ImFCS: A software for Imaging FCS data
analysis and visualization
Jagadish Sankaran,1, 2
Xianke Shi,2 Liang Yoong Ho,
3 Ernst H. K. Stelzer,
4 and Thorsten
Wohland1,2,5
1Singapore-MIT Alliance, National University of Singapore (NUS),
E4-04-10, 4 Engineering Drive 3, 117576, Singapore 2Department of Chemistry, NUS, 3 Science Drive 3, 117543, Singapore
3Bioinformatics Institute, 30 Biopolis Street #07-01 Matrix, 138671, Singapore 4Cell Biology and Biophysics Unit, European Molecular Biology Laboratory, Meyerhofstrasse 1,
69117 Heidelberg, Germany [email protected]
Abstract: The multiplexing of fluorescence correlation spectroscopy (FCS),
especially in imaging FCS using fast, sensitive array detectors, requires the
handling of large amounts of data. One can easily collect in excess of
100,000 FCS curves a day, too many to be treated manually. Therefore,
ImFCS, an open-source software which relies on standard image files was
developed and provides a wide range of options for the calculation of spatial
and temporal auto- and cross-correlations, as well as differences in Cross-
Correlation Functions (ΔCCF). ImFCS permits fitting of standard models to
correlation functions and provides optimized histograms of fitted
parameters. Applications include the measurement of diffusion and flow
with Imaging Total Internal Reflection FCS (ITIR-FCS) and Single Plane
Illumination Microscopy FCS (SPIM-FCS) in biologically relevant samples.
As a compromise between ITIR-FCS and SPIM-FCS, we extend the
applications to Imaging Variable Angle-FCS (IVA-FCS) where sub-critical
oblique illumination provides sample sectioning close to the cover slide.
© 2007 Optical Society of America
OCIS codes: (300.6280) Spectroscopy, fluorescence and luminescence; (040.1520) CCD,
charge-coupled device; (110.4155) Multiframe image processing; (110.0110) Imaging systems;
(300.0300) Spectroscopy; (040.1490) Cameras
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1. Introduction
Fluorescence Correlation Spectroscopy (FCS) records fluorescence fluctuations from small
observation volumes and extracts information about molecular processes which underlie these
fluctuations. FCS is typically performed in confocal systems at a single spot at a time.
Multiplexing started with the first two-foci measurements by Brinkmeier et al [1], later
followed by 4 foci measurements on a CMOS device with 4 detection elements [2]. This was
followed by the usage of electron multiplying charge coupled device (EMCCD) cameras for
the first time as detection elements with sufficient high read-out rates to perform confocal
FCS [3]. Although the time resolution could be improved by using selected regions of the
EMCCD [4], the number and density of confocal spots was limited since neighboring
confocal volume elements cross-talk to each other in dependence of their distance. Therefore
a minimum distance between focal volume elements of at least 10-15 confocal diameters was
required to perform FCS [3]. Therefore, despite a density of 250,000 pixels on a CCD, not
more than 3-400 confocal spots could be used. This was improved upon by spinning disk FCS
[5] at the expense of the observation time per pixel. With the introduction of total internal
reflection (TIR) [6–8], single plane illumination microscopy (SPIM) [9] and critical angle
illumination [10,11] in FCS, the creation of the observation volumes was facilitated by
selectively illuminating only a thin layer of the sample which lies in the focal plane of the
#133271 - $15.00 USD Received 12 Aug 2010; revised 21 Oct 2010; accepted 26 Oct 2010; published 22 Nov. 2010(C) 2010 OSA 6 December 2010 / Vol. 18, No. 25 / OPTICS EXPRESS 25469
detection objective. Recently, a stationary Nipkow disc based multiplexed FCS has also been
demonstrated [12]. Since these techniques only illuminate the parts of the sample which are
observed [9,13], the background and cross-talk between the detection elements is greatly
reduced making FCS in an imaging mode possible even on live cells and within living
organisms. Multiplexing can also be achieved by scanning the beam in a pre-determined
manner in a confocal laser scanning microscope. A wide variety of scanning FCS techniques
have been reported [14]. Scanning FCS has the advantages of reduced cross-talk since the
pixels are spatially well separated and higher temporal resolution whereas Imaging FCS has
the advantage of obtaining more measurements per sample per time interval with less
phototoxicity due to a low light exposure allowing measurements over for a longer time [9].
Imaging FCS is now routinely capable of recording FCS measurements on regions of
interest (ROI) of 4000 points or more. The limit of the ROI is here set by two requirements: i)
the frame rate of the camera, which decreases with increasing size of the ROI, but has to be
kept at a minimum value so that the time resolution is sufficient to observe single molecule
events of interest. This is typically between 250 and 3000 frames per second, for ROIs on the
order of 400-4000 pixels. The highest frame rate here is determined by the maximum
available camera speed at the moment. ii) The capacity of computers of handling the acquired
data in an acceptable time. At the time of writing, 32 × 32 pixels can be handled on a standard
PC (3 GHz Dual Core, 4 GB RAM, 32 bit Windows XP) in an acceptable time (~1 min for
correlation and ~4 mins for curve fitting). Higher pixel numbers can considerably slow down
calculations as well as data fitting.
Since we record typically 10,000 frames per measurement at a frame rate of 250-3000
frames per second, our recording time is between 3 and 40 s. This means that a typical
experimenter records easily 100,000 correlation curves per day. This is an amount of data that
cannot be treated manually anymore. Presently, to the best of our knowledge, no
commercially available software can read in image stacks and calculate correlations in each
pixel of the image stack. The goal of this work was therefore to provide a program that allows
the user to read-in the intensity files from different CCDs, to automatically calculate the
temporal autocorrelations and temporal and spatial cross-correlations, to fit all data with a set
of predefined models and to display images and histograms of all parameters. The program,
ImFCS, provided here is written in C++ for Windows XP/Vista, and is linked to the widely
available commercial software Igor Pro (WaveMetrics Inc, Lake Oswego, OR, USA) to
provide a graphical interface for the user. It should be noted though that the C++ routines can
as well be easily implemented into any other graphic user interface or adapted for any other
operating system. The article is divided into two parts, the first part deals with the description
of the software and the second part deals with examples of application of the software in
various camera-based FCS techniques (ITIR-FCS, IVA-FCS and SPIM-FCS).
2. Description of ImFCS
ImFCS is a data analysis tool for camera based FCS. Upon recording of a time series or stack
of images by a camera and providing the stacks to ImFCS, the software presents intensity time
traces for each pixel and calculates auto– and cross-correlations of and between pixels. The
correlation curves are fitted with suitable models to extract parameters. The fitted parameters
are displayed to the user as individual images. Figures S1-S3 in the supplement provide an
overview of the program functionalities, structure and screen shot respectively.
2.1 Input to the program
Correlations are performed on a stack of multiple images acquired at different time points.
Each image is made up of a certain number of pixels and each pixel has an associated
intensity value. The format which is required as input by ImFCS is the Tagged Image File
Format (tiff). The present specification of Tiff files 6.0 [15] allows an entire stack of frames to
be stored as a single “multi-plane” Tiff file and most commercial softwares allow saving data
#133271 - $15.00 USD Received 12 Aug 2010; revised 21 Oct 2010; accepted 26 Oct 2010; published 22 Nov. 2010(C) 2010 OSA 6 December 2010 / Vol. 18, No. 25 / OPTICS EXPRESS 25470
in this format. Conversion of other file formats for storing frame stacks into *.tif is available
with ImageJ [16]. The intensity values from the multi-plane tiff file are written into an
intensity array of dimensions n, w, l where n is the number of frames, w is the number of rows
in the image and l is the number of columns in the image. A detailed description of the
program is given in the supplement (Secs. 2.1-2.3). Each measurement has a background
value (bg) associated which originates from camera, environment and sample related issues.
The user has three options to remove the background. The background value can be
determined by a background file which was acquired without excitation of the fluorophores or
the background value can be entered directly into software or can be set to the minimum value
of the stack being correlated. For a full frame data treatment, the correlation is performed at
each pixel and upon completion the output consists of w × l number of correlation curves.
Note that ImFCS allows choosing subregions or cross-correlations between pixels in which
case the number of correlation curves will vary accordingly. The program provides as an
option to bin the data which is a process in which the adjacent pixels are added up. The
number of pixels to be binned (bin) is determined by the user. In case, binning is performed,
the output consists of w l
bin bin
number of correlations where x is the largest integer
less than or equal to x.
2.2 Correlation: Types and architecture
Correlations are performed between pixels which had been acquired at different times and/or
locations. Assuming stationary processes, the acquisition time of the first frame can be set to
0t . The pixels in the frame are correlated individually with pixels in another frame that was
acquired at t . The difference between the acquisition times of these two frames being
correlated, τ, is referred to as lag time. The cross-correlation GAB(τ) between the fluorescent
intensities in pixels A and B (FA and FB) is defined as
0A B
AB
A B
F FG
F t F t
(1)
Autocorrelation is a special case of cross-correlation when the correlation is performed on
the fluorescent intensity for a single pixel. The above formula is modified by replacing B with
A. The program calculates various types of cross-correlations, for instance, those between the
centre pixel and the pixels along the central row or central column or the leading and trailing
diagonal and the cross-correlation of the central pixels with the surrounding rectangular
region of pixels. It calculates the differences in forward and backward correlations referred to
as ΔCCF. Presently two formats of the calculation are permitted in the software.
( ) ( ) ( )
( ) ( ) ( )
AB BA AB BA
AB CB AB CB
G G G
G G G
(2)
These correlations are schematically displayed in Figs. S1 B and C in the supplement. The
software allows the user to draw region(s) on an average intensity map of the stack, which can
be auto- or cross-correlated. The details of how the above options are programmed are given
in Sec. 2.4 in the supplement.
There are a number of important time scales for the calculation of the correlations. First,
the frame rate of the camera limits the time resolution, and this time per frame is referred to as
Δτ. Note that this time includes the illumination of the camera as well as the readout time (in
our case, illumination times is between 0.2 and 1 ms and the readout time between 0.3 and
4.6 ms, resulting in overall frame rates between 171 and 2000 frames per second). All other
time scales are multiples of this basic unit time Δτ. Second, the measurement has to be taken
over a certain acquisition time tacq. Third, the correlations are calculated for different lagtimes
#133271 - $15.00 USD Received 12 Aug 2010; revised 21 Oct 2010; accepted 26 Oct 2010; published 22 Nov. 2010(C) 2010 OSA 6 December 2010 / Vol. 18, No. 25 / OPTICS EXPRESS 25471
τ (0< τ < tacq). Fourth, at different lagtimes τ, the width over which the intensity signal is
integrated before the correlation is calculated can vary and is referred to as the bin width
[17,18]. The program supports two correlator architectures
a. Linear (linear)
b. Semi-logarithmic (semilog)
2.2.1 Linear correlation
In linear correlation mode, the correlations are calculated at linearly increasing lagtimes
m where m ranges from 0 to M-1, if the correlations are calculated for M lagtimes. The
bin width for each lagtime is kept constant at Δτ. Theoretically, the last point of the correlation
is the acquisition time (tacq). It is not advisable to calculate the correlation till tacq since the
number of data points to average are very few as the lagtime approaches tacq. To display
correlations from 0t to , /end end acq endt t t t t + 1 number of calculations need to be
done. Substituting typical values, Δτ = 0.5 ms, tend = 1.0235 s, 2048 correlations at individual
lag times need to be performed. For linear correlation, the lagtime is
| 0 1linear
tendm m m m
(3)
Where is the set of natural numbers.
2.2.2 Semi-logarithmic correlation
The semi-logarithmic correlator architecture is used more frequently since this architecture
covers a larger range of lagtimes than the linear correlator using less number of computations.
This correlator architecture is based on the multi-tau algorithm [17]. In the most common
configuration, the first 16 correlations are at linearly increasing lagtimes m where m
ranges from 0 to 15 with a binwidth of Δτ. The next set of 8 correlations possess linearly
spaced lagtimes at intervals of 2Δτ beginning with (15 + 2)Δτ and a bin width of 2Δτ . The
next set of 8 correlations possess lagtimes at intervals of 4Δτ beginning with (31 + 4)Δτ and a
bin width of 4Δτ. This is repeated for bin widths of 8Δτ, 16Δτ, 32Δτ, 64Δτ and 128Δτ. The last
calculated lag time is at (2048-1)Δτ. Substituting Δτ = 0.5 ms, a lag time of 1.0235 s can be
achieved by just 72 (16 + (8-1) × 8) correlations. The same lagtime needs 2048 correlations in
the linear configuration. The above example was for the configuration of a (16, 8) multi tau
correlator but can be directly extended to any (p, q) correlator structure. In a (p, q) correlator,
the first p correlations are at linearly increasing lagtimes m where m ranges from 0 to
p-1 with a binwidth of Δτ. The next q groups possess p/2 lagtimes with bin width and lagtime
intervals which double from group to group. In this way a particular lagtime is always the sum
of all the bin widths of the previous lagtimes. A (p, q) correlator calculates a correlation
function at h = [p + (q-1) × q/2] number of lagtimes. The minimum number of frames (Frmin),
needed for a (p,q) correlator is
11 2
min 2 1
qp iFr p
i
(4)
For a (16,8) correlator, Frmin = 2047. Although 2047 frames are sufficient to carry out the
correlations, it is advised to perform the correlation with higher number of frames in order to
increase the precision of the calculated correlation. Here, all the correlations have been
calculated using 10000 frames. A detailed description of the semi-logarithmic correlator is
available in [18,19]. Thus the lagtime in this architecture can be represented by the formula
below
#133271 - $15.00 USD Received 12 Aug 2010; revised 21 Oct 2010; accepted 26 Oct 2010; published 22 Nov. 2010(C) 2010 OSA 6 December 2010 / Vol. 18, No. 25 / OPTICS EXPRESS 25472
2
12
2 1 1 12 2 2
semilog
| 0
m
p
m
m m m
m p p qm m p m p q
p
p
(5)
2.3 Implementation in the program
There are two ways, by which the correlation can be calculated, using the sums of products
method or by using Fourier transforms [20]. In this software, the correlation is calculated
using the former method. The continuous expression for correlation in Eq [1]. is converted to
discrete form and implemented in the program as in Eq [6]. for the linear and the first cycle of
the semi-logarithmic architecture. Symmetric normalization is performed where each
correlation is normalized by only those intensity values used in the calculation of the
autocorrelation [17].
1( )
0( )1 1
0
linear : 1| 0
Semi-logarithmic : =
n kn k F i F i k
A BiG k
n k nF i F i
A Bi i k
tendx
k k x
x p
(6)
1 2 1 12 1 12 22
0 22
2
12 1 122
0 22
2 1 12
2 2
ll
l
ll
ll
l
l
n p pk i k
i
A Blpi j i
j i k
n pk
i
A B
i j ij
pG k
n pk F j F j
F j F j
1 2 1 12 22
0
2
0, 2
1
l
l
l
n p pk i k
pii k
pk
k l
l q
(7)
In the case of semi-logarithmic architecture, the multi tau algorithm is implemented [17,18].
Stacks which have acquisition times which are integer multiples of Δτ are created by
summation and the correlations are calculated in these stacks as shown in Eq [7]. The
correlations are calculated for p/2 points at arithmetically progressing time intervals at twice
(21) the time resolution, Δτ, of the camera. This is followed for p/2 points with a time
difference of four times (22) the time resolution. This is repeated till the time difference has
reached 2q-1 times the time resolution. The procedure by which the formula below is computed
in the program is described in the supplement (Sec. 2.5).
#133271 - $15.00 USD Received 12 Aug 2010; revised 21 Oct 2010; accepted 26 Oct 2010; published 22 Nov. 2010(C) 2010 OSA 6 December 2010 / Vol. 18, No. 25 / OPTICS EXPRESS 25473
2.4 Fitting model
Two fitting models are included in the software to fit the data obtained above and to extract
the parameters. The generalized fitting model for cross-correlation of diffusion and flow
processes for square regions separated by rx and ry in the x and y axes respectively, for TIRF
based camera FCS [8] is given by Eq. [S1] in the supplement where N = <C>a2 where a is
the pixel size in object space, C is the surface concentration, D is diffusion coefficient, vx and
vy are the velocities in the x and y axes respectively. σ is the width of the Gaussian Point
Spread Function (PSF) [21,22] of the microscope in the x-y plane defined by Eq. [S2] in the
supplement. By setting rx and ry to zero, the model can be simplified to describe the
autocorrelation as provided in [7,23]. In the case of SPIM-FCCS [9] with a light sheet of
considerable thickness (σz) in z direction, the same model was modified to Eq. [S6] where N =
2<C>a2σz. Upon fitting with each of the models, the fitting parameters are displayed as image
plots. Using the histogram button in the software, a histogram of the fitted parameters can be
plotted. The number of histogram bins is calculated using the Freedman-Diaconis rule [24]
where max and min are the sample maximum and minimum respectively, s is the sample size
and Q1 and Q3 are the first and the third quartile respectively.
3
3 1
max min
2
sNumber of histogram bins
Q Q
(8)
3. Data collection modes in Imaging FCS analyzed by ImFCS
One of the critical needs of FCS is to create a small observation volume (order of 1015 l) to
observe the fluctuations of fluorescence. This is achieved in imaging FCS by restricting the
volume in which the sample is excited. In ITIR-FCS, a ~100 nm thin section close to the
cover slip is illuminated by an evanescent wave which is created when a laser beam impinges
on an interface coming from an optically more dense (µ1) to an optical less dense (µ2) medium
at angles greater than the critical angle (critical angle = sin1 (µ2/µ1)). In SPIM-FCS, the
volume isolation is provided by a diffraction limited light sheet created in the focal-plane of
the detection objective illuminating regions away from the cover slide [9].
Recently, other related illumination schemes with sectioning capability have been
introduced for imaging and FCS. Variable Angle Epi-fluorescent Microscopy (VAEM) [25]
and Highly Inclined and Laminated Optical Sheet (HILO) microscopy were utilized for
imaging of plant cells and single molecule imaging, respectively [26,27]. Critical angle
illumination based FCS was demonstrated on fluorescent beads [10]. These techniques make
use of sub-critical illumination. At sub-critical, oblique angles of illumination, the refracted
light is just above the surface of separation sufficient to illuminate fluorophores away from
the surface in the bulk sample. The use of sub-critical angles reduces the background
considerably and provides volume isolation in the bulk suitable to perform FCS. Performing
FCS in such illumination conditions is referred to as IVA-FCS (Imaging Variable Angle-
FCS). IVA-FCS does not need any separate add-on apparatus to a TIRF microscope. Using
IVA-FCS, diffusion of fluorescent beads in solution was studied. In comparison with ITIR-
FCS, IVA-FCS has the advantage of increased penetration depth into bulk of the sample away
from the surface of separation. A schematic of the illumination schemes is presented in Fig. 1.
Representative examples of data collected by any of the 3 aforementioned illumination
schemes and analyzed using ImFCS are presented here. The “materials and methods” are
available in the supplement in Sec. 5. Three different processes are probed using Imaging
FCS. The first part is an analysis of diffusive behavior of lipids and membrane proteins on
artificial and cell membranes respectively using ITIR-FCS and beads in solution using IVA-
FCS. The second part is an analysis of flow process using ΔCCF imaging in ITIR-FCCS. In
the last part, coupled diffusion and flow processes in a model system and in a living zebrafish
embryo are studied using ITIR-FCCS and SPIM-FCCS respectively.
#133271 - $15.00 USD Received 12 Aug 2010; revised 21 Oct 2010; accepted 26 Oct 2010; published 22 Nov. 2010(C) 2010 OSA 6 December 2010 / Vol. 18, No. 25 / OPTICS EXPRESS 25474
Fig. 1. Illumination schemes in camera based FCS are shown here. ITIR-FCS schematic is
shown in A in which super-critical illumination is performed and the volume isolation is
provided by an exponentially decaying evanescent wave exciting the fluorophores near the
cover slide. IVA-FCS is performed just by decreasing the angle of incidence to values less
than the critical angle leading to selective excitation in the bulk sample as seen in B. C is a
schematic of SPIM illumination where the fluorophores are excited by a diffraction limited
light sheet. A is restricted to surfaces like 2D lipid bilayers and cell membranes while B and C
are capable of exciting fluorophores in a physiologically relevant 3D environment inside
biological samples.
4. Results and Discussion
4.1 Analysis of diffusion by ITIR-FCS and IVA-FCS using ImFCS
A POPC bilayer doped with fluorescently labeled lipids was prepared and stacks were
acquired using ITIR-FCS. 21x21 pixels of 10000 images were acquired and analyzed by the
software. The entire set of 441 ACFs are shown along with two representative
autocorrelations in Fig. 2A. The fitting model fits properly to the experimental data. All the
correlation curves can be fitted and the parameters can be retrieved. Two of those parameters
namely, D and N are shown in Figs. 2B and 2C. All the values hereinafter are shown as mean
± SD. The average value of D and N are 1.37 ± 0.44 µm2/s and 8 ± 2 (441 values)
respectively. The values of the fitted parameters can be viewed as a histogram.
To demonstrate the applicability in live cells, a membrane protein called Epidermal
Growth Factor Receptor (EGFR) fused with EGFP at the C terminus was expressed in CHO
cells using transfection. The average value of D and N are 0.07 ± 0.04 µm2/s and 50 ± 12 (451
values) respectively (Figs. 2D-2F). In contrast to the previous case, not all the curves were
fitted properly. 7% of the curves exhibited bleaching and were not included in computing the
average D and N. This was done by discarding values with diffusion coefficients less than
0.01 µm2/s. Upon inspection, it can be seen that most of these values fall into four distinct
pockets in the D and N map. The regions centered at rows 5, 11 and 21 are characterized by a
sudden rise in intensity lasting for around 2 seconds during the 40 second acquisition period.
The intensity rise is twice the average intensity during all the other times. The sudden increase
in intensity could be attributed to aggregates of fluorescent proteins diffusing on the
membrane. Such problems can be overcome by implementing automatic FCS analysis
algorithms in ImFCS for removal of unwanted peaks corrupting the curves [28]. Half of the
pixels in the region centered at row 2 are characterized by intensities traces which could be
aggregates of fluorophores. On the contrary, the remaining half shows traces which exhibit a
loss in fluorescence with time. This may be the case where the molecule is immobile on the
cell membrane and hence the pixels exhibit bleaching. An option to correct for loss incurred
due to bleaching is available in the software. The details of this option can be found in the
supplement in Sec. 6.
Fluorescent beads were diffusing in solution and were studied using IVA-FCS. The
average value of D and N are 1.1 ± 0.7 µm2/s and 0.01 ± 0.006 (944 values) respectively. 2%
of the curves were not fitted. The theoretical value calculated from the Stokes Einstein’s
equation is 2.4 µm2/s. The deviations from the theoretical model are due to the facts that FCS
#133271 - $15.00 USD Received 12 Aug 2010; revised 21 Oct 2010; accepted 26 Oct 2010; published 22 Nov. 2010(C) 2010 OSA 6 December 2010 / Vol. 18, No. 25 / OPTICS EXPRESS 25475
is sensitive to bright and big particles and beads are prone to aggregation. Particles
comparable to the size of PSF will increase the apparent PSF [9]. The histograms of D and N
are provided in the supplement in Sec.8. The diffusion coefficients obtained in this example
are similar to the D’s obtained using SPIM-FCS [9]. Unlike the case of EGFR on cell
membranes, there are less number of curves which are not fitted. (Figs. 2G-2I). Illumination at
angles lower than the critical angle helps one to perform measurements in 3D environments.
This can be further extended for biological applications where measurements need to be
performed in native state. Different pixels are characterized by different correlation curves.
This variation is due to the inherent variability associated with the system under investigation.
Generally, it is observed that measurements on cells and biological samples have an increased
variability when compared to the measurements on solutions and model membranes. A few
guidelines to perform Imaging FCS are provided in the Sec. 9 of the supplement. A systematic
comparison of diffusion coefficients obtained from Imaging FCS and other fluorescent
techniques is available in Sec. 10 of the supplement.
4.2 Analysis of flow by ΔCCF imaging using ImFCS
ΔCCF imaging is demonstrated on two different systems, those exhibiting isotropic
phenomena like diffusion and anisotropic phenomena like flow. The cross-correlations were
calculated between adjacent pixels. For studying diffusion, a Rho-PE labeled POPC/POPG
(2:1 500 µM) lipid bilayer prepared using the protocol in [8] was used. The forward and
backward correlations for an isotropic process are similar and hence when the correlations are
subtracted, on an average, the area under such curves is zero.
Quantum dots were immobilized to coverslides and moved using a mechanical stage
simulating a flow process. For non-isotropic processes, the correlation in the direction of the
flow, exhibits a maximum at the time it takes to travel from the first region to the second
region being correlated. The intensity observed in any pixel is a sum total of the intensity of
the pixel and the contributions of cross-talk from pixels which are separated from each other
at distances on the order of the PSF. This cross-talk leads to a pseudo-autocorrelation term.
Hence, the correlation in the direction against the flow is a decaying curve which is only due
to the pseudo-autocorrelation between these two regions. When such curves are subtracted,
the area under the resulting curve is a non-zero number.
#133271 - $15.00 USD Received 12 Aug 2010; revised 21 Oct 2010; accepted 26 Oct 2010; published 22 Nov. 2010(C) 2010 OSA 6 December 2010 / Vol. 18, No. 25 / OPTICS EXPRESS 25476
Fig. 2. Diffusion in a fluorescently labeled lipid bilayer was studied using ITIR-FCS. The
entire set of 441 curves and 2 representative correlations are shown in A. The raw data is
shown in grey and the fitted curves are shown in black, the fitted parameters of D and N are
displayed as images in B and C. Diffusion of a fluorescently labeled protein (EGFR-EGFP) on
a living cell membrane was probed by ITIR-FCS. Unlike the previous set, all the curves are not
fitted. These are seen by regions of white pixels in the D and N plots shown in E and F. 2
illustrative curves out of the ensemble are displayed in D. Unlike the previous case, there is
more variability in the shape of the curves and the molecules exhibit a wide range of D values
as seen by the inset in D. G, H and I are measurements of diffusion of beads in solution by
IVA-FCS. The curves were fitted and parameters (D and N) were extracted and displayed as H
and I. 2 typical correlation curves along with the complete group is seen in G.
#133271 - $15.00 USD Received 12 Aug 2010; revised 21 Oct 2010; accepted 26 Oct 2010; published 22 Nov. 2010(C) 2010 OSA 6 December 2010 / Vol. 18, No. 25 / OPTICS EXPRESS 25477
Fig. 3. Forward and backward cross-correlations of an isotropic process (diffusion) and an
anisotropic diffusion (flow) are shown in A and B. 2 distinct populations are seen only in B and
not in A since the forward cross-correlation along the direction of flow exhibit a peak while the
cross-correlation against the direction of flow does not. The forward and backward cross-
correlations in diffusion do not exhibit any differences since diffusion is a random process.
Characteristic forward and backward cross-correlations from the above two processes are
shown in C. The ΔCCF distributions of flow and diffusion are shown in D. Diffusion exhibits a
Gaussian distribution centered at zero while the distribution for flow is centered at a non-zero
number. Hence the ΔCCF distribution can be used as a discriminant to differentiate isotropic
and anisotropic transport. The ΔCCF images of diffusion and flow are shown in A and B as
insets drawn to the same scale.
The distributions of these two processes are shown in Fig. 3. Flow being an anisotropic
process, shows two distinct populations of curves, the populations being the forward and the
backward correlation. On the contrary, the forward and backward correlations overlap each
other in the case of diffusion. Both the distributions are Gaussian which differs in the mean
value. The average values of ΔCCF are 0 ± 0.02 (380 values) and 0.03 ± 0.01 (420 values) for
diffusion and flow respectively. The Gaussian distribution of ΔCCF values of flow has a non-
zero mean characteristic of anisotropic processes. As expected, the SD of ΔCCF values of a
directed flow process is less than that of a random diffusion process. Thus ΔCCF distribution
serves as a way to distinguish processes exhibiting directed transport alone or in combination
with other processes. The reader is referred to Sec. 3.2 in the supplement for a theoretical
treatment of the above phenomena.
4.3 Analysis of diffusion and flow by ITIR-FCCS and SPIM-FCCS using ImFCS
In most of the cases, it is found that diffusion and flow processes are always seen in
conjunction. This was the primary motive behind defining the fitting model as a generalized
function to describe both processes. Imaging FCS was used to probe diffusion and flow
processes together. As a model system, a Rho-PE labeled POPC bilayer was moved using a
microscope stage and ITIR-FCCS measurements were performed. To extend the applicability
#133271 - $15.00 USD Received 12 Aug 2010; revised 21 Oct 2010; accepted 26 Oct 2010; published 22 Nov. 2010(C) 2010 OSA 6 December 2010 / Vol. 18, No. 25 / OPTICS EXPRESS 25478
of Imaging FCS to real, complex 3D environments; SPIM-FCS was used to study the
diffusion of fluorescent beads injected into a zebrafish embryo.
All the curves were fitted with Eq. [S3] in the case of the model system described above.
The average D and N obtained are 1.65 ± 0.48 µm2/s and 152 ± 20 (400 values) respectively.
As expected, the coefficients of variation (mean/SD) of the above two values are small since a
model system is being studied here. Apart from the D value, the system is characterized by the
velocity which is found to be 9.92 ± 0.11 µm/s (400 values). The microscope stage was
moved at a speed of 10 µm/s and the expected and obtained values are close to each other.
These values were obtained by fitting the autocorrelation data.
Please note that the autocorrelation expression as given in Eq. [S3] is an even function in
both vx and vy. Hence the autocorrelation cannot reveal the direction of the flow and the cross
correlation needs to be calculated which is not an even function in vx and vy. The cross-
correlation of the pixel in the center was performed with 4 other pixels, one each along the co-
ordinate axes separated from the center pixel by 4 pixel units. The cross-correlation curves
with pixels separated by 4 pixel units along the positive and negative y axis are identical and
close to the background noise. This indicates that there is no flow along these directions. On
the contrary, the cross-correlation curves of the center pixel with pixels separated by 4 pixel
units along the positive and negative x axis are different from each other. The cross-
correlation along the positive x axis shows a peak characteristic of processes exhibiting flow,
indicating the fact that the flow is along this axis. This is supported by the fact that, the cross-
correlation along the negative x axis is insignificant. This flow velocity in magnitude and
direction is displayed as an arrow plot.
To demonstrate the applicability of analyzing coupled diffusion and flow data in
biological systems, SPIM-FCCS was performed in the veins in a zebrafish embryo by
injecting fluorescent beads. The average D and N of the beads were found to be 1.18 ± 0.7
µm2/s and 0.38 ± 0.19 (356 values). 11% of the curves were not fitted. The curves which were
not fitted fall into 2 main regions, the regions in the top left and the region in the bottom
middle (Figs. 4H-4J). The curves in the top left region do not fit because there is no blood
flow in the top region as seen in the time-series raw data. The absence of flow in that region,
leads to correlation curves which are characteristic of diffusion only. As a result, the fitting
model fails to fit the data properly. The curves at the bottom middle failed to converge.
To obtain vectorial information about blood flow, the direction of flow is determined by
computing the cross-correlations. The four cross-correlations described in the previous case
were determined. The cross-correlations along x axis show that the flow is along the negative
x axis since a peak is seen only along this curve and not in the other. Unlike the case above,
where the flow was only along one of the directions, the flow here had a component along the
y axis as well. By similar reasoning, it was concluded that the flow is along the negative y
axis. This is confirmed by visual inspection of the time series movie from which the
correlations were calculated. The flow is at an angle of 45° from the horizontal. This agrees
with the finding the velocity has both x and y components. The exact angle was computed by
tan1(vy/vx). The magnitude and direction of the flow velocity was found to be (13 ± 5 µm/s)
and (44 ± 15°) respectively.
#133271 - $15.00 USD Received 12 Aug 2010; revised 21 Oct 2010; accepted 26 Oct 2010; published 22 Nov. 2010(C) 2010 OSA 6 December 2010 / Vol. 18, No. 25 / OPTICS EXPRESS 25479
Fig. 4. ITIR-FCCS and SPIM-FCCS provide vectorial information. A fluorescently labeled
lipid bilayer was moved using a microscope stage to simulate processes exhibiting both
diffusion and flow and was studied using ITIR-FCS (A-E). Beads were injected into the vein of
living zebra fish embryo and studied by SPIM-FCS (F-J). The autocorrelations (raw data-grey,
fitted curve–black) were fitted and D and N were obtained as seen in A(F), C(H), and D(I). To
identify the direction of flow, 4 different cross-correlations were performed in B and G. The
velocity in magnitude and direction is depicted as arrow plots in E and J.
#133271 - $15.00 USD Received 12 Aug 2010; revised 21 Oct 2010; accepted 26 Oct 2010; published 22 Nov. 2010(C) 2010 OSA 6 December 2010 / Vol. 18, No. 25 / OPTICS EXPRESS 25480
5. Conclusion
Camera based FCS technologies provide the user with a multiplexing advantage and can be
used to probe dynamics on 2D model/cell membranes and 3D living cells/embryos. Here,
ImFCS, an open source software is described which is a data analysis software to evaluate
image stacks acquired in imaging FCS. The software calculates a variety of spatiotemporal
auto- and cross-correlations and differences between spatial forward and backward cross-
correlations. Quantitative vectorial parameters can be retrieved by curve fitting using the
software. Selected applications of the software were demonstrated on data acquired using 3
different modes of imaging FCS (ITIR-FCS, IVA-FCS and SPIM-FCS). This user-interactive
and fast open-source software to evaluate imaging FCS data makes the analysis easier and
accessible for a larger community interested in the dynamic behavior of molecules in model
and living systems.
6. Supplementary material
The computational aspects of the program are described in detail in the supplement. The
supplement, the manual to the program ImFCS, the source code in VC++ .net2003 and the
Igor Pro Procedure files are available at http://staff.science.nus.edu.sg/~chmwt/ImFCS.html.
Acknowledgements
The authors thank Lin Guo for his help in sample preparation and imaging. The authors thank
Dr. Hwee Kuan Lee (Bioinformatics Institute, Singapore) and Dr. Joachim Wuttke
(Forschungszentrum Juelich GmbH) for helpful discussions. TW acknowledges funding from
the Alexander von Humboldt Foundation. This work was supported by a grant from the
Ministry of Education of Singapore (R-143-000-358-112). JS is supported by a scholarship of
the Singapore-MIT Alliance.
#133271 - $15.00 USD Received 12 Aug 2010; revised 21 Oct 2010; accepted 26 Oct 2010; published 22 Nov. 2010(C) 2010 OSA 6 December 2010 / Vol. 18, No. 25 / OPTICS EXPRESS 25481
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