AUTOMATIC QUANTIFICATION OF MICROTUBULE DYNAMICS Stathis Hadjidemetriou, James S. Duncan, Derek Toomre, and David Tuck Yale University, Department of Electrical Engineering and Diagnostic Radiology, Department of Cell Biology, Department of Pathology-Pathology Informatics New Haven, CT 06520 stathis, duncan@noodle.med.yale.edu,
[email protected],
[email protected] ABSTRACT The dynamics of the microtubule assembly are very significant both for cell function and structure. Abnormal function of the assembly is involved in neurodegenerative diseases and cancer. Currently, microtubule dynamics are typically analyzed manually, which is time consuming and limiting. We present an algorithm that quantifies the microtubule dynamics automatically. The quantification becomes simpler, easier, and more extensive. We examine the sensitivity of the algorithm using phantom as well as real data. 1. INTRODUCTION Microtubules are biopolymers. The starting point is close to the nucleus, and the ending point, the tip, is close to the cell cortex [1]. The microtubules are responsible both for cell function and structure. For example, they form the elongated axons of neurons. The microtubule tips is the most dynamic part of the assembly and is significant for many microtubule functions. Some of the functions in which the microtubules are involved are protein transport, cell polarity, cell migration, and mitosis [1]. Abnormalities in the microtubule assembly are involved in neurodegenerative diseases such as Alzheimer’s disease [2]. Also, abnormal cell division and migration can lead to cancer growth and metastasis [3]. Anticancer drugs, such as Taxol , act by targeting and stabilizing the microtubule assembly. Several novel anticancer drugs under clinical development, such as taxanes and epothilones, have a similar effect on the assembly [3]. Targeting microtubules, however, is also neurotoxic. Elucidating the effects of these novel compounds on microtubule dynamics might lead to improvements in the therapeutic index with reduced toxicity. To achieve this we have developed an algorithm that quantifies the dynamics of the microtubule assembly automatically in epifluorescent confocal microscopy of -tubulin. It enables simple, fast, and extensive quantification of the tip dynamics. The main design objective of the algorithm is to be robust with respect to the low signal to noise ratio
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caused by the attenuating fluorescence as well as the low interframe time required to capture the motion. We demonstrate and examine the sensitivity of the algorithm with respect to microtubule curvature, intersection angle between microtubules, and image noise with phantom and real data. The statistics of the microtubule tips are typically computed from manually annotated microscopy video sequences. This approach is time consuming and limiting. Many algorithms exist to track the motion of single molecules, cell particles [4, 5], as well as entire cells [6]. Motion tracking and compensation has also been significant at the organ imaging level, for example, for the motion of the lungs, the heart [7], and the retina, as well as tissue growth over longitudinal 4D data [8]. In a more general context, motion estimation has been used for video compression [9], body motion tracking, and vehicle tracking [10]. Motion estimation is also related to the problem of registration [6]. There has also been work on segmenting typically tree structured, stationary, curvilinear structures. For example, vasculature, the bronchial tree [11], and roads in remote sensing. Such algorithms often use edge detectors, corner detectors, and rely on spatial connectivity. Some algorithms also require the specification of the end points of the elongated structures [12].
2. METHOD All video frames are first preprocessed to decrease noise. The microtubules are then segmented in an arbitrary frame. To achieve this a clear initial point in each microtubule is automatically selected. Each point iteratively gives a stack of points representing a microtubule. The iteration steps first predict the next point and then adapt the prediction based on the image intensities. The iteration ends when adapted points lie in the background, or a maximum number of steps is exceeded. The motion of each microtubule is tracked in positive and negative time. The union of the microtubules and their motion gives the dynamics of the assembly. Finally, the dynamics of the assembly are quantified.
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2.1. Preprocessing We enhance microtubule regions with matched filters, , where is the orientation. The filter is shown in Figure 1. The shape of the filters is elliptical with eccentricity . The length of the major axis is , where is the width of a microtubule. The filters are positive within of the major axis and the remaining two regions are negative, with . Twenty of these filters with Æ orientations , where , were applied to all video frames.
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Matched filtering of each video frame, , of size , and time index , gives a stack of twenty filtered images. The stack of images is given by , where . We take the maximum over , to get the enhanced image . Fig , where ure 2 (a) and Figure 2 (c) show two original image frames. The corresponding enhanced images are in Figure 2 (b) and Figure 2 (d), respectively.
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Fig. 1. Horizontal matched filter.
2.2. Segmentation of Microtubules The extracellular region is set to zero in all frames ,
. The background is also set to zero by histogram thresholding. The image pixels above the threshold maintain their original values. The inner part of the microtubule assembly is very dense. Individual microtubules cannot be discriminated in 3D space and intensity with simple epifluorescent confocal microscopy and the resolution of the CCD. Thus, we null the inner part of the assembly. To achieve this we select a frame , where and approximate it with a sum of Gaussian distributions: , where are the coefficients of the Gaussians . The optimal values of ,
are estimated with expectation maximization. First, we set to zero the region of inside a circle whose center is the center of the cell and the peak of is on its periphery. Second, we set to zero the region of within an isointensity contour of that encloses 40% of the . The same regions are set to zero in the entire sequence, , .
(a) Inner region and selected (b) Inner region and selected band from starting frame band from starting frame of first sequence. of second sequence. Fig. 3. Original image and selected band.
Subsequently, we select an isointensity contour that corresponds to the outer region of the cell. We form a band around this contour of width and superimpose it upon . Figure 3 (a) and Figure 3 (b) show the inner regions set to zero as well as the selected bands. These images correspond to the images in Figure 2 (a) and Figure 2 (c), respectively. To segment the microtubules we start from pixels of maximum intensity in the band and proceed iteratively both toward the interior and exterior of . Each direction gives a segment of the microtubule expressed as a stack of points, as shown in Figure 4 (a). At each iteration we compute a predicted direction of angle , which is a weighted sum of microtubule tangents close to the tip. During adaptation we compute probabilities for several directions located symmetrically around . These directions, shown in Figure 4, are given by Æ , where . The probability , where depends on the correlation, , of the image with a rectangular window model of the microtubules, shown in Figure 4 (a). The window size is
(a) Starting frame of first sequence.
(b) Enhanced starting frame of first sequence.
(c) Starting frame of second sequence.
(d) Enhanced starting frame of second sequence.
Fig. 2. Two original frames from two different video sequences and the corresponding enhanced versions.
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dated position is given by . The tip can be polymerizing, depolymerizing or be stable [13]. We model this by computing the correlation with a window both behind and in front of the topmost point on the stack. The latter process is described in subsection 2.2. We possibly add or delete a point from the stack. The last step of the algorithm is to measure the position and velocity of the microtubule tips. We also superimpose and display the segmented microtubules on the video sequence.
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(a) Segmenting the microtubule with two stacks of points.
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(b) Lateral motion and tip motion tracking. Fig. 4. Segmenting in (a), and tracking the lateral and tip motion of the microtubule in (b).
, the orientation of its major axis is , and its starting point is the topmost point on the stack. A Gaussian prior
, so that is also a factor in the probability of an orientation. That is, . If , a new point is added to the stack along such that . The new point is given by , where is a fixed step
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size. Finally, we concatenate the two stacks to form a single stack for each microtubule, as shown in Figure 4 (b).
2.3. Motion Tracking and Output Measures We track the motion of each microtubule between consecu, and . We assume that tive frames in microtubule points move along the normal as shown in Figure 4 (b). To update the position of each point we use a variable step size , where . The probability of each step, , depends on the correlation, , of the image with a rectangular window model of the microtubule, shown in Figure 4 (b). The window is centered at and its major axis is parallel to the microtubule tangent, . The probability of a point also depends on a Gaussian prior , so that . That is, . We compute such that . The up-
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We used two phantom sequences. Both sequences consist of twenty frames of size . Each pixel of the sequence was corrupted with uncorrelated Gaussian noise of standard deviation of the maximum intensity corresponding to the microtubules. The microtubules are represented as sinu
and of amplitude six. soids of frequency The starting frame of the first sequence, the frame, is shown in Figure 5 (a). The algorithm correctly segments . It fails to the microtubules up to frequency segment part of the blue microtubule of the maximum fre . Figure 5 (b) shows the microtubules segquency, mented in the frame of the first sequence. Figure 5 (c) shows the trajectories and velocities of the tips in the entire sequence. The starting frame of the second sequence, the frame, is shown in Figure 5 (d). Figure 5 (e) shows the microtubules segmented in the last frame of the second sequence. The dark green microtubule is segmented only partly. Figure 5 (f) shows the trajectories and velocities of the tips in the entire sequence.
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Fig. 5. Segmented microtubules (MTs) together with their tip trajectories and velocities for two phantom sequences. In Figure 6 we show the application of the algorithm to two real sequences. The sequences show in vivo fibroblast
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or epithelial cells. Both sequences consist of twenty frames. In the first sequence the interframe time is 10 s and frame size is . In the second sequence the interframe time is 5 s and frame size is . The actual width of an individual microtubule is 25 nm. The width in the sequences is 2-3 pixels. The spatial resolution was approximately 10nm per pixel. Figure 6 (a) shows the microtubules segmented in the frame of the first sequence. The starting frame of this sequence, the frame, is shown in Figure 2 (a). Figure 6 (b) shows the trajectories and velocities of the tips in the entire sequence. The starting frame, the frame, of the second sequence is shown in Figure 2 (c). The segmentation results and statistics of the second sequence are shown in Figure 6 (c) and Figure 6 (d), respectively.
Subsequently we tracked their motion and quantified their tip statistics. We evaluated the algorithm with phantom as well as real sequences.
5. REFERENCES [1] E.D.P. De Robertis and E.M.F. De Robertis, Cell and Molecular Biology, Lea & Febiger, 1987. [2] M. Hutton, J. Lewis, D. Dickinson S.H. Yen, and E. McGowan, “Analysis of tauopathies with transgenic mice,” Trends in Molecular Medicine, vol. 7, no. 10, pp. 467–470, 2001. [3] L.A. Amos and J. Lowe, “How Taxol stabilizes microtubule structure,” Chemistry & Biology, vol. 6, no. 3, pp. 65–69, 1999. [4] M.K. Cheezum, W.F. Walker, and W.H. Guilford, “Quantitative comparison of algorithms for tracking single fluorescent particles,” Biophysical Journal, vol. 81, pp. 2378–2388, 2001.
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[5] G. Danuser, P.T. Tran, and E.D. Salmon, “Tracking differential interference contrast diffraction line images with nanometre sensitivity,” Journal of Microscopy, vol. 198, no. 1, pp. 34–53, 1999.
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[7] X. Papademetris, A.J. Sinusas, D.P. Dione, R.T. Constable, and J.S. Duncan, “Estimation of 3-D left ventricular deformation from medical images using biomechanical models,” IEEE Trans. on Medical Imaging, vol. 21, no. 7, pp. 786– 800, 2002.
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[6] S. Shemlon and S. Hawkins, “Non-rigid image alignment for layered cell representation and motion tracking,” in Proc. of the IEEE Northeast Bioengineering Conference, 1996, pp. 125–126.
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Fig. 6. Segmented microtubules together with their tip trajectories and velocities for two real sequences. Both the phantom and real sequences show that the algorithm is robust to noise. The first sequence also shows that the algorithm is robust to curvature. The second phantom sequence, however, shows that resolving microtubule intersections is a more difficult problem. 4. SUMMARY Microtubule dynamics are significant for cell structure, function, and understanding pathology. The objective of this work has been to automatically quantify the dynamics in epifluorescent confocal microscopy of -tubulin. To achieve this we first segmented microtubules close to the cell cortex.
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[8] T.J. Hutton, B.F. Buxton, P. Hammond, and H.W.W. Potts, “Estimating average growth trajectories in shape-space using kernel smoothing,” IEEE Trans. on Medical Imaging, vol. 22, no. 6, pp. 747–753, 2003. [9] H.S. Sawhney and S. Ayer, “Compact representations of videos through dominant and multiple motion estimation,” IEEE Trans. on Pattern Analysis and Machine Intelligence, vol. 18, no. 8, pp. 814–830, 1996. [10] J.L. Barron, D.J. Fleet, and S.S. Beauchemin, “Performance of optical flow techniques,” International Journal of Computer Vision, vol. 12, no. 1, pp. 43–77, 1994. [11] Y. Fridman, S.M. Pizer, S. Aylward, and E. Bullitt, “Segmenting 3D branching tubular structures using cores,” in Proc. of MiCCAI, 2003, vol. 2, pp. 570–577. [12] J.M. Geusebroek, A.W.M. Smeulders, and H. Geerts, “A minimum cost approach for segmenting networks of lines,” International Journal of Computer Vision, vol. 43, no. 2, pp. 99–111, 2001. [13] J. Howard and A. Hyman, “Dynamics and mechanics of the microtubule plus end,” Nature, vol. 422, pp. 753–758, 2003.
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