Modern Polymer Spect..

258 5 Vibrationul Spectroscopy oj' Polypeptides
extended-chain and helical structures. Not all known structures have been the subjects
of such analyses, but this approach will certainly be extended to them in the
future.
5.4.1 Extended-Chain Polypeptide Structures
5.4.1.1 General Features
Stereochemically acceptable extended-chain (so-called p-sheet) structures were first
described by Pauling and Corey from molecular model building (78, 791. In some
cases, specific structures of synthetic polypeptides have been determined from X-ray
diffraction studies. These have provided the bases for the vibrational analyses of this
class of polypeptide chain conformations.
In these analyses, some structural constraints have had to be imposed in order to
achieve a reasonable degree of transferability in the force fields. These constraints
have consisted of adopting a standard peptide group geometry, which is probably
not a serious problem, and accepting a completely planar peptide group (i.e., the
CN torsion angle, Q, equal to 180"), which may be more serious since departures
from planarity of 5-10' require relatively little energy (and are not uncoininon in
proteins) and may have an important effect on some of the modes. The standard
geometry of the peptide group is given in Table 5-4, based [XO] on the refined X-ray
structure of P-PLA [Sl]. (The dimensions for PGI are slightly different [19].) We
therefore assume that chain conforinations differ only in their q, $ torsion angles.
As Pauling and Corey first pointed out [78, 791, adjacent hydrogen-bonded chains
in a P-sheet can occur in two arrangements, parallel and antiparallel (with respect to
the direction of the chemical sequence along the chain). In addition, depending on
the axial stagger between adjacent chains, the sheet can be 'pleated' or 'rippled', the
latter being possible only if all-L and all-D chains alternate in the sheet. (In practice,
only PG can satisfy this requirement, since it has not as yet been possible to
Table 5-4. Standard geometry of the peptide group
Bond length
('4")
Bond angle
(degrees)
C"C 1.53 C"CN 115.4
co 1.24 C"C0 121.0
CN 1.32 CNC" 120.9
NH 1 .oo CNH 123.0
NC ' 1.47 NCT
1
C"H 1.07 NC"H
109.5
CC"H
OCNH 180.0
a From 180, 811.