the origin of attractive interactions between dna molecules author: matej kanduč mentor: prof. rudi...
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The origin of attractive interactions between DNA
molecules
Author: Matej KandučMentor: prof. Rudi Podgornik
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Outline
Introduction to DNA structure
DNA condensation
Mean-field approach
Kornyshev-Leikin theory
Strong coupling theory
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What is DNA?
DNA Proteins Live
DNA - deoxyribonucleic acidlong helical polymer
contains genetic information that encodes proteins
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Structure of double DNA strands
ssphosphate sugar
(deoxyribose)
bases
adenine thymine
guanine cytosineH-bonds
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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!
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2 nm
1 t
urn
= 1
0 b
ase
pair
s =
3.4
nm
minor groove1.2 nm
major groove2.2 nm
Double helix
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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
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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
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DNA compaction
Higher organisms (eukaryotes)
Bacteria (prokaryotes)
Viruses
In cell’s nucleus
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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
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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!
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Hud & Downing, 2001
Lambert et al., 2000
DNA condensation
Toroidal DNA condensate Condensate from many genomes
Local hexagonal order
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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+
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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!
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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!
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Kornyshev – Leikin theory
Explicitly treating of charge pattern on cylinders
Analitical solution in Debye-Hückel approximation
a
Boundary conditions
ε’ ε’ε
Linearization!
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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!
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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
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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
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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
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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
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Two charged surfaces in strong coupling
electrostatic pressure:
osmotic pressure:
total pressure:
One counterion between two charged plates
attraction
repulsion
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Two cylinders in strong coupling
homogenously charged cylinders
only counterions
(partition function)
Free energy
Naji et al., 2004
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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
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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
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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