Repulsive expansion dynamics in colony growth and gene expression.

Spatial expansion of a population of cells can arise from growth of microorganisms, plant cells, and mammalian cells. It underlies normal or dysfunctional tissue development, and it can be exploited as the foundation for programming spatial patterns. This expansion is often driven by continuous growth and division of cells within a colony, which in turn pushes the peripheral cells outward. This process generates a repulsion velocity field at each location within the colony. Here we show that this process can be approximated as coarse-grained repulsive-expansion kinetics. This framework enables accurate and efficient simulation of growth and gene expression dynamics in radially symmetric colonies with homogenous z-directional distribution. It is robust even if cells are not spherical and vary in size. The simplicity of the resulting mathematical framework also greatly facilitates generation of mechanistic insights.

Massive computational acceleration by using neural networks to emulate mechanism-based biological models.

For many biological applications, exploration of the massive parametric space of a mechanism-based model can impose a prohibitive computational demand. To overcome this limitation, we present a framework to improve computational efficiency by orders of magnitude. The key concept is to train a neural network using a limited number of simulations generated by a mechanistic model. This number is small enough such that the simulations can be completed in a short time frame but large enough to enable reliable training. The trained neural network can then be used to explore a much larger parametric space. We demonstrate this notion by training neural networks to predict pattern formation and stochastic gene expression. We further demonstrate that using an ensemble of neural networks enables the self-contained evaluation of the quality of each prediction. Our work can be a platform for fast parametric space screening of biological models with user defined objectives.

Bacterially driven cadmium sulfide precipitation on porous membranes: Toward platforms for photocatalytic applications.

The emerging field of biofabrication capitalizes on nature's ability to create materials with a wide range of well-defined physical and electronic properties. Particularly, there is a current push to utilize programmed, self-organization of living cells for material fabrication. However, much research is still necessary at the interface of synthetic biology and materials engineering to make biofabrication a viable technique to develop functional devices. Here, the authors exploit the ability of Escherichia coli to contribute to material fabrication by designing and optimizing growth platforms to direct inorganic nanoparticle (NP) synthesis, specifically cadmium sulfide (CdS) NPs, onto porous polycarbonate membranes. Additionally, current, nonbiological, chemical synthesis methods for CdS NPs are typically energy intensive and use high concentrations of hazardous cadmium precursors. Using biosynthesis methods through microorganisms could potentially alleviate these issues by precipitating NPs with less energy and lower concentrations of toxic precursors. The authors adopted extracellular precipitation strategies to form CdS NPs on the membranes as bacterial/membrane composites and characterized them by spectroscopic and imaging methods, including energy dispersive spectroscopy, and scanning and transmission electron microscopy. This method allowed us to control the localization of NP precipitation throughout the layered bacterial/membrane composite, by varying the timing of the cadmium precursor addition. Additionally, the authors demonstrated the photodegradation of methyl orange using the CdS functionalized porous membranes, thus confirming the photocatalytic properties of these composites for eventual translation to device development. If combined with the genetically programmed self-organization of cells, this approach promises to directly pattern CdS nanostructures on solid supports.

Programmable assembly of pressure sensors using pattern-forming bacteria.

Biological systems can generate microstructured materials that combine organic and inorganic components and possess diverse physical and chemical properties. However, these natural processes in materials fabrication are not readily programmable. Here, we use a synthetic-biology approach to assemble patterned materials. We demonstrate programmable fabrication of three-dimensional (3D) materials by printing engineered self-patterning bacteria on permeable membranes that serve as a structural scaffold. Application of gold nanoparticles to the colonies creates hybrid organic-inorganic dome structures. The dynamics of the dome structures' response to pressure is determined by their geometry (colony size, dome height, and pattern), which is easily modified by varying the properties of the membrane (e.g., pore size and hydrophobicity). We generate resettable pressure sensors that process signals in response to varying pressure intensity and duration.

Elements of biological oscillations in time and space.

Oscillations in time and space are ubiquitous in nature and play critical roles in dynamic cellular processes. Although the molecular mechanisms underlying the generation of the dynamics are diverse, several distinct regulatory elements have been recognized as being critical in producing and modulating oscillatory dynamics. These include negative and positive feedback, time delay, nonlinearity in regulation, and random fluctuations ('noise'). Here we discuss the specific roles of these five elements in promoting or attenuating oscillatory dynamics, by drawing on insights from quantitative analyses of natural or synthetic biological networks.

Collective Space-Sensing Coordinates Pattern Scaling in Engineered Bacteria.

Scale invariance refers to the maintenance of a constant ratio of developing organ size to body size. Although common, its underlying mechanisms remain poorly understood. Here, we examined scaling in engineered Escherichia coli that can form self-organized core-ring patterns in colonies. We found that the ring width exhibits perfect scale invariance to the colony size. Our analysis revealed a collective space-sensing mechanism, which entails sequential actions of an integral feedback loop and an incoherent feedforward loop. The integral feedback is implemented by the accumulation of a diffusive chemical produced by a colony. This accumulation, combined with nutrient consumption, sets the timing for ring initiation. The incoherent feedforward is implemented by the opposing effects of the domain size on the rate and duration of ring maturation. This mechanism emphasizes a role of timing control in achieving robust pattern scaling and provides a new perspective in examining the phenomenon in natural systems.

Temporal control of self-organized pattern formation without morphogen gradients in bacteria.

Diverse mechanisms have been proposed to explain biological pattern formation. Regardless of their specific molecular interactions, the majority of these mechanisms require morphogen gradients as the spatial cue, which are either predefined or generated as a part of the patterning process. However, using Escherichia coli programmed by a synthetic gene circuit, we demonstrate here the generation of robust, self-organized ring patterns of gene expression in the absence of an apparent morphogen gradient. Instead of being a spatial cue, the morphogen serves as a timing cue to trigger the formation and maintenance of the ring patterns. The timing mechanism enables the system to sense the domain size of the environment and generate patterns that scale accordingly. Our work defines a novel mechanism of pattern formation that has implications for understanding natural developmental processes.