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, CroatiaLorena Griparić, UCLA, LA, USAFrancoise Livolant, Laboratoire de Physique des Solides, Orsay, FranceRudi Podgornik, Faculty of Mathematics and Physics, University of Ljubljana, Institute J.Stefan, Ljubljana, Slovenia

http://real-science.ifs.hr

Group for dielectric spectroscopy and magnetotransport properties

http://ifs.hr

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 nmCounterion atmospheresurrounds charged polymer DNA

3.4 nm10 bpfull turn

m

0.34 nm2 nm

-2e / 0.34 nm

M

Monovalent counterions:Strong repulsive electrostaticinteraction; Debye screening length

Polyvalent counterions:Repulsive interactions turn intoattractive 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 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

Persistence length Lp 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, 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

Electrophoresis:

1) polydisperse Na-DNA most of the fragments: 2 – 20 kbpContour length: 0.7 - 7 mSemidilute regime: c > c* ≤ 0.006 mg/mL

2) monodisperse Na-DNAShort fragments: 146 bpContour length: 50 nmDilute regime: c < c* 1 mg/mL

Chamber for complex conductivity of samples in solution Conductivity range 1.5-2000 S/cm Small volume: 100 L Platinum electrodes Reproducibility 1.5 % Long term reproducibilty: 2 hours

Temperature control unit Temperature range: 10↔60oC Stability: ±10 mK

•Precision impedance analyzer Agilent 4294A: 40Hz - 100MHz

Dielectric Spectroscopy Set-Up

Dielectric spectroscopy

Frequency range: 40 Hz – 110 MHzMeasurement functions: Gexp(), Cexp ()

G()=Gexp() – Gbg()C()=Cexp() – Cbg()

Background: NaCl solutions of different molarities adjusted to have the same real part of admittances and capacitances as DNA solutions.

0

0

'

''

C

S

G

S

Counterion atmosphere in ac field

DNA

Applied ac field: Oscillating flow of net charge associated with intrinsic DNA counterions

(L) L2/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 regimecDNA > chain overlap

concentration

R

Na+

Lp

Solution correlation length

relaxation time length scale L

Dilute regimecDNA < chain overlap

concentration

Rad

Results: Complex dielectric relaxation

1

01

1

iHF

Cole-Cole function

long long short

Two broad (1- 0.8) relaxation modesHF mode: Long: 0.1 MHz – 15 MHz; Short: similarLF mode: Long: 0.5 kHz – 70 kHz; Short: 80 kHzAmplitude and position in frequency depend on DNA concentration

Long Na-DNA solutions Semidilute regime

Characteristic scale of HF relaxation

cDNA-0.5

cDNA-0.33

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)

cDNA-0.5

dGPD semidilute solution correlation length

cDNA-0.33

Low DNA concentrationsNo added salt

Locally fluctuating regionsWith exposed hydrophopic cores

1 mM added salt: cDNA > 2Is pertinent scale cDNA < 2Is Debye length ?

Characteristic scale of LF relaxation

cDNA-0.29±0.04

1 mM added salt: cDNA > 2Is R pertient scale cDNA < 2Is LLF 50 nm

R cDNA-0.25

Average size of the chainrandom walk of correlation blobs

A.V.Dobrynin et al., Prog.Polym.Sci.30, 1049 (2005)

Added salt vs own DNA screening

Odijk-Skolnick-FixmanLp = L0 + lB / (2b )2 = L0 + 0.324 Is

-1

Persistence length

2 Is < 0.4 ci :

DNA acts as its own salt

LLF R

Screening by added salt ions2 Is > 0.4 ci = 0.4 (3 cDNA)

LpLLF

Summary: semidilute solutions

HF response: solution propertyFree counterionsdGPD correlation length or mesh size cDNA

-0.5

Low DNA concentrations, low added salt: cDNA-0.33

Locally fluctuating regions with exposed hydrophobic cores

LF response: single-chain propertyCondensed (and free) counterionsHigh 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

Short Na-DNA solutions Dilute regime

Characteristic scale of HF relaxation

RadcDNA-0.33

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: cDNA < 0.4 mg/mL

cDNA = 0.5 mg/mL

2) 1 mM added salt: cDNA > 2Is Rad pertient scale cDNA < 2Is Debye length ?

3) LHF < Lc = 50 nmTwo zone model

LHF = R and not Rad; R = Lc / 2Intrinsic DNA counterions respondwithin cylindrical zone only

Rad

R

25 nm

3 nm

Characteristic scale of LF relaxation

Re Lc 50 nm

Contour length of the chain

A.V.Dobrynin et al., Prog.Polym.Sci.30, 1049 (2005)

Nonuniformly stretched chain in a dilutesalt-free solution

Added salt-independent behavior in low added salt limit:no OSF effects since Lc 50 nm

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 LLF25nm• Since Lc 50 nm, smaller effective contour length cannot be due to decrease of rigidity as quantified by the persistence length• Incipient dynamic dissociation inducesshort bubbles of separated strands

Is cin

cDNA

Rad

R

R

Summary: dilute solutions

HF response: solution propertyFree counterionsLow added salt:Reduced average distance between chains RcDNA

-0.33

High added salt:Debye length -1 ∞ Is

-1/2 ???

LF response: single-chain propertyCondensed (and free) counterionsLow added salt: Contour length of the chain, Lc, cDNA-independentHigh added salt: Smaller effective contour length due to formation of denaturation bubbles

Lc

Summary: dilute vs semidilute solutions HF response: solution property

Free counterions

Low added salt:Dilute regime: Reduced average distance between chains RcDNA

-0.33

Power law behavior independent on DNA conformation

Semidilute regime: dGPD correlation length cDNA-0.5

Power law behavior signals on DNA conformation: cDNA-0.33 but cannot

distinguish between dynamical and static aspect

High added salt:Debye length -1 ∞ Is

-1/2 ??? in both regimes

Summary: dilute vs semidilute solutions LF response: single-chain property

Condensed (and free) counterions

Low added salt: Dilute regimeContour length of the chain, Lc, cDNA-independent since interchain interactions negligible compared to intrachain onesSemidilute regimeAverage size of the chain, R cDNA

-0.25 since DNA acts as its own salt

High added salt: Dilute regimeSmaller effective contour length due to formation of denaturation bubbles; coupling between added salt and denaturation process not clear yetSemidilute regimeSmaller persistence length due to screening i.e. OSF effects: Lp Is

-1

Semidilute vs dilute regimeLF relaxation HF relaxation

Length scale Exponent, theoretical

Exponent, experimental

Length scale Exponent, theoretical

Exponent, experimental

Dilute Contour length 0 0+/-0.05 Average distance between chains

-0.33 -0.33+/-0.05

Semidilute Average size of the chain

-0.25 -0.29+/-0.05 deGennes correlation length

-0.5;-0.33 for

hydrophobic chains

for dsDNA -0.5+/-0.05;

for destabilized dsDNA

-0.33+/-0.05