Biological signal processing with a genetic toggle switch

Algorithmic Programming of Sequential Logic and Genetic Circuits for Recording Biochemical Concentration in a Probiotic Bacterium

Through the implementation of designable genetic circuits, engineered probiotic microorganisms could be used as noninvasive diagnostic tools for the gastrointestinal tract. For these living cells to report detected biomarkers or signals after exiting the gut, the genetic circuits must be able to record these signals by using genetically encoded memory. Complex memory register circuits could enable multiplex interrogation of biomarkers and signals. A theory-based approach to create genetic circuits containing memory, known as sequential logic circuits, was previously established for a model laboratory strain of Escherichia coli, yet how circuit component performance varies for nonmodel and clinically relevant bacterial strains is poorly understood. Here, we develop a scalable computational approach to design robust sequential logic circuits in probiotic strain Escherichia coli Nissle 1917 (EcN). In this work, we used TetR-family transcriptional repressors to build genetic logic gates that can be composed into sequential logic circuits, along with a set of engineered sensors relevant for use in the gut environment. Using standard methods, 16 genetic NOT gates and nine sensors were experimentally characterized in EcN. These data were used to design and predict the performance of circuit designs. We present a set of genetic circuits encoding both combinational logic and sequential logic and show that the circuit outputs are in close agreement with our quantitative predictions from the design algorithm. Furthermore, we demonstrate an analog-like concentration recording circuit that detects and reports three input concentration ranges of a biochemical signal using sequential logic.

Theoretical and computational tools to model multistable gene regulatory networks

The last decade has witnessed a surge of theoretical and computational models to describe the dynamics of complex gene regulatory networks, and how these interactions can give rise to multistable and heterogeneous cell populations. As the use of theoretical modeling to describe genetic and biochemical circuits becomes more widespread, theoreticians with mathematical and physical backgrounds routinely apply concepts from statistical physics, non-linear dynamics, and network theory to biological systems. This review aims at providing a clear overview of the most important methodologies applied in the field while highlighting current and future challenges. It also includes hands-on tutorials to solve and simulate some of the archetypical biological system models used in the field. Furthermore, we provide concrete examples from the existing literature for theoreticians that wish to explore this fast-developing field. Whenever possible, we highlight the similarities and differences between biochemical and regulatory networks and 'classical' systems typically studied in non-equilibrium statistical and quantum mechanics.

Theoretical and computational tools to model multistable gene regulatory networks

The last decade has witnessed a surge of theoretical and computational models to describe the dynamics of complex gene regulatory networks, and how these interactions can give rise to multistable and heterogeneous cell populations. As the use of theoretical modeling to describe genetic and biochemical circuits becomes more widespread, theoreticians with mathematical and physical backgrounds routinely apply concepts from statistical physics, non-linear dynamics, and network theory to biological systems. This review aims at providing a clear overview of the most important methodologies applied in the field while highlighting current and future challenges. It also includes hands-on tutorials to solve and simulate some of the archetypical biological system models used in the field. Furthermore, we provide concrete examples from the existing literature for theoreticians that wish to explore this fast-developing field. Whenever possible, we highlight the similarities and differences between biochemical and regulatory networks and 'classical' systems typically studied in non-equilibrium statistical and quantum mechanics.

Modelling genetic stability in engineered cell populations

Predicting the evolution of engineered cell populations is a highly sought-after goal in biotechnology. While models of evolutionary dynamics are far from new, their application to synthetic systems is scarce where the vast combination of genetic parts and regulatory elements creates a unique challenge. To address this gap, we here-in present a framework that allows one to connect the DNA design of varied genetic devices with mutation spread in a growing cell population. Users can specify the functional parts of their system and the degree of mutation heterogeneity to explore, after which our model generates host-aware transition dynamics between different mutation phenotypes over time. We show how our framework can be used to generate insightful hypotheses across broad applications, from how a device's components can be tweaked to optimise long-term protein yield and genetic shelf life, to generating new design paradigms for gene regulatory networks that improve their functionality.

A synthetic distributed genetic multi-bit counter

A design for genetically encoded counters is proposed via repressor-based circuits. An N-bit counter reads sequences of input pulses and displays the total number of pulses, modulo 2N. The design is based on distributed computation with specialized cell types allocated to specific tasks. This allows scalability and bypasses constraints on the maximal number of circuit genes per cell due to toxicity or failures due to resource limitations. The design starts with a single-bit counter. The N-bit counter is then obtained by interconnecting (using diffusible chemicals) a set of N single-bit counters and connector modules. An optimization framework is used to determine appropriate gate parameters and to compute bounds on admissible pulse widths and relaxation (inter-pulse) times, as well as to guide the construction of novel gates. This work can be viewed as a step toward obtaining circuits that are capable of finite automaton computation in analogy to digital central processing units.

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A single-bit counter is designed for a repressor-based genetic circuit

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A scalable multi-bit counter is enabled by distributing the design across cells

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A computational optimization framework is proposed to guide the design

Feasibility and reliability of sequential logic with gene regulatory networks

Gene regulatory networks exhibiting Boolean behaviour, e.g. AND, OR or XOR, have been routinely designed for years. However, achieving more sophisticated functions, such as control or computation, usually requires sequential circuits or so-called state machines. For such a circuit, outputs depend both on inputs and the current state of the system. Although it is still possible to design such circuits by analogy with digital electronics, some particularities of biology make the task trickier. The impact of two of them, namely the stochasticity of biological processes and the inhomogeneity in the response of regulation mechanisms, are assessed in this paper. Numerical simulations performed in two use cases point out high risks of malfunctions even for designed GRNs functional from a theoretical point of view. Several solutions to improve reliability of such systems are also discussed.

Four different mechanisms for switching cell polarity

The mechanisms and design principles of regulatory systems establishing stable polarized protein patterns within cells are well studied. However, cells can also dynamically control their cell polarity. Here, we ask how an upstream signaling system can switch the orientation of a polarized pattern. We use a mathematical model of a core polarity system based on three proteins as the basis to study different mechanisms of signal-induced polarity switching. The analysis of this model reveals four general classes of switching mechanisms with qualitatively distinct behaviors: the transient oscillator switch, the reset switch, the prime-release switch, and the push switch. Each of these regulatory mechanisms effectively implements the function of a spatial toggle switch, however with different characteristics in their nonlinear and stochastic dynamics. We identify these characteristics and also discuss experimental signatures of each type of switching mechanism.

Protein-protein interaction network controlling establishment and maintenance of switchable cell polarity

Cell polarity underlies key processes in all cells, including growth, differentiation and division. In the bacterium Myxococcus xanthus, front-rear polarity is crucial for motility. Notably, this polarity can be inverted, independent of the cell-cycle, by chemotactic signaling. However, a precise understanding of the protein network that establishes polarity and allows for its inversion has remained elusive. Here, we use a combination of quantitative experiments and data-driven theory to unravel the complex interplay between the three key components of the M. xanthus polarity module. By studying each of these components in isolation and their effects as we systematically reconstruct the system, we deduce the network of effective interactions between the polarity proteins. RomR lies at the root of this network, promoting polar localization of the other components, while polarity arises from interconnected negative and positive feedbacks mediated by the small GTPase MglA and its cognate GAP MglB, respectively. We rationalize this network topology as operating as a spatial toggle switch, providing stable polarity for persistent cell movement whilst remaining responsive to chemotactic signaling and thus capable of polarity inversions. Our results have implications not only for the understanding of polarity and motility in M. xanthus but also, more broadly, for dynamic cell polarity.

The asymmetric localization of cellular components (polarity) is at the core of many important cellular functions including growth, division, differentiation and motility. However, important questions still remain regarding the design principles underlying polarity networks and how their activity can be controlled in space and time. We use the rod-shaped bacterium Myxococcus xanthus as a model to study polarity and its regulation. Like many bacteria, in M. xanthus a well-defined front-rear polarity axis enables efficient translocation. This polarity axis is defined by asymmetric polar localization of a switch-like GTPase and its cognate regulators, and can be reversed in response to signaling cues. Here we use a combination of quantitative experiments and data-driven theory to deduce the network of interactions among the M. xanthus polarity proteins and to show how the combination of positive- and negative-feedback interactions give rise to asymmetric polar protein localization. We rationalize this network topology as operating as a spatial toggle switch, providing stable polarity for persistent cell movement whilst remaining responsive to chemotactic signaling and capable of polarity inversions. Our results have broader implications for our understanding of dynamic cell polarity and GTPase regulation in both bacteria and eukaryotic cells.

Balancing Cell Populations Endowed with a Synthetic Toggle Switch via Adaptive Pulsatile Feedback Control

The problem of controlling cells endowed with a genetic toggle switch has been recently highlighted as a benchmark problem in synthetic biology. It has been shown that a carefully selected periodic forcing can balance a population of such cells in an undifferentiated state. The effectiveness of these control strategies, however, can be hindered by the presence of stochastic perturbations and uncertainties typically observed in biological systems and is therefore not robust. Here, we propose the use of feedback control strategies to enhance robustness and performance of the balancing action by selecting in real-time both the amplitude and the duty-cycle of the pulsatile inputs affecting the toggle switch behavior. We show, via in silico experiments and realistic agent-based simulations, the effectiveness of the proposed strategies even in the presence of uncertainties, stochastic effects, cell growth, and inducer diffusion. In so doing, we confirm previous observations made in the literature about coherence of the population when pulsatile forcing inputs are used, but, contrary to what was proposed in the past, we leverage feedback control techniques to endow the balancing strategy with unprecedented robustness and stability properties. We compare via in silico experiments different external control solutions and show their advantages and limitations from an in vivo implementation viewpoint.

Quality and Capacity Analysis of Molecular Communications in Bacterial Synthetic Logic Circuits

Synthetic logic circuits have been proposed as potential solutions for theranostics of biotechnological problems. One proposed model is the engineering of bacteria cells to create logic gates, and the communication between the bacteria populations will enable the circuit operation. In this paper, we analyze the quality of bacteria-based synthetic logic circuit through molecular communications that represent communication along a bus between three gates. In the bacteria-based synthetic logic circuit, the system receives environmental signals as molecular inputs and will process this information through a cascade of synthetic logic gates and free diffusion channels. We analyze the performance of this circuit by evaluating its quality and its relationship to the channel capacity of the molecular communications links that interconnect the bacteria populations. Our results show the effect of the molecular environmental delay and molecular amplitude differences over both the channel capacity and circuit quality. Furthermore, based on these metrics, we also obtain an optimum region for the circuit operation resulting in an accuracy of 80% for specific conditions. These results show that the performance of synthetic biology circuits can be evaluated through molecular communications, and lays the groundwork for combined systems that can contribute to future biomedical and biotechnology applications.

Chemical Systems Involving Two Competitive Self-Catalytic Reactions

Self-catalytic reactions are chemical phenomena, in which a product catalyzes the reactions of substrates further to yield products. A significant amplification of product concentration occurs during the reactions in a dilute solution, which exhibit notable properties such as sigmoidal kinetics, seeding effects, and thermal hysteresis. Chemical systems involving two competitive self-catalytic reactions can be considered, in which the competitive formation of two products occurs, which is affected by environmental changes, subtle perturbations, and fluctuations, and notable chemical phenomena appear such as formation of different structures in response to slow/fast temperature changes, chiral symmetry breaking, shortcut in reaction time, homogeneous-heterogeneous transitions, and mechanical responses. Studies on such chemical systems provide understanding on biological systems and can also be extended to the development of novel functional materials.

Cellular checkpoint control using programmable sequential logic

Biological processes that require orderly progression, such as growth and differentiation, proceed via regulatory checkpoints where the cell waits for signals before continuing to the next state. Implementing such control would allow genetic engineers to divide complex tasks into stages. We present genetic circuits that encode sequential logic to instruct Escherichia coli to proceed through a linear or cyclical sequence of states. These are built with 11 set-reset latches, designed with repressor-based NOR gates, which can connect to each other and sensors. The performance of circuits with up to three latches and four sensors, including a gated D latch, closely match predictions made by using nonlinear dynamics. Checkpoint control is demonstrated by switching cells between multiple circuit states in response to external signals over days.

A novel optogenetically tunable frequency modulating oscillator

Synthetic biology has enabled the creation of biological reconfigurable circuits, which perform multiple functions monopolizing a single biological machine; Such a system can switch between different behaviours in response to environmental cues. Previous work has demonstrated switchable dynamical behaviour employing reconfigurable logic gate genetic networks. Here we describe a computational framework for reconfigurable circuits in E.coli using combinations of logic gates, and also propose the biological implementation. The proposed system is an oscillator that can exhibit tunability of frequency and amplitude of oscillations. Further, the frequency of operation can be changed optogenetically. Insilico analysis revealed that two-component light systems, in response to light within a frequency range, can be used for modulating the frequency of the oscillator or stopping the oscillations altogether. Computational modelling reveals that mixing two colonies of E.coli oscillating at different frequencies generates spatial beat patterns. Further, we show that these oscillations more robustly respond to input perturbations compared to the base oscillator, to which the proposed oscillator is a modification. Compared to the base oscillator, the proposed system shows faster synchronization in a colony of cells for a larger region of the parameter space. Additionally, the proposed oscillator also exhibits lesser synchronization error in the transient period after input perturbations. This provides a strong basis for the construction of synthetic reconfigurable circuits in bacteria and other organisms, which can be scaled up to perform functions in the field of time dependent drug delivery with tunable dosages, and sets the stage for further development of circuits with synchronized population level behaviour.

A Robust Molecular Network Motif for Period-Doubling Devices

Life is sustained by a variety of cyclic processes such as cell division, muscle contraction, and neuron firing. The periodic signals powering these processes often direct a variety of other downstream systems, which operate at different time scales and must have the capacity to divide or multiply the period of the master clock. Period modulation is also an important challenge in synthetic molecular systems, where slow and fast components may have to be coordinated simultaneously by a single oscillator whose frequency is often difficult to tune. Circuits that can multiply the period of a clock signal (frequency dividers), such as binary counters and flip-flops, are commonly encountered in electronic systems, but design principles to obtain similar devices in biological systems are still unclear. We take inspiration from the architecture of electronic flip-flops, and we propose to build biomolecular period-doubling networks by combining a bistable switch with negative feedback modules that preprocess the circuit inputs. We identify a network motif and we show it can be "realized" using different biomolecular components; two of the realizations we propose rely on transcriptional gene networks and one on nucleic acid strand displacement systems. We examine the capacity of each realization to perform period-doubling by studying how bistability of the motif is affected by the presence of the input; for this purpose, we employ mathematical tools from algebraic geometry that provide us with valuable insights on the input/output behavior as a function of the realization parameters. We show that transcriptional network realizations operate correctly also in a stochastic regime when processing oscillations from the repressilator, a canonical synthetic in vivo oscillator. Finally, we compare the performance of different realizations in a range of realistic parameters via numerical sensitivity analysis of the period-doubling region, computed with respect to the input period and amplitude. Our mathematical and computational analysis suggests that the motif we propose is generally robust with respect to specific implementation details: functionally equivalent circuits can be built as long as the species-interaction topology is respected. This indicates that experimental construction of the circuit is possible with a variety of components within the rapidly expanding libraries available in synthetic biology.

The emerging age of cell-free synthetic biology

The engineering of and mastery over biological parts has catalyzed the emergence of synthetic biology. This field has grown exponentially in the past decade. As increasingly more applications of synthetic biology are pursued, more challenges are encountered, such as delivering genetic material into cells and optimizing genetic circuits in vivo. An in vitro or cell-free approach to synthetic biology simplifies and avoids many of the pitfalls of in vivo synthetic biology. In this review, we describe some of the innate features that make cell-free systems compelling platforms for synthetic biology and discuss emerging improvements of cell-free technologies. We also select and highlight recent and emerging applications of cell-free synthetic biology.