ImFCS: A software for Imaging FCS data analysis and visualization

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

References and links:

1. M. Brinkmeier, K. Dorre, J. Stephan, and M. Eigen, “Two beam cross correlation: A method to characterize

transport phenomena in micrometer-sized structures,” Anal. Chem. 71(3), 609–616 (1999).

2. M. Gösch, A. Serov, T. Anhut, T. Lasser, A. Rochas, P. A. Besse, R. S. Popovic, H. Blom, and R. Rigler,

“Parallel single molecule detection with a fully integrated single-photon 2x2 CMOS detector array,” J. Biomed.

Opt. 9(5), 913–921 (2004).

3. B. Kannan, J. Y. Har, P. Liu, I. Maruyama, J. L. Ding, and T. Wohland, “Electron multiplying charge-coupled

device camera based fluorescence correlation spectroscopy,” Anal. Chem. 78(10), 3444–3451 (2006).

4. M. Burkhardt, and P. Schwille, “Electron multiplying CCD based detection for spatially resolved fluorescence

correlation spectroscopy,” Opt. Express 14(12), 5013–5020 (2006).

5. D. R. Sisan, R. Arevalo, C. Graves, R. McAllister, and J. S. Urbach, “Spatially resolved fluorescence correlation

spectroscopy using a spinning disk confocal microscope,” Biophys. J. 91(11), 4241–4252 (2006).

6. B. Kannan, L. Guo, T. Sudhaharan, S. Ahmed, I. Maruyama, and T. Wohland, “Spatially resolved total internal

reflection fluorescence correlation microscopy using an electron multiplying charge-coupled device camera,”

Anal. Chem. 79(12), 4463–4470 (2007).

7. L. Guo, J. Y. Har, J. Sankaran, Y. M. Hong, B. Kannan, and T. Wohland, “Molecular diffusion measurement in

lipid bilayers over wide concentration ranges: a comparative study,” ChemPhysChem 9(5), 721–728 (2008).

8. J. Sankaran, M. Manna, L. Guo, R. Kraut, and T. Wohland, “Diffusion, transport, and cell membrane

organization investigated by imaging fluorescence cross-correlation spectroscopy,” Biophys. J. 97(9), 2630–2639

(2009).

9. T. Wohland, X. Shi, J. Sankaran, and E. H. K. Stelzer, “Single plane illumination fluorescence correlation

spectroscopy (SPIM-FCS) probes inhomogeneous three-dimensional environments,” Opt. Express 18(10),

10627–10641 (2010).

#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 25468

10. M. Matsumoto, T. Sugiura, and K. Minato, “Spatially resolved fluorescence correlation spectroscopy based on

electron multiplying CCD - art. no. 663017,” in Confocal, Multiphoton, and Nonlinear Microscopic Imaging III,

T. Wilson, and A. Periasamy, eds. (2007), pp. 63017–63017.

11. M. Matsumoto, T. Sugiura, and K. Minato, “Illumination by Near-Critical-Angle Incidence for Imaging

Fluorescence Correlation Spectroscopy with Electron-Multiplying Charge-Coupled Device Camera,” Jpn. J.

Appl. Phys. 49(6), 060208 (2010).

12. D. J. Needleman, Y. Xu, and T. J. Mitchison, “Pin-hole array correlation imaging: highly parallel fluorescence

correlation spectroscopy,” Biophys. J. 96(12), 5050–5059 (2009).

13. J. Huisken, J. Swoger, F. Del Bene, J. Wittbrodt, and E. H. K. Stelzer, “Optical sectioning deep inside live

embryos by selective plane illumination microscopy,” Science 305(5686), 1007–1009 (2004).

14. R. Rigler, H. Vogel, Z. Petrášek, and P. Schwille, “Scanning Fluorescence Correlation Spectroscopy,” in Single

Molecules and Nanotechnology (Springer Berlin Heidelberg, 2008), pp. 83–105.

15. “Tiff 6.0 specification,” http://partners.adobe.com/public/developer/en/tiff/TIFF6.pdf.

16. W. S. Rasband, “ImageJ,” (U. S. National Institutes of Health, Bethesda, Maryland, USA,

http://rsb.info.nih.gov/ij/, 1997–2009).

17. K. Schaetzel, and R. Peters, “Noise on multiple-tau photon correlation data,” S. S. Kenneth, ed., (SPIE, 1991),

pp. 109–115.

18. T. Wohland, R. Rigler, and H. Vogel, “The standard deviation in fluorescence correlation spectroscopy,”

Biophys. J. 80(6), 2987–2999 (2001).

19. X. Shi, and T. Wohland, “Fluorescence Correlation Spectroscopy,” in Nanoscopy and Multidimensional Optical

Fluorescence Microscopy A. Diaspro, ed. (CRC Press, 2010).

20. W. Press, B. Flannery, S. Teukolsky, and W. Vetterling, Numerical Recipes in C: The Art of Scientific

Computing (Cambridge University Press, 1992).

21. B. Zhang, J. Zerubia, and J.-C. Olivo-Marin, “Gaussian approximations of fluorescence microscope point-spread

function models,” Appl. Opt. 46(10), 1819–1829 (2007).

22. B. Zhang, J. Zerubia, and J. C. Olivo-Marin, “A study of Gaussian approximations of fluorescence microscopy

PSF models - art. no. 60900K,” in Conference on Three-Dimensional and Multidimensional Microscopy - Image

Acquisition and Processing XIII, J. A. Conchello, C. J. Cogswell, and T. Wilson, eds., (SPIE, San Jose, CA,

2006), pp. K900–K900.

23. J. Ries, E. P. Petrov, and P. Schwille, “Total internal reflection fluorescence correlation spectroscopy: effects of

lateral diffusion and surface-generated fluorescence,” Biophys. J. 95(1), 390–399 (2008).

24. D. Freedman, and P. Diaconis, “On the histogram as a density estimator-L2 theory,” Probab. Theory Relat. Fields

57, 453–476 (1981).

25. C. A. Konopka, and S. Y. Bednarek, “Variable-angle epifluorescence microscopy: a new way to look at protein

dynamics in the plant cell cortex,” Plant J. 53(1), 186–196 (2008).

26. M. Tokunaga, N. Imamoto, and K. Sakata-Sogawa, “Highly inclined thin illumination enables clear single-

molecule imaging in cells,” Nat. Methods 5(2), 159–161 (2008).

27. M. Tokunga, N. Imamoto, and K. Sakata-Sogawa, “Addendum: Highly inclined thin illumination enables clear

single-molecule imaging in cells,” Nat. Methods 5(5), 455–455 (2008).

28. J. Ries, M. Bayer, G. Csúcs, R. Dirkx, M. Solimena, H. Ewers, and P. Schwille, “Automated suppression of

sample-related artifacts in Fluorescence Correlation Spectroscopy,” Opt. Express 18(11), 11073–11082 (2010).

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


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


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


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


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).


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.


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


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.


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.


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


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.


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.


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.


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ImFCS: A software for Imaging FCS data analysis and visualization

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