While natural phenomena may often appear to be complex and hence difficult to predict, in between those seemingly chaotic events, there can be moments of strikingly beautiful patterns and forms. In certain sense, synthetic biology is about identifying and reproducing these patterns and mathematics is about describing and understanding the mechanisms behind their formations. Although spatial patterns are ubiquitous in living organisms, the task of identifying the underlying mechanisms can be daunting due to the overwhelming complexity of living cells and organisms. Indeed, the study of natural patterns dates back to many centuries in the past. In this proposal, the team proposes to combine gene circuit engineering and mathematical analysis to advance our understanding of reaction-diffusion (RD) based biological pattern formation. Specifically, there are three main objectives the team hopes to achieve in the proposed research: Aim 1, Experimentally and mathematically characterize RD based cellular pattern formation driven by rationally designed gene circuits. Aim 2, Investigate implications of nutrient limitation on pattern formation. Aim 3, Engineering and testing of pattern formation of interacting populations. Specifically, the team proposes to engineer a set of gene circuits to direct bacterial cells to form self-organized patterns without predefined spatial cues. The role of network topology, nonlinearity, gene expression stochasticity, and environmental signals in contributions to observed spatially structured patterns will be examined. To this end, this interdisciplinary team plans to mechanistically formulate a series of plausible RD models that accurately describe gene regulation, protein production, quorum sensing, and dispersion driven by synthetic circuits. Moreover, the team plans to develop appropriate experimental, computational, and mathematical tools based on the single-cell agarose pad platform that shall allow us to quantitatively and experimentally probe the fundamental mechanisms of spatial patterns formation across molecular, single-cell, and colony scales.