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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