Automated quantification of cell endocytosis using active contours and wavelets. A. Dufour1, V. Meas-Yedid1, A. Grassart2 and J.-C. Olivo-Marin1.
Automated quantification of cell endocytosis using active contours and wavelets A. Dufour1 , V. Meas-Yedid1 , A. Grassart2 and J.-C. Olivo-Marin1 Institut Pasteur, CNRS URA 2582, 25-28 rue du Dr. Roux, 75015 Paris, France 1 Quantitative Image Analysis Unit, 2 Biology of Cell Interactions Unit {adufour,vmeasyed,jcolivo}@pasteur.fr
Abstract Cellular endocytosis is a mechanism of great interest in biology, for it regulates the communication between the cell and the external medium. With recent advances in fluorescence microscopy, endocytosis has become a popular candidate for image-based high content screening campains. In this context, we have developped an automated framework comprising robust cell segmentation using coupled shape-constrained active contours and efficient endosome extraction using an isotropic undecimated wavelet transform. The resulting method has few parameters and is able to analyze tens of cells per image in the order of seconds. Validation is performed by experimentally confirming previously published results obtained through manual analysis.
eters such as endosome count per cell and fluorescence intensity. We start by presenting the cell segmentation step in section 2, which is based on active contour models. Then, we describe in section 3 the endosome extraction method based on an isotropic undecimated wavelets transform (IUWT). Section 4 presents results on biological data, where we show that we obtain similar results to those published in recent work using manual analysis [3]. Finally, section 5 concludes the paper and discusses further extensions to this work in order to provide a robust and generic tool for endocytosis-based high-content screening applications.
2. Automated multi-cell segmentation
1. Introduction
This section describes the active contour model used to automatically extract the cell boundaries. We first recall the main principles of active contour models and then describe our segmentation method.
Receptor-mediated endocytosis allows cells to communicate with their environment via membrane receptors which transport macromolecules form the extracellular medium to intracellular compartement named endosomes. This phenomenon is now easily observable using fluorescence microscopy, however due to the lack of adapted algorithms and softwares, image analysis is usually performed by visual examination, which is a tedious task, time consuming, user-biased and provides poor quantitative measurements. Although new tools have been developped to quantitatively measure multiple features on individal cells (e.g. cycle, size, intensity, localization of subcellar compartments, etc.), none of them currently focuses on celullar endocytosis in an efficient, intuitive and automated manner. In this paper, we propose a fully automated method to detect cells and evaluate the endocytosis of IL-2 receptors (IL-2R) in Hep2β cells through quantitative param-
Recall on active contours The principal of active contours is to deform an initial contour placed on the image until it fits the boundary of the desired entity. The deformation can be mathematically expressed as the minimization of an energy functional, which comprises several terms related either to the image data (driving the contour toward features of interest) or to geometrical properties of the contour (regularizing the deformation to avoid local energy minima). Active contours come in two mathematical forms. Implicit models (also known as level sets [6]) express the contour as the zero-level of a higher dimensional function defined on the image domain. Explicit models (also known as snakes [4]) consider the contour as a parametric curve which is discretized into a set of control points evolving in the image domain. Thanks to their topological flexibility, level sets are well suited to segment an unknown number of non-touching objects using a sin-
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gle contour. In our case however, cells are clustered and would thus not be distinguished, unless multiple coupled level sets are employed [8], increasing the computational load substancially. Snakes are naturally rigid regarding topology, which suits our context, and have a lower complexity, yielding faster performance for a same number of contours. Initialization Using multiple active contours requires a specific initialization for each contour in the image, often provided manually for clustered objects. We propose to automatize this step using prior knowledge on the biological protocol. Cells are stained such that the nucleus appears brighter than the cytoplasm. Ideally, clustered cells would be distinguished by a simple threshold with the nuclei intensity. However, due to imperfect imaging conditions, intensity varies across the image, causing a global threshold to fail. Instead, we start by quantizing the image into N intensity classes using the K-Means algorithm, and produce a binary image for each threshold. Then, for each threshold in ascending order, objects smaller than a given value (e.g. the maximum nucleus size) are extracted from the binary image, polygonized into a contour, and erased from the remaining binary images to avoid duplicate extractions. This method is fast and robust since the maximum nucleus size is known a priori, and initialization results converge for increasing values of N (N > 6 in our experiments). Contour deformation The contours deformation toward cell boundaries is obtained by minimizing an energy functional of the form: E(C1..n , I) = λEI + µER + γEC + δES ,
(1)
where C1..n are the contours evolving on image I and λ, µ, γ, δ are non-negative empirical weights. EI is a data attachment term combining region information through the Mumford-Shah functional and edge information through image intensity gradients. ER is a regularizer (in the Tikhonov sense) that smooths the contours geometry during its deformation to avoid local energy minima. EC is a coupling term that penalizes overlaps between contours. These three first terms have been successfully employed in biological imaging ([9][10]), but are not sufficient to correctly determine the contact location between cells (cf. fig. 3). To improve contact localization, we have introduced in (1) a new term ES that will monitor the contour shape during its deformation. This term expresses our prior biological knowledge that Hep2β cells are generally elongated, and thus constrains each contour deformation along its major axis. For each
contour, this term reads Z ES (C) = e(C) 0
1
~ g N (p) · ~a1 dp,
(2)
where g is a positive definite non-increasing function, ~ is the outer normal to the contour at point p and e is N the contour eccentricity ratio computed p from the major axis ~a1 and minor axis ~a2 by e , ||~a1 ||2 − ||~a2 ||2 /2. Minimizing this term tends to constrain contour points to remain close to the main contour axis. The eccentricity ratio regularizes the shape constraint by cancelling its effect for circular contours (i.e. non-elongated cells). Contour evolution is then performed using a classical Euler-Lagrange gradient descent scheme, yielding an iterative deformation process where each contour point is progressively displaced by a force combining the four terms of eq. (1). Convergence is detected individually for each contour when the overall deformation falls under a small value close to 0.
3. Spots detection by IUWT filtering The fluorescence-labeled endosomes generally appear as small specific spots superimposed on an unspecific background. A number of methods have been proposed to detect and characterize spots in an automated manner, but none of them provides satisfactory answers on biological images. This can be explained by the fact that spots have an inhomogeneous grey level distribution over the image while, at the same time, the image may present a complex and non-uniform background. In [5], a multiresolution algorithm has been presented to handle these problems. It is based on an isotropic undecimated wavelet transform (IUWT) of the image and on the selective filtering of wavelet coefficients. Spot detection Three specificities are exploited: 1) the inherent adaptiveness of the analysis to the object size, 2) the correlation of the wavelet coefficients of an object across consecutive scales and 3) the low computational cost that allows fast reconstruction. The basic idea is to reconstruct the image from the thresholded wavelet bands such that the spots are denoised and enhanced. The wavelet scaling (approximation) bands is set to zero so that the smooth background is not reconstructed. Following the method proposed in [5], we consider that the spots are features of interest represented by a small number of coefficients, that are both large and correlated across the scales. On the contrary, the noise has smaller coefficients that do not propagate across levels. The IUWT [7] decomposition scheme is:
¯ ↑j−1 ? aj−1 aj = h dj = aj−1 − aj ,
(3)
where h is a symmetric low-pass filter, aj and dj are respectively the approximation and the wavelet coefficients at scale j (≤ J), h↑k [l] = h[l] if l/2k ∈ Z and 0 ¯ otherwise, h[n] = h[−n] and “?” denotes convolution. Detection of significant coefficients by FDR Wavelet spot detection can be achieved by zero-ing the insignificant coefficients while keeping the significant ones. We detect the significance of coefficients by testing the binary hypothesis: ∀ d, H0 : dj = 0 vs. H1 : dj 6= 0. Since a wavelet has a zero mean, if dj comes from a signal having a constant intensity within the wavelet support, then dj would be zero, if no noise was present. Thus dj ∈ H0 in this case. In order to control a global statistic error rate, multiple hypothesis tests should be used. Therefore, the false discovery rate (FDR) [1] [2] is chosen to control the significance of the wavelet coefficients. The FDR is the average fraction of false detections over the total number of detections. The FDR control has two advantages: 1) it usually has a greater detection power; 2) it can easily handle correlated data. The latter point is important since the IUWT is overcomplete. Finally, we compute the correlation images which corresponds to the multiscale spatial product between the detail images. Once the correlated image is thresholded and binarized, the connected components are considered as putative bright spots.
Figure 1. Sample image of IL-2 receptor endocytosis in Hep2β cells. Top-left: cells. Top-right: endosomes. Bottom-left: mycRac1 mutant. Bottom-right: merged view. fit the cell boundaries correctly, while touching cells are well distinguished. This is due to the incorporation of the new shape constraint, which improves the detection of elliptic shaped objects, as shown in fig.3. Without shape constraint (fig.3-left), contours fail to detect cell edges and contact locations correctly. This behavior is successfully corrected using the shape-constraint described in eq. (2) (fig. 3-right).
4. Experiments & results Imaging Fig.1 shows a multi-channel image of IL-2R endocytosis in Hep2β cells transfected with a Rac1 mutant. The top-left image shows cells labeled with HCS CellMask. The top-right image shows endosomes where IL-2R, labeled with the specific antibody 561 coupled to cy3, has been internalized. The bottom-left image shows transfected cells expressing the myc-Rac1 mutant, labeled with an anti-myc antibody and a secondary mouse antibody coupled to FITC. Images were aquired on a Zeiss Axiovert 200 epifluorescence microscope equipped with a 25× objective (NA 0,8) and a Roper Scientific Coolsnap HQ Camera. Images are obtained from three different experiments. A total of 96 images were obtained under the same acquisition settings, yielding around 800 cells. Cell segmentation Fig.2 presents segmentation results on the HCS labeled image (fig.1-top-left). Since the fluorescence marking is inhomogeneous and difficult to see, we superimpose the result on a maximum gradient map of the image, where real cell contours are easier to distinguish visually. One can see that the contours
Figure 2. Left: initialization on the HCS labeled image. Right: final contours superimposed on a gradient map of the image.
Figure 3. Segmentation results on touching cells. Left: without shape constraint. Right: with shape constraint.
Spots detection Fig.4-top-right shows spot detection results, which are robust to the variability of biological images and to the high level of noise. To validate the method, we quantified the endocytosis of IL-2R for two different cell populations, and compare the results with those published in [3]. The first population correspond to transfected cells expressing a myc-Rac1 mutant (known to inhibit endocytosis). The second population corresponds to control cells which do not express the mutant. To automatically sort the two populations, we use the K-means algorithm to cluster the cells mean intensity into 3 classes, so as to capture weakly transfected cells (an example of cell transfection is shown in fig.4-bottom-left). For the three experiments, 194 cells were found to be transfected and 594 were not, and the expression of myc-Rac1 mutant inhibited 38%±10.5 (mean ± standard deviation) of IL-2Rb entry as compared with the non-transfected cells. These results are similar to the previous published results [3] based on manual analysis. Processing time ranged from 5 to 10 seconds per image using a 2.4 GHz dual-core cpu, including initialization, cells segmentation and endosomes extraction, by comparison with manual analysis which takes from 5 to 10 minutes. The time mostly depends on the number of cells per image. 10 seconds is the worst case time needed for an image full of cells (around 30 cells).
Figure 4. Results on clustered cells. Topleft: IL-2R endosomes. Top-right: spot detection results. Bottom-left: myc-Rac1 mutant transfection. Bottom-right: cell segmentation results.
5. Conclusion and perspectives We have developped an automated framework for multiple cell segmentation and spot detection for the quantitative analysis of cell endocytosis. Segmentation is performed using multiple coupled active contours, to which we have added a shape-constraint to monitor the contours deformation according to our prior knowledge of the cells shape. Endosome extraction is performed using an isotropic undecimated wavelet transform, and a selective statistical filtering of the wavelet coefficients. Results show that the method is able to detect cells boundaries fast and efficiently, even in case of touching cells. Quantitative results coincide with previously published work on manual analysis, proving that the method is suited for larger-scale experiments, and more particularly high-content-screening campains. We can exploit the results to provide more accurate quantitative data, such as spatial distribution of the endosomes.
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