raster image correlation spectroscopy rics - … · we can have a combination of very high time...
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Raster Image Correlation
Spectroscopy
RICS
We can have a combination of very high time resolution with sufficient spatial
resolution.
Major benefits of RICS:
� It can be done with commercial laser scanning microscopes (either one
or two photon systems)
� It can be done with analog detection, as well as with photon counting
systems, although the characteristic of the detector must be accounted
for (time correlations at very short times due to the analog filter)
� RICS provides an intrinsic method to separate the immobile fraction
� It provides a powerful method to distinguish diffusion from binding
How does it work?
Novel Idea: Raster Image Correlation Spectroscopy
Raster Scanning
Start herePixel time Line time + retracing time
1
Situation 1:slow diffusion
Situation 2: fast diffusion
2 3 4
1 2 3 4 5 6 7
Temporal information hidden in the raster-scan image:
the RICS approach
PixelS
pati
al co
rrela
tio
n
Slower diffusion
Faster diffusion
How is the spatial correlation done?
Image 1
(0,0) (0,127)
Image 1shifted
(x,0+y) (0,127) ξ0 1 2 3…..………….127
Spatial CorrelationResults
Matrix 1 Matrix 2
x
Operation:
One number is obtained for x and y and is divided by the average intensity squared
)127,0127,0)...(2,02,0()1,01,0()0,00,0( ××+×+×
In the x direction
PLUS In the y direction
)127,1127,1)...(2,12,1()1,11,1()0,10,1( ××+×+×+
How to use a stack of images?
Spatially correlate each frameIndividually then take the average of all the framesFRAME #1
(0,0) (0,256)
FRAME #1
(0,0) (0,256)
FRAME #1
(0,0) (0,256)
FRAME #1
(0,0) (0,256)
FRAME #1
(0,0) (0,256)
FRAME #100
(0,0) (0,256)
1.
..
..100
2),(
),(),(),(
><
>++<=
yxI
yxIyxIGRICS
ψξψξ
In a raster-scan image, points are measured at different positions and at different times
simultaneously
If we consider the time sequence, it is not continuous in time
If we consider the pixel sequence, it is contiguous in space
In the RICS approach we calculate the 2-D spatial correlation function (similarly to the
ICS method of Petersen and Wiseman)
The variables x and y represent spatial increments
in the x and y directions, respectively
2-D spatial correlation can be computed very efficiently using FFT methods.
To introduce the “RICS concept” we must account for the relationship between time
and position of the scanning laser beam.
The RICS approach: 2-D spatial correlations
ψ
ξ
)4
exp()4(
1),(
2
2/3Dt
r
DttrP −=
π
The the dynamics at a point is independent on the scanning motion of the laser beam
),(),(),( ψξψξψξ GSG RICS x=
Consider now the process of diffusion. The diffusion kernel can be described by the
following expression
There are two parts:
(1) the temporal term,
(2) the spatial Gaussian term
For any diffusion the amplitude
decreases as a function of time and
the width of the Gaussian increases
as a function of time
The RICS approach for diffusion
SLOW
FAST
21
2
1
2
0
)(41
)(41),(
−−
++
++=
z
lplp
w
D
w
D
NG
ψτξτψτξτγψξ
At any position, the ACF due to diffusion takes the familiar form:
tp and tl indicate the pixel time and the line time.
The correlation due to the scanner movement is:
++
+
−=
))(4
1(
]2
)2
(2
)2
[(
exp),(
2
0
00
w
D
w
r
w
r
Slp ψτξτ
ψδξδ
ψξ
Where δδδδr is the pixel size. For D=0 the spatial correlation gives the autocorrelation of
the PSF, with an amplitude equal to γγγγ/N. As D increases, the correlation (G term)
becomes narrower and the width of the S term increases.
RICS: space and time relationships
Digman et al. Biophys. J., 2005
Sp
ati
al
co
rre
lati
on
Faster diffusion
Pixel
Slow diffusion
AutoCorrelation plot (log averaged)
Tau (s)14e-6 14e-5 14e-4 14e-3 14e-2
G(t
)
3.5
3
2.5
2
1.5
1
0.5
0
D = 0.1 µm2/s
(membrane
proteins)
D = 5.0 µm2/s
(40 nm beads)
D = 90 µm2/s
(EGFP)
RICS Simulations of three different diffusion rates:Box size=3.4µm sampling time: 1) 32µs/pixel 2) 8µs/pixel 3) 4µs/pixel
Horizontal and Vertical fits:Simulations of beads 300 frames, 128x128pixels, 8µs/pix, size of pixels=30nm
0.0 0.2 0.4 0.6 0.8 1.0
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
D = 100
D = 10
D = 1
D = 0.1
ψ(µ m)ξ (µm)
0.0 0.2 0.4 0.6 0.8 1.0
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
D = 100
D = 10
D = 1
D = 0.1
g(ξ
)
g(ξ
)
Horizontal ACF Vertical ACF
Brown et al, JMI, 2007In SIMFCS
� Scan Speeds (µµµµs/pixel):• 4µµµµs for fast molecules D >100µµµµm2/s
• 8 -32µµµµs for slower molecules D= 1 µµµµm2/s-100µµµµm2/s
• 32-100µµµµs for slower molecules D= 0.1 µµµµm2/s-10µµµµm2/s
� Pixel Size:• 3-4x smaller than the Point Spread Function (PSF���� 300nm)
� Molecular Concentrations•Same conditions as conventional FCS methods
How to Setup the Laser Scanning Confocal Microscope
Common Errors in RICS
Scanning Too Slow(100 us/pixel, D = 300 um2/s)
Pixels are separated too much relative to PSF
(pixel size = w0 = 0.3 um)
Courtesy of Jay Unruh
128x128, 4 µs/pixel, 5.4 ms/line, 0.023 µm/pixel
Digman et al. Biophys. J., 2005
RICS: Fits to spatial correlation functionsRICS: Fits to spatial correlation functionsOlympus Fluoview300 LSMOlympus Fluoview300 LSM
EGFP in solutionEGFP in solution Spatial ACFSpatial ACF
D = 105 D = 105 ±± 1010 µµµµµµµµmm22/s/s
Fit to Spatial ACFFit to Spatial ACF
What ROI size to use? How many frames to acquire?
Size of ROI square (pixels)
Number of Frames Analyzed100 50 10 5
0
20
40
60
80
100
120
140
160256x256128x12864x6432x32
D (
µm
2/s
)
100nM mEGFP
0.000
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0.008
256 128 64 32
g(0
) avera
ge
500 frames
100 frames
75 frames
50 frames
25 frames
10 frames
1 frame
ROI size
100nM mEGFP
Brown et al, JMI, 2007
y = 0.86x + 7.1
R2
= 0.9961
0
10
20
30
40
50
60
70
80
90
100
0 20 40 60 80 100
Co
ncen
trati
on
via
RIC
S
Fluorescein in 100mM TRIS pH 9
Concentration via Absorbance (nM)
Obtaining concentration from RICS
Brown et al, JMI, 2007
How we go from solutions to cells?
In cells we have an immobile fraction
The 2-D-spatial correlation of an image
containing immobile features has a very strong
correlation pattern
We need to separate this immobile fraction
from the mobile part before calculating the
transform
How is this achieved?
In a “truly immobile” bright region, the intensity fluctuates
according to the Poisson distribution due to shot noise.
The time correlation of the shot noise is zero, except at time
zero.
The spatial correlation of the intensity at any two pixels due
to shot noise is zero, even if the two points are within the
PSF.
If we subtract the average intensity and disregard the zero
time-space point, the immobile bright region totally
disappear from the correlation function
Attention!!!!This is not true for analog detection, not even in the first
order approximation. For analog detection the shot noise is
time (and space) correlated.
Does noise from the detectors correlate?
Photon counting:
ACF of a bright
immobile particle
τ
Analog detection:
ACF of a bright
immobile particle
τ
Formula used to subtract background:
Subtract the average
Spatial Correlation
x
ySpatial Correlationof entire imageAfter subtracting image
Average intensity of each pixel on the overall stack:
),(),( yxIyxI i −
),( yxI
The intensity of each pixel minus the average intensity from entire stack for
each pixel: However, this yields negative values.
A scalar must be added : Ia =
Spatial correlationbefore subtracting background
ayxIyxIyxFwhereyxFICS iii +−= ),(),(),()),((
Intensity profile
Pixels
Inte
nsit
y
How to subtract immobile features from images?
Average of the “sea of
molecules” only
Average of the image including the immobile part
Immobile feature
linePixels
Intensity before removal
Intensity after removal
linePixels
Inte
nsity
Inte
nsity
Frames
Inte
nsit
y
0 10 20 30 40
Start the analysis
50 60
End of the analysis
Subtraction of moving average
Average between 1-10Frame #5
-
Matrix1 Matrix 2
=
A scalar average is then added
Operation is repeated for frame #6 - average between 2-11frame #7 - average between 3-12
Moving average operation on frames:
Pixel size = 0.092μμμμmPixel time= 8 μμμμs Line time = 3.152 ms
Wo = 0.35 μμμμm
Spatial ACF
No removal
Spatial ACF
With removal
G1(0) = 0.0062
D1 = 7.4 μμμμm2/sG2(0) = 0.00023
D2 = 0.54 μμμμm2/sBkgd = -0.00115
Fit using 3-D diffusion formula
Example of the Removal of Immobile Structures and Slow Example of the Removal of Immobile Structures and Slow
Moving FeaturesMoving Features
What is left
after removal
Conclusions
10-6 10-3 10-0
τ (s)
SmallMolecule
CytosolicProtein
TransmembraneProtein
Large Protein Aggregates
G(τ
)
t=1t=2
t=0
t=3
t=n
Pixel
µsec
Linemsec
T-ICMSec to min
RICS
FCS
Temporal ICMRICS
Line ScanTemporal correlation
Techniques Time Res. Spatial Res. Used to Study
Temporal-ICM sec <0.5 µµµµm Protein aggregates
Transmembrane proteins
RICS µµµµsec-msec ~2 µµµµm Soluble proteins
Binding interactions
Line-RICS msec <0.5 µµµµm Soluble proteins
Binding interactions
Summary
• Measures dynamic rates from the µµµµsec-msec time scale
• Anyone with a commercially available instrument can use it
• Immobile structures can be filtered out and fast fluctuations can be detected
• RICS has high spatial and temporal resolution
• The range of these dynamic rates covers a wide range from immobile to cytosolic diffusions (0.2-12um2/s)
• Other types of processes and interactions are also measured
• Line scanning is essential for determination of binding process and complements the RICS analysis
We have expanded the RICS methods to do Cross-Correlation
RICS (ccRICS)
The ccRICS approach
1),(),(
),(),(),(
21
21 −>><<
>++<=
yxIyxI
yxIyxIGccRICS
ψξψξ
The spatial correlation function
ψξ
The variables ξ and ψ represent spatial increments in the x and y
directions, respectively
+++
+∝
2
222212112212211
2
11211
2222111211
)()0,0(
NffNNffffNff
NffNffG cc
The Gcc(0,0) value and bleedthrough
2211111 )( NfNftF += 2221122 )( NfNftF +=
Ch1 Ch2
450 500 550 600 650 7000
20
40
60
80
100
Wavelength (nm)
%T
Experimental issues
• The volume of excitation and emission at the two excitation wavelengths must superimpose (we are using the Olympus FV1000 LSCM for these experiments)
• Bleedthrough of the green into the red channel must be small (<5%)
• FRET will strongly decrease the ccRICS signal
• High ratio of labeled to unlabeled molecules are needed (if you have only 10% labeled, in a
complex of 1:1, you will only have 1% of the complexes labeled with both proteins)
Cells. MEF transfected Vinculin, FAK and paxillin. cDNA were ligated to EGFP or mCherry at the
C-terminal end.
Microscopy. Olympus FV1000 with 60x 1.2NA water objective, 12.5 us/pixel, 256x256 pixels
12.5 μm square, 100 to 200 frames collected for each sample. 1frame/s.
EGFP excitation at 488nm (0.5%) and mCherry at 559nm (adjusted to a max of 1.5%).
Emission filters at 505-540nm and 575-675 nm, for the green and red channels, respectively.
Overlap of the volume of observation was tested by imaging single 100 nm fluorescent beads
carrying two colors simultaneously
VIN (green)-PAX (red)
Pixels
140
133
126
119
0.003
0.002
0.001
0.000
Pixels
140
133
126
119
0.003
0.002
0.001
0.000
Pixels
140
133
126
119
0.006
0.004
0.002
0.000
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133
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119
0.006
0.004
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119
0.010
0.005
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0.010
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119
0.010
0.005
0.000
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119
0.003
0.002
0.001
0.000
Pixels
140
133
126
119
0.003
0.002
0.001
0.000
(d) (e) (f)
(g) (h) (i)
(b)(a) (c)
Channel green Channel red Cross-correlation
VIN and PAX co localize at adhesions but they are
moving independently in the cytoplasm
MAV=10s
MAV=40s
The cross-correlation increases for the slow fluctuations (at MAV=40s). It is round in
shape indicating that it is generated at single locations.
FAK (green)-PAX
(red)
FAK and PAX co localize at adhesions but they are
moving independently in the cytoplasm
MAV=10s
MAV=40s
The cross-correlation increases for the slow fluctuations (at MAV=40s). It is round in
shape indicating that it is generated at single locations and it is very small.
Pixels
140
133
126
119
0.003
0.002
0.001
0.000
Pixels
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133
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119
0.003
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0.000
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133
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119
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119
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0.000
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0.004
0.002
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0.002
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0.000
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0.000
Pixels
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133
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119
0.004
0.002
Pixels
140
133
126
119
0.004
0.002
(d) (e) (f)
(g) (h) (i)
(a) (b) (c)
Channel green Channel red Cross-correlation
15
0
13
5
12
0
10
5
3.000
2.000
1.000
Pixels
150135
120105
15
0
13
51
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5
2.000
1.500
1.000
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0.000
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120105
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0
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2.000
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5
3.000
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120105
1 2 3
Schematic representation for the interpretation of the ccRICS
experiment. Simulation of binding and diffusion
Diffusion
Few complexes
Fast bindingDifferent shape
Smaller than PSF
Slow binding
Round shape
Distribution of fraction of cross-correlation in the cell.
Correlation with adhesion disassembling
Gcc/A
vg
(g1,g
2)
2
1.5
1
0.5
0
Gcc/A
vg
(g1,g
2)
2
1.5
1
0.5
0
(a)
Gcc/A
vg
(g1,g
2)
2
1.5
1
0.5
0
Gcc/A
vg
(g1,g
2)
2
1.5
1
0.5
0
(b)
VIN-PAX MAV=10s VIN-PAX MAV=40s
There is “more” cross-correlation at the locations of adhesion disassembling
ccRICS by scanning a region of interest across the image
Calculating the ratio Gcc/AV(G1,G2)
Summary of ccRICS
• We developed a toolbox for biophysicists and cell biologists to address common questions regarding the formation of protein complex, their spatial distribution and their stoichiometry
• ccRICS is extremely powerful at detecting joint diffusing proteins and in separating diffusion from binding processes
• The Paxillin, vinculin and FAK never crosscorrelate in the cytoplasm before binding to the focal adhesion. We only detect cross correlation due to dissociation of large clusters of proteins.
What is the stoichiometry of these clusters and is this stoichiometry crucial for the
biological system?
Random 1:2
The Number & Molecular Brightness (N&B) Method
Existing Methods to determine protein concentration and aggregation of proteins in cells
1. Calibration of the free fluorophore based on intensity
However, it doesn’t give you the size distributionOnly concentration is given
INTENSITY
31,250counts/sec
93,750 counts/sec
If “free” EGFP at 10nM gave 30,000 counts/sec then the conclusion would be that :
=10nM
= 30nM
Average intensity of MEF cells expressing Paxillin-EGFP
A
B
A
B
2. Förster resonance energy transfer (FRET)
This method is very sensitive to detect the formation of pairs.
1
2
3
4
5
6
0 2 4 6 8 10 12
Position
t2
t5
t8
(in time)
PSF
t2 t5 t8
Photo
n c
ounts
t1The intensity distribution accounts for the fluctuations of photons from the molecule freely diffusing through the exitation profile. Thus, the overall
photon counting count distrubution is the weighted superposition of individual Poissonian distributions for each intensity values with a scaling
amplitude. The fluctuations light intensity results in a broadeing of photon count distribution with respect to a pure poisson distribution. As the
fluctuations increases, the photon count distribution broadens.
t2 t3 t4
“Photon Bursts”
The average photon count rate of bursts determines
the
molecular brightness of the labeled protein.
4. Photon Counting Histogram Analysis
Fre
qu
en
cy
Red is PCHBlack is Poisson
Singlepaxillin
Few paxillin Not aggregated large paxillin
self-aggregate
Fre
qu
en
cy
εεεε = 2x103 cpsm
εεεε = 2x103 cpsm
εεεε = 8x103 cpsm
cluster of 4 paxillins
counts
εεεε = 24x103 cpsm
Nodifference
countslarge cluster
Many paxillin Not aggregated
εεεε = 2x103 cpsm
Significantdifference
Largerdifference
εεεε >24x103 cpsm
Many particles one brightness One particle increasing brightness
3. Image correlation Spectroscopy (ICS)
However, the events must be slow >1sec (no movement during one frame)
and the aggregates must be large. Petersen and Wiseman:Biophys J. 1999
Purpose: Provide a pixel resolution map of molecular number and
aggregation in cells
Method: First and second moment of the fluorescence intensity distribution
at each pixel
Source: Raster scanned image obtained with laser scanning microscopes
TIRF with fast camerasSpinning disk confocal microscope
Output: The N and B maps, B vs intensity 2D histogram
Tools: Cursor selection of pixel with similar brightness
Quantitative analysis of center and std dev of the e and n
distributionTools for calibration of analog detectors
Tutorials: mathematical background, data import, analysis examples (our web
site
The Number and Brightness (N&B) analysis
• Given two series of equal average, the larger is the variance, the less molecules contribute to the average. The ratio of the square of the
average intensity (<k>2) to the variance (σσσσ2) is proportional to the average number of particles <N>.
* Originally developed by Qian and Elson (1990) for solution measurements.
0 5 10 15 20 25 30 3518.8
19.0
19.2
19.4
19.6
19.8
Time (s)
Inte
nsity (
kcp
s) at pixel k
0 5 10 15 20 25 30 3518.8
19.0
19.2
19.4
19.6
19.8
Time (s)
Inte
nsity (
kcp
s) at pixel j
Fre
qu
en
cy
19.4 khz
Fre
qu
en
cy
19.4 khz
0 5 10 15 20 25 30 3518.8
19.0
19.2
19.4
19.6
19.8
Time (s)
Inte
nsity (
kcp
s) at pixel k
0 5 10 15 20 25 30 3518.8
19.0
19.2
19.4
19.6
19.8
Time (s)
Inte
nsity (
kcp
s)
0 5 10 15 20 25 30 3518.8
19.0
19.2
19.4
19.6
19.8
Time (s)
Inte
nsity (
kcp
s) at pixel k
0 5 10 15 20 25 30 3518.8
19.0
19.2
19.4
19.6
19.8
Time (s)
Inte
nsity (
kcp
s) at pixel j
0 5 10 15 20 25 30 3518.8
19.0
19.2
19.4
19.6
19.8
Time (s)
Inte
nsity (
kcp
s) at pixel j
Fre
qu
en
cy
19.4 khz
Fre
qu
en
cy
19.4 khz
Fre
qu
en
cy
19.4 khz
Fre
qu
en
cy
19.4 khz
K
kki
i∑ ><−
=
2
2
)(
σ
K
k
k i
i∑>=<Average
(first moment)
Variance (second moment)
σ
k
How to distinguish pixels with many dim molecules from pixels with few bright molecules?
This analysis provides a map of <N> and brightness (B) for every pixel in the image. The units of
brightness are related to the pixel dwell time and they are “counts/dwell time/molecule”.
2
2
σ
><>=<
kN
><=
><
><=
kN
kB
2σ
σ2 = Variance<k>= Average countsN = Apparent number of moleculesB = Apparent molecular brightnessK = # of frames analyzed
time
K
k
k i
i∑>=<
K
kki
i∑ ><−
=
2
2
)(
σ
Calculating protein aggregates from images
To increase the apparent brightness we could increase the dwell time, since the brightness is
measured in counts/dwell time/molecule.
Increasing the dwell time decreases the amplitude of the fluctuation.
1 0-9
1 0-7
1 0-5
1 0-3
1 0-1
0 .0
0 .1
0 .2
0 .3
0 .4
T im e (s )
G( ττ ττ
)
1 µs dwell time 1 ms dwell time
Selecting the dwell time
What contributes to the variance?
nn
22 εσ = nd εσ =2
222
dnσσσ +=
The measured variance contains two terms, the variance due to the particle number fluctuation
and the variance due to the detector count statistics noiseThese two terms have different dependence on the m
Both depend on the intrinsic brightness and the number of molecules. We can invert the equations and obtain n and εεεε
(for the photon counting detector)
nn
22 εσ =Variance due to particle number fluctuations
nd εσ =2Variance due to detector shot noise
n is the true number of m
ε ε ε ε is the true molecular bri
1
22222
+=><
+=><
+><
=><
= εσ
ε
εσσσ
kn
n
kkkB ddn
How to Calculate n and ε
This ratio identifies pixels of different brightness due to mobile particles.
The “true” number of molecules n and the “true” molecular brightness for mobile particles can be obtained from
><−
><=
k
kn
2
2
σ ><
><−=
k
k2σ
ε
If there are regions of immobile particles, n cannot be calculated because for the immobile fraction the variance is = <k>. For this reason, several plots are offered to help the operator to identify regions of mobile and immobile particles. Particularly useful is the plot of NvsB.
y = 4.4321x2 + 0.9438x
0
0.5
1
1.5
2
2.5
3
3.5
0 0.5 1
Intensity (c/dwelltime/molecule)
Vari
an
ce
Quadratic dependence of the variance on particle brightness
20nM EGFP in solution as a function of laser power
2-photon excitation using photon counting dete
nn
22 εσ =
Identification of mobile and immobile molecules
If we change the laser power, a plot of the ratio variance/intensity vs intensity can distinguish the mobile from immobile fraction. The two curves are for different pixel integration times.
Intensity
Variance/inte
nsity
1
Immobile
Mobile
103
104
105
106
107
108
0.95
1.00
1.05
1.10
1.15
Slide
EGFP
B
Counts/s
Increase the laser power
Increase the concentration but laser power
stays the same
The effect of the immobile part: with photon counting detectorsFluorescent beads in a sea of 100nM Fluorescein.
intensity300200100
B
4
3
2
1
0
intensity300200100
B
4
3
2
1
0
Selectingfluorescein
Selectingbeads
Intensity B map
intensity
43210
Variance/n
tensity
4
3.5
3
2.5
2
1.5
1
0.5
0
Monomer-octamer serie
Immobile
Brightness and number of molecules can be measured independently
intensity210
B
2
1.5
1
0.5
00.0 0.5 1.0 1.5 2.0
0
500
1000
1500
εε εε (c
ou
nts
/s/m
ole
cu
le)
Counts/pixel
2D histogram Brightness vs laser intensity
0
1
40 80 120 160 2000
2000
4000
6000
8000
10000
εε εε (c
ou
nts
/s/m
ole
cu
le)
Concentration (nM)0 40 80 120 160 200
0
4
8
n
Concentration (nM)
Brightness vs concentrationNumber of particles vs concentration
EGFP in solution
C
D
0 250 500 750 10000
50
100
150
n
Intensity (digital levels)
0 250 500 750 1000
0
5000
10000
15000
20000
25000
30000
εε εε (c
ou
nts
/s/m
)
Intensity (digital levels)
0 50
B
A
0 100000
Average intensity
EGFP in CHO-k1 (1-Photon LSM)homogenous Brightness & heterogeneous Number of Molecules
Map of Number of molecules
Map of molecular Brightness
MEFCHOk1
Average intensityMolecular Brightness
Selected MonomersSelected >5mers
x= 1.90057 y= 1.03400 #pixels= 5702 in= 662
intensity321
Va
ria
nc
e/n
ten
sit
y 1.3
1.2
1.1
1
0.9
x= 1.88378 y= 1.27400 #pixels= 716 in= 1
intensity321
Va
ria
nc
e/n
ten
sit
y 1.3
1.2
1.1
1
0.9
Paxillin assembles as monomers and disassembles as aggregates as large as 8-12
Digman, M.A., et al, Biophys J. 2008 Mar 15;94(6):2320-32
Time (s)4003002001000
Co
un
ts
3.4
3.3
3.2
3.1
3
2.9
2.8
2.7
2.6
2.5
pixel 104,68 A= 0.00000 k= 0.00000 B= 0.00000
Linear tau4003002001000
Co
un
ts
4
3
2
pixel 67,120 Intensity chnage in a 8x8 region
Selecting large aggregates
1289664320
128
96
64
32
0
time (s)4003002001000
Co
un
ts
4
3
2
pixel 6,89 average intensity in a region 8x8
Selecting large aggregates
1289664320
128
96
64
32
0
Selecting large aggregates
1289664320
128
96
64
32
0
Selecting large aggregates
1289664320
128
96
64
32
0
Selecting large aggregates
1289664320
128
96
64
32
0
Selecting large aggregates
0 to 99 100 to 199200 to 299 300 to 399400 to 499
100 Frame averages
Assembly and disassembly occurs in the order of minutes
Digman, M.A., et al, Biophys J. 2008 Mar 15;94(6):2320-32
Cross N&B
Conceptual illustration of Cross N&B
N
GGRR ii
cc
∑ −−=
))((2σ
Uncorrelated Correlated
Cross-variance
Inte
nsity f
luctu
ations
Frames
Inte
nsity f
luctu
ations
Frames
543210-1-2-3-4-5
5
4
3
2
1
0
-1
-2
-3
-4
-5
Ch
an
ne
l 2
Channel 1intensity
242220181614121086420
24
22
20
18
16
14
12
10
8
6
4
2
0
Channel 1
Ch
an
ne
l 2
Cross N&B Analysis determines stoichiometry
No Cross-Brightness
x= 17.50000 y= 17.50000 #pixels= 0 in= 0
intensity
4035302520151050-5
Variance/in
tensity
40
35
30
25
20
15
10
5
0
-5
Green Channel
Red
Channel
1:12:1
1:2
x= 20.14170 y= -0.07143 #pixels= 0 in= 0
intensity
4035302520151050-5
Variance/in
tensity
40
35
30
25
20
15
10
5
0
-5
Green Channel
Red
Channel
Positive Cross-Variance
1:1
2:1
1:2
This example is only for ideal systems where the brightness is calibrated for both channels.
The co-variance principle and the derivation of the
ccN&B method
K
RRGG ii
cc
))((2
><−><−=∑σ
Definition of co-variance.
It is the average of product
of the fluctuations in the
Green and Red channel2
cc
cc
RGN
σ
>><<= Definition of the cross-
number of molecules. It is
the co-variance divided by
the product of the intensity
in the two channels
K is the number of frames, σ2 the variance and < > indicate
To calibrate the system we need to know the brightness of the
monomers
5 % correlated
5 % correlated
intensity ratio 2:1
x= 4.83673 y= 1.46602 #pixels= 10530 in= 82
B1
12840
ccB
4
2
0
-2
x= 3.06122 y= 1.46602 #pixels= 10530 in= 82
B2
12840
ccB
4
2
0
-2
x= 3.24490 y= 1.46602 #pixels= 10346 in= 139
B1
12840
ccB
4
2
0
-2
x= 3.24490 y= 1.46602 #pixels= 10346 in= 139
B2
12840
ccB
4
2
0
-2
x= 2.75100 y= 2.93689 #pixels= 0 in= 0
B2
420
B1
4
2
0
x= 2.73092 y= 2.71845 #pixels= 0 in= 0
B2
420
B1
4
2
0
x= 2.67068 y= 2.66990 #pixels= 0 in= 0
B2
420
B1
4
2
0
x= 2.87755 y= 0.00485 #pixels= 59425 in= 896
B1
12840
ccB
4
2
0
-2
x= 2.75510 y= 0.00485 #pixels= 59425 in= 896
B2
12840
ccB
4
2
0
-2
0 % correlated
B1-B2 Bcc1 Bcc2
(1)
25 % correlated
x= 3.06122 y= 1.60194 #pixels= 35178 in= 598
B1
12840
ccB
4
2
0
-2
x= 3.12245 y= 1.56796 #pixels= 35178 in= 598
B2
12840
ccB
4
2
0
-2
x= 2.77108 y= 2.76699 #pixels= 0 in= 0
B2
420
B1
4
2
0
(2)
(3)
(4)
(A) (B) (C)
1) calibrate the monomers in both channels The lack of symmetry is due to Poissonian rather than Gaussian distribution of counts
2) Add correlated molecules (still all monomers)
3) At 5% you can still distinguish the positive correlated fluctuations
4) Now we have 2:1 stoichiometry. We have more brightness in B1 but the same in B2
What to look for:
1) First we need to calibrate the monomers
2) We have to see if there is positive cross variance
3) We have to see where the cross variance occurs in respect to the brightness of Ch1 and Ch2
The unknown sample: Vinculin-EGFP and Paxillin-mcherry
x= 1.11885 y= 1.22857 #pixels= 17416 in= 495
B2
3210
B1
3
2.5
2
1.5
1
0.5
0
Selection map
250200150100500
240
220
200
180
160
140
120
100
80
60
40
20
0
x= 2.71084 y= 1.55238 #pixels= 376 in= 0
B1
543210
cc
B
3
2.5
2
1.5
1
0.5
0
-0.5
-1
x= 1.40625 y= 1.35238 B1= 7.48 B2= 3.42
B2
543210
cc
B
3
2.5
2
1.5
1
0.5
0
-0.5
-1
1,000
900
800
700
600
500
400
300
200
100
0
Stoichiometry histogram
Channel 11413121110987654321
Ch
an
ne
l 2
35
30
25
20
15
10
5
0
-5
A B
C D E
We must find for each value of B1 in one pixel, what is the
The fluctuations must be correlated, so we only look at the
2:3
Look at the brightnesses that coincide for Ch1 an
Selecting different regions of the image
Selection map
240220200180160140120100806040200
240
220
200
180
160
140
120
100
80
60
40
20
0
Stoichiometry histogram
Channel 11413121110987654321
Ch
an
ne
l 2
35
30
25
20
15
10
5
0
-5
Stoichiometry histogram
Channel 11413121110987654321
Ch
an
ne
l 2
35
30
25
20
15
10
5
0
-5
Selection map
240220200180160140120100806040200
240
220
200
180
160
140
120
100
80
60
40
20
0
A B
C D
AFH1
Slide 62
AFH1 Make sure I didnt mess this up.Rick Horwitz, 6/18/2008
Cross –correlations occur at specific pixels at the adhesions
Vinculin-EGFP and Paxillin-mcherry
Selection map Selection map
x= 1.71429 y= 2.89320 #pixels= 1644 in= 34
B1
6543210
ccB
6
5
4
3
2
1
0
-1
-2
x= 1.51837 y= 2.93204 #pixels= 1644 in= 34
B2
6543210
ccB
6
5
4
3
2
1
0
-1
-2
51s-100s0s-50s
A B0s-50s 0s-50s
Selection map
x= 1.71429 y= 2.89320 #pixels= 630 in= 0
B1
6543210
ccB
6
5
4
3
2
1
0
-1
-2
x= 1.51837 y= 2.93204 #pixels= 630 in= 0
B2
6543210
ccB
6
5
4
3
2
1
0
-1
-2
Selection map
51s-100s0s-50s
1.Large Cross variance is only seen at the adhesion
2.Points of large co-variance occur at different regions and
We determined that the brightness for monomers B1= 1.118 and B2=1.22. Thus the ccB1= 6x monomer and for ccB2= 3 x the monomer
Simulations: effect of bright immobile features
x= 0.98394 y= 0.99515 #pixels= 1977 in= 214
B2
420
B1
4
2
0
Selection map
x= 2.73092 y= 2.76699 #pixels= 43909 in= 467
B2
420
B1
4
2
0
Selection map
x= 2.69388 y= -0.09709 #pixels= 51932 in= 569
B1
420
ccB
2
0
-2
x= 1.02041 y= -0.07767 #pixels= 1234 in= 130
B1
420ccB
2
0
-2
A
B
FAK and Paxillin
x= 1.08434 y= 1.21053 #pixels= 37301
B2
6543210
B1
6
5
4
3
2
1
0
Selection map
x= 1.54286 y= 3.32039 #pixels= 2699 in= 18
B1
6543210
ccB
6
5
4
3
2
1
0
-1
-2
x= 1.30120 y= 3.14286 #pixels= 2699 in= 18
B2
6543210
ccB
6
5
4
3
2
1
0
-1
-2
Selection map
3:4Digman, M.A., et al, PNAS Jan.23, 2009 Ahead of print
mutFAK-PAX cell shows no cross-correlation although the cell
forms adhesion (endogenous FAK?)
x= 7.78591 y= 1.99247 #pixels= 0 in= 0
B1
7654321
ccB
1.5
1
0.5
0
-0.5
-1
Testing for artifacts: FAK mutant does not form complexes
FAK-EGFP
Pax-mCherry
Summary
• N&B distinguishes between number of molecules and molecular brightness in the same pixel
• The acquisition for the N&B can be done with a commercial Laser Scanning Microscope (LSM) and the same data used for RICS can be used to map N and B.
• The Immobile fraction can be separated since it has a Brightnessvalue =1
• The N&B analysis of paxillin at adhesions shows large aggregatesof protein during disassembly.
• Cross N&B allows us to determine the stoichiometry of the complexes.
Additional Reading
1) Jay R Unruh and Enrico Gratton.Analysis of molecular concentration and brightness from fluorescence fluctuation data with an electron multiplied CCD camera.Biophys J. 2008; [epub ahead of print].
2) Michelle A Digman, Rooshin Dalal, Alan R Horwitz, and Enrico Gratton.Mapping the number of molecules and brightness in the laser scanning microscope.Biophys J. 2008; 94(6): 2320-2332.
3) Rooshin B Dalal, Michelle A Digman, Alan R Horwitz, Valeria Vetri, and Enrico Gratton. Determination of particle number and brightness using a laser scanning confocal microscope operating in the analog mode. Microsc Res Tech. 2008; 71(1): 69-81.
4) Yan Chen, Joachim D Müller, Qiaoqiao Ruan, and Enrico Gratton. Molecular brightness characterization of EGFP in vivo by fluorescence fluctuation spectroscopy. Biophys J. 2002; 82(1): 133-44.
5) Alberto Garcia-Marcos, Susana A Sánchez, Pilar Parada, John S Eid, David M Jameson, Miguel Remacha, Enrico Gratton, and Juan P G Ballesta.Yeast ribosomal stalk heterogeneity in vivo shown by two-photon FCS and molecular brightness analysis. Biophys J. 2008; 94(7): 2884-2890.
6) Michelle A Digman, Paul W Wiseman, Colin K Choi, Alan R Horwitz, and Enrico Gratton. Mapping the stoichiometry of molecular complexes at adhesions in living cells.Proc Natl Acad Sci USA. 2008; [submitted].