In a recent study by researchers at the Massachusetts Institute of Technology, supporting evidence was found for the mathematics behind embryonic tissue folding. Embryonic tissue folding is the process of tissue forming that determines the shapes of most of our body’s inner workings. While scientists have been observing this phenomenon for quite a while now, there had previously been little information regarding why this process worked in the way that it does.

Embryonic tissue folding

During the 1970s and ‘80s, biologists researching tissue folding worked to identify the specific genes that encoded the process of tissue folding, but now, the focus of research has switched to the physical properties of the folding. Researchers hope that in understanding the physics of the folding, they will be able to engineer tissue folding outside of the body, which will provide insight into birth defects and other deformities that occur during embryonic tissue folding. Researchers at M.I.T. employed strategies similar to those used by astronomers observing the structure of galaxies to help grasp the physics behind these foldings.

Gastrulation in a fruit fly

In this particular study, researchers focused specifically on the process of gastrulation, during which the embryo transforms from a single layered sphere to a more complex shape. To observe this process, the researchers used fruit flies, whose gastrulation process is identical to that of humans. Adam Martin and Hannah Yevick – two lead authors of the study – have long hypothesized that the network of the proteins myosin and actin play a role in the process of tissue folding, but could not support their claim until now. In order to gain concrete evidence supporting their hypothesis, Martin and Yevick teamed up with Jörn Dunkel – an associate professor of physical applied mathematics at M.I.T.

Dunkel’s lab used a procedure in topology to identify features of a three-dimensional structure and trace the actomyosin networks across and between cells in a sheet of tissue. As Dunkel explains, “Once you have the network, you can apply standard methods from network analysis — the same kind of analysis that you would apply to streets or other transport networks, or the blood circulation network, or any other form of network.” An important part of the study was to determine how well the actomyosin network would respond to certain blockages and damages. The M.I.T. team found that the network contained substantial repetition. In other words, most of the “nodes” in the network are connected to many other “nodes” in the same network. This redundancy ensures that even if some of the cells in the network are damaged or blocked off, it can still fold correctly. “If you and I are holding a single rope, and then we cut it in the middle, it would come apart. But if you have a net, and cut it in some places, it still stays globally connected and can transmit forces, as long as you don’t cut all of it,” Dunkel says.

But the researchers are not yet done examining the processes of tissue folding. Martin says that he now plans to apply the techniques used during the fruit fly study to see if the same patterns occur in the neural tube of mice. The neural tube is important because if deformed, it can result in many different birth defects. “We would like to understand how it goes wrong,” Martin says. “It’s still not clear whether it’s the sealing up of the tube that’s problematic or whether there are defects in the folding process.” While many questions remain unanswered regarding tissue folding, it is clear that math will play a major role in solving these problems. In general, math is becoming an even more powerful tool for biologists by providing an algorithmic understanding of three-dimensional structures. Through close work with biologists, mathematicians like Jörn Dunkel are on the forefront of scientific research and are pushing boundaries previously thought not to exist.