Dynamics and Structure of Biopolyelectrolytes characterized by Dielectric Spectroscopy Silvia Tomic Institut za fiziku, Zagreb, Croatia S. Tomic et al., Phys. Rev. Lett. 97, (2006) S. Tomic et al., Phys.Rev.E 75, (2007) S. Tomic et al., Europhys. Lett. 81, (2008) T.Vuletic et al., Phys.Rev.E 82, (2010) T.Vuletic et al., Phys.Rev.E 83, (2011) S.Tomic et al., Macromolecular Symposia (2011)

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

Bio-polyelectrolytes Conformational properties of cellular components play a key role in determination of their functional behavior  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 Advanced tools for structural determination: single-molecule techniques Conformational and dynamical properties are tightly related Another route

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

Condensed counterions Free counterions Oosawa-Manning condensation Bjerrum length l B e 2 /       7.1 Å G.S.Manning, J.Chem.Phys.51, 924 (1969)) Na-DNANa-HA Strongly charged:  = 4.2 Weakly charged:  = 0.7 Charge-density (Manning) parameter  measures the relative strength of electrostatic interactions versus thermal motion  = zl B /b = e 2 /  0 b k B T

DNA and HA elasticity Persistence length L p 200 nm T.Odijk, J.Polim.Sci.Polym.Phys.Ed.15, 477 (1977). J.Skolnick and M.Fixman, Macromolecules 10, 944 (1977). L p = L 0 + L e = L 0 + l B /4 (b ) 2 Rigid chain: L p > L c Very low salt Flexible chain: L p < L c High salt ds-DNA: structural L 0  50 nm HA: structural L 0  9 nm

Counterion atmosphere in ac field Applied ac field: Oscillating flow of net charge associated with intrinsic DNA counterions  (L)  L 2 /D relaxation time  length scale L Displacement by diffusion D = 1.33·10 -9 m 2 /s for Na + counterions a)b) Semidilute regimeDilute regime

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 of concentration and added salt for two different chain lengths: LONG: polydisperse, average fragments 4  m SHORT: monodisperse nucleosomal fragments, 146 bp (50nm) LONG Na-HA: polydisperse, average fragments 4  m weaker electrostatic interactions and 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 the polyelectrolyte solution structure.

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): to minimize stray impedances including the free ion contribution and electrode polarization effects l/S= cm -1 ; S=0.98 cm 2 (100  L), l= cm

Results: Complex dielectric relaxation  Two broad (1-   0.8) relaxation modes in MHz (HF) and kHz (LF) range Fits to a formula representing a sum of two Cole-Cole functions (L)  L 2 /D: holds without rescaling and with prefactors roughly of the order of one a1>a2>a3>a4

MHz range: Collective properties 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) Intrinsic DNA counterions respond within cylindrical zone only R ad R 50 nm DNA fragments, dilute regime c DNA = 0.5 mg/mL 25 nm 3 nm R  c DNA c DNA -0.33

MHz range: Collective properties P.G.de Gennes et al.,J.Phys.(Paris), 37, 1461 (1976) Long chains, semidilute regime   c DNA -0.5 dGPD solution correlation length Long chains: local properties independent on N Correlation length: must be independent on N c  c* :   L c  N·b; c*  1 / L c 2 assumption :  L c · (c* / c) m  N ·b·(1 / N 2 c) m → (c·b) -0.5  Random walk of correlation blobs   c DNA Low DNA concentrations No added salt local conformational fluctuations sc denaturation bubbles partially expose the hydrophobic core of DNA. c c -0.5

DS and SAXS: complementary methods for quantifying the polyelectrolyte solution structure Pure water DNA solutions DS: Relaxation HF peak centred at 1/  0  (L 2 /D) -1 moves towards lower frequencies with decreasing concentrations (prefactor equals 1 in our experiments) SAXS: Scattering peak centred at q m  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

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

kHz range : single chain properties Average size of the chain, R  c DNA T.Odijk, J.Polim.Sci.Polym.Phys.Ed.15, 477 (1977).; J.Skolnick and M.Fixman, Macromolecules 10, 944 (1977). 0.05mg/mL Persistence length Odijk-Skolnick-Fixman: L p = L 0 + a I s -1 L 0 = 50 nm Added salt screening DNA screening LpLp ~c mg/mL Long chains, semidilute regime: strongly charged, semiflexible High added salt: 2 I s > c Screening by added salt ions R=√n ·  L c ≥ n ·  Low added salt: 2 I s < c DNA acts as its own salt

kHz range: single chain properties Long chains, semidilute regime: weakly charged, flexible c HA =0.03mg/mL Low added salt: 2 I s < c HA acts as its own salt (all counterions are free) renormalization takes into account the polyion properties High salt: 2 I s > c: r scr = C {B/ [b(c HA + 2AI s )]} -0.5 dGD electrostatic screening length Screening by added salt ions L p  I s -0.5 electrostatic persistence length OSF model L p  I s -1 for rigid rods not valid Flory-type flexible chain models apply HA screeningAdded 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). weakly charged flexible dGD renormalized Debye screening length r B = C (B/b c HA ) -0.5 ∞ const ( c HA ) -0.5 L p  I s -0.5

Dielectric strength  f ۰ c ۰   l B ۰ L 2 } →  f ۰ c ۰ l B ۰ L 2 → f   / c ۰ L 2 Standard theoretical approaches :  = 1/f is conc-independent f conc-independent for DNA and HA Long and short chains strongly charged, semiflexible Long chains weakly charged, flexible f conc-dependent: reduction due to increased screening f conc-independent Long and short chains pure water long DNA solutions MHz modekHz modec >> 2I s increase due to cond.counterions or: due to counterion clouds sqeezed closer to polyion reduction due to increased screening Long and short chains MHz modekHz modec << 2I s Long DNA solutions f added salt - dependent

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 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 L p  I s -1 for rigid and semi-flexible chains (Odijk-Skolnick-Fixman) L p  I s -0.5 for 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

 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

LF: long Na-DNA, semidilute regime c DNA ± 0.04 Average size of the chain random walk of correlation blobs R  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) for    L p :  g · a g monomers inside  blob → g  c ·  3 chain: N / g correlation blobs chain size: R 2  (N / g) ·  2 ;  c -0.5 → R  c mM added salt: c DNA > 2I s R pertient scale c DNA < 2I s L LF  50 nm: Structural persistence length