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