Mechanical Feedback in Regulating the Size of Growing Multicellular Spheroids

TL;DR

This paper introduces a thermodynamically motivated model incorporating energetic costs of growth to explain how mechanical feedback regulates the finite size of multicellular spheroids, aligning with experimental observations.

Contribution

It extends classical morphoelasticity by adding growth energy costs, enabling size control and realistic stress profiles in tissue growth models.

Findings

Model predicts finite spheroid size consistent with experiments.

Reproduces residual stress profiles observed in spheroids.

Emerges necrotic core naturally from the framework.

Abstract

The mechanism by which cells measure the dimension of the organ in which they are embedded, and slow down their growth when the final size is reached, is a long-standing problem of developmental biology. The role of mechanics in this feedback is considered important. Morphoelasticity is a standard continuum framework for modeling growing elastic tissues. However, in this theory, in the absence of additional variables, the feedback between growth and mechanical stress leads to either a collapse or unbounded growth of the tissue, but usually prohibits reaching a finite asymptotic size ('size control'). In this article, we modify this classical setting to include an energetic cost associated with growth, leading to the physical effect of size control. The present model simultaneously provides a qualitatively correct residual stress profile and has a naturally emerging necrotic core, all of which have previously been experimentally established in multicellular spheroids. This is achieved through a local feedback mechanism derived from a thermodynamical framework. The model delivers testable predictions for experimental systems and could be a step towards the understanding of the role of mechanics in the multifaceted question of how growing organs attain their final size.