Biological organisms rely on spatial variation in cell activity to coordinate diverse activities, such as microbial colonization and embryonic development. Interactions among neighboring cells play a crucial role in generating spatial patterns spontaneously from stochastic initial conditions or by refining simple spatially varying inputs, such as chemical concentration gradients, into complex outputs, such as stripes in gene expression. The ability to synthetically engineer multicellular patterning will facilitate advances in designing microbial communities, creating synthetic biomaterials, and programming tissue and organ growth, among other applications. Researchers face numerous theoretical and practical challenges to implementing patterning in synthetic biological setups, in part because living systems are extremely high dimensional and nonlinear. Thus, a handful of theories have guided most experimental efforts to implement multicellular patterning, and most successes have relied primarily on trial and error or numerical simulation. Future progress in synthetic multicellular patterning will benefit from interpretable mathematical theory for patterning phenomena, coupled with experimental platforms for validating these theories in practice. In this thesis, I develop methods for understanding and implementing multicellular patterning through the lens of networked dynamical systems, in which individual cells are modeled as dynamical systems and their interactions are modeled as networks. With this mathematical representation, cell behavior and network structure can be partially decoupled, facilitating both analysis and intuition building. In Chapter 2, I introduce a spatial filtering approach to biological pattern refinement, in which a network of interacting cells is treated as a "filter" for interpreting a prepattern into a different output pattern. This approach separates the exact form of the prepattern from the resulting readout, enabling a spatial frequency-based interpretation of pattern refinement that is conducive to analysis with extant intuition from signal processing. In the remaining two chapters, I apply theory for contrasting patterning to two unique synthetic biological setups. Chapter 3 focuses on a platform in which colonies of bacteria physically connected by channels interact through the exchange of diffusible molecules. Spatial parameters such as the distance between colonies and their placement is exploited to modulate patterning features, including contrast level and stability. Chapter 4 describes a setup in which chemical interaction among yeast cells is substituted with computer-controlled inputs that are adjusted in real time based on the measured gene expression levels. Theory predicted spontaneous contrasting patterning with qualitative and quantitative accuracy, demonstrating the potential benefits of this experimental platform for future avenues in multicellular patterning research. A central theme throughout this thesis is how exploiting a dynamical systems framework can provide new insights into (possible) patterning behaviors by considering them with a different perspective from the usual. For example, I show in Chapter 2 that random, constant-in-time spatial variation can generate Turing-like patterns when system dynamics are stable; conventional wisdom requires an instability to observe such patterns. Similarly, in Chapter 4, I show how "lateral inhibition" can be achieved without cells physically communicating or even physically neighboring each other---an impossible paradigm in customary biological setups. Moving forward, I hope this work will stand as just one example of how an interdisciplinary approach can shed light on the structure and function of living systems, evolved and engineered alike.




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