Skin cells flood by the thousands towards the site of the wound where they will lay down fresh layers of protective tissue.
Researchers from the University of Colorado Boulder have taken an important step towards unraveling the drivers behind this behavior. One day scientists might be able to understand how the body rebuilds skin, thanks to an equation learning technique developed by the team.
David Bortz, professor of applied mathematics at the University of Colorado Boulder and senior author of the new study, said that learning the rules for how individual cells respond to the motion of other cells is critical to understanding why cells migrate into a wound.
Bortz and the professor of biochemistry at the University of Colorado Boulder have been working together for a decade. The group's method can be applied to a wide range of phenomena in the natural world.
Messenger, a researcher in Bortz's lab, said that the math is applicable to a wide range of fields, including how flocks of birds avoid both predators and each other.
He and his colleagues published their results.
The research is dependent on a set of tools from the field of data-driven modeling. The group designed computer simulations of hundreds of cells moving toward an artificial wound, then built a method to learn the equations for each individual cell. The team's tools can be used to understand complex natural phenomena, like wound healing.
We want our wounds to close as quickly as possible to prevent infections. We plan to use these learned models to test pharmaceuticals and drug combinations that may be able to help heal wounds.
Errors and trials.
Most mathematical models use complex equations to try to capture a phenomenon in the real world.
Bortz was part of a team of scientists who used models to try to predict the spread of COVID-19 in Colorado. He said that it can take a lot of trial and error to get those equations right.
It can take a long time to develop an accurate and reliable model.
He and his colleagues used data to learn models of individuals in this study.
Bortz said that it was important to put the data first and let the mathematics follow.
Particles and cells.
He and his colleagues decided to look at the problem of cell migration from a data-driven perspective.
The skin cells surge together as a group in the laboratory. Like a herd of buffalo, skin cells will align their direction to the cells in front of them but also try not to get in the way of the leaders.
Bortz and Messenger created computer simulations that showed hundreds of digital cells moving together. Each and every one of those cells had equations built by the team that described their motions.
If you have 1,000 cells, you can learn more than one model.
They began clustering those models by drawing on more math. Bortz said that the patterns hiding in data are well-suited to being found with the help of the software. When the researchers mixed together two or more types of cells that moved in different ways, their suite of tools was able to spot and sort the cells into groups.
"We learn models for each cell, but those models can be sorted, revealing the dominant categories of cell behaviors that play a role in wound healing."
The goal is to use their approach to dig into the behavior of real cells in the lab. The technique could be used to study cancer. He said that cancer cells move from one organ to another.
"As a biochemist, we don't have a quantitative way to describe the migration of cells." We do now.
More information: Daniel A. Messenger et al, Learning anisotropic interaction rules from individual trajectories in a heterogeneous cellular population, Journal of The Royal Society Interface (2022). DOI: 10.1098/rsif.2022.0412 Journal information: Journal of the Royal Society Interface
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