Synthetic microbial consortia consist of two or more engineered strains that grow together and share the same resources. When intercellular signaling pathways are included in the engineered strains, close proximity of the microbes can generate complex dynamic behaviors that are difficult to obtain using a single strain. However, when a consortium is not cultured in a well-mixed environment the constituent strains passively compete for space as they grow and divide, complicating cell−cell signaling. Here, we explore the temporal dynamics of the spatial distribution of consortia cocultured in microfluidic devices. To do this, we grew two different strains of Escherichia coli in microfluidic devices with celltrapping regions (traps) of several different designs. We found that the size of the traps is a critical determinant of spatiotemporal dynamics. In small traps, cells can easily signal one another, but the relative proportion of each strain within the trap can fluctuate wildly. In large traps, the relative ratio of strains is stabilized, but intercellular signaling can be hindered by distances between cells. This presents a trade-off between the trap size and the effectiveness of intercellular signaling, which can be mitigated by increasing the initial seeding of cells in larger traps. We also built a mathematical model, which suggests that increasing the number of seed cells can also increase the strain ratio variability due to an increased number of strain interfaces in the trap. These results help elucidate the complex behaviors of synthetic microbial consortia in microfluidic traps and provide a means of analysis to help remedy the spatial heterogeneity inherent to different trap types.

Advances in synthetic biology allow us to engineer bacterial collectives with pre-specified characteristics. However, the behavior of these collectives is difficult to understand, as cellular growth and division as well as extra-cellular fluid flow lead to complex, changing arrangements of cells within the population. To rationally engineer and control the behavior of cell collectives we need theoretical and computational tools to understand their emergent spatiotemporal dynamics. Here, we present an agent-based model that allows growing cells to detect and respond to mechanical interactions. Crucially, our model couples the dynamics of cell growth to the cell’s environment: Mechanical constraints can affect cellular growth rate and a cell may alter its behavior in response to these constraints. This coupling links the mechanical forces that influence cell growth and emergent behaviors in cell assemblies. We illustrate our approach by showing how mechanical interactions can impact the dynamics of bacterial collectives growing in microfluidic traps.

The increased complexity of synthetic microbial biocircuits highlights the need for distributed cell functionality due to concomitant increases in metabolic and regulatory burdens imposed on single-strain topologies. Distributed systems, however, introduce additional challenges since consortium composition and spatiotemporal dynamics of constituent strains must be robustly controlled to achieve desired circuit behaviors. Here, we address these challenges with a modeling-based investigation of emergent spatiotemporal population dynamics using cell-length control in monolayer, two-strain bacterial consortia. We demonstrate that with dynamic control of a strain’s division length, nematic cell alignment in close-packed monolayers can be destabilized. We find that this destabilization confers an emergent, competitive advantage to smaller-length strains—but by mechanisms that differ depending on the spatial patterns of the population. We used complementary modeling approaches to elucidate underlying mechanisms: an agent-based model to simulate detailed mechanical and signaling interactions between the competing strains, and a reductive, stochastic lattice model to represent cell-cell interactions with a single rotational parameter. Our modeling suggests that spatial strain-fraction oscillations can be generated when cell-length control is coupled to quorum-sensing signaling in negative feedback topologies. Our research employs novel methods of population control and points the way to programming strain fraction dynamics in consortial synthetic biology.

Increased complexity of engineered microbial biocircuits highlights the need for distributed cell functionality due to concomitant increases of metabolic and regulatory burdens imposed on single-strain topologies. Distributed systems, however, introduce additional challenges since consortium composition and spatiotemporal dynamics of constituent strains must be robustly controlled to achieve desired circuit behaviors. Here, we address these challenges with a modeling-based investigation of emergent spatiotemporal population dynamics that result from cell-length control of monolayer, two-strain bacterial consortia. We demonstrate that with dynamic control of a strain's division length, nematic cell alignment in close-packed monolayers can be destabilized. We found this destabilization conferred an emergent, competitive advantage on smaller-length strains---but by mechanisms that differed depending on the spatial patterns of the population. We used complementary modeling approaches to elucidate underlying mechanisms: an agent-based model to simulate detailed mechanical and signaling interactions between the competing strains and a reductive, stochastic lattice model to represent cell-cell interactions with a single rotational parameter. Our modeling suggests that spatial strain-fraction oscillations can be generated when cell-length control is coupled to quorum-sensing signaling in negative feedback topologies. Our research employs novel methods of population control and points the way to programming strain fraction dynamics in consortial synthetic biology.

Abstract. Advances in synthetic biology allow us to engineer bacterial collectives with pre-specified characteristics. However, the behavior of these collectives is difficult to understand, as cellular growth and division as well as extra-cellular fluid flow lead to complex, changing arrangements of cells within the population. To rationally engineer and control the behavior of cell collectives we need theoretical and computational tools to understand their emergent spatiotemporal dynamics. Here, we present an agent-based model that allows growing cells to detect and respond to mechanical interactions. Crucially, our model couples the dynamics of cell growth to the cell's environment: Mechanical constraints can affect cellular growth rate and a cell may alter its behavior in response to these constraints. This coupling links the mechanical forces that influence cell growth and emergent behaviors in cell assemblies. We illustrate our approach by showing how mechanical interactions can impact the dynamics of bacterial collectives growing in microfluidic traps.

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Synthetic microbial consortia consist of two or more engineered strains that grow together and share the same resources. When intercellular signaling pathways are included in the engineered strains, close proximity of the microbes can generate complex dynamic behaviors that are dicult to obtain using a single strain. However, when a consortium is not cultured in a well-mixed environment the constituent strains passively compete for space as they grow and divide, complicating cell-cell signaling. Here, we explore the temporal dynamics of the spatial distribution of consortia co-cultured in microuidic devices. To do this, we grew two dierent strains of Escherichia coli in microuidic devices with cell-trapping regions (traps) of several dierent designs. We found that the size and shape of the traps are critical determinants of spatiotemporal dynamics. In small traps, cells can easily signal one another but the relative proportion of each strain within the trap can uctuate wildly. In large traps, the relative ratio of 1 strains is stabilized, but intercellular signaling can be hindered by distances between cells. This presents a trade-o between the trap size and the eectiveness of intercellular signaling, which can be mitigated by controlling the initial seeding of cells in the large trap. These results show how synthetic microbial consortia behave in microuidic traps and provide a method to help remedy the spatial heterogeneity inherent to dierent trap geometries.

We consider the numerical solution of a phase field model for polycrystallization in the solidification of binary mixtures in a domain Ω ⊂ R 2 . The model is based on a free energy in terms of three order parameters: the local orientation Θ of the crystals, the local crystallinity φ, and the concentration c of one of the components of the binary mixture. The equations of motion are given by an initial-boundary value problem for a coupled system of partial differential equations consisting of a regularized second order total variation flow in Θ, an L 2 gradient flow in φ, and a W 1,2 (Ω) * gradient flow in c. Based on an implicit discretization in time by the backward Euler scheme, we suggest a splitting method such that the three semidiscretized equations can be solved separately and prove existence of a solution. As far as the discretization in space is concerned, the fourth order Cahn-Hilliard type equation in c is taken care of by a C 0 Interior Penalty Discontinuous Galerkin approximation which has the advantage that the same finite element space can be used as well for the spatial discretization of the equations in Θ and φ. The fully discretized equations represent parameter dependent nonlinear algebraic systems with the discrete time as a parameter. They are solved by a predictor corrector continuation strategy featuring an adaptive choice of the time-step. Numerical results illustrate the performance of the suggested numerical method.