Fundamental length scales in Na- DNA solutions: semidilute versus dilute regime Sanja Dolanski Babić, Tomislav Vuletić, Tomislav Ivek, Silvia Tomić, Institut za fiziku, Zagreb, Croatia Sanja Krča, Rudjer Boskovic Institute, Zagreb, Croatia Lorena Griparić, UCLA, LA, USA Francoise Livolant, Laboratoire de Physique des Solides, Orsay, France Rudi Podgornik, Faculty of Mathematics and Physics, University of Ljubljana, Institute J.Stefan, Ljubljana, Slovenia Group for dielectric spectroscopy and magnetotransport properties

Key words Biological matter: Charged polymers: DNA, RNA, HA, proteins functions and structure are intimately connected connection via dynamics depend on the local environment

DNA: highly charged polymer Effective density: 1 e - / 0.17 nm Counterion atmosphere surrounds charged polymer DNA 3.4 nm 10 bp full turn m 0.34 nm 2 nm -2e / 0.34 nm M Monovalent counterions: Strong repulsive electrostatic interaction; Debye screening length Polyvalent counterions: Repulsive interactions turn into attractive interactions Grosberg et al., Rev.Mod.Phys.74, 329 (2002) Richness of phenomena in soft matter is Comparable with those in low-temperature physics

DNA: wide elasticity range 200 nm Elongated coil conformation in aqueous solutions 50 nm In cells L c  4 cm folded in dense and compact states to fit within micron-sized nucleus Rigid chain: L p > L c Very low salt Flexible chain L p < L c High salt Persistence length L p  I -1

DNA structure from DNA dynamics “Tube” experiment: System of many DNA chains in solution Technique: Dielectric spectroscopy 40 Hz – 100 MHz Varying parameters: DNA concentration and added salt (ionic strength) Theoretical models: Fundamental length scales describing the structure of a single- chain and solution composed of many chains S. Tomic, T.Vuletic, S.Dolanski et al., Phys. Rev. Lett. 97, (2006) S. Tomic et al., Phys.Rev.E 75, (2007) S. Tomic, S.Dolanski, T.Ivek, T.Vuletic, et al., submitted to EPL

Electrophoresis: 1) polydisperse Na-DNA most of the fragments: 2 – 20 kbp Contour length:  m Semidilute regime: c > c* ≤ mg/mL 2) monodisperse Na-DNA Short fragments: 146 bp Contour length: 50 nm Dilute regime: c < c*  1 mg/mL

 Chamber for complex conductivity of samples in solution Conductivity range  S/cm Small volume: 100  L Platinum electrodes Reproducibility 1.5 % Long term reproducibilty: 2 hours  Temperature control unit Temperature range: 10↔60 o C Stability: ±10 mK Precision impedance analyzer Agilent 4294A: 40Hz - 100MHz Dielectric Spectroscopy Set-Up

Dielectric spectroscopy Frequency range: 40 Hz – 110 MHz Measurement functions: G exp (  ), C exp (  ) G(  )=G exp (  ) – G bg (  ) C(  )=C exp (  ) – C bg (  ) Background: NaCl solutions of different molarities adjusted to have the same real part of admittances and capacitances as DNA solutions.

Counterion atmosphere in ac field DNA Applied ac field: Oscillating flow of net charge associated with intrinsic DNA counterions  (L)  L 2 /D S.S.Dukhin et al, Adv.Coll. Interface Sci. 13, 153 (1980) R.W.O’Brian, J. Coll. Interface Sci 113, 81 (1986). F.Bordi et al., J.Phys.:CondensedMatter 16, R1423 (2004)  Semidilute regime c DNA > chain overlap concentration R Na + LpLp Solution correlation length relaxation time  length scale L Dilute regime c DNA < chain overlap concentration R ad

Results: Complex dielectric relaxation Cole-Cole function long short Two broad (1-   0.8) relaxation modes HF mode: Long: 0.1 MHz – 15 MHz; Short: similar LF mode: Long: 0.5 kHz – 70 kHz; Short:  80 kHz Amplitude and position in frequency depend on DNA concentration

Long Na-DNA solutions Semidilute regime

Characteristic scale of HF relaxation c DNA -0.5 c DNA P.G.de Gennes et al.,J.Phys.(Paris), 37, 1461 (1976) A.V.Dobrynin et al., Prog.Polym.Sci.30, 1049 (2005) T.Odijk, Macromolecules 12, 688 (1979)   c DNA -0.5 dGPD semidilute solution correlation length   c DNA Low DNA concentrations No added salt Locally fluctuating regions With exposed hydrophopic cores 1 mM added salt: c DNA > 2I s  pertinent scale c DNA < 2I s Debye length ?

Characteristic scale of LF relaxation c DNA ± mM added salt: c DNA > 2I s R pertient scale c DNA < 2I s L LF  50 nm R  c DNA Average size of the chain random walk of correlation blobs A.V.Dobrynin et al., Prog.Polym.Sci.30, 1049 (2005)

Added salt vs own DNA screening Odijk-Skolnick-Fixman L p = L 0 + l B / (2b  ) 2 = L I s -1 Persistence length 2 I s < 0.4 c i : DNA acts as its own salt L LF R Screening by added salt ions 2 I s > 0.4 c i = 0.4 (3 c DNA ) LpLp L LF

Summary: semidilute solutions HF response: solution property Free counterions dGPD correlation length or mesh size  c DNA -0.5 Low DNA concentrations, low added salt:   c DNA Locally fluctuating regions with exposed hydrophobic cores  LF response: single-chain property Condensed (and free) counterions High added salt: OSF persistence length, L p  I s -1 Low added salt (DNA acts as its own salt): Average size of the chain, R  c DNA -0.25

Short Na-DNA solutions Dilute regime

Characteristic scale of HF relaxation R ad   c DNA Average distance between chains A.V.Dobrynin et al., Prog.Polym.Sci.30, 1049 (2005) A.Deshkovski, et al., Phys.Rev.Lett. 86, 2341 (2001) 1) Denaturation threshold: c DNA < 0.4 mg/mL c DNA = 0.5 mg/mL 2) 1 mM added salt: c DNA > 2I s R ad pertient scale c DNA < 2I s Debye length ? 3) L HF < L c = 50 nm Two zone model L HF = R and not R ad ; R = L c / 2 Intrinsic DNA counterions respond within cylindrical zone only R ad R 25 nm 3 nm

Characteristic scale of LF relaxation R e  L c  50 nm Contour length of the chain A.V.Dobrynin et al., Prog.Polym.Sci.30, 1049 (2005) Nonuniformly stretched chain in a dilute salt-free solution Added salt-independent behavior in low added salt limit: no OSF effects since L c  50 nm 1 mM added salt: 1.c DNA > 2I s : L c pertinent scale L LF is c DNA -independent since interchain interactions are negligible in dilute regime (not the case in semidilute regime) 2.c DNA < 2I s : shrinks in size L LF  25nm Since L c  50 nm, smaller effective contour length cannot be due to decrease of rigidity as quantified by the persistence length Incipient dynamic dissociation induces short bubbles of separated strands I s  c in  c DNA

R ad R R Summary: dilute solutions HF response: solution property Free counterions Low added salt: Reduced average distance between chains R  c DNA High added salt: Debye length  -1 ∞ I s -1/2 ??? LF response: single-chain property Condensed (and free) counterions Low added salt: Contour length of the chain, L c, c DNA -independent High added salt: Smaller effective contour length due to formation of denaturation bubbles LcLc

Summary: dilute vs semidilute solutions HF response: solution property Free counterions Low added salt: Dilute regime: Reduced average distance between chains R  c DNA Power law behavior independent on DNA conformation Semidilute regime: dGPD correlation length   c DNA -0.5 Power law behavior signals on DNA conformation:   c DNA but cannot distinguish between dynamical and static aspect High added salt: Debye length  -1 ∞ I s -1/2 ??? in both regimes

Summary: dilute vs semidilute solutions LF response: single-chain property Condensed (and free) counterions Low added salt: Dilute regime Contour length of the chain, L c, c DNA -independent since interchain interactions negligible compared to intrachain ones Semidilute regime Average size of the chain, R  c DNA since DNA acts as its own salt High added salt: Dilute regime Smaller effective contour length due to formation of denaturation bubbles; coupling between added salt and denaturation process not clear yet Semidilute regime Smaller persistence length due to screening i.e. OSF effects: L p  I s -1

Semidilute vs dilute regime LF relaxationHF relaxation Length scaleExponent, theoretical Exponent, experimental Length scaleExponent, theoretical Exponent, experimental DiluteContour length00+/-0.05Average distance between chains /-0.05 SemidiluteAverage size of the chain /-0.05deGennes correlation length -0.5; for hydrophobic chains for dsDNA /-0.05; for destabilized dsDNA /-0.05