Serg

e Le

may

DN

A-ba

sed

na

note

chno

logy

:Co

nstr

uctio

n, m

echa

nics

, and

ele

ctro

nics

11 M

ay 2

008

Char

ge in

vers

ion

acco

mpa

nies

DN

A co

nden

satio

n

by m

ultiv

alen

t io

ns

Kavl

i Ins

titut

e of

Nan

osci

ence

Del

ft U

nive

rsity

of

Tech

nolo

gyTh

e N

ethe

rland

s

Ove

rvie

w:

rese

arch

line

sEl

ectr

osta

tics

in li

quid

Nan

o-io

nics

DN

A co

nden

satio

n

Nan

opor

esN

anot

ubes

Char

ge in

vers

ion

-+

Volta

mm

etry

Elec

trop

hore

sis

Sing

le-m

olec

ule

dete

ctio

n

Intr

oduc

tion

1. A

tom

ic F

orce

Mic

rosc

opy

2. M

agne

tic t

wee

zers

3. E

lect

roph

ores

is

Sum

mar

y

Out

line

Basi

cs o

f io

nic

scre

enin

g

Pois

son-

Boltz

man

n eq

uatio

n:

Deb

ye, G

ouy

&

Cha

pman

(19

20’s

)

+

-

--

- --

---

--

++

+

+

+++

+

++

+

2

2ex

p(/

)ii

i

i

ezc

ze

kTxφ

φε

∞∂

=−

−∂

∑

()

exp(

/)

ii

cx

cze

kTφ

∞=

−

Ioni

c co

ncen

trat

ions

:

Elec

tros

tatic

pot

entia

l

λ D +

+

22

Di

ii

kT zec

ελ

∞=∑

Deb

ye

leng

th

-H

igh

surf

ace

ch

arge

:

“Com

pact

laye

r”“H

elm

holtz

la

yer”

“Ste

rn la

yer”

“Man

ning

con

dens

ate”

Basi

cs o

f io

nic

scre

enin

g

Elec

trop

hore

tic

mob

ility

rev

erse

s si

gn a

t hi

gh c

once

ntra

tion

of

mul

tival

ent

coun

terio

ns

Jam

es &

Hea

ley,

J. C

oll.

Int.

Sci

. 40

, 42

(197

2)Q

uesa

da-P

erez

et

al.,

Chem

Phys

Chem

4,

234

(200

3)

1. C

harg

e in

vers

ion

Forc

e-di

stan

ce a

ppar

atus

Pash

ley,

J. C

oll.

Int.

Sci

. 102

, 23

(198

4)Pe

trov

, Mik

lavi

c

& N

ylan

der,

J. P

hys.

Che

m. 98

2602

(19

94)

Atom

ic f

orce

mic

rosc

opy

Vith

ayav

eroj

, Yia

coum

i

& T

sour

is, J

. Dis

p. S

ci. T

echn

. 24,

517

(20

03)

Best

eman

et a

l, PR

L 93

, 170

802

(200

4)

Stre

amin

g cu

rren

tsva

n de

r H

eyde

n

et a

l, PR

L 96

, 224

502

(200

6)

-NEl

ectr

icfie

ld

+3

+3

+3

+3

+3

+3

Som

e od

d ob

serv

atio

ns…

Actin

fil

amen

ts c

onde

nsed

by

Ba2+

Ange

lini

et

al,

PNAS

100

, 863

4 (2

003)

DN

A co

nden

satio

n by

spe

rmin

e4+

2.

Like

-cha

rge

attr

actio

n Lam

bert

et

al.,

PNAS

97,

724

8 (2

000)

Som

e od

d ob

serv

atio

ns…

Prop

osed

mec

hani

sms

W. M

. Gel

bart

et

al,

Phys

ics

To

day

53

, 38

(200

0)

[ove

rvie

w]

F. O

osaw

a, B

iopo

lym

ers

6

, 163

3 (1

968)

Rou

zina

&

Blo

omfie

ld, J

PC 100

, 997

7 (1

996)

Korn

yshe

v &

Lei

kin,

PRL 82

, 413

8 (1

999)

Gol

esta

nian

, Kar

dar

&

Liv

erpo

ol,

PRL 82

, 445

6 (1

999)

, PRE

66

, 051

802

(200

2)

Zhan

g &

Shk

lovs

kii,

Phys

ica

A 349

, 563

(20

05)

…

and

man

y ot

hers Bu

t

no

smok

ing

gun

expe

rimen

t!!!

Why

stud

y D

NA

con

dens

atio

n?100 nm

DN

A co

nden

sed

by

sper

min

e4+

Hud

et

al,

PNAS

98

(2

001)

•

Beca

use

it’s

fun!

•

Prot

otyp

ical

sys

tem

for

stu

dyin

g el

ectr

osta

tic e

ffec

ts (

high

cha

rge

dens

ity)

•

Hig

h le

vel o

f co

ntro

l

•

Biol

ogic

al r

elev

ance

(D

NA

pack

agin

g, c

hrom

atin

str

uctu

re)

•

Pote

ntia

l app

licat

ion

to g

ene

ther

apy

100 nm

Hud

et a

l, PN

AS 98

(200

1)

TEM

, AFM

Sedi

men

-ta

tion

C 3+

% uncondensed

Ras

paud

et a

l, Bi

ophy

s. J

. 74,

381

(19

98)

Pelta

, Li

vola

nt

& S

ikor

av, J

. Bio

l. Ch

em. 2

71, 5

656

(199

6)

Prev

ious

exp

erim

enta

l wor

k

Opt

ical

tw

eeze

rs

Exte

nsio

nEx

tens

ion

(μ

m)

Force(pN)

Mur

ayam

a et

al,

PRL 90

, 018

102

(200

3)

TEM

imag

es

Scal

e ba

r 50

nM

10 m

M

sper

mid

ine

(3

+)

Hig

hly-

char

ged

surf

aces

POSI

TIVE

CH

ARG

E: P

olyl

ysin

e-co

ated

mic

a

NEG

ATIV

E SU

RFA

CE:

bare

mic

a

100 μM

1 m

M10

mM

100

mM

900

mM

100 μM

1 m

M10

mM

100

mM

900

mM

1 μm

×

1 μm

Sp

erm

idin

e

(3+

)

Imag

ing

in li

quid

Bare

mic

a

PL-c

oate

dm

ica

Scal

e ba

r 50

nm

1 m

M

sper

mid

ine

(3

+)

Gra

phite Ta

ke-h

ome

mes

sage

s

Don

’t us

e AF

M t

o le

arn

abou

t co

nden

sate

mor

phol

ogy!

At m

M

conc

entr

atio

ns o

f tr

ival

ent

ions

, hig

hly-

char

ged

obje

cts

stic

k to

geth

er

Wha

t’s w

rong

with

mea

n-fie

ld t

heor

ies?

No

char

ge in

vers

ion

3-

3+

3-3-

No

like-

char

ge a

ttra

ctio

n

Coul

omb’

s la

w

Char

ge in

vers

ion

poss

ible

3-3+

3+

Like

-cha

rge

attr

actio

n po

ssib

le

New

ele

men

ts:

•di

scre

tene

ss o

f ch

arge

•sp

atia

l cor

rela

tions

•el

ectr

osta

tic e

nerg

ies

mus

t be

> k

T

In g

ener

al, m

inim

ize

free

ene

rgy

G=

U–

TS

Udo

min

ates

for

low

T,

high

ZS

“

“hi

gh T

, low

Z3-3-3+

3+

Corr

elat

ed li

quid

- +Z

ion

-

Rou

zina

& B

loom

field

, JP

C 100,

997

7 (1

996)

Zhan

g &

Shk

lovs

kii,

Phys

ica

A 349,

563

(20

05)

“Ele

ctro

stat

ic z

ippe

r”

Korn

yshe

v &

Lei

kin,

PR

L 82,

413

8 (1

999)

Prop

osed

ele

ctro

stat

ic m

echa

nism

s

Zhan

g &

Shk

lovs

kii

Phys

ica

A 349

, 563

(20

05)2

SCL

cond

1(

)2

Gn

Cφ

=−

+Fr

eeen

ergy Sh

ort-

rang

eat

trac

tion

Repu

lsio

ndu

e

to n

et c

harg

e

0(

/)l

n(/

)kT

Zecc

φ=

c 0

= c

harg

e in

vers

ion

co

ncen

trat

ion

DN

A po

sitiv

e

whe

n

c>

c0

- +Z

ion

-

Rou

zina

&

Blo

omfie

ldJP

C 100

, 997

7 (1

996)

Effe

ctiv

e

DN

A po

tent

ial

-

Free energy

+

Expe

rimen

tal

te

st:

Mea

sure

as

fun

ctio

n

of c

once

ntra

tion

1.Fr

ee e

nerg

y

of c

onde

nsat

ion

2.N

et c

harg

e of

con

dens

ates

Char

ge in

vers

ion

Like

-cha

rge

at

trac

tion

Stro

ngly

cor

rela

ted

liqui

d m

echa

nism

Cond

ense

De-

cond

ense

Yang

& R

au, B

ioph

ys. J

. 89,

193

2 (2

005)

Mag

netic

tw

eeze

rs

8kbp

nic

ked

DN

A, 1

0mM

TRIS

, pH

7.5

Wor

m-li

ke-c

hain

fit

L =

2.8

5 μm

, p =

51.

6 nm

Cond

ensa

tion

is

a f

irst-

orde

r, n

ucle

ated

pr

oces

s

Mon

oval

ent

Triv

alen

t

1mM

[C 1

2

H30

CoN

8

]3+

DN

A co

nden

satio

n

DN

A-D

NA

DN

A-su

rfac

eBo

th

Pote

ntia

lpr

oble

m

Solu

tion

Stiff

spa

cers

ss-d

s-ss

D

NA

Coat

ss-

DN

A

with

Rec

A

Impl

emen

tatio

n

Rul

ing

out

DN

A-su

rfac

e in

tera

ctio

ns (

1/3)

81nmss-d

s-ss

-DN

ARec

A-co

ated

310n

m

120n

m

Rul

ing

out

DN

A-su

rfac

e in

tera

ctio

ns (

2/3)

•Rec

A-co

ated

ss

-DN

A

beha

ves

as

stif

f

rod

•Co

nden

satio

n

conc

entr

atio

n

and

dyna

mic

s

unaf

fect

ed

by

surf

aces

Rul

ing

out

DN

A-su

rfac

e in

tera

ctio

ns (

3/3)

•

Ree

ntra

nt

beha

vior

m

anife

st a

t si

ngle

-

mol

ecul

e

leve

l

•

Som

e

ion

spec

ifici

ty

(esp

ecia

lly

sper

mid

ine)

•

Appr

oxim

atel

y

quad

ratic

in

ln

(c

/c0

)“a

s ex

pect

ed”

Cond

ensa

tion

forc

e F c

ΔG‡

ΔGco

ndG

F c

= f

ree

ener

gy

of c

onde

nsat

ion

pe

r un

it le

ngth

Mur

ayam

a et

al,

PRL 90

, 018

102

(200

3)

(exp

’t)Zh

ang

et a

l, Ph

ysic

a

A 349

, 563

(20

05)

(the

ory)

Wha

t ar

e w

e pr

obin

g?

ΔG‡

ΔGco

nd

But

we

obse

rve

nucl

eatio

n ki

netic

s!

Hyp

othe

sis:

tra

nsiti

on s

tate

is a

loop

sper

min

esp

erm

idin

e

2b

loop

kTp

URF

Rπ

π=

+

bend

ing

ener

gyw

ork

agai

nst

forc

e

Low

est-

ener

gy lo

op:

2bkTp

RF

=

T. R

. Str

ick

et

al.,

Pro

g. B

ioph

ys. M

olec

. Bio

l. 74

, 115

(20

00)

Hyp

othe

sis:

the

tra

nsiti

on s

tate

is a

loop

bend

twis

tel

eccr

it(

)(

)...

GU

FU

nG

GΔ

=+

++

=‡

Loop

en

ergy

Win

ding

the

spr

ing:

Pr

e-tw

istin

g

a to

rsio

nally

co

nstr

aine

d

mol

ecul

e lo

wer

s

the

ener

gy

for

fo

rmin

g

a lo

op

Tors

iona

l

ener

gy

per

turn

2be

nd(

)8

bU

FkTpF

π=

2

twis

t

4(

)Cn

Un

Lπ

=−

twis

tbe

nd0

UU

δδ

+=

T. R

. Str

ick

et

al.,

Pro

g. B

ioph

ys. M

olec

. Bio

l. 74

, 115

(20

00)

Test

ing

the

loop

hyp

othe

sis

22

()

(0)

12

(0)

cb

ccC

nF

LkTpFn

Fn

π⎛

⎞=

+⎜

⎟⎜

⎟=

⎝⎠

F c

(0)

= f

it pa

ram

eter

C =

86

nmk b

T

p=

50

nm

Nuc

leat

ion

st

ate

cont

ains

a

DN

A lo

op

Test

ing

the

loop

hyp

othe

sis

loop

elec

crit

...‡

Δ=

++

=G

UG

G

()

2el

ecln

1/

Dc

LG

Rπε

φλ

=+

Appr

oxim

ate

as

tw

o

cylin

ders

loop

elec

0U

Gδ

δ+

=

0(

/)l

n(

/)

kTZe

cc

φ=

2

00

()

()

1ln

cc

Lc

Fc

Fc

ac

⎛⎞

⎛⎞

=−

⎜⎟

⎜⎟

⎜⎟

⎝⎠

⎝⎠

a=

kno

wn

co

nsta

nt

So

wha

t

caus

es

the

conc

entr

atio

n

depe

nden

ce?

L

•

Qua

litat

ivel

y

good

fit

(ex

cept

sp

erm

idin

e)

•

Fits

yie

ldL

=40

nm

(c

ompa

re

to lo

op

perim

eter

>34

nm

)

2

00

()

1ln

cc

Lc

FFc

ac

⎛⎞

⎛⎞

=−

⎜⎟

⎜⎟

⎜⎟

⎝⎠

⎝⎠

Fit

to o

ur s

impl

e m

odel

Prob

lem

:N

obod

y

had

ever

rep

orte

d

posi

tive

D

NA

in e

lect

roph

ores

is!

But

no

t

a st

raig

htfo

rwar

d

expe

rimen

t:•

Cond

ensa

tes

ge

t

stuc

k

in t

he g

el•

Mob

ility

is

ver

y

low

•El

ectr

oosm

otic

flo

ws

+-

Pred

ictio

n: F

or c

>c 0

, the

DN

A sh

ould

be

po

sitiv

ely

ch

arge

d

Acid

tes

t

Slop

e

∝

elec

trop

hore

tic

mob

ility

3 m

M0.

1 m

M

Raw

da

ta

Sper

min

e4+

Mal

vern

ze

ta-s

izer

ZS

(M

3-PA

LS m

ode)

5 ng

/μL

DN

A10

min

incu

batio

n

Dyn

amic

ligh

t sc

atte

ring

•

Sper

min

e ca

n

char

ge-in

vert

DN

A•

Ch

arge

inve

rsio

n

inhi

bite

d

by

mon

oval

ent

salt

(pro

babl

y

why

it

w

as n

ot

obse

rved

be

fore

)

Elec

trop

hore

tic

mob

ility

We

obse

rve

a

corr

elat

ion

be

twee

n•

the

max

imum

for

ce

conc

entr

atio

n•

the

char

ge in

vers

ion

co

ncen

trat

ion

Triv

alen

t ca

tions

Salm

on p

rota

min

e

(sal

min

e)

8 kb

p

DN

A•

Sm

all

ca

tioni

c

prot

ein

(21

argi

nine

s

out

of

32 a

min

o

acid

s) t

hat

re

plac

es

hist

ones

in

sp

erm

ioge

nesi

s

•

Char

ge in

vers

ion

cl

early

ob

serv

ed(s

eeal

soRa

spau

det

al

., PR

L 20

06, f

or15

0 bp

DN

A)

•

Forc

e

decr

ease

s

at

high

pro

tam

ine

co

nc)

•

Rob

ust

up

to

300

mM

Mul

tival

ent

io

ns

can

ch

arge

-inve

rt

DN

A at

low

sal

t

Cond

ensa

tion

of

DN

A un

der

te

nsio

n

occu

rs

via

a di

scre

te, a

ctiv

ated

pr

oces

s

Obs

erva

tions

ar

e qu

alita

tivel

y

cons

iste

nt w

ith

SCL

mec

hani

smc

μ

Tran

sitio

n

stat

e in

volv

es

the

form

atio

n

of a

loop

Biop

olym

ers

87

, 14

1 (2

007)

Phys

. Rev

. Let

t.

98, 0

5810

3 (2

007)

Nat

ure

Phys

ics

3,

641

(20

07)

Conc

lusi

ons

Fund

ing:

Koe

n

Bes

tem

an

Ackn

owle

dgm

ents

Mar

cel Z

even

berg

enN

ynke

Dek

ker

Koe

rt

van

Eijk

150n

m

Susa

nne

Hag

e

(ss-

ds

DN

A co

nstr

ucts

)Ig

or V

ilfan

, U. Z

iese

(T

EM)

I will

disc

uss

the

prob

lem

of h

ow s

tiff,

high

ly c

harg

ed D

NA

can

be

cond

ense

d in

to d

ense

stru

ctur

es b

y m

ultiv

alen

t ion

s. W

e st

udie

d in

real

tim

e th

e co

nden

satio

n of

sin

gle

DN

A m

olec

ules

usi

ng m

agne

tic

twee

zers

and

foun

d th

at c

onde

nsat

ion

occu

rs v

ia d

iscr

ete

nucl

eate

d ev

ents

. By

mea

surin

g th

e in

fluen

ce o

f an

impo

sed

twis

t, w

e sh

owed

that

con

dens

atio

n is

initi

ated

by

the

form

atio

n of

a p

lect

onem

ic

supe

rcoi

l. Th

is d

emon

stra

tes

a st

rong

inte

rpla

y be

twee

n th

e co

nden

satio

n tra

nsiti

on a

nd e

xter

nally

impo

sed

mec

hani

cal c

onst

rain

ts. W

e al

so p

erfo

rmed

ele

ctro

phor

esis

mea

sure

men

ts s

how

ing

that

DN

A c

an b

e ch

arge

-inve

rted

by tr

i-

or q

uadr

ival

ent

ions

at s

uffic

ient

ly lo

w m

onov

alen

t

salt

conc

entra

tion.

The

se re

sults

su

gges

t a d

irect

con

nect

ion

betw

een

char

ge in

vers

ion

and

DN

A c

onde

nsat

ion,

and

are

qua

litat

ivel

y co

nsis

tent

with

the

theo

retic

al p

ropo

sal t

hat b

oth

effe

cts

are

inte

rdep

ende

nt, p

urel

y el

ectro

stat

ic

phen

omen

a.

Cha

rge

inve

rsio

n ac

com

pani

es D

NA

con

dens

atio

n by

mul

tival

ent i

ons