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 technique2) Instrumentation3) 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

IttItI

tG

III

T

t

0 2 4 6 8 10 12 14 16 18 205600

5800

6000

6200

6400

6600

6800

7000

7200

7400

II

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

)()()(

IttItI

tG t

NN

NN

NI

tItItG t

1

)()()0(

22

2

2

0)()(

)()()(

2

2

IItI

IItI

tG t

D

wxy2

~

NNqNqINqIqNI

zxyxy

zxydiff

diffdiff

zxy

wwcNww

Dw

ttNtG

wz

wyxr

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

wwcNww

Dw

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

ItGII

ItG 2221

22

1221

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

pttN

tG

co

diffdiff

111

exp1111

11)(

2

FCS on Molecular beacons: two processes – two characteristic time scales

kkNkNNeNNN

NkNkkt

NNNN

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

pttN

tG

diffdiff

exp1111

11)(

2

structuralfluctuations

diffusion

Control:

GC (t) 1N

1

1t

diff

GB(t) 1N

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 (

µs)

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 (

µs)

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 (

µs)

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 (A21)Opening and closing timesof 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 a

nd 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

321

321

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 ,

c q ,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 12

qx2 x j

2 t q y2 y j

2 t qz2 zj

2 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 123

r 2 t w xy

2

1

23

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

NDND

G

GtDG6

Zimm

Rouse 32tt

Rouse theory of Polymer Dynamics:

dr n

dt1F n

Kspring 3kBT

b2

dr n

dt

3kBTb2

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

21cos2

kNFX

dtXd

nNkXXr

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

NTk

NbD B

bG

2

Mean-square displacement of an end-monomer:

1

122

22 1146

N

k

t

Gnke

kNbtDtr

21

248

tTbkB

Center-of-mass internal

Rouse model: connectivity + friction of polymer segments

Exact: 21

22 48

tTbkr B

segment a oft coefficienfriction

VFD

equation sEinstein'

friction :segments for

NTkD

NN

BG

21

22

22

2

22

6

666

tTbkr

bNrNTkD

trbTkt

NTktDr

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

18Rij

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

cos kN

n 12

dX kdt

X kk

F k k

3b3

kBTN

3k

32

100 102 104

100

101

102

103

104

105

t2

3

6DGt

DG 8 63

kBT6b N

kBT

6Reet b

r 2 t b2

Zimm model: Rouse model + hydrodynamic interactions

NRTkD

ee

BG

16

Hydrodynamic shell:

32

23

2

6

666

tTkrtTkr

rTkD

tr

TktDr

BB

Br

Br

r

32

2 2

tTkr 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

321

321

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

12Interpretation 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

rTkD B

r 6

2

2

rTbkD 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

316

dbbrc222 ln

316

For dsDNA b=100nm, d=2nm: rc2 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

0,60,70,80,9

1

20 30 40 50 60 80 100

23100bp

32

2 2

tTkr B

Zimm regime:No free parameters,No polymer parameters

dbbrc222 ln

316

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

2400670023000Zimm regime

t (ms)

r2

( m2)

32

2 2

tTkr 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