theoretical study of the interaction between sodium ion and a cyclopeptidic tubular structure
TRANSCRIPT
Theoretical Study of the Interaction Between Sodium
Ion and a Cyclopeptidic Tubular Structure
FRANCESCO FERRANTE, GIANFRANCO LA MANNA
Dipartimento di Chimica Fisica ‘‘F. Accascina’’, Universita degli Studi di Palermo,Viale delle Scienze, 90128 Palermo, Italy
Received 31 October 2005; Revised 16 March 2006; Accepted 17 March 2006DOI 10.1002/jcc.20677
Published online 20 April 2007 in Wiley InterScience (www.interscience.wiley.com).
Abstract: DFT calculations have been carried out to describe the pathway of a sodium ion along the stacking
direction of a tubular structure set up by five cyclopeptidic units, which can be considered a suitable model of a
hollow tubular structure of indefinite length. A lattice of points inside the tubular structure is defined and the DFT
interaction energy values with a sodium ion are obtained. The data allow predicting a zigzag path of the ion inside
the hosting structure.
q 2007 Wiley Periodicals, Inc. J Comput Chem 28: 2085–2090, 2007
Key words: tubular structure; cyclopeptide; nanotube; macrocyclic system
Introduction
Several classes of organic tubular structures are known, which
are made up of self-assembling of macrocyclic units;1,2 among
these, the hollow tubular systems set up by stacking of cyclopep-
tides derived from alternating D- and L-aminoacids, where the
self-complementary of the NH��CO group allows for intermo-
lecular hydrogen bonding, can be used as suitable devices for
building intermembrane ionic channels with performances com-
parable to those of the natural counterparts.3 The side groups of
the aminoacids can be chosen so that the resulting tubular struc-
ture can be inserted inside a lipidic double layer4 or inside a
monolayer adsorbed on a support.5 Moreover, a large variety of
hybrid cyclopeptides self-assembling into tubular structures
has been designed with potential applications in several fields of
physics and chemistry.6
We attempt here to study, using accurate quantum–mechanical
methods in the framework of the computational study of cyclo-
peptidic tubular systems undertaken by our research group,7 the
interaction between a cyclopeptidic tubular system and a sodium
ion, to give some insight in the transport process of a cation
through a tubular system.
The importance of such a study relies on the possible under-
standing of the basic elementary processes regulating the con-
ductivity properties inside artificial devices mimicking natural
systems. An example of this kind of study is reported in the
case of the insertion of lithium ion into carbon nanotubes.8
In the first part of the article, the choice of a suitable tubular
structure is dealt with, whereas in the second section the interac-
tion energy values between the chosen system and Naþ ion are
reported and discussed.
Computational Details
The full geometry optimization of the tubular aggregates was
carried out at the density functional theory level, using the gen-
eralized gradient BP86 functional9 and a split valence plus polari-
zation basis set (SVP) whose contraction scheme is (7s4p1d/
4s1p)/[3s2p1d/2s1p]. To reduce the computational time, the reso-
lution of identity (RI-DFT) approximation10 was used. In the
RI scheme, the electron density is expressed in terms of an
auxiliary basis set, which results in a better scaling behavior of
the Coulombian integrals relative to the number of basis set
functions, without consistent loss in accuracy. Its reliability was
already tested in the literature11 and also by us in the case of
the geometry optimization of dimeric and trimeric aggregates of
some cyclopeptides (Ferrante, F.; La Manna, G. unpublished
data). The auxiliary basis set corresponds to the SVP basis; its
contraction scheme is (8s3p3d1f/4s2p)/[6s3p3d1f/2s1p]. The
same model was used to calculate the energy values of all the
671 systems generated by placing, one at a time, a sodium
ion in a point of the lattice built up inside the cavity of the
aggregate, as described in The Interaction Between the Tubular
Structure and the Naþ Ion. The SVP and auxiliary basis set
Contract/grant sponsor: MIUR, Universita di Palermo
Correspondence to: G. La Manna; e-mail: [email protected]
q 2007 Wiley Periodicals, Inc.
contraction schemes for sodium atom are (10s5p1d)/[4s2p1d]
and (12s4p4d1f)/[5s2p2d1f], respectively. All calculations were
performed by using the package TURBOMOLE, Version 5.6.12
Results and Discussion
Definition of the Tubular Structure
The aim is to define the geometry of a tubular structure (TuS),
having the properties of an ideal system set up by an indefinite
number of monomeric units. So, once the monomeric unit was
selected, we optimized the geometries of the polymeric struc-
tures obtained, by stacking an increasing number of monomeric
units; when the geometry of the inner part of the polymeric
structure was independent on further addition of monomers, that
geometry was considered as representative of the whole TuS.
Cyclo[(Gly)8] was chosen as the monomeric unit because
glycine is the simplest aminoacidic structure and it is possible to
make computations on relatively large polymers. The presence
of side groups, in case different aminoacids were considered,
should not affect the conclusions, as the side groups are outside
the region under study, and the distortions on the structure of the
backbone, as well as the effects on the interaction of the TuS
with the ion, should be negligible.
The optimized geometrical parameters of the monomer are
given in Table1. The bond length values are similar to those
reported for cyclo[(Gly-D-Ala)4],13 with the largest deviation of
0.04 A in the case of the C���C bond. Conversely, dihedral
angles values are rather different, with the backbone torsional
angle ! less planar than in cyclo[(Gly-D-Ala)4].The dimer and the trimer were built up by bringing together
the monomers along the axis perpendicular to the plane of the
rings according to the most stable ‘‘antiparallel 1’’ geometry, as
Table 1. Relevant Geometrical Parameters of the Optimized Structure of cyclo [(Gly)8].
Bond lenghts (A) Bond angles (8) Dihedral angles (8)
C��O 1.233 C���C��N 115.4 C��N��C���C (�) 6128.4
C��N 1.364 C���C��O 120.4 N��C���C��N ( ) 6156.3
N��H 1.030 N��C��O 124.1 C���C��N��C� (!) 6170.8
N��C� 1.451 C���N��C 122.4
C���C 1.542 C���N��H 113.5
C��N��H 120.1
Figure 1. (a) Linearized schemes of the three stacking modes of a dimeric cyclopeptidic structure.
The antiparallel 1 stacking mode was shown to be the most stable structure. (b) Linearized scheme of
the trimer according to the antiparallel 1 stacking mode.
2086 Ferrante and La Manna • Vol. 28, No. 13 • Journal of Computational Chemistry
Journal of Computational Chemistry DOI 10.1002/jcc
shown in Figure 1. The minimum energy geometry of the dimer
corresponding to the ‘‘antiparallel 1’’ stacking mode is more
stable than the parallel mode by about 30 kJ mol�1 and by about
50 kJ mol�1 with respect to the ‘‘antiparallel 2’’ stacking mode,
which is in agreement with experimental data.14 In the trimer,
shown in Figure 1b, the same ‘‘antiparallel 1’’ arrangement was
adopted for both AB and BA0 couples of monomers.
The N��H���O¼¼C hydrogen bond lengths obtained for the
optimized dimer (AB) and the trimer (ABA0) of cyclo[(Gly)8]are reported in Table2. In the case of the dimer, the hydrogen
bond lengths are all approximately identical, whereas in the
trimer an alternation of shorter and longer hydrogen bonds is
observed. This can be rationalized in terms of the rotation of the
amidic groups of the central unit in the trimer that causes
the carbonylic oxygens to be closer to the amidic hydrogens of
the upper unit and farther from those of the lower unit. The val-
ues of the hydrogen bond lengths are in agreement with those
obtained in DFT calculations on aggregates of linear chains of
polyglycine.15
Afterwards, the tetramer and the pentamer were similarly built
up by adopting the same ‘‘antiparallel 1’’ stacking mode; the
hydrogen bond lengths obtained for the pentamer B0ABA0B@,whose optimized structure is shown in Figure 2a, are reported in
Table 2. We noted that the hydrogen bond lengths involving the
three central units were all in the range 1.870–1.877 A, whereas
the values concerning the terminal units showed noticeable
differences, as previously observed in the trimer. We conclude
that, since the geometry of the central monomer of the pentamer
is essentially replicated in the two adjacent monomers, the
pentamer can be considered as a representative structure of a
tubular {cyclo[(Gly)8]}n of indefinite length. Hence, the inner
trimer can be a good descriptor of the whole tubular structure
and our analysis will be limited to points lying inside it.
Table 2. N��H���O¼¼C Hydrogen Bond Lengths, in A, for the Optimized
Aggregates {cyclo[(Gly)8]}2 (AB), {cyclo[(Gly)8]}3 (ABA0), and
{cyclo[(Gly)8]}5 (B0ABA0B0 0).
Dimer Trimer Pentamer
AB AB BA0 B0A AB BA0 A0B@
1.908 1.921 1.889 1.912 1.877 1.876 1.902
1.907 1.890 1.918 1.878 1.870 1.875 1.876
1.907 1.915 1.889 1.905 1.872 1.875 1.901
1.908 1.885 1.919 1.883 1.875 1.873 1.887
1.908 1.917 1.890 1.907 1.874 1.874 1.918
1.907 1.889 1.923 1.883 1.876 1.8701 1.886
1.908 1.915 1.892 1.910 1.873 1.874 1.911
1.907 1.886 1.918 1.881 1.877 1.870 1.881
Figure 2. (a) Optimized structure of the pentamer tubular structure. (b) Scheme of the points inside
the tubular structure where the sodium ion was placed and interaction energy values were computed.
2087Interaction Between Sodium Ion and a Cyclopeptidic Tubular Structure
Journal of Computational Chemistry DOI 10.1002/jcc
It is to be outlined that, given the antiparallel arrangement,
the central monomeric unit of the pentamer is not a symmetry
plane.
The resulting main features of {cyclo[(Gly)8]}5 are the fol-
lowing: height, 20.1 A; interring distance, 4.8 A, very close to
the experimental values found in several cyclopeptide nano-
tubes;1,3,13 and diameter of the cavity (central monomer), 9.1 A.
The Interaction Between the Tubular Structure
and the Na+ Ion
The transport of ions inside the tubular structure (TuS), driven
by some external force, is strongly dependent on the relative
values of the inner energetic barriers. The interaction energy
between the chosen ion, Naþ, and the pentamer was calculated
for a lattice of points that was built inside the cavity of the pen-
tamer, taking as reference element the longitudinal axis of the
tubular structure, which is defined as the straight line passing
through the two points at intermediate distance from two carbonylic
oxygens at opposite sides of the second and of the fourth unit.
The distance between the second and the fourth monomeric
unit of the pentamer, 9.6 A, was divided into 10 identical parts
and each one of the resulting 11 points was the center of a circle
perpendicular to the axis. Moreover, every circular contour was
divided into a number of parts, so that each resulting point was
at about the same distance, ranging from 0.8 to 1.0 A, from the
adjacent considered points. This allowed a homogeneous distri-
bution of the points, where the interaction with the sodium ion
was evaluated. The distance between two adjacent circular surfa-
ces along the axis is 0.96 A; the radius of the inner circle was
chosen as 0.83 A (r1) and the radii of the other three concentric
circles were 1.66 (r2), 2.49 (r3), and 3.32 A (r4), respectively.
The total number of the considered points, lying on 11 parallel
planes, resulted 671. The set of the points considered is shown
in Figure 2b.
An analysis of the interaction energy values is reported here
for the most representative regions, namely the circular contours
corresponding to the third plane (p3), crossing the H-bonds
between the second and the third monomeric unit, those in the
sixth plane (p6), crossing the central monomeric unit of the pen-
tamer and those in the ninth plane (p9), crossing the H-bonds
between the third and fourth unit of the pentamer.
The interaction energy values obtained for the points lying
on the outermost circular contour are reported in Figure 3. An
approximate periodicity of �/2 is apparent, and so we can draw
our attention on angular values lower than �/2.Some attractive energy minima are present in the cases of
the p3 and p9 planes, but the general aspect shows that the
region corresponding to this outer contour is repulsive every-
where, except for some small intervals of the angular coordinate.
This indicates that the presence of the sodium ion at distances
from the axis of the TuS larger than 3.3 A can be ruled out.
When going inside the TuS, the interaction energy values
show all negative (attractive) values, as shown in Figure 4. In
the case of the distance 2.49 A from the axis (Fig. 4a), the sec-
tions p3 and p9 show the deepest minima, corresponding to
Figure 3. Interaction energy between the tubular structure and a
Naþ ion placed at the outermost circular contour (r4) as a function
of its angular coordinate for three representative planes (see text).
Figure 4. Interaction energy between the tubular structure and a
Naþ ion placed at the circular contours r3 (a) and r2 (b) as a function
of its angular coordinate for three representative planes (see text).
2088 Ferrante and La Manna • Vol. 28, No. 13 • Journal of Computational Chemistry
Journal of Computational Chemistry DOI 10.1002/jcc
interactions between the ion and the oxygen atoms of the TuS,
whereas the minima found in the section p6 can be referred to
interactions with the nitrogens; in all cases, the maxima have
been found in correspondence to interactions with the carbon
atoms of the carbonylic groups. For the distance of 1.66 A from
the axis, all sections show attractive values, with a less signifi-
cant angular modulation, especially in the case of the section p6,
and the energy values are all within the range of 25 kJ mol�1.
In Figure 5 an analysis of the interaction energies as a func-
tion of the distance from the central axis of the pentamer, for a
fixed value of the angular parameter and different sections p3,
p6 and p9, is reported. The minima of interaction energy are
located in the range of distances of 2.2–2.5 A, with lower
distance values in the case of the central section p6.
A further analysis of the interaction can be done by examin-
ing the energy values along the longitudinal direction (stacking
direction). Figure 6 shows the interaction energy values as a
function of the longitudinal coordinate z for different values of
the distance from the axis 0, r1, r2, and r3, at the fixed 0 value
of the angular coordinate. We observe the presence of two
minima and an energy barrier, approximately corresponding to
the p6 plane, which is less pronounced by decreasing the
distance of the ion from the longitudinal axis of the TuS.
Similar trends are observed in the case of different values of
the angular coordinate.
Conclusion
The overall information obtained from the analysis of the inter-
action energy values between the sodium ion and the cyclope-
ptidic tubular structure allows hypothesizing, in the presence of
a driving force along the stacking direction, going from p3
Figure 5. Interaction energy as a function of the ion’s radial coordi-
nate, at 0 radians, for three representative planes (see text).
Figure 6. Interaction energy as a function of the ion’s longitudinal coordinate, at 0 radians, for differ-
ent values of the radial coordinate [0 (a); r1 (b); r2 (c); r3 (d), see text].
2089Interaction Between Sodium Ion and a Cyclopeptidic Tubular Structure
Journal of Computational Chemistry DOI 10.1002/jcc
towards p9, a sort of zigzag pathway. In fact, after an initial
optimal interaction at a distance around 2.3 A from the longitu-
dinal axis, corresponding to the energy minimum found in corre-
spondence with the p3 plane, it is necessary the ion gets closer
to the axis so as to overcome the lowest energetic barrier, and
then goes along, away from the axis, for experimenting the larg-
est attractive energy (minimum energy distance about 2.4 A at
the p9 plane).
Moreover, the ion’s movement shows an angular modulation;
according to the observed interaction energy values, it is likely
to expect a decreasing of the angular coordinate, from initial
values of 0.8–1.2 rad (plane p3) to about 0.2 rad (plane p9).
The apparent asymmetry shown from the initial to the final
values of the radial and angular coordinates is due to the intrin-
sic asymmetry of the pentamer because of the antiparallel
arrangement adopted in the building of the TuS.
This result can be considered as a first static computational
approach in the study of the ionic conductivity inside a tubular
structure and could be extended by a molecular dynamics
simulation.
Acknowledgment
We thank the Computing Center of the University of Palermo
(C.U.C.) for technical support.
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2090 Ferrante and La Manna • Vol. 28, No. 13 • Journal of Computational Chemistry
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