====== Drosophila invagination: cell dynamics ======
''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 (x_{t}, y_{t}) 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).
{plainnat}
{page} {1}{Standard}
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
{ 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}
[^1]: Good for overviewing FRAP; but I don’t agree with statement such
as below; Quote: “*When motion due to active transport or
unidirectional flow can be discounted, protein mobility in a cell is
due to brownian motion.*”, because mobility in this case is defined
by Brownian motion *and *the structural environment, which makes the
FRAP curve fitting difficult.