It is hard to bridge the gap between mathematical formulations and biological implementations of Turing patterns, yet this is necessary for both understanding and engineering these networks with synthetic biology approaches. Here, we model a reaction–diffusion system with two morphogens in a monostable regime, inspired by components that we recently described in a synthetic biology study in mammalian cells.1 The model employs a single promoter to express both the activator and inhibitor genes and produces Turing patterns over large regions of parameter space, using biologically interpretable Hill function reactions. We applied a stability analysis and identified rules for choosing biologically tunable parameter relationships to increase the likelihood of successful patterning. We show how to control Turing pattern sizes and time evolution by manipulating the values for production and degradation relationships. More importantly, our analysis predicts that steep dose–response functions arising from cooperativity are mandatory for Turing patterns. Greater steepness increases parameter space and even reduces the requirement for differential diffusion between activator and inhibitor. These results demonstrate some of the limitations of linear scenarios for reaction–diffusion systems and will help to guide projects to engineer synthetic Turing patterns.

Engineering spatial patterning in mammalian cells, employing entirely genetically encoded components, requires solving several problems. These include how to code secreted activator or inhibitor molecules and how to send concentration-dependent signals to neighboring cells, to control gene expression. The Madin–Darby Canine Kidney (MDCK) cell line is a potential engineering scaffold as it forms hollow spheres (cysts) in 3D culture and tubulates in response to extracellular hepatocyte growth factor (HGF). We first aimed to graft a synthetic patterning system onto single developing MDCK cysts. We therefore developed a new localized transfection method to engineer distinct sender and receiver regions. A stable reporter line enabled reversible EGFP activation by HGF and modulation by a secreted repressor (a truncated HGF variant, NK4). By expanding the scale to wide fields of cysts, we generated morphogen diffusion gradients, controlling reporter gene expression. Together, these components provide a toolkit for engineering cell–cell communication networks in 3D cell culture.

Single-cell RNA sequencing studies on gene co-expression patterns could yield important regulatory and functional insights, but have so far been limited by the confounding effects of differentiation and cell cycle. We apply a tailored experimental design that eliminates these confounders, and report thousands of intrinsically covarying gene pairs in mouse embryonic stem cells. These covariations form a network with biological properties, outlining known and novel gene interactions. We provide the first evidence that miRNAs naturally induce transcriptome-wide covariations and compare the relative importance of nuclear organization, transcriptional and post-transcriptional regulation in defining covariations. We find that nuclear organization has the greatest impact, and that genes encoding for physically interacting proteins specifically tend to covary, suggesting importance for protein complex formation. Our results lend support to the concept of post-transcriptional RNA operons, but we further present evidence that nuclear proximity of genes may provide substantial functional regulation in mammalian single cells.