Quantifying biological pattern formation: a time-dynamic persistent homology approach

Pattern formation and self-organization is present across scales in biology, and one example is cells interacting to form tissues during development. As more detailed experimental data becomes available, especially in developmental-biology applications, this raises exciting questions in mathematics about how to quantify this data and understand relevant information that is not captured by traditional statistical analyses. Here we will show how persistent homology can be used to study pattern formation in the skin of zebrafish. This mathematical tool provides a quantitative way of measuring dynamic changes in spots, stripes, and other biologically relevant pattern features in zebrafish during their development.

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