Designing modular reaction-diffusion programs for complex pattern formation

Abstract

Cells use sophisticated, multiscale spatial patterns of chemical instructions to control cell fate and tissue growth. While some types of synthetic pattern formation have been well studied1-6, it remains unclear how to design chemical processes that can reproducibly create similar spatial patterns. Here we describe a scalable approach for the design of processes that generate such patterns, which can be implemented using synthetic DNA reaction-diffusion networks7,8. In our method, black-box modules are connected together into integrated programs for arbitrarily complex pattern formation. These programs can respond to input stimuli, process information, and ultimately produce stable output patterns that differ in size and concentration from their inputs. To build these programs, we break a target pattern into a set of patterning subtasks, design modules to perform these subtasks independently, and combine the modules into networks. We demonstrate in simulation how programs designed with our methodology can generate complex patterns, including a French flag and a stick figure.

Stable DNA-based reaction–diffusion patterns

“…49,50 This process enables chemical patterns formed by reaction-diffusion processes to regenerate when perturbed, and could serve as a building block for the modular design of reaction-diffusion processes that form more complex patterns such as a stick gure.…”

Microscopic agents programmed by DNA circuits

“…Many of these man-made systems are inspired by regulatory networks observed within single cells: logic circuits seen in signaling cascades 3,4 ; circadian oscillators pacing the metabolism of light-harvesting microorganisms 5,6 ; all-ornothing switches embedded in genetic regulation pathways 4,7,8 , shape-forming morphogen fronts in developing embryos [9][10][11][12] . These systems are based on homogeneous mixtures where a unique computation happens in one bulk solution.…”

A self-regulating biomolecular comparator for processing oscillatory signals

“…A growing set of tools for engineering in vivo RNA-based logic could be used to design these mechanisms [30][31][32][33]. In vitro, transcriptional circuits [13,34,35] or strand displacement circuits [9,36] could potentially also implement the mechanisms we describe.…”

“…The same condition holds for P T and P A , which are used to produce T and A respectively, so these species are also modelled as having constant concentrations. In vivo, the stability of precursor concentrations could be achieved through buffering [19], whereas in vitro, high concentrations of these precursors could cause them to remain effectively constant over long time periods [9,20].…”