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Fluorescence Correlation Spectroscopy technique and its applications to DNA
dynamics
Oleg Krichevsky
Ben-Gurion University in the Negev
Outline
• Tutorial on FCS1) The basic idea of the technique
2) Instrumentation
3) Standard applications:
- measurements of concentrations
- diffusion kinetics
- binding assay
• DNA dynamics
1) DNA hairpin opening-closing kinetics o (k-)
c (k+)
2) DNA “breathing”
3) Polymer conformational dynamics- flexible polymers (ssDNA)- semi-flexible polymers (dsDNA) - semi-rigid polymers (F-actin)
Tools:
• specific fluorescence labeling:attaching fluorophores at precise positions
• Fluorescence Correlation Spectroscopy (FCS)
Fluorescence Correlation Spectroscopy (FCS)Magde, Elson & Webb (1972); Rigler et al (1993)
10-2
100
102
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
G
t (ms)2
02
2
)()0()(
)()(11
)()()(
I
tIItG
tdttItITI
I
ttItItG
III
T
t
0 2 4 6 8 10 12 14 16 18 205600
5800
6000
6200
6400
6600
6800
7000
7200
7400
I
I
t
10-2
100
102
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
G
(ms) t
I
I
t
General Properties of FCSCorrelation Function
2
)()()(
I
ttItItG t
NN
N
N
N
I
tItItG t
1
)()()0(
22
2
2
0)()(
)()()(
2
2
I
ItII
ItItG t
D
wxy2
~
NNqNqI
NqIqNI
zxyxy
zxydiff
diffdiff
zxy
wwcNw
w
D
w
ttNtG
w
z
w
yxr
2232
2
2
2
2
22
4
1
1
1
11)(
22exp0
10-2
10-1
100
101
102
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
G
t (ms)
Rh6G
Correlation functionfor simple diffusion:
laser
Principles of confocal setup
Sampling volume 0.5 fl (Ø 0.45 x 2 m)Incident light power 10 - 50W0.1-300 molecules per sampling volumeon average
Enhancements and variations of the standard setup:
1) Two-color FCS (Schwille et al)2) Two-photon FCS (Berland et al) 3) Scanning FCS (Petersen et al)
References and technical details in G. Bonnet and O.K., Reports on Progress in Physics, 65(2002), 251-297
Standard applications:
zxyxy
zxydiff
diffdiff
wwcNw
w
D
w
ttNtG
2232
2
4
1
1
1
11)(
1) Amplitude of G(t) → concentration of moving molecules
2) Decay → diffusion kinetics (in vitro and in vivo)
3) Binding assay
FCS as a Binding Assay
Few nm
Protein DNA
Few m
+
Fast Diffusion
Slow Diffusion
Methyltransferase + Lambda-DNA
(methyltransferase – courtesy of Albert Jeltsch and Vikas Handa)
In general, for two-component diffusion:
tGII
ItG
II
ItG 22
21
22
12
21
21
1) DNA hairpin opening-closing kinetics o (k-)
c (k+)
withGrégore Altan-BonnetNoel GoddardAlbert LibchaberRockefeller University
t RNA
Diag.H Brezski
DNA hairpin fluctuations:
Molecular beacon designTyagi&Kramer (1996)
5’ - Rh6G – CCCAA – (Xn) – TTGGG – [DABCYL] – 3’ (n=12-30) Signal/background: Io/ Ic ~ 50-100
0
50
100
150
200
250
300
350
0 10 20 30 40 50 60 70
o (k-)
c (k+)
I (kHz)
T (oC)
p T I T Imin
Imax Imin
K T c
o
p T
1 p T
kk
tp
p
ttNtG
co
diffdiff
111
exp1
1
11
11)(
2
FCS on Molecular beacons: two processes – two characteristic time scales
kk
NkNNeNNN
NkNkkt
N
NNN
NkNkt
N
ootkk
ooo
oo
oc
coo
0
motion) (no closedopen
G
t (ms)0
0.1
0.2
0.3
0.4
0.5
0 0.01 0.1 1 10
Correlation function of a molecular beacon:
10-4
10-2
100
102
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
G
HOPE!!!
tp
p
ttNtG
diffdiff
exp1
1
11
11)(
2
structuralfluctuations
diffusion
Control:
GC (t) 1
N
1
1t
diff
GB(t) 1
N
1
1t
diff
11 p
pexp t
o (k-)
c (k+)
o (k-)
c (k+)
Beacon:
Correlation functions of beacon & control
0
0.1
0.2
0.3
0.4
0.5
0 0.01 0.1 1 10
t (ms)
1
1.2
1.4
1.6
1.8
2
2.2
0.01 0.1
Gbeacon
/GcontrolRatio of the correlation functions:
pure conformational kinetics
Gconf A exp t B
0.1
1
0 0.02 0.04 0.06 0.08 0.1
T = 30C
T = 42C
T = 48C
t (ms)
Gconf
Conformational kinetics at different temperatures:
0
50
100
150
200
250
300
350
0 10 20 30 40 50 60 70
1) Melting curves: I(T)
p T I T Imin
Imax Imin
K T p T 1 p T
c
o
2) FCS on beacons:3) FCS on controls:
Gbeacon t Gdiff t Gconf t Gcontrol t Gdiff t
Gconf t Gbeacon
GcontrolA exp( t
) B
1 1
o 1
c
The experimental procedure:
0
0.1
0.2
0.3
0.4
0.5
0 0.01 0.1 1 10
I
T
1
1.2
1.4
1.6
1.8
2
2.2
0.01 0.1
Gbeacon
/Gcontrol
101
102
103
104
3.1 3.2 3.3 3.4 3.5 3.6
o,
c (µ
s)
1000/T (K-1)
o (T
21)
c (T
21)
Characteristic time scales of opening and closing of T21 loop hairpin:
101
102
103
104
105
3.1 3.2 3.3 3.4 3.5 3.6
o,
c (µ
s)
1000/T (K-1)
T12
T16
T21
T30
Different lengths of T-loops:
101
102
103
104
3.1 3.2 3.3 3.4 3.5 3.6
o,
c (µ
s)
1000/T (K-1)
o (T
21)
o (A
21)
c (A
21)
c (T
21)
The loops of equal length but different sequence: T21 vs. A21
Stacking interaction between bases
10
102
103
104
3.1 3.2 3.3 3.4 3.5 3.6
o, c (s
)
1000/T
c (A
8)
o (A
8)
c (A
21)
o (A
21)Opening and closing times
of different poly-A loops
0
5
10
15
20
0 5 10 15 20 25 30 35
Closing enthalpy (kcal/mol) vs. loop length (poly-A)
0.55 kcal/mol/stacked base
10
100
1000
10000
3.1 3.2 3.3 3.4 3.5 3.6
clos
ing
an
d op
enin
g (
s)
1000/T (K-1)
c (loop: A
8CA
12)
c (loop: A
5CA
15)
c (loop: A
10CA
10)
c (loop: A
21)
o
Placing a defect in a
poly-A loop
no defect
PNAS 95, 8602-8606 (1998) Phys. Rev. Letters 85, 2400-2403 (2000)
In some simple situations we have some understanding of the sequence-dependence of hairpin closing kinetics
In a number of other situations we have no undersanding
- poly-C loops- short poly-T loops (below 7 bases(
TTT
T
-G-C-G-G-C-G-G-G- -C-G-C- C- G-C-C-C
G-C-G-C-C-G-C-G-
fluctuation box (AT basepairs)
3'
5'
The experimental construct:
= end-tagging on opposite backbones (DABCYL-Rhodamine 6G)
= internal tagging on opposite basepairs (DABCYL-Rhodamine 6G)
2) DNA “breathing”
0
0.2
0.4
0.6
0.8
1
1.2
0 20 40 60 80 100
Melting curves showing the opening of the "bubble" and of the end regions
open
frac
tion
Temperature (C)
middle labeling
end labeling
G t A exp t B
0,2
0,22
0,24
0,26
0,28
0,3
0,32
0,34
10-5 0,0001 0,001 0,01 0,1 1 10
Relaxation of the breathing modes
G(t)
lag (ms)
18 base pairs AT region
T=40oC
0,2
0,22
0,24
0,26
0,28
0,3
0,32
0,34
10-5 0,0001 0,001 0,01 0,1 1 10
Relaxation of the breathing modes
G(t)
lag(ms)
18 base pairs AT region
T=40oC
G t A exp t B
40s
Phys. Rev. Letters 90, 138101 (2003)
Conformational dynamics ofpolymers in good solvents:
on the model ofdsDNA and ssDNA molecules
lag (ms)
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,01 0,1 1 10 100 1000 104
G(t)
lag (ms)
diffdiff
ttNtG
211
1
0
5
10
15
20
0,01 0,1 1 10 100 1000
Diffusion of dsDNA 6700bp
22
2
2
2
32
132
1
1
xyxy w
tr
w
trN
tG
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,01 0,1 1 10 100 1000 104
G t r2 t
G t c
,0 c
,t
dd
c 2 d 2
c
q ,0 c *
q ,t
q 2dq
c 2 d 2
j
j trtc ,
cq ,0 c
q , t e
iq r j t r j 0
j exp i qxx j t qyy j t qzz j t
j
exp 1
2qx
2 x j2 t q y
2 y j2 t qz
2 zj2 t
j c exp qx
2 qy2 qz
2 r2 t 6
0 exp
2 x2 y2 w xy
2
2z 2
wz2
G t 1
N 12
3
r 2 t w xy
2
1
2
3
r2 t wz
2
Polymer Statistics
Freely Jointed Chain model: Random Walks in Space
Ree
Ree
b
Ree
2 Nb2
Polymer conformational dynamics:
center of mass
polymer end
Dt6The kinetics of monomer random motion:
• double-stranded DNA (dsDNA)• single-stranded DNA (ssDNA)
tr 2
Rouse (1953)Zimm (1956)
t b
tr 2
t
Theory:
b2
2eeR
Zimm1
Rouse 1
ND
ND
G
GtDG6
Zimm
Rouse 32t
t
Rouse theory of Polymer Dynamics:
dr n
dt1F n
Kspring 3kBT
b2
dr n
dt
3kBT
b2
r n1
r n
r n r n 1
f n n 2,..,N 1
b b2
kBT
Basic length scale: b
Basic timescale: Polymer size:
N
b
22
2
1
10
3
2
1cos2
k
NF
X
dt
Xd
nN
kXXr
bkk
k
kk
N
kkn
Rouse modes:
0 10 20 30 40 50 60 70 80 90 100-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
n0 N
N
Tk
N
bD B
bG
2
Mean-square displacement of an end-monomer:
1
122
22 1
146
N
k
t
Gnke
kN
btDtr
21
248
t
TbkB
Center-of-mass internal
Rouse model: connectivity + friction of polymer segments
Exact: 21
22 48
t
Tbkr B
segment a oft coefficienfriction
VFD
equation sEinstein'
friction :segments for
N
TkD
NN
BG
2
12
2
22
2
22
6
666
tTbk
r
bNrN
TkD
tr
bTkt
N
TktDr
B
rr
Br
B
r
Br
r
Rouse model is nice but wrong:
NDG
1
1) Experimental measurements of polymer coil diffusion(dynamic light scattering)
2) Hydrodynamic interactions between polymer segments cannot be neglected
F j
v i
dr n
dt ij
F j
ii 1
6Rij
1
8Rij
1
8b i j
ij N
4b
Diverge with N => cannot be neglected even for distant monomers
Zimm model: Rouse model + hydrodynamic interactions
r n
X 0 2
X k
k1
N 1
coskN
n 1
2
dX kdt
X kk
F k k
3b3
kBT
N
3k
32
100 102 104
100
101
102
103
104
105
t2
3
6DGt
DG 8 6
3 kBT
6b N
kBT
6Reet b
r 2 t b2
Zimm model: Rouse model + hydrodynamic interactions
NR
TkD
ee
BG
1
6
Hydrodynamic shell:
32
23
2
6
666
tTk
rtTk
r
r
TkD
tr
TktDr
BB
Br
Br
r
32
2 2
t
Tkr B
Exact
Zimm model is right
Rouse model is wrong
From polymer coil diffusion measurements:
ttr
ttr
2
322
What about monomer motion?
Zimm
Rouse
Real polymers: limited flexibility
b b - Kuhn length: defines polymer flexibility
b ~ several monomers: flexible polymerb >> monomer size: semi-flexible or stiff polymer
Polymer can be considered as flexible at the length scale > b
N Lb Ree
2 Nb2 Lb
dsDNA: semi-flexible, b=100nm~340bp, dsDNA width d=2nm
ssDNA: flexible, b~1-5nm~2-10bases
22
2
2
2
32
132
1
1
xyxy w
tr
w
trN
tG
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,01 0,1 1 10 100 1000 104
G t r2 t
Results:2400 bp fragment
t (ms)
r2
(m2)
t
t
b
Ree
R2ee
b2
b - Kuhn length ) b=2lp~100nm~340bp(
Ree – end-to-end distance :
Why no Zimm behavior?
2400bp = 7b
small polymer
still small ?t
9400bp = 30 b
still small
r2
t
9400bp = 30 b
6700bp = 20 b
23000bp = 70 b
hmm... t
48000bp = 140 b
t
10-2
10-1
100
101
10-2 10-1 100 101 102
t (ms)
r2 (m)
r 2 48kBTb2
t
12
Interpretation of the friction of cylinder with length b=100nm and diameter d=2nm:
3b ln b d
Why not Zimm-model behavior?dsDNA is semi-flexible, the hydrodynamic interactions are weak
r
TkD B
r 6
2
2
r
TbkD B
r
Korteweg-Helmholtz theorem: when inertia can be neglected, the flow is organized to have minimal viscous losses
Rouse model:
Zimm model:
Rouse regime below:
3b ln b d
dbbrc222 ln
3
16
dbbrc222 ln
3
16
For dsDNA b=100nm, d=2nm: rc
2 b2 18
Rouse regime from b2 (0.01 m2) to 18b2 (0.2 m2) or R2ee
Above r2c: Zimm behavior
23000bp
Best power fit gives power 0.64
0,2
0,3
0,4
0,5
0,6
0,70,80,9
1
20 30 40 50 60 80 100
23100bp
32
2 2
t
Tkr B
Zimm regime:No free parameters,No polymer parameters
dbbrc222 ln
3
16
For flexible polymer:
No Rouse regime, Zimm regime only
b d rc2 b2
10-3
10-2
10-1
100
101
0,01 0,1 1 10 100
2400
6700
23000
Zimm regime
t (ms)
r2
( m2)
32
2 2
t
Tkr B
Single-stranded DNA:
10-3
10-2
10-1
100
101
10-3 10-2 10-1 100 101 102 103
dsDNA 2400dsDNA 6700HWR theory 2400HWR theory 6700Rouse regime
Theory for semi-flexible polymers: parameters b,d.Harnau, Winkler, Reineker (1996)
Conclusions:
10-3
10-2
10-1
100
101
0,01 0,1 1 10 100t (ms)
r2
( m2)
Phys. Rev. Lett. 92, 048303 (2004)
1 (First measurements of individual monomer dynamics within large polymer coil
2 (There is a large range of dsDNA dynamics unaffected by hydrodynamic interactions (Rouse model)
3 (The dynamics of ssDNA is dominated by hydrodynamic interactions (Zimm theory)
Thanks to my group:
Roman ShustermanSergey AlonTatiana GavrinyovCarmit Gabay
And to friends and collaborators
Grégoire Altan-BonnetNoel GoddardAlbert LibchaberDidier Chatenay Rony GranekDavid MukamelAlbert JeltschVikas HandaDina RavehAnna Bakhrat