The origin of attractive interactions between DNA

molecules

Author: Matej KandučMentor: prof. Rudi Podgornik

Outline

Introduction to DNA structure

DNA condensation

Mean-field approach

Kornyshev-Leikin theory

Strong coupling theory

What is DNA?

DNA Proteins Live

DNA - deoxyribonucleic acidlong helical polymer

contains genetic information that encodes proteins

Structure of double DNA strands

ssphosphate sugar

(deoxyribose)

bases

adenine thymine

guanine cytosineH-bonds

Why a helix?

van der Waals force

hydrophobic force

twist angle = 36°

Adjacent base pairs attract themselves!

force

(bases are not solubale in water)

Rigid bonds

sugar-phosphate distance: 0.6 nm

consequence: twist!

2 nm

1 t

urn

= 1

0 b

ase

pair

s =

3.4

nm

minor groove1.2 nm

major groove2.2 nm

Double helix

DNA under physiological conditions

persistence length= 50 nm

dissociation of phosphate groups

-e0 per 0.17nm

charge screening due to salt ions

screening length: 1nm

H+

In 0.1M solution of NaCl

Disordered coil

2Rg

LRg size of coil

Peterlin, 1953

10-6 10-5 10-4 10-3 10-2 10-1 100 101 102 meters

viruses

bacteria

fungi

plants

reptiles

insects

mammals

Total DNA sizes

bacteriophage T4: 50 μmhuman: 1.8 mamoeba: 230 m

Eukaryotes -chromosomes

DNA compaction

Higher organisms (eukaryotes)

Bacteria (prokaryotes)

Viruses

In cell’s nucleus

Kleinschmidt et al., 1962

Disordered DNA

DNA size: 50 μm

Bacteriophage T4

Disorderd coil: 1 μm

Packing size: 50 nm

In usual conditions:parts of DNA repel each other

Effect of polyvalent ions

Cholesteric phase Columnar hexagonal phase

Pelta et al., 1996

Isotropic phase

Dilute solution= small concentration of DNA

depends on NaCl/agents concentration

polyvalent ions

++ (2+), 3+, 4+

liquid crystalfragments 50 nmhigh pitch: 22 μm (0.05°/molecule)

monocrystalline

condensation

Polyvalent ions induce attraction between DNA

molecules!

Hud & Downing, 2001

Lambert et al., 2000

DNA condensation

Toroidal DNA condensate Condensate from many genomes

Local hexagonal order

Condensing agents

Co

NH3

NH3

NH3

NH3H3N

H3N

NH2

H2N N

H

N

H

NH2

H2N N

H

(spermine)

(spermidine)

(cobalt hexamine)

Mn2+

Cd2+

+1

+2

+3

+4

valency causing condensationno effect

Mg2+

Ca2+

Na+

K+

Mean-field theory (Poisson-Boltzmann)

Poisson-Boltzmann

only Coulombic interactions

no dipole interactions

charges are point-like

aqueous solution – continuos medium

mean-field potential of all ions

Assumptions

Very successful in describing soft charged systems

...counterion

...coion

Solving electrostatics

collective effects!

R

a

Poisson-Boltzmann for charged cylinders

DNA molecules as two homogenously charged cylindersSimple salt (Na+Cl-): 000 nnn

Boundary condition

Only re

pulsive

forc

e

Fails fo

r poly

vale

nt ions!

Kornyshev – Leikin theory

Explicitly treating of charge pattern on cylinders

Analitical solution in Debye-Hückel approximation

a

Boundary conditions

ε’ ε’ε

Linearization!

Kornyshev-Leikin theory – implementation for DNA

two thin spirals of negative charge – DNA phosphates

two thin spirals of positive charge – cations adsorbed in the grooves

some counterions possess chemical affinity to sites on DNA

θ - fraction of phosphate charges neutralized by adsorbed cations

fraction f in minor groovethe rest (1-f ) in major groove

by hand!

Kornyshev and Leikin, 1999

Kornyshev – Leikin theory

R=26 Å Δz = optimal

0.9 < θ < 1.1

Electrostatic zipper

Condensation possible

minor groove: 30%

major groove: 70%

Dz

Intrinsic structure not the only effect...

28°-42°

??

sequence dependent twist

finite elasticity reduced interaction

Non-ideality in structure

Other examples of different structures

F-actin Microtubules Viruses

Correlation effects

Mean-field

(Oosawa, 1968)

no correlations

no correlations

Poisson-Boltzmann

repulsive force for homogenous surfaces

Perturbative correction

thermal fluctuations

attractive force for homogenous surfaces

Strong-coupling theorystrong correlations

2D Wigner crystal formation

strong correlations

attractive correction

(Kornyshev-Leikin)

Intrinsic structure

Geometrical details

attraction

2az

q

Counterion correlations – Strong coupling theory

za

counterions form 2D layer

Neutrality condition:

Potential energy:

no lateral degrees fo freedom

Criterion

electrostatic energy >> thermal energy

Netz, 2000

Coupling parameter

one-particle effects

Two charged surfaces in strong coupling

electrostatic pressure:

osmotic pressure:

total pressure:

One counterion between two charged plates

attraction

repulsion

Two cylinders in strong coupling

homogenously charged cylinders

only counterions

(partition function)

Free energy

Naji et al., 2004

Two cylinders in strong coupling - results

long-range attraction

local minimum at small separations

Free energy Force

relevanceq=3, 4...

relevant for small distances and q >2

Monte Carlo simulations

Allahyarov et al., 2005

local minimum ~ counterion diameter

competition: monovalent vs. polyvalent ions

local attraction for polyvalent salt

repulsion for large distances

Explicit DNA structureExplicit ion-ion interactions

25 mM monovalent65 mM polyvalent

monovalent + polyvalent ions

Conclusion

2az

q

Ion correlations

Solution with polyvalent ions

Strong couplingGeometrical structure

Monovalent solution

repulsion between DNA molecules

No complete theory!

mean-field for ions

attraction between DNA molecules

adsorption of polyvalent ions

electrostatic zipper one-particle effects

only for polyvalent ions