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1. Dynamics and Structure of Biopolyelectrolytes characterized by Dielectric SpectroscopySilvia TomicInstitut za fiziku, Zagreb, Croatia S. Tomic et al., Phys. Rev. Lett.97, 098303 (2006) S. Tomic et al.,Phys.Rev.E 75, 021905 (2007) S. Tomic et al., Europhys. Lett. 81, 68003 (2008) T.Vuletic et al., Phys.Rev.E 82, 011922 (2010) T.Vuletic et al., Phys.Rev.E 83, 041803 (2011) S.Tomic et al., Macromolecular Symposia (2011) http://real-science.ifs.hr

2. Acknowledgments Institut za fiziku, Zagreb T.Vuletić, S.Dolanski Babić (Medical School, Zgb University) T.Ivek, D.Grgičin Institute of Biophysics and Nanosystems Research, Austrian Academy of Sciences, Graz G.Pabst LPS, Universite Paris Sud F.Livolant, UCLA, LA L.Griparić Dept of Physics, University of Ljubljana, JSI, NIH R.Podgornik

3. Bio-polyelectrolytes Conformational properties of cellular components play a key role in determination of their functional behavior Advanced tools for structural determination: single-molecule techniques Conformational and dynamical properties are tightly related Another route • Measurement of dynamics of many polyelectrolyte chains in solution (tube experiment) • Can the tools applied in the tube experiment provide information about the single-chain structure? Dielectric spectroscopy technique (kHz-MHz) enables to detect and discern • structural organization of the solution as an ensemble composed of many chains and • structural properties of a single-chain

4. Na-DNA Na-HA • Highly asymmetric salts with positive counterions • In aqueous solutions: charged polyions plus Na+ atmosphere -2e / 0.34 nm 2 nm 0.34 nm m 3.4 nm 10 bp full turn M Counterion atmosphere • Dynamics of counterion charge cloud can be • studied by the DS

5. Free counterions Condensed counterions Na-DNA Na-HA Charge-density (Manning) parameter h measures the relative strength of electrostatic interactions versus thermal motion h = zlB/b = e2 / 4pee0 b kBT Weakly charged: h= 0.7 Strongly charged: h= 4.2 Bjerrum length lB e2 / 4pee0kBT 7.1 Å Oosawa-Manning condensation G.S.Manning, J.Chem.Phys.51, 924 (1969))

6. 200 nm DNA and HA elasticity Persistence length Lp Rigid chain: Lp> Lc Very low salt Flexible chain: Lp< Lc High salt ds-DNA: structural L0 50 nm HA: structural L0 9 nm T.Odijk, J.Polim.Sci.Polym.Phys.Ed.15, 477 (1977). J.Skolnick and M.Fixman, Macromolecules 10, 944 (1977). Lp= L0 + Le = L0 + lB /4 (bk)2

7. relaxation time t length scale L t(L) L2/D Displacement by diffusion a) b) Counterion atmosphere in ac field Semidilute regime Dilute regime Applied ac field: Oscillating flow of net charge associated with intrinsic DNA counterions D =1.33·10-9m2/s for Na+ counterions

8. This work • Parameters relevant for counterion dynamics: • Valency, chain length, concentration of polyions and of added salt ions • Dielectric relaxation properties of monovalent Na-DNA aqueous solutions as a function ofconcentration and added salt for two different chain lengths: • LONG: polydisperse, averagefragments 4 mm • SHORT: monodisperse nucleosomal fragments, 146 bp (50nm) • LONGNa-HA: polydisperse, averagefragments 4 mm • weaker electrostatic interactionsand much higher chain flexibility DS measurements → parameters characterizing the counterion dynamics → polyelectrolyte structural properties predicted by theoretical models SAXS experiments: a complementary method for quantifying thepolyelectrolyte solution structure.

9. 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): to minimize stray impedances including the free ion contribution and electrode polarization effects l/S=0.1042cm-1; S=0.98 cm2 (100mL), l=0.1021 cm

10. Results: Complex dielectric relaxation • Two broad(1-a 0.8)relaxation modes in MHz (HF) and kHz (LF) range a1>a2>a3>a4 Fits to a formula representing a sum of two Cole-Cole functions • (L) L2/D: holds without rescalingand with prefactors roughly of the order of one

11. cDNA = 0.5 mg/mL 25 nm R 3 nm Rad MHz range: Collective properties 50 nm DNA fragments, dilute regime cDNA-0.33 Intrinsic DNA counterions respond within cylindrical zone only A.V.Dobrynin et al., Prog.Polym.Sci.30, 1049 (2005) A.Deshkovski, et al., Phys.Rev.Lett. 86, 2341 (2001) Average distance between chains R  cDNA-0.33

12. Low DNA concentrations No added salt x  cDNA-0.33 local conformational fluctuations scdenaturation bubbles partially expose the hydrophobic core of DNA. • Long chains: local properties independent on N • Correlation length: • must be independent on N • c c* : x Lc  N·b; • c* 1 / Lc2 • assumption: x  Lc · (c* / c)m • x  N·b·(1 / N2c)m → (c·b)-0.5  MHz range: Collective properties Long chains, semidilute regime x cDNA-0.5 c-0.5 c-0.33 c-0.5 dGPD solution correlation length Random walk of correlation blobs P.G.de Gennes et al.,J.Phys.(Paris), 37, 1461 (1976)

13. DS and SAXS: complementary methods for quantifying the polyelectrolyte solution structure Pure water DNA solutions DS: Relaxation HF peak centred at 1/t0 (L2/D)-1moves towards lower frequencies with decreasing concentrations (prefactor equals 1 in our experiments) SAXS: Scattering peak centred at qm  L-1 moves towards lower wave vectors with decreasing concentrations (prefactor is interaction dependent) DS L is the length scale along which counterions oscillate SAXS L is the size of the exclusion volume around a polyion in solution a1>a2>a3>a4

14. MC simulated Lp (WLC) FRET and SAXS: C.Yuan et al., Phys.Rev.Lett. 100, 018102 (2008) 89bp (30 nm) 10bp (3 nm) • ds-DNA appears softer as its length decreases • Softening originates from dynamic base flip-out • or base-pair breathing at msec time scales Flip-out probability kHz range: single chain properties 50 nm fragments, dilute regime Nonuniformly stretched chain in a dilute salt-free solution Contour length of the chain Lc = N·b A.V.Dobrynin et al., Prog.Polym.Sci.30, 1049 (2005) • High added salt regime (2Is > cDNA): • 50nm DNA shrinks in size Lceff25nm • Smaller effective contour length cannot be due to decrease of rigidity as quantified • by Lp since Lc  50 nm • Incipient dynamic dissociation induces • short bubbles of separated strands • Model calculations confirm that bubbles lead to lower Lp O.Lee et al., Phys.Rev.E81, 021906 (2010)

15. Lp ~c-0.25 DNA screening Persistence length 0.05mg/mL Odijk-Skolnick-Fixman: Lp = L0 + aIs-1 L0 = 50 nm Added salt screening kHz range: single chain properties Long chains, semidilute regime: strongly charged, semiflexible Average size of the chain, R  cDNA-0.25 R=√n ·x Lc ≥ n · x Low added salt: 2 Is < c DNA acts as its own salt 0.05mg/mL High added salt: 2 Is > c Screening by added salt ions T.Odijk, J.Polim.Sci.Polym.Phys.Ed.15, 477 (1977).; J.Skolnick and M.Fixman, Macromolecules 10, 944 (1977).

16. kHz range: single chain properties Long chains, semidilute regime: weakly charged, flexible weakly charged dGD renormalized Debye screening length rB= C (B/bcHA)-0.5 ∞ const (cHA)-0.5 Low added salt: 2 Is < c HA acts as its own salt (all counterions are free) renormalization takes intoaccount the polyion properties flexible High salt: 2 Is > c: rscr= C {B/ [b(cHA + 2AIs)]}-0.5 dGD electrostatic screening length Lp Is-0.5 Screening by added salt ions Lp Is-0.5electrostaticpersistence length OSF model LpIs-1for rigid rodsnot valid Flory-type flexible chain models apply cHA=0.03mg/mL HA screening Added salt screening P.G.de Gennes et al.,J.Phys.(Paris), 37, 1461 (1976) A.V.Dobrynin et al., Macromolecules.28, 1859 (1995) M.Ullner, J.Phys.Chem.B107, 8097 (2003).

17. MHz mode MHz mode c << 2Is c >> 2Is kHz mode kHz mode Long and short chains Long and short chains strongly charged, semiflexible Long chains weakly charged, flexible Long and short chains Long and short chains f added salt - dependent Long DNA solutions pure water long DNA solutions increase due to cond.counterions or: due to counterion clouds sqeezed closer to polyion f conc-independent f conc-dependent: reduction due to increased screening reduction due to increased screening f conc-independent for DNA and HA Dielectric strength De  f۰c۰a a  lB ۰L2 }→ De f۰c۰ lB۰L2→f  De / c۰L2 Standard theoretical approaches: h = 1/f is conc-independent

18. Summary and open issues • Dielectric spectroscopy is a technique which reliably reveals the structural features of a single chain and the structural organization of the solution composed of many chains in the tube experiments • DS (at c<10g/L) complements SAXS and SANS (c>1g/L) • 1) Repulsive regime: univalent counterions, mean-field approaches apply • 2) Well defined regime: dilute or semidilute • How specific the observed results are for DNA and HA; whether some of them can be taken as generic properties of biopolyelectrolytes • Some features are generic like dGPD semidilute solution correlation length • Some features are specific like 1) Extremely high flexibility for short ds-DNA fragments 2) Locally fluctuating regions with exposed hydrophopic cores of long DNA 3) Chain flexibility: the key parameter which determines scaling of the electrostatic persistence length • Lp Is-1for rigid and semi-flexible chains (Odijk-Skolnick-Fixman) • Lp Is-0.5for more flexible chains (Ullner-Dobrynin) • DNA structure in the case of polyvalent counterions in the vicinity of attractive (correlation) regime of electrostatic interactions • Mg-DNA pure water: ds conformation stability increased compared to NaDNA

19. 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

20. RcDNA-0.25 Average size of the chain random walk of correlation blobs cDNA-0.29±0.04 LF: long Na-DNA, semidilute regime 1 mM added salt: cDNA > 2IsR pertient scale cDNA < 2IsLLF 50 nm: Structural persistence length • for x Lp:x  g · a • g monomers inside x blob → g c·x3 • chain: N / g correlation blobs • chain size: R2 (N / g) ·x2 ; x  c-0.5 • → R c-0.25 P.G.de Gennes et al.,J.Phys.(Paris), 37, 1461 (1976) A.V.Dobrynin et al., Prog.Polym.Sci.30, 1049 (2005)