Statistical Analysis of Skin Cell Geometry and Motion

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Statistical Analysis of Skin Cell Geometry and Motion
Amy Werner-Allen (Applied Mathematics), Corey O’Hern (Mechanical Engineering and
Material Science, Physics), Eric Dufresne (Mechanical Engineering and Material Science,
Physics, Chemical Engineering, Cell Biology), Valerie Horsley (Molecular and Developmental
Biology), Aaron Mertz (Physics)
Background
Keratinocytes are the predominant type of cell in the epidermis. One feature of these cells
is their tendency to adhere into layers of relatively uniform height, providing a cell packing
whose geometry is relatively straight-forward to analyze. Adherence requires the cells to
differentiate, or change from a less-specified to a more specific cell type, which is mediated
through the addition of calcium. Another feature is their ability to regroup after an incision has
broken through the cell layer, allowing the wound to repair itself. This healing is mitigated in
part by proliferation, or the dividing of cells. These two characteristics – the ability to pack
consistently and the ability to fill open spaces – indicate that these cells have some intrinsic sense
of their neighbors and surrounding space. Understanding the interconnectedness of the driving
forces for cellular migration and structure is a challenging task that requires integrating
biological aspects – internal and external signals within and between cells – as well as physical
ones – surface tension minimization, velocity force fields, and mechanical stress.
In addition to adhesion, proliferation plays an important role in the growth and packing of
keratinocytes. The epidermis consists of two important layers. The outer layer consists of
differentiated keratinocytes, which form cell-cell adhesions and a structured packing formation
that serves as a protective barrier. Underneath, the basal layer contains continually proliferative
epithelial cells, which serve to replenish cells from the outer layer that have died and been cast
off. Once a basal cell has differentiated and entered the outer layer, the cell cycle terminates and

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it is unable to proliferate. Steady state is reached when mean cell apoptosis matches the
proliferation rate. However, the rate of proliferation has not been studied as a function of local
physical and geometrical quantities such as density, cell shape, and motion. Cancerous situations
arise when the proliferation rate continues to increase despite the fact that a fully dense packing
of cells has been established. Quantifying normal proliferative cell behavior may help us
understand what causes hyper-proliferation of epithelial cells.
The overarching scope of this project encompasses both packing and wound healing
characterization. We began by processing the images and studying trends in cell characteristics –
such as area, perimeter, number of sides and average curvature – over various time intervals.
Next we examined cell motion and interactions at low-densities as an alternative way to replicate
wound healing assays. Lastly, we studied proliferation patterns in various cluster sizes to
determine the role of replication in packing formations.
I. Image Processing and Cell Characterization
To begin, we wanted to quantify some basic physical properties of epithelial cells. In
order to generate a large amount of data, we started with a set of twenty microscope images of
mouse keratinocytes stained for the E-Cadherin protein, which is a transmembrane protein that
congregates on cell-to-cell adhesions and delineates cellular boundaries in dense packings. Once
the cell outlines were established, we developed a method for determining vertices, which
allowed us to determine number of sides per cell and the curvature of the sides. We then studied
cultures at various time points to see whether and how these properties would change over time.

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Figure 1: unprocessed microscope image of
fluorescent staining of MKCs.
Figure 2: bwlabel of cells from a traced image
Method
Mouse keratinocytes (MKCs) were grown in cultures with a high cellular density around
4x105
cells/mL to ensure confluence. The cells had been passaged ten to eleven times since being
procured from the mouse; cell passaging allows a culture to be maintained for an extended
period of time and involves splitting cells once they become confluent. The cells are grown in
high-calcium medium in order to promote cell-cell adhesions. Figure 1 shows a pre-processed
image that has been stained with two fluorescent dyes.
The DNA in the nucleus was stained with DAPI, which
is a blue stain; the E-Cadherin protein was stained with
GFP, which is a green stain. Although the position of the
nucleus relative to the cell’s center of mass is also of
interest, we began by first tracing the cell boundaries
and disregarding the nucleus.
Once the cell boundaries were traced (figure 2), individual cells needed to be identified.
To do this, the MATLAB function bwlabel was implemented. This function computes connected
components in binary images and designates a
label to each region. Each individual cell can
then be accessed by its unique label; figure 2
shows a depiction of each cell, colored with a
different color gradient for demarcation. Once
the labels were assigned, areas and perimeters
were calculated for each cell using MATLAB
programs.

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Figure 3: two frames containing vertices
Figure 4: final model of original image
In order to determine number of sides and curvature, vertices needed to be pinpointed.
We define a vertex as the convergence of three or more cell sides at a single point. To identify
vertex locations, we overlaid a grid of small square frames onto the image outline. For each
frame, we determined the number of labels present, which is indicative of the number of cells;
any frame that has three or more labels must contain a
vertex. Figure 3 shows examples of two frames, each
containing three or more labels, hence a vertex (the blue
diamond). Once vertices were established, we could then
compile the number of sides of each cell. Also of interest is the average curvature of the sides
and cells; this was calculated by fitting fourth-order
polynomial functions to each side; the final model of
the initial image in figure 1 is shown in figure 4.
Next, we took time-series images at six-hour
intervals up until 24 hours. Time was measured from
when the calcium was added. We plotted the
distributions of normalized areas and perimeters,
number of sides, and average curvature.
Results
The area of each cell was calculated and normalized based on the average over all areas
(figure 5). Similar calculations were performed for the perimeters of each cell (figure 6). Based
on log-linear plots (not shown), the distributions appear to be exponential.

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Figure 5: Area distribution for twenty initial images Figure 6: Perimeter distribution for twenty initial images
The average curvature and the average curvature multiplied by the square root of the area were
calculated for each cell. The distributions show these values normalized to the average curvature
for each image (figure 7.1 and 7.2). Curvature was computed using the following equation:
Here κ stands for curvature, and y is the best-fit forth-order polynomial function that was
calculated for each side.
Figures 7.1 and 7.2: distributions of average curvature of a cell and average curvature of a side

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Figure 8.1 and 8.2: the distribution of the number of sides per cell and a plot of the log of areas to the log of the perimeter squares.
The red dots represent individual data points; the blue line is the ratio of log(area) to log(perimeter2
) for a circle, which is the smallest
possible value
The number of sides for each cell was calculated based on the number of vertices associated with
each cell. The average number of sides is 5.6, which is nearly hexagonal. The plot of the log of
area versus log of perimeter squared confirms that our calculations did not violate acceptable
area to perimeter ratios.
The distributions of the above quantities were replicated at various time points. The distributions
showed little to no change over time, indicating that the packing, once confluent, is stable. This
implies that time-dependence is not relevant for densely-packed cells.
II. Scratch Wound Replication
The standard method for generating a wound is by performing a scratch assay. This
procedure requires a confluent cell culture, in this case of keratinocytes, which are then scratched
using a pipette tip. The scratch is then imaged over set time intervals, usually every four hours
until the wound has fully closed, around 24 hours. Although this is the most accurate

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reproducible depiction of an actual wound, several complications arise using this method. For
one, many of the cells become damaged during the process, which may impede or alter their
natural reactions to the changed environment. In addition, dispersal of the cytoplasmic elements
of the damaged cells into the nearby surroundings may induce unwanted intercellular signaling.
Some of the cells die and become dispersed throughout the media, making imaging less clear and
more prone to improper processing.
These issues were addressed through a study completed by Poujade et. al (2007). They
devised a method for replicating wounded-cell collective motion by growing a monolayer of
epithelial cells in restricted strips and then studying the motion induced when the boundaries
were removed. This procedure eliminates any effects that may be triggered through cell damage
or death. Instead of adopting this method, we chose to explore a non-traditional and simpler way
of addressing wound healing. We examined the movement, proliferation, and cluster formation
of keratinocytes over time, beginning in a low-density state. As the cells live and grow, they are
constantly responding to factors in their local environment, such as the number of neighbors
surrounding them and the availability of free space nearby. This environment is not adulterated
with damaged or dead cells, as in the conventional scratch wound assay. Understanding and
quantifying how cells react to changes in density and cluster size has pertinent applicability to
the study of wound healing.
Research motivations
There are several aspects to this research that need to be examined. Some of these aspects have
not yet been assessed, and are therefore left as future directions for the continuation of this
project. One important correlation is the rate of proliferation and its dependency on the density of

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the local environment. Do cells divide more slowly when surrounded by a large cluster of other
cells? It is also of interest to investigate how cell size and shape change as a function of the
surrounding environment. Once cells become fully packed into a monolayer, they form a
characteristic packing pattern with a hexagonal formation. Some exterior cue, presumably at
some transitional density, must initiate the transformation in cell shape from low-density to high-
density packing.
In addition to cell proliferation, velocity of migration is also a crucial feature to study.
The first step would be to obtain a distribution of velocities for each cell at given time points.
This would allow us to quantify the relationship between cellular motion and local environment
traits, such as density and cluster size. It would also be of interest to study the impact of cluster
size on velocity: do larger clusters move or respond to their environments differently than
smaller ones? All of these unresolved questions guide the motivation for this project.
Methods
In order to examine the properties of the growth, proliferation and cluster formation of
mouse keratinocytes, I took time-series images from cell cultures plated at low-density (~1x105
cells/mL) in 10 mL wells. The cells had been passaged eleven times since being procured from
the mouse. For this study, the cells were grown in low-calcium medium, with a concentration of
0.05 millimolar; additional calcium would cause the cells to differentiate, stop proliferating, and
adhere to one another. Cells were imaged using bright field microscopy with 10 x magnification.
Images produced have dimensions 23.5 by 17.6 centimeters (9.25 by 6.93 inches).

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Figure 9: diagram of a 10 mL well depicting method of image
gathering in culture 1; figure is not to scale – about thirty frames
span the length of the reference line
Figure 10: diagram of image gathering for culture 2 using
reference points
Using one of the cultures, I took
approximately one hundred images of
consecutive, non-overlapping screen shots at
0, 10, 24 and 32 hours (Figure 9).
Characteristics of interest include cluster size
(i.e. number of cells in a cluster), average cell
size and shape, and density of cells per image,
each as a function of time. Although
corresponding images cannot be precisely
overlaid at each time point (i.e. image 33 at
time 0 may not be the exact frame as image 33 at time 24, etc.), their compilation represents a
specific and discrete area of the plated culture. With the second culture, I made a grid of about
twenty equally-spaced reference points on the
bottom of the well. At each coordinate we took four
non-overlapping images at 0, 24 and 32 hours
(figure 10). This systemization allowed us to return
to relatively the exact same image frame at each
time point. Ideally, this will permit us to study
individual cell motion and specific cluster
formations.
Examples of images procured can be found on page 13. Most of the images are similar to
figure 14.1; the cell membranes are difficult to delineate, while the nuclei are prominently
darkened. Figure 14.2 is a sample image from the first culture that has been traced using a photo-

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editing program, and figure 14.3 shows a standard cluster. Time-sequential images from the
second culture can be used for single-cell analysis, as highlighted in figure 15.1. Calculations
pertaining to number of cells per image and cluster sizes were tabulated by hand. In order to
make further assessments regarding cellular area and shape, the outlines of cell membranes must
be traced. Once this has been completed, either by hand or by an image processing program, I
have written matlab scripts that determine cell area, perimeter and shape.
Results
Cluster sizes (number of cells per cluster) for each image were recorded and complied,
and the following histogram (figure 11) shows the distribution of normalized cluster sizes at each
of the four time intervals:
Figure 11: distribution of cluster sizes at 0, 10, 24 and 32 hours (left to right)

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We can see that, while the initial distribution was heterogeneous at the onset, it became more and
more uniform as time progressed, with each cluster becoming more likely to be of average size.
We also can plot the average cluster size over time, shown in figure 12:
Although we would expect the average cluster size to increase over time, there is a slight dip at
10 hours. In addition, we would like to examine the proliferation of cells by looking at the
average number of cells per image over time, shown here in figure 13:
Figure 12: change in average cluster size versus time
Figure 13: average cells per image versus time

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As expected, the number of cells is steadily increasing. By 32 hours, the cell population has
doubled. The proliferation rate for epithelial cells is generally considered to be 24 hours.
Raw data
0 hours:
total number of cells: 1797
average cluster size: 2.9411
average # cells per image: 19.9667
10 hours:
24 hours:
32 hours:
Proliferation:
time cells/image ratio
0 19.9667 1
10 22.6556 1.134669224
24 32.3626 1.62082868
32 40.6742 2.037101774

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Images
Figure 14.1-sample image from culture 1, 0 hours Figure 14.2 – same image as left, this time with cell outlines traced
Figure 14.3 – close-up of cluster with nine cells
Figure 15.1 – sequence in same frame at 0, 24, and 32 hours (yellow outlines cell trajectory)

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Figure 16: BrdU stain on a small cluster
III. Proliferation Studies
It is also of interest to study proliferation rates of plated cells over various time intervals
to examine the relationship between proliferation, cell packing and cluster size. This requires
pulsing the cells with BrdU, a synthetic nucleotide that serves as a thymidine replacement. The
system is then visualized at fixed time points to determine the cells that have incorporated BrdU
into their DNA, which indicates the cells that have successfully divided. Another technique that
is useful for preliminary cell cultures is the incorporation of an intracellular membrane labeling
counterstain to enhance cell boundaries, which will increase the efficiency of image processing
and analysis. The new experimental techniques would allow the proliferative cells to be clearly
identified and the rate of proliferation to be calculated as a function of cluster size. Our research
is guided by the following important set of specific questions: 1) Does proliferation occur from
the interior, or nearer to the cluster borders? 2) Does the proliferation rate of a cell depend on the
number of nearest neighbors, or its distance from the cluster boundary? 3) How does the shape of
a cell vary as a function of density and position within a cluster? 4) Does the history of cell
division affect the probability that it will divide in the future?
Method
We began by culturing two plates of MKCs at
three initial densities: 4x105
, 5x105
and 9x105
cells/mL. One plate was fixed and pulsed with
BrdU immediately after the cells settled; the
second plate allowed the cells to grow for
another 24 hours before being pulsed. All six

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plates were pulsed with BrdU for six hours and then stained for DAPI (cell nuclei) and GFP
(BrdU). Cells that proliferated within the six hour BrdU pulse showed up with bright green
nuclei; cells that did not proliferate within the pulse had regular blue nuclei. Figure 16 shows an
example image of a cluster of twenty-one cells of which five have proliferated. The proliferation
rate of an average cell in a confluent packing is once every twenty-four hours. Forty-five images
of various clusters at sizes ranging from five to twenty-five cells were taken.
Continued Research
The next step in this project would be to continue to collect more images of
appropriately-sized clusters, process the images to quantify the characteristics discussed
previously, and identify the proliferative cells. Distance from center of mass of proliferative cells
to cluster center of mass would quantify the position of proliferation in clusters. Other important
factors would be the rate of proliferation as a function of cluster size, the shape of the cell (area,
perimeter, number of sides, average curvature) as a function of the rate of proliferation, and the
rate of proliferation conditioned on number of previous cell divisions.

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Interactions, and Proliferation on Epithelial Packing”. Current Biology. December 18, 2007. vol.
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