Fundamental length scales in Na-DNA solutions: semidilute versus dilute regime

1. Group for dielectric spectroscopy and magnetotransport properties http://real-science.ifs.hr http://ifs.hr 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

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

3. -2e / 0.34 nm 2 nm 0.34 nm m 3.4 nm 10 bp full turn M DNA: highly charged polymer Effective density: 1 e- / 0.17 nm Counterion atmosphere surroundscharged polymer DNA 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

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

5. 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, 098303 (2006) S. Tomic et al., Phys.Rev.E 75, 021905 (2007) S. Tomic, S.Dolanski, T.Ivek, T.Vuletic, et al., submitted to EPL

6. Electrophoresis: 1) polydisperse Na-DNA most of the fragments: 2 – 20 kbp Contour length: 0.7 - 7 mm Semidilute regime: c > c* ≤ 0.006 mg/mL 2) monodisperse Na-DNA Short fragments: 146 bp Contour length: 50 nm Dilute regime: c < c*  1 mg/mL

7. Temperature control unit Temperature range: 10↔60oC Stability: ±10 mK • Precision impedanceanalyzer Agilent 4294A: 40Hz - 100MHz Dielectric Spectroscopy Set-Up • Chamber for complex conductivity of samples in solution Conductivity range 1.5-2000 mS/cm Small volume: 100 mL Platinum electrodes Reproducibility 1.5 % Long term reproducibilty: 2 hours

8. Dielectricspectroscopy Frequency range: 40 Hz – 110 MHz Measurement functions: Gexp(w), Cexp (w) G(w)=Gexp(w) – Gbg(w) C(w)=Cexp(w) – Cbg(w) Background: NaCl solutions of different molarities adjusted to have the same real part of admittances and capacitances as DNA solutions.

9. Na+ Lp Rad R  Counterion atmosphere in ac field Applied ac field: Oscillating flow of net charge associated with intrinsic DNA counterions Solution correlation length Dilute regime cDNA < chain overlap concentration Semidilute regime cDNA > chain overlap concentration DNA relaxation time t length scale L 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) t(L) L2/D

10. long long short Cole-Cole function Results: Complex dielectric relaxation Two broad (1-a 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

11. Long Na-DNA solutions Semidilute regime

12. Low DNA concentrations No added salt cDNA-0.33 cDNA-0.5 x  cDNA-0.33 Locally fluctuating regions With exposed hydrophopic cores 1 mM added salt: cDNA > 2Isx pertinent scale cDNA < 2Is Debye length ? x cDNA-0.5 dGPD semidilute solution correlation length Characteristic scale of HF relaxation 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)

13. RcDNA-0.25 cDNA-0.29±0.04 Average size of the chain random walk of correlation blobs A.V.Dobrynin et al., Prog.Polym.Sci.30, 1049 (2005) Characteristic scale of LF relaxation 1 mM added salt: cDNA > 2IsR pertient scale cDNA < 2IsLLF 50 nm

14. Screening by added salt ions 2 Is > 0.4 ci = 0.4 (3 cDNA) LLF Lp DNA acts as its own salt LLF R 2 Is < 0.4 ci : Added salt vs own DNA screening Odijk-Skolnick-Fixman Lp = L0 + lB / (2b k)2 = L0 + 0.324 Is-1 Persistence length

15.  Summary: semidilute solutions HF response: solution property Free counterions dGPD correlation length or mesh size x  cDNA-0.5 Low DNA concentrations, low added salt: x  cDNA-0.33 Locally fluctuating regions with exposed hydrophobic cores LF response: single-chain property Condensed (and free) counterions High added salt: OSF persistence length, Lp Is-1 Low added salt (DNA acts as its own salt): Average size of the chain, R  cDNA-0.25

16. Short Na-DNA solutions Dilute regime

17. R Rad Characteristic scale of HF relaxation cDNA = 0.5 mg/mL 25 nm 3 nm Average distance between chains 3) LHF < Lc = 50 nm Two zone model LHF = R and not Rad;R = Lc / 2 Intrinsic DNA counterions respond within cylindrical zone only Rad cDNA-0.33 1) Denaturation threshold: cDNA < 0.4 mg/mL 2) 1 mM added salt: cDNA > 2IsRad pertient scale cDNA < 2Is Debye length ? A.V.Dobrynin et al., Prog.Polym.Sci.30, 1049 (2005) A.Deshkovski, et al., Phys.Rev.Lett. 86, 2341 (2001)

18. Re Lc  50 nm Contour length of the chain Is cin  3 cDNA Nonuniformly stretched chain in a dilute salt-free solution A.V.Dobrynin et al., Prog.Polym.Sci.30, 1049 (2005) Characteristic scale of LF relaxation 1 mM added salt: 1.cDNA > 2Is:Lc pertinent scale LLF is cDNA-independent since interchain interactions are negligible in dilute regime (not the case in semidilute regime) • 2.cDNA < 2Is: shrinks in size LLF25nm • Since Lc 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 Added salt-independent behavior in low added salt limit: no OSF effects since Lc  50 nm

19. R Rad R Lc Summary: dilute solutions HF response: solution property Free counterions Low added salt: Reduced average distance between chains R cDNA-0.33 High added salt: Debye length k-1∞Is-1/2 ??? LF response: single-chain property Condensed (and free) counterions Low added salt: Contour length of the chain, Lc, cDNA-independent High added salt: Smaller effective contour length due to formation of denaturation bubbles

20. Summary: dilute vs semidilute solutionsHF response: solution property Free counterions Low added salt: Dilute regime: Reduced average distance between chains R cDNA-0.33 Power law behavior independent on DNA conformation Semidilute regime:dGPD correlation length x cDNA-0.5 Power law behavior signals on DNA conformation: x  cDNA-0.33but cannot distinguish between dynamical and static aspect High added salt: Debye length k-1∞Is-1/2 ??? in both regimes

21. Summary: dilute vs semidilute solutionsLF response: single-chain property Condensed (and free) counterions Low added salt: Dilute regime Contour length of the chain, Lc, cDNA-independent since interchain interactions negligible compared to intrachain ones Semidilute regime Average size of the chain, R  cDNA-0.25since 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: Lp Is-1

22. Semidilute vs dilute regime