Quorum-Sensing Synchronization of Synthetic Toggle Switches: A Design Based on Monotone Dynamical Systems Theory

A computational design of a programmable biological processor

Basic synthetic information processing structures, such as logic gates, oscillators and flip-flops, have already been implemented in living organisms. Current implementations of these structures have yet to be extended to more complex processing structures that would constitute a biological computer. We make a step forward towards the construction of a biological computer. We describe a model-based computational design of a biological processor that uses transcription and translation resources of the host cell to perform its operations. The proposed processor is composed of an instruction memory containing a biological program, a program counter that is used to address this memory, and a biological oscillator that triggers the execution of the next instruction in the memory. We additionally describe the implementation of a biological compiler that compiles a sequence of human-readable instructions into ordinary differential equation-based models, which can be used to simulate and analyse the dynamics of the processor. The proposed implementation presents the first programmable biological processor that exploits cellular resources to execute the specified instructions. We demonstrate the application of the described processor on a set of simple yet scalable biological programs. Biological descriptions of these programs can be produced manually or automatically using the provided compiler.

Controlling spatiotemporal pattern formation in a concentration gradient with a synthetic toggle switch

The formation of spatiotemporal patterns of gene expression is frequently guided by gradients of diffusible signaling molecules. The toggle switch subnetwork, composed of two cross-repressing transcription factors, is a common component of gene regulatory networks in charge of patterning, converting the continuous information provided by the gradient into discrete abutting stripes of gene expression. We present a synthetic biology framework to understand and characterize the spatiotemporal patterning properties of the toggle switch. To this end, we built a synthetic toggle switch controllable by diffusible molecules in Escherichia coli. We analyzed the patterning capabilities of the circuit by combining quantitative measurements with a mathematical reconstruction of the underlying dynamical system. The toggle switch can produce robust patterns with sharp boundaries, governed by bistability and hysteresis. We further demonstrate how the hysteresis, position, timing, and precision of the boundary can be controlled, highlighting the dynamical flexibility of the circuit.

Multi-modality in gene regulatory networks with slow promoter kinetics

Phenotypical variability in the absence of genetic variation often reflects complex energetic landscapes associated with underlying gene regulatory networks (GRNs). In this view, different phenotypes are associated with alternative states of complex nonlinear systems: stable attractors in deterministic models or modes of stationary distributions in stochastic descriptions. We provide theoretical and practical characterizations of these landscapes, specifically focusing on stochastic Slow Promoter Kinetics (SPK), a time scale relevant when transcription factor binding and unbinding are affected by epigenetic processes like DNA methylation and chromatin remodeling. In this case, largely unexplored except for numerical simulations, adiabatic approximations of promoter kinetics are not appropriate. In contrast to the existing literature, we provide rigorous analytic characterizations of multiple modes. A general formal approach gives insight into the influence of parameters and the prediction of how changes in GRN wiring, for example through mutations or artificial interventions, impact the possible number, location, and likelihood of alternative states. We adapt tools from the mathematical field of singular perturbation theory to represent stationary distributions of Chemical Master Equations for GRNs as mixtures of Poisson distributions and obtain explicit formulas for the locations and probabilities of metastable states as a function of the parameters describing the system. As illustrations, the theory is used to tease out the role of cooperative binding in stochastic models in comparison to deterministic models, and applications are given to various model systems, such as toggle switches in isolation or in communicating populations, a synthetic oscillator, and a trans-differentiation network.

Reprogramming cooperative monotone dynamical systems

Multistable dynamical systems are ubiquitous in nature, especially in the context of regulatory networks controlling cell fate decisions, wherein stable steady states correspond to different cell phenotypes. In the past decade, it has become experimentally possible to "reprogram" the fate of a cell by suitable externally imposed input stimulations. In several of these reprogramming instances, the underlying regulatory network has a known structure and often it falls in the class of cooperative monotone dynamical systems. In this paper, we therefore leverage this structure to provide concrete guidance on the choice of inputs that reprogram a cooperative dynamical system to a desired target steady state. Our results are parameter-independent and therefore can serve as a practical guidance to cell-fate reprogramming experiments.

Computing with biological switches and clocks

The complex dynamics of biological systems is primarily driven by molecular interactions that underpin the regulatory networks of cells. These networks typically contain positive and negative feedback loops, which are responsible for switch-like and oscillatory dynamics, respectively. Many computing systems rely on switches and clocks as computational modules. While the combination of such modules in biological systems leads to a variety of dynamical behaviours, it is also driving development of new computing algorithms. Here we present a historical perspective on computation by biological systems, with a focus on switches and clocks, and discuss parallels between biology and computing. We also outline our vision for the future of biological computing.

Combining a Toggle Switch and a Repressilator within the AC-DC Circuit Generates Distinct Dynamical Behaviors

Although the structure of a genetically encoded regulatory circuit is an important determinant of its function, the relationship between circuit topology and the dynamical behaviors it can exhibit is not well understood. Here, we explore the range of behaviors available to the AC-DC circuit. This circuit consists of three genes connected as a combination of a toggle switch and a repressilator. Using dynamical systems theory, we show that the AC-DC circuit exhibits both oscillations and bistability within the same region of parameter space; this generates emergent behaviors not available to either the toggle switch or the repressilator alone. The AC-DC circuit can switch on oscillations via two distinct mechanisms, one of which induces coherence into ensembles of oscillators. In addition, we show that in the presence of noise, the AC-DC circuit can behave as an excitable system capable of spatial signal propagation or coherence resonance. Together, these results demonstrate how combinations of simple motifs can exhibit multiple complex behaviors.

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.

Mapping quorum sensing onto neural networks to understand collective decision making in heterogeneous microbial communities

Microbial communities frequently communicate via quorum sensing (QS), where cells produce, secrete, and respond to a threshold level of an autoinducer (AI) molecule, thereby modulating gene expression. However, the biology of QS remains incompletely understood in heterogeneous communities, where variant bacterial strains possess distinct QS systems that produce chemically unique AIs. AI molecules bind to 'cognate' receptors, but also to 'non-cognate' receptors found in other strains, resulting in inter-strain crosstalk. Understanding these interactions is a prerequisite for deciphering the consequences of crosstalk in real ecosystems, where multiple AIs are regularly present in the same environment. As a step towards this goal, we map crosstalk in a heterogeneous community of variant QS strains onto an artificial neural network model. This formulation allows us to systematically analyze how crosstalk regulates the community's capacity for flexible decision making, as quantified by the Boltzmann entropy of all QS gene expression states of the system. In a mean-field limit of complete cross-inhibition between variant strains, the model is exactly solvable, allowing for an analytical formula for the number of variants that maximize capacity as a function of signal kinetics and activation parameters. An analysis of previous experimental results on the Staphylococcus aureus two-component Agr system indicates that the observed combination of variant numbers, gene expression rates and threshold concentrations lies near this critical regime of parameter space where capacity peaks. The results are suggestive of a potential evolutionary driving force for diversification in certain QS systems.

A Blueprint for a Synthetic Genetic Feedback Controller to Reprogram Cell Fate

To artificially reprogram cell fate, experimentalists manipulate the gene regulatory networks (GRNs) that maintain a cell's phenotype. In practice, reprogramming is often performed by constant overexpression of specific transcription factors (TFs). This process can be unreliable and inefficient. Here, we address this problem by introducing a new approach to reprogramming based on mathematical analysis. We demonstrate that reprogramming GRNs using constant overexpression may not succeed in general. Instead, we propose an alternative reprogramming strategy: a synthetic genetic feedback controller that dynamically steers the concentration of a GRN's key TFs to any desired value. The controller works by adjusting TF expression based on the discrepancy between desired and actual TF concentrations. Theory predicts that this reprogramming strategy is guaranteed to succeed, and its performance is independent of the GRN's structure and parameters, provided that feedback gain is sufficiently high. As a case study, we apply the controller to a model of induced pluripotency in stem cells.