The origin of attractive interactions
between DNA molecules
Author: Matej Kanduč
Mentor: prof. Rudi Podgornik
Outline
Introduction to DNA structure
DNA condensation
Mean-field approach
Kornyshev-Leikin theory
Strong coupling theory
What is DNA?
DNA - deoxyribonucleic acid
long helical polymer
contains genetic information that encodes proteins
DNA
Proteins
Live
Structure of double DNA strands
phosphate
s
sugar
(deoxyribose)
bases
adenine
guanine
thymine
H-bonds
cytosine
Why a helix?
Adjacent base pairs
attract themselves!
hydrophobic force
(bases are not solubale
in water)
Rigid bonds
sugar-phosphate
distance: 0.6 nm
van der Waals force
consequence: twist!
force
twist angle = 36°
1 turn = 10 base pairs = 3.4 nm
Double helix
minor groove
1.2 nm
major groove
2.2 nm
2 nm
DNA under physiological conditions
Disordered coil
In 0.1M solution of NaCl
dissociation of
phosphate groups
H+
-e0 per 0.17nm
2Rg
charge screening due
to salt ions
size of coil
Rg  L
screening length: 1nm
persistence length
= 50 nm
Peterlin, 1953
Total DNA sizes
viruses
bacteria
Eukaryotes chromosomes
fungi
plants
insects
reptiles
mammals
10-6
10-5
10-4
10-3
10-2
10-1
100
101
102 meters
bacteriophage T4: 50 μm
human: 1.8 m
amoeba: 230 m
DNA compaction
Viruses
Higher organisms (eukaryotes)
Bacteria (prokaryotes)
In cell’s nucleus
Disordered DNA
Bacteriophage T4
DNA size: 50 μm
Disorderd coil: 1 μm
Packing size: 50 nm
In usual conditions:
parts of DNA repel
each other
Kleinschmidt et al., 1962
Effect of polyvalent ions
Isotropic phase
Dilute solution
= small concentration
of DNA
+
polyvalent ions
(2+), 3+, 4+
Cholesteric phase
Columnar hexagonal phase
Polyvalent ions induce attraction
between DNA molecules!
condensation
liquid crystal
fragments 50 nm
high pitch: 22 μm (0.05°/molecule)
depends on
NaCl/agents
concentration
monocrystalline
Pelta et al., 1996
DNA condensation
Toroidal DNA condensate
Condensate from many genomes
Hud & Downing, 2001
Local hexagonal order
Lambert et al., 2000
Condensing agents
no effect
causing condensation
valency
Na+
K+
+1
Mg2+
Ca2+
Mn2+
+2
Cd2+
NH2
H2N
N
(spermidine)
H
+3
NH3
H3N
NH3
(cobalt hexamine)
Co
H3N
NH3
NH3
H
+4
N
H2N
N
H
NH2
(spermine)
Mean-field theory (Poisson-Boltzmann)
Solving electrostatics
Assumptions
only Coulombic interactions
no dipole interactions
charges are point-like
aqueous solution – continuos medium
mean-field potential of all ions
collective effects!
...counterion
...coion
Poisson-Boltzmann
Very successful in describing
soft charged systems
Poisson-Boltzmann for charged cylinders
DNA molecules as two homogenously charged cylinders
Simple salt (Na+Cl-): n  n  n
0
Boundary condition
R
a
0
0
Kornyshev – Leikin theory
Explicitly treating of charge pattern on cylinders
Analitical solution in Debye-Hückel approximation
Linearization!
a
ε’
ε
ε’
Boundary conditions
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
by hand!
fraction f in minor groove
the rest (1-f ) in major groove
Kornyshev – Leikin theory
Δz = optimal
R=26 Å
Electrostatic zipper
Kornyshev and Leikin, 1999
Condensation possible
0.9 < θ < 1.1
minor groove: 30%
major groove: 70%
Dz
Intrinsic structure not the only effect...
Non-ideality in structure
?
28°-42°
sequence
dependent twist
finite elasticity
reduced interaction
Other examples of different structures
F-actin
Microtubules
Viruses
Correlation effects
strong correlations
no correlations
Mean-field
Poisson-Boltzmann
no correlations
Perturbative
correction
thermal fluctuations
attractive correction
repulsive force
for homogenous
surfaces
Intrinsic structure
Geometrical details
(Kornyshev-Leikin)
attraction
(Oosawa, 1968)
Strong-coupling
theory
strong correlations
2D Wigner crystal
formation
attractive force
for homogenous
surfaces
Counterion correlations – Strong coupling theory
electrostatic energy >> thermal energy
Criterion
counterions form 2D layer
q
Neutrality condition:
z
2a
a  z
Potential energy:
no lateral degrees fo freedom
Coupling parameter
one-particle effects
Netz, 2000
Two charged surfaces in strong coupling
One counterion between two charged plates
electrostatic pressure:
osmotic pressure:
total pressure:
repulsion
attraction
Two cylinders in strong coupling
homogenously charged cylinders
only counterions
Free energy
(partition function)
Naji et al., 2004
Two cylinders in strong coupling - results
Free energy
relevance
q=3, 4...
long-range attraction
local minimum at small separations
relevant for small distances and q >2
Force
Monte Carlo simulations
Explicit DNA structure
Explicit ion-ion interactions
monovalent + polyvalent ions
competition: monovalent vs. polyvalent ions
local attraction for polyvalent salt
local minimum ~ counterion diameter
repulsion for large distances
25 mM monovalent
65 mM polyvalent
Allahyarov et al., 2005
Conclusion
Monovalent solution
repulsion between DNA molecules
Solution with polyvalent ions
attraction between DNA molecules
Ion correlations
Geometrical structure
mean-field for ions
adsorption of polyvalent
ions
electrostatic zipper
Strong coupling
q
z
2a
one-particle effects
only for polyvalent ions
No complete theory!