# (627b) Analyzing Individual Cancer Cell Motility with Chemotaxis Perspective

#### AIChE Annual Meeting

#### 2006

#### 2006 Annual Meeting

#### Computational Molecular Science and Engineering Forum

#### Computational Biology: Systems Modeling II

#### Friday, November 17, 2006 - 8:46am to 9:02am

The importance of cell migration during metastasis has pioneered several studies in the area of cell motility. The objective is to understand the role of chemotaxis (directed migration of cells in a gradient of chemoattractant) during the cancer invasion process.

?*Cellular dynamics'* simulation, originally developed to simulate the chemotaxis during bacterial migration could be used for studying mammalian cell migration. The pre-requisite for doing such a simulation is the knowledge of parameters extracted from experimental data such as the distribution of turn angles and turn frequency in the presence or absence of chemoattractant gradient.

Here we show the different data analysis methods used to generate the turn angle distribution of MCF10A-pbabe, neuN and neuT cells. The pbabe is the control and neuT is the full oncogene.

Materials and methods

Experimental data:

*(Margaret Hollister, Weaver lab, Department of Cancer biology, Vanderbilt University)*

Semi-confluent layer of cells were detached, re-suspended and plated over bare tissue culture wells and tracked using time-lapse video microscopy. Cells were tracked for 4.5 hours with one frame collected every 5 minutes and x, y data obtained using MetaMorph. Data Analysis:

The position data (in the form of t, x and y) of different cells at different times was analyzed using two methods to develop a turn angle distribution. The turn angle was found using cross product and ranged from -pi to +pi.

Two methods namely, 2-point (involving use of two points to find turn angle between two consecutive vectors) and 3-point (involving use of three points to find turn angle between two consecutive vectors) were used to generate turn angle distribution.

*Advantage of 3-point method:* The use of multiple points to determine turn angle gives better picture of cellular turns on longer time scale rather than looking into short time fluctuations Distributions:

Turn angle distribution from 3-point method seems more reasonable and has more spread in values compared to 2-point method where the turn angle values are very small. The 3-point method indeed picked up the turns (analogous to tumbles in bacterial motion) made by a cell in a trajectory by applying a criterion of average turn angle > 45 degree and hence the use of turn angle distribution from this method seems to be more appropriate.

The turn angle distributions of the three types of MCF10A cells were determined and found to be similar.

Identifying the turning points in a cell trajectory (by applying a criterion of average turn angle > 45 degree) and finding the distance and time between these points, the run length and run time distributions were constructed. Parameter estimation:

The mean run time (<t>) and mean run length (<*l*>) for each cell type were determined by linear fitting of the logarithm of the complement of the cumulative distribution functions (cdf) of run time and run length against run time and run length respectively.

The average speed was found by dividing the entire distance traveled by cell by time. The following equations were used to estimate various parameters.

S: average speed, m: random motility coefficient, P: persistence time, n: number of dimensions, y: persistence index and h(q) : turn angle probability distribution.

y was determined by using probability distribution function of turn angles. Persistence times were also determined by plotting degree of orientation versus time. **Results and discussion**

It is found that the more invasive cell line (neuT) seems to display longer persistence and have larger mean run time in 2-D. The persistence index y is relatively higher for these cells in 2-D.

Persistence time values (in minutes) determined by noting that time is equal to persistence value when degree of orientation decays to 37% of its initial value are as follows:

*Pbabe: 30, neuN: 45 and neuT: 75.*

These values are smaller compared to 3-point method as the cosine of deviation was obtained by performing dot product between consecutive vectors, which is similar to 2-point method.

Random motility coefficient in 2-D is found to decrease from the control pbabes to the more invasive neuTs. However, the scenario in actual tumor environment in 3-D might be completely different. The results in 2-D may indicate that the invasive cells might be exhibiting higher random motility coefficients values in 3-D.

Summary

Turn angle distributions and turn frequencies of MCF10A-pbabe, neuN and neuT cells under conditions of zero chemoattractant gradient (and in 2-D) developed.

The random motility coefficient values (in 2-D) for invasive and noninvasive cells determined. Future work

The data analysis needs to be repeated for cell migration under different gradients of attractant for instance, in a microfluidic chamber. The results from unbiased migration in 2-D show that invasive cells might have characteristics entirely different in 3-D like higher random motility coefficient and thus turn angle distribution in 3-D need to be developed. The persistence time and mean speed values obtained from the 4.5 hour data analysis could be used to perform a cell migration simulation based on persistent random walk model. The next step would be to perform ?cellular dynamics' simulation for the cells using the turn angle distributions and turn frequencies under different gradients, first in 2-D and then extend to 3-D.