The energy of an amide hydrogen bond in vacuo
is arguably the upper limit of its free energy since the entropic contribution is presumably unfavorable and anything more polarizable than a vacuum will reduce the contribution of the electrostatic interactions [17
]. Quantum mechanical calculations of amide hydrogen bond strengths using a formamide-formaledehyde model suggest that an amide hydrogen bond has an in vacuo
energy of 6.6 kcal/mol[17
]. Calculations for an N-methylacetamide dimer also agree that the energy of the hydrogen bond in a vacuum is about 6.6 kcal/mol [18
]. Experimentally determined vapor phase enthalpies of hydrogen bonds between neutral species range from 3-6 kcal/mol[19
]. Thus, it appears that the upper end for neutral hydrogen bonds is around 6 kcal/mol, but could be even higher in special cases [20
], particularly charge stabilized hydrogen bonds [19
]. Clearly, there is potential for hydrogen bonds to be a powerful stabilizing force.
Hydrogen bond energies will be reduced from the optimal values by a number of factors. First, hydrogen bond strength is very sensitive to geometry [17
] and geometry may not be optimized. Second, solvent polarizability decreases hydrogen bond strength, which is dominated by electrostatics [17
]. Third, the entropy cost for fixing the donors and acceptors decreases the free energy of the interaction. Finally, the ability of the solvent to participate in hydrogen bonds can reduce the net energy difference. For example, in water (W) the making and breaking of a backbone hydrogen bond can be written as follows [22
Thus, a simple hydrogen bond inventory approach implies no net change in the number of hydrogen bonds. If all hydrogen bonds were equal (and they are certainly not), the net contribution of a hydrogen bond should be zero. While the hydrogen bond inventory concept is overly simplistic [23
], it is clear that for the formation of a protein hydrogen bond to be energetically favorable, it must be more favorable than solvation of the broken hydrogen bond by water.
How much more stable can a protein hydrogen bond be compared to water solvation? It seems that a good place to look is in functional binding sites or enzymes where there may be strong evolutionary pressure to optimize particular hydrogen bonds. Indeed, Shan & Herschlag argue that an optimized neutral hydrogen bond in an enzyme active site could be around 9 kcal/mol more stable than an alternative hydrogen bond to water [24
]. A Tyr to Phe mutation in the active site of ketosteroid isomerase reduces transition state stabilization by 6.3 kcal/mol [25
]. Thus, even in water solution, optimized hydrogen bonds can be very important contributors to intermolecular complexes.
In an apolar solvent like the center of a membrane bilayer that has a low dielectric constant and no competitive hydrogen bonding potential, hydrogen bond contributions could be even stronger. As discussed below, however, most hydrogen bonds in both water soluble and membrane proteins seem to be far from these optimized limits.