SESIÓN DE APRENDIZAJE Nº 2 I DATOS INFORMATIVOS

The phases of the clock and cell cycle signals were calculated using Equation 7.3. θ= tan−1 ( c dc/dt ) (7.3) where c is the fitted clock or FUCCI signal. Figure 7.7a illustrates the relationship between the oscillating signal and the phase.

The division times were obtained from the LineageTracker software, taken from the positions of branches in the lineage data structure (Appendix A.2.1). The phases of each oscillator were obtained at these timepoints.

Given that the FUCCI markers indicate the phase of the cell cycle, it is expected that the cell divisions occur at defined phases of the FUCCI signals (at the end of the M-phase). This is illustrated in Figure 7.7b, where the division time, as obtained from the lineage data, occurred during the steep drop in the S-G2-M marker.

The phases were measured for all 39 divisions identified earlier. Figure 7.8a displays the phases of the FUCCI cycle for all divisions. Since the cell divisions occur during the drop in S-G2-M, it would be expected that the measured phases would be between 4 and 2π. All of the divisions did occur within, or close to, this range: below 0.5 radians (equivalent to 27◦) or above 4.2 (245◦). The divisions occurred while the G1 signal was in the phase range 1.84–3.33 (equivalent to 105.5◦–190.6◦).

The phases of the clock at point of division are shown in Figure 7.8b. Although divisions occur at all phases of the clock, most are concentrated in a peak between 2–4 radians.

A Rayleigh Test was performed to test whether the phase distribution of the divisions is randomly distributed. Lower p-values from this test indicate that the data exhibits a unimodal deviation from uniformity [138]. The results from the FUCCI measurements (Figure 7.8a) are 5.7×10−9 _{for the G1 signal and}

2.0×10−12 _{for the S-G2-M signal. Low values such as these verify that the}

measurements are reporting realistic or consistent phase angles since divisions will only occur at the termination of the M-phase.

0 2 4 6 8 P h a s e time (minutes) 0 500 1000 1500 2000 2500 3000 0.2 0.4 0.6 0.8 1 C lo c k ( fi tt e d )

a) Relationship between signal and phase

0 500 1000 1500 2000 0 200 400 600 800 1000 1200 Time (minutes) Signal Clock (fitted) S−G2−M Divisions

b) Cell division takes place during drop in S-G2-M

Figure 7.7: a) Phase (in radians, from 0→2π) takes the form of a sawtooth wave. b) Sudden drop in the S-G2-M FUCCI marker from a single cell during division. Times of division are indicated by red circles over the FUCCI signal.

5 10 30 210 60 240 90 270 120 300 150 330 180 0 G1 S−G2−M

a) Phase of FUCCI marker at division

5 10 30 210 60 240 90 270 120 300 150 330 180 0 Clock Phase

b) Clock phase at cell division

Figure 7.8: Phases of the FUCCI marker and cell cycle at division. a) The phases of the G1 and S-G2-M FUCCI markers at the point of division. b) The phase of the clock marker at division.

The Rayleigh p-value obtained from the Circadian signal was 1.2×10−6_.

This indicates that divisions do not occur uniformly throughout the circadian cycle but since this is higher than the p-values for the FUCCI signals, the distribution is not as narrow.

7.4

Circadian and Cell Cycles are not indepen-

dent of each other

Although the durations of the circadian and FUCCI oscillations were found to be unrelated, the cell divisions predominantly occurred during a restricted range of phases of the clock. This is in agreement to previous studies [139] which have observed that divisions occur preferentially at particular times of day, and is contrary to the observations of Yeom et.al [24].

Chapter 8

Discussion

The cell segmentation and tracking methods described here are similar to methods which have been published elsewhere [50, 81, 82, 84, 91, 92, 140] but the implementation is unique in that it provides a flexibility to choose from a range of methods (similar to CellProfiler [59]) but with the novel feature of interactive modifications to the segmentation, tracking and lineages.

Since a automated system rarely reaches 100% accuracy compared to ground- truth data, the ability to correct the automatic analysis will increase the numbers of cells available for analysis and allow complete timecourses and lineages to be obtained for cells which would be impossible to analyse otherwise, such as the Zebrafish FUCCI cells described in Chapter 7 where the low contrast between cells and background pose too great a challenge for automatic segmentation.

The original analysis methods were developed for Hoechst-stained C2C12 cells but a change in circumstances during the PhD resulted in the necessity of applying the software to other cell types. Few changes were required to allow the segmentation and tracking to perform successfully onSz.pombe cells, the major modifications being to the lineage construction element of the tracking, since the movement of the nuclei during mitosis were largely constrained along the cell axis, different daughter cell identification methods were required. Ultimately the software demonstrated its utility and flexibility in the analysis of 4 different cell types, extracting fluorescence timecourse, lineage and oscillatory information from the cells.

approach, where different parts of the task are handled as separate steps. This allows different methods to be used as more sophisticated techniques become available. The first step in segmentation is cell detection which uses two very simple operations, a Gaussian convolution followed by maxima detection. This provides a very rapid cell detection which, as shown in Chapter 5, also leads to good accuracy. The high cell densities and rapid motion rule out methods which rely on cell positions or shape within a previous frame, as often utilised in active- contour segmentation and tracking systems. The cell detection can perform poorly if a bright cell overlaps a faint cell, where the Gaussian convolution can mask the maxima which would be present from the fainter companion. Situations such as these remain challenging to any segmentation method.

The tracking system is also implemented as a two stage modular system where the first stage builds the transition matrix while the second module assigns the trajectories based on the matrix. A similar approach is used by a number of other systems [46, 50, 57], where short tracks are often created then linked together to create full lineages. The current system solves the optimisation problem for each frame by creating single links connecting adjacent frames. It may be possible to solve the global tracking for multiple frames but this may be impractical for large populations where the computational cost will rapidly rise to unmanageable levels.

8.1

LineageTracker is a unique solution to HTS

The LineageTracker software described here attempts to solve a problem which is addressed by other software, such as CellProfiler. One disadvantage with existing systems is the lack of ability to correct mistakes made by the computer. There have been attempts at solving this problem by rejecting unreliable tracks [108] but this increases overall accuracy at the expense of volume of data. The interactive data viewer in LineageTracker allows any inevitable segmentation or tracking errors to be corrected, increasing both quantity and quality of data, the tradeoff being time required for analysis.

The analysis of circadian systems in single cells is reliant on the accurate measurement of fluorescent oscillators in those cells. While LineageTracker was in development, a dedicated circadian analysis package was released [85] which

was also based around ImageJ. While the latter software would seem to offer sufficient tools to enable it to be used in the C5Sys analysis, the handling of cell division was incomplete, with only a single daughter being followed, which would restrict its use where lineage construction is required.

New software has recently (September 2011) been made available which provides a similar solution. Cell Evaluator [141] utilises seed based or threshold based segmentation and tracking is provided by minimising a cost matrix in a similar manner as described in Section 3.4.8. This software works in a similar manner to LineageTracker: it is installed as an ImageJ plugin but largely operates as a self-contained application. Additionally it provides rudimentary cell editing to correct for errors made by the segmentation algorithms.