A GRAPH PARTITIONING APPROACH TO PREDICTING PATTERNS IN LATERAL INHIBITION SYSTEMS

Cell-in-the-loop pattern formation with optogenetically emulated cell-to-cell signaling

Designing and implementing synthetic biological pattern formation remains challenging due to underlying theoretical complexity as well as the difficulty of engineering multicellular networks biochemically. Here, we introduce a cell-in-the-loop approach where living cells interact through in silico signaling, establishing a new testbed to interrogate theoretical principles when internal cell dynamics are incorporated rather than modeled. We present an easy-to-use theoretical test to predict the emergence of contrasting patterns in gene expression among laterally inhibiting cells. Guided by the theory, we experimentally demonstrate spontaneous checkerboard patterning in an optogenetic setup, where cell-to-cell signaling is emulated with light inputs calculated in silico from real-time gene expression measurements. The scheme successfully produces spontaneous, persistent checkerboard patterns for systems of sixteen patches, in quantitative agreement with theoretical predictions. Our research highlights how tools from dynamical systems theory may inform our understanding of patterning, and illustrates the potential of cell-in-the-loop for engineering synthetic multicellular systems.

Designing Spatially Distributed Gene Regulatory Networks To Elicit Contrasting Patterns

Pattern formation and differential interactions are important for microbial consortia to divide labor and perform complex functions. To obtain further insight into such interactions, we present a computational method for simulating physically separated microbial colonies, each implementing different gene regulatory networks. We validate our theory by experimentally demonstrating control over gene expression patterns in a diffusion-mediated lateral inhibition circuit. We highlight the importance of spatial arrangement as a control knob for modulating system behavior. Our systematic approach provides a foundation for future applications that require understanding and engineering of multistrain microbial communities for sophisticated, synergistic functions.

Pattern Formation over Multigraphs

Two of the most common pattern formation mechanisms are Turing-patterning in reaction-diffusion systems and lateral inhibition of neighboring cells. In this paper, we introduce a broad dynamical model of interconnected modules to study the emergence of patterns, with the above mentioned two mechanisms as special cases. Our results do not restrict the number of modules or their complexity, allow multiple layers of communication channels with possibly different interconnection structure, and do not assume symmetric connections between two connected modules. Leveraging only the static input/output properties of the subsystems and the spectral properties of the interconnection matrices, we characterize the stability of the homogeneous fixed points as well as sufficient conditions for the emergence of spatially non-homogeneous patterns. To obtain these results, we rely on properties of the graphs together with tools from monotone systems theory. As application examples, we consider patterning in neural networks, in reaction-diffusion systems, and contagion processes over random graphs.

A Compartmental Lateral Inhibition System to Generate Contrasting Patterns

We propose a lateral inhibition system and analyze contrasting patterns of gene expression. The system consists of a set of compartments interconnected by channels. Each compartment contains a colony of cells that produce diffusible molecules to be detected by the neighboring colonies. Each cell is equipped with an inhibitory circuit that reduces its production when the detected signal is sufficiently strong. We characterize the parameter range in which steady-state patterns emerge.