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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 www.biotechniques.com 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. functions: 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 www.biotechniques.com 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 � % k1 % k2 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)] 2 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 � 1 instead. Of course, the existence of Model B: CCmax (t ) � CC0 t .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 www.biotechniques.com ı BioTechniques ı 109 Research Reports 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 2 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 Time 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 www.biotechniques.com 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 www.biotechniques.com 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 2.5 2 MCF7 2 normalized cross-correlation BZ R 1.5 BZ R 16HBE 1 MCF7 0.5 16HBE 0 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 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 2 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 2 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 2 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 www.biotechniques.com 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. 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