Characterizing the spatio-temporal behavior of cell populations

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					                                                                                                          Research Reports

      Characterizing the spatio-temporal behavior
        of cell populations through image auto-
           and cross-correlation microscopy
                                Noël Bonnet, Franck Delavoie, and Jean-Marie Zahm

                                                    BioTechniques 43:107-114 (July 2007)
                                                          doi 10.2144/000112478

     We propose two methods for characterizing the spatio-temporal behavior of cell populations in culture. The first method, image
     auto-correlation microscopy (IACM), allows us to characterize the variation in the number of objects as a function of time, thus
     enabling the quantification of the clustering properties of cell populations to be performed. The second method, image cross-
     correlation microscopy (ICCM), allows us to characterize the migration properties of cell populations. The latter method does
     not require estimation or measurement of the trajectories of individual cells, which is very demanding when populations of >100
     cells are examined. The capabilities of the two methods are demonstrated with simulated cell populations, and their usefulness is
     illustrated with experiments involving invasive and noninvasive tumor cell populations.

INTRODUCTION                                   point-of-view, the quantitative charac-             The aim of the work presented here
                                               terization of these different properties        is to find an alternative to the tracking
    In different physio-pathological           (formation of clusters and migration)           of individual cells in order to quantify
situations, such as embryogenesis,             is usually very demanding.                      the migration characteristics of cell
wound repair, and tumor invasion,                  To quantify the agglomerative               populations in culture. The main idea
isolated cells or cell populations             behavior implies that the coordinates           is to consider the whole set of cells in
exhibit changes to their normal                of all cells must be known. Since the           the field-of-view of a microscope at
behavior. Studying the spatio-temporal         automatic detection of cells in a field-        once rather than considering each cell
behavior of cell populations in cultures       of-view containing one or several               individually, and to perform statistics
provides a way to assess alterations           hundred cells is not obvious, this often        while computing parameters rather
in their functions in relation to the          means that the user has to pick these           than applying statistical analysis after
mechanisms leading to pathology. This          cell coordinates interactively with a           computing these parameters.
behavior is generally complex and              pointing device.                                    The method we propose is an
involves different processes such as               To quantify the migration character-        extension to cell populations of a
migration, aggregation, proliferation,         istics of cells is even more demanding,         method originally proposed for the
adhesion, and spreading.                       since the knowledge of cell coordinates         characterization of biomolecules.
    Here, we will concentrate on the           in all the images of a temporal series is       This method, image correlation
first two of these aspects: aggregation        not sufficient. What is necessary is the        spectroscopy (ICS), is itself an
and migration. In the general context          coordinates of each cell as a function          extension of another method called
of tumor metastasis, we are involved           of time. In principle, this data could          fluorescence correlation spectroscopy
in the study of the specific behavior          be obtained by tracking procedures.             (FCS). FCS was developed to
of invasive cells compared with that           However, again, automatic tracking              estimate macromolecule transport
of noninvasive cells. We have previ-           procedures are not reliably able to cope        and concentration properties via the
ously shown that the sociological              with dense populations of cells located         auto-correlation analysis of a temporal
behavior of these two populations of           very close to each other, especially            signal—the fluorescence amplitude
cells is fundamentally different (1–3).        when non-directed migration is                  variation arising from spontaneous
Starting from a random seeding,                involved. Thus, we often rely on inter-         fluctuations in molecular occupation
noninvasive cells have a tendency to           active tracking of cells rather than            number within a small volume (4–6).
form clusters, while invasive cells tend       on automatic tracking. This is a very               ICS has the same goal as FCS, but
to remain isolated. From a practical           tedious, error-prone procedure.                 relies on spatial fluctuations recorded

                            UMRS, Inserm 514, Université de Reims Champagne-Ardenne, Reims, France

Vol. 43 ı No. 1 ı 2007                                                               ı BioTechniques ı 107
Research Reports

through a series of images (7–10). The        Imaging
                                                                                                 →                  →
acronym STICS, for spatio-temporal                                                       where x = (x,y) and x i = (xi ,yi).
image-correlation spectroscopy,                   One hour after seeding, the culture    The auto-correlation of image k can be
has also been used (11,12). Since             dish was placed on the stage of a Zeiss    written as:
the acronym ICS was not very well             Axiovert 200 inverted microscope
adapted to the technique it represents,       (Zeiss, Oberkochen, Germany) and
                                              enclosed in a small transparent culture                    � I k �x, y �.� I k �x � � , y � � �
a new acronym, ICM (image-corre-                                                         ACk �� ,� � �                              2
lation microscopy), was suggested             chamber with 5% CO2 in air at 37°C.                                    I k � x, y �
(13). Here, we adopt this terminology.        Image sequences were recorded at
It should also be mentioned that the          10× magnification with a sampling
idea of using image cross-correlation         rate of one image per minute for up                                                       [Eq.2]
to characterize migration of molecules        to 17 h. The high-sampling frequency
was described previously (14,15).             was useful to build movies that helped     where
                                              us to interpret the behavior of cell
                                                                                                     r          r          r
                                              populations on a qualitative basis.             � I k �x � � I k �x � � I k �x � �
MATERIALS AND METHODS                         One image out of 20, corresponding
                                              to a time interval of 20 min, was then
                                              analyzed quantitatively. The coordi-       and 〈.〉 represents the mean of the
Cell Cultures                                 nates of the center of each cell in the    bracketed quantity.
                                              field-of-view were determined. For             In fact, we will show below that it is
   The human bronchial cell lines used
                                              the phase contrast images used in this     better to work on an image that reflects
in this study, 16HBE14o- (16HBE)
and BZR, were derived from normal             study, we found that manual processing     the
                                                                                         ~ local density of cells (denoted
                                              (i.e., mouse clicking) provided results    I k (x,y)), rather than on the image
human bronchial cells immortalized
                                              with better confidence than automatic      composed of Dirac delta functions.
after transfection with the simian virus
                                              segmentation, owing to the difficulty in   Equation 2 can be rewritten using the
40 (SV40) large T-antigen gene. The
                                              segmenting such images.                    local cell density I k
BZR cell line was also infected with
the v-Ha-ras oncogene. The human                                                                         � I k �x, y �.� I k �x � � , y � � �
                                                                                                           %             %
mammary epithelial cell line MCF-7            Simulations                                ACk �� ,� � �                              2
was obtained from ATCC (accession                                                                                    I k �x, y �
no. HTB-22; Manassas, VA, USA).                   Besides the analysis of live-cell
These cell lines display different            data, sequences of images simulated
invasive potentials in vitro, as well         with well-known characteristics were                                                      [Eq. 3]
as tumorigenicity and metastatic              analyzed in order to check the capabil-
ability in athymic nude mice. Cells           ities of the proposed method. Using the       This local density of cells can
were cultured in a 5% CO2 fully               simulator previously described (17),       be obtained by the so-called Parzen
humidified atmosphere at 37°C in              we could model the formation of cell       method (18), convolving the point
Dulbecco’s modified Eagle’s medium            clusters as a function of time and any     distribution of cells with a kernel:
(DMEM) (Gibco®; Invitrogen, Grand             combination of directed migration and
Island, NY, USA) supplemented with            random diffusion, with different distri-                    Nk
penicillin, streptomycin, and 10%             butions of migration speed.                      % r                r r
                                                                                               I k �x � � � Ker � x � xi ��
fetal calf serum. Into each culture dish                                                                     i �1
(diameter 3.5 cm), 2 × 105 cells/mL           Image Auto-Correlation
were plated.                                  Analysis (or Microscopy)
   In order to further check the validity                                                                                               [Eq. 4]
of our approach, we also submitted               We consider that all the Nk cells
BZR-invasive cells to the main                                                           where Ker(.) is a normalized kernel
                                              present in the field-of-view of each
polyphenolic component of green                                                          function. Although other kernel
                                              image (k) have been marked: every
tea, epigallocatechin-gallate (EGCG).                                                    functions could also be used [e.g., the
                                              cell is represented by a “white” pixel
Since many studies associated EGCG                                                       Epanechnikov kernel (19)], the choice
                                              located at the center of that cell. So,
with inhibition of cancer metastasis                                                     of a Gaussian kernel can be justified
                                              the kth image of the sequence can
(16), we expect it could also inhibit                                                    by its similarity with what is obtained
                                              be described by a set of Dirac delta
the migratory behavior of invasive                                                       experimentally in the traditional ICS.
cell lines such as BZR (unpublished                                                      Gaussian kernels were also used for
data). EGCG was therefore added to                                                       computer simulations of scanning
                                                                 Nk                      fluorescence-correlation spectroscopy
                                                           r          r r
cell cultures at concentrations of 5
μg/mL and 7.5 μg/mL, respectively.
                                                      I k �x � � � � �x � xi ��          experiments (20). Note that the kernel
                                                                i �1                     size σ is an important parameter
                                                                                         that will be the subject of further
                                                                              [Eq. 1]    discussion.

108 ı BioTechniques ı                                                                         Vol. 43 ı No. 1 ı 2007
                                                                                                                                   Research Reports

    Several characteristics of the cell             Image Cross-Correlation
distribution can be obtained from the               Analysis (or Microscopy)                                         where α stands for the anomalous
full auto-correlation function ACk (ξ,η),                                                                            diffusion parameter: α = 1 corresponds
such as the number of objects in the                   The migration properties of the cell                          to a normal diffusion process, α < 1
image and the mean size of these                    populations can be estimated through                             to sub-diffusion, and α > 1 to super-
objects.                                            the computation of cross-correlation                             diffusion (24,25).
    As was demonstrated previously                  functions associated with pairs of
in the context of ICS (7,21,22), the                images, recorded at different time                                   Model C:
amplitude value of the auto-corre-                  settings.
lation function at the origin is inversely             Again, it is better to work with cells
proportional to the number of objects               represented by a kernel or, alterna-                                 < d 2 (t) > = 4D.t + S 2.t 2
present in image k:                                 tively, a disc. Thus the cross-correlation                                                                      [Eq. 10]
                                                    function can be written as:
   ACk (0,0) ≈ 1 / Nk                                                                                                   Model C makes explicit the two
                                                                        � I k1 �x, y �.� I k 2 �x � � , y � � �
                                                                          %              %                           possible contributions to migration,
                                          [Eq. 5]   CCk1, k 2 �� ,� � �                                         �    the first term on the right hand side
                                                                              I �x, y � . I �x, y �
                                                                                                                     representing diffusion, with a diffusion
   When the auto-correlation function                                                                                coefficient D, and the second term
is computed for all the images of the                                                                [Eq. 7]         representing directed migration, with
temporal series, one can deduce the                                                                                  migration speed S (24,26).
evolution of the number of objects as a                Considering the cross-correlation                                For each of these migration models,
function of time (i.e., of the process of           between different pairs of images, we                            a model for the variation of the cross-
cluster formation):                                 now end up with a function of time,                              correlation decay function has been
                                                    CC(ξ,η,t), where t = (k 2 - k 1).Δt . The                        devised (11,13,27) as follows:
                                                    position (ξmax,ηmax) and value (CCmax) of
     ˆ        ˆ
     N (t ) � N (k .�t ) � 1 / AC k (0,0) �         the maximum of this two-dimensional                                  Model A (13):
                                                    function can be used for the character-
where Δt is the time interval between               ization of the migration properties. The                                                            1
                                                    position of the maximum (ξmax,ηmax)                                      CCmax (t ) � CC0                 � CC� �
two image acquisitions, and N stands                                                                                                                      t
                                                    indicates the amount of directed                                                                1�
for the estimated value of N.                                                                                                                            �D
   More precisely, in order to cope with            migration (see Equation 10) that takes
proliferation, the existence of clusters            place in the experiment. The variation                                                                          [Eq. 11]
can be ascertained by comparing the                 of the maximum value (CCmax) as a
number of objects estimated through                 function of time provides information
the auto-correlation of the density of              related to the diffusion characteristics                         where CC0 + CC∞ = CCmax(t = 0) and
objects [Nσ(t)] with the number of                  of the phenomena. For capturing this                             τ D is the characteristic diffusion time.
elementary objects (i.e., the number                information, we have to model the
of cells) N0(t). We can define a cluster            function CCmax(t).                                                   Model B (27):
index as:                                              Many models have been proposed
                                                    for describing the mean quadratic
                         ˆ                          displacement < d2 (t) > as a function                                                   1                     1
                         N� (t )                    of time. We considered the following                             CCmax (t ) � CC0             � CC� � CC0            � CC� �
            CI� (t ) �            �                                                                                                     1 � A.t �                 �
                                                                                                                                                              1 � 2 .t �
                         N 0 (t )                   three models:                                                                                                �

                                          [Eq. 6]       Model A:
                                                                                                                                                                    [Eq. 12]
   At this stage, it is appropriate to                   <d (t) > = 4D [t-P.exp(-t/P)]

specify our definition of a cluster
in this context. Clearly, if we were                                                                 [Eq. 8]         where ω is the e-2 radius of the Gaussian
working with cells characterized by                                                                                  kernel function (hence, ω = 2σ).
the coordinates of a single pixel (Dirac            where P is the directional persistence
delta functions), clusters could not be             time and D = (S 2P) /2, where S is the                               Model C (11):
considered. This justifies the repre-               average speed (23).
                                                                                                                                                  �                     �
sentation of a cell by a local kernel                                                                                                             � � S .t � 2 1        �
instead. Of course, the existence of                    Model B:                                                      CCmax (t ) � CC0
                                                                                                                                             .exp � � � 2 � .           � � CC� �
                                                                                                                                       1�         � � � � 1� t          �
clusters is clearly dependent upon the                                                                                                    �D      �
                                                                                                                                                  �             �D      �
kernel size σ: the number of objects
decreases when the size of the kernel is                < d 2 (t) > = 4D.tα = Γ.t α
increased.                                                                                           [Eq. 9]                                                        [Eq. 13]

Vol. 43 ı No. 1 ı 2007                                                                                     ı BioTechniques ı 109
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                                                        Model B:                                invasive potentials in vitro as well
                                                                                                as tumorigenicity in athymic nude
                                                                                                mice. This could be a consequence
                                                            DICCM � � / 4 � A� 2 �
                                                                             .                  of a difference in the expression of
                                                                                                adhesion molecules: 16HBE cells
                                                                                                express membranous E-cadherin and
                                                                                    [Eq. 15]    β-catenin, while BZR cells do not
                                                                                                express E-cadherin and present a
                                                     where, again, 2σ is assumed to play the    cytoplasmic localization of β-catenin.
                                                     same role as the e-2 radius of the laser   In addition, the shape of these cells is
                                                     beam.                                      very different: 16HBE cells display
                                                        To validate the suggested approach,     an epithelial cuboidal shape, while
                                                     these estimated effective diffusion        BZR cells display a mesenchymal
                                                     coefficients DICCM should be compared,     elongated shape.
                                                     at least qualitatively, to the diffusion      The image auto-correlation
                                                     coefficients (called D<d >) estimated
                                                                                                approach was applied to real
                                                     through cell tracking procedures.          temporal sequences of these invasive
                                                                                                and noninvasive cell lines (data not
                                                                                                shown). In Figure 3, the estimated
                                                     RESULTS                                    density of objects (individual cells
                                                                                                and clusters) is displayed as a function
                                                     Characterization of Cluster                of time for two different values of the
                                                     Formation by Image Auto-                   Gaussian kernel standard deviation
                                                     Correlation Analysis                       (σ = 8 and σ = 16 pixels). It is also
Figure 1. Snapshots of simulated temporal                                                       compared with the density of objects
image series and corresponding local density            Simulations. We simulated               counted manually. As can be seen,
maps. (A–C) Cells move randomly in the field-
                                                     image series where cells are moving        the results indicate that whatever the
of-view. (A′–C′) Corresponding local cell densi-
ty, computed according to the Parzen method [the     but remain isolated (simulating
kernel has a two-dimensional (2-D) Gaussian          invasive cells), and other image series    A
shape with a standard deviation of 16 pixels         where cells form clusters (simulating
(i.e. 16/512 of the image size)]. (D–F) Cells at-    noninvasive cells).
tract each other and thus form clusters. (D′–F′)
Corresponding local cell density.
                                                        Figure 1 displays some images
                                                     selected from two such series and
where the different terms have the same              the image function (local density)
meaning as previously stated.                        used to compute the correlation
   From the estimated parameters (τD for             functions. The standard deviation
Models A and C, Γ or A for Model B), we              of the Gaussian kernel was equal to
defined an effective diffusion coefficient           16 pixels, for a field-of-view of 512 ×
according to the following relations:                512 pixels.
                                                        Figure 2 shows the number of            B
   Models A and C:                                   objects (isolated cells and clusters)
                                                     estimated as a function of time and as
                                                     a function of the kernel size (standard
   DICCM = σ 2/τ D                                   deviation 8 and 16 pixels). As can
                                                     be seen, the method clearly differ-
                                          [Eq. 14]   entiates the case of invasive cells,
                                                     where the number of detected objects
where σ stands for the standard                      remains constant as a function of
deviation of the Gaussian kernel.                    time (Figure 2A), from the case of
   This relation comes from the usual                noninvasive cells where the number
relation between                                     of objects diminishes as a function of     Figure 2. Density of objects estimated as a
                                                     time (Figure 2B), due to the formation     function of time for simulations. (A) Without
                              w2                                                                attraction nor repulsion, the density of objects
   D and τ D (i.e., D �           �   )              of clusters.                               remains approximately constant. (B) With at-
                             4� D
                                                        Analysis of live-cell data. The         traction, the density of objects is reduced as a
when w is the e-2 radius of the Gaussian             behavior of invasive and noninvasive       function of time, as a result of cluster formation.
kernel function. Within this approach,               cells (BZR and 16HBE, respectively)        In both cases, the two curves correspond to two
                                                                                                sizes of the kernel used to compute the local den-
the kernel function is assumed to play               was studied as a function of time.         sity of objects (the plain curve corresponds to the
the same role as the focused laser beam              These two cell lines were previously       smallest kernel size, σ = 8 pixels, and the dashed
in confocal experiments.                             described (1): they display different      curve to the largest kernel size, σ = 16 pixels).

110 ı BioTechniques ı                                                                                Vol. 43 ı No. 1 ı 2007
                                                                                                                                                                                                                                                                                                              Research Reports

A                                                    speed defined. We simulated four                                                                                                                        true for other values of the kernel size
                                                     image series, with maximum speeds                                                                                                                       (data not shown).
                                                     of 5, 10, 15, and 20 spatial units (i.e.,                                                                                                                  Modeling CCmax(t) with Equations
                                                     pixels) per time unit. Then we inves-                                                                                                                   11–13, we were able to estimate
                                                     tigated whether our proposed image                                                                                                                      different values of the diffusion
                                                     cross correlation microscopy (ICCM)                                                                                                                     parameter D ICCM. Simultaneously,
                                                     method is able to differentiate these                                                                                                                   we estimated the diffusion coeffi-
                                                     four different situations.                                                                                                                              cient through the computation and
                                                        The results from ICCM, CCmax(t),                                                                                                                     modeling of the mean quadratic
                                                     are displayed in Figure 4A for the                                                                                                                      displacement. All three models could
B                                                    four situations (different migration                                                                                                                    be fitted very well and gave similar
                                                     speeds), and one value of the Gaussian                                                                                                                  results for the estimated value of
                                                     kernel size (standard deviation) equal                                                                                                                  the diffusion coefficient D <d > (the                                                                                                   2

                                                     to 16 spatial units from a field-of-                                                                                                                    relative difference between minimum
                                                     view of 512 × 512 spatial units. It                                                                                                                     and maximum estimated values
                                                     appears that the four situations can                                                                                                                    was approximately 20%). It should
                                                     be clearly differentiated. The same is                                                                                                                  be mentioned that the modeling
                                                                                                                                                                                                             according to Model C did not show

                                                      A                                                                                                                                               B
Figure 3. Evolution of the estimated density of                                                                                         ��������������������������������������������
                                                                                                                                                                                                                                                                                                    �������������������������������������������� ��

                                                                                                                                                                                                                 � �� ���� � �� � ���� � ��� � � ��� �� ��� ���� ��� � ���
objects (individual cells + clusters) as a func-

tion of time, for (A) invasive BZR cells and                                                                                                                  speed=5 pixels/time step

(B) noninvasive 16HBE14o- (16HBE) cells.                                                                                          ���                             ��������������������                                                                                                                      A

The two curves in each graph represent the esti-


mations obtained with a Gaussian Parzen kernel
                                                                                                                                  ���                                                ����                                                                                                      ��
with a standard deviation equal to 8 pixels (plain
curves) and 16 pixels (dashed curves). The num-                                                                                   ���
ber of objects counted manually is also displayed                                                                                                                                                                                                                                              ��
as triangle symbols.                                                                                                                                                                                                                                                                                  ����
                                                                                                                                                 ���������������������                                                                                                                         ��

                                                                                                                                    �        �        �      �       �         ��        ��   ��
                                                                                                                                                      ����������������������                                                                                                                     �           ��      ��        ��         ��         ��
kernel size, the number of objects                                                                                                                                                                                                                                                                     ������������������� ����������������������
remains approximately constant for
invasive cells (i.e., BZR cells) while
                                                     C                                                                                  �������������������������������������������� ��
                                                                                                                                                                                                      D                                                                                                                                          �
                                                                      � �� ���� � �� � ���� � ��� � � ��� �� ��� ���� ��� � ���

                                                                                                                                                                                                                   � � � � � � � � � � � � � � � � � � � � � � � � � � ������������� � � � �

                                                                                                                                                                                                                                                                                                     �������������������������������������������� �
                                                                                                                                  ��                                                                                                                                                           ��
it diminishes for noninvasive cells

                                                                                                                                                                                                                       ����������������������������� � � � � � � � �

(i.e., 16HBE cells). This illustrates                                                                                                            B
                                                                                                                                           ��������                                                                                                                                                          C
                                                                                                                                  ��                                                                                                                                                           ��
the fact that invasive cells remain

                                                                                                                                                                                                                         �                                                 �

isolated while noninvasive cells                                                                                                  ��                                                                                                                                                           ��
form clusters with passage of time.
This result corroborates our previous                                                                                             ��                                                                                                                                                           ��
results obtained with a completely
different approach, using tools from                                                                                              ��                                                                                                                                                           ��

algorithmic geometry (1).
                                                                                                                                   �                                                                                                                                                            �
                                                                                                                                    �            ��        ��            ��         ��        ��                                                                                                 �          ��        ��        ��         ��        ��
                                                                                                                                           ������������������� ����������������������              �����                                                                                                ������������������� ����������������������
Characterization of Migration
Properties by Image Cross-
Correlation Analysis
                                                     Figure 4. Results from the image cross-correlation microscopy (ICCM) procedure applied
                                                     to a simulated dataset. (A) Evolution of the cross-correlation coefficient CCmax(t), as a function
   Simulations. We simulated series                  of the time delay between image pairs, for simulated image series. The four curves correspond to
of images where cells were allowed                   four values of the migration speed S. (B–D) Scatterplots relating the values of DICCM, estimated via
to move at different speeds. More                    ICCM, to the values of D〈d 〉, estimated via the modeling of the mean quadratic distance <d2(t)>, for        2

specifically, the parameter we define                four simulated image series, repeated five times. Rectangles represent the means plus or minus the
is the maximum speed at which                        standard deviations. The cross-correlation analyses, repeated for two values of the Gaussian kernel
                                                     standard deviation: σ = 8 (× symbol and plain line rectangles) and σ = 16 (symbol + and dotted line
cells are allowed to move. Then, the                 rectangles) are displayed. The scatterplot is displayed for the three models described in the text: (B)
migration speed of each individual                   Model A, (C) Model B, and (D) Model C. The oblique line represents the perfect correlation.
cell is chosen randomly, at each time
step, between zero and the maximum
Vol. 43 ı No. 1 ı 2007                                                                                                                                                                       ı BioTechniques ı 111
Research Reports

                                       A                                                                                              B
                                                                                     Experimental and fitted cross-                                                                          D estimated from ICCM vs D estimated from <d2>
                                                                                        correlation coefficient                                                                         3

                                                                                                                                      D eD testimated ffrom ICCMM ( µ/min) i n )
                                                                                                                                                                                                Model A

                                                                                                                                         s i m a t e d r o m I C C (�m m2 / m

                        normalized cross-correlation

                                                                                                          BZ R

                                                                                                                                                                                       1.5               BZ R
                                                                                                                                                                                         0               0.5              1             1.5
                                                                                                time (x100 mn)                                                                                    D estimated from <d2> (µm2/min)

                        C                                                         D estimated from ICCM vs D estimated from <d2>                  D                                          D estimated from ICCM vs D estimated from <d2>
                                                                             3                                                                                                          3
                                                                                                                                      D e s t iestimated rfrom ICCM (�m m2 / m i n )
                        D e s t iestimated rfrom ICCM (�m m2 / m i n )

                                                                                    Model B                                                                                                     Model C
                            D m a t e d f o m I C C M ( µ /min)

                                                                                                                                          D m a t e d f o m I C C M ( µ /min)

                                                                         2.5                                                                                                           2.5


                                                                             2                                                                                                          2

                                                                         1.5                                                                                                           1.5

                                                                             1                                                                                                          1

                                                                         0.5                                                                                                           0.5

                                                                             0                                                                                                          0
                                                                              0                 0.5              1              1.5                                                      0               0.5             1              1.5
                                                                                         D estimated from <d2> (µm /min)                                                                          D estimated from <d2> (µm2/min)

Figure 5. Cross-correlation analysis of temporal image series of three cell populations; 16HBE14o- (16HBE;∇), BZR (®), and MCF7 (Ο). (A) Evolution
of the cross-correlation coefficient CCmax(t), as a function of time delay between image pairs. The continuous curves represent the data modeled using Equation
11; the dashed curve for 16HBE cells, the plain curve for BZR cells, and the dotted curve for MCF7 cells. The three curves were normalized to CC(t = 0) in
order to facilitate display. (B–D) Scatterplots relating values of the diffusion coefficient DICCM, estimated via the image cross-correlation approach to values of
the diffusion coefficient D〈d 〉, estimated through the cell tracking procedure for the three cell populations. D was estimated for Models A, B, and C, which are

described in the text. (B) Model A, (C) Model B, and (D) Model C. DICCM was estimated for two values of σ: σ = 8 (open symbols), and σ = 16 pixel units (filled
symbols). The oblique line represents the perfect correlation.

evidence of directed motion and the                                                                        do not claim that the method allows us                                                                cantly in terms of migration speeds. This
modeling according to Model B led                                                                          to estimate the diffusion coefficient on                                                              result corroborates a result obtained
to an estimated value of the exponent                                                                      an absolute basis.                                                                                    previously using a different approach
α between 0.92 and 1.09, close to                                                                             Analysis of live-cell data. Three cell                                                             (i.e., by quantifying the migration
normal diffusion.                                                                                          populations in culture were considered:                                                               speed of individual cells) (2). We also
   Figure 4, B–D display the scatter-                                                                      the BZR and 16HBE cell populations                                                                    note that the behavior of these two cell
plots of the values of D<d > and the                                                 2                     already considered for their different                                                                populations is notably different from
values of DICCM for the different situa-                                                                   clustering behavior and another cell                                                                  the behavior of the MCF7 population.
tions described above (i.e., for different                                                                 population, MCF7, characterized by                                                                    We checked that these results are not
values of the maximum speed allowed                                                                        a very weak motility. The results of                                                                  sensitive to the choice of the kernel
and for different values of the kernel                                                                     ICCM, [i.e. CCmax(t)], are displayed in                                                               shape (i.e., Gaussian, Epanechnikow,
size). The scatterplot is constructed                                                                      Figure 5A for these three cell popula-                                                                Mollifier).
for the three models of diffusion                                                                          tions and for one value of the Gaussian                                                                   We also compared the estimation
mentioned above. These figures show                                                                        kernel standard deviation (σ = 16 pixel                                                               of DICCM obtained by ICCM with the
that there is a good proportionality                                                                       units). We note that the BZR and 16HBE                                                                estimation of D<d >. The results are

between the estimated values of D<d >                                                                 2    populations display a similar behavior,                                                               displayed in Figure 5, B–D, for two
and DICCM. However, at this stage, we                                                                      indicating that they do not differ signifi-

112 ı BioTechniques ı                                                                                                                                                                                                   Vol. 43 ı No. 1 ı 2007
                                                                                                Research Reports

values of the Gaussian kernel standard     time, this reflects the formation of       and a larger estimated diffusion
deviation, σ = 8 and σ = 16 pixel units.   clusters. We were able to show that        coefficient). As a consequence, we
   It should be stressed that the          the IACM procedure can be used             cannot claim that we can estimate the
discrepancy in the values of D <d >   2    to demonstrate the significantly           diffusion coefficient on an absolute
estimated from the three models of         different behavior of noninvasive and      basis. We expect that in the future
<d2(t)> was significantly higher than      invasive cells—the former showing          we will be able to define an optimum
for the simulations, but the corre-        a strong tendency to form clusters,        value of the kernel parameter. For the
lation remains highly positive. For        while the latter having a strong           time being, we assume that a kernel
the specific case of the BZR cell line,    tendency to remain isolated. We think      size close to the cell size (i.e., a
we think that the strong discrepancy       that this new approach can be used to      radius of 8–10 pixels with our exper-
comes more from a problem in the           complement other approaches, such          imental conditions) is a reasonable
estimation of D <d > (a bad fit was
                    2                      as computational geometry and point        approximation. For the simula-
observed) than from a problem in the       fields statistics.                         tions and the live-cell experiments,
estimation of DICCM. Empirically, the         ICCM consists of computing the          this value provided the better
correlation appears to be better for σ     cross-correlation coefficient between      agreement for the comparison of the
= 8 than for σ = 16 pixel units.           the spatial cell densities within          two groups of methods (cell tracking
                                           consecutive images of a temporal           and cross-correlation).
Effect of EGCG on the                      series. The rate of decrease of this          The only claim we can make
                                           cross-correlation coefficient can          based on this work is that, provided
Migration of BZR Cells
                                           be related to an equivalent of the         our estimations are always made
   Preliminary results relative to the     diffusion coefficient, at least qualita-   under very similar conditions, we
effect of EGCG on the migration of         tively. Contrary to traditional methods    can compare the diffusion coefficient
invasive BZR cells can be summa-           for estimating the diffusion coeffi-       estimated for different cell popula-
rized as follows. The diffusion            cient, this method does not require        tions, or with the same cell population

coefficient, estimated according to        tracking individual cells, but only the    in different conditions. We plan to
the ICCM procedure (Models A and           position of all cells in the field-of-     apply the method for testing the
C), of BZR cells, is estimated to be 1     view, which we consider to be a great      effects of molecules involved in the
μm2/min. When EGCG at a concen-            advantage. We demonstrated that            phenotypic transformation of cells
tration of 5 μg/mL is added, the           there is a strong correlation between      (noninvasive toward invasive, or the
diffusion coefficient estimated in the     the diffusion coefficient estimated        converse) and in the inhibition of the
same conditions drops to 0.67 μm 2/        through trajectory estimation (cell        cell migratory behavior. Preliminary
min, and when EGCG is added at a           tracking) and the diffusion coefficient    results enclosed herein show that the
concentration of 7.5 μg/mL, a further      estimated by the ICCM procedure.           method allows to demonstrate the
drop to 0.3 μm2/min is observed.           This correlation was higher for            inhibitory effect of EGCG on the
                                           Models A and C (which are equiv-           migration of invasive BZR cells.
                                           alent when the percentage of directed
DISCUSSION                                 motion is negligible) than for Model
                                           B. The reasons for that remain to          ACKNOWLEDGMENTS
    Throughout this work we have           be elucidated.
tried to evaluate a method that could         One drawback of the ICCM                   All reviewers are warmly thanked
provide estimates of the dynamic           procedure is that the point distri-        for their very helpful comments. We
characteristics of a cell population, in   bution of cells (each cell being           also thank Salma Hazgui for her help
terms of formation of clusters and in      described by the position of its           in the experiments with EGCG.
terms of migration. The method does        center of mass, for instance) has to
not rely on the explicit determination     be replaced by a continuous distri-
of individual cell trajectories, which     bution, each cell being described          COMPETING INTERESTS
is usually very demanding.                 by an extended distribution. Going         STATEMENT
    Image auto-correlation microscopy      from the point distribution to the
(IACM) involves computing the auto-        continuous distribution can be                The authors declare no competing
correlation of the spatial cell density    done through the Parzen approach,          interests.
as a function of time. When the            replacing each point by a kernel.
auto-correlation coefficient remains       Unfortunately but logically, the
constant, this means that the density      estimated values of the number of
of cells also remains constant, which      objects and of the diffusion coeffi-       1. Nawrocki-Raby, B., M. Polette, C. Gilles,
can be interpreted as an absence of        cient depend on the size of the kernel        C. Clavel, K. Strumane, M. Matos,
clustering. When the auto-correlation      used (a larger kernel size induces a          J.-M. Zahm, F. Van Roy, et al. 2001.
coefficient decreases as a function of     smaller estimated number of objects           Quantitative cell dispersion analysis: new
Research Reports

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114 ı BioTechniques ı                                                                                     Vol. 43 ı No. 1 ı 2007