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Cargèse, 2002 - 1. DNA AS A POLYELECTROLYTE. Eric Raspaud Laboratoire de Physique des Solides Bât. 510, Université Paris –Sud 91405 Orsay, France Email : [email protected] Cargèse, 2002 - 2.

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Dna as a polyelectrolyte

Cargèse, 2002 - 1

DNA AS A POLYELECTROLYTE

Eric Raspaud

Laboratoire de Physique des Solides

Bât. 510,

Université Paris –Sud

91405 Orsay, France

Email : [email protected]


Dna as a polyelectrolyte

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


Dna as a polyelectrolyte

Cargèse, 2002 - 3

For proteins,

5 / 20 basic units may be ionized :

basic : lysine, arginine, histidine (-NH2+)

acidic : aspartic, glutamic (-COO-)

Amino-acid size ~ 4 Å

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

For the Cell membrane,

Typical Surface Charge Density~ 0.1- 1 e / nm2


Dna as a polyelectrolyte

105 Å

60 Å

Proteins + (RNA or DNA) complexes :

Cargèse, 2002 - 4

Nucleosome Core Particle

Tobacco Mosaic Virus

Linear Charge density

TMV ~ 2 e / nm

fd-virus ~ 5 e / nm

Surface Charge Density~ 6 e / nm2


Dna as a polyelectrolyte

Cargèse, 2002 - 5

(Bloomfield, 1999)


Dna as a polyelectrolyte

Cargèse, 2002 - 6

 3


Dna as a polyelectrolyte

Menu

Cargèse, 2002 - 7

1_ Brief Introduction on the Ionic dissociation and hydration

1_a) simple salt

1_b) DNA

2_ Simple salts : the Debye-Hückel model

2_a) spatial distribution

2_b) thermodynamic consequences

3_ Polyelectrolyte and the counterions distribution

3_a) the Poisson-Boltzmann equation

3_b) the Manning model

4_ Thermodynamic coefficients and the « free » counterions

4_a) the radius effect

4_b) the length effect

5_ Conformation and Interaction

5_a) Thermal denaturation

5_b) Interaction and chain conformation

6_ MultivalentCounterions

6_a) collapse and phase diagram

6_b) ionic correlation


1 brief introduction on the ionic dissociation and hydration 1 a simple salt

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

Cargèse, 2002 - 8

Thermal Energy,

kT 10-21Joules (0.6 kcal/mol)

Coulomb’s law(1780)

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

Roughly

and its associated energy :

The salt dissociates

in water

In water,

For a typical ionic crystal,


Dna as a polyelectrolyte

Cargèse, 2002 - 9

In general, one defines a characteristic length

of the ions dissociation/association :

The Bjerrum lengthlB

In water,

lB = 7.14

Å

if d < lB then

ion pairing occurs

For a multivalent salt zi : zj

|zizj | lB 


Dna as a polyelectrolyte

Cargèse, 2002 - 10

Similar notion

for the couple

Ion - charged monomer

d

Site – bound :

ion immobilized

and dehydrated

(Oosawa, 1971; Bloomfield, 2000)

strong electrolytes

Ex. : sulfonate group – SO3-

pKa and weak electrolytes

Ex. : acrylate group - COO- and Mg2+

(Sabbagh & Delsanti, 2000)


1 b dna

1_b) DNA

Cargèse, 2002 - 11

NMR relaxation :

Na+ associated with DNA

are not dehydrated or

immobilized

(Bleam et al., 1980)

Lost of Mn2+ hydration

upon binding to DNA

(Granot & Kearns, 1982)

18 – 23 water molecules per nucleotide

(from IR

Spectroscopy)

(Bloomfield, 2000)


Dna as a polyelectrolyte

Cargèse, 2002 - 12

For the phosphate group,

For the bases,

Neutral at pH 7


2 simple salts the debye h ckel model 1923

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

Cargèse, 2002 - 13

Solution of strong electrolytes (McQuarrie, 1976) :

Positive and negative charges in a continuum

medium of dielectric constant ee0

rj

The Coulombic potential acting upon the ith ion located at ri

rij

ri

or at the arbritary point r :

with r (r) the total charge density at r

How does the charges distribution r(r) change with respect to

the distance r from a central ion ?


2 a spatial distribution

2_a) spatial distribution

Cargèse, 2002 - 14

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

r

Dy(r) = -r(r )/ee0

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

with Fi= ziey(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.


Dna as a polyelectrolyte

k2 = 4p lB (z-2C-0+ z+2C+0)

1/k : the Debye screening length

  • (r) = A e-kr/ r

    a screened coulombic potential

    with A = (z0 lB eks)/(1+ks)

Cargèse, 2002 - 15

Solving the Poisson-Boltzmann equation :

ziey(r) << kT(kT/e  25mV)

Expanding the exponential, one gets

the linearized Poisson-Boltzmann or the Debye-Hückel equation :

Df (r) = k2f(r)

withf(r)= ey(r) / kT

Boundary conditions :

r→ , f → 0

r = s, E = - df /dr = - z0 lB /s2

(from the Gauss theorem with

z0thevalence of the central ion)


Dna as a polyelectrolyte

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

r

f(r)

monotonic increase

Charge

distribution

r(r)

opposite sign

r/s

r

same sign

z0= -1

« Ionic atmosphere » around the central ion

Cargèse, 2002 - 16

for a 1:1 salt (NaCl,…)

1/k s

s= 5 Å

1/k s = 6


2 b thermodynamic consequences

2_b) thermodynamic consequences

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= - (k3/12p) t(k s)

Felec < 0due to the ionic atmosphere

Predict then the thermodynamic coefficients


3 polyelectrolyte and the counterions distribution

3_ Polyelectrolyte and the counterions distribution

Cargèse, 2002 - 18

A polyelectrolyte

into an ionic solution

Simple salt

r

r

Apply

similar

calculation ?

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

  • No, the approximation ziey(r) << kT is no more valid


3 a the poisson boltzmann equation

3_a) the Poisson-Boltzmann equation

Dy(r) ~r(r)

In cylindrical geometry,

Dy(r) = (1/r)  (r  y/  r) /  r

Dy(r)~ e-zey(r) /kT

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

Cargèse, 2002 - 19

The central ion becomes the polyelectrolyte :

y(r) its electrostatic potential at a distance r

r (r)the charge density of the surrounded ions

a non-linear differential equation


Dna as a polyelectrolyte

Cargèse, 2002 - 20

  • a exact solution if there is no added salt :

    (Fuoss et al., 1951); (Zimm & Le Bret, 1983); (Deserno et al., 2000)

Neglected : * the finite size and spatial correlations of the small ions

* the non-uniformity of the dielectric constant (water)

The monomeric unit : Size b and valence zm

The chain :

an infinitely long cylinder of radius r0

The linear charge density : zme/b

For B – DNA,

a dinucleotide

b = 3.4 Å and zm = -2

-2e /3.4

Or equivalently :

-1e /1.7

with b = 1.7 Å and zm = -1

r0 = 10 Å

2r0


Dna as a polyelectrolyte

Counterions distribution ?

Cargèse, 2002 - 21

Number of charges per Bjerrum length lB :

xM = lB /b the Manning parameter

For B – DNA, b = 1.7 Å:xM = 4.2

Without added salt :

Only the counterions are present

b

zc e Cctotal + zm e Cmtotal = 0

Counterions

zc = + 1

monovalent (Na+, K+,…)

Monomers

zm = - 1

a nucleotide

(Phosphate-)

2r0


Dna as a polyelectrolyte

The Cell model : each chain enclosed in a coaxial cylindric cell

Cargèse, 2002 - 22

- ionic distribution :

the whole solution

=

a single cylindric cell

- concentration effect :

DNA dilution

=

R increase

Cmtotal = Cctotal = 1/pbR2

2r0

2R


Dna as a polyelectrolyte

Cargèse, 2002 - 23

Returning to the Poisson-Boltzmann equation,

Dy(r) = -r(r) /ee0 with r(r) the counterions charge density at a radial distance r from the chain

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

Assumption :y(r = R)=0

f(r)= k2 ef(r)

with f(r)= - zcey(r) / kT

The screening length 1/k becomes :

k2 = 4plBzc2C(R)

[ for the simple salt,k2 = 4p lB (z-2C-0+ z+2C+0) ]

0

r

r0

R


Dna as a polyelectrolyte

Cargèse, 2002 - 24

Boundary conditions :

a whole cell is neutral,

for r = Rf(r)/r = 0

the chain is charged withxM = lB /b = 4.2,

for r = r0f(r)/r = - 2 xM /r0

r0 = 10 Å

R = 50 Å (40 g/l DNA)

1/ k 25 Å

xM =

4.2

f(r)

1.5

f(r) = -2 ln( [kr /g2] cos (g ln[r/RM])) !!!

0.8

with g and RM two numerical constants

dependent on xM , r0 , R

r

r0

R


Dna as a polyelectrolyte

Cargèse, 2002 - 25

Fraction of counterions within a cylinder of radius r

R = 50 Å

xM =

4.2

1.5

Counterions accumulation

0.8

r/r0

0

Monotonic increase for xM < 1

r0

R

r


Dna as a polyelectrolyte

Cargèse, 2002 - 26

R = 250 Å (1.7 g/l DNA)

similar variation

xM =

4.2

Similar to simple salt;

Debye – Hückel or linearised Poisson-Boltzmann equation

zey(r) << kT orf(r) <<1

1.5

Counterions accumulation

0.8

r/r0


Dna as a polyelectrolyte

Cargèse, 2002 - 27

Using the linearised equation,

f(r)= k2f(r)

f(r)= - [2 xM/ kr0K1(kr0) ]K0(kr)

withf(kr <0.5) ln(kr)

0.8

xM= 0.8

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

For DNA xM= 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.


Dna as a polyelectrolyte

Cargèse, 2002 - 28

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

C (r) (M)

local concentration

of countreions

  • regular spacing of

  • the phosphate charge

  • on a cylinder

  • charges set along the

  • double-helix

0

r

r0

R


Dna as a polyelectrolyte

Experimentally :

Cargèse, 2002 - 29

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

Contrast matching

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

Heavy counterions (Thallium+)


3 b the manning model and the limiting laws

3_b) the Manning model and the limiting laws

Cargèse, 2002 - 30

  • An infinite line charge with a charge density xM

  • Simple salt is present in excess over polyelectrolyte

(Manning, 1969; 1978)

Two-states model for xM> 1:

« free » ions treated in the

Debye-Hückel approximation

« condensed » ions reducing the monomer charge

to an effective charge qeff.


Dna as a polyelectrolyte

Cargèse, 2002 - 31

Calculation of the effective charge qeff. :

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

  • gel. = (q eff.2 /4pee0)  e-krij/ rij

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

  • gel. = - (q eff.2 /4pee0b) ln kb

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

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

with zczm<0

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


Dna as a polyelectrolyte

Cargèse, 2002 - 32

-The mixing entropy decreases the number of condensed ions :

Concentration of the free salt : Cs

As q ions are confined in Vp,

the lost of mixing energy is

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

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

The ionic local concentration : Clocal = 103 q /Vp


Dna as a polyelectrolyte

Cargèse, 2002 - 33

Minimization of the free energy g el. + g mix. with respect to q :

1 - ln(Vp Cs/103) - zczm [1+ (zc/zm)q ]xMln (kb)2=0

Focus on the salt concentration Cs dependence with k2~ Cs

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

The only solution to cancel the Csdependence (in particular when Cs0) :

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

q = 1- 1/xM

For  zm =  zc = 1


Dna as a polyelectrolyte

radial extension of the

condensation region

Cargèse, 2002 - 34

76 % of the phosphates

have 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-q) = (L/b)/xM= L/lB!

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


4 thermodynamic coefficients and the free counterions

4_ Thermodynamic coefficients and the « free » counterions

Cargèse, 2002 - 35

« free » in the Manning sense :

For xM < 1, all the counterions are « free »

For xM > 1, only 1/ xM 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


Dna as a polyelectrolyte

Cargèse, 2002 - 36

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

Only the counterions far from the chain

or located at r = R

are thermodynamically « free »

C(R)

y(r = R) = 0

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

For xM > 1 and the limiting law,

Only 1/ 2xM counterions are thermodynamically « free »


Dna as a polyelectrolyte

Cargèse, 2002 - 37

The Donnan effect :

Semi-permeable membrane

reservoir

At the thermodynamical equilibrium,

the ions chemical potentials

from both sides are equal :

m(Cc Na+ , Cs ) = m( Cs0 )

Na-DNA

+

Salt Cs

Salt Cs0

(NaCl)

Cs= C Cl-

C Na+= Cs + Cc Na+

Cs0 = C Na+0 = C Cl-0

Counterions

coming from Na-DNA


4 a the radius effect

4_a) the radius effect

Cargèse, 2002 - 38

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

Cs0 - Cs’ ( 1/ 2xM)Cc Na+ /2

The salt exclusion factor : G = lim (Cs0 - Cs )/ CDNAfor Cc Na+ or CDNA 0

and2G 1/ 2xM

Information on the fraction of thermodynamically « free » counterions


Dna as a polyelectrolyte

Cargèse, 2002 - 39

Experimentally,

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

Simple salt limit 2G =1

2G

  • Theoretically,

  • by solving the P-B equation and averaging C Na+(r)and C Cl-(r)

  • 2G = (1/ 2xM) f( kr0 )

  • with

  • f(kr0 0) = 1 the limiting law

1/ 2xM

kr0

Cs0

10 mM

0.1 M

1 M

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


Dna as a polyelectrolyte

Cargèse, 2002 - 40

The osmotic pressure p :

p = r g h

h

Na-DNA +

Salt Cs

Salt Cs0

In excess of Na-DNA compared to NaCl,

Cs’0 the salt is excluded

with fosm the osmotic coefficient

p / kT = fosmCc Na+

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

fosm = C(R) / Cc Na+;fosm = ( 1+g(kr0 ) ) / 2xMwith g(kr0 ) 0

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


Dna as a polyelectrolyte

1/k

r0

Cargèse, 2002 - 41

fosm

2G

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

1/ 2xM

kr0

CDNA

1 g/l

100 g/l

  • Theories and Experiments are

  • qualitatively in good agreement.

  • Quantitatively…..

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


Dna as a polyelectrolyte

2

Cargèse, 2002 - 42

q/qeff

(Nicolai & Mandel, 1989)

(Stigter, 1978)

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

(Griffey, unpublished) 4.2

(Padmanabhan et al., 1988) 2.1

(Braulin et al., 1987) 2.5

  • Permeability of the double-helix

  • Specific interactions…

  • different sensibilities of

  • the different technics

To be compared withxM = 4.2


4 b the length effect

4_b) the length effect

(Alexander et al.,1984)

For charged spheres, ion chemical potential :

far from the spheres, mainly entropic kT ln C

on its surface, mainly enthalpic (electrostatic)

-qeffe2/4pee0a

qeff ~ - ln C

The effective charge increases with dilution

Counterions evaporation

Cargèse, 2002 - 43

Counterions evaporation

End effects

1/k

L


Dna as a polyelectrolyte

Cargèse, 2002 - 44

fraction of condensed counterions

qeff ~ - ln C

1/k

1/k

dilution

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


Dna as a polyelectrolyte

2G 1

Nucleotides

behave

like simple salt

denaturated

DNA

native DNA

( N = number of nucleotides per chain)

N = 25

N = 10

5 base-pairs

Returning to DNA, Importance of end effects

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

Cs= 1.8 mM1/k = 73 Å

Cargèse, 2002 - 45

kLend effects

2G =

(1/ 2xM) f( kr0 )

1/k

Cs (mM)


Dna as a polyelectrolyte

Cargèse, 2002 - 46

N  72

The local

concentration

at the DNA surface

N = 24

Ends effect

becomes negligeable on average

but evaporation still

occurs at the ends.

N = 12

1/k

(Olmsted et al., 1989)


5 conformation and interaction 5 a thermal denaturation

5_ Conformation and Interaction5_a) Thermal denaturation

Cargèse, 2002 - 47

Calculation of the free energy using the charge renormalisation

(Manning, 1972)

Interaction energy

of the chain with its ionic atmosphere

Entropic term

of the salt, of the « free » ions

Non-electrostatic term

+

+…

+

- (np/xM )kT ln k

+(np/xM )kT ln Cs

Addition

of salt

Destabilizes

Stabilizes

Ionic atmosphere

(ns salt + np/xM« free » ions)

(salt in excess but at low concentration)

the double-helix

L/lB or np/xM

charged phosphate

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


Dna as a polyelectrolyte

Cargèse, 2002 - 48

- (np/xM )kT ln k

+(np/xM )kT ln Cs

k ~ Cs 1/2

The dominant term

is entropic

+(np/2xM )kT ln Cs

  • 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

    D Gele=Gelesingle-stranded– Geledouble-stranded< 0


Dna as a polyelectrolyte

Tm (°C)

CNa+(M)

Cargèse, 2002 - 49

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

After manipulation :

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

with A = kTm2/DHm

T4 DNA (Record, 1975)


Dna as a polyelectrolyte

kT

D G non-ele > 0 G non-eledenaturated > G non-elenative

Cargèse, 2002 - 50

From experimentalTm and calculated D Gele

  • Gnon-ele

    per

    nucleotide

*Tm= k log Cs + 0.41 XGC + 81.5

(Schildkraut & Lifson, 1965)

*d Tm /d log Cs ~D (1/2xM )

~ D (2G )

(Olmsted et al., 1991)

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


5 b interaction and chain conformation

5_b) Interaction and chain conformation

Cargèse, 2002 - 51

Intermolecular interactions :

between short DNAL = Lp = 50 nm (150 bp)

For neutral rods,

excluded volume v0 L2 d

d = 2r0

For DNA rods,v L2deff

with an effective diameter

deff = 2r0 + (1/k) f( xM , k r0 )

e-kr

(Brenner & Parsegian, 1972)

At low salt , deff >> d andv >> v0

In the high salt limit, deff = d andv = v0


Dna as a polyelectrolyte

Cargèse, 2002 - 52

v L2deff

v

isotropic

50 v0

C i - a

anisotropic

v0

fi-a~ deff / L

CNaCl(M)

Ci – a ~ 1 / v

(Nicolai & Mandel, 1989)

CDNA increases with Cs


Dna as a polyelectrolyte

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 (kLp >>1),

  • lele = lOSF = lB/ 4 (kb)2withblB

  • (Odijk, 1977; Skolnick & Fixman, 1977)

  • Using the P-B equation, lele = lOSF f(k r0)

  • (Fixman, 1982; Le Bret, 1982)


Dna as a polyelectrolyte

6360 bp (Maret & Weill, 1983)

587 bp (Hagerman, 1981)

T7 DNA (Sobel & Harpst, 1991)

T2 DNA (Harrington, 1978)

Cargèse, 2002 - 54

Lp (nm)

Lp = l0 + lOSF

Lp = l0 + lOSF f(k r0 )

l0= 50 nm

k r0

linear Col E1 plasmid

(Borochov et al., 1981)

CNaCl

0.01

0.1

1 M


Dna as a polyelectrolyte

Cargèse, 2002 - 55

Rg: radius of gyration

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

Experimental data

(Sobel & Harpst, 1991)

  • Including :

  • excluded volume

  • with deff

  • persistence length

    • with lOSF f(k r0 ), l0= 40 nm

  • (Stigter, 1985)

Random coil

CNaCl


6 multivalent counterions 6 a collapse and phase diagram

6_ MultivalentCounterions6_a) collapse and phase diagram

Cargèse, 2002 - 56

In the Manning approach,

The charge fraction zcq of condensed ions increases like

zcq = 1- 1/zcxM

the effective charge is reduced by 94 %

m

zc

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

Linear plasmid in 50 mM monovalent salt

+ 0.2 mM of zc-valent

(Ma & Bloomfield, 1994)


Dna as a polyelectrolyte

Cargèse, 2002 - 57

Low monovalent salt (1 mM) + Cobalt Hexamine zc= 3 on l DNA

Light scattering (Widom & Baldwin, 1980-83)

Toroidal globule

Diffusion coefficient

Scattered

Intensity

RH 40 nm

with spermidine (zc= 3),

RH 50 nm

Cobalt Hexamine Concentration

(Wilson & Bloomfield, 1979)


Dna as a polyelectrolyte

Cargèse, 2002 - 58

For higher DNA concentrations :aggregation

My first clichés !

Cryo-electron microscopy


Dna as a polyelectrolyte

  • For

  • Nucleosome core particles

  • H1-depleted chromatine fragments

  • short single-stranded DNA

Cargèse, 2002 - 59

Phase diagram

DNA redissolution

In excess of

spermine

Spermine

Concentration (M)

DNA precipitation

DNA concentration (M)

(Raspaud et al., 1998-99)


Dna as a polyelectrolyte

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


Dna as a polyelectrolyte

  • a salt bridge model : « ion-bridging » model ?

  • Intermolecular interactions in dilute solutions with an excluded volume v :

Cargèse, 2002 - 61

(Olvera de la Cruz et al., 1995)

electrostatic repulsion

between like-charged chains

short-range attraction

local

charge

inversion

-

-

-

-

The reduced effective charge : - qeff xM

1

Cspermine (mM)

1 / zc

Cmultivalent salt

CDNA (mM)


6 b ionic correlation

6_b) ionic correlation

zc= 4

zc= 1

r/r0

Cargèse, 2002 - 62

Fraction of counterions

within a cylinder of radius r

(from the P-B equation)

Strong charge accumulation

near the surface ( one layer)

Few Angstroms


Dna as a polyelectrolyte

Cargèse, 2002 - 63

Coulomb energy between neighboring ions

Coupling parameter :

W=Wc / kT

Wc= (zce)2/4pee0az

az

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

Important longitudinal correlations between ions

« strongly correlated liquid »

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


Dna as a polyelectrolyte

Cargèse, 2002 - 64

Two-dimensional lattice of

the multivalent counterions

around the surface

Correlation Energy ec

per ion < 0 (attractive)

If n : local concentration of

the correlated liquid

ec – Wc

ec(2n) < ec(n )

Attraction between DNA


Dna as a polyelectrolyte

- qeff xM

-

+

Phase diagram

log Cmultivalent salt

Cobalt-hexamine

Energy

of DNA condensation

per nucleotide

- ec = 0.07 kT

+

log Cmultivalent salt

-

log CDNA

(Rau & Parsegian, 1992)

Cargèse, 2002 - 65

  • In the dissolved state,

  • Free energy per DNA molecule with qeff

  • - In the condensed state, using ec

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


Dna as a polyelectrolyte

About the charge inversion,

Cargèse, 2002 - 66

Short DNA

fragments

+

T4 DNA

-

Spermine concentration (zc = + 4)

-

Nucleosome

Core Particles

+ 4

+

+ 3

-

-

zc = + 2

Spermidine concentration (zc = + 3)

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

(Yamasaki et al., 2001)


Dna as a polyelectrolyte

  • specific effects : polyamine is a polycation

  • at long length scale, behaves like azc-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 ion

  • attenuated correlation effect

  • (Lyubartsev & Nordenskiöld, 1997)

  • - the electrophoretic mobility and its associated zeta potential

Cargèse, 2002 - 67

+

rz

-

Slipping surface located at rz

during the electrophoretic migration

Comparison between

rz and the ionic size s

r / s

rz = s rz = 2s

(Deserno et al., 2001)


Dna as a polyelectrolyte

Cargèse, 2002 - 68

  • mixture of mono and zc-valent cations condensed onto the DNA

  • attenuated correlation effect

  • - non-ideal behavior of the “free” multivalent salt

  • Debye-Hückel ionic atmosphere and the ionic size effect

  • reduced and may suppressed the DNA overcharging

  • (Solis & Olvera de la Cruz, 2001)


Dna as a polyelectrolyte

Cargèse, 2002 - 69

As a conclusion,

DNA IS A POLYELECTROLYTE

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 changes

without specific effects

- DNA - charged proteins interactions

Course limited to Simple Naked DNA study with ions,

more complex behavior for Chromatin,…


References

References

Cargèse, 2002 - 70

  • S. Alexander, P.M. Chaikin, P. Grant, G.J. Morales, P. Pincus, D. Hone, J.Chem.Phys., 80, p 5776, 1984.

  • P. Atkins, Physical Chemistry, 6th ed., W.H. Freeman and Co., NY, 1998.

  • H.E. Auer, Z. Alexandrowicz, Biopolymers, 8, p 1, 1969.

  • M.L. Bleam, C.F. Anderson, M.T. Jr Record, P.N.A.S., 77, p 3085, 1980.

  • V.A. Bloomfield, in « Nucleic Acids structures, properties, and functions »V.A. Bloomfield, D.M. Crothers and I. Tinocco Jr, Eds (University Science Books, Sausalito CA), p 475-528, 2000.

  • N. Borochov, H. Eisenberg, Z. Kam, Biopolymers, 20, p 231, 1981.

  • W.H. Braulin, C.F. Anderson, Record M.T. , Biochemistry, 26, p 7724, 1987.

  • S.L. Brenner and V.A. Parsegian, Biophys. J., 14, p 327, 1974.

  • S.-L. Chang, S.H. Chen, R.L. Rill and J.S. Lin, J.Phys.Chem., 94, p 8025, 1990.

  • M. De Frutos, E. Raspaud, A. Leforestier, F. Livolant, Biophys. J., 81, p 1127, 2001.

  • M. Deserno, C. Holm, and S. May, Macromolecules, 33, p 199, 2000.

  • M. Deserno, F. Jimenez-Angeles, C. Holm, M. Lozada-Cassou, J.Phys.Chem. B, 105, p 10983, 2001.

  • M. Fixman, J. Chem. Phys., 76, p 6346, 1982.

  • R.M. Fuoss, A. Katchalsky, S. Lifson, P.N.A.S., 37, p 579, 1951.

  • P. Gonzales-Mozuelos, M.Olvera de la Cruz, J.Chem.Phys., 103, p 3145, 1995.

  • J. Granot and D.R. Kearns, Biopolymers, 21, p 203, 1982.

  • L.M. Gross, U.P. Strauss, in « Chemical Physics of ionic solutions », B.E. Conway and R.G. Barradas, Eds (John Wiley & Sons, Inc., NY), p 361-389, 1966.

  • A.Y. Grosberg, T.T. Nguyen, and B.I. Shklovskii, Rev. Modern Physics, 74, p 329, 2002.

  • P. J. Hagerman, Biopolymers, 20, p 1503, 1981.


Dna as a polyelectrolyte

Cargèse, 2002 - 71

  • R.E. Harrington, Biopolymers, 17, p 919, 1978.

  • N.I. Korolev, A.P Lyubartsev, and L. Nordenskiöld, Biophys. J., 75, p 3041, 1998.

  • M. Le Bret, J. Chem. Phys., 76, p 6243, 1982.

  • M. Le Bret and B. H. Zimm, Biopolymers, 23, p 287, 1984.

  • M. Le Bret and B. H. Zimm, Biopolymers, 23, p 271, 1984.

  • H. Liu, L. Skibinska, J. Gapinski, A. Patkowski, E.W. Fisher, R. Pecora, J.Chem.Phys., 109, p 7556, 1998.

  • A.P. Lyubartsev and L. Nordenskiöld, J.Phys.Chem. B, 101, p 4335, 1997.

  • T. Odijk, J. Pol. Sci. Phys. Ed., 15, 477, 1977.

  • T. Odijk, Biophys. J., 75, p 1224, 1998.

  • C. Ma and V.A. Bloomfield, Biopolymers, 35, p 211, 1994.

  • D.A. Mac Quarrie, « Statistical Mechanics », Harper’s chemistry series, Harper Collins, 1976.

  • G. Maret and G. Weill, Biopolymers, 22, p 2727, 1983.

  • G.S. Manning, J. Chem. Phys., 51, 3, p 924, 1969.

  • G.S. Manning, Biopolymers, 11, p 937, 1972.

  • G.S. Manning, Q. Rev. Biophys. II, 2, p 179, 1978.

  • T.T. Nguyen, I. Rouzina, B.I. Shklovskii, J. Chem. Phys., 112, p 2562, 2000.

  • T.T. Nguyen, and B.I. Shklovskii, J.Chem. Phys., 115, p 7298, 2001.

  • T. Nicolai and M. Mandel, Macromolecules, 22, p 438, 1989.

  • M. Olmsted, C.F. Anderson, and M.T. Record Jr., Proc. Natl. Acad.Sci. USA, 86, p 7760, 1989.

  • M. Olmsted, C.F. Anderson, and M.T. Record Jr., Biopolymers, 31, p 1593, 1991.

  • M. Olvera de la Cruz, L. Belloni, M. Delsanti, J.P. Dalbiez, O. Spalla, M. Drifford, J.Chem.Phys., 103, p 5871, 1995.

  • F. Oosawa, « Polyelectrolytes », Marcel Dekker, NY, p 160, 1971.

  • S.Padmanabhan, B. Richay, C.F. Anderson, M.T. Record Jr, Biochemistry, 27, p 4367, 1988.


Dna as a polyelectrolyte

Cargèse, 2002 - 72

  • E. Raspaud, M. Olvera de la Cruz, J.-L. Sikorav, F. Livolant, Biophys. J., 74, p 381, 1998.

  • E. Raspaud, I. Chaperon, A. Leforestier, F. Livolant, Biophys. J., p 1547, 1999.

  • E. Raspaud, M. da Conceiçao, F. Livolant, Phys. Rev.Lett., 84, p 2533, 2000.

  • D.C. Rau and V.A. Parsegian, Biophys. J., 61, p 246, 1992.

  • M.T. Record Jr, Biopolymers, 14, p 2137, 1975.

  • I. Rouzina, V.A. Bloomfield, J. Phys. Chem., 100, p 9977, 1996.

  • I. Rouzina, V.A. Bloomfield, Biophys. J., 77, p 3242, 1999.

  • I. Sabbagh and M. Delsanti, Eur. Phys. J. E, 1, p 75, 2000.

  • C. Schildkraut, S. Lifson, Biopolymers, 3, p 195, 1965.

  • J. Shack, R.J. Jenkins, and J.M. Thompsett, J. Biol. Chem., 198, 85, 1952.

  • J. Skolnick and M. Fixman, Macromolecules, 10, p 944, 1977.

  • E.S. Sobel and J.A. Harpst, Biopolymers, 31, p 1559, 1991.

  • F.J. Solis, and M. Olvera de la Cruz, Eur.Phys.J. E, 4, p 143, 2001.

  • D. Stigter, J. Phys. Chem., 82, p 1603, 1978.

  • D. Stigter, Macromolecules, 18, p 1619, 1985.

  • U.P. Strauss, C. Helfgott, and H. Pink , J. Phys. Chem., 71, 8, p 2550, 1967.

  • J.R.C. van der Maarel, L.C.A. Groot, M. Mandel, W. Jesse, G. Jannink and V. Rodriguez, J.Phys.II France, 2, p 109, 1992.

  • J. Widom and R.L. Baldwin, J. Mol. Biol., 144, p 431, 1980.

  • J. Widom and R. Widom, Biopolymers, 22, p 1595, 1983.

  • R.W. Wilson and V.A. Bloomfield, Biochemistry, 18, p 2192, 1979.

  • Y. Yamasaki, Y. Teramoto, K. Yoshikawa, Biophys. J., 80, p 2823, 2001.


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