A feedback quenched oscillator produces turing patterning with one diffuser

Stability Analysis for Large-Scale Multi-Agent Molecular Communication Systems

Molecular communication (MC) is recently featured as a novel communication tool to connect individual biological nanorobots. It is expected that a large number of nanorobots can form large multi-agent MC systems through MC to accomplish complex and large-scale tasks that cannot be achieved by a single nanorobot. However, most previous models for MC systems assume a unidirectional diffusion communication channel and cannot capture the feedback between each nanorobot, which is important for multi-agent MC systems. In this paper, we introduce a system theoretic model for large-scale multi-agent MC systems using transfer functions, and then propose a method to analyze the stability for multi-agent MC systems. The proposed method decomposes the multi-agent MC system into multiple single-input and single-output (SISO) systems, which facilitates the application of simple analysis technique for SISO systems to the large-scale multi-agent MC system. Finally, we demonstrate the proposed method by analyzing the stability of a specific large-scale multi-agent MC system and clarify a parameter region to synchronize the states of nanorobots, which is important to make cooperative behaviors at a population level.

Spatiotemporal Patterning Enabled by Gene Regulatory Networks

Spatiotemporal pattern formation plays a key role in various biological phenomena including embryogenesis and neural network formation. Though the reaction-diffusion systems enabling pattern formation have been studied phenomenologically, the biomolecular mechanisms behind these processes have not been modeled in detail. Here, we study the emergence of spatiotemporal patterns due to simple, synthetic and commonly observed two- and three-node gene regulatory network motifs coupled with their molecular diffusion in one- and two-dimensional space. We investigate the patterns formed due to the coupling of inherent multistable and oscillatory behavior of the toggle switch, toggle switch with double self-activation, toggle triad, and repressilator with the effect of spatial diffusion of these molecules. We probe multiple parameter regimes corresponding to different regions of stability (monostable, multistable, oscillatory) and assess the impact of varying diffusion coefficients. This analysis offers valuable insights into the design principles of pattern formation facilitated by these network motifs, and it suggests the mechanistic underpinnings of biological pattern formation.

A Tug-of-War Mechanism for Pattern Formation in a Genetic Network

Synthesizing spatial patterns with genetic networks is an ongoing challenge in synthetic biology. A successful demonstration of pattern formation would imply a better understanding of systems in the natural world and advance applications in synthetic biology. In developmental systems, transient patterning may suffice in order to imprint instructions for long-term development. In this paper we show that transient but persistent patterns can emerge from a realizable synthetic gene network based on a toggle switch. We show that a bistable system incorporating diffusible molecules can generate patterns that resemble Turing patterns but are distinctly different in the underlying mechanism: diffusion of mutually inhibiting molecules creates a prolonged "tug-of-war" between patches of cells at opposing bistable states. The patterns are transient but longer wavelength patterns persist for extended periods of time. Analysis of a representative small scale model implies the eigenvalues of the persistent modes are just above the threshold of stability. The results are verified through simulation of biologically relevant models.

Delay-induced wave instabilities in single-species reaction-diffusion systems

The Turing (wave) instability is only possible in reaction-diffusion systems with more than one (two) components. Motivated by the fact that a time delay increases the dimension of a system, we investigate the presence of diffusion-driven instabilities in single-species reaction-diffusion systems with delay. The stability of arbitrary one-component systems with a single discrete delay, with distributed delay, or with a variable delay is systematically analyzed. We show that a wave instability can appear from an equilibrium of single-species reaction-diffusion systems with fluctuating or distributed delay, which is not possible in similar systems with constant discrete delay or without delay. More precisely, we show by basic analytic arguments and by numerical simulations that fast asymmetric delay fluctuations or asymmetrically distributed delays can lead to wave instabilities in these systems. Examples, for the resulting traveling waves are shown for a Fisher-KPP equation with distributed delay in the reaction term. In addition, we have studied diffusion-induced instabilities from homogeneous periodic orbits in the same systems with variable delay, where the homogeneous periodic orbits are attracting resonant periodic solutions of the system without diffusion, i.e., periodic orbits of the Hutchinson equation with time-varying delay. If diffusion is introduced, standing waves can emerge whose temporal period is equal to the period of the variable delay.

Turing Patterning Using Gene Circuits with Gas-Induced Degradation of Quorum Sensing Molecules

The Turing instability was proposed more than six decades ago as a mechanism leading to spatial patterning, but it has yet to be exploited in a synthetic biology setting. Here we characterize the Turing instability in a specific gene circuit that can be implemented in vitro or in populations of clonal cells producing short-range activator N-Acyl homoserine lactone (AHL) and long-range inhibitor hydrogen peroxide (H2O2) gas. Slowing the production rate of the AHL-degrading enzyme, AiiA, generates stable fixed states, limit cycle oscillations and Turing patterns. Further tuning of signaling parameters determines local robustness and controls the range of unstable wavenumbers in the patterning regime. These findings provide a roadmap for optimizing spatial patterns of gene expression based on familiar quorum and gas sensitive E. coli promoters. The circuit design and predictions may be useful for (re)programming spatial dynamics in synthetic and natural gene expression systems.

Signaling Delays Preclude Defects in Lateral Inhibition Patterning

Lateral inhibition represents a well-studied example of biology's ability to self-organize multicellular spatial patterns with single-cell precision. Despite established biochemical mechanisms for lateral inhibition (e.g., Delta-Notch), it remains unclear how cell-cell signaling delays inherent to these mechanisms affect patterning outcomes. We investigate a compact model of lateral inhibition highlighting these delays and find, remarkably, that long delays can ensure defect-free patterning. This effect is underscored by an interplay with synchronous oscillations, cis interactions, and signaling strength. Our results suggest that signaling delays, though previously posited as a source of developmental defects, may in fact be a general regulatory knob for tuning developmental robustness.

Modular Synthetic Inverters from Zinc Finger Proteins and Small RNAs

Synthetic zinc finger proteins (ZFPs) can be created to target promoter DNA sequences, repressing transcription. The binding of small RNA (sRNA) to ZFP mRNA creates an ultrasensitive response to generate higher effective Hill coefficients. Here we combined three “off the shelf” ZFPs and three sRNAs to create new modular inverters in E. coli and quantify their behavior using induction fold. We found a general ordering of the effects of the ZFPs and sRNAs on induction fold that mostly held true when combining these parts. We then attempted to construct a ring oscillator using our new inverters. Our chosen parts performed insufficiently to create oscillations, but we include future directions for improvement upon our work presented here.

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.

Feedback, receptor clustering, and receptor restriction to single cells yield large Turing spaces for ligand-receptor-based Turing models

Turing mechanisms can yield a large variety of patterns from noisy, homogenous initial conditions and have been proposed as patterning mechanism for many developmental processes. However, the molecular components that give rise to Turing patterns have remained elusive, and the small size of the parameter space that permits Turing patterns to emerge makes it difficult to explain how Turing patterns could evolve. We have recently shown that Turing patterns can be obtained with a single ligand if the ligand-receptor interaction is taken into account. Here we show that the general properties of ligand-receptor systems result in very large Turing spaces. Thus, the restriction of receptors to single cells, negative feedbacks, regulatory interactions among different ligand-receptor systems, and the clustering of receptors on the cell surface all greatly enlarge the Turing space. We further show that the feedbacks that occur in the FGF10-SHH network that controls lung branching morphogenesis are sufficient to result in large Turing spaces. We conclude that the cellular restriction of receptors provides a mechanism to sufficiently increase the size of the Turing space to make the evolution of Turing patterns likely. Additional feedbacks may then have further enlarged the Turing space. Given their robustness and flexibility, we propose that receptor-ligand-based Turing mechanisms present a general mechanism for patterning in biology.

Autonomous bacterial localization and gene expression based on nearby cell receptor density

Escherichia coli were genetically modified to enable programmed motility, sensing, and actuation based on the density of features on nearby surfaces. Then, based on calculated feature density, these cells expressed marker proteins to indicate phenotypic response. Specifically, site-specific synthesis of bacterial quorum sensing autoinducer-2 (AI-2) is used to initiate and recruit motile cells. In our model system, we rewired E. coli's AI-2 signaling pathway to direct bacteria to a squamous cancer cell line of head and neck (SCCHN), where they initiate synthesis of a reporter (drug surrogate) based on a threshold density of epidermal growth factor receptor (EGFR). This represents a new type of controller for targeted drug delivery as actuation (synthesis and delivery) depends on a receptor density marking the diseased cell. The ability to survey local surfaces and initiate gene expression based on feature density represents a new area-based switch in synthetic biology that will find use beyond the proposed cancer model here.

BioFNet: biological functional network database for analysis and synthesis of biological systems

In synthetic biology and systems biology, a bottom-up approach can be used to construct a complex, modular, hierarchical structure of biological networks. To analyze or design such networks, it is critical to understand the relationship between network structure and function, the mechanism through which biological parts or biomolecules are assembled into building blocks or functional networks. A functional network is defined as a subnetwork of biomolecules that performs a particular function. Understanding the mechanism of building functional networks would help develop a methodology for analyzing the structure of large-scale networks and design a robust biological circuit to perform a target function. We propose a biological functional network database, named BioFNet, which can cover the whole cell at the level of molecular interactions. The BioFNet takes an advantage in implementing the simulation program for the mathematical models of the functional networks, visualizing the simulated results. It presents a sound basis for rational design of biochemical networks and for understanding how functional networks are assembled to create complex high-level functions, which would reveal design principles underlying molecular architectures.

Synthetic multicellularity

The ability to synthesize biological constructs on the scale of the organisms we observe unaided is probably one of the more outlandish, yet recurring, dreams humans have had since they began to modify genes. This review brings together recent developments in synthetic biology, cell and developmental biology, computation, and technological development to provide context and direction for the engineering of rudimentary, autonomous multicellular ensembles.