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Structure of Homopolymer DNA-CNT Hybrids
Suresh Manohar, Tian Tang*
*University of Alberta (Canada)
What governs the structure of DNA-CNT?Is there an optimal wrapping geometry?
Contributing Terms in the formation of hybrid: Adhesion Entropy loss of DNA backbone Electrostatics Bending and torsion of DNA backbone Deformation of CNT Base-Base Stacking Hydrogen bonding
+ (ns)
Contributions to the Binding EnergyContributing Term Estimate (kT/nm for a 1-nm tube)
1 Base-CNT Adhesion 13-35(based on base-graphite adsorption
data)
2 Entropic free energy increase due to chain confinement
0.4 – 1.3
3 Electrostatics 1.8 – 3.8(100 M salt)
4 Enthalpy increase due to DNA/CNT deformation
Negligible for DNA and for CNT’s < 1 nm in diameter
5 Base-base stacking Order of base-CNT adhesion, absorbed into it.
6 Hydrogen bonding Potentially very important – sequence dependent (upto 28 kT for GC in vacuum). Negligible
for cases studied here.
•Nucleotide base adsorption on inorganic surfaces (graphite in particular)
Edelwirth et al. Surface Science 1998Sowerby et al. Biosystems 2001
G
TC
A (2 0 k J /m o l )
Sowerby et al. PNAS (2001)
Adsorption Strong
lossentropy 2D-3D~Hads kTnb
Vdw stacking interactionsHydrophobic interactionsInterfacially enhanced hydrogen bonding
DNA on the nanotube: strong binding
0.5 1 1.5 2 2.5 3 3.5-500
0
500
1000
1500
2000
2500
3000
3500
4000
4500
R(Wad/D)1/2
-
L p/k
TL
molecular simulations--(n,0)molecular simulations--(2n,n)molecular simulations--(n,n)elastica solution
Twisting: (14,7)
Wrinkling: (16,16)
/
ext
vdw
PU
LkT
L
/flatR W D
Contribution due to nanotube deformability can be neglected for small-diameter tubes
Bending/Twisting ssDNA
dsDNA 100
ssDNA 5.1 : LengthKuhn
nm
nm
Bustamante, Bryant, Smith Nature, 421 423 (2003)
Very small ‘null’ Kuhn length?
Large effective Kuhn length at low ionic strength: long range electrostatic repulsion
Enthalpic effects?
Entropy Loss Due to Backbone Confinement
Order of kbT per nm (and smaller at low ionic strength)
Important at high ionic strength
Negligible at low ionic strength
NkTNb
bNkTU
k
ke 2
3
2
32
22
Enthalpic terms (stretch, bend, twist) – negligible!
Small ‘null’ Kuhn length!
Electrostatics
• Line of Charges Interacting Through the Debye-Huckel Potential• Account for nonlinearity using Manning Condensation
2 21, 0 , 0r z r z
2
1 1 1 12 log 1 expelU b
z z z z
100 M monovalent salt (T = 300K), 1.8 – 3.8 TkB per nm
Contributions to the Binding EnergyContributing Term Estimate (kT/nm for a 1-nm tube)
1 Base-CNT Adhesion 13-35(based on base-graphite adsorption
data)
2 Entropic free energy increase due to chain confinement
0.4 – 1.3
3 Electrostatics 1.8 – 3.8(100 M salt)
4 Enthalpy increase due to DNA/CNT deformation
Negligible for DNA and for CNT’s < 1 nm in diameter
5 Base-base stacking Order of base-CNT adhesion, absorbed into it.
6 Hydrogen bonding Potentially very important – sequence dependent (upto 28 kT for GC in vacuum). Negligible
for cases studied here.
Molecular Dynamics (MD) Simulation
MD was done using CHARMM program and forcefield.
Systematic study of poly(T) with 12 bases around (10,0) CNT.
CNT interacts with other atoms through vdw interactions only.
PME Method was used.
Equilibration
0 50 100 150 200 250 300 350 400-2.615
-2.61
-2.605
-2.6
-2.595
-2.59
-2.585
-2.58
-2.575
-2.57
-2.565x 10
4
Time (ps)T
otal
Sys
tem
Ene
rgy
(kca
l/mol
)
Pitch = 17.7 nmMinimized Equilibrated at 300K
Phosphate Group Solvated
Location of P atoms (for DNA with helical pitch of 61.5 nm).
Yellow – Starting loactions
Red – Final locations
P distance = 9.8 ± 0.5 Å from CNT axis
Solvated P atoms.
Blue – P atoms
Several Bases Un-Stack
Stacked Base Unstacked BAse
Stacked Base is at a distance of 3.45 Å from CNT surface
Water envelope starts at a distance of 6.8 ± 0.5 Å from CNT axis
Unstacking of Bases
Reduction of Effective Adhesion Energy
W = Adhesion energy for single base
WAdenine = -7.8 kcal/mol
WThymine = -6.3 kcal/mol
A > T
γ = Adhesion energy of base in chain
γAdenine = -2.4 kcal/mol
γThymine = -3.3 kcal/mol
Poly-dT > Poly-dA
α ≤ 35o stacked base
α > 35o unstacked base
Lateral Mobility of Base
Projection of nearest CNT carbon atom onto base plane
Mean bond length for T base ~ 1.39 Ao
Energy Barrier ~ 2 kBT
Kuhn Length
Klsji err /2
lk, Kuhn length = 5 nm for poly-dT on CNT surface
Analytical Model
1. At low ionic strengths, the competition between electrostatics and effective adhesion lead to an optimal wrapping geometry.
2. Free energy due to adhesion, Gad = -lγ, where l is the arc length of DNA per unit length of CNT, γ is the adhesion energy per unit arc length of DNA.
3. Electrostatics is handled using counterion condenstaion theory.
Pitch = 2πc
a = 9 Ao, d = 2 Ao, δ = 7 Ao
ε1 = 80, ε2 = 1
Q = -1.609 e-19 C
Sum charge-charge interactions on a Helix
Apply counterion-condensation theory
2 2 2
1 1 1
1 11 1 1 1 1
4 2B
el
k Tg f h
b
21/ / 4B o Bl b q k Tb
2 2 2 2 2 2 22 / 1 cos / 2 / 1 cos / 4 2
2 2 2 2 2 2 21 22 / 1 cos / 2 / 1 cos / 4
b n a b nb c b n a b nb c b
n
e e ef
n a b nb c n a b nb c
222 2 2 2
220 0 2 1
2 / 1 cos /2
/
b
o
n
e J n a b nb ch d
b
g = gad + gelFree energy of hybrid,
For low-ionic strength, competition between electrostatics & adhesion gives an optimal helical wrap
Summary Scaling analysis, molecular dynamics and an
analytical model were used to study the hybrid.
At low limit of ionic strengths, competition between electrostatics and adhesion leads to optimum wrapped geometry.
Poly-dT adheres better than poly-dA even though A>T for single bases.
Methodology
Starting structure was created in Materials StudioTM (MS). Sodium ions placed at a distance of 3.5 Å from P atoms. A pre-equilibrated water box of dimension 102x39x33 Å3 was used. The solute (DNA+CNT+ions) was placed at the center of water box. Periodic boundary conditions were employed using CRYSTAL
command in CHARMM. Initial structure was minimized for 500 steps using Newton Raphson. Two stage heating and equilibration done in NPT ensemble. 400 ps production phase done in NVT ensemble. This procedure was followed for structures with varying helical
pitches.
Gold coated AFM tip
Do Force Measurements on samples with Graphite or CNT in water
Attach thiolated ssDNA to the tip
Extract pull-off force and adhesion energy
Get Force-Deflection plot
Scheme for AFM experiment
Force plot for (DNA + 2-mercaptoethanol) tip on graphite in water
Force plot for Au tip on graphite in water
CNT Sample in water Graphite in water
Ongoing Work AFM experiments. Molecular simulations to estimate the binding free energy
between Graphite/CNT and single DNA base (A,T,C,G) using Thermodynamic Integration and Density of States method.