¹ , Zagreb, Croatia² School of Medicine, University of Zagreb, Croatia³ Institut Ruđer Bošković, Zagreb, Croatia4 Dept. of Biological Chemistry, UCLA David Geffen School of Medicine, Los Angeles, USA

T.Vuletić T.Vuletić ¹¹,, S.Dolanski Babi S.Dolanski Babićć ²², , S.Tomić S.Tomić ¹¹,D.Vurnek ,D.Vurnek ¹¹, S.Krča, S.Krča³³, , D.IvankovićD.Ivanković³³, L.Griparić, L.Griparić44

•tvuletic@ifs.hrtvuletic@ifs.hr ; www.ifs.hr/real_science ; www.ifs.hr/real_science

Dielectric Spectroscopy ofDielectric Spectroscopy of Genomic DNA SolutionsGenomic DNA Solutions

Lyophillized DNA: salmon testes, Lyophillized DNA: salmon testes, Sigma-Aldrich (D1626, Type III); Sigma-Aldrich (D1626, Type III); calf thymus, Rockland (MB –102-0100) calf thymus, Rockland (MB –102-0100)Pure water: MilliPore, Milli-Q, 0.056 Pure water: MilliPore, Milli-Q, 0.056 S/cmS/cm

Range of DNA solutions: 0.011 – 18 mg/mLRange of DNA solutions: 0.011 – 18 mg/mLquantified spectroquantified spectrophphotomotomeetrically trically at 260 at 260 nmnm

SAMPLES & MATERIALS

Precision impedance analyzerPrecision impedance analyzer

Agilent 4294A: 40 Hz-100 MHzAgilent 4294A: 40 Hz-100 MHz

C-G, capacitance C-G, capacitance && real part real part of conductance measured of conductance measured amplitude 20-50 mVamplitude 20-50 mV

AgilentBNCs

Chamber for complex conductivity of liquid Chamber for complex conductivity of liquid samples – water solutions, conductivity samples – water solutions, conductivity range: 1.5-2000range: 1.5-2000S/cm; volume: 50-200 S/cm; volume: 50-200 LL

Reproducibility 1%, Long term (2 h) 2%Reproducibility 1%, Long term (2 h) 2%

Temperature Temperature

control unitcontrol unit

Temp. range: Temp. range:

00°° to 60 to 60°°CC

Stability: Stability:

±±10 mK10 mK

Pt

cham

ber

steelcasing

Pt

Low-frequency Dielectric Spectroscopy

CONDUCTIVITY of DNA-solution vs. temperature and concentrationRESULT: Conductivity follows the power Conductivity follows the power

law with exponent smaller than 1 for law with exponent smaller than 1 for both salmon-DNA and calf-DNAboth salmon-DNA and calf-DNA p percolation character ofercolation character of the the conduction path in DNA solutionsconduction path in DNA solutionsNote: measured conductivity Note: measured conductivity (gray line) of DNA (gray line) of DNA solution was subtracted for 1.5 solution was subtracted for 1.5 S/cm - the S/cm - the conductivity of pure water when measured in conductivity of pure water when measured in our chamber.our chamber.

(T) – ion mobility = e/6R(T)

(T) – H2O viscosity ~ e-H/RT

– ionic conductivity = NAe~ eH/RT

H=-18 kJ/mol (Source: CRC Handbook)

ionic solutions theory:

Note: H, enthalpy is related to energy required for a molecule to escape from its “neighbors”

RESULT: DNA solution conductivity shows a temperature dependence typical for ionic solutions

Resulting (GDNA-GNaCl, CDNA-CNaCl)

Complex dielectric function

1

01

1

iHF∞

relaxation process strength = (0) - ∞

0 – central relaxation time

symmetric broadening of the relaxation time distribution 1 -

0

'B

S

l

0

0''GG

S

l

Note: C=B/

generalized Debye function

FITS to a sum of two generalized Debye functions

Worldwide motivation: Worldwide motivation: Transport of electrical Transport of electrical signals in bio-materials on signals in bio-materials on a molecular scale a molecular scale is of fundamental interest is of fundamental interest in the life sciencesin the life sciences

Our motivation: pOur motivation: physical hysical and biological functions of and biological functions of DNADNA are strongly affected are strongly affected by its local environmentby its local environment

Our aim: to Our aim: to revealreveal dynamical and dynamical and conformational propertiesconformational propertiesof native DNAof native DNA as a function as a function of its aqueous of its aqueous environmentenvironment

MOTIVATION Experimental characterization Experimental characterization of the counter-ion atmospheres of the counter-ion atmospheres around DNA in solution is around DNA in solution is essential for an understanding of essential for an understanding of DNA physical properties and DNA physical properties and biological functionsbiological functions

Low frequency dielectric Low frequency dielectric spectroscopy (LFDS) to study spectroscopy (LFDS) to study genomic DNAgenomic DNA as a function of as a function of electrolyte concentration, electrolyte concentration, counter-ion and pH counter-ion and pH

LFDS: powerful tool to probe LFDS: powerful tool to probe charge entities and their charge entities and their backgroundbackground structure in various structure in various bio-macromolecular structures bio-macromolecular structures

R.Das et al.,Phys.Rev.Lett.90, 188103 (2003)

N.Nandi et al., Chem.Rev.100, 2013 (2000)M. Sakamoto et al., Biopolymers 18, 2769 (1979)S.Bone et al., Biochymica et Biophysica Acta 1306, 93 (1996)

• G() and C()=B()/ of DNA solutions are measured• These are subtracted for (G, C) of background (reference) NaCl solution with matching (1-100kHz) conductivity This procedure enables to eliminate the electrode polarization effects, as well as other stray impedance effects. That is, since these influences are nearly the same in DNA and reference solutions, they are reduced by the subtraction.

=’()-i’’()Y()= G()+iB()

From complex conductance to complex dielectric function

B.Saif et al., Biopolymers 31, 1171 (1991)

DNA IN SOLUTION Coulomb repulsion between POCoulomb repulsion between PO44

-- groups groups, , DNA DNA is stretched outis stretched out to the rod-like conformationto the rod-like conformation Worm-like Worm-like mmodelodel: c: chain of N segments of hain of N segments of length a;length a; Contour length L = N · aContour length L = N · a

Rigid over short distance and Rigid over short distance and becomes flexiblebecomes flexible over largeover large distancesdistances Persistance length L Persistance length Lpp determines a determines a boundaryboundary between the two types of between the two types of bbehaviorehavior iin 0.1 M NaCln 0.1 M NaCl; ; LLpp = = 50 nm : 150 bp length50 nm : 150 bp length

200 nm

M. Daune, Molecular Biophysics (Oxford, 2003)

Kratky and Porod (1949) Kuhn

Results: Two Relaxation Modes in 10 kHz – 10 MHz range

HF mode: 10, 1- 0.8Same features for both salmon and calf DNA

LF mode: 100, 1- 0.8 calf DNA salmon DNA

: c-independent strong drop at low c0 : no change at low c levels off at low c

?

Electro-kinetics of Electrical Double Layer

S.S.Dukhin et al, Adv.Coll. Interface Sci. 13, 153 (1980)

R.W.O’Brian, J. Coll. Interface Sci 113, 81 (1986).

Na+ ions redistributed in the vicinity of DNA chain in Na+ ions redistributed in the vicinity of DNA chain in order to screenorder to screen phosphate groupsphosphate groups Electrical double layer with thickness Electrical double layer with thickness -1-1 is created is created Suggestion: Suggestion: Under applied ac fieldUnder applied ac field two types of two types of dielectric dispersion dielectric dispersion two characteristic length two characteristic length scales: scales: -1-1 - Debye-H- Debye-Hüückel length & contour length of ckel length & contour length of moleculemolecule

????? LLHF,LFHF,LF= (= (HF.LFHF.LFD)D)1/21/2 , , from experiments from experiments D=kD=kBBT/6T/6R,R, D(25°C) = 1.5 ·10D(25°C) = 1.5 ·10-9 -9 mm22/s/s

LLHFHF:: 4 nm – 45 nm 4 nm – 45 nmDDH screening lengthH screening length?? or DNA mesh size or DNA mesh size??

LLLLFF:: 6060 nm – nm – 750750 nm nm Persistence Persistence lengthlength??

(Source: CRC Handbook)

Temperature dependent relaxation

MMode characteristic lengthode characteristic lengthss appearappear temperature independent temperature independent Since characteristic length L=(D(T)·Since characteristic length L=(D(T)·(T))(T))1/21/2

Thus, Thus, (T)~ 1/D(T) ~ 1/(T(T)~ 1/D(T) ~ 1/(T··ee--H/RTH/RT)) Therefore, Therefore, should be FIT to e should be FIT to eH/RTH/RT/T/T

Energy scaleEnergy scaless of of thethe mode modess areare quite similar tquite similar to energy o energy scale of ionic conductivityscale of ionic conductivity:: H= -18 kJ/molH= -18 kJ/mol

H= -H= -2020±±22 kJ/mol kJ/mol

ConclusionConclusion - - Origin of dielectric dispersion in DNA solutionsOrigin of dielectric dispersion in DNA solutionsDNA chain:DNA chain: Random sequence of Random sequence of segments placed insegments placed in counter-ion counter-ion atmosphereatmosphere. With. With ac field ac field applied, applied, appearappear broad broad relaxation modes relaxation modes due to oscillating counter-ions at due to oscillating counter-ions at different length and time scalesdifferent length and time scales

Modes:Modes:1) Contour length; f1) Contour length; f00 < 1 kHz < 1 kHz

M. Sakamoto et al., Biopolymers 18, 2769 (1979)S.Takashima, J.Phys.Chem.70, 1372 (1966)

L

-1

Na+, Cl-

Lp

LHF

--

---

- - -

-

2) LF mode: 2) LF mode: 1 kHz < f1 kHz < f00 < 70 kHz < 70 kHz Persistence length: Persistence length: distance bound by distance bound by potential barriers potential barriers due to variation of due to variation of local conformationlocal conformationAs expected LAs expected Lpp ~~ I I-1/2-1/2 when salt is addedwhen salt is added

3) HF mode: 3) HF mode: 0.1 kHz < f0.1 kHz < f00 < 15 MHz < 15 MHz Mesh size:Mesh size: DNA chains form a DNA chains form a loose mesh defining a loose mesh defining a characteristic length for characteristic length for relaxation– attribution is relaxation– attribution is strongly supported by Lstrongly supported by LHFHF independence of added salt I.independence of added salt I.LLHFHF ~~ c c1/2-1/31/2-1/3, indicates , indicates dimensionality of the web dimensionality of the web between 2 & 3.between 2 & 3.

HF Mode Characteristic Length: DNA mesh size

Inherent Inherent (I(INaClNaCl=0) Na=0) Na+ +

ions only:ions only: /c /c ~~ L LHFHF

22 in accord within accord withMandel-Mandel-Manning Manning modelmodel

Added salt ions (IAdded salt ions (INaClNaCl≠0) do not ≠0) do not contribute to relaxation. contribute to relaxation. On the contrary, they increase On the contrary, they increase screening and strongly reduce Nascreening and strongly reduce Na++ ions ions active in HF relaxationactive in HF relaxation

LLHF HF is DNA concentration dependent, but added salt is DNA concentration dependent, but added salt independent independent LLHFHF can not be can not be -1 -1 ~~ I I-1/2 -1/2 , Debye-H, Debye-Hüückel length ckel length LLHFHF given by mesh sizegiven by mesh size, , ie.ie. average distance average distance between DNA chains in solution (this length scale between DNA chains in solution (this length scale does not vary with added salt, Idoes not vary with added salt, INaClNaCl≠0)≠0)M.N. Spiteri et al., Phys.Rev.Lett.77, 5218 (1996)

LF Mode Characteristic Length: Persistence Length

Similar effect of inherent and added Similar effect of inherent and added Na+ ionsNa+ ions All ions contribute to screeningAll ions contribute to screening LLLFLF ~~ I I-1/2-1/2 implying L implying LLFLF ~~ -1-1 as expected for as expected for persistence lengthpersistence length

Important Important difference in Ldifference in Lpp of salmon and calf DNA of salmon and calf DNA at low concentration at low concentration

Certainly Certainly LFLF ~~ L L22 and we found and we found /c /c ~~ L LLFLF22

Both relaxation parameters should be Both relaxation parameters should be proportional to characteristic length, Lproportional to characteristic length, L22 according to :according to : M.Mandel, Ann.NY Acad.Sci. 303,

74 (1977)G.S.Manning, Biophys.Chem. 9,

65 (1978)

P.G.de Gennes et al.,J.Phys.(Paris), 37, 1461 (1976)M.N. Spiteri et al., Phys.Rev.Lett.77, 5218 (1996)