Dynamics and Structure of Biopolyelectrolytes characterized by

Dielectric Spectroscopy

Silvia TomicInstitut za fiziku, Zagreb, Croatia

http://real-science.ifs.hr

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)

Acknowledgments

Institut za fiziku, ZagrebT.Vuletić, S.Dolanski Babić (Medical School, Zgb University)T.Ivek, D.Grgičin

LPS, Universite Paris SudF.Livolant,UCLA, LAL.Griparić

Dept of Physics, University of Ljubljana, JSI, NIHR.Podgornik

Institute of Biophysics and Nanosystems Research, Austrian Academy of Sciences, GrazG.Pabst

Bio-polyelectrolytes

Conformational properties of cellular componentsplay 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 nm10 bpfull turn

m

0.34 nm2 nm

-2e / 0.34 nm

M

Na-DNA Na-HA

• Highly asymmetric salts with positive counterions

• In aqueous solutions: charged polyions plus Na+ atmosphere

• Dynamics of counterion charge cloud can bestudied by the DS

Condensedcounterions

Freecounterions

Oosawa-Manning condensation

Bjerrum length lB e2 / 7.1 Å

G.S.Manning, J.Chem.Phys.51, 924 (1969))

Na-DNA Na-HA

Strongly charged: = 4.2 Weakly charged: = 0.7

Charge-density (Manning) parameter measures the relative strength of electrostatic interactions versus thermal motion

= zlB/b = e2 / 0 b kBT

DNA and HA elasticity

Persistence length Lp

200 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 (b )2

Rigid chain: Lp > Lc

Very low saltFlexible chain: Lp < Lc

High saltds-DNA: structural L0 50 nmHA: structural L0 9 nm

Counterion atmosphere in ac field

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

(L) L2/Drelaxation time length scale LDisplacement by diffusion

D = 1.33·10-9 m2/s for Na+ counterions

Na+ a) b)

Semidilute regime Dilute 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 MHzMeasurement functions: Gexp(), Cexp ()

G()=Gexp() – Gbg()C()=Cexp() – Cbg()

Background (NaCl solutions): to minimizestray impedances including the free ion contribution and electrode polarization effects

0

0

'

''

C

S

G

S

l/S=0.1042 cm-1; S=0.98 cm2 (100L), l=0.1021 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) L2/D:holds without rescaling and with prefactors roughly of the order of one

a1>a2>a3>a4

(Hz)

101 102 103 104 105 106 107 108

1

10

100

a2

a3

a1

pure water HA solutions

25°C

(Hz)

101 102 103 104 105 106 107 108

1

10

100

25°C

b1

b2

b3

added saltHA solutions

proceeding.JNB/016

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 respondwithin cylindrical zone only

Rad

R

50 nm DNA fragments, dilute regime

cDNA = 0.5 mg/mL

25 nm

3 nm

R cDNA-0.33

cDNA-0.33

MHz range: Collective properties

P.G.de Gennes et al.,J.Phys.(Paris), 37, 1461 (1976)

Long chains, semidilute regime

cDNA-0.5

dGPD solutioncorrelation length

Long chains: local properties independent on NCorrelation length:

• must be independent on N

• c c* : Lc N·b; • c* 1 / Lc

2

• assumption: Lc · (c* / c)m

• N ·b·(1 / N2 c)m → (c·b)-0.5

Random walk of correlation blobs

cDNA-0.33

Low DNA concentrationsNo added salt

local conformational fluctuations sc denaturation bubbles partially expose the hydrophobic core of DNA.

cHA (mg/mL)0.01 0.1 1 10 100

pure waterNa-HA solutions 25°C

added saltNa-HA solutions

b)

Is (mM)0.1 1

LH

F (

nm)

102040

cDNA (mg/mL)0.01 0.1 1 10 100

LH

F (

nm)

1

10

100

25oC

a) Na-DNA solutions

c-0.33

c-0.5

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 (L2/D)-1 moves 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)

DNA in water

q-1 (nm)

0 2 4 6 8 10 12 14

I (a

rb. u

nits

)

5

10a1

a2

a5a3

a4

pure water Na-DNA solutions

25oC

DSL 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 dilutesalt-free solution

50 nm fragments, dilute regime

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 Lc

eff 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)

cDNA (mg/mL)0.01 0.1 1 10

LL

F (

nm)

10

100

1000 25 °C

Lc = 50 nm

146 bp Na-DNAsolutions

proc

eedi

ng.J

NB

/002

FRET and SAXS: C.Yuan et al., Phys.Rev.Lett. 100, 018102 (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 Lp (WLC)

89bp (30 nm)

10bp (3 nm)

Flip-out probability

kHz range: single chain properties

Average size of the chain, R cDNA-0.25

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:

Lp = L0 + a Is-1

L0 = 50 nmAdded salt screening

DNA screening

Lp

~c-0.25

0.05mg/mL

Long chains, semidilute regime: strongly charged, semiflexible

High added salt: 2 Is > cScreening by added salt ions

R=√n ·Lc ≥ n ·Low added salt: 2 Is < c

DNA acts as its own salt

kHz range: single chain propertiesLong chains, semidilute regime: weakly charged, flexible

cHA=0.03mg/mL

Low added salt: 2 Is < cHA acts as its own salt (all counterions are free)renormalization takes into account the polyion properties

High salt: 2 Is > c: rscr = C {B/ [b(cHA + 2AIs)]}-0.5

dGD electrostatic screening length

Screening by added salt ions

Lp Is-0.5 electrostatic persistence length

OSF model Lp Is-1 for rigid rods not valid

Flory-type flexible chain models applyHA 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).

weakly charged

flexible

dGD renormalized Debye screening length

rB = C (B/bcHA)-0.5 ∞ const (cHA)-0.5

Lp Is-0.5

Dielectric strengthf ۰ c ۰ lB ۰ L2 } → f۰c ۰ lB۰L2 → f / c ۰ L2

Standard theoretical approaches: = 1/f is conc-independent

f conc-independent for DNA and HA

Long and short chainsstrongly charged, semiflexible

Long chainsweakly charged, flexible

f conc-dependent:reduction due to increased screening

f conc-independent

Long and short chains

pure water longDNA solutions

MHz mode kHz modec >> 2Is

increase due to cond.counterionsor: due to counterion clouds sqeezed closer to polyion

reduction due to increased screening

Long and short chainsLong and short chains

MHz mode kHz modec << 2Is

Long DNA solutions

f added salt - dependent

Summary and open issuesDielectric 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 experimentsDS (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 semidiluteHow 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 lengthSome 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-1 for rigid and semi-flexible chains (Odijk-Skolnick-Fixman)

Lp Is-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 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

LF: long Na-DNA, semidilute regime

cDNA-0.29±0.04 Average size of the chain

random walk of correlation blobs

R cDNA-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)

• for Lp: g · a

• g monomers inside blob → g c · 3

• chain: N / g correlation blobs • chain size: R2 (N / g) · 2 ; c-0.5

→ R c-0.25

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