Search

MiS Preprint Repository

Delve into the future of research at MiS with our preprint repository. Our scientists are making groundbreaking discoveries and sharing their latest findings before they are published. Explore repository to stay up-to-date on the newest developments and breakthroughs.

MiS Preprint
67/2019

Signaling gradients in surface dynamics as basis for planarian regeneration

Arnd Scheel, Angela Stevens and Christoph Tenbrock

Abstract

We introduce and analyze a mathematical model for the regeneration of planarian flatworms. This system of differential equations incorporates dynamics of head and tail cells which express positional control genes that in turn translate into localized signals that guide stem cell differentiation. Orientation and positional information is encoded in the dynamics of a long range wnt-related signaling gradient. We motivate our model in relation to experimental data and demonstrate how it correctly reproduces cut and graft experiments. In particular, our system improves on previous models by preserving polarity in regeneration, over orders of magnitude in body size during cutting experiments and growth phases. Our model relies on tristability in cell density dynamics, between head, trunk, and tail. In addition, key to polarity preservation in regeneration, our system includes sensitivity of cell differentiation to gradients of wnt-related signals measured relative to the tissue surface. This process is particularly relevant in a small tissue layer close to wounds during their healing, and modeled here in a robust fashion through dynamic boundary conditions.

Supplementary materials (videos, mp4, 1MB)

Received:
Aug 15, 2019
Published:
Aug 15, 2019

Related publications

inJournal
2021 Repository Open Access
Arnd Scheel, Angela Stevens and Christoph Tenbrock

Signaling gradients in surface dynamics as basis for planarian regeneration

In: Journal of mathematical biology, 83 (2021) 1, p. 6