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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statistical analysis of skin cell geometry and motion

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