# Modeling Cellular Movement Inside Collagen Gels

## School Name

South Carolina Governor's School for Science & Mathematics

## Grade Level

12th Grade

## Presentation Topic

Mathematics

## Presentation Type

Mentored

## Abstract

Our goal was to explain why human cells, when sprinkled onto a collagen gel, formed a torus after one day and a sphere a day later. The chemical properties of the cells and collagen gel can’t be used because of the large size of the gels. A new approach was taken by analyzing the physical forces instead of the chemical properties. We hypothesized that we could model the formation of these geometric shapes because the collagen gel contains so many intermolecular forces that it affects cellular movement. To model the collagen gel, we created a three-dimensional phantom lattice with a coordination number of six. We ran millions of random walks along the connections of the phantom lattice, each of which represented a unique polymer chain configuration. We then took the gradient of an energy equation to derive a force equation that models the individual bending and stretching forces of each polymer chain. Through this research project, we also hoped to gain insight as to why cancer cells don’t move similarly to regular cells. When cancerous human cells instead of noncancerous cells are used, no recognizable shape was formed. By understanding why regular human cells form a torus and then a sphere, we hoped to gain insight as to why cancerous cells move differently than noncancerous cells.

## Recommended Citation

Lu, John and Pence, Travis, "Modeling Cellular Movement Inside Collagen Gels" (2019). *South Carolina Junior Academy of Science*. 130.

https://scholarexchange.furman.edu/scjas/2019/all/130

## Location

Founders Hall 140 B

## Start Date

3-30-2019 8:45 AM

## Presentation Format

Oral Only

## Group Project

Yes

Modeling Cellular Movement Inside Collagen Gels

Founders Hall 140 B

Our goal was to explain why human cells, when sprinkled onto a collagen gel, formed a torus after one day and a sphere a day later. The chemical properties of the cells and collagen gel can’t be used because of the large size of the gels. A new approach was taken by analyzing the physical forces instead of the chemical properties. We hypothesized that we could model the formation of these geometric shapes because the collagen gel contains so many intermolecular forces that it affects cellular movement. To model the collagen gel, we created a three-dimensional phantom lattice with a coordination number of six. We ran millions of random walks along the connections of the phantom lattice, each of which represented a unique polymer chain configuration. We then took the gradient of an energy equation to derive a force equation that models the individual bending and stretching forces of each polymer chain. Through this research project, we also hoped to gain insight as to why cancer cells don’t move similarly to regular cells. When cancerous human cells instead of noncancerous cells are used, no recognizable shape was formed. By understanding why regular human cells form a torus and then a sphere, we hoped to gain insight as to why cancerous cells move differently than noncancerous cells.