Table Of ContentElectron channels in biomolecular nanowires
Arrigo Calzolari*,1 Rosa Di Felice,1 Elisa Molinari,1 and Anna Garbesi2
1 INFM-S3 - National Research Center on nanoStructures and Biosystems at Surfaces,
4 and Dipartimento di Fisica Universit`a di Modena e Reggio Emilia, I-41100 Modena, Italy
0 2 CNR ISOF, Area della Ricerca, Bologna, Italy
0
2 We report a first-principle study of the electronic and conduction properties of a quadruple-
helix guanine wire (G4-wire), a DNA-derivative, with inner potassium ions. The analysis of the
n
electronic structure highlights the presence of energy manifolds that are equivalent to the bands
a
J of (semi)conducting materials, and reveals the formation of extended electron channels available
forcharge transport along thewire. Thespecific metal-nucleobase interactionsaffect theelectronic
2
properties at theFermi level, leading thewire to behaveas an intrinsically p-doped system.
]
t
f
o *email: [email protected] molecules (variable between 10 µm and 10 nm). Thus,
s due to its apparent poor intrinsic conductivity, DNA
.
t mightbereasonablyconsideredasabadinsulatorrather
a
than a viable electrical molecular wire.
m I. INTRODUCTION
Besidesthe standardDNA, othernucleotide-basedhe-
-
d lical molecules, such as guanine quadruple helices (G4-
Fueled by the ever increasing drive for miniaturiza-
n wires) or ”metal-manipulated” duplexes, may offer the
tion and improved performance in electronic devices
o
desired mechanical, recognition, and self-assembly prop-
c and by potential applications in the nanotechnologies,
erties, that make DNA so attractive. With respect to
[ the research effort to investigate the properties of novel
native DNA, these derivatives have metal cations in the
nanowire materials is undergoing an impressive growth.
1 innercoreofthebasestack. Whereastheinteractionsbe-
It is foreseen that the conventional solid-state technol-
v
tweenexternalionsandthedoublehelixhavebeenlargely
2 ogy could be replaced by new generations of devices
studiedbothexperimentallyandtheoretically,theeffects
1 based on molecular components, which take advantage
of their inclusion inside the helix are largely unknown.
0 ofthe quantummechanicaleffects thatrulethe nanome-
1 ter scale. Molecular electronics1 is currently explored as The presence of internal metal ions may drastically af-
0 fect the bonding pattern with and among the bases, in-
a long-term alternative for increasing the device density
4 troducing novel features in the structural and electronic
in integrated circuits. However, to keep up with these
0 properties of the system.12 A promising pathway for the
expectations,thenew trendmustprovideflexible,repro-
/
t ducible andwellstructuredarchitectures,easytowirein exploitationofDNA as a conductor inmolecular devices
a
isindicatedbytheevidencethatmetalionsincorporated
m a programmable way.
in the helix core may modify the conductivity of DNA-
Byvirtueoftheirrecognitionandself-assemblingprop-
- based wires.13,14
d erties, DNA molecules seem particularly suitable to ful-
n fill these requirements. Both the intrinsic combinatory In this paper, we focus on nanowires known as G4-
o principles ofnucleic acids andtheir chemistry canbe ex- wires15 (or quadruplexes), consisting of stacked guanine
c
ploited to build precise, miniaturized and locally mod- (G) tetrads (G4): the structure of these systems is illus-
:
v ulated patterns, where the drawing of functional arrays tratedanddescribedinFigure 1. These one-dimensional
i
X is obtained through a series of programmed chemical re- polymers are becoming appealing as prospective candi-
actions and not by the physical handling of the sam- dates for bio-molecular electronics because, due to the
r
a ples. The realization of DNA-based wired architectures low ionization potential of guanine (the lowest among
via self-assembly is a viable route to scale down the size nucleic-acid bases), they might be suitable to medi-
of devices to the molecular level.2,3,4 However, whereas ate charge transport by hole conduction along the he-
it was demonstrated that the self-assembling capabil- lix, and have even been suggested as nano-mechanical
ities of DNA make it suitable as a template to wire extension-contractionmachines.16 In the presence of ap-
metallic materials,5 its ability as an intrinsic conduc- propriate metal cations (especially K+ and Na+), solu-
tor is questioned by experimental results.6 Depending tions of homoguanylic strands in water,17,18 as well as
on base sequence, molecule length, environmentalcondi- lipophilicguanosinemonomersinorganicsolvents,19self-
tions,substrates,andelectrodematerials,thedirectmea- assemble in right-handed quadruple helices. The G4-
surements of the dc conductivity of DNA-based struc- motif has been identified in both cases; however, while
tures in solid-state devices7 reportinsulating character,8 the quadruplexes obtained from guanylate strands have
semiconductor-like transport characteristics,9 ohmic be- an outer mantle of sugars and phosphates (as in DNA)
havior,10 andproximity-inducedsuperconductivity.11 In- that connects the adjacent G4 planes, those obtained
deed, even in the cases in which charge transport has from lipophilic guanosine derivatives have no interpla-
been observed, the current is very low, with resistances nar connection: a continuous linker between consecutive
of the order of 0.1-1 GΩ cross the length of the DNA tetramersisnotnecessarytoformthewires. Theguanine
whereas the electronic properties of these materials were
so far investigated to a much lesser extent.27
In the following, we present a first-principle investiga-
tion of the electronic and conduction properties of pe-
riodically repeated G4-wires. Recently,27 we described
the structure and the energetics, as well as some basic
features of the electronic structure, of an infinite G4-
wire with and without the presence of K+ ions in the
inner cavity. In this paper,we focus entirely on the elec-
tronic properties of the same system and present a com-
plete and thorough analysis of the guanine-guanine and
metal-guanine interactions, discussing the effects on the
conduction properties of the tubular system.
II. COMPUTATIONAL APPROACH
FIG. 1: (a) Side view of a short quadruplex from which
thesimulatedG4-wirewasextracted. Theimagewasderived We performed ab-initio calculations of the electronic
from an experimental X-ray structure.21 The central core of andconductionpropertiesofinfiniteG4-wiresinthepres-
thehelix(red)isconstitutedofstackedsupramolecularstruc- ence of K+ ions, within the Density Functional Theory
tures,theG-quartets(G4),andtheK+ions(bluespheres)are (DFT)approach,28 usingthePW9129 gradient-corrected
hostedinthecentralcavityoftheG-quartetstack. Thelateral
exchange-correlationfunctional. DFT is lately gaining a
gray sticks describe the external sugar-phosphate backbone,
large credit in the scientific community as a reliable and
excludedinoursimulations. ByvirtueoftheoverallC4 sym-
accuratemethod todescribe large-scalebiomolecularag-
metry of the helix, it is possible to extract a periodic unit of
gregates,30 including guanine-based stacks.31
threeG4tetradsfromthisfinitequadruplex,thatconstitutes
theelementary building-blockof thesimulated infinitewires. Ourtotal-energy-and-forcecalculations32allowedusto
(b)IsolatedG-quartetthatformsoneplaneofthestackedG4- attainasimultaneousdescriptionoftheoptimizedatomic
wire. Each G4 consists of four co-planar H-bondedguanines, configuration and of the corresponding electronic struc-
arrangedinasquare-likeconfiguration. Theimageshowsthe ture for the selected systems (see Figure 1): the finite
relaxed geometry and an isosurface plot of theHOMOmani- planar guanine tetrad (G-quartet) and the infinite heli-
fold. (c) Schemeof the bypiramidal K+-O coordination. cal G4-wire filled with K+ ions in the inner cavity (label
3G4/K+). The single-particle electron wave-functions
were expanded in a plane-wave basis set with a kinetic-
quadruplexes have recently attracted interest because of energy cutoff of 25 Ry. Two special k-points in the ir-
theirpossibleroleinbiologicalsystems:20 theirbiological reducible wedge were employed for Brillouin Zone (BZ)
relevance has propelled a large number of investigations sums in the case of the G4-wire. The infinite helix was
(e.g. X-ray21 and NMR22) aimed at characterizing such simulatedby repeatedsupercellcontainingthree stacked
unusual supramolecular structures. Quadruple helices G4tetrads,27 employingperiodicboundaryconditionsin
have been obtained in the presence of different monova- the three spatial direction a thick vacuum layer (∼ 16
lent (K+, Na+, NH4+)19a,23 and divalent (Ca2+, Ba2+, ˚A)inthedirectionsperpendiculartothehelicalaxispre-
Sr2+,Pb2+)19b,24 cations. Despite the differentchemical ventedspuriousinteractionsbetweenadjacentreplicasof
nature ofthe constituents,allthese G4-wiresarecharac- the wire. For the isolated G-quartet, the same vacuum
terized by an inner core of stacked G4’s intercalated by thickness was employed also in the third direction per-
metal cations: one cation in every tetrad and one cation perdiculartotheplaneofthetetrad,andonlytheΓpoint
in every other tetrad, in the case of mono- and di-valent was used in the BZ sampling.
ions,respectively. Theself-assemblycapabilityoftheG4- The electron-ion interaction was described by non-
helices allows for the formation of quite long (100-1000 norm-conserving pseudopotentials33 for all the species
nm) and stiff wires. AFM images25 of four-stranded he- (C, N, O, H) except K, for which a norm-conserving
lices obtained fromG-richoligonucleotidesonsubstrates pseudopotential34 was used. For the latter species, both
revealed the G4-wires to be uniform and relatively rigid the valence 4s and the semi-core 3p shells contributed
polymers, with few bends, kinks, or branches. to the system with valence electrons. This treatment
Despite the large amount of structural investigations, represented a significant refinement towards a complete
theconductionpropertiesofthesenanowiresarebasically description of the electronic structure, with respect to
unknown and a direct measurement of electrical proper- the simplified results27 obtained by fixing the 3p shell in
ties of G4-wires is still missing. From the theoretical the frozen core and by applying Non Linear Core Cor-
pointofview,quantumchemistryandmoleculardynam- rections35 (NLCC)toaccountforpartialcorerelaxation.
icsstudiesfocusedontheenergeticsandonthegeometry The starting atomic configuration was obtained from
ofisolatedG-quartetsorfiniteclustersofstackedG4’s,26 the results of the X-ray analysis21 of the d(TG4T)
quadruple helix. Motivated by the observation that G4-
wires form with17,18 and without19 the covalentskeleton
andbyourspecificinterestinthebasestackasachannel
for charge mobility, we neglected the external backbone
in our simulations and focused on the centralcore of the
helix,constitutedofguaninesandmetalcations(seeFig.
1a). This choice is supported by theoretical reports36
for approximated DNA structural models, which assert
thatifanycurrentflowsinsuchsystems,itdoesthrough
the base-stacking, without involving the external man-
tle in the transport phenomena. The same evidence was
morerecentlyconfirmedbyDFTcalculationsoftheelec-
tronic properties of real DNA sequences (A-DNA8a and
Z-DNA37): these simulations showed that the orbitals
related to the sugar-phosphate backbone are a few eV
below the HighestOccupied MolecularOrbital(HOMO)
and above the Lowest Unoccupied Molecular Orbital
(LUMO) of the system. In principle, one should expect
thattheenvironmentsurroundingthebasestackplaysan
FIG. 2: (a) Band-structure along the GA direction parallel
important role in the overall conductivity properties of totheaxisof the3G4/K+ G4-wire, which coincideswith the
DNA molecules.37,38,39 Recent studies37,39b pointed out directionalongwhichtheplanartetradsstack. (b)Totaland
that a random distribution of counter-ions in the unit Projected Density of States (DOS) of the wire. The shaded
cell modifies the electrical properties of DNA both re- grayarearepresentsthetotalDOS.Thethinred(thickblue)
ducing the bulk quantum conductance and introducing solidcurvemarkstheprojectionoftheDOSontoG(K).Note
localized empty states in the energy gap. However, this thatthetotalDOSandtheG-DOScoincideinalargepartof
result is coherent with a picture where the external ions thespectrum,wherethethinredcurvealmost coincideswith
the border of the shaded area. The dashed horizontal curve
quantitativelyaffecttheglobaltransportpropertiesofthe
indicates the Fermilevel.
system,but donotconstitute analternativepathwayfor
the electron/hole transport through the helix.7 There-
fore, we believe that the bare guanine core will be well
identical character and are localized on the individual
representativeoftheessentialelectronicpropertiesofthe
G molecules. Figure 1b shows an isosurface plot of the
quadruplexes, allowing for the inspection of the charge-
convolution of four electron states (the HOMO’s of the
migration mechanisms and of the key features of metal-
fourguaninesinthetetrad)whichformtheπ-likeHOMO
molecule interaction. An explicit account for the effects
manifold.
of the backbone and of the surrounding counterions37,39
By exploiting the square-symmetry of the planar
wouldinsteadbedemandedforaquantitativeevaluation ◦
tetrad and the 30 twist angle between consecutive
of the quantum conductance to be compared with mea-
tetrads,wesimulatedaquadruplexofinfinitelengthwith
sured transport characteristics,which is way beyond the
a periodically repeated unit supercell containing three
purpose of the present work.
stacked G-quartets and three intercalated K+ ions in
the unit cell.27 Each potassium ion was symmetrically
located between two consecutive tetrads, and bipyrami-
III. RESULTS AND DISCUSSIONS
dally coordinated with the eight (four above and four
below)nearest-neighboringoxygenatoms(Fig. 1c). The
By means of the first-principle approach outlined atomic positions were relaxed until the forces vanished,
above,weoptimizedboththeisolatedG-quartetandthe within an accuracy of 0.03 eV/˚A. The structure, the en-
periodic G4-stack. ergetics,andthemetal-inducedstabilityofthetubewere
The analysis of the electronic structure of the planar described elsewhere.27 We find now that the explicit in-
G-quartet shows interesting features that will help un- clusion of the semi-core 3p electrons of K in the valence
derstandingtheelectricalpropertiesofG4-wires. Asalso shell for the pseudopotential calculations does not alter
foundfortheotherplanarG-aggregates(e.g. dimers,rib- theresultsobtainedpreviouslywithintheNLCCapprox-
bons),31 the H-bonds among the guanines do not favor imation,27 anddoesnotchangethe understandingofthe
theformationofsupramolecularorbitalsextendedonthe system from the structural point of view. The refined
whole G-quartet and the existence of dispersive bands. treatmentof the semi-core 3p electrons of K allows us to
On the other hand, the intermolecular interactions split gain a deeper insight into the electronic structure.
eachguanineenergylevelintoamultipletstructure: each The band-structure of the G4-wire 3G4/K+ is shown
multiplet is composed of four (the number of G’s in the in Figure 2a: the unoccupied states (above 3.5 eV) are
tetrad) energy levels and has a total width of about 200 separated from the occupied states (below 0 eV) by a
meV. The orbitals that contribute to a manifold have large energy gap (affected by the typical DFT underes-
timation28), and some of the states around zero energy helixwithrespecttothetetrad. Thiseffectisduetotwo
are partially filled. We previously demonstrated31 that factors: (i) the number of energy levels in each multi-
π-π coupling among guanines may give rise to delocal- plet; (ii) the in-plane and out-of-plane guanine-guanine
ized Bloch-type orbitals, whose band dispersion along and guanine-metal interactions, that couple the electron
the stacking direction depends on the relative rotation statesstemmingfromthevariousstructuralelements(ei-
angle between nucleobases in adjacent planes. Taking ther from G or from K) in the supercell. The number
into account the detected rotation angle21 of 30◦ for the of electron states in each manifold depends upon the
guanine quadruple helices, we now report that the elec- number of molecules and ions in the unit cell: there-
tronic band-structure of the 3G4/K+ column is repre- fore, whereas each manifold of the G-quartet contains
sentedbydispersionlessenergybands,indicatingthatno four levels, the manifolds of the 3G4/K+ wire contain
complete supramolecular orbital delocalization is to be twelve levels from the twelve guanines, and additional
expectedforsuchadegreeofhelicity. Thisbehaviorleads twelvelevelsfromthe K+ ionsintheenergyrangewhere
to the conclusion that in G4-wires the π-π superposition metal-base hybridization occurs. We come back to this
is not sufficient to induce a sizable coupling between the point later when we discuss the DOS. The number of
molecular states of guanines and/or the atomic orbitals levels in a manifold is not the only element that deter-
ofpotassium,whichwouldleadtopurelydispersivebands mines the details of the bandstructure: another key fea-
similartothoseof(semi)conducting materials. However, ture is the band-width, which is instead controlled by
as for the isolated G-quartet, the band-structure of the the specific interactions. Whereas in the case of the G4
3G4/K+ columnidentifiesthepresenceofmanifoldsthat tetrad only H-bonding plays a role, in the case of the
are equivalentto effective bands: eachmanifoldcontains 3G4/K+ wire there are different contributions from H-
a number (or multiplet) of levels that can be explained bonding and stacking between the bases, and from the
in terms of the number of nucleobase molecules and of coupling between the bases and the metal ions. It is
potassium ions in the periodic supercell, as we discuss worth noting that the formation of dense manifolds and
later. The orbitals in a multiplet have identical symme- the consequent establishment of effective band-like po-
tries and some degree of hybridization between neigh- tential conduction channels is a common characteristic
boring bases. The levels within a manifold are so close of stacked H-bonded nucleobase aggregates. In fact, not
(dense) in energy (∆E ≤ 20meV) that an external weak only we identified the same features in guanine quadru-
interaction (e.g. the thermal fluctuations or an exterinal plexes both in the presence and absence of inner metal
electricfield)maylettheorbitalsmix,givinganeffective cations,27butsimilarenergymanifoldswerealsodetected
dispersive band. This interpretation suggests a descrip- in the electronic band-structure of two different DNA
tionoftheelectronicstructurewherethespreadingofthe duplexes.7,8a,37 For instance, in their simulation of an
energy levels of the manifold leads to the formation of elevenbase-pairpoly(dG)-poly(dC)8asequence,dePablo
effective band-like peaks in the Density of States (DOS) andcoworkersfoundaHOMO-manifoldderivedfromthe
(Fig. 2b, shaded gray area). The DOS of the 3G4/K+ eleven states of guanines. In that case, the topmost va-
wire thus appears similar to those of materials with a lencebandhadabandwidthofonly40meV,smallerthan
dispersive band-structure. that calculated in our G4-wire (∼ 700 meV). This con-
firms that, while the splitting of the energy levels into
It is important to note that there is a one-to-one cor-
multiplets is a fingerprint of stacked rotated H-bonded
respondence between the band structure and the ground
nucleobases, the peculiar characteristic of the manifolds
state conduction properties (e.g., the quantum conduc-
depend on the intrinsic stacking properties (e.g. the π-π
tance spectrum) of a periodic system in the coherent
transport regime:40 at any given energy, the quantum coupling) of each type of helix.
conductanceisaconstantvalueproportionaltothenum-
To investigate more closely the effects of the metal
beroftransmittingchannelsavailableforchargemobility,
cations and of the metal-molecule interaction, we pro-
which are equal (in the absence of external leads) to the jected41 the total density of states of 3G4/K+ (shaded
number of bands at the same energy. Therefore,the for-
grayareain Fig. 2b)on G(thin redcurve)andK (thick
mation of effective dispersive bands in the investigated
blue curve) atomic orbitals. The G- and K-Projected
G4-wire is a signal of the intrinsic capability of the ma-
DOS’s(PDOS’s)showthatinalargeportionofthespec-
terial of hosting electron ”energy channels” available for
trum (below -2 eV and above 3.5 eV) only the guanine
chargemigration, whithin continuous energy ranges. On
electron states contribute to the DOS. For instance, the
the contrary, the energy spikes that would characterize LUMO peak at 3.5 eV has a pure guanine character,be-
a discrete spectrum would not be efficient for transport.
ing the convolution of the only twelve LUMO orbitals of
Theextendedorbitals(seebelow)relatedtotheeffective twelve G’s. The contribution of the K+ ions to the total
bands turn out to be the corresponding viable ”space
DOS is mainly localized at the top of the valence band
channels”forcarriermobility,e.g. thepathwaysthrough
(between-2 eV and0 eV). The presence ofboth guanine
which the carriers may migrate in the wire.
and potassium contributions to the DOS (as seen from
AcomparisonbetweenthemanifoldsoftheisolatedG- the superposition of the blue and red peaks in Fig. 2b)
quartet and of the G4-wire highlights an increased den- at the top of the occupied bands is the consequence of
sity of energy levels in the manifolds of the quadruple a metal-molecule interaction. The HOMO peak of the
planeperpendiculartotheG-quartets,wefurtherinspect
the features of the metal-molecule interaction (Fig. 3b).
Due to the high degree of charge delocalization along
the wire axis, the G4-wires may be described as good
electron/hole channels for mobile charges. Two types
of pathways for such mobile charges can be identified in
Figure 3b and contribute to the conductivity channels.
The first one stems from the low-energy component of
FIG.3: (a)Isosurfaceplotoftheconvolutionoforbitalsthat the HOMO double-peak, is extended through the gua-
representstheHOMOmanifoldoftheG4-wire,sideview. (b)
nine core of the helix, and is due to the base-base inter-
Contour plot of the same orbital in a plane perpendicular to
action. Similar channels are also observed for the other
thetetrameric planes and containing theK+ ions.
manifold-derived peaks (e.g. LUMO) and in the empty
(K free) quadruple helix.27 The second type of pathway
is due to the high-energycomponentof the HOMOpeak
3G4/K+ wire (see the double-peak indicated by an ar-
andresults fromthe metal-base interaction. This hybrid
row in Figure 2b) is due to a convolution of 24 electron
pathwayiscenteredaroundthepotassiumionsinthecen-
states deriving from the coupling between the twelve G
tral cavity of the wire, and it clearly shows the coupling
HOMO’s andthe twelve potassiumorbitals. Indeed, one
with the coordinated oxygen atoms of the G molecules.
would expect that the K+ ions would contribute to the
Hence, the inclusion of the metal cations inside the he-
DOS only with the filled p orbitals, after the s electrons
lix drastically influences the electronic properties of the
are removed upon ionization of the system. However, if
system. The details of the metal-nucleobase interactions
thiswerethecase,bycountingthelevelsinthemanifolds
dependuponthe natureofthe cationincludedinthehe-
wewouldfindonlyninecompletelyoccupiedlevelsdueto
lix. In the present case of potassium, its coupling with
the metal (three p orbitals from each K ion), in addition
the G bases modifies the topmostvalence band, favoring
to the guanine-based manifolds containing twelve levels
the formationof extended orbitals alongthe stackingdi-
each. Instead, the number of computed occupied levels
rection and enhancing the conduction properties of the
(twelvemorethanthosecomingfromthe guaninecount-
empty guanine structure.27
ing,andallconcentratedintheHOMOdouble-peak)and
the occurrence of partial occupation for some of them Togetfurtherinsightsintothemetal-basecoupling,we
(those around the computed Fermi level, see Figure 2b) compared the 3G4/K+ wire with other two similar neu-
indicates sp hybridizationin potassium when insertedin tral systems: the empty quadruple helix (labeled 3G4)
the helical guanine complex. Therefore, potassium does andthe G4-wirewith neutral K atoms (labeled 3G4/K).
not contribute separately with the 4s and the filled 3p The structures 3G4 and3G4/Kdo notdescribe realsys-
shells, but with a partially occupied sp shell: 7 equiva- tems,but areuseful modelsfor better understandingthe
lent electrons in 4 orbitals, which become 6 electrons in 3G4/K+ quadruplexes. The changes of the inner core
4 orbitals when the system is ionized as the 3G4/K+ do not basically modify the geometry (bond lengths and
wire. Consequently, the highest-energy component of angles) of the quadruple helix, but affect the electronic
the HOMO double-peak has an occupation factor of 3/4 structure. Figure 4 shows the comparison among the
the Fermi level is pinned at the top of the effective va- DOS (shaded gray areas) and the PDOS (thin red and
lence band (Fig. 2b) and the G4-wire in the presence of thick blue curves) of the systems. To compare the three
K+ ionsbehavesasanintrinsicallyp-typedopedsystem. structureswealignedthebottomenergylevels,andfixed
The observation of delocalized holes at the topmost va- the origin of the energy scale at the top of the valence
lence band is in agreement with the description of the band of the empty 3G4 helix (taken as reference), with
electronic structure of potassiumdiscussed above,where the purposetooutline the effects ofthe inclusionofmet-
eachionizedK+ atomcontributestothewholeelectronic als into the empty guanine supramolecular structure.
structurenotwiththreefully occupiedp-levels,butwith As already mentioned, in the DOS of all the studied
four partially occupied sp-states. G4-wires we observe the occurrence of broad G-derived
The spread sp-orbitals of potassium easily interact peaks, reflecting the same guanine aggregation state.
with the surrounding molecular orbitals of the tetrads, The empty tube has the valence band completely occu-
giving hybrid metal-molecule states. We visualized this pied and the Fermi level lays in the middle of the gap;
effectby drawingthe convolutionofthe effective HOMO in the presence of potassium (3G4/K and 3G4/K+), the
of the wire. Figure 3a shows anisosurface of the HOMO Fermi level is pinned at the top of a partially occupied
charge density in the unit cell, obtained from the convo- valence band. In the 3G4 case, the HOMO peak is the
lutionofthe 24highestoccupiedorbitalsthatcontribute convolution of the HOMO’s of guanines (HG in Fig. 4),
to the HOMO double-peak. By comparison with Figure whicharecompletelyoccupied;intheothertwocases,in-
1b, it is possible to recognize a uniform distribution of stead, the HOMO derives from the interactions between
the p orbitals deriving from the tetrads, but also the in- the HOMO’s of guanine (HG) and the hybrid states of
nerdelocalizeddensitystemmingfromtheorbitalsofthe potassium (labeled K in Fig. 4), which are partially
K+ ions. By cutting the HOMO charge density with a filled. One may consider the 3G4/K structure as ob-
the sp orbitals of the K+ ions shifts the position of this
peak to lower energies and reduces its height. All the
other peaks in Fig. 4 havea p-like characterandare less
influenced by the G-K+ coupling. The displacement of
peakdalsomodifies peakc, whichis sharperandhigher
in 3G4/K+ than in the free-standing tube. In the neu-
tral 3G4/K helix, the electrostatic coupling between K
and G is more effectively screened because of the larger
numberofelectronsinthe system: asaconsequence,the
shift of peak d is reduced with respect to the 3G4/K+
case, and peak d remains similar to that of the empty
wire. Another difference that we remark is the compo-
sition of the HOMO peaks: whereas for the 3G4 empty
tube the HOMO is purely G-like (HG), it is a mixed G-
K-like double-peak (HG+K) for the charged 3G4/K+
wire. For the neutral 3G4/K wire, the HOMO (Fig. 4,
middle panel) is split into two sharper peaks (Fig. 4,
bottom panel): a lower energy component similar to the
peak HG and a higher component with a prevalent K
character. The decrease in the degree of K-G orbital
mixing in 3G4/K with respect to 3G4/K+ is most likely
attributable to the increased occupation of the sp shell
of potassium, which becomes more inert because more
similar to a closed shell.
These changes in the electronic structure due to dif-
FIG.4: Total andProjected DensityofStates(DOS)ofdif-
ferent charge states of the inner metals underline the
ferentquadruplehelicalG4-wires: withoutinnermetal(3G4)
inthetoppanel,withK+ions(3G4/K+)inthemiddlepanel, delicate equilibrium that rules the stability and the
mutual interactions in this hybrid organic/inorganic
with neutral K atoms (3G4/K) in the bottom panel. In each
panel, the shaded gray area represents the total DOS, the molecule/metal complex. Differently from M-DNA,13
thin red (thick blue) curve marks the contribution of gua- wherethe metalcationsubstitutes foranimmino hydro-
nine (potassium) to the DOS. HG (LG) labels the band-like genatomandiscovalentlybondedtoanucleobase,inG4-
peakderivingfrom theHOMO’s(LUMO’s)of singleguanine wiresthereisnodirectchargesharingbetweenthemetal
moleculesintheunitcell. ThelabelKidentifiespeakswitha and the guanines. The stability and the electronic prop-
pronouncedpotassiumcontribution. Theoriginoftheenergy erties of the system are ruled by the coordination ratio
scaleisconsistentlysetattheHOMOoftheemptycolumnin amongthe K+ andthe eightnearest-neighboringoxygen
thethreeplots. The3G4isaninsulatorwithalargeHOMO-
atoms, symmetrically located above and below the ion
LUMO gap. In the metal-containing quadruplexes 3G4/K+
(Fig. 1c). The metal cations stabilize the structure via
and 3G4/K, instead, the Fermi level is pinned at the top of
electrostatic interactions,but also constitute aneffective
theHG+K and of the K peaks, respectively, dueto partially
occupied electron states. bridge between the electronic charge density around the
oxygenatoms: the HOMO contour plot shown in Figure
3b is the result of the π-π coupling between the oxygens
tained by adding three electrons to the 3G4/K+. The of consecutive tetrads, mediated by the electronic struc-
ture of the K+ ion.
inclusionofsuchelectronsincreases(from3/4to7/8fill-
The possibility of changing the electronic properties
ing factor) but does not complete the occupation of the
of the G4-wire, by using different metal ions to stabilize
topmost band; thus, the helix with the atomic K would
the stack, is expected to be a powerful tool for tuning
also be an intrinsic p-type doped wire.
the conduction properties of the nanowires. We are cur-
By analyzing the position and the width of the band-
rently exploring the inclusion of other cations with dif-
likepeaksforthethreesystems,wecanunderlinefurther
ferentouter-shellelectronicconfigurations(e.g. thetran-
details about the K-G interactions. As the K-derived
sition metals), that may be exploited to further change
states are found atthe topof the valence band, far away
the conductivity of G4-wires.
from that range the spectra are identical, e.g. peaks
a,b,e,f have the same width, shape and positions in
thethreeplots. AlsotheG-likeLUMOpeakLG remains
basically unchanged. On the contrary, in the 3G4/K+ IV. CONCLUSIONS
wire (central panel in Figure 4) the occurrence of a non-
vanishing K-PDOSin the [-2;-1]eV range strongly mod- The first principle study of the electronic and conduc-
ifies the peaks c and d with respect to the empty wire: tion properties of infinite G4-wires, stabilized by K+ in-
the electrostatic coupling between the s-like peak d and ner cations, shows that the π-π coupling among stacked
planar tetrads is insufficient to induce the formation of ical and self-assembly properties, suggest that G4-wires
dispersive bands in the wires. However, the presence of may be explored as viable DNA-based conductors for
closely spaced energy levels leads to the formation of nanoscale molecular electronics. The computed proper-
manifolds, whose density of states suggests a band-like ties are the equivalent of those of a bulk material: of
behavior. Thecouplingamongguanine-localizedmolecu- course, the actual behavior as a wire in a device setting
larorbitals,whichmaybeeasilyinducedbyaweakexter- dependonthespecific deviceimplementation,isaffected
nal interaction, gives rise to extended electron channels, fromconditionssuchaselectrode-wireandsubstrate-wire
suitable to host mobile charge carriers along the wire. coupling,andleavesseveralopenissuesforfurtherinves-
While the formation of split manifolds seems to be tigation and exploitation.
a general feature of base-base interactions in H-bonded
stackedsupramolecularnucleobaseaggregates,theeffects
due to the presence ofthe metals depend onthe identity
V. ACKNOWLEDGMENTS
of the cations. In the case of potassium, the inclusion
of the cations enhances the conduction properties of the
system, generating additional extended electronic chan- We gratefully thank Joshua Jortner for illuminating
nels stemming from the metal-guanine interaction. The discussions. This work was partially supported by the
mixed sp-orbitals of K+ hybridize with the HOMO’s of EC through project ”DNA-based nanowires” IST-2001-
guanine,andthiscouplinggivesorigintoapartiallyfilled 38951, by INFM through ”Progetto calcolo parallelo”
HOMOband,whichmakesthe systemequivalentto ap- which provided computer time at CINECA (Bologna,
doped wide-bandgap semiconductor. Italy), and by MIUR (Italy) through grant ”FIRB-
Theaboveresults,alongwiththeirattractivemechan- NOMADE”.
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