A comparative analysis of synthetic genetic oscillators

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.

Long negative feedback loop enhances period tunability of biological oscillators

Oscillatory phenomena play a major role in organisms. In some biological oscillations such as cell cycles and heartbeats, the period can be tuned without significant changes in the amplitude. This property is called (period) tunability, one of the prominent features of biological oscillations. However, how biological oscillators produce tunable oscillations remains largely unexplored. We tackle this question using computational experiments. It has been reported that positive-plus-negative feedback oscillators produce tunable oscillations through the hysteresis-based mechanism. First, in this study, we confirmed that positive-plus-negative feedback oscillators generate tunable oscillations. Second, we found that tunability is positively correlated with the dynamic range of oscillations. Third, we showed that long negative feedback oscillators without any additional positive feedback loops can produce tunable oscillations. Finally, we computationally demonstrated that by lengthening the negative feedback loop, the Repressilator, known as a non-tunable synthetic gene oscillator, can be converted into a tunable oscillator. This work provides synthetic biologists with clues to design tunable gene oscillators.

Structure, function, and mechanism of the core circadian clock in cyanobacteria

Circadian rhythms enable cells and organisms to coordinate their physiology with the cyclic environmental changes that come as a result of Earth's light/dark cycles. Cyanobacteria make use of a post-translational oscillator to maintain circadian rhythms, and this elegant system has become an important model for circadian timekeeping mechanisms. Composed of three proteins, the KaiABC system undergoes an oscillatory biochemical cycle that provides timing cues to achieve a 24-h molecular clock. Together with the input/output proteins SasA, CikA, and RpaA, these six gene products account for the timekeeping, entrainment, and output signaling functions in cyanobacterial circadian rhythms. This Minireview summarizes the current structural, functional and mechanistic insights into the cyanobacterial circadian clock.

Proliferation of cells with aggregation and communication

Cell proliferation is often considered to occur via front propagation with constant velocity. This scenario proposed by Fisher, Kolmogorov, Petrovsky, and Piskunov is based on the solution of the corresponding mean-field reaction-diffusion equations and does not take into account that due to adhesion the cells have tendency to aggregate and that the rate of cell division may depend on the cell-cell communication. Herein, the author presents extensive Monte Carlo simulations taking both these factors into account and illustrating that the former factor can dramatically modify the spatio-temporal kinetics of cell proliferation. In particular, the conventional relation between the front velocity and diffusion coefficient may fail, the front velocity may appreciably increase with increasing time, and/or the front may be partly or fully smeared on the realistic length scales.

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.

mRNA function after intracellular delivery and release

Nanocarrier-mediated mRNA delivery and release into the cells with subsequent translation to protein is of interest in the context of the development of a new generation of drugs. In particular, this protein can play a role of a transcription factor and be used as a tool to regulate temporarily the genetic networks. The corresponding transient kinetics of gene expression are expected to depend on the mechanism and duration of mRNA release. Assuming the release to be rapid on the time scale of other steps, the author shows theoretically the mRNA-related transient features of gene expression occurring in stable, bistable, and oscillatory regimes in a single cell. Qualitatively, the results obtained are found to be fairly similar to those reported earlier for the situation when the release is slow. Thus, the features of the transient kinetics under consideration appear to be less sensitive to the duration of mRNA release compared to what one might expect.

Systems and synthetic biology approaches in understanding biological oscillators

Background

Self-sustained oscillations are a ubiquitous and vital phenomenon in living systems. From primitive single-cellular bacteria to the most sophisticated organisms, periodicities have been observed in a broad spectrum of biological processes such as neuron firing, heart beats, cell cycles, circadian rhythms, etc. Defects in these oscillators can cause diseases from insomnia to cancer. Elucidating their fundamental mechanisms is of great significance to diseases, and yet challenging, due to the complexity and diversity of these oscillators.

Results

Approaches in quantitative systems biology and synthetic biology have been most effective by simplifying the systems to contain only the most essential regulators. Here, we will review major progress that has been made in understanding biological oscillators using these approaches. The quantitative systems biology approach allows for identification of the essential components of an oscillator in an endogenous system. The synthetic biology approach makes use of the knowledge to design the simplest, de novo oscillators in both live cells and cell-free systems. These synthetic oscillators are tractable to further detailed analysis and manipulations.

Conclusion

With the recent development of biological and computational tools, both approaches have made significant achievements.

Kinetics of lipid-nanoparticle-mediated intracellular mRNA delivery and function

mRNA delivery into cells forms the basis for one of the new and promising ways to treat various diseases. Among suitable carriers, lipid nanoparticles (LNPs) with a size of about 100 nm are now often employed. Despite high current interest in this area, the understanding of the basic details of LNP-mediated mRNA delivery and function is limited. To clarify the kinetics of mRNA release from LNPs, the author uses three generic models implying (i) exponential, (ii) diffusion-controlled, and (iii) detachment-controlled kinetic regimes, respectively. Despite the distinct differences in these kinetics, the associated transient kinetics of mRNA translation to the corresponding protein and its degradation are shown to be not too sensitive to the details of the mRNA delivery by LNPs (or other nanocarriers). In addition, the author illustrates how this protein may temporarily influence the expression of one gene or a few equivalent genes. The analysis includes positive or negative regulation of the gene transcription via the attachment of the protein without or with positive or negative feedback in the gene expression. Stable, bistable, and oscillatory schemes have been scrutinized in this context.

Understanding and engineering plant form

A plant's form is an important determinant of its fitness and economic value. Here, we review strategies for producing plants with altered forms. Historically, the process of changing a plant's form has been slow in agriculture, requiring iterative rounds of growth and selection. We discuss modern techniques for identifying genes involved in the development of plant form and tools that will be needed to effectively design and engineer plants with altered forms. Synthetic genetic circuits are highlighted for their potential to generate novel plant forms. We emphasize understanding development as a prerequisite to engineering and discuss the potential role of computer models in translating knowledge about single genes or pathways into a more comprehensive understanding of development.

Grip on complexity in chemical reaction networks

A new discipline of "systems chemistry" is emerging, which aims to capture the complexity observed in natural systems within a synthetic chemical framework. Living systems rely on complex networks of chemical reactions to control the concentration of molecules in space and time. Despite the enormous complexity in biological networks, it is possible to identify network motifs that lead to functional outputs such as bistability or oscillations. To truly understand how living systems function, we need a complete understanding of how chemical reaction networks (CRNs) create function. We propose the development of a bottom-up approach to design and construct CRNs where we can follow the influence of single chemical entities on the properties of the network as a whole. Ultimately, this approach should allow us to not only understand such complex networks but also to guide and control their behavior.

Serotyping, antibiotic susceptibility, and virulence genes screening of Escherichia coli isolates obtained from diarrheic buffalo calves in Egyptian farms

AIM

In Egypt as in many other countries, river water buffalo (Bubalus bubalis) is considered an important source of high-quality milk and meat supply. The objective of this study was to investigate serotypes, virulence genes, and antibiotic resistance determinants profiles of Escherichia coli isolated from buffalo at some places in Egypt; noticibly, this issue was not discussed in the country yet.

MATERIALS AND METHODS

A number of 58 rectal samples were collected from diarrheic buffalo calves in different regions in Egypt, and bacteriological investigated for E. coli existence. The E. coli isolates were biochemically, serologicaly identified, tested for antibiotic susceptibility, and polymerase chain reaction (PCR) analyzed for the presence of antibiotic resistance determinants and virulence genes.

RESULTS

Overall 14 isolates typed as E. coli (24.1%); 6 were belonged to serogroup O78 (10.3%), followed by O125 (4 isolates, 6.9%), then O158 (3 isolates, 5.2%) and one isolate O8 (1.7%), among them, there were 5 E. coli isolates showed a picture of hemolysis (35.7%). The isolates exhibited a high resistance to β lactams over 60%, followed by sulfa (50%) and aminoglucoside (42.8%) group, in the same time the isolates were sensitive to quinolone, trimethoprim-sulfamethoxazole, tetracycline (100%), and cephalosporine groups (71.4%). A multiplex PCR was applied to the 14 E. coli isolates revealed that all were carrying at least one gene, as 10 carried blaTEM (71.4%), 8 Sul1 (57.1%), and 6 aadB (42.8%), and 9 isolates could be considered multidrug resistant (MDR) by an incidence of 64.3%. A PCR survey was stratified for the most important E. coli virulence genes, and showed the presence of Shiga toxins in 9 isolates carried either one or the two Stx genes (64.3%), 5 isolates carried hylA gene (35.7%), and eae in 2 isolates only (14.3%), all isolates carried at least one virulence gene except two (85.7%).

CONCLUSION

The obtained data displayed that in Egypt, buffalo as well as other ruminants could be a potential source of MDR pathogenic E. coli variants which have a public health importance.

Computational Modelling of Cancer Development and Growth: Modelling at Multiple Scales and Multiscale Modelling

In this paper, we present two mathematical models related to different aspects and scales of cancer growth. The first model is a stochastic spatiotemporal model of both a synthetic gene regulatory network (the example of a three-gene repressilator is given) and an actual gene regulatory network, the NF-[Formula: see text]B pathway. The second model is a force-based individual-based model of the development of a solid avascular tumour with specific application to tumour cords, i.e. a mass of cancer cells growing around a central blood vessel. In each case, we compare our computational simulation results with experimental data. In the final discussion section, we outline how to take the work forward through the development of a multiscale model focussed at the cell level. This would incorporate key intracellular signalling pathways associated with cancer within each cell (e.g. p53-Mdm2, NF-[Formula: see text]B) and through the use of high-performance computing be capable of simulating up to [Formula: see text] cells, i.e. the tissue scale. In this way, mathematical models at multiple scales would be combined to formulate a multiscale computational model.

Agent-based modelling in synthetic biology

Biological systems exhibit complex behaviours that emerge at many different levels of organization. These span the regulation of gene expression within single cells to the use of quorum sensing to co-ordinate the action of entire bacterial colonies. Synthetic biology aims to make the engineering of biology easier, offering an opportunity to control natural systems and develop new synthetic systems with useful prescribed behaviours. However, in many cases, it is not understood how individual cells should be programmed to ensure the emergence of a required collective behaviour. Agent-based modelling aims to tackle this problem, offering a framework in which to simulate such systems and explore cellular design rules. In this article, I review the use of agent-based models in synthetic biology, outline the available computational tools, and provide details on recently engineered biological systems that are amenable to this approach. I further highlight the challenges facing this methodology and some of the potential future directions.

Parametric Sensitivity Analysis of Oscillatory Delay Systems with an Application to Gene Regulation

A parametric sensitivity analysis for periodic solutions of delay-differential equations is developed. Because phase shifts cause the sensitivity coefficients of a periodic orbit to diverge, we focus on sensitivities of the extrema, from which amplitude sensitivities are computed, and of the period. Delay-differential equations are often used to model gene expression networks. In these models, the parametric sensitivities of a particular genotype define the local geometry of the evolutionary landscape. Thus, sensitivities can be used to investigate directions of gradual evolutionary change. An oscillatory protein synthesis model whose properties are modulated by RNA interference is used as an example. This model consists of a set of coupled delay-differential equations involving three delays. Sensitivity analyses are carried out at several operating points. Comments on the evolutionary implications of the results are offered.

Classical Mechanics Approach Applied to Analysis of Genetic Oscillators

Biological oscillators present a fundamental part of several regulatory mechanisms that control the response of various biological systems. Several analytical approaches for their analysis have been reported recently. They are, however, limited to only specific oscillator topologies and/or to giving only qualitative answers, i.e., is the dynamics of an oscillator given the parameter space oscillatory or not. Here, we present a general analytical approach that can be applied to the analysis of biological oscillators. It relies on the projection of biological systems to classical mechanics systems. The approach is able to provide us with relatively accurate results in the meaning of type of behavior system reflects (i.e., oscillatory or not) and periods of potential oscillations without the necessity to conduct expensive numerical simulations. We demonstrate and verify the proposed approach on three different implementations of amplified negative feedback oscillator.

Bridging the gap between modules in isolation and as part of networks: A systems framework for elucidating interaction and regulation of signalling modules

While signalling and biochemical modules have been the focus of numerous studies, they are typically studied in isolation, with no examination of the effects of the ambient network. In this paper we formulate and develop a systems framework, rooted in dynamical systems, to understand such effects, by studying the interaction of signalling modules. The modules we consider are (i) basic covalent modification, (ii) monostable switches, (iii) bistable switches, (iv) adaptive modules, and (v) oscillatory modules. We systematically examine the interaction of these modules by analyzing (a) sequential interaction without shared components, (b) sequential interaction with shared components, and (c) oblique interactions. Our studies reveal that the behaviour of a module in isolation may be substantially different from that in a network, and explicitly demonstrate how the behaviour of a given module, the characteristics of the ambient network, and the possibility of shared components can result in new effects. Our global approach illuminates different aspects of the structure and functioning of modules, revealing the importance of dynamical characteristics as well as biochemical features; this provides a methodological platform for investigating the complexity of natural modules shaped by evolution, elucidating the effects of ambient networks on a module in multiple cellular contexts, and highlighting the capabilities and constraints for engineering robust synthetic modules. Overall, such a systems framework provides a platform for bridging the gap between non-linear information processing modules, in isolation and as parts of networks, and a basis for understanding new aspects of natural and engineered cellular networks.

Spatio-temporal models of synthetic genetic oscillators

Signal transduction pathways play a major role in many important aspects of cellular function e.g. cell division, apoptosis. One important class of signal transduction pathways is gene regulatory networks (GRNs). In many GRNs, proteins bind to gene sites in the nucleus thereby altering the transcription rate. Such proteins are known as transcription factors. If the binding reduces the transcription rate there is a negative feedback leading to oscillatory behaviour in mRNA and protein levels, both spatially (e.g. by observing fluorescently labelled molecules in single cells) and temporally (e.g. by observing protein/mRNA levels over time). Recent computational modelling has demonstrated that spatial movement of the molecules is a vital component of GRNs and may cause the oscillations. These numerical findings have subsequently been proved rigorously i.e. the diffusion coefficient of the protein/mRNA acts as a bifurcation parameter and gives rise to a Hopf bifurcation. In this paper we first present a model of the canonical GRN (the Hes1 protein) and show the effect of varying the spatial location of gene and protein production sites on the oscillations. We then extend the approach to examine spatio-temporal models of synthetic gene regulatory networks e.g. n-gene repressilators and activator-repressor systems.

Impact of time delays on oscillatory dynamics of interlinked positive and negative feedback loops

Interlinking a positive feedback loop (PFL) with a negative feedback loop (NFL) constitutes a typical motif in genetic networks, performing various functions in cell signaling. How time delay in feedback regulation affects the dynamics of such systems still remains unclear. Here, we investigate three systems of interlinked PFL and NFL with time delays: a synthetic genetic oscillator, a three-node circuit, and a simplified single-node model. The stability of steady states and the routes to oscillation in the single-node model are analyzed in detail. The amplitude and period of oscillations vary with a pointwise periodicity over a range of time delay. Larger-amplitude oscillations can be induced when the PFL has an appropriately long delay, in comparison with the PFL with no delay or short delay; this conclusion holds true for all the three systems. We unravel the underlying mechanism for the above effects via analytical derivation under a limiting condition. We also develop a stochastic algorithm for simulating a single reaction with two delays and show that robust oscillations can be maintained by the PFL with a properly long delay in the single-node system. This work presents an effective method for constructing robust large-amplitude oscillators and interprets why similar circuit architectures are engaged in timekeeping systems such as circadian clocks.

Kinetic aspects of enzyme-mediated repair of DNA single-strand breaks

In cells and bacteria, DNA can be damaged in different ways. The efficient damage repair, mediated by various enzymes, is crucial for their survival. Most frequently, the damage is reduced to single-strand breaks. In human cells, according to the experiments, the repair of such breaks can mechanistically be divided into four steps including (i) the break detection, (ii) processing of damaged ends, (iii) gap filling, and (iv) ligation of unbound ends of the broken strand. The first and second steps run in parallel while the third and fourth steps are sequential. The author proposes a kinetic model describing these steps. It allows one to understand the likely dependence of the number of breaks in different states on enzyme concentrations. The dependence of these concentrations on the rate of the formation of breaks can be understood as well. In addition, the likely role of unzipping and zipping of the fragments of broken ends of the strand in the ligation step has been scrutinized taking the specifics of binding of DNA stands into account.

A Statistical Approach Reveals Designs for the Most Robust Stochastic Gene Oscillators

The engineering of transcriptional networks presents many challenges due to the inherent uncertainty in the system structure, changing cellular context, and stochasticity in the governing dynamics. One approach to address these problems is to design and build systems that can function across a range of conditions; that is they are robust to uncertainty in their constituent components. Here we examine the parametric robustness landscape of transcriptional oscillators, which underlie many important processes such as circadian rhythms and the cell cycle, plus also serve as a model for the engineering of complex and emergent phenomena. The central questions that we address are: Can we build genetic oscillators that are more robust than those already constructed? Can we make genetic oscillators arbitrarily robust? These questions are technically challenging due to the large model and parameter spaces that must be efficiently explored. Here we use a measure of robustness that coincides with the Bayesian model evidence, combined with an efficient Monte Carlo method to traverse model space and concentrate on regions of high robustness, which enables the accurate evaluation of the relative robustness of gene network models governed by stochastic dynamics. We report the most robust two and three gene oscillator systems, plus examine how the number of interactions, the presence of autoregulation, and degradation of mRNA and protein affects the frequency, amplitude, and robustness of transcriptional oscillators. We also find that there is a limit to parametric robustness, beyond which there is nothing to be gained by adding additional feedback. Importantly, we provide predictions on new oscillator systems that can be constructed to verify the theory and advance design and modeling approaches to systems and synthetic biology.

The Intracellular Dynamics of Circadian Clocks Reach for the Light of Ecology and Evolution

A major challenge for biology is to extend our understanding of molecular regulation from the simplified conditions of the laboratory to ecologically relevant environments. Tractable examples are essential to make these connections for complex, pleiotropic regulators and, to go further, to link relevant genome sequences to field traits. Here, I review the case for the biological clock in higher plants. The gene network of the circadian clock drives pervasive, 24-hour rhythms in metabolism, behavior, and physiology across the eukaryotes and in some prokaryotes. In plants, the scope of chronobiology is now extending from the most tractable, intracellular readouts to the clock's many effects at the whole-organism level and across the life cycle, including biomass and flowering. I discuss five research areas where recent progress might be integrated in the future, to understand not only circadian functions in natural conditions but also the evolution of the clock's molecular mechanisms.

Proteolytic crosstalk in multi-protease networks

Processive proteases, such as ClpXP in E. coli, are conserved enzyme assemblies that can recognize and rapidly degrade proteins. These proteases are used for a number of purposes, including degrading mistranslated proteins and controlling cellular stress response. However, proteolytic machinery within the cell is limited in capacity and can lead to a bottleneck in protein degradation, whereby many proteins compete ('queue') for proteolytic resources. Previous work has demonstrated that such queueing can lead to pronounced statistical relationships between different protein counts when proteins compete for a single common protease. However, real cells contain many different proteases, e.g. ClpXP, ClpAP, and Lon in E. coli, and it is not clear how competition between proteins for multiple classes of protease would influence the dynamics of cellular networks. In the present work, we theoretically demonstrate that a multi-protease proteolytic bottleneck can substantially couple the dynamics for both simple and complex (oscillatory) networks, even between substrates with substantially different affinities for protease. For these networks, queueing often leads to strong positive correlations between protein counts, and these correlations are strongest near the queueing theoretic point of balance. Furthermore, we find that the qualitative behavior of these networks depends on the relative size of the absolute affinity of substrate to protease compared to the cross affinity of substrate to protease, leading in certain regimes to priority queue statistics.

Mammalian synthetic biology: emerging medical applications

In this review, we discuss new emerging medical applications of the rapidly evolving field of mammalian synthetic biology. We start with simple mammalian synthetic biological components and move towards more complex and therapy-oriented gene circuits. A comprehensive list of ON-OFF switches, categorized into transcriptional, post-transcriptional, translational and post-translational, is presented in the first sections. Subsequently, Boolean logic gates, synthetic mammalian oscillators and toggle switches will be described. Several synthetic gene networks are further reviewed in the medical applications section, including cancer therapy gene circuits, immuno-regulatory networks, among others. The final sections focus on the applicability of synthetic gene networks to drug discovery, drug delivery, receptor-activating gene circuits and mammalian biomanufacturing processes.

How to make an oscillator

A cell-free approach reveals how genetic circuits can produce robust oscillations of proteins and other components.

Advances in synthetic dynamic circuits design: using novel synthetic parts to engineer new generations of gene oscillations

As bioengineering applications expand, the need to design and implement circuits that exhibit dynamic properties increases. In particular, schemes that control precise patterns of gene expression as a function of time are essential for balancing multiple metabolic objectives in natural and synthetic systems. Given that modularity has been an important component of dynamic circuits, recent efforts to improve dynamic circuits have focused on replacing old parts for new components that increase the robustness, stability, and tunability. In this review, we show that incorporation of novel components such as regulatory noncoding RNAs (ncRNAs), promoter-transcription factor pairs, and metabolite sensors have allowed traditional dynamic circuits to obtain more robust functionality and improved dynamic properties.

Design principles for robust oscillatory behavior

Oscillatory responses are ubiquitous in regulatory networks of living organisms, a fact that has led to extensive efforts to study and replicate the circuits involved. However, to date, design principles that underlie the robustness of natural oscillators are not completely known. Here we study a three-component enzymatic network model in order to determine the topological requirements for robust oscillation. First, by simulating every possible topological arrangement and varying their parameter values, we demonstrate that robust oscillators can be obtained by augmenting the number of both negative feedback loops and positive autoregulations while maintaining an appropriate balance of positive and negative interactions. We then identify network motifs, whose presence in more complex topologies is a necessary condition for obtaining oscillatory responses. Finally, we pinpoint a series of simple architectural patterns that progressively render more robust oscillators. Together, these findings can help in the design of more reliable synthetic biomolecular networks and may also have implications in the understanding of other oscillatory systems.

Influence of parameter values on the oscillation sensitivities of two p53-Mdm2 models

Biomolecular networks that present oscillatory behavior are ubiquitous in nature. While some design principles for robust oscillations have been identified, it is not well understood how these oscillations are affected when the kinetic parameters are constantly changing or are not precisely known, as often occurs in cellular environments. Many models of diverse complexity level, for systems such as circadian rhythms, cell cycle or the p53 network, have been proposed. Here we assess the influence of hundreds of different parameter sets on the sensitivities of two configurations of a well-known oscillatory system, the p53 core network. We show that, for both models and all parameter sets, the parameter related to the p53 positive feedback, i.e. self-promotion, is the only one that presents sizeable sensitivities on extrema, periods and delay. Moreover, varying the parameter set values to change the dynamical characteristics of the response is more restricted in the simple model, whereas the complex model shows greater tunability. These results highlight the importance of the presence of specific network patterns, in addition to the role of parameter values, when we want to characterize oscillatory biochemical systems.

Forging patterns and making waves from biology to geology: a commentary on Turing (1952) 'The chemical basis of morphogenesis'

Alan Turing was neither a biologist nor a chemist, and yet the paper he published in 1952, 'The chemical basis of morphogenesis', on the spontaneous formation of patterns in systems undergoing reaction and diffusion of their ingredients has had a substantial impact on both fields, as well as in other areas as disparate as geomorphology and criminology. Motivated by the question of how a spherical embryo becomes a decidedly non-spherical organism such as a human being, Turing devised a mathematical model that explained how random fluctuations can drive the emergence of pattern and structure from initial uniformity. The spontaneous appearance of pattern and form in a system far away from its equilibrium state occurs in many types of natural process, and in some artificial ones too. It is often driven by very general mechanisms, of which Turing's model supplies one of the most versatile. For that reason, these patterns show striking similarities in systems that seem superficially to share nothing in common, such as the stripes of sand ripples and of pigmentation on a zebra skin. New examples of 'Turing patterns' in biology and beyond are still being discovered today. This commentary was written to celebrate the 350th anniversary of the journal Philosophical Transactions of the Royal Society.

Multi-stable dynamics of the non-adiabatic repressilator

The assumption of the fast binding of transcription factors (TFs) to promoters is a typical point in studies of synthetic genetic circuits functioning in bacteria. Although the assumption is effective for simplifying the models, it becomes questionable in the light of in vivo measurements of the times TF spends searching for its cognate DNA sites. We investigated the dynamics of the full idealized model of the paradigmatic genetic oscillator, the repressilator, using deterministic mathematical modelling and stochastic simulations. We found (using experimentally approved parameter values) that decreases in the TF binding rate changes the type of transition between steady state and oscillation. As a result, this gives rise to the hysteresis region in the parameter space, where both the steady state and the oscillation coexist. We further show that the hysteresis is persistent over a considerable range of the parameter values, but the presence of the oscillations is limited by the low rate of TF dimer degradation. Finally, the stochastic simulation of the model confirms the hysteresis with switching between the two attractors, resulting in highly skewed period distributions. Moreover, intrinsic noise stipulates trains of large-amplitude modulations around the stable steady state outside the hysteresis region, which makes the period distributions bimodal.

Stochastic oscillations induced by intrinsic fluctuations in a self-repressing gene

Biochemical reaction networks are subjected to large fluctuations attributable to small molecule numbers, yet underlie reliable biological functions. Thus, it is important to understand how regularity can emerge from noise. Here, we study the stochastic dynamics of a self-repressing gene with arbitrarily long or short response time. We find that when the mRNA and protein half-lives are approximately equal to the gene response time, fluctuations can induce relatively regular oscillations in the protein concentration. To gain insight into this phenomenon at the crossroads of determinism and stochasticity, we use an intermediate theoretical approach, based on a moment-closure approximation of the master equation, which allows us to take into account the binary character of gene activity. We thereby obtain differential equations that describe how nonlinearity can feed-back fluctuations into the mean-field equations to trigger oscillations. Finally, our results suggest that the self-repressing Hes1 gene circuit exploits this phenomenon to generate robust oscillations, inasmuch as its time constants satisfy precisely the conditions we have identified.

Evolution of lifespan

Present-day evolutionary theory, modern synthesis and evo-devo, appear to explain evolution. There remain however several points of contention. These include: biological time, direction, macroevolution verses microevolution, ageing and the extent of internal as opposed to external mediation. A new theoretical model for the control of biological time in vertebrates/bilaterians is introduced. Rather than biological time being controlled solely by a molecular cascade domino effect, it is suggested there is also an intracellular oscillatory clock. This clock (life's timekeeper) is synchronised across all cells in an organism and runs at a constant frequency throughout life. Slower frequencies extend lifespan, increase body/brain size and advance behaviour. They also create a time void which could aid additional evolutionary change. Faster frequencies shorten lifespan, reduce body/brain size and diminish behaviour. They are therefore less likely to mediate evolution in vertebrates/mammals. It is concluded that in vertebrates, especially mammals, there is a direction in evolution towards longer lifespan/advanced behaviour. Lifespan extension could equate with macroevolution and subsequent modifications with microevolution. As life's timekeeper controls the rate of ageing it constitutes a new genetic theory of ageing. Finally, as lifespan extension is internally mediated, this suggests a major role for internal mediation in evolution.

Delays induce novel stochastic effects in negative feedback gene circuits

Stochastic models of reaction networks are widely used to depict gene expression dynamics. However, stochastic does not necessarily imply accurate, as subtle assumptions can yield erroneous results, masking key discrete effects. For instance, transcription and translation are not instantaneous processes-explicit delays separate their initiation from the appearance of their functional products. However, delays are often ignored in stochastic, single-gene expression models. By consequence, effects such as delay-induced stochastic oscillations at the single-cell level have remained relatively unexplored. Here, we present a systematic study of periodicity and multimodality in a simple gene circuit with negative feedback, analyzing the influence of negative feedback strength and transcriptional/translational delays on expression dynamics. We demonstrate that an oscillatory regime emerges through a Hopf bifurcation in both deterministic and stochastic frameworks. Of importance, a shift in the stochastic Hopf bifurcation evidences inaccuracies of the deterministic bifurcation analysis. Furthermore, noise fluctuations within stochastic oscillations decrease alongside increasing values of transcriptional delays and within a specific range of negative feedback strengths, whereas a strong feedback is associated with oscillations triggered by bursts. Finally, we demonstrate that explicitly accounting for delays increases the number of accessible states in the multimodal regime, and also introduces features typical of excitable systems.

Integration of microfluidics into the synthetic biology design flow

One goal of synthetic biology is to design and build genetic circuits in living cells for a range of applications. Major challenges in these efforts include increasing the scalability and robustness of engineered biological systems and streamlining and automating the synthetic biology workflow of specification-design-assembly-verification. We present here a summary of the advances in microfluidic technology, particularly microfluidic large scale integration, that can be used to address the challenges facing each step of the synthetic biology workflow. Microfluidic technologies allow precise control over the flow of biological content within microscale devices, and thus may provide more reliable and scalable construction of synthetic biological systems. The integration of microfluidics and synthetic biology has the capability to produce rapid prototyping platforms for characterization of genetic devices, testing of biotherapeutics, and development of biosensors.

Strategy revealing phenotypic differences among synthetic oscillator designs

Considerable progress has been made in identifying and characterizing the component parts of genetic oscillators, which play central roles in all organisms. Nonlinear interaction among components is sufficiently complex that mathematical models are required to elucidate their elusive integrated behavior. Although natural and synthetic oscillators exhibit common architectures, there are numerous differences that are poorly understood. Utilizing synthetic biology to uncover basic principles of simpler circuits is a way to advance understanding of natural circadian clocks and rhythms. Following this strategy, we address the following questions: What are the implications of different architectures and molecular modes of transcriptional control for the phenotypic repertoire of genetic oscillators? Are there designs that are more realizable or robust? We compare synthetic oscillators involving one of three architectures and various combinations of the two modes of transcriptional control using a methodology that provides three innovations: a rigorous definition of phenotype, a procedure for deconstructing complex systems into qualitatively distinct phenotypes, and a graphical representation for illuminating the relationship between genotype, environment, and the qualitatively distinct phenotypes of a system. These methods provide a global perspective on the behavioral repertoire, facilitate comparisons of alternatives, and assist the rational design of synthetic gene circuitry. In particular, the results of their application here reveal distinctive phenotypes for several designs that have been studied experimentally as well as a best design among the alternatives that has yet to be constructed and tested.

Theory on the dynamics of oscillatory loops in the transcription factor networks

We develop a detailed theoretical framework for various types of transcription factor gene oscillators. We further demonstrate that one can build genetic-oscillators which are tunable and robust against perturbations in the critical control parameters by coupling two or more independent Goodwin-Griffith oscillators through either -OR- or -AND- type logic. Most of the coupled oscillators constructed in the literature so far seem to be of -OR- type. When there are transient perturbations in one of the -OR- type coupled-oscillators, then the overall period of the system remains constant (period-buffering) whereas in case of -AND- type coupling the overall period of the system moves towards the perturbed oscillator. Though there is a period-buffering, the amplitudes of oscillators coupled through -OR- type logic are more sensitive to perturbations in the parameters associated with the promoter state dynamics than -AND- type. Further analysis shows that the period of -AND- type coupled dual-feedback oscillators can be tuned without conceding on the amplitudes. Using these results we derive the basic design principles governing the robust and tunable synthetic gene oscillators without compromising on their amplitudes.

A Novel Synthesizing Genetic Logic Circuit: Frequency Multiplier

This paper presents a novel synthesizing genetic logic circuit design based on an existing synthetic genetic oscillator, which provides a function of frequency multiplier to synthesize a clock signal whose frequency is a multiple of that of the genetic oscillator. In the renowned literature, the synthetic genetic oscillator, known as a repressilator, has been successfully built in Escherichia coli to generate a periodic oscillating phenomenon through three repressive genes repress each other in a chain. On the basis of this fact, our proposed genetic frequency multiplier circuit utilizes genetic Buffers in series with a waveform-shaping circuit to reshape the genetic oscillation signal into a crisp logic clock signal. By regulating different threshold levels in the Buffer, the time length of logic high/low levels in a fundamental sinusoidal wave can be engineered to pulse-width-modulated (PWM) signals with various duty cycles. Integrating some of genetic logic XOR gates and PWM signals from the output of the Buffers, a genetic frequency multiplier circuit can be created and the clock signal with the integer-fold of frequency of the genetic oscillator is generated. The synthesized signal can be used in triggering the downstream digital genetic logic circuits. Simulation results show the applicability of the proposed idea.

Synthesizing genetic sequential logic circuit with clock pulse generator

Background

Rhythmic clock widely occurs in biological systems which controls several aspects of cell physiology. For the different cell types, it is supplied with various rhythmic frequencies. How to synthesize a specific clock signal is a preliminary but a necessary step to further development of a biological computer in the future.

Results

This paper presents a genetic sequential logic circuit with a clock pulse generator based on a synthesized genetic oscillator, which generates a consecutive clock signal whose frequency is an inverse integer multiple to that of the genetic oscillator. An analogous electronic waveform-shaping circuit is constructed by a series of genetic buffers to shape logic high/low levels of an oscillation input in a basic sinusoidal cycle and generate a pulse-width-modulated (PWM) output with various duty cycles. By controlling the threshold level of the genetic buffer, a genetic clock pulse signal with its frequency consistent to the genetic oscillator is synthesized. A synchronous genetic counter circuit based on the topology of the digital sequential logic circuit is triggered by the clock pulse to synthesize the clock signal with an inverse multiple frequency to the genetic oscillator. The function acts like a frequency divider in electronic circuits which plays a key role in the sequential logic circuit with specific operational frequency.

Conclusions

A cascaded genetic logic circuit generating clock pulse signals is proposed. Based on analogous implement of digital sequential logic circuits, genetic sequential logic circuits can be constructed by the proposed approach to generate various clock signals from an oscillation signal.

Cyclic negative feedback systems: what is the chance of oscillation?

Many biological oscillators have a cyclic structure consisting of negative feedback loops. In this paper, we analyze the impact that the addition of a positive or a negative self-feedback loop has on the oscillatory behavior of the three negative feedback oscillators proposed by Tsai et al. (Science 231:126-129, 2008) where, in contrast with numerous oscillator models, the interactions between elements occur via the modulation of the degradation rates. Through analytical and computational studies we show that an additional self-feedback affects the oscillatory behavior. In the high-cooperativity limit, i.e., for large Hill coefficients, we derive exact analytical conditions for oscillations and show that the relative location between the dissociation constants of the Hill functions and the ratio of kinetic parameters determines the possibility of oscillatory activities. We compute analytically the probability of oscillations for the three models and show that the smallest domain of periodic behavior is obtained for the negative-plus-negative feedback system whereas the additional positive self-feedback loop does not modify significantly the chance to oscillate. We numerically investigate to what extent the properties obtained in the sharp situation applied in the smooth case. Results suggest that a switch-like coupling behavior, a time-scale separation, and a repressilator-type architecture with an even number of elements facilitate the emergence of sustained oscillations in biological systems. An additional positive self-feedback loop produces robustness and adaptability whereas an additional negative self-feedback loop reduces the chance to oscillate.

Chaos and robustness in a single family of genetic oscillatory networks

Genetic oscillatory networks can be mathematically modeled with delay differential equations (DDEs). Interpreting genetic networks with DDEs gives a more intuitive understanding from a biological standpoint. However, it presents a problem mathematically, for DDEs are by construction infinitely-dimensional and thus cannot be analyzed using methods common for systems of ordinary differential equations (ODEs). In our study, we address this problem by developing a method for reducing infinitely-dimensional DDEs to two- and three-dimensional systems of ODEs. We find that the three-dimensional reductions provide qualitative improvements over the two-dimensional reductions. We find that the reducibility of a DDE corresponds to its robustness. For non-robust DDEs that exhibit high-dimensional dynamics, we calculate analytic dimension lines to predict the dependence of the DDEs’ correlation dimension on parameters. From these lines, we deduce that the correlation dimension of non-robust DDEs grows linearly with the delay. On the other hand, for robust DDEs, we find that the period of oscillation grows linearly with delay. We find that DDEs with exclusively negative feedback are robust, whereas DDEs with feedback that changes its sign are not robust. We find that non-saturable degradation damps oscillations and narrows the range of parameter values for which oscillations exist. Finally, we deduce that natural genetic oscillators with highly-regular periods likely have solely negative feedback.

Engineered temperature compensation in a synthetic genetic clock

Synthetic biology promises to revolutionize biotechnology by providing the means to reengineer and reprogram cellular regulatory mechanisms. However, synthetic gene circuits are often unreliable, as changes to environmental conditions can fundamentally alter a circuit's behavior. One way to improve robustness is to use intrinsic properties of transcription factors within the circuit to buffer against intra- and extracellular variability. Here, we describe the design and construction of a synthetic gene oscillator in Escherichia coli that maintains a constant period over a range of temperatures. We started with a previously described synthetic dual-feedback oscillator with a temperature-dependent period. Computational modeling predicted and subsequent experiments confirmed that a single amino acid mutation to the core transcriptional repressor of the circuit results in temperature compensation. Specifically, we used a temperature-sensitive lactose repressor mutant that loses the ability to repress its target promoter at high temperatures. In the oscillator, this thermoinduction of the repressor leads to an increase in period at high temperatures that compensates for the decrease in period due to Arrhenius scaling of the reaction rates. The result is a transcriptional oscillator with a nearly constant period of 48 min for temperatures ranging from 30 °C to 41 °C. In contrast, in the absence of the mutation the period of the oscillator drops from 60 to 30 min over the same temperature range. This work demonstrates that synthetic gene circuits can be engineered to be robust to extracellular conditions through protein-level modifications.