A mathematical model connects the evolution of chickens, fish and frogs

"How does it happen?" is one of the most fundamental and persistent questions in existence. For example, how can cells self-organize into muscles, bones, or skin throughout human development? How do they develop into a finger, a brain, a spine?

One area of scientific study focuses on comprehending gastrulation, the process by which embryo cells change from a single layer to a multidimensional structure with a major body axis, even though the answers to such concerns are yet unclear. In humans, gastrulation occurs around 14 days following fertilization.

Since studying human embryos at this point is not feasible, scientists from Harvard University, the University of Dundee (UK), and the University of California San Diego were able to examine the process of gastrulation in chick embryos, which at this stage are quite comparable to human embryos.

This research was carried out via an interdisciplinary, back-and-forth mix of theoretical and experimental science—what UC San Diego Assistant Professor of Physics Mattia Serra refers to as an ideal loop. Theorist Mattia is interested in complicated biophysical systems and emergent patterns within them.

Here, he developed a mathematical model with the assistance of the biologists at the University of Dundee. The mobility of tens of thousands of cells throughout the whole chick embryo, known as the gastrulation flows, was observed under a microscope and could be precisely predicted by the model. This is the first time that these fluxes in chick embryos have been replicated in a self-organizing mathematical model.

Subsequently, the scientists aimed to determine if the model could not only reproduce their experimental findings but also forecast potential outcomes in other scenarios. By altering the current settings or the starting circumstances, Serra's team "perturbed" the model.

The model produced cellular fluxes that were not normally detected in the chick but were observed in two other vertebrate species, fish and frog. These results were unexpected.

Collaborators in biology replicated the precise perturbations from the model on the chick embryo in the lab to make sure these outcomes were not just a mathematical dream of the model. Interestingly, these artificially created chick embryos also displayed gastrulation fluxes that are found in fish and frogs in the wild.

These results, which were published in Science Advances, imply that different vertebrate species may have evolved different fundamental principles underlying multicellular self-organization.

"Fish, frogs and chicks all live in different environments, so over time, the evolutionary pressure may have changed the parameters and the initial conditions of embryo development," said Serra. "But some of the self-organizing core principles, at least in this early stage of gastrulation, may be the same in all three."

These days, Serra and his associates are investigating additional processes that result in self-organizing patterns at the embryonic stage. They believe that by advancing biomaterials design and regenerative medicine, their research will contribute to a longer and better life for people.

"The human body is the most complex dynamical system in existence," he said. It's fascinating to think about the numerous intriguing biological, physical, and mathematical mysteries surrounding our body. The discoveries we can make are endless."