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.