DNA AS A POLYELECTROLYTE

Eric Raspaud

Laboratoire de Physique des SolidesBât. 510,Université Paris –Sud91405 Orsay, FranceEmail : raspaud@lps.u-psud.fr

Cargèse, 2002 - 1

Cargèse, 2002 - 2

Unlike proteins, each of the DNA basic units (the base pair) is composed of two identical ionisable groups, the phosphate groups.

Projection of the two phosphates on the double-helix axis :

(B-DNA)

Linear charge density : 2 e / 3.4 Å ~ 6 e / nm

equivalently, 1 e / 1.7 Å

One of the most highly charged systems

Cargèse, 2002 - 3

Amino-acid size ~ 4 Å

Typical Linear Charge density ~ 1 /( 4 4 Å) ~ 0.6 e / nm

For proteins,

5 / 20 basic units may be ionized :

basic : lysine, arginine, histidine (-NH2

+)

acidic : aspartic, glutamic (-COO-)

For the Cell membrane,

Typical Surface Charge Density ~ 0.1- 1 e / nm2

Proteins + (RNA or DNA) complexes : Cargèse, 2002 - 4

105 Å

60 Å

Nucleosome Core Particle

Surface Charge Density ~ 6 e / nm2

Linear Charge density

TMV ~ 2 e / nmfd-virus ~ 5 e / nm

Tobacco Mosaic Virus

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(Bloomfield, 1999)

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3

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1_ Brief Introduction on the Ionic dissociation and hydration

1_a) simple salt1_b) DNA

2_ Simple salts : the Debye-Hückel model2_a) spatial distribution2_b) thermodynamic consequences

3_ Polyelectrolyte and the counterions distribution3_a) the Poisson-Boltzmann equation3_b) the Manning model

4_ Thermodynamic coefficients and the « free » counterions

4_a) the radius effect4_b) the length effect

5_ Conformation and Interaction5_a) Thermal denaturation5_b) Interaction and chain conformation

6_ Multivalent Counterions6_a) collapse and phase diagram6_b) ionic correlation

Menu

Cargèse, 2002 - 8

Coulomb’s law (1780)

Attraction force between two elemantary charges e separated by a distance d

and its associated energy :

deW 1

4 0

2

deF 2

0

14

2

For a typical ionic crystal,

JoulesW 10 18

Thermal Energy,kT 10-21 Joules (0.6 kcal/mol)

In water, 80

kTW

The salt dissociatesin water

1_ Brief Introduction on the Ionic dissociation and hydration1_a) simple salt

Roughly

In general, one defines a characteristic lengthof the ions dissociation/association :

The Bjerrum length lB

Cargèse, 2002 - 9

lekT

B 04

2

In water,

lB = 7.14 Å

For a multivalent salt zi : zj

|zizj | lB

if d < lB thenion pairing occurs

d

(Oosawa, 1971; Bloomfield, 2000)

Similar notionfor the coupleIon - charged monomer

Site – bound :ion immobilizedand dehydrated

pKa and weak electrolytes

Ex. : acrylate group - COO- and Mg2+

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(Sabbagh & Delsanti, 2000)

strong electrolytes

Ex. : sulfonate group – SO3-

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18 – 23 water molecules per

nucleotide(from IR

Spectroscopy)

(Bloomfield, 2000)

NMR relaxation :

Na+ associated with DNAare not dehydrated orimmobilized

(Bleam et al., 1980)

Lost of Mn2+ hydrationupon binding to DNA

(Granot & Kearns, 1982)

1_b) DNA

Cargèse, 2002 - 12For the phosphate group,

For the bases,

Neutral at pH 7

Cargèse, 2002 - 13

Solution of strong electrolytes (McQuarrie, 1976) :

Positive and negative charges in a continuum medium of dielectric constant 0

rij

ri

rj

The Coulombic potential acting upon the ith ion located at ri

ij ij

jii r

qr

04)(

or at the arbritary point r : '4

')'()(0 rr

drrr

with (r) the total charge density at r

2_ Simple salts : the Debye-Hückel model (1923)

How does the charges distribution (r) change with respect tothe distance r from a central ion ?

Cargèse, 2002 - 14

r(r) is related to the electrostatic potential r by the Poisson’s law and by the Boltzmann’s distribution :

- Ionic size : s- cations and anions charges : z+e and z- e- concentration of the bulk solution : C+

0, C-0

z+ e C+0 + z- e C-

0 = 0 (Electroneutrality)

(r ) = z+e C+0 e-z+e(r)/kT + z-e C-

0 e-z-e(r)/kT

with Fi = zie(r) the energy of the charge zie located at the distance r from the central ion or equivalently the electrostatic work required to bring the charge from the reference state to the distance r.

(r) = -(r )/0

2_a) spatial distribution

Solving the Poisson-Boltzmann equation :zie(r) << kT (kT/e 25mV)

Expanding the exponential, one getsthe linearized Poisson-Boltzmann or the Debye-Hückel equation :

(r) = 2(r)

Cargèse, 2002 - 15

with (r)= e(r) / kT

2 = 4lz-2C-

0 z+2C+

0 : the Debye screening length

Boundary conditions :r → , → 0r = s, E = - d/dr = - z0 l /s2 (from the Gauss theorem with

z0 the valence of the central ion)

(r) = A e-r/ r

a screened coulombic potential

with A = (z0 l es)/(1+s)

Cargèse, 2002 - 16

1 3 5 7 9

r/s

(r)

Csalt (mM)

1/ (Å)

1 100

10 30

100 10

103 3

for a 1:1 salt (NaCl,…)

s = 5 Å

s = 6

s

r

z0= -1

0

1

2

3

4

1 3 5 7 9

Chargedistribution(r)

opposite sign

same sign

« Ionic atmosphere » around the central ion

1 3 5 7 9

rFraction of charge within a sphere of radius r and concentric to the central ion

monotonic increase

Cargèse, 2002 - 17

Knowing the ion spatial distribution and the electrostatic potential and charging the ions, one can calculate the electrostatic free energies of the system :

electrostatic energy

Felec / V kT= - (3/12) ( s)

Felec < 0 due to the ionic atmosphere

Predict then the thermodynamic coefficients

2_b) thermodynamic consequences

Cargèse, 2002 - 183_ Polyelectrolyte and the counterions distribution

r

Simple salt

r

A polyelectrolyteinto an ionic solution

Applysimilarcalculation ?

-Yes, we can start from the Poisson-Boltzmann equation

- No, the approximation zie(r) << kT is no more valid

3_a) the Poisson-Boltzmann equation

Cargèse, 2002 - 19

The central ion becomes the polyelectrolyte :

(r) its electrostatic potential at a distance r

(r) the charge density of the surrounded ions

(r) ~ (r)

(r) ~ e-ze(r)/kT(r) ~ e-ze(r) /kT

In cylindrical geometry, (r) = (1/r) (r / r) / r

a non-linear differential equation

Neglected : * the finite size and spatial correlations of the small ions* the non-uniformity of the dielectric constant (water)

Cargèse, 2002 - 20 a exact solution if there is no added salt :(Fuoss et al., 1951); (Zimm & Le Bret, 1983); (Deserno et al., 2000)

The chain :an infinitely long cylinder of radius r0

2r0

The monomeric unit : Size b and valence zm

For B – DNA,

r0 = 10 Å a dinucleotideb = 3.4 Å and zm = -2-2e /3.4

Or equivalently :-1e /1.7with b = 1.7 Å and zm = -1

The linear charge density : zme/b

Cargèse, 2002 - 21Number of charges per Bjerrum length lB :

M = lB b the Manning parameter

For B – DNA, b = 1.7 Å : M = 4.2

2r0

b

Without added salt :Only the counterions are present

zc e Cctotal + zm e Cm

total = 0

Counterions

zc = + 1monovalent (Na+, K+,…)

Monomers

zm = - 1a nucleotide(Phosphate-)

Counterions distribution ?

Cargèse, 2002 - 22The Cell model : each chain enclosed in a coaxial cylindric cell

2r0

2R

- ionic distribution :

the whole solution =

a single cylindric cell

- concentration effect :

DNA dilution=

R increase

Cmtotal = Cc

total = 1/bR2

Cargèse, 2002 - 23Returning to the Poisson-Boltzmann equation,

(r) = - (r) /0 with (r) the counterions charge density at a radial distance r from the

chain

(r) = zce C(R) e-zce (r) /kT

0

r0 R

r

Assumption : (r = R)=0

(r)= 2 e(r) with(r)= - zce(r) / kT

The screening length 1/ becomes :

2 = 4lB zc2C(R)

[ for the simple salt, 2 = 4lz-2C-

0 z+2C+

0 ]

Cargèse, 2002 - 24

Boundary conditions :

a whole cell is neutral,for r = R (r)/r = 0

the chain is charged with M = lB b = 4.2,for r = r0 (r)/r = - 2 M /r0

(r) = -2 ln( [r /2] cos ( ln[r/RM])) !!!

with and RM two numerical constantsdependent on M , r0 , R

0

1

2

3

4

5

0 10 20 30 40 50

r0 R

r

(r)

r0 = 10 ÅR = 50 Å (40 g/l DNA)1/ 25 Å

M =

4.2

1.5

0.8

Cargèse, 2002 - 25Fraction of counterions within a cylinder of radius r

0

r0 R

r

1 2 3 4 50

1

0.5

r/r0

R = 50 Å

M =4.2

1.5

0.8

Counterions accumulation

Monotonic increase for M < 1

Cargèse, 2002 - 26

1 10

1

0

0.5

2 5 20

R = 250 Å (1.7 g/l DNA)

Counterions accumulation

similar variation

Similar to simple salt;

Debye – Hückel or linearised Poisson-Boltzmann equation

ze(r) << kT or (r) <<1

0.8

1.5

4.2M =

r/r0

Cargèse, 2002 - 27

Using the linearised equation,(r)= 2(r)

(r)= - [2 M / r0 K1(r0) ] K0(r)

with (r <0.5) ln(r)

M = 0.80.8

For M < 1, the electrostatic potential (r) is lower than kT and no counterions accumulation or condensation occurs. Counterions may be treated like simple salts.

For DNA M= 4.2 > 1, a strong counterion condensation occurs near the chain; only the counterions far from the chain are submitted to a low electrostatic potential and may be treated like simple salts.

Cargèse, 2002 - 28

C (r) (M)

local concentrationof countreions

0

r0 Rr

- regular spacing ofthe phosphate chargeon a cylinder

-charges set along thedouble-helix

Monte-Carlo simulation (Le Bret & Zimm, 1984) :

Cargèse, 2002 - 29Experimentally :

X-Ray scattering (Chang et al., 1990)

Heavy counterions (Thallium+)

Neutron scattering (van der Maarel et al., 1992)

Contrast matching

3_b) the Manning model and the limiting laws

-An infinite line charge with a charge density M

- Simple salt is present in excess over polyelectrolyte

Two-states model for M > 1:

Cargèse, 2002 - 30

« free » ions treated in theDebye-Hückel approximation

« condensed » ions reducing the monomer chargeto an effective charge qeff.

(Manning, 1969; 1978)

Cargèse, 2002 - 31Calculation of the effective charge qeff. :

-The condensed ions decrease the repulsions between the chain charges :

gel. = (q eff. 2 /40) e-rij/ rij

By summing over all pairs of effective charges of the chain, the electrostatic contribution to the free energy per monomer becomes for b << 1:

gel. = - (q eff. 2 /40b) ln b

Set the number of condensed ions per monomer, the effective charge per monomer becomes:

q eff. = zme + zce = zme [1+ (zc/zm)]

with zczm<0

gel. / kT = - zm2 [1+ (zc/zm)]2 M

ln b

Cargèse, 2002 - 32

- The mixing entropy decreases the number of condensed ions :

Volume of the region where ions are said to be condensed : Vp

The ionic local concentration : Clocal = 103 /Vp

Concentration of the free salt : Cs

As ions are confined in Vp,the lost of mixing energy is

gmix../ kT = ln (Clocal/Cs)

Cargèse, 2002 - 33Minimization of the free energy g el. + g mix. with respect to :

1 - ln(Vp Cs/103) - zczm [1+ (zc/zm)] M ln (b)2 =0

Focus on the salt concentration Cs dependence with 2 ~ Cs

- ln Cs ~ zczm [1+ (zc/zm)] M ln Cs

The only solution to cancel the Cs dependence (in particular when Cs 0) :

-1 = zczm [1+ (zc/zm)] M

For zm = zc = 1 = 1- 1/ M

Cargèse, 2002 - 34

b (Å)

M salt

zc : 1

zc Clocal (M)

x (Å)

B-DNA 1.7 4.2

1 0.76 1.17 7.4

2 0.88 0.39 11.2

4 0.94 0.12 16.9

Single-stranded DNA

4 1.8

1 0.44 0.21 12.5

4 0.86 0.021 32.2

radial extension of thecondensation region

76 % of the phosphateshave a condensed counterion or the effective charge is reduced by 1/4

For a long DNA chain (of size L) in a monovalent salt,its structural charge is proportional to L/b

and its effective charge to (L/b) (1-) = (L/b)/M = L/lB !

The DNA chain behaves like a chain where the distance between charged monomers is equal to lB

Cargèse, 2002 - 35

4_ Thermodynamic coefficients and the « free » counterions

« free » in the Manning sense :

For M < 1, all the counterions are « free »For M > 1, only 1/ M counterions are « free »

But they are submitted to the electrostatic potential created by the DNA chains;Similar to the ionic atmosphere of the Debye-Hückel interations for simple salts

thermodynamically « free » : where ions are only submitted to the thermal agitation

C(R)

(r = R) = 0

Cargèse, 2002 - 36

- For the Poisson-Boltzmann cell model without added salt,

Only the counterions far from the chainor located at r = Rare thermodynamically « free »

- For DNA in excess of salt, only the ions far from the chain are thermodynamically « free »

For M > 1 and the limiting law,

Only 1/ 2M counterions are thermodynamically « free »

Cargèse, 2002 - 37

Na-DNA

+Salt Cs

Salt Cs0

Cs0 = C Na+

0 = C Cl-0Cs

= C Cl-

C Na+ = Cs + Cc Na+

Counterionscoming from Na-DNA

Semi-permeable membrane

At the thermodynamical equilibrium,the ions chemical potentialsfrom both sides are equal :

(Cc Na+ , Cs ) = ( Cs0 )

The Donnan effect :

(NaCl)

reservoir

4_a) the radius effect

Cargèse, 2002 - 38

In an excess of salt (NaCl) with diluted Na-DNA,

Cs0 - Cs’ ( 1/ 2M Cc Na+ /2

and 21/ 2M

The salt exclusion factor : limCs0 - Cs CDNA for Cc Na+ or CDNA 0

Information on the fraction of thermodynamically « free » counterions

Cargèse, 2002 - 39

-Theoretically,

by solving the P-B equation and averaging C Na+

(r) and C Cl-(r)

2M ) fr0

with

fr0 0the limiting law

0

0.2

0.4

0.6

0.8

1

0.1 1

2

r02M

Cs0

10 mM 0.1 M 1 M

(Strauss et al., 1966-67; Shack et al., 1952)

Simple salt limit 2=1

Experimentally,the salt concentration in the DNA compartment Cs isdetermined by selective electrodes

Cargèse, 2002 - 40

with osm the osmotic coefficient

The osmotic pressure

Na-DNA +

Salt Cs

Salt Cs0

h = g h

Used by T. Odijk for the free energy of DNA in bacteriophage (1998)

In excess of Na-DNA compared to NaCl,

Cs’ 0 the salt is excluded

/ kT = osm Cc Na+

Returning to the P-B equation in salt-free conditions,

osm = C(R) / Cc Na+ ; osm = ( 1+g(r0 ) ) / 2M with g(r0 ) 0

Cargèse, 2002 - 41

0

0.2

0.4

0.6

0.8

1

0.1 1

2 osm

2M r0

100 g/l1 g/l

CDNA

(Auer & Alexandrowicz, 1969); (Raspaud et al., 2000)

- Strong deviation from the limiting law due to the finite radius r0

r0

1/

-Theories and Experiments arequalitatively in good agreement.Quantitatively…..

Cargèse, 2002 - 42

(Stigter, 1978)

2

(Nicolai & Mandel, 1989)

(Liu et al., 1998) q/qeff= 5.9

(Griffey, unpublished) 4.2(Padmanabhan et al., 1988) 2.1(Braulin et al., 1987) 2.5

To be compared withM = 4.2

- Permeability of the double-helix- Specific interactions…- different sensibilities of

the different technics

q/qeff

Cargèse, 2002 - 43

End effects

L1/

Counterions evaporation

For charged spheres, ion chemical potential :

far from the spheres, mainly entropic kT ln Con its surface, mainly enthalpic (electrostatic)

-qeffe2/40a

qeff ~ - ln C

(Alexander et al.,1984)

The effective charge increases with dilutionCounterions evaporation

4_b) the length effect

1/1/

Cargèse, 2002 - 44fraction of condensed counterions

(Gonzalez-Mozuelos & Olvera de la Cruz, 1995) dilution

qeff ~ - ln C

Cargèse, 2002 - 45Returning to DNA, Importance of end effects

for short oligonucleotide helices : Simulations of Olmsted et al. (1991)

Cs = 1.8 mM 1/= 73 Å

( N = number of nucleotides per chain)

N = 105 base-pairs

N = 25

native DNA

denaturatedDNA

2M )

fr0

2Nucleotidesbehavelike simple salt

1/0

0.5

1

1.5

2

0 5 10 15

Cs (mM)

Lend effects

Cargèse, 2002 - 46

(Olmsted et al., 1989)

The localconcentrationat the DNA surface

N = 12

N = 24

N 72

Ends effectbecomes negligeable on averagebut evaporation stilloccurs at the ends.

1/

Cargèse, 2002 - 475_ Conformation and Interaction5_a) Thermal denaturation

Calculation of the free energy using the charge renormalisation

(Manning, 1972)

Non-electrostatic term

+

L/lB or np/M

charged phosphate

Ionic atmosphere (ns salt + np/M « free » ions)(salt in excess but at low concentration)

Interaction energyof the chain with its ionic atmosphere

+Entropic termof the salt, of the « free » ions

- (np/M ) kT ln + (np/M ) kT ln Cs

Destabilizes Stabilizes

the double-helix

Additionof salt

(np/M ) denaturated > (np/M )native DNA

+…

Cargèse, 2002 - 48

+ (np/2M ) kT ln Cs

- (np/M ) kT ln + (np/M ) kT ln Cs

~ Cs 1/2

The dominant term is entropic

Finally, the electrostatic free energy Gele= H –TS > 0

and dominated by the entropy S

Entropic cost to condense or confine the counterions

Gain in electrostatic free energy to denaturate DNA

Gele = Gelesingle-stranded – Gele

double-stranded < 0

Cargèse, 2002 - 49

At the melting temperature Tm, Gnon-ele + Gele = 0

After manipulation :

d Tm /d log Cs A [ (1/2M )denaturated-(1/2M )native]

with A = k Tm2/Hm

0

20

40

60

80

100

10-4 10-3 10-2 10-1

Tm (°C)

CNa+ (M)

T4 DNA (Record, 1975)

kT

From experimental Tm and calculated Gele

Gnon-ele

pernucleotide

** Tm = k log Cs + 0.41 XGC + 81.5

(Korolev et al., 1998; see also Rouzina & Bloomfield, 1999)

(Schildkraut & Lifson, 1965)

** d Tm /d log Cs ~ (1/2M ) ~ (2)

(Olmsted et al., 1991)

Cargèse, 2002 - 50

G non-ele > 0 G non-eledenaturated > G non-ele

native

Cargèse, 2002 - 515_b) Interaction and chain conformation

Intermolecular interactions :

between short DNA L = Lp = 50 nm (150 bp)

For neutral rods,

excluded volume v0 L2 dd = 2r0

For DNA rods, v L2deff

with an effective diameter

deff = 2r0 + (1/) f( M , r0 )

At low salt , deff >> d and v >> v0

In the high salt limit, deff = d and v = v0

e-r

(Brenner & Parsegian, 1972)

Cargèse, 2002 - 52

0

5

10

15

20

10-3 10-2 10-1 100

v

v0

CNaCl (M)

(Nicolai & Mandel, 1989)

50 v0

v L2deff

isotropic

anisotropic

C i - a

i-a ~ deff / L

Ci – a ~ 1 / v

CDNA increases with Cs

Cargèse, 2002 - 53

Intramolecular interactions :

The persistence length Lp : the bending flexibility

Bending makes the phosphate charges lie closer

from one another : electrostatic contribution to Lp

Lp = l0 + lele

- Using the Debye-Hückel approximation and the limiting law ( Lp >>1),

lele = lOSF = lB / 4 (b)2 with b lB

(Odijk, 1977; Skolnick & Fixman, 1977)

- Using the P-B equation, lele = lOSF f(r0 ) (Fixman, 1982; Le Bret, 1982)

0

50

100

150

200

0.01 0.1 1 10

Cargèse, 2002 - 54

Lp (nm)

r0

1 M0.10.01

CNaCl

6360 bp (Maret & Weill, 1983)

T2 DNA (Harrington, 1978)

587 bp (Hagerman, 1981)

T7 DNA (Sobel & Harpst, 1991)

linear Col E1 plasmid(Borochov et al., 1981)

Lp = l0 + lOSF

Lp = l0 + lOSF f(r0 )

l0 = 50 nm

400

500

600

700

800

10-3 10-2 10-1 1 101

Rg : radius of gyration

Rg (nm) of T7 DNA (40 103 bp)

Cargèse, 2002 - 55

CNaCl

Experimental data(Sobel & Harpst, 1991)

Including : - excluded volume

with deff

- persistence lengthwith lOSF f(r0 ), l0 = 40 nm

(Stigter, 1985)

Random coil

6_ Multivalent Counterions6_a) collapse and phase diagram

Cargèse, 2002 - 56

b (Å)

M salt

zc : 1

zc Clocal (M)

x (Å)

B-DNA 1.7 4.2

1 0.76 1.17 7.4

2 0.88 0.39 11.2

4 0.94 0.12 16.9

Single-stranded DNA

4 1.8

1 0.44 0.21 12.5

4 0.86 0.021 32.2

In the Manning approach,

The charge fraction zcof condensed ions increases like

zc = 1- 1/ zcM

the effective charge is reduced by 94 %

Experimentally, electrophoretic mobility (cm2/V.s. × 10-4) :1.47 1

1.31 2

0.92 3

zc

Linear plasmid in 50 mM monovalent salt+ 0.2 mM of zc-valent

(Ma & Bloomfield, 1994)

Cargèse, 2002 - 57Low monovalent salt (1 mM) + Cobalt Hexamine zc = 3 on DNA

Cobalt Hexamine Concentration

Light scattering (Widom & Baldwin, 1980-83)

Toroidal globule

ScatteredIntensity

Diffusion coefficient

RH 40 nm

with spermidine (zc = 3),

RH 50 nm

(Wilson & Bloomfield, 1979)

Cargèse, 2002 - 58For higher DNA concentrations : aggregation

My first clichés !

Cryo-electron microscopy

Cargèse, 2002 - 59

10-6

10-4

10-2

1

10-6 10-4 10-2 1

Phase diagram

SpermineConcentration (M)

DNA concentration (M)

DNA redissolutionIn excess ofspermine

DNA precipitation

For

-Nucleosome core particles

- H1-depleted chromatine fragments

- short single-stranded DNA

(Raspaud et al., 1998-99)

Cargèse, 2002 - 60

Attractive interaction : in violation of the basic P-B theory

- a simple charge (quasi)-neutralization with a non-Coulombic attractive force ?

doesn’t explain the redissolution in excess of multivalent salt

Cargèse, 2002 - 61- a salt bridge model : « ion-bridging » model ?

Intermolecular interactions in dilute solutions with an excluded volume v :

electrostatic repulsionbetween like-charged chains

short-range attraction

--

--

localchargeinversion

The reduced effective charge : - qeff M

1

1 / zc

Cmultivalent salt

Csp

erm

ine (m

M)

CDNA (mM)

(Olvera de la Cruz et al., 1995)

Cargèse, 2002 - 62Fraction of counterionswithin a cylinder of radius r(from the P-B equation)

0

0.2

0.4

0.6

0.8

1

1 102 5 20

r/r0

zc = 1

zc = 4

Few AngstromsStrong charge accumulationnear the surface ( one layer)

6_b) ionic correlation

Cargèse, 2002 - 63

Coulomb energy between neighboring ions

az

Wc = (zce)2/40 az

Coupling parameter :

= Wc / kT

For multivalent ions, zc > 1 and > 1 strong coupling

Important longitudinal correlations between ions« strongly correlated liquid »

(Rouzina & Bloomfield, 1996; Grosberg et al., 2002 and references therein)

Cargèse, 2002 - 64

Two-dimensional lattice ofthe multivalent counterionsaround the surface

Correlation Energy c

per ion < 0 (attractive)

c – Wc

If n : local concentration ofthe correlated liquid

cncn

Attraction between DNA

Cargèse, 2002 - 65- In the dissolved state,

Free energy per DNA molecule with qeff

- In the condensed state, using c

- qeff M

log Cmultivalent salt

-

+

+

-lo

g C

mul

tival

ent s

alt

log CDNA

Phase diagram

(Nguyen et al., 2000 ; Nguyen & Shklovskii, 2001)

Cobalt-hexamine

Energyof DNA condensationper nucleotide

- c = 0.07 kT

(Rau & Parsegian, 1992)

Cargèse, 2002 - 66About the charge inversion,

Spermidine concentration (zc = + 3)

-

-

-

+

Spermine concentration (zc = + 4)

NucleosomeCore Particles

zc = + 2

+ 3

+ 4

-

+

(Yamasaki et al., 2001) (Raspaud et al., 1999; De Frutos et al., 2001)

Short DNAfragments

T4 DNA

Cargèse, 2002 - 67- specific effects : polyamine is a polycation

at long length scale, behaves like a zc-valent ions

similar shape of the phase diagram

at short length scale (az), each of the zc charged groups

may be considered as a monovalent ionattenuated correlation effect

(Lyubartsev & Nordenskiöld, 1997)

- the electrophoretic mobility and its associated zeta potential

Slipping surface located at rduring the electrophoretic migration

Comparison between

r and the ionic size s

r

r = s r = 2s

+

-r / s

(Deserno et al., 2001)

Cargèse, 2002 - 68

- mixture of mono and zc-valent cations condensed onto the DNAattenuated correlation effect

- non-ideal behavior of the “free” multivalent saltDebye-Hückel ionic atmosphere and the ionic size effect

reduced and may suppressed the DNA overcharging(Solis & Olvera de la Cruz, 2001)

Cargèse, 2002 - 69

DNA IS A POLYELECTROLYTE

As a conclusion,

which behaves like others charged systems (for instance, synthetic materials)and which behavior may be understood in a first approach by electrostatics notion.

Salt may regulate - DNA-DNA interactions and their conformational changeswithout specific effects

- DNA - charged proteins interactions

Course limited to Simple Naked DNA study with ions,more complex behavior for Chromatin,…

Cargèse, 2002 - 70References

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