Mechanical feedback as a possible regulator of tissue growth

doi:10.1073/pnas.0404782102

Mechanical feedback as a possible regulator of tissue growth

Boris I. Shraiman†

Kavli Institute for Theoretical Physics, Kohn Hall, University of California, Santa Barbara, CA 93106

Edited by Eric F. Wieschaus, Princeton University, Princeton, NJ (received for review July 8, 2004)

Abstract

Regulation of cell growth and proliferation has a fundamental role in animal and plant development and in the progression of cancer. In the context of development, it is important to understand the mechanisms that coordinate growth and patterning of tissues. Imaginal discs, which are larval precursors of fly limbs and organs, have provided much of what we currently know about these processes. Here, we consider the mechanism that is responsible for the observed uniformity of growth in wing imaginal discs, which persists in the presence of gradients in growth inducing morphogens in spite of the stochastic nature of cell division. The phenomenon of “cell competition,” which manifests in apoptosis of slower-growing cells in the vicinity of faster growing tissue, suggests that uniform growth is not a default state but a result of active regulation. How can a patch of tissue compare its growth rate with that of its surroundings? A possible way is furnished by mechanical interactions. To demonstrate this mechanism, we formulate a mathematical model of nonuniform growth in a layer of tissue and examine its mechanical implications. We show that a clone growing faster or slower than the surrounding tissue is subject to mechanical stress, and we propose that dependence of the rate of cell division on local stress could provide an “integral-feedback” mechanism stabilizing uniform growth. The proposed mechanism of growth control is not specific to imaginal disc growth and could be of general relevance. Several experimental tests of the proposed mechanism are suggested.

Footnotes

↵ † E-mail: shraiman{at}kitp.ucsb.edu.
This paper was submitted directly (Track II) to the PNAS office.
Abbreviation: Dpp, Decapentaplegic.
↵ ‡ Another problem involves the proposed notion that morphogen gradient decreases in inverse proportion with the size of the tissue. The latter behavior does not follow from the laws of diffusion without an additional assumption that the rate of Dpp secretion at the antero-posterior boundary itself decreases in inverse proportion with the size.
↵ § For simplicity of presentation, we discuss here 2D pressure in an idealized 2D tissue. In reality, this 2D pressure would be the uniaxial stress in the cell layer corresponding to the modulation of layer thickness and cell (apical) area.
↵ ¶ The right side of Eq. 1 vanishes for uniform γ, which thus yields stress-less growth. More generally, stress-less growth can be produced by a special class of nonuniform growth patterns: those with γ satisfying Δ²γ = 0 (see Supporting Appendix).
↵ ∥ One can imagine an alternative mechanism in which cells communicate their proliferation rate (or their local density) to their neighbors by means of a chemical messenger (or cell contact interaction). However, to compare their own growth rate with that of the surrounding tissue, cells would have to correctly calibrate the received signal by fine tuning signal-transduction parameters.
↵ ** This characteristic length does not necessarily correspond to the thickness of the disc, because the elasticity of the tissue is likely to reside in a much thinner apical cytoskeleton layer.