Cooperativity to increase Turing pattern space for synthetic biology.

Luis Diambra,Diego Barcena Menendez,Vivek Raj Senthivel,Mark Isalan

doi:10.1021/sb500233u

Luis Diambra, Diego Barcena Menendez + Show 2 more

Open Access

https://doi.org/10.1021/sb500233u

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Abstract

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.

Highlights

The self-organization of spatial patterns and structures is a fundamental problem in many fields, especially in developmental biology
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
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]

Summary

Introduction

The self-organization of spatial patterns and structures is a fundamental problem in many fields, especially in developmental biology. Even though many biological patterns resemble Turing patterns in appearance, this alone does not constitute a compelling proof of such mechanisms operating in living systems.[12] Alternatively, due to recent advances in biotechnology, the synthetic generation of Turing patterns in cell culture should be possible in the near future.[25,26] This will increase our fundamental understanding of these systems as well as provide tools for biotechnology applications To implement such engineered biological systems, we need to know a priori the requisite properties of the gene and protein building blocks. The key aim, was to develop a biologically interpretable model that would show us the most flexible parameter relationships for making patterns

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