The shape changing is no mere curiosity. Volvox embryos do it in two ways, and the one the Cambridge researchers studied is remarkably similar to something that occurs in the embryos of humans and other animals, when a ball of cells turns into a doughnut shape, with an inside and an outside. Although it’s not immediately obvious, grown up humans are still kind of messy doughnuts, with arms, head, legs and most of our internal organs all part of the doughnut itself. The hole, in terms of geometry, at least, is the digestive system, from beginning to end.

That process is called gastrulation, and it is enormously significant in the embryo’s growth, the beginning of a crucial distinction between what’s inside and what’s outside. The paper in Physical Review Letters describing the new research begins with a quote from the embryologist Lewis Wolpert: “It is not birth, marriage or death, but gastrulation which is truly the most important time in your life.”

Humans and other large, complicated animals are, however, very difficult to study. Even when they are embryos, their cells not only change shape during gastrulation but move around and turn into different kinds of tissues.

For Stephanie Höhn, Raymond E. Goldstein and their Cambridge colleagues who did the research, Volvox presented a process that is a little bit simpler. The spherical skin of a Volvox embryo is one cell deep. Each cell has a tail, and just before inversion they are all pointing inward. They need to point outward, so they can flutter and move the Volvox along, so the embryo turns inside out.

All the cells stay in place, maintaining their connections with other cells. But they change shape. Dr. Goldstein said, “If you were to take a basketball and you tried to turn the thing inside out,” that would be similar to what Volvox has to do.