Dynamic positioning and precision of bistable gene expression boundaries through diffusion and morphogen decay

Abstract

1Traditional models for how morphogen gradients guide embryonic patterning fail to account for experimental observations of temporal refinement in gene expression domains. Dynamic positional information has recently emerged as a framework to address this shortcoming. Here, we explore two central aspects of dynamic positional information--the precision and placement of gene expression boundaries--in bistable genetic networks driven by morphogen gradients. First, we hypothesize that temporal morphogen decay may increase the precision of a boundary by compensating for variation in initial conditions that would otherwise lead neighboring cells with identical inputs to diverge to separate steady states. Second, we explore how diffusion of gene products may play a key role in placing gene expression boundaries. Using an existing model for Hb patterning in embryonic fruit flies, we show that diffusion permits boundaries to act as near-traveling wavefronts with local propagation speed determined by morphogen concentration. We then harness our understanding of near-traveling fronts to propose a method for achieving accurate steady-state boundary placement independent of initial conditions. Our work posits functional roles for temporally varying inputs and cell-to-cell coupling in the regulation and interpretation of dynamic positional information, illustrating that mathematical theory should serve to clarify not just our quantitative, but also our intuitive understanding of patterning processes. 2 Author SummaryIn many developmental systems, cells interpret spatial gradients of chemical morphogens to produce gene expression boundaries in exact positions. The simplest mathematical models for "positional information" rely on threshold detection, but such models are not robust to variations in the morphogen gradient or initial protein concentrations. Furthermore, these models fail to account for experimental results showing dynamic shifts in boundary placement and increased boundary precision over time. Here, we propose two theoretical mechanisms for enhancing boundary precision and placement using a bistable toggle switch. Distinct from existing research in "dynamic positional information", this work posits a functional role for temporal decay in morphogen concentration and for diffusion of gene expression products, the latter of which is often omitted in quantitative models. We suggest that future research into dynamic positional information would benefit from perspectives that link local (cellular) and global (patterning) behaviors, as well as from mathematical theory that builds our intuitive understanding alongside more data-driven approaches.