Mechanics dictate where and how freshwater planarians fission.

Asexual freshwater planarians reproduce by tearing themselves into two pieces by a process called binary fission. The resulting head and tail pieces regenerate within about a week, forming two new worms. Understanding this process of ripping oneself into two parts poses a challenging biomechanical problem. Because planarians stop "doing it" at the slightest disturbance, this remained a centuries-old puzzle. We focus on fission and show that it proceeds in three stages: a local constriction ("waist formation"), pulsation-which increases waist longitudinal stresses-and transverse rupture. We developed a linear mechanical model with a planarian represented by a thin shell. The model fully captures the pulsation dynamics leading to rupture and reproduces empirical time scales and stresses. It asserts that fission execution is a mechanical process. Furthermore, we show that the location of waist formation, and thus fission, is determined by physical constraints. Together, our results demonstrate that where and how a planarian rips itself apart during asexual reproduction can be fully explained through biomechanics.