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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
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