Cross, T.A.

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A Solid State Nuclear Magnetic Resonance Approach for Determining the Structure of Gramicidin a without Model Fitting 

SOLID STATE NUCLEAR MAGNETIC RESONANCE
APPROACH FOR DETERMINING THE STRUCTURE
OF GRAMICIDIN A WITHOUT MODEL FITTING
T. A. CROSS
Department of Chemistry, Florida State University, Tallahassee, Florida 32306-3006
Recently, solid state nuclear magnetic resonance (NMR)
methods have been used with magnetically aligned samples
to determine bond orientations with respect to the mag-
netic field in the backbone of polypeptides (1, 2). From the
bond orientations the orientation of the planar peptide
linkages can be determined. In these initial efforts the
presence of a distorted a helix was inferred from the
peptide linkage orientations and model-fitting the data (2).
However, it is possible to take advantage of the tetrahedral
geometry of the a carbon joining adjacent peptide linkage
planes and steric considerations to determine the three-
dimensional structure without model-fitting.
It has been shown that the ion-conducting channel
conformation of Gramicidin A in a phospholipid bilayer
can be magnetically aligned (3). While a structural model
of this channel (4) has withstood many challenges over the
last 14 years, it remains a model for which there is very
little direct structural data. The model does not explain
physical data such as the sequence specificity of ion
conductance (5) and the location of a specific site for ion
binding in the channel (6). To illustrate the solid state
NMR approach for determining the structure of Grami-
cidin a priori, the NMR data has been predicted for a
tripeptide sequence, -D Val8-L Trpg-D Leu10-, from the
atomic coordinates of the structural model. The Val8-Trpg
peptide linkage will be referred to as linkage A and the
Trp9-Leulo linkage as B (see Fig. 1).
The only NMR data used in this analysis are the N-H
(N-H) and N-C1 (N-Cl) dipolar interactions predicted
for the Gramicidin channel aligned such that the channel
axis is parallel with the magnetic field as shown by Van
Echteld et al.. The predicted values of the dipolar cou-
plings, Av, were obtained from the following equation and
the values are given in Table I.
AP =vg(3 cos2O- 1).
the N-H bonds. This is true for Gramicidin oriented in a
lipid bilayer as shown in Table I (3). The two values for
COSONH of linkage B will lead to duplicate sets of torsion
angles-in effect, one set where the molecule is oriented
with respect to the positive field direction and one where
the molecule is similarly oriented with respect to the
"negative" field direction. This duplication is eliminated
by considering only one of these ON-H angles. This is a
one-time elimination, for all other dipolar couplings both
values of 0 will be considered.
For N-C1 dipolar couplings, which ,are typically small
when the N-H couplings are large, four values of 0 are
obtained. This leads to four possible combinations ofN-H
and N-C, orientations in linkage B. Two of these combina-
tions are eliminated because they are inconsistent with the
HNC, bond angle. The orientation of two bonds with
respect to the magnetic field does not uniquely define the
orientation of a plane with respect to the field. An ambigu-
ity exists for the sign of the direction cosine relating the
axis normal to the plane with the field. Therefore, for
linkage B, four possible orientations need to be considered.
For these orientations a laboratory axis frame can be
assigned (see Fig. 2) with the Z axis parallel with the field
and the X and Y axes arbitrarily placed for an orthogonal
axis system. By defining the orientation of this peptide
NMR DETERMINED BOND ORIENTATIONS
Bo
L NKAGEA INKAGE
(1)
o is the angle between the bond and the magnetic field.
From the absolute value of Av' the possible bond orienta-
tions are determined (Fig. 1). The determination of 0 using
this equation will result in an ambiguity in the sign of cos0.
Because the absolute value of Av is obtained from the
NMR spectrometer, for values of As' c vPI there are a total
of four values of cos0 obtained. When Av > vll there is only
one possible sign for AP' and therefore, two possible values
for cos0. A property of helical structures oriented approxi-
mately parallel with the field is that AP' is generally >PI, for
R
FIGURE 1 A tripeptide sequence in Gramicidin A illustrating the planar
nature of the peptide linkages and the bonds in boldface for which the
NMR data was predicted. The orientation of these vectors with respect to
the field, Bo, is determined from the dipolar coupling between directly
bonded atoms in an oriented sample. The carbonyl carbons are referred to
as the Cl atoms throughout this communication.
BIOPHYS. J. ©Biophysical Society * 0006-3495/86/01/124/03 $1.00
Volume 49 January 1986 124-126
124
TABLE I
THE PREDICTED DIPOLAR COUPLINGS: AP, FOR
THE TWO PEPTIDE LINKAGES OF THE
TRIPEPTIDE, Val - Trp - Leu, IN GRAMICIDIN
Dipolar Couplings Val8 - Trpg Trp9 - Leul0Dipolaroupli Linage A Linkage B
*N-H + 15.30 kHz + 17.08 kHz
tN-C, ± 1.03 kHz ±0.51 kHz
*p-= +9.45 kHz (2).
tl = -1.33 kHz (2).
linkage the locations of six atoms are determined, includ-
ing the location of the Trpg and Leulo a carbons. The
NMR data for the adjacent peptide linkage, A, can be used
to determine the possible orientations for the N-Ca bond of
linkage A. Two possible orientations must be considered
for the N-H bond and four orientations for the N-C1 bond,
resulting in eight possible combinations. Only four of these
combinations allow for the known HNC, bond angle and
therefore, four N-Ca bond orientations are to be considered
with the four linkage B orientations. Of the sixteen combi-
nations of N-Ca and N-C1 orientations two are inconsis-
tent with the NCaCi bond angle. Again the orientation of
two bonds with respect to the field describes a plane for
which the normal to the plane is defined relative to the field
with an ambiguity in the sign of the direction cosine.
Twenty-eight values of the it torsion angle result. Of these
only nine fall in stable regions of the Ramachandran
diagram. To determine the X torsion angle the location of
C1 in linkage A must also be determined. The ambiguity in
the sign of the direction cosine relating the axis of the
normal to the plane of linkage A with the field doubles the
number of coordinate sets. Of the 18 sets of direction
cosines only 10 fall in sterically allowed regions of the
Ramachandran diagram. These 10 possible relative orien-
tations of the two peptide linkages are described by the
torsion angles given in Table II. The X angle of -1440 and
L/NKAGEA - | | LINKAGE 8
Val-8 ' // ' Leu-10
C6 / CC,a
c N~I
I~~~~~
R H
FIGURE 2 The same sequence as shown in Fig. 1, but here the orienta-
tion of the laboratory frame is shown. Z is parallel with the field and X
and Yand placed in orthogonal relationships to form an axis system. This
frame is first defined for the atoms of linkage B and then the bond
orientations in linkage A are determined with respect to the lab frame.
The 4 and 4' torsion angles that characterize the relative orientation of the
peptide linkage planes are also shown.
TABLE II
THE POSSIBLE RELATIVE ORIENTATIONS FOR
THE TWO PEPTIDE LINKAGES OF THE
TRIPEPTIDE, Val - Trp - Leu, IN GRAMICIDIN
DETERMINED WITHOUT MODEL FITTING FROM
PREDICTED NMR DATA
Conformation X 4A
1 -142.80 + 132.70
2 -142.80 +98.70
3 -129.60 +101.80
4 -128.90 + 163.90
5 -128.90 + 142.60
6 -122.90 +112.80
7 -122.60 + 132.70
8 -122.60 +98.70
9 -109.40 +101.80
10 -102.70 +112.80
t angle of 1320 correspond to the torsion angles of the
model structure from which the NMR data was pre-
dicted.
From the dipolar NMR data for two bonds in a single
peptide linkage it is conceivable that up to 16 sets of
coordinates can be generated. For an adjacent peptide
linkage up to 32 sets of coordinates are possible resulting in
as many as 1,024 possible relative orientations of the
peptide linkages. By taking into consideration the geome-
try of the atoms involved and steric hindrance, this number
has been reduced to 10 possible solutions. These solutions
all fall in the region of the fi secondary structures, none of
them is near either the collagen triple helix or a-helix
regions of the Ramachandran diagram.
The number of possible solutions for the structure of
Gramicidin, as it is further elaborated will decrease, as
many of the solutions will not result in reasonable secon-
dary structures. Furthermore, from these sets of orienta-
tions it is clear that as more NMR data is accumulated
that the number of solutions can also be reduced. For
instance, determining any of the C0 bond orientations
directly will reduce the possible solutions by approximately
a factor of two. Another attractive possibility is to interpret
the Cl chemical shift anisotropy, which has a high asym-
metry coefficient and would therefore provide information
about the orientation of the axis normal to the plane of the
peptide linkage. For now, it is shown that the solid-state
NMR approach for determining polypeptide backbone
structures does not have to depend on model-fitting the
observed data.
The author would like to thank Professor Dan Urry for providing the
coordinates of the structural model of Gramicidin A.
Receivedfor publication 11 May 1985.
REFERENCES
1. Cross, T. A., P. Tsang, and S. J. Opella. 1983. Comparison of protein
and DNA backbone structures in fd and Pfl1 bacteriophages.
Biochemistry. 22:721-726.
POSTER SUMMARIES 125
2. Cross, T. A., and S. J. Opella. 1985. Protein structures by solid state
NMR: residues 40-45 of fd coat protein. J. Mol. Biol. 182:367-
381.
3. Van Echteld, C. J. A., B. de Kruijff, A. J. Verkleij, J. Leunissen-
Bijvelt, and J. de Gier. 1982. Gramicidin induces the formation of
non-bilayer structures in phosphatidylcholine dispersions in a fatty
acid chain length dependent way. Biochim. Biophys. Acta.
692:126-138.
4. Urry, D. W. 1971. The Gramicidin A transmembrane channel: a
proposed ir(L,D) helix. Proc. Natl. Acad. Sci. USA. 68:672-676.
5. Bamberg, E., K. Noda, E. Gross, and P. Lauger. 1976. Single-channel
parameters of Gramicidin A, B, and C. Biochim. Biophys. Acta.
419:223-228.
6. Urry, D. W., K. U. Prasad, and T. L. Trapane. 1982. Location of
monovalent cation binding sites in the Gramicidin A channel. Proc.
Nati. Acad. Sci. USA. 79:390-394.
126 NMR Approach to Gramicidin Structure


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A Solid State Nuclear Magnetic Resonance Approach for Determining the Structure of Gramicidin a without Model Fitting

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