Abstract
The Turing reaction-diffusion model explains how identical cells can self-organize to form spatial patterns. It has been suggested that extracellular signaling molecules with different diffusion coefficients underlie this model, but the contribution of cell-autonomous signaling components is largely unknown. We developed an automated mathematical analysis to derive a catalog of realistic Turing networks. This analysis reveals that in the presence of cell-autonomous factors, networks can form a pattern with equally diffusing signals and even for any combination of diffusion coefficients. We provide a software (available at http://www.RDNets.com) to explore these networks and to constrain topologies with qualitative and quantitative experimental data. We use the software to examine the self-organizing networks that control embryonic axis specification and digit patterning. Finally, we demonstrate how existing synthetic circuits can be extended with additional feedbacks to form Turing reaction-diffusion systems. Our study offers a new theoretical framework to understand multicellular pattern formation and enables the wide-spread use of mathematical biology to engineer synthetic patterning systems.
Highlights
How cells self-organize to form ordered structures is a central question in developmental biology (Hiscock and Megason, 2015), and identifying self-organizing mechanisms promises to provide new tools for synthetic biology and regenerative medicine (Chen and Weiss, 2005; Guye and Weiss, 2008; Isalan et al, 2008; Bansagi et al, 2011; Chau et al, 2012; Mishra et al, 2014; Schaerli et al, 2014; Wroblewska et al, 2015)
Our results show that reaction-diffusion systems have three types of requirements for the diffusible signals depending on the network topology: Type I networks require differential diffusivity, Type II networks allow equal diffusivities, and Type III networks allow for unconstrained diffusivity
Understanding how complex gene regulatory networks control cellular behavior is a challenging problem in biology; even small networks can contain regulatory feedbacks that make systems behaviors difficult to predict (Le Novere, 2015)
Summary
How cells self-organize to form ordered structures is a central question in developmental biology (Hiscock and Megason, 2015), and identifying self-organizing mechanisms promises to provide new tools for synthetic biology and regenerative medicine (Chen and Weiss, 2005; Guye and Weiss, 2008; Isalan et al, 2008; Bansagi et al, 2011; Chau et al, 2012; Mishra et al, 2014; Schaerli et al, 2014; Wroblewska et al, 2015). More than six decades ago, Alan Turing proposed a theoretical model in which interactions between diffusible substances can break the initial symmetry of cell fields to form periodic patterns (Turing, 1952). Numerous studies have proposed models based on these concepts to explain pattern formation during development, including skin appendage specification (Sick et al, 2006; Harris et al, 2005), lung branching (Menshykau et al, 2012; Hagiwara et al, 2015), tooth development (Salazar-Ciudad and Jernvall, 2010), rugae formation (Economou et al, 2012), and digit patterning (Sheth et al, 2012; Raspopovic et al, 2014). The evidence in support of specific activator-inhibitor pairs has been limited, and few studies have provided experimental support for the differential diffusivity of activators and inhibitors (Kondo and Miura, 2010; Marcon and Sharpe, 2012; Muller et al, 2012)
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