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