Threshold Response to Stochasticity in Morphogenesis

TL;DR

This paper investigates how biological development, specifically in Drosophila eye formation, maintains ordered structures despite stochastic gene expression, revealing a threshold response that ensures robustness against noise.

Contribution

It introduces a mathematical model demonstrating a universal sigmoidal response of developmental patterning to stochasticity, highlighting a robustness threshold in morphogenesis.

Findings

Ordered patterns persist below a noise threshold

Beyond the threshold, patterns rapidly become disordered

Robustness allows genetic variation without phenotypic change

Abstract

During development of biological organisms, multiple complex structures are formed. In many instances, these structures need to exhibit a high degree of order to be functional, although many of their constituents are intrinsically stochastic. Hence, it has been suggested that biological robustness ultimately must rely on complex gene regulatory networks and clean-up mechanisms. Here we explore developmental processes that have evolved inherent robustness against stochasticity. In the context of the Drosophila eye disc, multiple optical units, ommatidia, develop into crystal-like patterns. During the larva-to-pupa stage of metamorphosis, the centers of the ommatidia are specified initially through the diffusion of morphogens, followed by the specification of R8 cells. Establishing the R8 cell is crucial in setting up the geometric, and functional, relationships of cells within an ommatidium and among neighboring ommatidia. Here we study a mathematical model of these spatio-temporal processes in the presence of stochasticity, defining and applying measures that quantify order within the resulting spatial patterns. We observe a universal sigmoidal response to increasing transcriptional noise. Ordered patterns persist up to a threshold noise level in the model parameters. As the noise is further increased past a threshold point of no return, these ordered patterns rapidly become disordered. Such robustness in development allows for the accumulation of genetic variation without any observable changes in phenotype. We argue that the observed sigmoidal dependence introduces robustness allowing for sizable amounts of genetic variation and transcriptional noise to be tolerated in natural populations without resulting in phenotype variation.