Fluorescence microscopy IIIFluorescence correlation spectroscopy
(FCS)
CZECH TECHNICAL UNIVERSITY IN PRAGUE
FACULTY OF BIOMEDICAL ENGINEERING
Detection volume in confocal microscopy:
x ~ 200 nm
z ~ 1 m
the volume from which fluorescence is collected in a confocal (or a multiphoton) is defined by the diffraction limited focusing and the
collection efficiency of the objective - Point spread function (PSF) of the microscope
typically of femtoliter volume
In a diluted solution (~ nM) the average number of molecules
in detection volume ~ 1
The measured fluorescence signal is then very noisy due to fluctuations in the number of
molecules in detection volume, their transitions to
nonfluorescent states (triplet, …)~ 3D Gaussian profile
Autocorrelation of fluorescence fluctuations:
The timescale of fluorescence fluctuation provides information on the kinetics of the underlying processes. They are studied by correlation
analysis.
2
1
1
1
t [ms]
fluore
scence
inte
nsi
ty
[ms]G
()
1
2
1/2
1)(
)()()( 2
tI
tItIG
1/2 – characteristic timescale of the fluctuations
Note: Sometimes a different definition of G () – converges to 1!!!
Timescale of fluctuations in FCS:
The timescale of fluorescence fluctuation provides information on the kinetics of the underlying processes. They are studied by correlation
analysis.
from Schwille and Haustein: Fluorescence Correlation Spectroscopy
[ms]
G ()
A single fluorophore molecule emits photons with intervals which are related to its lifetime. More fluorophores in a complex can emit with shorter intervals –
investigation of antibunching provides information on molecular oligomerization
antibunching
rotational movement
photophysical processes (triplet state, …)
diffusion
Free diffusion and FCS:
The autocorrelation function G () is fitted by a theoretical model
For free diffusion (e.g. in a solution) and assuming a 3D Gaussian shape of the detection volume following model has been derived:
2/1
0 )/)(/(11
)/(111
)(
zDDN
G
[ms]
G ()
D
x direction
z direction
1/N
z/0 – structure parameter, usually ~ 5-8Number of molecules and diffusion time in detection volume
Free diffusion and FCS:
The autocorrelation function G () is fitted by a theoretical model
When considering the transition to triplet state:
2/1
0 )/)(/(11
)/(11
)1(1
)/exp(1)(
zDD
T TNTTG
characteristic time of triplet transitionfraction of molecules in triplet
When considering more fluorophore species with different diffusion times:
[ms]
G ()
D2
D1
2/1
0
2
1
1
2
)/)(/(11
)/(11
)(
)()(
zDiDii
M
iii
M
iiii
M
g
FQN
gFQG
brightness
fraction
Diffusion coefficient D determination:
Diffusion coefficient D of the fluorophore can be calculated from its diffusion time D
In a similar manner concentration can be calculated from N and the detection volume size
D
D
4
20
The detection volume diameter 0 is usually determined by a calibration measurement with a solution of a fluorophore with known diffusion
coefficient
for example Rhodamine 6G has D = 426 m2s-1
DNA compaction investigated by FCS:
DNA molecules have pharmaceutical potential in gene therapy, they are however large and negatively charged – difficult transport over cellular membrane
E1
Natural solution – compaction of DNA by polycationic molecules such as spermine (+4)
amonium/phosphate ratio
DNA labelled by intercalating dye PicoGreen is condensed by spermine and the required ration of condenser/base-pair is searched
Particle number decreases as the multiple-labelled DNA becomes smaller than the detection volume
Adjimatera et al. (2006) Pharm Res 23:1564-1573
Dual-color fluorescence cross-correlation spectroscopy (FCCS):
Simultaneous measurement of FCS of 2 different fluorophores excited by 2 different lasers. The emission is divided by an emission dichroic mirror to 2
channels and detected by 2 detectors with appropriate emission filters.
400 450 500 550 600 650 700 750 8000,0
0,2
0,4
0,6
0,8
1,0
No
rmal
ized
Inte
nsi
ty
Wavelength [nm]
emission dichroic
detector
major dichroic (double)
1)()(
)()()(
tItI
tItIG
BA
BACC
Autocorrelation of individual fluorophores and cross-correlation between
them can be measured
Problems:
o crosstalk between the two excitation and detection channels
o difference in detection volumes in the two channels (diffraction limited focus is larger for longer wavelength)
Dual-color fluorescence cross-correlation spectroscopy (FCCS):
Cross-correlation is related to interactions of molecules.
E2
Positive cross-correlation indicates that molecules move together (complex). The higher the amplitude of the cross-correlation, the higher complex concentration
Negative cross-correlation (anti-correlation) – molecules avoid each other
Interaction of 2 membrane proteins:
negative control – noninteracting molecules, only crosstalk
positive control – double-labeled protein
Experiment:
Liu et al. (2007) Biophys J 93:684-698
Fluorescence lifetime correlation spectroscopy (FLCS):
Uses differences in fluorescence lifetime (instead of in fluorescence spectra) to distinguish contributions to FCS signal
Lifetime is sensitive to fluorophore environment FLCS can separate contributions from fluorophores in different environments (different conformation of proteins, …)
The method combines FCS with pulsed time-resolved fluorescence spectroscopy (typically TCSPC), arrival time on 2 different scales is measured for each photon
4500 4600 4700 4800 4900
Macro Time [ns]
Laser pulse photon
Relative Time [ps]2480 31201240
0 10 20 30 40 500
20000
40000
60000
80000
100000
Co
un
ts
Channel Time [ns]1E-3 0,01 0,1 1 10 100 1000 10000
1,00
1,04
1,08
1,12
Co
rre
lati
on
G()
Lag Time [ms]
Fluorescence lifetime correlation spectroscopy (FLCS):
Each component has its characteristic fluorescence decay (decay pattern)
0 200 400 600 800 1000 12001E-8
1E-7
1E-6
1E-5
1E-4
1E-3
0,01
0,1
No
rma
lize
d p
att
ern
pj(i)
Channel j
5 ns comp 2 ns comp
Statistical (numerical) filters (instead of optical filters) are use to separate the photons according to their arrival time after the excitation pulse
5 ns component2 ns component
2j
21j
1j ptwptwtI
For each channel j the measured intensity Ij is a linear combination of patterns:
0 200 400 600 800 1000-4-3-2-1012345
Filt
er fj(i)
Channel j
5 ns 2 ns
5 ns component2 ns component
Filt
er
f j(i)
The probability with photons in jth channel contribute to ith pattern. Sum over i equals 1 for each j.
Fluorescence lifetime correlation spectroscopy (FLCS):
Optical filters can improve the data by filtering out scattered light. The statistical filters can do the same – scattered light and noise can be filtered out thanks to their
different decay pattern
Dark counts (detector afterpulsing) results in a constant background – influence correlation at short lag times (can be misinterpreted as triplet transition)
5 ns component2 ns componentafterpulsing
Filt
er
f j(i)
Channel j
Note: after separating the contributions of individual patterns we can find autocorrelation for each of them and cross-correlations between them
If we do not know one of the patterns (it cannot be measured individually), we can still separate the respective contribution by filtering out everything else
DNA compaction investigated by FLCS:
What is the compaction mechanism (gradual or all-or-none transition)? For large DNA molecules investigated by single-molecule fluorescence microscopy, but for smaller
plasmids below resolution
E3
The lifetime of PicoGreen changes upon compaction (change in local polarity)
Patterns for uncondensed (4 ns) and fully condensed (3 ns) DNA measured separately and used for investigation of the titration midpoint by FLCS
DNA compaction investigated by FLCS: E3
Patterns for uncondensed (4 ns) and fully condensed (3 ns) DNA measured separately and used for investigation of the titration midpoint by FLCS
10-3 102
1.6
2.4
G()
(ms)
Good agreement of the autocorrelation of the filtered out components with the pure forms equilibrium between uncondensed and fully condensed form at the midpoint
(all-or-none transition)
Analysis of cross-correlation between the 2 components reveals further details
Humpolíčková et al. (2008) Biophys J 94:L17-L19
DNA compaction investigated by FLCS: E3
Its amplitude between the amplitudes of the two components suggests presence of dynamics between the two forms.
Analysis of cross-correlation between the 2 components reveals further details
10-4 101
30
60
G()
(ms)
Fitting with a model indicates dynamics on ms scale with independent compaction of approximately 5 domains in the DNA molecule.
FLCS also showed that another DNA condenser HTAB (+1) exhibits gradual compaction mechanism
Humpolíčková et al. (2008) Biophys J 94:L17-L19
FLCS and lifetime tuning:Not always is the process we investigate accompanied by a sufficient
change in lifetime.
E4
Fluorescence lifetime can be influenced externally for example by the vicinity of a conductive surface (quenching)
1.8 ns in supported lipid bilayer (SLB) on ITO surface
5.6 ns in small unilamellar vesicles (SUVs)
0.01 0.1 1 10 100 10001.0
1.5
2.0
2.5 SLBs SUVs filtred SUVs filtred SLBs
Co
rre
lati
on
G()
Lag Time [ms] [ms]
G ()
FLCS
FCS of planar samples:
In planar samples (lipid bilayers, molecular layers on interfaces, …) the detection volume is reduced to a 2-dimensional Gaussian intensity profile
)/(111
)(DN
G
D
D
4
20
Determination of 0 is a problem:
o positioning problem: small axial displacement – significant change in , N and D.
o difference in detection volume in the reference and the sample due to difference in refractive index
4nm2m0 ≈ 200 nm
A need to avoid extrinsic calibration by introducing an intrinsic ruler
Calibration-free FCS:extrinsic calibration avoided by introducing an intrinsic ruler:
•axial step between several FCS measurements – Z-scan FCS
• parameters of continuous scanning during the FCS measurement – scanning FCS, scanning continuously over a circle of known radius or a line with a defined speed
• distance between more points in which FCS is simultaneously measured, multiple measurement points can be generated by:
two overlapping foci generated by doubling the focus by a Wollaston prism (like in DIC) or Michelson interferometer – 2-focus FCS.
different pixels of a microscope image (recorded for example in TIRF configuration) – Image correlation spectroscopy (ICS, STICS, …)
• combination of scanning and imaging in laser scanning microscopy (LSM) – known pixel size and scanning speed – RICS, STICS, …
Z-scan FCS:known axial step between measurements serves as intrinsic calibration
Z
parabolic dependence of 2, N and D on Z:
-0,8 -0,6 -0,4 -0,2 0,0 0,2 0,4 0,6 0,80
2
4
6
8
10
12
14
0
2
4
6
8
10
12
14
D [
ms]
Pa
rtic
le n
um
be
r
Z [m]
Determination of surface concentration cS and diffusion coefficient D of the fluorophore
4
02
222
040
2
2220 1)(,1
4)(
Z
cZNZ
DZ SD
ICS:spatial correlation between image pixels (distances along x and y axes play the role
of lag time)
The amplitude of the correlation peak is inversely proportional to fluorophore
density
additional temporal information allows investigation of diffusion:
• correlations between images in a temporal series (spatio-temporal ICS – STICS)
• imaging by LSM with defined scanning speed spatial correlation contains temporal information (Raster image correlation spectroscopy – RICS), 2 axes – 2 timescales
diffusion – broadening of the peak
oriented flow – broadening + shift
possibility to construct velocity maps
temporal resolution defined by imaging speed
Hebert et al. (2005) Biophys J 88:3601-3614
Acknowledgement
The course was inspired by courses of:
Prof. David M. Jameson, Ph.D.
Prof. RNDr. Jaromír Plášek, Csc.
Prof. William Reusch
Financial support from the grant:
FRVŠ 33/119970
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