How do zebrafish get their stripes? A new data analysis tool could provide an answer

The iconic zebrafish stripes are a classic example of natural self-organization. As zebrafish embryos develop, three types of pigment cells move around the skin, eventually jostling into positions that form yellow and blue stripes the length of the body.

Scientists want to understand the genetic rules that direct this delicate dance, and a new algorithm developed by Brown University mathematicians could help them get there. The algorithm, described this week in Proceedings of the National Academy of Sciences, is able to quantify various shape and pattern attributes, allowing scientists to more objectively test ideas about how zebrafish stripes — and potentially other developmental patterns — form.

“The overarching goal of studying zebrafish stripes is to understand the early development of organisms — how genes are expressed to form structures and phenotypes,” said Bjorn Sandstede, professor in the Brown Division of Mathematics. applied and lead author of the research. “People have developed simulations to help understand these processes, but the challenge is that you look at a few zebrafish or a few images of simulations, and you basically look at what the similarities and differences are. We wanted to create something that was automated and more objective.”

Of scratches and stains

Zebrafish prove to be excellent test beds for evaluating how genetic changes can influence pattern formation. Their embryos are transparent and develop rapidly, which gives scientists the opportunity to study the development of stripes in detail. Over the years, researchers have discovered a number of genetic mutations that alter the pigment patterns of zebrafish. Some mutations change the straightness of fish stripes, some introduce small breaks in the stripes, and others create a fan of spots rather than stripes. These mutations provide a better understanding of the rules governing the formation of stripes.

These different patterns are the result of changes in the way pigment cell types interact with each other and move around during development. To understand the rules that these cells follow, scientists have developed computer models that simulate the formation of cell movement patterns. By adjusting the rules governing the simulation, and then seeing if the output matches models of real fish, scientists can begin to determine which rules are important.

Sandstede and Alexandria Volkening, who earned her doctorate. to Brown and is now a postdoctoral researcher at Northwestern University, previously developed such a simulation, and it has yielded new insights into how the scratches form. But the new algorithm described in this latest paper, which Volkening co-authored on, provides a new way to assess the performance of this model and others, the researchers say.

The form of the data

The new algorithm uses a technique known as topological data analysis.

“This is a newer area of ​​math and statistics that focuses on the quantification of shape,” said Melissa McGuirl, a graduate student at Brown and the study’s lead author. “Essentially, it’s a tool that allows us to track connected components and loops that match shape features that represent specks or stripes.”

In this case, these connected components are made up of individual pigment cells in zebrafish images or from simulations of zebrafish scratch development. The algorithm assesses how well each cell’s position correlates with others, and therefore whether the cells are part of a pattern element – a stripe, spot, or something else. The beauty of the technique, the researchers say, is that it can quantify patterns on a wide range of spatial scales, from the scale of a few individual cells to whole fish.

“What we can do with this is determine a variety of descriptors that allow us to talk about things like the straightness or curvature of the stripes, the number of pauses in the stripes, or the average cell-to-cell distances,” Sandstede mentioned. “If there are spots, how many cells are included in each spot? Are they round or more elongated?”

With these more objective feature measurements in hand, researchers can better assess how well their model and others are capturing the dynamics of zebrafish pattern formation. And that, the researchers say, could lead to key insights into how genetic instructions manifest in natural structures.

And the technique isn’t just limited to zebrafish, Sandstede said.

“It’s much more general than zebrafish pigment cells,” he said. “This is designed to quantify patterns and shapes, and it really could do that in any type of system.”

The research was supported by the National Science Foundation (1644760, DMS-1714429, CCF-1740741, DMS-1440386, DMS-1764421) and the Simons Foundation (597491).

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