Multiscale model of electronic behavior and localization in stretched dry DNA

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Multiscale model of electronic behavior and
localization in stretched dry DNA

• R. L. Barnett, P. Maragakis, A. Turner, M. Fyta ,
  E. Kaxiras
• J Mater Sci (2007) 42 8894 - 8903
• Presented by
• Pooja Shrestha

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Introduction

• The mechanism of charge transport has been
  subject of numerous studies in past few years.
  These works address the problem of DNA stretching
  effects on the electronic states and the electron
  localization.
• Eley and Spivey 1 introduced the notion of
  efficient charge transport along the stacked
  pi-orbitals of the DNA bases.
• More recent electron transport experiments on DNA
  have widely varying results showing alternatively
  insulating behavior, semi-conducting behavior,
  ohmic conductivity and proximity induced
  superconductivity.
• There is a large diversity of the DNA forms in
  terms of its composition, length and structure.
  The electronic and transport properties of DNA
  are directly influenced by its different
  conformations as well as by environmental factors
  such as counterions, impurities or temperature.
  DNA electrode contact and rich variety of
  structures that it assume are cause of
  variability in experimental measurements.
• (1). Eley DD, Spivey DI
  (1961) Trans Faraday Soc 58 411

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DNA can be used to

• Build nanostructure
• Guide material synthesis
• Construct nanomaterial device
• Perform computations

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A short introduction to DNA

• DNA is a nucleic acid that contains the genetic
  information used in development and functioning
  of all known living organism and some virus.
• Nucleic acid is a macromolecule composed of
  chains of monomeric nucleotide which is a
  chemical compound that consists of three
  portions nitrogenous base, sugar and phosphate
  groups.
• Chemically, DNA is long polymer made from
  repeating units called nucleotides, with a
  backbone made of sugars and phosphate groups.

Single strand DNA
http//www.nanoroadmap.it/events/first_conference/
presentations/simmel.pdf
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Continued..

• DNA exist as the pair of molecule in the shape
  of double helix which is stabilized by hydrogen
  bonds between base attached to two stands

Form of double helix
http//www.nanoroadmap.it/events/first_conference/
presentations/simmel.pdf
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Continued..

• Each types of base on one strand forms a bond
  with just one type of base in other strand which
  is called complementary base pairing. Eg
• A-T
• C-G
• T-A
• G-C
• where, A Adenine
• C Cytosine
• G Guanine
• T Thymine

Base pairing
http//www.nanoroadmap.it/events/first_conference/
presentations/simmel.pdf
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Continued..

• Double helix is also stabilized by hydrophobic
  effect and pi stacking.
• An aromatic interaction (or pi-pi interaction) is
  a noncovalent interaction between organic
  compounds containing aromatic moieties.
• pi-pi interaction is caused by intermolecular
  overlapping of p-orbitals.
• In DNA pi stacking occurs between adjacent
  nucleotides. Aromatic ring are positioned nearly
  perpendicular to the length of the DNA strands
  and arranged parallel to each other allowing the
  bases to participate in aromatic interaction.

http//www.quantumconsciousness.org/images/DNA02.g
if
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Theoretical methods

• Theoretical efforts to understand the electronic
  behavior and transport in DNA can be divided into
  two general categories

• Model calculations using effective Hamiltonian
  and master equations to describe the dynamics of
  electrons and holes in DNA 4. The main
  limitation of such approach lies in the
  difficulty of determining accurate values for the
  parameters in effective Hamiltonian.
• Ab initio calculations can provide an accurate
  and detailed description of the electronic
  features but this approach is typically limited
  to a small number of atoms due to computational
  cost and cannot handle the full complexity of DNA
  molecule in various conformations.
• (4). Caetano RA, Schulz PA (2005) Phys Rev Lett
  95 126601

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Continued..

• The calculations are based on density-functional
  theory and some approximations are employed to
  handle computational demands. The results have
  been compared to an efficient and realistic
  semi-empirical model 2 in order to establish
  the validity of the latter approach.
• The poly(CG)-poly(CG) structures obtained in the
  pioneering study of Lebrun and Lavery 3 are
  used as representative structure for stretching
  effects which models two different modes of
  stretching
• pulling on opposite 3- 3 ends unwound helix
  leading to ribbon like structure and
• pulling on opposite 5- 5 ends leads helix
  contraction
• Dry and neutral DNA structure has been taken
  where the negatively charged groups on the
  backbone are passivated by protons water
  molecules or counterions (such as Na ion) are not
  considered in the calculations.

(2). Elstner M, et.al. (1998) Phys Rev B 58
7260 (3). Lebrun A, Lavery R (1996) Nucl Ac Res
24 2260
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Ab initio calculations

• Three different implementations of
  density-functional theory have been used to study
  the nature of electronic states in individual
  bases and in base pairs a method that uses
  atomic-like orbitals as the basis, one that uses
  plane waves and third that uses a real-space
  grid.
• For consistency and simplicity same
  exchange-correlation functional has been used in
  local-density approximation 5.
• In each methods pseudopotentials are represented
  by the Trouiller-Martins type in SIESTA, the
  Vanderbilt ultrasoft type in VASP and the
  Hammann-Schluter-Chiang type in HARES with
  computational parameters that ensure high level
  of convergence.
• (5). Perdew JP. Zunger A, (1981) Phys Rev B
  23 7260

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SIESTA a linear scaling density functional method

• Siesta (Spanish Initiative for Electronic
  Simulations with Thousands of Atoms) is both a
  method and its computer program implementation,
  to perform electronic structure calculations and
  ab initio molecular dynamics simulations of
  molecules and solids.
• It uses the standard Kohn-Sham selfconsistent
  density functional method in the local density
  (LDA-LSD) or generalized gradient (GGA)
  approximations.
• It uses norm-conserving pseudopotentials in its
  fully nonlocal form.
• The basis set is a very general and flexible
  linear combination of numerical atomic orbitals
  (LCAO).
• It projects the electron wavefunctions and
  density onto a real-space grid in order to
  calculate the Hartree and exchange-correlation
  potentials and their matrix elements.

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Continued..

• It allows the use of localized linear
  combinations of the occupied orbitals
  (valence-bond or Wannier-like functions), making
  the computer time and memory scale linearly with
  the number of atoms. Simulations with several
  hundred atoms are feasible with modest
  workstations.
• It also provides

• Total and partial energies.
• Atomic forces.
• Stress tensor.
• Electric dipole moment.
• Atomic, orbital and bond populations (Mulliken).
  
• Electron density

http//www.uam.es/departamentos/ciencias/fismateri
ac/siesta/
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Semi-empirical model

• 18 base pairs of poly(CG)-poly(CG) DNA sequence
  is used which has been stretched by 30, 60 and
  90. Within the semi-empirical scheme the
  electronic eigenfunctions are expressed as
• where the basis set includes the s and p atomic
  orbitals for each atom in the system. The
  coefficients are numerical constants.
• This method uses second order expansion in the
  electronic density to obtain the total energy.
• The result for band gaps is in excellent
  agreement with those of the ab initio simulation.

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Results and discussion

• The structure of base pairs is shown with
  labeled atoms in each base Figure (1).

Figure (1) The DNA base pairs AT (top) and CG
(bottom), with the atoms labeled. The purines (A,
G) are on the right, the pyrimidines (T, C) on
the left. Atom labeling follows standard notation
convention.
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Continued..

• The HOMO (highest occupied molecular orbital)
  state of AT pair is exactly the same as that of
  the HOMO state of the isolated A and the LUMO
  (lowest unoccupied molecular orbital) state of AT
  is same as that of the isolated T.
• The HOMO state of CG pair is exactly the same as
  that of the HOMO state of the isolated G and the
  LUMO state of CG is same as that of the isolated
  C.
• This shows that purines (A or G) give rise to the
  HOMO state, while the pyrimidines (C or T) are
  responsible for the LUMO states of each pair.
  Thus it is clear that all p-orbitals which
  belongs to purine or pyrimidine contribute to
  respective HOMO or LUMO state of base pair.
  This is in agreement with calculation with
  absorption spectra of DNA base and base pairs 6
• (6). Varsano D, Felice RI, Marques MAL, Rubio A
  (2006) J Phys Chem B 110 7129

Figure (2) The frontier states in the base pairs
and their identification with corresponding
orbitals in the isolated bases. The middle figure
in each panel shows the total charge density on
the plane of the base pair, with higher values of
the charge density in red and lower values in
blue. The figure on the left shows the HOMO state
and the figure on the right shows the LUMO state,
where red and blue isosurfaces correspond to
positive and negative values of the wave
functions. The labels on the left denote the type
of bases and base pairs.
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Continued..

• HOMO and LUMO states are slightly affected when
  the two components of base pair are separated
  along the direction of hydrogen-bond.
• Only in the reason where the backbone distance is
  significantly smaller than equilibrium value,
  interaction between the two bases shifts the
  eigenvalues of electronic state appreciably but
  the shift is relatively small for the HOMO and
  LUMO states.
• Band gap of the AT pair is significantly larger
  (3 eV) than that of CG pair (2 eV) and the HOMO
  and LUMO states of CG pair lie within band gap of
  AT pair.

Figure (3) Eigenvalues of states in the AT and
CG base pairs as a function of backbone distance.
In each case three states are included above and
below the band gap. Lines are results from SIESTA
calculations, points are results from HARES
calculations (see text). The frontier orbitals in
both pairs are related to one component of the
pair as indicated by the labels. The equilibrium
backbone distance is denoted by a vertical dashed
line.
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Continued..

• Eigenvalue shows slight dependence on axial
  distance and the angle of rotation except for
  small values of the axial distance which
  correspond to unphysical small separation between
  two base pairs.

Figure (4) Eigenvalues of states in the AT-AT,
CG-CG and ATCG base pair combinations as a
function of the distance along the helical axis
(at zero angle of rotation) and the rotation
angle around the helical axis (at the equilibrium
axial distance).
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Continued..

• The radius of the sphere centered on a particular
  atom is proportional to the magnitude of the
  dominant coefficient at this site which is
  essentially proportional to the local electronic
  density.
• As DNA becomes more elongated, orbitals overlap
  is less and become localized for high stretching.

Figure (5) The DNA structures for the
unstretched (top) and the different amounts of
stretching in the 3-3 and the 5-5 modes with
features of the frontier orbitals described by
the blue (HOMO) and red (LUMO) spheres. For both
modes theamount of stretching is (a) 30, (b)
60, and (c) 90 relative to the unstretched
structure, which is the BDNA form. The 3-5
orientations of the poly(CG)-poly(CG) sequence
are shown in the left panel at 90 stretching,
whereth ese the structure is easier to visualize.
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Conclusions

• The external force subjected to DNA double helix
  stretch elastically and have a dramatic effect on
  electronic properties at the atomic scale and on
  electrical transport along DNA.
• Purines are found to be associated with the HOMO
  states while the pyrimidines with the LUMO
  states.
• In the AT-CG combination the HOMO and LUMO states
  are identified with those of CG pair.
• For all combinations of bases and base pairs the
  nature of these states is not affected by
  separation of bases or base pairs along different
  directions or rotation along the helical axis.
• Electron hopping along DNA molecule is the
  function of stretching which is stronger for 3-
  3 mode than 5- 5 mode.

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ANY QUESTION ?
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THANK YOU !