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? DNAProteinsLive DNA - deoxyribonucleic acid long helical polymer contains genetic information that encodes proteins

Structure of double DNA strands phosphate sugar ( deoxyribose ) bases adeninethymine guanine cytosine H-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 turn = 10 base pairs = 3.4 nm minor groove 1.2 nm major groove 2.2 nm Double helix

DNA under physiological conditions persistence length = 50 nm dissociation of phosphate groups -e 0 per 0.17nm charge screening due to salt ions screening length: 1nm H+H+ In 0.1M solution of NaCl Disordered coil 2Rg2Rg size of coil Peterlin, 1953

Total DNA sizes bacteriophage T4: 50 μm human: 1.8 m amoeba: 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 phaseColumnar 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 crystal fragments 50 nm high 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 (spermine) (spermidine) (cobalt hexamine) Mn 2+ Cd valency causing condensationno effect Mg 2+ Ca 2+ Na + K+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!

Poisson-Boltzmann for charged cylinders DNA molecules as two homogenously charged cylinders Simple salt (Na + Cl - ): Boundary condition Only repulsive force Fails for polyvalent ions!

Kornyshev – Leikin theory Explicitly treating of charge pattern on cylinders Analitical solution in Debye-Hückel approximation a Boundary conditions ε’ε’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 groove the rest (1-f ) in major groove by hand!

Kornyshev and Leikin, 1999 Kornyshev – Leikin theory R=26 ÅΔz = optimal 0.9 < θ < 1.1 Electrostatic zipper Condensation possible minor groove: 30% major groove: 70%

Intrinsic structure not the only effect... 28°-42° ? sequence dependent twist finite elasticityreduced interaction Non-ideality in structure Other examples of different structures F-actin MicrotubulesViruses

Correlation effects Mean-field (Oosawa, 1968) no correlations Poisson-Boltzmann repulsive force for homogenous surfaces Perturbative correction thermal fluctuations attractive force for homogenous surfaces Strong-coupling theory strong correlations 2D Wigner crystal formation strong correlations attractive correction (Kornyshev-Leikin) Intrinsic structure Geometrical details attraction

Counterion correlations – Strong coupling theory 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 energyForce relevance q=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 structure Explicit ion-ion interactions 25 mM monovalent 65 mM polyvalent monovalent + polyvalent ions

Conclusion Ion correlations Solution with polyvalent ions Strong coupling Geometrical 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