A comparative analysis of synthetic genetic oscillators

Complexity reduction by symmetry: uncovering the minimal regulatory network for logical computation in bacteria

Symmetry principles play an important role in geometry, and physics, allowing for the reduction of complicated systems to simpler, more comprehensible models that preserve the system's features of interest. Biological systems are often highly complex and may consist of a large number of interacting parts. Using symmetry fibrations, the relevant symmetries for biological "message-passing" networks, we introduce a scheme, called Complexity Reduction by Symmetry or ComSym, to reduce the gene regulatory networks of Escherichia coli and Bacillus subtilis bacteria to core networks in a way that preserves the dynamics and uncovers the computational capabilities of the network. Gene nodes in the original network that share isomorphic input trees are collapsed by the fibration into equivalence classes called fibers, whereby nodes that receive signals with the same "history" belong to one fiber and synchronize. Then we reduce the networks to its minimal computational core via k-core decomposition. This computational core consists of a few strongly connected components or "signal vortices", in which signals can cycle through. While between them, these "signal vortices" transmit signals in a feedforward manner. These connected components perform signal processing and decision making in the bacterial cell by employing a series of genetic toggle-switch circuits that store memory, plus oscillator circuits. These circuits act as the central computation device of the network, whose output signals then spread to the rest of the network. Our reduction method opens the door to narrow the vast complexity of biological systems to their minimal parts in a systematic way by using fundamental theoretical principles of symmetry.

On Emergence of Spontaneous Oscillations in Kombucha and Proteinoids

An important part of studying living systems is figuring out the complicated steps that lead to order from chaos. Spontaneous oscillations are a key part of self-organisation in many biological and chemical networks, including kombucha and proteinoids. This study examines the spontaneous oscillations in kombucha and proteinoids, specifically exploring their potential connection to the origin of life. As a community of bacteria and yeast work together, kombucha shows remarkable spontaneous oscillations in its biochemical parts. This system can keep a dynamic balance and organise itself thanks to metabolic processes and complex chemical reactions. Similarly, proteinoids, which may have been primitive forms of proteins, undergo spontaneous fluctuations in their structure and function periodically. Because these oscillations happen on their own, they may play a very important part in the development of early life forms. This paper highlights the fundamental principles governing the transition from chaos to order in living systems by examining the key factors that influence the frequency and characteristics of spontaneous oscillations in kombucha and proteinoids. Looking into these rhythms not only helps us understand where life came from but also shows us ways to make self-organising networks in synthetic biology and biotechnology. There is significant discussion over the emergence of biological order from chemical disorder. This article contributes to the ongoing discussion by examining at the theoretical basis, experimental proof, and implications of spontaneous oscillations. The results make it clear that random oscillations are an important part of the change from nonliving to living matter. They also give us important information about what life is all about.

Light-driven synchronization of optogenetic clocks

Synthetic genetic oscillators can serve as internal clocks within engineered cells to program periodic expression. However, cell-to-cell variability introduces a dispersion in the characteristics of these clocks that drives the population to complete desynchronization. Here, we introduce the optorepressilator, an optically controllable genetic clock that combines the repressilator, a three-node synthetic network in E. coli, with an optogenetic module enabling to reset, delay, or advance its phase using optical inputs. We demonstrate that a population of optorepressilators can be synchronized by transient green light exposure or entrained to oscillate indefinitely by a train of short pulses, through a mechanism reminiscent of natural circadian clocks. Furthermore, we investigate the system's response to detuned external stimuli observing multiple regimes of global synchronization. Integrating experiments and mathematical modeling, we show that the entrainment mechanism is robust and can be understood quantitatively from single cell to population level.

From resonance to chaos by modulating spatiotemporal patterns through a synthetic optogenetic oscillator

Oscillations are a recurrent phenomenon in biological systems across scales, but deciphering their fundamental principles is very challenging. Here, we tackle this challenge by redesigning the wellcharacterised synthetic oscillator known as "repressilator" in Escherichia coli and controlling it using optogenetics, creating the "optoscillator". Bacterial colonies manifest oscillations as spatial ring patterns. When we apply periodic light pulses, the optoscillator behaves as a forced oscillator and we systematically investigate the properties of the rings under various light conditions. Combining experiments with mathematical modeling, we demonstrate that this simple oscillatory circuit can generate complex dynamics that are transformed into distinct spatial patterns. We report the observation of synchronisation, resonance, subharmonic resonance and period doubling. Furthermore, we present evidence of a chaotic regime. This work highlights the intricate spatiotemporal patterns accessible by synthetic oscillators and underscores the potential of our approach in revealing fundamental principles of biological oscillations.

Dynamics and bifurcations in genetic circuits with fibration symmetries

Circuit building blocks of gene regulatory networks (GRN) have been identified through the fibration symmetries of the underlying biological graph. Here, we analyse analytically six of these circuits that occur as functional and synchronous building blocks in these networks. Of these, the lock-on, toggle switch, Smolen oscillator, feed-forward fibre and Fibonacci fibre circuits occur in living organisms, notably Escherichia coli; the sixth, the repressilator, is a synthetic GRN. We consider synchronous steady states determined by a fibration symmetry (or balanced colouring) and determine analytic conditions for local bifurcation from such states, which can in principle be either steady-state or Hopf bifurcations. We identify conditions that characterize the first bifurcation, the only one that can be stable near the bifurcation point. We model the state of each gene in terms of two variables: mRNA and protein concentration. We consider all possible 'admissible' models-those compatible with the network structure-and then specialize these general results to simple models based on Hill functions and linear degradation. The results systematically classify using graph symmetries the complexity and dynamics of these circuits, which are relevant to understand the functionality of natural and synthetic cells.

Classification of 2-node excitatory-inhibitory networks

We classify connected 2-node excitatory-inhibitory networks under various conditions. We assume that, as well as for connections, there are two distinct node-types, excitatory and inhibitory. In our classification we consider four different types of excitatory-inhibitory networks: restricted, partially restricted, unrestricted and completely unrestricted. For each type we give two different classifications. Using results on ODE-equivalence and minimality, we classify the ODE-classes and present a minimal representative for each ODE-class. We also classify all the networks with valence ≤2. These classifications are up to renumbering of nodes and the interchange of 'excitatory' and 'inhibitory' on nodes and arrows. These classifications constitute a first step towards analysing dynamics and bifurcations of excitatory-inhibitory networks. The results have potential applications to biological network models, especially neuronal networks, gene regulatory networks, and synthetic gene networks.

Transcriptional rewiring of an evolutionarily conserved circadian clock

Circadian clocks temporally coordinate daily organismal biology over the 24-h cycle. Their molecular design, preserved between fungi and animals, is based on a core-oscillator composed of a one-step transcriptional-translational-negative-feedback-loop (TTFL). To test whether this evolutionarily conserved TTFL architecture is the only plausible way for achieving a functional circadian clock, we adopted a transcriptional rewiring approach, artificially co-opting regulators of the circadian output pathways into the core-oscillator. Herein we describe one of these semi-synthetic clocks which maintains all basic circadian features but, notably, it also exhibits new attributes such as a "lights-on timer" logic, where clock phase is fixed at the end of the night. Our findings indicate that fundamental circadian properties such as period, phase and temperature compensation are differentially regulated by transcriptional and posttranslational aspects of the clockworks.

Beyond microtubules: The cellular environment at the endoplasmic reticulum attracts proteins to the nucleus, enabling nuclear transport

All proteins are translated in the cytoplasm, yet many, including transcription factors, play vital roles in the nucleus. While previous research has concentrated on molecular motors for the transport of these proteins to the nucleus, recent observations reveal perinuclear accumulation even in the absence of an energy source, hinting at alternative mechanisms. Here, we propose that structural properties of the cellular environment, specifically the endoplasmic reticulum (ER), can promote molecular transport to the perinucleus without requiring additional energy expenditure. Specifically, physical interaction between proteins and the ER impedes their diffusion and leads to their accumulation near the nucleus. This result explains why larger proteins, more frequently interacting with the ER membrane, tend to accumulate at the perinucleus. Interestingly, such diffusion in a heterogeneous environment follows Chapman's law rather than the popular Fick's law. Our findings suggest a novel protein transport mechanism arising solely from characteristics of the intracellular environment.

Enhanced precision of circadian rhythm by output system

Circadian rhythms are biological rhythms with a period of approximately 24 h that persist even under constant conditions without daily environmental cues. The molecular circadian clock machinery generates physiological rhythms, which can be transmitted into the downstream output system. Owing to the stochastic nature of the biochemical reactions and the extracellular environment, the oscillation period of circadian rhythms exhibited by individual organisms or cells is not constant on a daily basis with variations as high as 10%, as reflected by the coefficient of variation. Although the fluctuations in the circadian rhythm are measured through a reporter system such as bioluminescence or fluorescence, which is an example of output systems, experimentally confirming whether the fluctuations found in the reporter system are the same as those in the circadian clock is challenging. This study investigated a coupled system of a circadian clock and its output system numerically and analytically, and then compared the fluctuations in the oscillation period of the two systems. We found that the amount of fluctuations in the output system is smaller than that in the circadian clock, assuming the degradation rate of the molecules responsible for the output system is a typical value for protein degradation. The results indicate that the output system can improve the accuracy of the circadian rhythm without the need for any denoising processes.

A universal description of stochastic oscillators

Many systems in physics, chemistry, and biology exhibit oscillations with a pronounced random component. Such stochastic oscillations can emerge via different mechanisms, for example, linear dynamics of a stable focus with fluctuations, limit-cycle systems perturbed by noise, or excitable systems in which random inputs lead to a train of pulses. Despite their diverse origins, the phenomenology of random oscillations can be strikingly similar. Here, we introduce a nonlinear transformation of stochastic oscillators to a complex-valued function [Formula: see text](x) that greatly simplifies and unifies the mathematical description of the oscillator's spontaneous activity, its response to an external time-dependent perturbation, and the correlation statistics of different oscillators that are weakly coupled. The function [Formula: see text] (x) is the eigenfunction of the Kolmogorov backward operator with the least negative (but nonvanishing) eigenvalue λ1 = μ1 + iω1. The resulting power spectrum of the complex-valued function is exactly given by a Lorentz spectrum with peak frequency ω1 and half-width μ1; its susceptibility with respect to a weak external forcing is given by a simple one-pole filter, centered around ω1; and the cross-spectrum between two coupled oscillators can be easily expressed by a combination of the spontaneous power spectra of the uncoupled systems and their susceptibilities. Our approach makes qualitatively different stochastic oscillators comparable, provides simple characteristics for the coherence of the random oscillation, and gives a framework for the description of weakly coupled oscillators.

OsTOC1 plays dual roles in the regulation of plant circadian clock by functioning as a direct transcription activator or repressor

Plant clock function relies on precise timing of gene expression through complex regulatory networks consisting of activators and repressors at the core of oscillators. Although TIMING OF CAB EXPRESSION 1 (TOC1) has been recognized as a repressor involved in shaping oscillations and regulating clock-driven processes, its potential to directly activate gene expression remains unclear. In this study, we find that OsTOC1 primarily acts as a transcriptional repressor for core clock components, including OsLHY and OsGI. Here, we show that OsTOC1 possesses the ability to directly activate the expression of circadian target genes. Through binding to the promoters of OsTGAL3a/b, transient activation of OsTOC1 induces the expression of OsTGAL3a/b, indicating its role as an activator contributing to pathogen resistance. Moreover, TOC1 participates in regulating multiple yield-related traits in rice. These findings suggest that TOC1's function as a transcriptional repressor is not inherent, providing flexibility to circadian regulations, particularly in outputs.

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.

Design of Oscillatory Networks through Post-Translational Control of Network Components

Many essential functions in biological systems, including cell cycle progression and circadian rhythm regulation, are governed by the periodic behaviors of specific molecules. These periodic behaviors arise from the precise arrangement of components in biomolecular networks that generate oscillatory output signals. The dynamic properties of individual components of these networks, such as maturation delays and degradation rates, often play a key role in determining the network's oscillatory behavior. In this study, we explored the post-translational modulation of network components as a means to generate genetic circuits with oscillatory behaviors and perturb the oscillation features. Specifically, we used the NanoDeg platform-A bifunctional molecule consisting of a target-specific nanobody and a degron tag-to control the degradation rates of the circuit's components and predicted the effect of NanoDeg-mediated post-translational depletion of a key circuit component on the behavior of a series of proto-oscillating network topologies. We modeled the behavior of two main classes of oscillators, namely relaxation oscillator topologies (the activator-repressor and the Goodwin oscillator) and ring oscillator topologies (repressilators). We identified two main mechanisms by which non-oscillating networks could be induced to oscillate through post-translational modulation of network components: an increase in the separation of timescales of network components and mitigation of the leaky expression of network components. These results are in agreement with previous findings describing the effect of timescale separation and mitigation of leaky expression on oscillatory behaviors. This work thus validates the use of tools to control protein degradation rates as a strategy to modulate existing oscillatory signals and construct oscillatory networks. In addition, this study provides the design rules to implement such an approach based on the control of protein degradation rates using the NanoDeg platform, which does not require genetic manipulation of the network components and can be adapted to virtually any cellular protein. This work also establishes a framework to explore the use of tools for post-translational perturbations of biomolecular networks and generates desired behaviors of the network output.

The ups and downs of biological oscillators: a comparison of time-delayed negative feedback mechanisms

Many biochemical oscillators are driven by the periodic rise and fall of protein concentrations or activities. A negative feedback loop underlies such oscillations. The feedback can act on different parts of the biochemical network. Here, we mathematically compare time-delay models where the feedback affects production and degradation. We show a mathematical connection between the linear stability of the two models, and derive how both mechanisms impose different constraints on the production and degradation rates that allow oscillations. We show how oscillations are affected by the inclusion of a distributed delay, of double regulation (acting on production and degradation) and of enzymatic degradation.

A synthetic population-level oscillator in non-microfluidic environments

Synthetic oscillators have become a research hotspot because of their complexity and importance. The construction and stable operation of oscillators in large-scale environments are important and challenging. Here, we introduce a synthetic population-level oscillator in Escherichia coli that operates stably during continuous culture in non-microfluidic environments without the addition of inducers or frequent dilution. Specifically, quorum-sensing components and protease regulating elements are employed, which form delayed negative feedback to trigger oscillation and accomplish the reset of signals through transcriptional and post-translational regulation. We test the circuit in devices with 1 mL, 50 mL, 400 mL of medium, and demonstrate that the circuit could maintain stable population-level oscillations. Finally, we explore potential applications of the circuit in regulating cellular morphology and metabolism. Our work contributes to the design and testing of synthetic biological clocks that function in large populations.

Computational characterization of recombinase circuits for periodic behaviors

Recombinases are site-specific proteins found in nature that are capable of rearranging DNA. This function has made them promising gene editing tools in synthetic biology, as well as key elements in complex artificial gene circuits implementing Boolean logic. However, since DNA rearrangement is irreversible, it is still unclear how to use recombinases to build dynamic circuits like oscillators. In addition, this goal is challenging because a few molecules of recombinase are enough for promoter inversion, generating inherent stochasticity at low copy number. Here, we propose six different circuit designs for recombinase-based oscillators operating at a single copy number. We model them in a stochastic setting, leveraging the Gillespie algorithm for extensive simulations, and show that they can yield coherent periodic behaviors. Our results support the experimental realization of recombinase-based oscillators and, more generally, the use of recombinases to generate dynamic behaviors in synthetic biology.

Degradation-driven protein level oscillation in the yeast Saccharomyces cerevisiae

Generating robust, predictable perturbations in cellular protein levels will advance our understanding of protein function and enable the control of physiological outcomes in biotechnology applications. Timed periodic changes in protein levels play a critical role in the cell division cycle, cellular stress response, and development. Here we report the generation of robust protein level oscillations by controlling the protein degradation rate in the yeast Saccharomyces cerevisiae. Using a photo-sensitive degron and red fluorescent proteins as reporters, we show that under constitutive transcriptional induction, repeated triangular protein level oscillations as fast as 5-10 min-scale can be generated by modulating the protein degradation rate. Consistent with oscillations generated though transcriptional control, we observed a continuous decrease in the magnitude of oscillations as the input modulation frequency increased, indicating low-pass filtering of input perturbation. By using two red fluorescent proteins with distinct maturation times, we show that the oscillations in protein level is largely unaffected by delays originating from functional protein formation. Our study demonstrates the potential for repeated control of protein levels by controlling the protein degradation rate without altering the transcription rate.

Combined multiple transcriptional repression mechanisms generate ultrasensitivity and oscillations

Transcriptional repression can occur via various mechanisms, such as blocking, sequestration and displacement. For instance, the repressors can hold the activators to prevent binding with DNA or can bind to the DNA-bound activators to block their transcriptional activity. Although the transcription can be completely suppressed with a single mechanism, multiple repression mechanisms are used together to inhibit transcriptional activators in many systems, such as circadian clocks and NF-κB oscillators. This raises the question of what advantages arise if seemingly redundant repression mechanisms are combined. Here, by deriving equations describing the multiple repression mechanisms, we find that their combination can synergistically generate a sharply ultrasensitive transcription response and thus strong oscillations. This rationalizes why the multiple repression mechanisms are used together in various biological oscillators. The critical role of such combined transcriptional repression for strong oscillations is further supported by our analysis of formerly identified mutations disrupting the transcriptional repression of the mammalian circadian clock. The hitherto unrecognized source of the ultrasensitivity, the combined transcriptional repressions, can lead to robust synthetic oscillators with a previously unachievable simple design.

Matryoshka and disjoint cluster synchronization of networks

The main motivation for this paper is to characterize network synchronizability for the case of cluster synchronization (CS), in an analogous fashion to Barahona and Pecora [Phys. Rev. Lett. 89, 054101 (2002)] for the case of complete synchronization. We find this problem to be substantially more complex than the original one. We distinguish between the two cases of networks with intertwined clusters and no intertwined clusters and between the two cases that the master stability function is negative either in a bounded range or in an unbounded range of its argument. Our proposed definition of cluster synchronizability is based on the synchronizability of each individual cluster within a network. We then attempt to generalize this definition to the entire network. For CS, the synchronous solution for each cluster may be stable, independent of the stability of the other clusters, which results in possibly different ranges in which each cluster synchronizes (isolated CS). For each pair of clusters, we distinguish between three different cases: Matryoshka cluster synchronization (when the range of the stability of the synchronous solution for one cluster is included in that of the other cluster), partially disjoint cluster synchronization (when the ranges of stability of the synchronous solutions partially overlap), and complete disjoint cluster synchronization (when the ranges of stability of the synchronous solutions do not overlap).

Synthetic Genetic Reversible Feynman Gate in a Single E. coli Cell and Its Application in Bacterial to Mammalian Cell Information Transfer

Reversible computing is a nonconventional form of computing where the inputs and outputs are mapped in a unique one-to-one fashion. Reversible logic gates in single living cells have not been demonstrated. Here, we constructed a synthetic genetic reversible Feynman gate in single E. coli cells, and the input-output relations were measured in a clonal population. The inputs were extracellular chemicals, isopropyl β-d-1-thiogalactopyranoside (IPTG), and anhydrotetracycline (aTc), and the outputs were two fluorescence proteins. We developed a simple mathematical model and simulation to capture the essential features of the circuit and experimentally demonstrated that the behavior of the circuit was ultrasensitive and predictive. We showed an application by creating an intercellular Feynman gate, where input information from bacteria was computed and transferred to HeLa cells through shRNAs delivery and the output signals were observed as silencing of native AKT1 and CTNNB1 genes. The introduction of reversible logics in synthetic biology is new, and given that one-to-one input-output mapping, such reversible genetic systems might have applications in sensing, diagnostics, cellular computing, and synthetic biology.

Synthetic biology tools for engineering Goodwin oscillation in Trypanosoma brucei brucei

Kinetoplastid protozoa possess properties that are highly divergent from the mammalian, yeast and bacterial cells more commonly used in synthetic biology and represent a tantalisingly untapped source of bioengineering potential. Trypanosoma brucei brucei (T. b. brucei), an established model organism for studying the Kinetoplastida, is non-pathogenic to humans and provides an interesting test case for establishing synthetic biology in this phylogenetic class. To demonstrate further the tractability of Kinetoplastida to synthetic biology, we sought to construct and demonstrate a Goodwin oscillator, the simplest oscillatory gene network, in T. b. brucei for the first time. We report one completed iteration of the archetypal synthetic biology Design-Build-Test-Learn (DBTL) cycle; firstly, using Ab initio mathematical modelling of the behaviour a theoretical, oscillatory, trypanosomal synthetic gene network (SGN) to inform the design of a plasmid encoding that network. Once assembled, the plasmid was then used to generate a stable transfectant T. b. brucei cell line. To test the performance of the oscillatory SGN, a novel experimental setup was established to capture images of the fluorescent signal from motion-restricted live cells. Data captured were consistent with oscillatory behaviour of the SGN, with cellular fluorescence observed to oscillate with a period of 50 min, with varying amplitude and linear growth trend. This first DBTL cycle establishes a foundation for future cycles in which the SGN design and experimental monitoring setup can be further refined.

A frequency-amplitude coordinator and its optimal energy consumption for biological oscillators

Biorhythm including neuron firing and protein-mRNA interaction are fundamental activities with diffusive effect. Their well-balanced spatiotemporal dynamics are beneficial for healthy sustainability. Therefore, calibrating both anomalous frequency and amplitude of biorhythm prevents physiological dysfunctions or diseases. However, many works were devoted to modulate frequency exclusively whereas amplitude is usually ignored, although both quantities are equally significant for coordinating biological functions and outputs. Especially, a feasible method coordinating the two quantities concurrently and precisely is still lacking. Here, for the first time, we propose a universal approach to design a frequency-amplitude coordinator rigorously via dynamical systems tools. We consider both spatial and temporal information. With a single well-designed coordinator, they can be calibrated to desired levels simultaneously and precisely. The practical usefulness and efficacy of our method are demonstrated in representative neuronal and gene regulatory models. We further reveal its fundamental mechanism and optimal energy consumption providing inspiration for biorhythm regulation in future.

Applications of Bacterial Degrons and Degraders - Toward Targeted Protein Degradation in Bacteria

A repertoire of proteolysis-targeting signals known as degrons is a necessary component of protein homeostasis in every living cell. In bacteria, degrons can be used in place of chemical genetics approaches to interrogate and control protein function. Here, we provide a comprehensive review of synthetic applications of degrons in targeted proteolysis in bacteria. We describe recent advances ranging from large screens employing tunable degradation systems and orthogonal degrons, to sophisticated tools and sensors for imaging. Based on the success of proteolysis-targeting chimeras as an emerging paradigm in cancer drug discovery, we discuss perspectives on using bacterial degraders for studying protein function and as novel antimicrobials.

Immobilization of Proteins of Cell Extract to Hydrogel Networks Enhances the Longevity of Cell-Free Protein Synthesis and Supports Gene Networks

Herein, we constructed a new type of hydrogel based artificial cells supporting long-lived protein synthesis, post-translational modification, and gene networks. We constructed the artificial cells by immobilizing the transcription and translation system from E. coli cytoplasmic extract onto the polyacrylamide hydrogel. With the continuous supply of energy and nutrition, the artificial cells were capable of stable protein expression for at least 30 days. Functional proteins which were difficult to produce in vivo, including colicin E1 and urokinase, were synthesized in the artificial cells with high bioactivity. Furthermore, we constructed a sigma factor based genetic oscillator in the artificial cells. The artificial cells not only provide a powerful platform for continuous protein synthesis and convenient design and testing of genetic networks, but also hold great promise for the development of metabolic engineering, drug delivery, and biosensors.

Qualitative Modeling, Analysis and Control of Synthetic Regulatory Circuits

Qualitative modeling approaches are promising and still underexploited tools for the analysis and design of synthetic circuits. They can make predictions of circuit behavior in the absence of precise, quantitative information. Moreover, they provide direct insight into the relation between the feedback structure and the dynamical properties of a network. We review qualitative modeling approaches by focusing on two specific formalisms, Boolean networks and piecewise-linear differential equations, and illustrate their application by means of three well-known synthetic circuits. We describe various methods for the analysis of state transition graphs, discrete representations of the network dynamics that are generated in both modeling frameworks. We also briefly present the problem of controlling synthetic circuits, an emerging topic that could profit from the capacity of qualitative modeling approaches to rapidly scan a space of design alternatives.

Self-assembly-based posttranslational protein oscillators

Recent advances in synthetic posttranslational protein circuits are substantially impacting the landscape of cellular engineering and offer several advantages compared to traditional gene circuits. However, engineering dynamic phenomena such as oscillations in protein-level circuits remains an outstanding challenge. Few examples of biological posttranslational oscillators are known, necessitating theoretical progress to determine realizable oscillators. We construct mathematical models for two posttranslational oscillators, using few components that interact only through reversible binding and phosphorylation/dephosphorylation reactions. Our designed oscillators rely on the self-assembly of two protein species into multimeric functional enzymes that respectively inhibit and enhance this self-assembly. We limit our analysis to within experimental constraints, finding (i) significant portions of the restricted parameter space yielding oscillations and (ii) that oscillation periods can be tuned by several orders of magnitude using recent advances in computational protein design. Our work paves the way for the rational design and realization of protein-based dynamic systems.

Topology-induced dynamics in a network of synthetic oscillators with piecewise affine approximation

In synthetic biology approaches, minimal systems are used to reproduce complex molecular mechanisms that appear in the core functioning of multi-cellular organisms. In this paper, we study a piecewise affine model of a synthetic two-gene oscillator and prove existence and stability of a periodic solution for all parameters in a given region. Motivated by the synchronization of circadian clocks in a cluster of cells, we next consider a network of N identical oscillators under diffusive coupling to investigate the effect of the topology of interactions in the network's dynamics. Our results show that both all-to-all and one-to-all coupling topologies may introduce new stable steady states in addition to the expected periodic orbit. Both topologies admit an upper bound on the coupling parameter that prevents the generation of new steady states. However, this upper bound is independent of the number of oscillators in the network and less conservative for the one-to-all topology.

Computer-Aided Whole-Cell Design: Taking a Holistic Approach by Integrating Synthetic With Systems Biology

Computer-aided design (CAD) for synthetic biology promises to accelerate the rational and robust engineering of biological systems. It requires both detailed and quantitative mathematical and experimental models of the processes to (re)design biology, and software and tools for genetic engineering and DNA assembly. Ultimately, the increased precision in the design phase will have a dramatic impact on the production of designer cells and organisms with bespoke functions and increased modularity. CAD strategies require quantitative models of cells that can capture multiscale processes and link genotypes to phenotypes. Here, we present a perspective on how whole-cell, multiscale models could transform design-build-test-learn cycles in synthetic biology. We show how these models could significantly aid in the design and learn phases while reducing experimental testing by presenting case studies spanning from genome minimization to cell-free systems. We also discuss several challenges for the realization of our vision. The possibility to describe and build whole-cells in silico offers an opportunity to develop increasingly automatized, precise and accessible CAD tools and strategies.

Developmental function and state transitions of a gene expression oscillator in Caenorhabditis elegans

Gene expression oscillators can structure biological events temporally and spatially. Different biological functions benefit from distinct oscillator properties. Thus, finite developmental processes rely on oscillators that start and stop at specific times, a poorly understood behavior. Here, we have characterized a massive gene expression oscillator comprising > 3,700 genes in Caenorhabditis elegans larvae. We report that oscillations initiate in embryos, arrest transiently after hatching and in response to perturbation, and cease in adults. Experimental observation of the transitions between oscillatory and non-oscillatory states at high temporal resolution reveals an oscillator operating near a Saddle Node on Invariant Cycle (SNIC) bifurcation. These findings constrain the architecture and mathematical models that can represent this oscillator. They also reveal that oscillator arrests occur reproducibly in a specific phase. Since we find oscillations to be coupled to developmental processes, including molting, this characteristic of SNIC bifurcations endows the oscillator with the potential to halt larval development at defined intervals, and thereby execute a developmental checkpoint function.

Quorum sensing for population-level control of bacteria and potential therapeutic applications

Quorum sensing (QS), a microbial cell-to-cell communication process, dynamically regulates a variety of metabolism and physiological activities. In this review, we provide an update on QS applications based on autoinducer molecules including acyl-homoserine lactones (AHLs), auto-inducing peptides (AIPs), autoinducer 2 (AI-2) and indole in population-level control of bacteria, and highlight the potential in developing novel clinical therapies. We summarize the development in the combination of various genetic circuits such as genetic oscillators, toggle switches and logic gates with AHL-based QS devices in Gram-negative bacteria. An overview is then offered to the state-of-the-art of much less researched applications of AIP-based QS devices with Gram-positive bacteria, followed by a review of the applications of AI-2 and indole based QS for interspecies communication among microbial communities. Building on these general-purpose QS applications, we highlight the disruptions and manipulations of QS devices as potential clinical therapies for diseases caused by biofilm formation, antibiotic resistance and the phage invasion. The last part of reviewed literature is dedicated to mathematical modelling for QS applications. Finally, the key challenges and future perspectives of QS applications in monoclonal synthetic biology and synthetic ecology are discussed.

Modeling the tunability of the dual-feedback genetic oscillator

Oscillatory gene circuits are ubiquitous to biology and are involved in fundamental processes of cell cycle, circadian rhythms, and developmental systems. The synthesis of small, non-natural oscillatory genetic circuits has been increasingly used to test the fundamental principles of genetic network dynamics. While the "repressilator" was used to first demonstrate the proof of principle, a more recently developed dual-feedback, fast, tunable genetic oscillator has demonstrated a greater degree of robustness and control over oscillatory behavior by combining positive- and negative-feedback loops. This oscillator, combining lacI (negative-) and araC (positive-) feedback loops, was, however, modeled using multiple layers of differential equations to capture the molecular complexity of regulation, in order to explain the experimentally measured oscillations. In the search for design principles of such minimal oscillatory circuits, we have developed a reduced model of this dual-feedback loop oscillator consisting of just six differential equations, two of which are delay differential equations. The delay term is optimized, as the only free parameter, to fit the experimental dynamics of the oscillator period and amplitude tunability by the two inducers isopropyl β-D-1-thiogalactopyranoside (IPTG) and arabinose. We proceed to use our reduced and experimentally validated model to redesign the network by comparing the effect of asymmetry in gene expression at the level of (a) DNA copy numbers and the rates of (b) mRNA translation and (c) degradation, since experimental and theoretical work had predicted a need for an asymmetry in the copy numbers of activator (araC) and repressor (lacI) genes encoded on plasmids. We confirm that the minimal period of the oscillator is sensitive to DNA copy number asymmetry, and can demonstrate that while the asymmetry in the translation rate has an identical effect as the plasmid copy numbers, modulating the asymmetry in mRNA degradation can improve the tunability of the period and amplitude of the oscillator. Thus, our model predicts control at the level of translation can be used to redesign such networks, for improved tunability, while at the same time making the network robust to replication "noise" and the effects of the host cell cycle. Thus, our model predicts experimentally testable principles to redesign a potentially more robust oscillatory genetic network.

A Model for the Spatiotemporal Design of Gene Regulatory Circuits †

Mathematical modeling assists the design of synthetic regulatory networks by providing a detailed mechanistic understanding of biological systems. Models that can predict the performance of a design are fundamental for synthetic biology since they minimize iterations along the design-build-test lifecycle. Such predictability depends crucially on what assumptions (i.e., biological simplifications) the model considers. Here, we challenge a common assumption when it comes to the modeling of bacterial-based gene regulation: considering negligible the effects of intracellular physical space. It is commonly assumed that molecules, such as transcription factors (TF), are homogeneously distributed inside a cell, so there is no need to model their diffusion. We describe a mathematical model that accounts for molecular diffusion and show how simulations of network performance are decisively affected by the distance between its components. Specifically, the model focuses on the search by a TF for its target promoter. The combination of local searches, via one-dimensional sliding along the chromosome, and global searches, via three-dimensional diffusion through the cytoplasm, determine TF-promoter interplay. Previous experimental results with engineered bacteria in which the distance between TF source and target was minimized or enlarged were successfully reproduced by the spatially resolved model we introduce here. This suggests that the spatial specification of the circuit alone can be exploited as a design parameter in synthetic biology to select programmable output levels.

Computational analysis of viable parameter regions in models of synthetic biological systems

Background

Gene regulatory networks with different topological and/or dynamical properties might exhibit similar behavior. System that is less perceptive for the perturbations of its internal and external factors should be preferred. Methods for sensitivity and robustness assessment have already been developed and can be roughly divided into local and global approaches. Local methods focus only on the local area around nominal parameter values. This can be problematic when parameters exhibits the desired behavior over a large range of parameter perturbations or when parameter values are unknown. Global methods, on the other hand, investigate the whole space of parameter values and mostly rely on different sampling techniques. This can be computationally inefficient. To address these shortcomings ’glocal’ approaches were developed that apply global and local approaches in an effective and rigorous manner.

Results

Herein, we present a computational approach for ’glocal’ analysis of viable parameter regions in biological models. The methodology is based on the exploration of high-dimensional viable parameter spaces with global and local sampling, clustering and dimensionality reduction techniques. The proposed methodology allows us to efficiently investigate the viable parameter space regions, evaluate the regions which exhibit the largest robustness, and to gather new insights regarding the size and connectivity of the viable parameter regions. We evaluate the proposed methodology on three different synthetic gene regulatory network models, i.e. the repressilator model, the model of the AC-DC circuit and the model of the edge-triggered master-slave D flip-flop.

Conclusions

The proposed methodology provides a rigorous assessment of the shape and size of viable parameter regions based on (1) the mathematical description of the biological system of interest, (2) constraints that define feasible parameter regions and (3) cost function that defines the desired or observed behavior of the system. These insights can be used to assess the robustness of biological systems, even in the case when parameter values are unknown and more importantly, even when there are multiple poorly connected viable parameter regions in the solution space. Moreover, the methodology can be efficiently applied to the analysis of biological systems that exhibit multiple modes of the targeted behavior.

Degradation rate uniformity determines success of oscillations in repressive feedback regulatory networks

Ring oscillators are biochemical circuits consisting of a ring of interactions capable of sustained oscillations. The nonlinear interactions between genes hinder the analytical insight into their function, usually requiring computational exploration. Here, we show that, despite the apparent complexity, the stability of the unique steady state in an incoherent feedback ring depends only on the degradation rates and a single parameter summarizing the feedback of the circuit. Concretely, we show that the range of regulatory parameters that yield oscillatory behaviour is maximized when the degradation rates are equal. Strikingly, this result holds independently of the regulatory functions used or number of genes. We also derive properties of the oscillations as a function of the degradation rates and number of nodes forming the ring. Finally, we explore the role of mRNA dynamics by applying the generic results to the specific case with two naturally different degradation timescales.

The Usual Suspects 2019: of Chips, Droplets, Synthesis, and Artificial Cells

Synthetic biology aims to understand fundamental biological processes in more detail than possible for actual living cells. Synthetic biology can combat decomposition and build-up of artificial experimental models under precisely controlled and defined environmental and biochemical conditions. Microfluidic systems can provide the tools to improve and refine existing synthetic systems because they allow control and manipulation of liquids on a micro- and nanoscale. In addition, chip-based approaches are predisposed for synthetic biology applications since they present an opportune technological toolkit capable of fully automated high throughput and content screening under low reagent consumption. This review critically highlights the latest updates in microfluidic cell-free and cell-based protein synthesis as well as the progress on chip-based artificial cells. Even though progress is slow for microfluidic synthetic biology, microfluidic systems are valuable tools for synthetic biology and may one day help to give answers to long asked questions of fundamental cell biology and life itself.

Slow relaxation during and after perturbation of bistable kinetics of gene expression

After a short perturbation of a bistable genetic network, it returns to its initial steady state or transits to another steady state. The time scale characterizing such transient regimes can be appreciably longer compared to those of the degradation of the perturbed mRNAs and proteins. The author shows in detail the specifics of this slowdown of the transient kinetics using mean-field kinetic equations and Monte Carlo simulations. Attention is focused on nanocarrier-mediated delivery and release of short non-coding RNA (e.g., miRNA or siRNA) into cells with subsequent suppression of the populations of the targeted mRNA and corresponding protein.

Synthetic Switches and Regulatory Circuits in Plants

Synthetic biology is an established but ever-growing interdisciplinary field of research currently revolutionizing biomedicine studies and the biotech industry. The engineering of synthetic circuitry in bacterial, yeast, and animal systems prompted considerable advances for the understanding and manipulation of genetic and metabolic networks; however, their implementation in the plant field lags behind. Here, we review theoretical-experimental approaches to the engineering of synthetic chemical- and light-regulated (optogenetic) switches for the targeted interrogation and control of cellular processes, including existing applications in the plant field. We highlight the strategies for the modular assembly of genetic parts into synthetic circuits of different complexity, ranging from Boolean logic gates and oscillatory devices up to semi- and fully synthetic open- and closed-loop molecular and cellular circuits. Finally, we explore potential applications of these approaches for the engineering of novel functionalities in plants, including understanding complex signaling networks, improving crop productivity, and the production of biopharmaceuticals.

Parameter estimation in models of biological oscillators: an automated regularised estimation approach

BACKGROUND

Dynamic modelling is a core element in the systems biology approach to understanding complex biosystems. Here, we consider the problem of parameter estimation in models of biological oscillators described by deterministic nonlinear differential equations. These problems can be extremely challenging due to several common pitfalls: (i) a lack of prior knowledge about parameters (i.e. massive search spaces), (ii) convergence to local optima (due to multimodality of the cost function), (iii) overfitting (fitting the noise instead of the signal) and (iv) a lack of identifiability. As a consequence, the use of standard estimation methods (such as gradient-based local ones) will often result in wrong solutions. Overfitting can be particularly problematic, since it produces very good calibrations, giving the impression of an excellent result. However, overfitted models exhibit poor predictive power. Here, we present a novel automated approach to overcome these pitfalls. Its workflow makes use of two sequential optimisation steps incorporating three key algorithms: (1) sampling strategies to systematically tighten the parameter bounds reducing the search space, (2) efficient global optimisation to avoid convergence to local solutions, (3) an advanced regularisation technique to fight overfitting. In addition, this workflow incorporates tests for structural and practical identifiability.

RESULTS

We successfully evaluate this novel approach considering four difficult case studies regarding the calibration of well-known biological oscillators (Goodwin, FitzHugh-Nagumo, Repressilator and a metabolic oscillator). In contrast, we show how local gradient-based approaches, even if used in multi-start fashion, are unable to avoid the above-mentioned pitfalls.

CONCLUSIONS

Our approach results in more efficient estimations (thanks to the bounding strategy) which are able to escape convergence to local optima (thanks to the global optimisation approach). Further, the use of regularisation allows us to avoid overfitting, resulting in more generalisable calibrated models (i.e. models with greater predictive power).

Dynamical Task Switching in Cellular Computers

We present a scheme for implementing a version of task switching in engineered bacteria, based on the manipulation of plasmid copy numbers. Our method allows for the embedding of multiple computations in a cellular population, whilst minimising resource usage inefficiency. We describe the results of computational simulations of our model, and discuss the potential for future work in this area.

Period-amplitude co-variation in biomolecular oscillators

The period and amplitude of biomolecular oscillators are functionally important properties in multiple contexts. For a biomolecular oscillator, the overall constraints in how tuning of amplitude affects period, and vice versa, are generally unclear. Here, the authors investigate this co-variation of the period and amplitude in mathematical models of biomolecular oscillators using both simulations and analytical approximations. The authors computed the amplitude-period co-variation of 11 benchmark biomolecular oscillators as their parameters were individually varied around a nominal value, classifying the various co-variation patterns such as a simultaneous increase/decrease in period and amplitude. Next, the authors repeated the classification using a power norm-based amplitude metric, to account for the amplitudes of the many biomolecular species that may be part of the oscillations, finding largely similar trends. Finally, the authors calculate 'scaling laws' of period-amplitude co-variation for a subset of these benchmark oscillators finding that as the approximated period increases, the upper bound of the amplitude increases, or reaches a constant value. Based on these results, the authors discuss the effect of different parameters on the type of period-amplitude co-variation as well as the difficulty in achieving an oscillation with large amplitude and small period.

Reconstitution of an Ultradian Oscillator in Mammalian Cells by a Synthetic Biology Approach

The Notch effector gene Hes1 is an ultradian clock exhibiting cyclic gene expression in several progenitor cells, with a period of a few hours. Because of the complexity of studying Hes1 in the endogenous setting, and the difficulty of imaging these fast oscillations in vivo, the mechanism driving oscillations has never been proven. Here, we applied a "build it to understand it" synthetic biology approach to construct simplified "hybrid" versions of the Hes1 ultradian oscillator combining synthetic and natural parts. We successfully constructed a simplified synthetic version of the Hes1 promoter matching the endogenous regulation logic. By mathematical modeling and single-cell real-time imaging, we were able to demonstrate that Hes1 is indeed able to generate stable oscillations by a delayed negative feedback loop. Moreover, we proved that introns in Hes1 contribute to the transcriptional delay but may not be strictly necessary for oscillations to occur. We also developed a novel reporter of endogenous Hes1 oscillations able to amplify the bioluminescence signal 5-fold. Our results have implications also for other ultradian oscillators.

Biological Oscillators in Nanonetworks-Opportunities and Challenges

One of the major issues in molecular communication-based nanonetworks is the provision and maintenance of a common time knowledge. To stay true to the definition of molecular communication, biological oscillators are the potential solutions to achieve that goal as they generate oscillations through periodic fluctuations in the concentrations of molecules. Through the lens of a communication systems engineer, the scope of this survey is to explicitly classify, for the first time, existing biological oscillators based on whether they are found in nature or not, to discuss, in a tutorial fashion, the main principles that govern the oscillations in each oscillator, and to analyze oscillator parameters that are most relevant to communication engineer researchers. In addition, the survey highlights and addresses the key open research issues pertaining to several physical aspects of the oscillators and the adoption and implementation of the oscillators to nanonetworks. Moreover, key research directions are discussed.

Inferring a nonlinear biochemical network model from a heterogeneous single-cell time course data

Mathematical modeling and analysis of biochemical reaction networks are key routines in computational systems biology and biophysics; however, it remains difficult to choose the most valid model. Here, we propose a computational framework for data-driven and systematic inference of a nonlinear biochemical network model. The framework is based on the expectation-maximization algorithm combined with particle smoother and sparse regularization techniques. In this method, a “redundant” model consisting of an excessive number of nodes and regulatory paths is iteratively updated by eliminating unnecessary paths, resulting in an inference of the most likely model. Using artificial single-cell time-course data showing heterogeneous oscillatory behaviors, we demonstrated that this algorithm successfully inferred the true network without any prior knowledge of network topology or parameter values. Furthermore, we showed that both the regulatory paths among nodes and the optimal number of nodes in the network could be systematically determined. The method presented in this study provides a general framework for inferring a nonlinear biochemical network model from heterogeneous single-cell time-course data.

Computational Re-design of Synthetic Genetic Oscillators for Independent Amplitude and Frequency Modulation

To perform well in biotechnology applications, synthetic genetic oscillators must be engineered to allow independent modulation of amplitude and period. This need is currently unmet. Here, we demonstrate computationally how two classic genetic oscillators, the dual-feedback oscillator and the repressilator, can be re-designed to provide independent control of amplitude and period and improve tunability-that is, a broad dynamic range of periods and amplitudes accessible through the input "dials." Our approach decouples frequency and amplitude modulation by incorporating an orthogonal "sink module" where the key molecular species are channeled for enzymatic degradation. This sink module maintains fast oscillation cycles while alleviating the translational coupling between the oscillator's transcription factors and output. We characterize the behavior of our re-designed oscillators over a broad range of physiologically reasonable parameters, explain why this facilitates broader function and control, and provide general design principles for building synthetic genetic oscillators that are more precisely controllable.