When you cut yourself, a massive migration begins inside your body: skin cells flock in their thousands to the wound site, where they will soon deposit new layers of protective tissue.
In a new study, researchers at the University of Colorado at Boulder have taken an important step in unraveling the drivers of this collective behavior. The team has developed an equation-learning technique that could one day help scientists understand how the body rebuilds skin and could potentially inspire new therapies to speed up wound healing.
“Learning the rules of how individual cells respond to the proximity and relative motion of other cells is key to understanding why cells migrate in a wound,” said David Bortz, professor of applied mathematics at CU Boulder and author. principal of the new study.
The research is the latest in a decade of collaboration between Bortz and Xuedong Liu, professor of biochemistry at CU Boulder. The group’s method, called Weak form Sparse Identification of Nonlinear Dynamics (WSINDy), can be applied to a wide range of phenomena in the natural world, said the study’s lead author Dan Messenger.
“While this article is about cells, the math also applies to a wide range of areas, including how flocks of birds avoid both predators and each other,” Messenger said, postdoctoral researcher in Bortz’s laboratory.
He and his colleagues published their results on October 12 in the Journal of the Royal Society Interface.
The research revolves around a set of tools from the field of “data-driven modeling”, an emerging field at the intersection of applied mathematics, statistics and data science. Using this approach, the group designed computer simulations of hundreds of cells moving toward an artificial wound, then constructed a method to learn the equations to describe and examine the movement of each individual cell. The team’s tools are potentially much faster and more accurate than traditional modeling approaches, a boon to understanding complex natural phenomena like wound healing.
“To prevent infections, we want our wounds to close as soon as possible,” Liu said. “We plan to use these learned models to test pharmaceuticals and treatment regimens that may stimulate wound healing.”
trial and error
Mathematical models come in many shapes and sizes, but most use a complex series of equations to try to capture a real-world phenomenon.
Bortz, for example, joined a team of scientists in 2020 that relied on models to try to predict the spread of COVID-19 in Colorado. But, he noted, it can take a lot of trial and error, and even supercomputers, to validate these equations.
“Developing an accurate and reliable model can be a very long and laborious process,” Bortz said.
In this new study, he and his colleagues extended their newly developed WSINDy method to directly use data to learn patterns of individuals.
“It’s about putting the data first and letting the math follow,” Bortz said.
From cells to particles
In the current study, he and his colleagues, including biochemistry graduate student Graycen Wheeler, decided to turn this data-driven lens toward the problem of cell migration.
Liu and his colleagues observed how skin cells clump together in the lab. The migrating skin cells, they found, tend to follow certain rules: Like a herd of fleeing buffaloes, the skin cells will align their direction with the cells in front of them, but also try not to bump into the leaders from behind.
To see if WSINDy could shed light on this mass movement, Bortz and Messenger designed computer simulations showing hundreds of digital cells moving in tandem. The team deployed their WSINDy approach to construct precise equations describing the motion of each of these cells.
“With WSINDy, if you have 1,000 cells, you can learn 1,000 different patterns,” Bortz said.
They then relied on even more math to start grouping these patterns. Bortz noted that WSINDy is particularly well suited for finding hidden patterns in data. When researchers, for example, mixed two or more cell types that moved in different ways, their suite of tools could pinpoint and precisely sort the cells into groups.
“We not only learn patterns for each cell, but those patterns can be sorted, revealing the dominant categories of cellular behaviors that play a role in wound healing,” Messenger said.
In the future, the collaborators hope to use their approach to begin digging into the behavior of real cells in the lab. Liu noted that the technique could be particularly useful for studying cancer. Cancer cells, he said, undergo similar mass migrations as they spread from one organ to another.
“As biochemists, we don’t usually have a quantitative way to describe this cell migration,” Liu said. “But now we do.”
Mathematician on the front lines of Colorado’s coronavirus response
Daniel A. Messenger et al, Learning anisotropic interaction rules from individual trajectories in a heterogeneous cell population, Journal of the Royal Society Interface (2022). DOI: 10.1098/rsif.2022.0412
Provided by the University of Colorado at Boulder
Quote: New study shows how to learn cell migration equations (2022, October 27) Retrieved October 27, 2022 from https://phys.org/news/2022-10-equations-cell-migration.html
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