Cross-inhibition of Turing patterns explains the self-organized regulatory mechanism of planarian fission

Abstract

Planarian worms reproduce asexually by fission, resulting in two separated pieces each repatterning and regenerating a complete animal. The induction of this process is known to be dependent on the size of the worm as well as on environmental factors such as population density, temperature, and light intensity. However, despite much progress in understanding the signaling mechanisms of planarian regeneration and the biomechanics of fissioning, no induction mechanism has been proposed for the signaling of fission. Here, we propose and analyze a cross-inhibited Turing system in a growing domain for the signaling of fission in planaria and the regeneration of the anterior-posterior opposite head and tail gene expression gradient patterns. This self-regulated mechanism explains when and where growing planaria fission, and its dependence on the worm length. Furthermore, we show how a delayed control mechanism of the cross-inhibited Turing system explains the asymmetry of the resulting fragments, the induction of fission with an anterior amputation even in a short worm, the consecutive multiple fissions called fragmentation, and the effects of environmental factors in the signaling of fission. We discuss the possible molecular and biophysical implementations of the proposed model and suggest specific experiments to elucidate them. In summary, the proposed controlled cross-inhibited Turing system represents a completely self-regulated model of the fission and regeneration signaling in planaria.