Physico-Chemical Methods in Systems Biology
Monday,
Monday July 06
Tuesday, July 07
Fluorescence dynamics methods
to st
study
d diffusion
diff sion and binding of
biomolecules in vivo
Malte Wachsmuth
Cell Biology & Biophysics Unit, EMBL
[email protected]
www.embl.de/~wachsmut/downloads
MW 2015/07/06
Molecular mobilities and interactions on the cellular level
Vital processes on a cellular level rely on
• transport and diffusion
• establishment and maintenance of
concentration gradients
• distribution, accessibility, and occupation of
specific binding sites
• specific interactions of molecules
Based on Spiller et al., Nature 465, 2010
The measurement of molecular mobilities
and dynamics yields quantitatively
• biochemical parameters (dissociation
constant degree of binding/multimerization,
constant,
binding/multimerization
ion concentration, pH)
• biophysical properties (diffusion coefficient,
viscosity connectivity of cellular
viscosity,
compartments, elastic parameters)
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Morphogen gradients during development
Gurdon & Bourillot, Nature 413 (2001)
MW 2015/07/06
Overview
I. Dynamic aspects of fluorescence
II. Random walks and diffusion
III. Fluorescence correlation spectroscopy (FCS)
IV. Fluorescence recovery after photobleaching (FRAP)
V Fluorescence lifetime imaging microscopy (FLIM)
V.
VI. Experimental
p
examples
p
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The first observations of fluorescence
or: how drinking
g helped
p
• In 1845,
1845 Sir John Frederick William Herschel observed blue light glowing at
the surface of a solution of quinine in water (vulgo Tonic water) upon
illumination with sunlight that became stronger when adding ethanole
(vulgo Gin Tonic).
Herschel, J.F.W., Phil. Trans. R. Soc. London (1845) 133:143–145
• In 1852, Sir George Gabriel Stokes repeated this experiment using filters:
from the sunlight, the UV region was selected employing the blue glass of
a church window that shone on a bottle of quinine in solution. The emitted
light was filtered with a yellow glass of wine (sic).
Stokes, G.G., Phil. Trans. R. Soc. London (1852) 142:463
142:463–562
562
Lakowicz, J. R.: Principles of Fluorescence Spectroscopy
(2nd ed.). Kluwer Academic, New York (1999)
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Fluorescence in cell biology
Olympus Microscopy Resource Center
http://www.olympusmicro.com
Molecular Probes FluoCells
Blue:
Red:
Green:
DAPI (nucleus)
Mitotracker Red (mitochondria)
Alexa488 (actin)
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Fluorescence microscopy in cell biology
Robert Hooke, ~1665
~10 µm
commercial light
microsocpe, ~1880
~1 µm
commercial fluorescence
microscope, ~1998
~200 nm
Over the last 20 years:
significant improvements of the components of modern
fl
fluorescence
microscopes:
• objectives, filters
• detectors
superresolution fluorescence
microscopes, ~2010
<100 nm
• lasers
• stepper motors, galvanometer scanners
• electronics, computers
• concepts and ideas
MW 2015/07/06
What is fluorescence
Classification:
Cl
ifi ti
Luminescence is the capability of a
substance (solid, molecule, atom, ...) to
emit a photon following the decay of an
electronically excited state independent of
the nature of the excitation process
Excitation by
Other processes
Photon absorption
Photoluminescence
Decay from
Singlet state
Fluorescence
Triplet state
Phosphorescence
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What is a fluorophore
• Certain molecules generally being or
containing polyaromatic hydrocarbons or
heterocycles are called fluorophores or
fluorescent dyes
• They undergo fluorescence that is
simplistically defined as
high energy light in – low energy light out
• For fluorescein or GFP:
blue light
g in – g
green light
g out
modifiend from
Brejc et al.,
PNAS (1997);
C
Creemers
et al.,
l
Nat. Struct. Biol. (1999)
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The steps of the fluorescence process
In 1953, Alexander Jablonski described fluorescence for the first time using
a diagram of the different energy levels involved in the fluorescence process
emiission
~1
10-9 s
S1,2
relax
xation
~10-12 s
electronic
states
{
abso
orption/
excitation
~1
10-15 s
ene
ergy
vibrational
ib ti
l llevels
l off
the electronic states
Jablonski diagram
pictorially:
S0
singlet
i l states
Olympus Microscopy Resource Center
http://www.olympusmicro.com
MW 2015/07/06
Stokes’ shift and the Franck-Condon principle
• Different electronic states have different
configurations of the molecule as
described with a configuration coordinate
Franck-Condon diagram
• The vibrational levels of each electronic
state stem from the effective potential
around the stable configuration (LenardJones, harmonic approximation)
• Excitation takes place from the S0 ground
level to an S1 higher level with good
overlap of wave functions
e
energy
• From a Boltzmann occupation
distribution: mainly the ground states are
occupied in thermal equilibrium
S1
S0
• Th
The actuall transition
ii
iis so ffast that
h no
rearrangement of the molecule is possible
• Thermal equilibration with the
environment: relaxation to ground level
• Excitation takes place from the S1 ground
level to an S0 higher
g
level with g
good
overlap of wave functions
configuration coordinate
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Stokes’ shift and the Franck-Condon principle
Franck-Condon diagram
• That is why Stokes could observe in his
bottle yellow light upon illumination with
blue light!
S1
• But: we do not have a single wavelength
(colour) for both excitation and emission
• To some extent also the other vibrational
levels can be occupied and transitions can
take place between various combinations
of levels...
e
energy
• That is why it is called Stokes’ shift, a
very fundamental and useful property of
fluorophores allowing to separate
excitation and emission light spectrally
S0
• ... resulting in more or less broad
absorption and emission spectra
configuration coordinate
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Absorption and emission spectra and the mirror rule
• The distribution of
vibrational levels
generally determines
the absorption and
emission spectra
• For various
fluorophores, the
mirror rule applies:
the very similar
vibrational levels of
different electronic
states result in very
similar though
mirrored absorption
and emission spectra
S1
absorption
spectrum
S0
emission
spectrum
• The spectra are specific properties of the fluorophores that allow to identify them
• They can be measured with fluorescence spectrometers
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fluoresce
ence yield [a
a.u.]
Spectral properties of fluorophores
100
TMR
80
60
40
20
0
450
500
550
600
wavelength [nm]
650
700
taken from Invitrogen/
Molecular Probes website
http://www.probes.com
modifiend from
Patterson et al.,
J Cell Sci.
J.
Sci (2001)
Shaner et al., Nat. Meth. (2008)
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Labelling of different structures with different fluorophores
Fluorophores emit across the whole
spectrum
340-400 nm
Near Ultraviolet (UV, invisible)
400-430 nm
Violet
430-500 nm
Blue
500-560 nm
Green
560-620 nm
Yellow to Orange
620-700 nm
Red
>700
700 nm
Mole l Probes
Molecular
P obe Fl
FluoCells
oCell
Blue:
Red:
Green:
DAPI (nucleus)
Mitotracker Red (mitochondria)
Alexa488 (actin)
N
Near
IInfrared
f
d (IR,
(IR invisible)
i i ibl )
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Autofluorescent proteins: green fluorescent protein GFP
jellyfish Aequorea victoria (Cnidaria)
bioluminescent organism
Timeline:
1962: Discovery by Shimomura et al., J. Cell. Comp.Physiol. 59, 223
│
1992: Cloning and sequencing of GFP by Prasher, et al., Gene 111, 229
│
1995: Expression of fluorescent protein by Chalfie et al., Science 263, 802
│
thousands of publications...
│
2008 Nobel
2008:
N b l Prize
P i ffor O
Osamu Shimomura,
Shi
M
Martin
ti Ch
Chalfie,
lfi Roger
R
T i
Tsien
│
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Aequorea victoria bioluminescence
Aequorin Emission
Wavelength (nm)
Aequorin: 22 kDa Ca2+-sensitive protein with coelenterazine cofactor as luminophore
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Aequorea victoria bioluminescence
Aequorin Emission
Detected emission
Wavelength (nm)
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Aequorea victoria bioluminescence
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The structure of GFP
MW ~ 27 kDa
238 amino acids
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The chromophore of GFP
Tyr66
Gly67
2
1
Ser65
p-hydroxybenzylideneimidazolinone
1) Cyclization of Ser-Tyr-Gly
2) Oxidation
O d
off Tyr66
66
Conjugation of Tyr phenol group with the imidazolinone
No co-factor for fluorescence required!
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Excitation and emission spectra
400nm
508 nm
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The chromophore and fluorescence process of GFP
• GFP has a complex state diagram
• A is the dominant configuration in wtGFP
 UV excitation, blue emission
• upon illumination with UV and rarely
spontaneously it can switch rapidly
between A* and I*
• the chromophore is protonated
 blue excitation, green emission
• slow non-radiative transition from I* to
B a more stable
B,
bl configuration
fi
i
 blue excitation, green emission
fast
slow or
rare
• pH-dependent transient protonation of
th chromophore
the
h
h
from
f
the
th solvent
l
t
 UV excitation, blue emission
• thus, the (blue excitation, green
emi ion) fluorescence
emission)
fl o e en e of GFP shows
ho
ttwo
o
blinking processes due to chromophore
protonation
modifiend from
Brejc et al.,
PNAS (1997);
C
Creemers
ett al.,
l
Nat. Struct. Biol. (1999)
MW 2015/07/06
Excitation and emission spectra
GFP Excitation
GFP Emission
E i i
Wavelength (nm)
Chalfie et al., Science (1994)
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Mutagenesis provides spectral variants
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Fluorescent proteins from different species
Aequorea victoria
Discosoma spec.
Hydromedusae
Renilla reniformis
Anemonia sulcata
Anthozoa
Lukyanov et al., 2005, Nat Rev. Mol. Biol., 6:885
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Problem: FPs tend to oligomerize
Aequorea GFP (dimer)
Zhang et al., Nature Rev.
Mol. Cell. Biol., 2002
Miyawaki, Nature Rev.
Mol. Cell. Biol., 2011
Discosoma RFP (tetramer)
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Cure: Mutagenesis
Aequorea GFP (dimer)
Monomeric GFP (mGFP)
A206K
Zhang et al., Nature Rev.
Mol. Cell. Biol., 2002
Miyawaki, Nature Rev.
Mol. Cell. Biol., 2011
33 mutations
Discosoma RFP (tetramer)
Monomeric RFP (mRFP)
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Some non-oligomerizing FPs
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Some spectral variants
Shaner et al., Nat. Meth. (2008)
Miyawaki et al., Nat. Cell Biol. (2003)
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Examples of photoactivatable/-switchable FPs
Lukyanov (2005)
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And more to come…
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Chromophore maturation as a timer tool
Tyr66
Gly67
2
1
Ser65
Different maturation of
different fluorescent
proteins rates can be used
to measure protein
degradation and lifetime
Khmelinski et al.,
Nature Biotechnol. (2012)
MW 2015/07/06
The whole fluorescence story
bleaching
1s
~1
bleaching
~1 s
FRET
10-9 s
intersystem
crossing
10-8 s
S0
singlet
in
nt. conversion,
quenching
10-99 s
fluoresc
cence
~10--9 s
relaxa
ation
~10-12 s
absorp
ption
/excita
ation
-1
~10 15 s
S1
T
phosphorescence,
nonradiative
transition
10-6 s
triplet
MW 2015/07/06
States and rates
q
p
Rate equations
for the occupation
of states:
For each state, the differential equation for the
p
occupation
p
can be stated:
respective
S 0
  I  k12 S 0  k 21S1  k31T1
t
S1
 I  k12 S 0  k 21  k 23 S1
t
T1
 k 23 S1  k31T1
t
Typical
yp ca rates
a es for
o typical
yp ca fluorophores
uo op o es are:
a e
k12  0.004 cm 2 J 1s 1
k 21  4 108 s 1
k 23  2.5 106 s 1
k31  2 105 s 1
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Fluorescence lifetime
p
pp
Simplified
approach:
Only excitation of singlet states considered:
S 0
  I  k12 S 0  k 21S1
t
S1
 I  k12 S 0  k 21S1
t
After excitation to S1:
S1 0  1, S 0 0   0
S1
 k 21S1 , F t   k 21S1 t 
t
S1 t   exp k 21t , F t   F0 exp k 21t 
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ad
dditional process
ses
knr
emis
ssion
kr
excittation
S1
S0
 natt 
 red
1
kr
1
kr

  nat
  nat
k r  k nr
k r  k nr
fluores
scence siignal
Fluorescence lifetime
exponential decay
red
nat
 t
exp  
 
time after excitation
fluorescence lifetime:
• ave. time betw. excitation and emission
• characteristic property of dyes, ~ns
• depends on environment (ions,
(ions pH
pH, …))
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How to measure the fluorescence lifetime (time domain)
t
• excitation with a pulsed laser
• measuring the time between laser
pulse
l and
d fluorescence
fl
photon
h t
• calculation of a histogram
• Fitting exponential decays to
histograms
N
t
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Intersystem crossing and occupation of non-fluorescent states
q
p
Rate equations
for the occupation
of states:
For each state, the differential equation for the
p
occupation
p
can be stated:
respective
S 0
  I  k12 S 0  k 21S1  k31T1
t
S1
 I  k12 S 0  k 21  k 23 S1
t
T1
 k 23 S1  k31T1
t
Typical
yp ca rates
a es for
o typical
yp ca fluorophores
uo op o es are:
a e
k12  0.004 cm 2 J 1s 1
k 21  4 108 s 1
k 23  2.5 106 s 1
k31  2 105 s 1
MW 2015/07/06
Intersystem crossing and occupation of non-fluorescent states
q
p
Rate equations
for the occupation
of states:
A solution where excitation is turned on at t = 0:
F t   S1 t   1 
1 
1
1
exp 1t  
exp  21t 
1  1
1  1
k12 k 23
k12 k 23  k12 k31  k 21k31
1  k12  k 21
1  k31  k 23
k12
k12  k 21
F(t)
t [µs]
MW 2015/07/06
The chromophore and fluorescence process of GFP
• GFP has a complex state diagram
• A is the dominant configuration in wtGFP
 UV excitation, blue emission
• upon illumination with UV and rarely
spontaneously it can switch rapidly
between A* and I*
• the chromophore is protonated
 blue excitation, green emission
• slow non-radiative transition from I* to
B a more stable
B,
bl configuration
fi
i
 blue excitation, green emission
fast
slow or
rare
• pH-dependent transient protonation of
th chromophore
the
h
h
from
f
the
th solvent
l
t
 UV excitation, blue emission
• thus, the (blue excitation, green
emi ion) fluorescence
emission)
fl o e en e of GFP shows
ho
ttwo
o
blinking processes due to chromophore
protonation
modifiend from
Brejc et al.,
PNAS (1997);
C
Creemers
ett al.,
l
Nat. Struct. Biol. (1999)
MW 2015/07/06
Fluorescence photobleaching
q
p
Rate equations
for the occupation
of states:
For each state, the differential equation for the
p
occupation
p
can be stated:
respective
S 0
  I  k12 S 0  k 21S1  k31T1
t
S1
 I  k12 S 0  k 21  k 23 S1
t
T1
 k 23 S1  k31T1
t
Typical
yp ca rates
a es for
o typical
yp ca fluorophores
uo op o es are:
a e
k12  0.004 cm 2 J 1s 1
k 21  4 108 s 1
k 23  2.5 106 s 1
k31  2 105 s 1
MW 2015/07/06
Overview
I. Dynamic aspects of fluorescence
II. Random walks and diffusion
III. Fluorescence correlation spectroscopy (FCS)
IV. Fluorescence recovery after photobleaching (FRAP)
V Fluorescence lifetime imaging microscopy (FLIM)
V.
VI. Experimental
p
examples
p
MW 2015/07/06
Diffusion on a microscopic scale
6000
MS
SD [m2]
5000
6D
4000
3000
4D
2000
2D
1000
0
0
2
4
6
8
10
time [sec]
simulated random walks of
106 steps on a 15001500
MSD measurement:
mean square displacement
for 1D, 2D, and 3D diffusion
= t
= 4t
MW 2015/07/06
The random walk of a particle
Freely and randomly moving particle:
Consider a particle/molecule that undergoes randomly
oriented jumps of length b for every time step t. Each jump
is caused by collisions with solvent or gas molecules which
transfer a random force on the particle such that the
directional information is lost from one jump to the next. The
direction of each jump is the vector ui. After N jumps and the
time t = N t, the travelled vector is
N
R   ui ,
i 1
u i  b.
However, this is not a good measure to characterise a
polymer Instead
polymer.
Instead, the mean squared displacement
is used:
MSD  R
2
 N 
   ui 
 i 1 
2
N
t
  u i2   u i u j  b 2
t
i 1
i  j 
0
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The ideal polymer chain
Freely jointed/Gaussian chain:
Consider N stiff sticks of length b that form a linear chain.
The directional information is lost from one stick to the next.
The direction of each stick is the vector ui. Then the end-toend to
end vector is
N
R   ui ,
i 1
u i  b.
However, this is not a good measure to characterise a
polymer Instead
polymer.
Instead, the mean squared end-to-end
end to end distance
is used:
R
2
 N 
   ui 
 i 1 
2
N
  u i2   u i u j  Nb 2  Lb
i 1
i  j 
0
Here, b is the monomer length and L the overall contour
Here
length.
MW 2015/07/06
The random walk of a particle
Freely and randomly moving particle:
Consider a particle/molecule that undergoes randomly
oriented jumps of length b for every time step t. Each jump
is caused by collisions with solvent or gas molecules which
transfer a random force on the particle such that the
directional information is lost from one jump to the next. The
direction of each jump is the vector ui. After N jumps and the
time t = N t, the travelled vector is
N
R   ui ,
u i  b.
i 1
However, this is not a good measure to characterise a
polymer Instead
polymer.
Instead, the mean squared displacement
is used:
MSD  R
2
 N 
   ui 
 i 1 
2
N
t
  u i2   u i u j  b 2  t
t
i 1
i  j 
0
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Diffusion on a microscopic scale
6000
MS
SD [m2]
5000
6D
4000
3000
4D
2000
2D
1000
0
0
2
4
6
8
10
time [sec]
simulated random walks of
106 steps on a 15001500
MSD measurement:
mean square displacement
for 1D, 2D, and 3D diffusion
= t
= 4t
MW 2015/07/06
Diffusion on a macroscopic scale
simulated FRAP experiment: 3 x 10 µm2 strip bleached into 2D fluorescent layer
movements of single molecules equilibrate the distribution
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Diffusion on a macroscopic scale
c
Fick’s
i k’ 1stt law
l
off diffusion
diff i
j  x, t    D
j
c x, t 
x
x
the law of mass conservation
 Fick’s
2nd
law of diffusion
c x, t 
j  x, t 

t
x
j
j
c x, t 
 2 c  x, t 
D
t
x 2
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Diffusion on a macroscopic scale
c
j
Fick’s
i k’ 1stt law
l
off diffusion
diff i
jr, t    Dcr, t 
x
the law of mass conservation
cr, t 
 jr, t 
t
 Fick’s 2nd law of diffusion
cr, t 
 D 2 cr, t 
t
j
j
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Diffusion on a microscopic scale
cr, t 
 D 2 cr, t 
t
A solution for Fick’s 2nd law of diffusion
for a molecule that starts diffusing at r0:
0.30
1 sec
5 sec
9 sec
13 sec
17 sec
cr,0   r  r0 
cr, t   4Dt 
d 2
 r  r0  
exp 
  PD r, t r0 , t 
4
Dt


2
conce
entration
0.25
0.20
0.15
0.10
0.05
0.00
30
40
50
60
70
spatial coordinate
MW 2015/07/06
Diffusion on a microscopic scale
0.30
1 sec
5 sec
9 sec
13 sec
17 sec
This solution allows to derive the mean
squared displacement MSD:
MSD  r  r0 
2
  d 3 r r  r0  PD r, t r0 , t 
2
 2dDt
concenttration
0.25
0 25
0.20
0.15
0 15
0.10
0.05
0.00
30
Here, d is the dimensionality of the system
(1D, 2D, 3D) and D the diffusion
coefficient of the molecules studied.
40
50
60
70
spatial coordinate
6000
MSD [m2]
5000
6D
4000
3000
4D
2000
2D
1000
0
mean square displacement
for 1D, 2D, and 3D diffusion
0
2
4
6
time [sec]
8
10
MW 2015/07/06
Einstein-Smoluchowski relation for the diffusion coefficient
Viscosity and friction force:
Consider two parallel plates of area A at a distance d in a liquid. One plate is fixed, the
other one is dragged through the liquid parallel to the other one. Then, a counteracting
f
force
is transmitted
d via the
h solvent
l
with
h the
h following
f ll
properties:
Ffriction  A
v
1 d
Av
d
Av
v

 A
d
y

Ffriction
The proportionality factor η is called (dynamic) viscosity.
MW 2015/07/06
Einstein-Smoluchowski relation for the diffusion coefficient
Viscosity and friction force for a sphere:
Consider a sphere of radius R that is dragged through a liquid. The friction force is
given by the effective area of the sphere and the velocity gradient. The velocity of
solvent
l
molecules
l
l d
decays over a d
distance off approximately
l R. Thus,
h
we obtain
b
Ffriction   v
4R 2
 
v
R
6R 2
 
v
R
 6Rv
  6R
v
Ffriction = -v
∂v/∂y
For the zero order relaxation mode of a polymer, we could show
D
k BT

D
k BT
6R
which is the so-called Einstein-Smoluchowski relation for the diffusion coefficient
MW 2015/07/06
Different modes of diffusion
impact of physical properties and topology
trajectory
free diffusion, free random walk
MSD = 6Dt, linear in time
MSD
D
free
anomalous
l
diff
diffusion,
i
obstructed
b t t d random
d
walk
lk

MSD = t , 0 <  < 1, “square root” curve
anomalous
confined diffusion, constrained random walk
MSD = t,  « 1, runs into a plateau
confined/
moving corrall
time
time
temperature
diffusion coefficient
Wachsmuth et al.,
Biochim. Biophys. Acta
(2008)
D
viscosity
kBT
6Rh
h d d
hydrodynamic
i radius
di
MW 2015/07/06
Mobility = diffusion + binding
impact of biological interactions
complex formation can result in:
• reduced real diffusion coefficient
1
1
D
,   1

MW
3
• reduced apparent diffusion coefficient

k 
Dapp  Dreal 1  on 
koff 

• transient and long-term immobilization
MW 2015/07/06
Overview
I. Dynamic aspects of fluorescence
II. Random walks and diffusion
III. Fluorescence correlation spectroscopy (FCS)
IV. Fluorescence recovery after photobleaching (FRAP)
V Fluorescence lifetime imaging microscopy (FLIM)
V.
VI. Experimental
p
examples
p
MW 2015/07/06
Confocal fluorescence correlation spectroscopy (FCS)
objective lens
laser
filters
dic
chroic
mirrors
Single color FCS:
• concentrations c of
fluorescent molecules
• properties of diffusion/
transport processes
detectors
dic
chroic
mirror
m
pinhole
• diffusion coefficients D
G()
Dual-color FCCS:
• bimolecular interaction
properties
• kinetic rates kon, koff
1/N  1/c
• dissociation constants KD
log 
corr  1/D
MW 2015/07/06
FCS – counting single molecules
Diffusion induces
fluctuations of the
number of
molecules
N=3
N=4
N=2
<N> = 3
I(t)
<I>
This results in
fluctuations of the
fluorescence signal
t
MW 2015/07/06
FCS – autocorrelation analysis
I(t)
t
0
G()
GO    
I  t  I  t   
I t 
2
l
log

MW 2015/07/06
FCS – autocorrelation analysis
I(t)
t
0
G()
GO    
I  t  I  t   
I t 
2
l
log

MW 2015/07/06
FCS – autocorrelation analysis
I(t)
t
0
G()
GO    
I  t  I  t   
I t 
2
l
log

MW 2015/07/06
FCS – autocorrelation analysis
I(t)
t
0
G()
GO    
I  t  I  t   
I t 
2
l
log

MW 2015/07/06
FCS – autocorrelation analysis
G()
1/N  1/c
log 
corr  1/D
Fitting the autocorrelation function to appropriate model functions results in
• properties of the diffusion process
• the concentration
of several species with different hydrodynamic properties
MW 2015/07/06
Mobility = diffusion + binding
impact of biological interactions
complex formation can result in:
• reduced real diffusion coefficient
1
1
D
,   1

MW
3
• reduced apparent diffusion coefficient

k 
Dapp  Dreal 1  on 
koff 

• transient and long-term immobilization
MW 2015/07/06
Different species in the autocorrelation function
+


kon
koff
I(t)
I(t)
G(()
t
t
log 
Properties of ligand-receptor interactions:
dissociation constants, reaction rates, concentrations
MW 2015/07/06
FCCS – fluorescence cross correlation spectroscopy
kas
kdis
3 Enzyme
1
3.
1.
Both
Substrate
molecules
labelled
labelled
Significant
→change
Crosschange
correlation
of diffusion
2
2.
labelled
→→Small
of diffusion
time time
MW 2015/07/06
FCCS – fluorescence cross correlation spectroscopy
Extended
E t d d concept:
t
• labeling of potential binding partners with spectrally different fluorophores
• looking
g for correlations between the corresponding
p
g signals
g
I(t)
G(()
no correlation
t
log 


kas
kdis
I(t)
G()
t
correlation
log 
MW 2015/07/06
FCCS – model application


kon
+
koff
G()
log 
MW 2015/07/06
FCCS – model application


kon
+
koff
G()
log 
MW 2015/07/06
FCCS – model application


kon
+
koff
G()
log 
MW 2015/07/06
FCS – theoretical approach
Properties of the
optical system
Properties of the
diffusion process

I ((r)) = ...
Analytical
autocorrelation
function 
concentration,
t ti
brightness, diffusion
properties of up to 3
species
=
c (r,t) = ...
G()
log 
MW 2015/07/06
FCS – theoretical approach
Properties of the
optical system
I ((r)) = ...
assuming that the product of the illumination PSF and the detection PSF can be
approximated as a 3D Gaussian, giving the
detection efficieny
 x2  y 2
z2 
 k  r   exp  2
2 2 
2
w
z0 
0

MW 2015/07/06
FCS – theoretical approach
Properties of the
diffusion process
c (r,t) = ...
solving the diffusion equation for different cases:
1D, 2D, 3D diffusion; anomalous/obstructed diffusion; directed motion;
confined diffusion; diffusion and binding; intramolecular fluctuations;
as an example:
Green‘ss function for free 3D diffusion
Green
P  r1 , r2 ,     4D 
3 2
  r2  r1 2 
exp  



D

4


MW 2015/07/06
Correlation function for free diffusion in 3D
 x2  y2
z2 
 k  r   exp  2
2 2 
2
w
z0 
0

detection efficieny
c  r, t 
 D 2c  r, t 
t
Fick‘s diffusion equation
c  r,00     r  r1 
boundary condition
P  r1 , r2 ,     4D 
Green‘s function for free 3D diffusion
Gkl
  r2  r1 2 
exp  



4
D



d r d r  r  P r ,r ,   r 
    
 d r  r   d r  r 
3
definition of the correlation function
3 2
3
l
2

1  
  
1 
 1  2

 diff    diff 
1 2
1
2
k
1
3
correlation
co
e at o function
u ct o
diffusion time, concentration,
focal volume, structure
parameter, focus radius
diff
2
3
k
1
Gkl    
cVeff
1
l
1
w02
z0
wk2  wl2
32 2
2

, Veff   w0 z0 ,   , w0 
4D
w0
2
MW 2015/07/06
Different modes of diffusion as seen with FCS
impact of physical properties and topology
free diffusion
normal ACF
anomalous
l
diff
diffusion
i
ACF “smeared out”
confined
“sharper decay” of ACF
free:
in solution
solution, in dilute cellular compartments
compartments, in homogenous
membranes
anomalous:
nuclear proteins/complexes, Golgi-based proteins,
in the plasma membrane
confined:
inside cellular and artificial vesicles, chromatin-embedded
MW 2015/07/06
Different modes of diffusion
impact of physical properties and topology
trajectory
free diffusion, free random walk
MSD = 6Dt, linear in time
MSD
D
free
anomalous
l
diff
diffusion,
i
obstructed
b t t d random
d
walk
lk

MSD = t , 0 <  < 1, “square root” curve
anomalous
confined diffusion, constrained random walk
MSD = t,  « 1, runs into a plateau
confined/
moving corrall
time
time
temperature
diffusion coefficient
Wachsmuth et al.,
Biochim. Biophys. Acta
(2008)
D
viscosity
kBT
6Rh
h d d
hydrodynamic
i radius
di
MW 2015/07/06
Different modes of diffusion as seen with FCS
impact of physical properties and topology
free diffusion
normal ACF
anomalous
l
diff
diffusion
i
ACF “smeared out”
confined
“sharper decay” of ACF

1     
1 
Gkl  
 


cVeff
  Diff  
1

1  1
 2

   

 

 Diff  

1 2
MW 2015/07/06
Diffusion in different dimensions
membrane
fraction
soluble
fraction
membrane
fraction
soluble
fraction
MW 2015/07/06
Correlation function for free diffusion in 3D
 x2  y2
z2 
 k  r   exp  2
2 2 
2
w
z0 
0

detection efficieny
c  r, t 
 D 2c  r, t 
t
Fick‘s diffusion equation
c  r,0
0     r  r1 
boundary condition
P  r1 , r2 ,     4D 
Green‘s function for free 3D diffusion
Gkl
  r2  r1 2 
exp  



D

4


d r d r  r  P r ,r ,   r 
    
 d r  r   d r  r 
3
definition of the correlation function
3 2
3
1
2
l
2

1  
  
1 
 1  2

 diff    diff 
1 2
k
1
3
correlation
co
e at o function
u ct o
diffusion time, concentration,
focal volume, structure
parameter, focus radius
diff
2
3
k
1
Gkl    
cVeff
1
l
1
w02
z0
wk2  wl2
32 2
2

, Veff   w0 z0 ,   , w0 
4D
w0
2
MW 2015/07/06
Different species and nonfluorescent states
If the sample contains more than one distinct species, the resulting CF is a
sum off normalized
li d single
i l species
i CFs
CF weighted
i h d with
i h the
h relative
l i
concentrations
i
and the square of the quantum yields at the wavelengths used
1
G   
N tot
 c  G  
c 
s
2
s
s
s
s
nr
s
S1
s
Assuming that the fluorophore has emitted a photon
at t=0 and then solving the rate equations for the three
state system results in an additional factor for the CF
1   trip exp     trip 
T
nr
S0
MW 2015/07/06
FCS/FCCS applications
Binding
interactions
Chemical
kinetics
Sparse
molecule
l
l
detection
FCS
FCCS
Intramolecular
dynamics
in vivo
o
in vvitro
Cell
structure
t
t
dynamics
Membrane
dynamics
Diffusion
Molecular
concentration
MW 2015/07/06
Setting up an FCS experiment in living cells
Fluorophores
Fluorescent proteins
• all constructs used for imaging can be used for FCS... in principle
• blinking/flickering and photobleaching with different rates
Synthetic dyes
• in vitro labelling of target molecules
• introduction of labelled molecules into cells
Quantum dots
• very
y bright
g
• complex and environment-dependent photophysical properties: complex
blinking/flickering, changes of lifetime
• relatively large
Avoid photobleaching!
MW 2015/07/06
Confocal fluorescence correlation spectroscopy (FCS)
objective lens
laser
filters
dic
chroic
mirrors
Single color FCS:
• concentrations c of
fluorescent molecules
• properties of diffusion/
transport processes
detectors
dic
chroic
mirror
m
pinhole
• diffusion coefficients D
G()
Dual-color FCCS:
• bimolecular interaction
properties
• kinetic rates kon, koff
1/N  1/c
• dissociation constants KD
log 
corr  1/D
MW 2015/07/06
Setting up an FCS experiment in living cells
Concentrations and expression levels
• Concentration range accessible with FCS: 1 nM – 1 M
• Choose cells/clones that appear “dim”
• Photobleaching to reduce concentration of labelled molecules
• Coexistence of endogenous/non-labelled proteins: limiting especially for FCCS
experiments
strategies: genome editing techniques (CRISPR/Cas9, ...), RNAi knockout, ...
HeLa cells expressing
p
gp
pure EGFP which is expected
p
to be freely
y mobile
~11 m
cellll ttoo b
bright!
i ht!
same image with
5fold increased
values (offline)
FCS measurementt spott
MW 2015/07/06
Diffusion of EGFP in HeLa cells
0.025
autocorrelation function of free EYFP in
HeLa cell nucleus:
0.020
• ~45 molecules in the focus,
concentration
t ti off ~60
60 nM
M for
f
focal size of 0.15 fl
G()
0.015
0.010
0.005
0.000
0.01
0.1
1
10
100
• diffusion correlation time
~500 
sec, i.e., diffusion
coefficient of ~22 m2/sec,
i.e., viscosity ~4fold higher
than in water
lag time  [ms]
0.0
0
0 sec
0.1 sec
0.2 sec
0.3 sec
0.4 sec
MW 2015/07/06
Blinking of EGFP in HeLa cells
Two p
protonation/deprotonation
p
p
paths:
• result in blinking/flickering/intermittence
• one is pH-dependent
• time scale comparable diffusion
MW 2015/07/06
Overview
I. Dynamic aspects of fluorescence
II. Random walks and diffusion
III. Fluorescence correlation spectroscopy (FCS)
IV. Fluorescence recovery after photobleaching (FRAP)
V Fluorescence lifetime imaging microscopy (FLIM)
V.
VI. Experimental
p
examples
p
MW 2015/07/06
Confocal fluorescence excitation and detection
objective lens
filters
dic
chroic
mirrors
laser
dic
chroic
mirror
m
pinhole
detectors
• confocal/observation volume confined in 3D
• rater-scanning and synchronized detection:
image formation in the confocal laser scanning microscope
• flexible targeting of every point in the field of view
MW 2015/07/06
Fluorescence recovery after photobleaching (FRAP)
Re lt of FRAP experiments:
Results
e e i e t
• properties of diffusion/transport
processes
• diffusion coefficients D
• properties of interactions
• association
association, dissociation rates
kon, koff
• relative concentrations of
different fractions
MW 2015/07/06
Fluorescence recovery after photobleaching (FRAP)
Mueller et al., Curr. Op. Cell. Biol. (2010)
Redistribution of molecules and recovery
y of the fluorescence signal:
g
• After the bleach step, bleached molecules leave the bleach region and fluorescent ones
enter it owing to diffusion
• Bleached molecules bound to immobile binding sites are released to join the mobile
pool
• The binding sites can be re
re-occupied
occupied by mobile fluorescent molecules
• This redistribution due to exchange of both bound and mobile bleached molecules by
fluorescent ones results in the recovery of the fluorescence signal
MW 2015/07/06
Fluorescence recovery after photobleaching (FRAP)
Mueller et al., Curr. Op. Cell. Biol. (2010)
Redistribution of molecules and recovery
y of the fluorescence signal:
g
• A major challenge in FRAP experiments is to
dissect the contributions from the different
classes of molecules…
fluorescent
• …and the exchange between these classes
• This requires proper modelling of the data
including diffusion and binding reactions
bleached
mobile
immobile
MW 2015/07/06
Fluorescence recovery after photobleaching (FRAP)
Mueller et al., Curr. Op. Cell. Biol. (2010)
Redistribution of molecules and recovery
y of the fluorescence signal:
g
Model-independent interpretation
of recovery curve yields:
•
•
•
•
half-time of recovery
immobile fraction
fully mobile fraction
transiently bound fraction
MW 2015/07/06
Corrections in a FRAP experiment
Experimental limitations
that require corrections:
Bleaching of a certain
fraction of molecules
reduces the overall pool and
thus the maximum signal to
which it can recover.
Photobleaching during the
postbleach sequence affects
the temporal behaviour.
behaviour
Overall background signal
biases the apparent
fractions.
MW 2015/07/06
Spatially resolved FRAP analysis
So far:
The signal in the bleach region was averaged and monitored over time. Any other
spatial information was disregarded.
disregarded
Improvement:
• Division of cell/nucleus/… into a set of discrete regions
• Analysis of integrated intensity for each region
MW 2015/07/06
Spatially resolved FRAP analysis
Next step:
Complete spatio-temporal analysis
Here: projection in one direction and profile in the other direction
Plot of squared width of blech strip over time reveals diffusive behaviour
MW 2015/07/06
Quantitative modelling of spatially resolved FRAP data
p
Simulated FRAP experiment:
• 3 x 10 µm2 strip bleached into 2D fluorescent layer
• molecular diffusion to equilibrate the distribution
• can be described analytically (see next slides)
How do we set up a FRAP experiment in a living cell such that we can
simplify it to a 2D or even a 1D system?
MW 2015/07/06
FRAP: Bleaching of a pseudo-2D strip
Problem: complex 3D distribution of molecules after the bleach step
Solution, step 1: longer bleach profile by using a smaller aperture (NA) -> 2D
Solution, step 2: bleaching of a strip across the whole cell/nucleus ->
> 1D
MW 2015/07/06
Concept of Green‘s function to solve diffusion equation
c r , t    d r  c r , t  PD r, t r ,0 , PD r , t r ,0   cr , t   4Dt 
3 2
3
j

c
concen
ntration
c
 r  r 2 
exp 

4
Dt


=
x
x
spatial coordinate
MW 2015/07/06
Modelling the postbleach redistribution
t=0
t = 20
t=5
t = 40
t = 10
t = 80
Concentration distribution
directly after bleaching:
cx,0  c0  c0 px  a   x  a 
Using the proposed concept, we
can obtain the postbleach
distribution:
p   ax 
c x, t   c0  c0 erf 

2   4 Dt 
 a  x 
 erf 

4
Dt


MW 2015/07/06
What about binding and diffusion?
p
Coupled
diffusion and reaction:
Consider a diffusive fraction A and an immobile, bound
fraction B that exchange
g according
g to
AB
k on



k off
AB
This can be described with the diffusion-reaction equations
cdiff r, t 
 D  2 cdiff r, t   cB kon cdiff r, t   koff cbound r, t  ,
t
cbound r, t 
  koff cbound r, t   cB k on cdiff r, t 
t
This system of coupled differential equations is difficult or
impossible to solve, especially for complex boundary
conditions (bleach geometry, molecular kinetics)
MW 2015/07/06
What about binding and diffusion?
Diffusion and binding on different time scales:
Then, the diffusion and the reaction contribution can be treated independently
cdiff r, t 
 D  2 cdiff r, t   cB kon cdiff r, t   koff cbound r, t  ,
t
cbound r, t 
  koff cbound r, t   cB k on cdiff r, t 
t
MW 2015/07/06
What about binding and diffusion?
Diffusion and binding on different time scales:
The diffusive contribution is described as shown above. The binding contribution is just
cbound r, t   cbound r,    cbound r,    cbound r,0 exp koff t  ,
Fbound t   Fbound    Fbound    Fbound 0 exp koff t .
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What about binding and diffusion?
Diffusion and binding on the same time scales:
The full coupled reaction-diffusion scheme must be solved.
cdiff r, t 
 D  2 cdiff r, t   cB kon cdiff r, t   koff cbound r, t  ,
t
cbound r, t 
  koff cbound r, t   cB k on cdiff r, t 
t
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What about binding and diffusion?
Diffusion and binding on the same time scales:
The full coupled reaction-diffusion scheme must be solved. Strategies are
1 Numerical solution of the
1.
differential equations on a
finite difference
spatio-temporal
spatio
temporal grid
2. Application of coordinate tranforms that convert the coupled non-linear differential
equations into uncoupled linear differential equations
e g : Laplace transform,
e.g.:
transform Fourier transform
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Overview
I. Dynamic aspects of fluorescence
II. Random walks and diffusion
III. Fluorescence correlation spectroscopy (FCS)
IV. Fluorescence recovery after photobleaching (FRAP)
V Fluorescence lifetime imaging microscopy (FLIM)
V.
VI. Experimental
p
examples
p
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ad
dditional process
ses
knr
emis
ssion
kr
excittation
S1
S0
 natt 
 red
1
kr
1
kr
  nat

  nat
k r  k nr
k r  k nr
fluores
scence siignal
Fluorescence lifetime
exponential decay
red
nat
 t
exp  
 
time after excitation
fluorescence lifetime:
• ave. time betw. excitation and emission
• characteristic property of dyes, ~ns
• depends on environment (ions
(ions, pH
pH, …))
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How to measure the fluorescence lifetime (time domain)
t
• excitation with a pulsed laser
• measuring the time between laser
pulse
l and
d fluorescence
fl
photon
h t
• calculation of a histogram
• Fitting exponential decays to
histograms
N
t
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Confocal fluorescence excitation and detection
objective lens
filters
dic
chroic
mirrors
laser
dic
chroic
mirror
m
pinhole
detectors
• confocal/observation volume confined in 3D
• rater-scanning and synchronized detection:
image formation in the confocal laser scanning microscope
• flexible targeting of every point in the field of view
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Fluorescence lifetime as a spectral information
405 nm
405+488+543 nm
Molecular Probes FluoCells
Blue:
DAPI (nucleus)
Blue:
DAPI (nucleus)
Red:
Mitotracker
Red (mitochondria)
Red:
Mitotracker
Red (mitochondria)
Green:
Alexa488
(actin)
Green:
Alexa488 (actin)
Blue:
Red:
Green:
1.5 - 2.2 ns
2.2 - 2.6 ns
2.6 - 4.0 ns
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Fluorescence resonance energy transfer (FRET)
distance
dipole moments
modifiend from
Wouters et al.,
Trends in Cell Biology
(2001);
Gadella Trends in
Gadella,
Plant Science (1999)
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Fluorescence resonance energy transfer (FRET)
FRET efficiency (single FRET pair):
E=
quanta of energy transferred from excited donor to acceptor
total quanta of energy absorbed by donor
E r  
RF6
RF6  r 6
 1
 r 
D
with: RF – Förster radius
D – donor lifetime w/o FRET
E > 0 is thus a (qualitative) proof of interaction.
However, the biochemically relevant/interesting number is the fraction of donor molecules
involved in FRET when measuring E for an ensemble of molecules (the usual case).
This can be determined provided that positive and negative controls (100%/0% interaction)
are available.
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FRET-based fluorescent reporters
Zhang et al. (2002)
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Overview
I. Dynamic aspects of fluorescence
II. Random walks and diffusion
III. Fluorescence correlation spectroscopy (FCS)
IV. Fluorescence recovery after photobleaching (FRAP)
V Fluorescence lifetime imaging microscopy (FLIM)
V.
VI. Experimental
p
examples
p
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Chromatin organization in interphase
From histones to the chromatin fiber:
• compaction
• conservation and protection
• dynamic organisation
• regulation of transcription,
replication repair
replication,
• adoption of different epigenetic states
Wachsmuth et al., Biochim. Biophys. Acta 1783, 2008
Controversial:
• 30 nm chromatin fiber –
as observed under
(semi-)dilute conditions
• poorly structured –
sea of nucleosomes,
polymer melt
Maeshima et al., Curr. Op. Cell. Biol. 22, 2010
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H1 large scale binding and mobility
Imaging FRAP:
D~1 m2 s-1
results inconsistent
with other data,
require two bound
and one diffusive
component
Point CP/FRAP:
D = 20 µm2s-1
kon = 3.8
3 8 s-11
koff,1 = 0.89 s-1
koff,2 = 0.008 s-1
kswitch = 0.89 s-1
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FRAP of splicing factors in different nuclear locations
Rino et al. (2007) PLoS Comp. Biol. 3
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Dynamics of the exon-exon junction complex
Schmidt et al., RNA, 2009
Exon-exon junction complex (EJC):
• forms upon intron excision on maturating mRNA molecules in the nucleus
• serves as adaptor for nuclear
nuclear-cytoplasmic
cytoplasmic export and for mRNP quality control
• core-shell model of the EJC: core formed from proteins binding after, shell formed from proteins
binding prior to intron excision
• strong nuclear localization with accumulation in splicing speckles
• highly dynamic and mobile
What contributes to the mobilities of the EJC components Magoh and REF2-II?
REF2 II?
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Point FRAP and FCS of EJC factors REF2-II and Magoh
REF2-II-EGFP
scale bar 5 μm
Magoh-EGFP
scale bar 5 μm
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Point FRAP and FCS of EJC factors REF2-II and Magoh
REF2-II-EGFP
scale bar 5 μm
Magoh-EGFP
scale bar 5 μm
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Binding and diffusion properties of REF2-II and Magoh
slowly
y diffusive comp.
fas
st
FCS
immo
ob.
trans. bound
diff. comp
p.
FRAP
Im et al., Cytometry A, in press
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FCCS of mRNA-binding proteins
Y14/Magoh
dimer
NXF1/p15
dimer
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Cross correlation of GFP-p15 and RFP-NXF1 in the cytoplasm
Ratio G = 0.55
tD(GFP-p15) = 306 +/- 13 s
tD(RFP-NXF1) = 835 +/- 335 s
tD(cross) = 348 +/- 23 s
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No cross correlation of GFP-Y14 and RFP-NXF1RBM
Ratio G < 0.08
tD(GFP-Y14)
(GFP Y14) = 801 +// 93 s
tD(RFP-NXF1RBM) = 491 +/- 167 s
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Cross correlation of GFP-Y14 and RFP-NXF1
Ratio G = 0.19
tD(GFP
(GFP-Y14)
Y14) = 749 +/+/ 132 s
tD(RFP-NXF1) = 239 +/- 43 s
tD(cross) = 1098 +/- 167 s
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RNAi “rescue”
Endogenous mRNA
5‘ m7G-cap
5‘ UTR
CDS
3‘ UTR
AAAAAAA 3‘
knockdown of the
endogenous mRNA
R/GFP fusion mRNA
5‘ m7G-cap
R/GFP
CDS
AAAAAAA 3‘
UTR = untranslated region
CDS = coding sequence
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RNAi improves cross correlation measurements
Ratio G = 0
0.5
5
tD(GFP-Y14)
(GFP Y14) = 566 +/
+/- 118 s
s
tD(RFP-NXF1) = 579 +/- 414 s
tD(cross) = 481 +/- 102 s
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RNAi improves cross correlation measurements
RNAi Oligo
O
Ratio G
Y14 Oligo(A)/NXF1 Oligo(A)
0.24 +/- 0.07
Y14 Oligo(A)/NXF1 Oligo(B)
0.48 +/- 0.08
Y14 Oligo(B)/NXF1 Oligo(A)
0.23 +/- 0.21
Y14 Oligo(B)/NXF1
g ( )
Oligo(B)
g ( )
0.17 +/- 0.11
Control Oligo
0.28 +/- 0.05
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Cross correlation of GFP-Y14 and RFP-NXF1
Ratio G = 0
0.5
5
tD(GFP-Y14)
(GFP Y14) = 566 +/
+/- 118 s
s
tD(RFP-NXF1) = 579 +/- 414 s
tD(cross) = 481 +/- 102 s
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EJC core and shell model – mRNA transport
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3T3 cells expressing HP1-EGFP: diffusion and binding
Heterochromatin protein 1 isoform  (HP1):
• involved in heterochromatin formation
• binds
bi d globally
l b ll tto chromatin
h
ti
• and with higher affinity to heterochromatin
Cheutin et al. ((2003)) Science 299
Müller et al. ((2009)) Biophys.
p y J. 97
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2D-FCS of 3T3 cells expressing HP1-EGFP
Capoulade et al. (2011) Nature Biotechnology 29
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Further reading
More general biophysics:
•
•
•
•
C. Cantor & P. Schimmel, Biophysical Chemistry, Vol I, II & III, Freeman Press,
1980
I. N. Serdyuk, N. R. Zaccai & J. Zaccai, Methods in Molecular Biophysics:
Structure, Dynamics, Function, Cambridge University Press, 2007
B. Berne & R. Pecora, Dynamic Light Scattering, Wiley, 1976
T. A. Waigh, Applied Biophysics, Wiley, 2007
Diffusion, FCS, FRAP:
•
•
•
•
•
•
H. C. Berg, Random Walks in Biology, Princeton University Press, 1993
J. Crank, The Mathematics of Diffusion, Oxford University Press, 1999
H. S. Carslaw, J. C. Jaeger, Conduction of heat in solids, Clarendon Press, 1980
S. L. Shorte, F. Frischnecht, Imaging Cellular and Molecular Biological Functions,
Springer, 2007
D. Spector, D. Goldman, Live Cell Imaging - A Laboratory Manual, CSHL Press,
2005
R. Rigler, E. Elson, Fluorescence Correlation Spectroscopy: Theory and
Applications, Springer, 2001
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