) and partially negatively charged O− or N− atoms.
Interaction of charged with uncharged groupse	Noncovalent	All proteins	Moderate	Unit charge interacting with methyl groupd At the protein/water interface: ∼+0.1 Inside the protein in water: ∼+1 At the protein/vacuum interface or inside the protein in vacuum: ∼−1	Less specific	Electrostatic repulsion of charged Lys+, Arg+, His+, Asp−, Glu− from weakly polarizable protein medium to more polarizable water, and attraction of these groups to weakly polarizable protein medium from non-polarizable vacuum
Salt bridgese of two charged atoms	Noncovalent	Most proteins	Few	At the protein/water interface: ∼−2 At the protein/vacuum interface: ∼−40 Inside the protein (water or vacuum): ∼−25	Specific	Electrostatic interaction between positively charged Lys+, Arg+ or His+ and negatively charged Asp− or Glu−.
Coordinate bondse	Covalent	Metal-binding proteins	Very few	In water: ∼−6 and higher In vacuum: very high (∼−100), as for usual covalent bond	Highly specific	One metal cation is coordinated by several (e.g. six) O and/or N atoms in the protein (or balanced by interacting H2O molecules in water).
Disulfide bondse	Covalent	Mostly secreted proteins	Very few	Inside the cell: ∼0 Outside the cell: very high (∼−100), as for usual covalent bond	Highly specific	Inside the cell a special enzyme and glutathiones make the formation of disulfide bonds reversible. Outside the cell disulfide bonds are fixed.

^aData were compiled from or calculated after [8,70–73]. Covalent bonds (except for coordinate bonds and disulfides) are not included since they are the same in the native and unfolded protein structure and are canceled out. The strength of residue–residue and atom–atom contacts depends on the defined distance cutoff between interacting atoms. Usually, for VdW, hydrophobic interactions and interactions between charged and uncharged atoms the cutoff is defined as ≈4–8 Å (e.g. see [45,74]), ≈5 Å for salt bridges, ≈4 Å for H-bonds, ≈2.5 Å for coordinate and disulfide bonds. For in-vacuum interactions the stabilizing effect is energetic in nature, while for the in-water interactions the stabilizing free energy (i.e. mean force potentials) is mainly connected with entropy. Water is considered implicitly, as a medium rather than as particles.

^bVan der Waals interactions are the London dispersion forces, present in both the folded and unfolded state of the protein. In the folded state many interactions are between amino acid residues (and with water molecules at the surface). In the unfolded state the interactions are mostly between amino acid residues and the surrounding water molecules.

^cVan der Waals interactions are ‘sometimes used loosely for the totality of nonspecific attractive or repulsive intermolecular forces’ [72].

^dFor aromatic rings, the strength of interaction is approximately twofold larger.

^eThe stabilizing effect in water is mostly entropic in nature [8], which means that when a protein is folded, the entropy of water molecules increases stabilizing the folded protein structure. At the same time the enthalpy of the ‘protein-water’ system remains relatively unchanged. The formation of disulfide bonds inside the cell is assisted by thiol-disulfide exchange, which increases entropy of glutathione molecules and preserves enthalpy of S–S bonds.

^fThe free energy of hydrophobic interaction of nonpolar atoms with water was estimated as 45 cal/M for Ų of the molecular surface (i.e. 20–25 cal/M for Ų of the water-accessible surface area) [71]. An isolated methyl group (approximated by a sphere with a radius of ∼2 Å) can contact about twelve neighboring groups of the same dimensions and, thus, has about −0.3 kcal/M per contact as the cost of exclusion of water from the contact.