This paper presents a computational algorithm
for the detection and compensation for intracellular
movement in the FRAP experiments with focal adhesions
in living cells. The developed approach is based on the
calculation of correlation coefficient. It was validated on
the series of the experimental datasets and shows the
successful results in the comparison with other widelyestablished
methods

Apanasovich, V.

Friederich, E.

Hadzic, E.

Halavatyi, A.

Lisitsa, Y.

Yatskou, M.

English

Электронная библиотека БГУ

8 
The Correlation-Based Method for the Movement Compensation in 
the Analysis of the Results of FRAP Experiments 
Y. Lisitsa
1
, A. Halavatyi
2
, E. Hadzic
2
, E. Friederich
2
, M. Yatskou
1
, V. Apanasovich
1
 
1) Belarusian State University, Minsk, Belarus, ylisitsa@gmail.com 
2) The University of Luxembourg, Luxembourg, Luxembourg 
 
Abstract: This paper presents a computational algorithm 
for the detection and compensation for intracellular 
movement in the FRAP experiments with focal adhesions 
in living cells. The developed approach is based on the 
calculation of correlation coefficient. It was validated on 
the series of the experimental datasets and shows the 
successful results in the comparison with other widely-
established methods. 
Keywords: correlation, FRAP, cell movement, image 
processing, actin, focal adhesion. 
1. INTRODUCTION  
The cytoskeleton plays a major role in the cell 
motility. Actin forms part of the cytoskeleton in cells and 
is involved in the maintenance of cell shape as well as cell 
dynamics. The active form of actin is a helical polymer, 
called F-actin (F for filamentous), assembled from the 
monomeric subunits of G-actin (G for globular). The actin 
filaments are in the continuous process called 
treadmilling, when the G-actin molecules are added to the 
plus end of the filament and simultaneously they are 
removed from the minus end, without changing the 
filament length. Many proteins take part in the 
treadmilling, some of them are well-established, for 
example, Arp2/3 complex, which initiates new branches 
on the actin filaments, or capping proteins that block the 
growth of the branch of the actin filaments[1]. However, 
there are still a lot of proteins, such as testin, which 
functions in actin cytoskeleton are not well-studied [2]. 
The dynamic characteristac of the actin polimerization 
are studied by the Fluorescence Recovery After 
Photobleaching (FRAP) technique. Typically FRAP is 
used to examine the dynamics of fluorescently-labelled 
macromolecules in the living cells. In the FRAP 
experiment a small region of the fluorescent specimen is 
bleached rapidly (Fig 1A,B). As the photochemical 
bleaching of fluorophores is essentially irrevisible, the 
changes of fluorescent intensity in the bleached and 
unbleached regions are due to the exchange of bleached 
and fluorescent molecules between those regions(Fig 1C). 
Fluorescence recovery is quantified as average 
fluorescence intensity in the bleached region at each 
acquisition time point. The fitting of the recovery curve 
by the solution of the reaction-diffusion equation allows 
to estimate the parameters the intracellular processes, 
which change the mobility of fluorescently-labelled 
molecules (diffusion coefficients, association/dissociation 
rate constants, etc). However the accuracy of this analysis 
depends on the quality of quantification of recovery 
curves, which is very sensitive to the data artefacts due to 
the cell movement or a contamination [3]. 
A method based on modelling the received data with a 
parametric matrix model have been developed recently as 
an attempt to compensate for the image movement [4]. 
However this method is tackled by the definite 
assumption for the single particular experiment. On the 
other hand there are the specific approaches to consider 
the cell movement [5,6]. Nevertheless these methods are 
not well adjusted for to the inhomogeneous fluorescent 
distribution and the studies of the important cell 
structures, such as focal adhesions.  
The aim of our work is the development of an 
automated procedure for the tracking of the movement of 
focal adhesions (the part of the cytoskeleton connecting to 
the extracellular matrix), suitable for the analysis of 
FRAP experiments. The proposed method is based on the 
alignment of the images by finding maximum of the 
correlation coefficient. The developed method was 
implemented as the plugin for ImageJ [7]. We tested our 
method on the collected experimental data and compared 
it with one of the popular tracking methods [5].  
2. EXPERIMENTAL METHODS  
The monkey kidney epithelial Vero cells were 
transfected with the actin-GFP by the electroporation 
method. FRAP experiments with these cells were 
performed with the laser scanning confocal microscope 
(LSM-510 Meta, Carl Zeiss, Jena, Germany) using a 
63x/1.4NA oil-immersion objective. 
In each experiment 20 prebleach images and 400 
postbleach images were acquired with argon laser (488 
nm laser line) and time interval of 1 s between scans. The 
size of every image was 512×128 pixels with 0.14 μm per 
pixel. The circular region for bleaching with the diameter 
(Dr) of 19 pixels was selected on focal adhesion before 
start of acquisition. The bleaching was performed in 0.11 
s with 3 bleaching iterations using the same laser line at 
100% power. The result of every experiment was stored 
as a stack of images in multi-tiff format. 
3. COMPUTATIONAL ALGORITHM 
The developed method is based on the calculation of 
the correlation coefficient (r), which characterises the 
linear dependence between two signals (Eq.1). 







N
i
i
N
i
i
N
i
ii
BBAA
BBAA
r
1
2
1
2
1
)()(
))((
, (1) 
where A={A1,…AN},B={B1,…BN} are studied signals,     
are their mean values. 
Firstly the preparation of the reference image is 
described. Secondly the comparative procedure is 
presented. 
9 
Alternative for the previous paragraph: The algorithm 
consists of the several steps: i) preparation of the 
reference image for last prebleach time point and ii) 
alignment of images for other prime points to the 
prepared reference image. These steps are described in 
detail further. 
Reference image preparation. Because different 
parts of the cell can move differently during the FRAP 
acquisition and the region of the interest (ROI) is smaller 
than 1 percent of the whole image area (I), therefore the 
image comparison was not considered for entire slides in 
the stacks (Fig.1). The shifting was defined only for the 
small region (RI), which contains the ROI (Fig. 2A). The 
linear size of the region (Dr) is considered as the doubled 
size of the ROI (Droi), which means that 25 percent of the 
processing pixels belongs to the ROI. The center of the 
ROI coincides with the center of the RI.  
 
Fig. 1 –The FRAP experiment. A) The first image in the time 
series. B) The first image after bleaching (the 21st time point) 
C) Last acquired image in time series D-F) The enlargement 
of the region (RI) containing the ROI outlined in A with 
white square. 
In the FRAP experiment the intensity recovery in the 
ROI with time occurs because of the diffusion labelled 
molecules, which leads to non-linear increase among the 
pixels in the ROI. In order to prevent the reduction of the 
correlation coefficient because of intensity changes at 
different time points, the intensities of the pixels 
belonging to the ROI are not taken into account by putting 
their intensities to zero. 
The first image acquired after bleaching (S21) was 
used to create the references image (RI). Hence the pixels 
belonging the RI, can be described by Eq.2 
0),(
),(Sy)RI(x, 
) D|>)D-(y| (&) D|>)D-(x| If(
21
roiroiroiroi


yxelseRI
yDYxDX roicroic  (2) 
where Xc, Yc are the coordinates of the centre of the 
bleached region, x,y={0,..,Dr} – coordinates of the 
selected pixel. The prepared reference image (RI) is  
shown on the fig. 2B. 
As the correlation coefficient can be calculated only 
for the one-dimensional arrays, the RI was transformed to 
the one-dimensional reference array (RA) using eq.3.  
}D {0,...,yx,
y)RI(x,=y)+D_r*RA(x
r
 (3) 
The profile for the RA is shown in the Fig. 2C. 
Image alignment.  
Let’s assume that the processing slide (Sk) number is 
k, where k={0,…, 419} and the ROI shifting  during an 
experiment does not exceed the half size of the ROI. Then 
the location of the ROI centre on the Sk can belong the 
area (AREA) as described by eq.4.   
} Y,{X=AREA kjkikij  
i+Y=Yi,+X=X ckjcki  
}D*,0.5…,D*{-0.5=ji, roiroi  
(4) 
For the each position of the centre calculated by the Eq.4 
the pixel intensities for shifted image (PIkij) were found 
by the Eq.5. 
0,=y)PI(x, else
y)+D-Yx,+D-(X S=y)PI(x,
) D|>)D-(y| (&) D|>)D-(x| If(
roikjroikik
roiroiroiroi
 (5) 
 
Fig. 2- Reference image preparation. A) The RI B) The 
pixels belonging the ROI are nulled C) The linear 
interpretation of the RI (Eq,3). 
Then the linear array PAkij containing the PIkij is 
constructed using the Eq. 3. The correlation coefficients 
(Ck(i,j)) are calculated for the each PAkij with the RA by 
Eq.1. The desired shift values (  
        
     
) along both 
axes are determined as the the values of i,j which lead to 
the maximum of the correlation coefficients (Ck(i,j)) 
(Eq.6). 
) j)(i, Cmaxarg(=) J,(I k
j)(i,
shift
k
shift
k  (6) 
4. IMPLEMENTATION 
The algorithm was implemented as the plugin for 
ImageJ [5] with the simple interface shown in the Fig. 3. 
The parameters are set before processing the image time 
series: the number of first postbleach image, the type of 
the bleaching region (square or circle), the size of the 
bleached region in pixels. As the OK button is pressed the 
image processing starts. After the image was analyzed the 
table containing the shift values and the mean intensities 
10 
in the ROI for each slice is automatically generated (Fig. 
3B) 
 
Fig. 3- The interface of plugin for ImageJ. A) Window for 
specification of initial parameters B) The result table 
5. RESULTS 
The developed method was compared with the well-
established method for tracking on the experimental data 
of the actin dynamics at focal adhesions[3]. The set of 
tested images contains 28 undependable stacks, where 
there are four images with the strong contamination, two 
images has the gradual defocusing. The developed 
method showed tracked the movement of focal adhesions 
correctly for 86% of the images. The TurboReg plugin [5] 
has the successfully tracked 79% of images. Both 
methods do not process correctly only one image, for 
which cell parts moved a lot during the experiment.  
All other uncorrected results for the proposed 
approach are received only for the contracting cells, 
which are not usually considered in the further analysis; 
in contrast TurboReg plugin was not resistant to the 
defocusing during time-series acquisition. 
The use of the described tracking algorithm allows to 
improve the representativeness of the received data by 
diminishing effect of the movement of focal adhesions for 
the calculated recovery curves (Fig. 4). 
 
Fig. 4 – The recovery curves with and without compensation 
for the movement of focal adhesion. 
6. REFERENCES 
[1] Creighton T. E. The encyclopedia of molecular 
biology Vol 1-4 T. E. Creighton, A Wiley-Interscience 
Publication: 1999.  
[2] Garvalov B.K., Higgins T.E., Sutherland J.D. et all 
The conformational state of Tes regulates its zyxin-
dependent recruitment to focal adhesion J Cell Biol. 
2003 Apr V.14;161(1):33-9. 
[3] Goldman R. D. Live Cell Imaging: A Laboratory 
Manual, R. D. Goldman, D. L. Spector, Cold Spring 
Harbor Laboratory Press: 2004 p. 239-276 
[4] Pölönen H, Jansen M, Ikonen E, Ruotsalainen U. 
Automatic FRAP Analysis with Inhomogeneous 
Fluorescence Distribution and Movement 
Compensation, Adv Exp Med Biol. 2010;680:717-24.  
[5] Thevenaz P., Ruttimann U. E., Unser M. A pyramind 
Approach to Subpixel Registration Based on Intensity. 
IEEE Transaction on Image Processing V.7 (1). 1998 
Jan.  pp. 27-41  
[6] Y. Lisitsa A. Halavatyi, E. Hadzic, E. Friederich, M. 
Yatskou, V. Apanasovich,  Processing of FRAP 
Images. The proceeding of “International Congress 
on Computer Science: Information Systems and 
Technologies”, Republic of Belarus, Minsk, October' 
31 – November' 3, 2011. pp. 238-242 
[7] Collins TJ. ImageJ for microscopy. Biotechniques. 
2007 Jul;43(1 Suppl):25-30.  
 
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The Correlation-Based Method for the Movement Compensation in the Analysis of the Results of FRAP Experiments

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The Correlation-Based Method for the Movement Compensation in the Analysis of the Results of FRAP Experiments

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