Kota Miura

Aim

Analysis of cell shape dynamics before/during the invagination of Drosophila embryo.\ last update: 20110920

Methods

To study the details of cell shape changes during the invagination in Drosophila, each cell should be segmented. Image sequences were preprocessed and segmented by following procedure. Unless some notice is made, native function and modules of ImageJ was used.

Firstly, image sequences were corrected for bleaching by excitation laser by a custom ImageJ plugin that uses the general histogram matching algorithm . Secondly, to attenuate noise in image sequence, frames were running averaged by three frames using ImageJ plugin "Running Z Projector" developed by . Thirdly, to flatten the background intensity gradient, each image in each frame was subtracted with Gaussian-blurred image of that frame. Fourthly, bandpass filter was applied to eliminate patterns below three pixels and above 40 pixels to further reduce noise. Fifthly, cell boundary was refined by gray-scale erosion. Images were then segmented using TrainableSegmentation plugin in Fiji with constant training data for all strains. Finally, watershed and skeltonize algorithms were applied to minimize the thickness of the cell boundary.

After segmentation, cells were measured for their centroid and occupying area. The particle analysis module in ImageJ was used for this measurement with constant parameter setting for all strains. To link cells between successive frame, a particle linking algorithm developed by was modified. In short, following cost function was designed and used to evaluate the cost for the linking and globally optimize the linking between cells.

\[ Cost=((x_{t+1}-x_{t})^{2}) + (y_{t+1}-y_{t})^{2}) + \frac{2}{A_{t}}abs(A_{t} - A_{t+1}) \]
where <jsm>(x_{t}, y_{t})</jsm> is the centroid coordinate and \(A_{t}\) is cell area at time point $t$.

The cost is thus the squared displacement between two frames added with the normalized change in the area in between. During preprocessing and segmentation, some cells were oversegmented due to the limits in the capability of preprocessing. Such artifacts degrades the tracking quality. By using above cost function, wrongly segmented cells were automatically rejected from the track estimation and track linking algorithm steps over such badly segmented time point and links to the corresponding cell in successive frame. Only cells successfully tracked for more than 100 frames were used for the analysis. Note that though with such rejection algorithm, rejection is not 100% perfect and there are minor number of some cells with wrong contour are included in the analysis. Further improvements in the preprocessing and segmentation protocol are required in future.

1. Bleach Correction by Histogram matching. To attenuate the decreasing contrast of images due to fluorescence bleaching, histogram matching to the initial frame was applied to successive frames. Histogram matching algorithm and source code is from Burger and Burge.

2. Running average. To reduce the noise, three frames were averaged for each time point using a frame a frame after that time point. ImageJ plugin "Running Z Projector" developed by Nico Stuurman was used .

3. Background subtraction. To flatten the background intensity gradient, each image in each frame was subtracted with Gaussian-blurred image of that frame.

4. BandPass filtering to remove noise. To further reduce noise, each image was band passed by eliminating patterns below 3 pixels and above 40 pixels.

5. Grayscale-erosion to refine the segmented cell boundary.

6. Trainable segmentation using common training data. "Trainable Segmentation" is a part of the ImageJ bundle "Fiji" .

7. Watershed processing to separate some cells undersegmented and overlapping.

8. Skeltonize and dilate the binary image to minimize the thickness of cell boundary.

Results

Changes in cell area over time

Cell areas at each time point were plotted against time (frames). In wild type, gradual increase of variance of measured cell area was observed. This is due to the fact that some cells become smaller as they invaginate while the others increase cell area. This increase, from what could be seen in time-lapse sequence, seems to be due to stretching pulled by invaginating cells (fig 1 first plot).

Compared to the wild type, variance of cell area in the strain BOB was larger, indicating that cell area is with more variety in this mutant (fig 1, second plot). Such difference is also visible in the plot with relative area plotted against time (figure 2). Relative area of cell was calculated against the first time point of the same cell. (so "1" is various depending on the initial size, but all are area with 1 in the first frame. see next section). In case of wild type, cells become smaller in overall by time, indicated by the increase of area below 1.0. This trend was also seen in Tom. On the other hand in Bob, overall area decrease could be seen in the initial phase, but then the variance becomes large. Such time course suggests that after initial compaction (due to invagination) of cells, some cells become larger and some stay with the same size.

I should note that the image quality of BOB cell at the cell boundary was worse than other strains, wild type, TOM and M4. This caused more wrongly segmented cells in BOB. Accordingly area measurement/tracking has more error in this sample. This could be seen as more number of none tracked cells (painted in gray) in the BOB. Over/under segmentation becomes severe especially in the mid zone of the embryo where cells became smaller.

Cell area dynamics and local differences

Color coding of relative area

To compare the difference in individual cell area dynamics, cell tracks were analyzed in detail by color coding of relative cell area in time lapse sequences. For each cell that was tracked successfully for more than 100 time points, measured cell area (I will call this ’absolute area’; corresponds to fig. 1) was normalized against the area of that cell in the first time point (I will call this relative area; corresponds to fig.2).

See movie wtskel_Col.avi (also fig. 3a wtMontage.tif for still frames) for the wildtype area dynamics. In the first frame of the movie, all cells are painted in orange. Color scale is placed in the right bottom corner of the image stack. Orange color corresponds to 1.0 relative area. As time proceeds, minute and seemingly random fluctuation of cell area initially continues for a while, indicated by alternating color between dark orange (ca 0.8) to light orange (ca. 1.2). From around frame 98, some cells starts to become purple (ca 0.5) and then these cells start to disappear from the observed plane by invagination (frame > 120-130).

To visualize the distribution of cell compaction, color-coded sequence was time-projected to 2D by minimum value algorithm (fig. 4a, Cell Compaction Distribution ). Color code scale is the same as the one used for the above mentioned sequence. Cell compaction occurred mostly at the midzone of the embryo, indicated by dark blue signal mostly concentrated in the mid zone. Peripheral cells are also slightly blue, since these cells slightly decrease their size as they move towards the midzone. Strong compaction seems to be occurring at the two ends of invagination zones, but this could be due to the timing of the sequence capturing (for wild type, a bit earlier phase of invagination seems to be captured).

Compared to the wild type, much wider area of midzone showed cell compaction in BOB (fig. 4b). Approximately cells in approximately 2/3 of the width centered at the midzone underwent compaction, while in wild type, this zone is much narrower, about 1/2. Note that in this figure, enlargement of cell area that is seen in BOB is masked due to the minimum projection method. Enlargement of cells will be explained in the next section.

In m4 strain, cell compaction distribution is broad and inconsistent. Cells starts to decrease their area in more random manner, as it could be seen with the area color-code projection (fig,4c). Dark blue spots appeared not only in the mid zone, but also in the peripheral area of the embryo. This suggests that cell compaction and invagination are two events that is normally occurring simultaneously in wild type, but in this m4 strain these two events are decoupled and only cell compaction seems to be happening while activity of invagination being low. If invagination process and cell compaction process are timed independently, such decoupling may occur.

In the TOM strain, compaction of cells were concentrated at the midzone, but interestingly the compaction happened only in one side of the midzone. This could be clearly seen by one-sided blue streaks in the projection image (fig.4d). In the side where cell compaction at the midzone was not happening, cells at the very periphery seems to be showing shrinking of cell area. Although such left-right asymmetry in cell compaction activity is evident, cell tracks show only slight difference in their path (compaction active zone moves slightly more) (fgi5. d).

Single cell behavior

To examine in more detail, individual cells were analyzed with their area dynamics, relative positioning within the tissue and tracks.

In the wild type, cells located midzone starts to decrease cell area spontaneously, and when such cells become majority, invagination seems to take place. Cell labeled 280, 31, 48 are the ones which were in the midzone already before the invagination started (fig. 6a). Cell area shows small fluctuations, and then suddenly decrease in cell area initiates in all three cases (fig7a, area plots). In case of cells which were at relatively away from the midzone (cell 121, 93, 359), cells first moved towards the midzone (fig.6a). While they move towards the midzone, increase in cell area was observed (fig.7a, area plots). Cell compaction happened after cell reached the midzone, such as the case with cell 121.

In the bob strain, cell area dynamics at the midzone is more various than in the wild type (fig.6b). Some cells behaved like wild type, in which that they spontaneously starts to decrease their area and disappears (cells 103, 178). On the other hand, some cells do starts to decrease their area but then abort shrinking to recover the cell area, then even get larger than initially (cell 184, 124, 60, 160, 131). Such behavior in the end seems to contribute to the halt in the invagination process. Cells at the periphery initial moves towards the midzone, but as such stop in invagination happens, they move back to periphery again as if they are "pushed back"(cell 290).

In the m4 strain, cells starts to shrink spontaneously similar to the wild type (fig.6c). The difference is that the small area phase (corresponds to blue-dark blue color in the figure) is prolonged compared to the wild type (fig.7c, cell 188, 213, 214), and also some cells that increases cell area also co-exists in the midzone (cell 309). In addition, many cells starts to shrink still when they are in the periphery (cell 519, 468). Not all cells in the periphery starts compaction, and some cells remain with similar area (216) or get larger (cell 20), see Fig 7c, area plots. There are also cells in periphery, that behaves just like in wild type: move towards the midzone, and progressively decrease cell area (cell 416).

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 Measuring Time-Lapse Experiments: An Overview

 Kota Miura (Centre for Molecular and Cellular Imaging, EMBL), 29.June.2006

{ EMBO Practical Course 2006}

{ “Microinjection and Detection of Probes” }

Abstract

Time series of digital images, usually called ‘a stack’, contains temporal dynamics of position and intensity. By analyzing these dynamics, we can extract numerical parameter which then enables us to characterize the biological system. There are three types of dynamics. (i) Position does not change but intensity changes over time. (ii) Position changes but the intensity does not change. (iii) Both Position and Intensity change over time. Since (iii) is a combination of (i) and (ii), I will explain the basics of the measurement of type (i) and (ii). An example of type (i) is the measurement of cargo transport dynamics in vesicle trafficking (Hirschberg et al., 1998). Transition of protein localization from ER to Golgi then to the plasma membrane was measured over time by measuring the signal intensity in each statically positioned compartment. This type of technique has evolved to various sophisticated methods based on the same principle such as FRAP technique. Type (ii) corresponds to the measurement of movement, or object tracking, and an example is the single particle tracking of membrane surface proteins (Murase et al., 2004).

{ Notes}

{ Single Particle Tracking (SPT)}

(Saxton and Jacobson, 1997)  A review on SPT, also discusses about mean-square-displacement plot and interpretations.

(Kusumi et al., 1993)  Excellent application of SPT on constrained diffusion.

(Qian et al., 1991) Theoretical Comparison of SPT and FRAP

(Miura, 2005) A review on tracking techniques in cell biology.

Active Contour (SNAKES) Demo

http://www.markschulze.net/snakes/

{ FRAP reviews}

Reviews on FRAP (Phair et al., 2004; Sprague and McNally, 2005). Another review is a bit older, but good for overviewing classic literatures (Reits and Neefjes, 2001)¹.

{ Models for FRAP analysis}

Diffusion: Axelrod et. al.’s paper is a frequently cited classic paper on FRAP (Axelrod et al., 1976). They measured pure diffusion. Closed solution for Axelrod’s model was proposed later and still used by many researchers (Soumpasis, 1983).

Several empirical formula for fitting diffusion-FRAP can be found in other literatures (Ellenberg et al., 1997; Yguerabide et al., 1982).

Reaction: Jacquez ‘s book is good for learning the compartmental analysis used for modelling reaction-dominant FRAP recovery  (Jacquez, 1972) The book is also informative and excellent for modelling biochemical dynamics in general. Recent advances in biochemistry incorporate interaction with immobile (non-diffusive) entity, which radically changes the interpretation of parameter acquired by fitting exponential equations (Bulinski et al., 2001; Sprague et al., 2004)  

{ Advanced Models for FRAP}

Diffusion-Reaction: Formula considering both diffusion and reaction were recently proposed (Sprague et al., 2004). This paper is interesting not only for this diffusion-reaction approach but also for derivation of pure-diffusion, effective diffusion and reaction dominant FRAP.

Considerations on Membrane Architecture: Mobility of proteins is generally constrained by the complex architecture of intracellular space, the shape of organelle. Such steric effects has been omitted from FRAP analysis for the estimation mobility parameters e.g. diffusion coefficient.  Recent literature includes this effect for the FRAP analysis by reconstructing the ER membrane geometry by 3D rendering and simulating the movement of protein along that geometry (Sbalzarini et al., 2006; Sbalzarini et al., 2005).  

{ Cytoplasmic Architecture}

Diffusion within cytoplasm is not a simple pure-diffusion. Cytoskeletons, organelle and supramolecular complexes become obstacles to the movement of proteins. In a very small scale, the vacant spaces between these structures allow the molecule to move around without encountering these structures. In this vacant space, the cytoplasmic viscosity is said to be similar to water, or 2-3 folds higher than water. Measurement of small scale diffusion needs special techniques. On the other hand, we also can measure the movement of molecules in a larger scale. In this case, diffusion encounters steric hindrances and bindng/reaction with other molecules. Diffusion coefficient that includes this slowing factor is thus an apparent diffusion. More specifically when the molecule mobility is slowed down due to binding/reactions, this type pf diffusion is called effective diffusion.

To know more about microscopic diffusion and macroscopic diffusion inside cell, refer to Luby-Phelps papers (Luby-Phelps, 1994; Luby-Phelps, 2000).

{ ImageJ website}

Free and powerful software for quantitative image analysis.

http://rsb.info.nih.gov/ij/

{ EAMNET (European Advanced Microscopy Network) website}

http://www.embl.de/eamnet/

The website is maintained by Stefan Terjung (ALMF, EMBL). Download page links to many useful Macros for analyzing image-stacks.

{ References}