Electrostatic complexation of spheres and chains under elastic stress

R. D.

 

Kornberg

and

A.

 

Klug

,  , ();

K.

 

Luger

,

A. W.

 

Mäder

,

R. K.

 

Richmond

,

D. F.

 

Sargent

, and

T. J.

 

Richmond

,  , ();

J.

Widom

, , ().

F.

Ganachaud

,

A.

Elaı̈ssari

,

F.

Pichot

,

A.

Laayoun

, and

P.

Cros

, , ().

G. B.

Sukhorukov

,

E.

Donath

,

S.

Davis

,

H.

Lichtenfeld

,

F.

Caruso

,

Vi. I.

Popov

, and

H.

Möhwald

, , ().

D. W.

McQuigg

,

J. I.

Kaplan

, and

P. L.

Dubin

, , (), and references therein.

W. H.

Braunlin

,

T. J.

Strick

, and

M. T.

Record

, , ().

D. P.

Mascotti

and

T. M.

Lohmann

, , ().

J. O.

Rädler

,

I.

Koltover

,

T.

Salditt

, and

C. R.

Safinya

, , ().

I.

Koltover

,

T.

Salditt

, and

C. R.

Safinya

, , ().

M. T.

Record

,

C. F.

Anderson

, and

T. M.

Lohmann

, , ().

S. Y.

Park

,

R. F.

Bruinsma

, and

W. M.

Gelbart

, , ().

R.

Bruinsma

, , ().

D.

Harries

,

S.

May

,

W. M.

Gelbart

, and

A.

Ben-Shaul

, , ().

P.

Sens

and

J.-F.

Joanny

, , ().

N. L.

Marky

and

G. S.

Manning

, , ().

R. A.

Harries

and

J. E.

Hearst

, , ().

T. T.

Nguyen

,

A. Yu.

Grosberg

, and

B. I.

Shklovskii

, , ().

T. T.

Nguyen

and

B. I.

Shklovskii

, , ().

T. T.

Nguyen

and

B. I.

Shklovskii

, cond-mat/0105078.

M.

Rief

,

M.

Gautel

,

F.

Oesterhelt

,

J. M.

Fernandez

, and

H. E.

Gaub

, , ().

M. B.

Viani

,

T. E.

Schaffer

,

G. T.

Paloczi

et al., , ().

P. A.

Pincus

,

C. J.

Sandroff

, and

T. A.

Witten

, , ().

T. T.

Nguyen

and

B. I.

Shklovskii

, , ().

F. Oosawa, Polyelectrolytes (Decker, New York, 1971).

G. S.

Manning

, , ().

Ω follows from the ratio of $ccond,$ the concentration of counterions within the sheet of condensed counterions, to $cbulk,$ their concentration in the bulk: $Ω=ln(ccond/cbulk).$ The condensed counterions are confined within the Gouy–Chapman distance $λchain=1/4πσlB$ from the charged surface of the chain. σ denotes the number density of surface charges on the chain: $σ=1/2πrb.$ If we assume, for simplicity, that most of the counterions are condensed (highly charged chain) then $ccond≅σ/λchain$ leading to $Ω=2 ln(4ξκ−1/r).$ Similarly, in the sphere case we have $σ=Z/4πR2,$ leading to $Ω̃=2 ln(ZlB κ−1/R2).$ This derivation is consistent with the nonlinear Poisson–Boltzmann approach, cf. Ref. 26, for $λchain≪r$ and $λsph≪R.$

I.

Rouzina

and

V. A.

Bloomfield

, , ().

S.

Alexander

,

P. M.

Chaikin

,

P.

Grant

,

G. J.

Morales

,

P.

Pincus

, and

D.

Hone

, , ().

Due to the presence of the charged rod the value of $Zmax$ is slightly different from that for an isolated sphere. The electrostatic charging energy includes now the sphere-chain interaction term, Eq. (6), i.e., $lBZmax2/2R+ln(κR)Zmax$ leading to a $Zmax$ value of the order $(Ω̃−ln(κR))R/lB.$

Complexes formed by DNA and histone octamers show overcharging. In these complexes 147 base pairs of DNA (carrying 294 negative charges) are wrapped in a 1 $34;$ left-handed superhelical turn around the octamer containing 220 cationic residues (for details, cf. Ref. 30). This clearly indicates that the histone octamer is overcharged by the wrapped part of the DNA. The notion of overcharging is, however, only reasonable when the charging energy is operative—favoring an isoelectric complex. For high ionic strength where the size of the complex exceeds vastly the screening length of the solution this concept might be less useful. The nucleosome core particle (the histone octamer plus the 147 base pairs of wrapped DNA) is a cylindrical particle with a radius of about 5 nm and a height of 6 nm (Ref. 1). Its size is therefore large compared to the screening length at physiological conditions (roughly 100 mM salt, corresponding to $κ−1≈1 nm$⁠).

S. N.

Khrapunov

,

A. I.

Dragan

,

A. V.

Sivolob

, and

A. M.

Zagariya

, , ().

R. R.

Netz

and

J.-F.

Joanny

, , ().

H.

Schiessel

,

J.

Rudnick

,

R.

Bruinsma

, and

W. M.

Gelbart

, , ().

O. V.

Borisov

and

A.

Halperin

, , ().

A. V.

Dobrynin

,

M.

Rubinstein

, and

S. P.

Obukhov

, , ().

Y.

Kantor

and

M.

Kardar

, , ().

T.

Soddemann

,

H.

Schiessel

, and

A.

Blumen

, , ().

M. N.

Tamashiro

and

H.

Schiessel

, , ().

T.

Vilgis

,

A.

Johner

, and

J.-F.

Joanny

, , ().

A.

Halperin

and

E. B.

Zhulina

, , ().

Y.

Cui

and

C.

Bustamante

, , ().

T.

Odijk

, , ().

P.

Haronska

,

T. A.

Vilgis

,

R.

Grottenmüller

, and

M.

Schmidt

, , ().

E.

Gurovitch

and

P.

Sens

, , ().

E. M.

Mateescu

,

C.

Jeppesen

, and

P.

Pincus

, , ().

K. K.

Kunze

and

R. R.

Netz

, , ().

T.

Wallin

and

P.

Linse

, , ().

T.

Wallin

and

P.

Linse

, , ().

R. Messina, C. Holm, and K. Kremer (unpublished).

M.

Jonsson

and

P.

Linse

, , ().