Pattern formation: engineering, evolution, and applications

Abstract

Pattern formation is essential to the arrangement and organization of biomolecules, cells, and tissues that define the structure and function of diverse organisms or systems, at a wide range of length scales (from sub-microns to kilometers). Examples include the formation of the division ring in a bacterial cell, the development of embryonic cells, the growth of bacterial colonies, as well as the organization of macroscopic ecosystems. The importance of pattern formation has been well recognized in biology for decades, as evidenced by the classical book, On Growth and Form (published in 1917), by D'Arcy Wentworth Thompson. Ever since, extensive efforts have been made to dissect mechanisms underlying pattern formation or to explain (by modeling) pattern formation from plausible mechanisms. The reaction-diffusion model proposed by Alan Turing in 1952, is a representative example of the latter.Building upon these mathematical frameworks, synthetic biologists have aimed to engineer self-organized pattern formation using gene circuits. This has led to the creation of simple patterns such as core-ring structures, spots, 3D multi-layered patterns, and symmetry-breaking configurations. However, synthetic patterns remain far less complex than those found in nature, indicating that our understanding of pattern formation is still rudimentary, and the engineering of such systems is far from mature. In this dissertation, I will discuss the progress of engineering pattern formation and present my research on investigating pattern formation from three major aspects: engineering, evolution, and applications. First, pattern engineering is challenging due to two major reasons – the systems are intrinsically complex, leading to patterns arising within an extremely narrow parameter space; computation-aided design is also computationally costly due to the curse of dimensionality. To address these challenges, I developed a method that leverages the complementary advantages of mechanistic modeling and deep learning. This approach uncovered human-interpretable pattern formation rules and enabled the robust generation of rare patterns. Second, natural microbiome forms spatial patterns when growing on a surface. However, our understanding of how cells interact under the spatial structures and give rise to collective behaviors is limited. Utilizing Pseudomonas aeruginosa swarming colonies as a model system, a new mechanism of how the spatial structure quantitatively regulates the microbial interactions and was uncovered. Finally, pattern formation is a self-organizing process, which represents a form of computation. It converts environmental and genetic inputs into a two-dimensional morphology, with the patterning mechanisms defining the computational rules. I demonstrated that such systems can be used to encode information and enhance information security.