Reviews in Computational Chemistry Volume 18

126 Polarizability in Computer Simulations
indicate cooperativity in the hydrogen-bond energies, 226 and dielectric measurements
on polypeptide chains show an enhancement of the dipole moment
of the peptide group in an a-helix. 227 Other quantum mechanical studies have
addressed the importance of polarizability on protein folding, 228 enzyme catalysis,
229 DNA base pair stacking, 230 and nucleic acid interactions with
ions. 231
Several polarizable models for proteins and the peptide group have been
developed, using polarizable point dipoles, 32,44,45,232 electronegativity equalization
models, 10,146 and the two-state empirical model. 183 Simulations using
point polarizable dipole models by Warshel and co-workers 44,45 and by
Wodak and co-workers 46 examined the role of polarizability on protein stability,
dielectric properties, and enzymatic activity. For example, Van Belle et al. 46
found that the helix dipoles are enhanced, in agreement with the dielectric
measurements of Wada, 227 and, further, the helix dipoles are enhanced not
only through hydrogen bonds to the backbone, but also through association
with side chain atoms. Polarization has also been shown to influence the folding
time scales for small polypeptides. 183 For nucleic acids, a point polarizable
dipole model was recently introduced. 232 Despite these studies and acknowledgment
of the importance of polarizability from both electronic structure and
experimental studies, not many simulations of proteins or nucleic acids using
polarizable models have been done to date.
An implication of resonance-assisted hydrogen bonding is that as the
charges are polarized, through hydrogen bonds or other interactions, the
hybridization of the atoms involved can change. For example, studies of crystal
structures of formamide reveal that the C O bond length increases and the
C N bond length decreases due to the formation of hydrogen bonded
dimers. 233 Other crystal structures and ab initio quantum calculations on
amides further validate the fact that hydrogen bonds can change those bond
lengths. 234 The hydrogen bonds in these structures are in the amide plane
and promote the double bond, zwitterionic state. On the other hand, the interactions
in which the amino nitrogen serves as a hydrogen-bond acceptor
would stabilize the single bond form. Partial sp 3 hybridization of the amino
nitrogen leads to pyramidalization. Indeed, nonplanarities of some peptide
bonds have been observed in atomic-resolution structures of proteins.
183,235,236 In addition, the planarity of the peptide bond is dependent
on a protein’s secondary structure, with residues in an a-helix being more planar
than elsewhere. 183 For nucleic acids, ab initio calculations indicate that the
amino group can be pyramidalized through interactions with neighboring
molecules or ions. 237 For both the peptide bond and nucleic acid bases, there
is reason to believe that a significant degree of nonplanarity can be induced by
the environment. To treat these effects, the polarization of the electrostatic
degrees of freedom—charges or dipoles—would have to be coupled to the
bonded interactions, as has been developed for the peptide bond. 183