Researchers use 'hole-y' math and machine learning to study cellular self-assembly
The field of mathematical topology is often described in terms of donuts and pretzels.
To most of us, the two differ in the way they taste or in their compatibility with morning coffee. But to a topologist, the only difference between the two is that one has a single hole and the other has three. There’s no way to stretch or contort a donut to make it look like a pretzel — at least not without ripping it or pasting different parts together, both of which are verboten in topology. The different number of holes make two shapes that are fundamentally, inexorably different.
In recent years, researchers have drawn on mathematical topology to help explain a range of phenomena like phase transitions in matter, aspects of Earth’s climate and even how zebrafish form their iconic stripes. Now, a Brown University research team is working to use topology in yet another realm: training computers to classify how human cells organize into tissue-like architectures.
In a study published in the May 7 issue of the journal Soft Matter, the researchers demonstrate a machine learning technique that measures the topological traits of cell clusters. They showed that the system can accurately categorize cell clusters and infer the motility and adhesion of the cells that comprise them.
“You can think of this as topology-informed machine learning,” said Dhananjay Bhaskar, a recent Ph.D. graduate who led the work. “The hope is that this can help us to avoid some of the pitfalls that affect the accuracy of machine learning algorithms.”
Bhaskar developed the algorithm with Ian Y. Wong, an assistant professor in Brown’s School of Engineering, and William Zhang, a Brown undergraduate. More