15.5 Proteins

231

integrity requires that the backbone H-bonds be kept dry. The energetic importance of

H-bond wrapping (i.e., protection from water) can be seen by noting that the energy

of a hydrogen bond is strongly context-dependent. In water, it is about 2 kJ/mol;

in vacuo, it increases eightfold to tenfold. Wrapping will therefore greatly contribute

to the enthalpic stabilization of globular protein conformation.

A poorly desolvated H-bond is called a dehydron.¹²

The dehydron is under-

wrapped and, therefore, overexposed to water (i.e., wet), because there are insuffi-

cient apolar groups in its vicinity. The only way for a protein to diminish the presence

of water around a hydrogen bond is to bring apolar residues unable to form H-bonds

with water into its vicinity; by keeping water away, hydrophobic groups, such as

methyl and ethyl, are powerful intramolecular H-bond enhancers. The dehydronic

force is thus a three-body force involving the H-bond donor, the H-bond acceptor,

and the apolar residue. It is formally defined as the drag exerted by a dehydron on a

test residue; that is,

upper F equals minus nabla Subscript bold upper R Baseline left parenthesis StartFraction 1 Over 4 pi epsilon bold upper R EndFraction StartFraction q q Superscript prime Baseline Over r 0 EndFraction right parenthesis commaF = −∇R

(

1

4πεR

qq^,

r0

)

,

(15.7)

where bold upper RR is the position of the hydrophobic test residue measured perpendicularly

from the H-bond, qq and q primeq^, are the net charges, and r 0r0 is the O–H distance of the

H-bond. Typically, upper FF is about 7 pN at bold upper R equals 6R = 6 Å.

The three-dimensional structure of a protein (as encoded in a pdb file) can be

interrogated to reveal dehydrons. Hydrogen bonds are operationally defined as sat-

isfying the criteria of an N–O distance of 2.5–3.5 Å and the angle between the NH

and CO bonds equal to 45Superscript degrees^◦. The dehydration domain of an H-bond is defined as

two spheres of equal size centred on the CSuperscript left parenthesis alpha right parenthesis^(α)s of the amino acids paired by the

H-bond. The radius of the spheres (around 6.5–7 Å) is chosen to slightly exceed the

typical distance between nonadjacent CSuperscript left parenthesis alpha right parenthesis^(α)s; hence, the spheres necessarily interact.

The extent of wrapping is given by the number rhoρ of hydrocarbon groups within the

dehydration domains. A well-wrapped H-bond hasrho equals 15ρ = 15; most soluble monomeric

globular proteins have arhoρ around this value, averaged over all the backbone H-bonds.

Wrapping defects are decisive determinants of protein–protein (and other) inter-

actions. If the stable conformation of a globular protein is such that there are some

unavoidably underwrapped H-bonds on their solvent-accessible surfaces, then that

protein will be sticky; the underwrapped H-bonds will be hotbeds of stickiness.¹³

Any other surface able to provide an appropriate arrangement of apolar groups

will strongly bind to the dehydronic region (provided that geometric constraints—

shape complementarity—are satisfied). The completion of the desolvation shell of

a structure-determining H-bond has the same significance in understanding protein

structure and interactions as completing electron shells has in understanding the peri-

12 The dehydron concept is due to A. Fernández. See, for example, Fernández and Scott (2003) and

Fernández et al. (2002, 2003).

13 Empirically, a certain threshold density of dehydrons per unit area should be exceeded for a

surface to qualify as sticky.