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

Automated Design of Synthetic Gene Circuits in the Presence of Molecular Noise

Microorganisms (mainly bacteria and yeast) are frequently used as hosts for genetic constructs in synthetic biology applications. Molecular noise might have a significant effect on the dynamics of gene regulation in microbial cells, mainly attributed to the low copy numbers of mRNA species involved. However, the inclusion of molecular noise in the automated design of biocircuits is not a common practice due to the computational burden linked to the chemical master equation describing the dynamics of stochastic gene regulatory circuits. Here, we address the automated design of synthetic gene circuits under the effect of molecular noise combining a mixed integer nonlinear global optimization method with a partial integro-differential equation model describing the evolution of stochastic gene regulatory systems that approximates very efficiently the chemical master equation. We demonstrate the performance of the proposed methodology through a number of examples of relevance in synthetic biology, including different bimodal stochastic gene switches, robust stochastic oscillators, and circuits capable of achieving biochemical adaptation under noise.

Bayesian Optimization for Design of Multiscale Biological Circuits

Recent advances in synthetic biology have enabled the construction of molecular circuits that operate across multiple scales of cellular organization, such as gene regulation, signaling pathways, and cellular metabolism. Computational optimization can effectively aid the design process, but current methods are generally unsuited for systems with multiple temporal or concentration scales, as these are slow to simulate due to their numerical stiffness. Here, we present a machine learning method for the efficient optimization of biological circuits across scales. The method relies on Bayesian optimization, a technique commonly used to fine-tune deep neural networks, to learn the shape of a performance landscape and iteratively navigate the design space toward an optimal circuit. This strategy allows the joint optimization of both circuit architecture and parameters, and provides a feasible approach to solve a highly nonconvex optimization problem in a mixed-integer input space. We illustrate the applicability of the method on several gene circuits for controlling biosynthetic pathways with strong nonlinearities, multiple interacting scales, and using various performance objectives. The method efficiently handles large multiscale problems and enables parametric sweeps to assess circuit robustness to perturbations, serving as an efficient in silico screening method prior to experimental implementation.

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.

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.

BMSS2: A Unified Database-Driven Modeling Tool for Systematic Biomodel Selection

Modeling in synthetic biology constitutes a powerful means in our continuous search for improved performance with a rational Design-Build-Test-Learn approach. Particularly, kinetic models unravel system dynamics and enable system analysis for guiding experimental design. However, a systematic yet modular pipeline that allows one to identify the appropriate model and guide the experimental designs while tracing the entire model development and analysis is still lacking. Here, we develop BMSS2, a unified tool that streamlines and automates model selection by combining information criterion ranking with upstream and parallel analysis algorithms. These include Bayesian parameter inference, a priori and a posteriori identifiability analysis, and global sensitivity analysis. In addition, the database-driven design supports interactive model storage/retrieval to encourage reusability and facilitate automated model selection. This allows ease of model manipulation and deposition for the selection and analysis, thus enabling better utilization of models in guiding experimental design.

Stochastic Differential Equations for Practical Simulation of Gene Circuits

The Chemical Langevin Equation approach allows simple stochastic simulation of gene circuits under many practical situations where the number of molecules of the species involved is not extremely low. Here, we describe methods and a computational framework to simulate a population of cells containing gene circuits of interest. These methods account for both intrinsic and extrinsic noise sources, and allow us to have both individual cell-related species and population-related ones. The protocol covers aspects related to proper description of the system and setting the software tools. It also helps to deal with the optimization of data storage and the simulation precision versus computational time issue. Finally, it also gives practical tests to assess the validity of the underlying technical assumptions.

Single strain control of microbial consortia

The scope of bioengineering is expanding from the creation of single strains to the design of microbial communities, allowing for division-of-labour, specialised sub-populations and interaction with “wild” microbiomes. However, in the absence of stabilising interactions, competition between microbes inevitably leads to the removal of less fit community members over time. Here, we leverage amensalism and competitive exclusion to stabilise a two-strain community by engineering a strain of Escherichia coli which secretes a toxin in response to competition. We show experimentally and mathematically that such a system can produce stable populations with a composition that is tunable by easily controllable parameters. This system creates a tunable, stable two-strain consortia while only requiring the engineering of a single strain.

Engineered microbial communities can divide labour between their members and interface with natural microbiomes. Here the authors demonstrate how a single toxin producing engineered strain can tune the composition of a two-strain community.

Automated design of synthetic microbial communities

Microbial species rarely exist in isolation. In naturally occurring microbial systems there is strong evidence for a positive relationship between species diversity and productivity of communities. The pervasiveness of these communities in nature highlights possible advantages for genetically engineered strains to exist in cocultures as well. Building synthetic microbial communities allows us to create distributed systems that mitigate issues often found in engineering a monoculture, especially as functional complexity increases. Here, we demonstrate a methodology for designing robust synthetic communities that include competition for nutrients, and use quorum sensing to control amensal bacteriocin interactions in a chemostat environment. We computationally explore all two- and three- strain systems, using Bayesian methods to perform model selection, and identify the most robust candidates for producing stable steady state communities. Our findings highlight important interaction motifs that provide stability, and identify requirements for selecting genetic parts and further tuning the community composition.

Novel Tunable Spatio-Temporal Patterns From a Simple Genetic Oscillator Circuit

Multicellularity, the coordinated collective behavior of cell populations, gives rise to the emergence of self-organized phenomena at many different spatio-temporal scales. At the genetic scale, oscillators are ubiquitous in regulation of multicellular systems, including during their development and regeneration. Synthetic biologists have successfully created simple synthetic genetic circuits that produce oscillations in single cells. Studying and engineering synthetic oscillators in a multicellular chassis can therefore give us valuable insights into how simple genetic circuits can encode complex multicellular behaviors at different scales. Here we develop a study of the coupling between the repressilator synthetic genetic ring oscillator and constraints on cell growth in colonies. We show in silico how mechanical constraints generate characteristic patterns of growth rate inhomogeneity in growing cell colonies. Next, we develop a simple one-dimensional model which predicts that coupling the repressilator to this pattern of growth rate via protein dilution generates traveling waves of gene expression. We show that the dynamics of these spatio-temporal patterns are determined by two parameters; the protein degradation and maximum expression rates of the repressors. We derive simple relations between these parameters and the key characteristics of the traveling wave patterns: firstly, wave speed is determined by protein degradation and secondly, wavelength is determined by maximum gene expression rate. Our analytical predictions and numerical results were in close quantitative agreement with detailed individual based simulations of growing cell colonies. Confirming published experimental results we also found that static ring patterns occur when protein stability is high. Our results show that this pattern can be induced simply by growth rate dilution and does not require transition to stationary phase as previously suggested. Our method generalizes easily to other genetic circuit architectures thus providing a framework for multi-scale rational design of spatio-temporal patterns from genetic circuits. We use this method to generate testable predictions for the synthetic biology design-build-test-learn cycle.

From Microbial Communities to Distributed Computing Systems

A distributed biological system can be defined as a system whose components are located in different subpopulations, which communicate and coordinate their actions through interpopulation messages and interactions. We see that distributed systems are pervasive in nature, performing computation across all scales, from microbial communities to a flock of birds. We often observe that information processing within communities exhibits a complexity far greater than any single organism. Synthetic biology is an area of research which aims to design and build synthetic biological machines from biological parts to perform a defined function, in a manner similar to the engineering disciplines. However, the field has reached a bottleneck in the complexity of the genetic networks that we can implement using monocultures, facing constraints from metabolic burden and genetic interference. This makes building distributed biological systems an attractive prospect for synthetic biology that would alleviate these constraints and allow us to expand the applications of our systems into areas including complex biosensing and diagnostic tools, bioprocess control and the monitoring of industrial processes. In this review we will discuss the fundamental limitations we face when engineering functionality with a monoculture, and the key areas where distributed systems can provide an advantage. We cite evidence from natural systems that support arguments in favor of distributed systems to overcome the limitations of monocultures. Following this we conduct a comprehensive overview of the synthetic communities that have been built to date, and the components that have been used. The potential computational capabilities of communities are discussed, along with some of the applications that these will be useful for. We discuss some of the challenges with building co-cultures, including the problem of competitive exclusion and maintenance of desired community composition. Finally, we assess computational frameworks currently available to aide in the design of microbial communities and identify areas where we lack the necessary tools.

Asymmetry between Activators and Deactivators in Functional Protein Networks

Are “turn-on” and “turn-off” functions in protein-protein interaction networks exact opposites of each other? To answer this question, we implement a minimal model for the evolution of functional protein-interaction networks using a sequence-based mutational algorithm, and apply the model to study neutral drift in networks that yield oscillatory dynamics. We study the roles of activators and deactivators, two core components of oscillatory protein interaction networks, and find a striking asymmetry in the roles of activating and deactivating proteins, where activating proteins tend to be synergistic and deactivating proteins tend to be competitive.

Robustness of a biomolecular oscillator to pulse perturbations

Biomolecular oscillators can function robustly in the presence of environmental perturbations, which can either be static or dynamic. While the effect of different circuit parameters and mechanisms on the robustness to steady perturbations has been investigated, the scenario for dynamic perturbations is relatively unclear. To address this, the authors use a benchmark three protein oscillator design - the repressilator - and investigate its robustness to pulse perturbations, computationally as well as use analytical tools of Floquet theory. They found that the metric provided by direct computations of the time it takes for the oscillator to settle after pulse perturbation is applied, correlates well with the metric provided by Floquet theory. They investigated the parametric dependence of the Floquet metric, finding that the parameters that increase the effective delay enhance robustness to pulse perturbation. They found that the structural changes such as increasing the number of proteins in a ring oscillator as well as adding positive feedback, both of which increase effective delay, facilitates such robustness. These results highlight such design principles, especially the role of delay, for designing an oscillator that is robust to pulse perturbation.

A non-linear reverse-engineering method for inferring genetic regulatory networks

Hematopoiesis is a highly complex developmental process that produces various types of blood cells. This process is regulated by different genetic networks that control the proliferation, differentiation, and maturation of hematopoietic stem cells (HSCs). Although substantial progress has been made for understanding hematopoiesis, the detailed regulatory mechanisms for the fate determination of HSCs are still unraveled. In this study, we propose a novel approach to infer the detailed regulatory mechanisms. This work is designed to develop a mathematical framework that is able to realize nonlinear gene expression dynamics accurately. In particular, we intended to investigate the effect of possible protein heterodimers and/or synergistic effect in genetic regulation. This approach includes the Extended Forward Search Algorithm to infer network structure (top-down approach) and a non-linear mathematical model to infer dynamical property (bottom-up approach). Based on the published experimental data, we study two regulatory networks of 11 genes for regulating the erythrocyte differentiation pathway and the neutrophil differentiation pathway. The proposed algorithm is first applied to predict the network topologies among 11 genes and 55 non-linear terms which may be for heterodimers and/or synergistic effect. Then, the unknown model parameters are estimated by fitting simulations to the expression data of two different differentiation pathways. In addition, the edge deletion test is conducted to remove possible insignificant regulations from the inferred networks. Furthermore, the robustness property of the mathematical model is employed as an additional criterion to choose better network reconstruction results. Our simulation results successfully realized experimental data for two different differentiation pathways, which suggests that the proposed approach is an effective method to infer the topological structure and dynamic property of genetic regulations.

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.

Incoherent Inputs Enhance the Robustness of Biological Oscillators

Robust biological oscillators retain the critical ability to function in the presence of environmental perturbations. Although central architectures that support robust oscillations have been extensively studied, networks containing the same core vary drastically in their potential to oscillate, and it remains elusive what peripheral modifications to the core contribute to this functional variation. Here, we have generated a complete atlas of two- and three-node oscillators computationally, then systematically analyzed the association between network structure and robustness. We found that, while certain core topologies are essential for producing a robust oscillator, local structures can substantially modulate the robustness of oscillations. Notably, local nodes receiving incoherent or coherent inputs respectively promote or attenuate the overall network robustness in an additive manner. We validated these relationships in larger-scale networks reflective of real biological oscillators. Our findings provide an explanation for why auxiliary structures not required for oscillation are evolutionarily conserved and suggest simple ways to evolve or design robust oscillators.

A Bayesian framework for the analysis of systems biology models of the brain

Systems biology models are used to understand complex biological and physiological systems. Interpretation of these models is an important part of developing this understanding. These models are often fit to experimental data in order to understand how the system has produced various phenomena or behaviour that are seen in the data. In this paper, we have outlined a framework that can be used to perform Bayesian analysis of complex systems biology models. In particular, we have focussed on analysing a systems biology of the brain using both simulated and measured data. By using a combination of sensitivity analysis and approximate Bayesian computation, we have shown that it is possible to obtain distributions of parameters that can better guard against misinterpretation of results, as compared to a maximum likelihood estimate based approach. This is done through analysis of simulated and experimental data. NIRS measurements were simulated using the same simulated systemic input data for the model in a ‘healthy’ and ‘impaired’ state. By analysing both of these datasets, we show that different parameter spaces can be distinguished and compared between different physiological states or conditions. Finally, we analyse experimental data using the new Bayesian framework and the previous maximum likelihood estimate approach, showing that the Bayesian approach provides a more complete understanding of the parameter space.

Systems biology models are mathematical representations of biological processes that reproduce the overall behaviour of a biological system. They are comprised by a number of parameters representing biological information. We use them to understand the behaviour of biological systems, such as the brain. We do this by fitting the model’s parameter to observed or simulated data; and by looking at how these values change during the fitting process we investigate the behaviour of our system. We are interested in understanding differences between a healthy and an injured brain. Here we outline a statistical framework that uses a Bayesian approach during the fitting process that can provide us with a distribution of parameters rather than single parameter number. We apply this method when simulating the physiological responses between a healthy and a vascular compromised brain to a drop in oxygenation. We then use experimental data that demonstrates the healthy brain response to an increase in arterial CO2 and fit our brain model predictions to the measurements. In both instances we show that our approach provides more information about the overlap between healthy and unhealthy brain states than a fitting process that provides a single value parameter estimate.

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).

Distilling Robust Design Principles of Biocircuits Using Mixed Integer Dynamic Optimization

A major challenge in model-based design of synthetic biochemical circuits is how to address uncertainty in the parameters. A circuit whose behavior is robust to variations in the parameters will have more chances to behave as predicted when implemented in practice, and also to function reliably in presence of fluctuations and noise. Here, we extend our recent work on automated-design based on mixed-integer multi-criteria dynamic optimization to take into account parametric uncertainty. We exploit the intensive sampling of the design space performed by a global optimization algorithm to obtain the robustness of the topologies without significant additional computational effort. Our procedure provides automatically topologies that best trade-off performance and robustness against parameter fluctuations. We illustrate our approach considering the automated design of gene circuits achieving adaptation.

A Combinatorial Solution to Point Symbol Recognition

Recent work has shown that recognizing point symbols is an essential task in the field of map digitization. For the identification of symbols, it is generally necessary to compare the symbols with a specific criterion and find the most similar one with each known symbol one by one. Most of the works can only identify a single symbol, a small number of works are to deal with multiple symbols simultaneously with a low recognition accuracy. Given the two deficiencies, this paper proposes a deep transfer learning architecture, where the task is to learn a symbol classifier with AlexNet. For the insufficient dataset, we develop a method for transfer learning that uses a MNIST dataset to pretrain the model, which makes up for the problem of small training dataset and enhances the generalization of the model. Before the recognition process, preprocessing the point symbols in the map to coarse screening out the areas suspected of point symbols. We show a significant improvement over using point symbol images to keep a high performance in being able to deal with many more categories of symbols simultaneously.

Towards an Aspect-Oriented Design and Modelling Framework for Synthetic Biology

Work on synthetic biology has largely used a component-based metaphor for system construction. While this paradigm has been successful for the construction of numerous systems, the incorporation of contextual design issues—either compositional, host or environmental—will be key to realising more complex applications. Here, we present a design framework that radically steps away from a purely parts-based paradigm by using aspect-oriented software engineering concepts. We believe that the notion of concerns is a powerful and biologically credible way of thinking about system synthesis. By adopting this approach, we can separate core concerns, which represent modular aims of the design, from cross-cutting concerns, which represent system-wide attributes. The explicit handling of cross-cutting concerns allows for contextual information to enter the design process in a modular way. As a proof-of-principle, we implemented the aspect-oriented approach in the Python tool, SynBioWeaver, which enables the combination, or weaving, of core and cross-cutting concerns. The power and flexibility of this framework is demonstrated through a number of examples covering the inclusion of part context, combining circuit designs in a context dependent manner, and the generation of rule, logic and reaction models from synthetic circuit designs.

Computing with biological switches and clocks

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

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

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

Designing synthetic networks in silico: a generalised evolutionary algorithm approach

Background

Evolution has led to the development of biological networks that are shaped by environmental signals. Elucidating, understanding and then reconstructing important network motifs is one of the principal aims of Systems & Synthetic Biology. Consequently, previous research has focused on finding optimal network structures and reaction rates that respond to pulses or produce stable oscillations. In this work we present a generalised in silico evolutionary algorithm that simultaneously finds network structures and reaction rates (genotypes) that can satisfy multiple defined objectives (phenotypes).

Results

The key step to our approach is to translate a schema/binary-based description of biological networks into systems of ordinary differential equations (ODEs). The ODEs can then be solved numerically to provide dynamic information about an evolved networks functionality. Initially we benchmark algorithm performance by finding optimal networks that can recapitulate concentration time-series data and perform parameter optimisation on oscillatory dynamics of the Repressilator. We go on to show the utility of our algorithm by finding new designs for robust synthetic oscillators, and by performing multi-objective optimisation to find a set of oscillators and feed-forward loops that are optimal at balancing different system properties. In sum, our results not only confirm and build on previous observations but we also provide new designs of synthetic oscillators for experimental construction.

Conclusions

In this work we have presented and tested an evolutionary algorithm that can design a biological network to produce desired output. Given that previous designs of synthetic networks have been limited to subregions of network- and parameter-space, the use of our evolutionary optimisation algorithm will enable Synthetic Biologists to construct new systems with the potential to display a wider range of complex responses.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-017-0499-9) contains supplementary material, which is available to authorized users.

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.

Engineered Control of Genetic Variability Reveals Interplay among Quorum Sensing, Feedback Regulation, and Biochemical Noise

Stochastic fluctuations in gene expression trigger both beneficial and harmful consequences for cell behavior. Therefore, achieving a desired mean protein expression level while minimizing noise is of interest in many applications, including robust protein production systems in industrial biotechnology. Here, we consider a synthetic gene circuit combining intracellular negative feedback and cell-to-cell communication based on quorum sensing. Accounting for both intrinsic and extrinsic noise, stochastic simulations allow us to analyze the capability of the circuit to reduce noise strength as a function of its parameters. We obtain mean expression levels and noise strengths for all species under different scenarios, showing good agreement with system-wide available experimental data of protein abundance and noise in Escherichia coli. Our in silico experiments, validated by preliminary in vivo results, reveal significant noise attenuation in gene expression through the interplay between quorum sensing and negative feedback and highlight the differential role that they play in regard to intrinsic and extrinsic noise.

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.

L p -Adaptation: Simultaneous Design Centering and Robustness Estimation of Electronic and Biological Systems

The design of systems or models that work robustly under uncertainty and environmental fluctuations is a key challenge in both engineering and science. This is formalized in the design-centering problem, which is defined as finding a design that fulfills given specifications and has a high probability of still doing so if the system parameters or the specifications fluctuate randomly. Design centering is often accompanied by the problem of quantifying the robustness of a system. Here we present a novel adaptive statistical method to simultaneously address both problems. Our method, L_p-Adaptation, is inspired by the evolution of robustness in biological systems and by randomized schemes for convex volume computation. It is able to address both problems in the general, non-convex case and at low computational cost. We describe the concept and the algorithm, test it on known benchmarks, and demonstrate its real-world applicability in electronic and biological systems. In all cases, the present method outperforms the previous state of the art. This enables re-formulating optimization problems in engineering and biology as design centering problems, taking global system robustness into account.

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.

Molecular Engineering of Robustness and Resilience in Enzymatic Reaction Networks

Living systems rely on complex networks of chemical reactions to control the concentrations 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. One of the greatest challenges in chemistry is the creation of such functionality from chemical reactions. A key limitation is our lack of understanding of how molecular structure impacts on the dynamics of chemical reaction networks, preventing the design of networks that are robust (i.e., function in a large parameter space) and resilient (i.e., reach their out-of-equilibrium function rapidly). Here we demonstrate that reaction rates of individual reactions in the network can control the dynamics by which the system reaches limit cycle oscillations, thereby gaining information on the key parameters that govern the dynamics of these networks. We envision that these principles will be incorporated into the design of network motifs, enabling chemists to develop "molecular software" to create functional behavior in chemical systems.

Identifying stochastic oscillations in single-cell live imaging time series using Gaussian processes

Multiple biological processes are driven by oscillatory gene expression at different time scales. Pulsatile dynamics are thought to be widespread, and single-cell live imaging of gene expression has lead to a surge of dynamic, possibly oscillatory, data for different gene networks. However, the regulation of gene expression at the level of an individual cell involves reactions between finite numbers of molecules, and this can result in inherent randomness in expression dynamics, which blurs the boundaries between aperiodic fluctuations and noisy oscillators. This underlies a new challenge to the experimentalist because neither intuition nor pre-existing methods work well for identifying oscillatory activity in noisy biological time series. Thus, there is an acute need for an objective statistical method for classifying whether an experimentally derived noisy time series is periodic. Here, we present a new data analysis method that combines mechanistic stochastic modelling with the powerful methods of non-parametric regression with Gaussian processes. Our method can distinguish oscillatory gene expression from random fluctuations of non-oscillatory expression in single-cell time series, despite peak-to-peak variability in period and amplitude of single-cell oscillations. We show that our method outperforms the Lomb-Scargle periodogram in successfully classifying cells as oscillatory or non-oscillatory in data simulated from a simple genetic oscillator model and in experimental data. Analysis of bioluminescent live-cell imaging shows a significantly greater number of oscillatory cells when luciferase is driven by a Hes1 promoter (10/19), which has previously been reported to oscillate, than the constitutive MoMuLV 5’ LTR (MMLV) promoter (0/25). The method can be applied to data from any gene network to both quantify the proportion of oscillating cells within a population and to measure the period and quality of oscillations. It is publicly available as a MATLAB package.

Technological advances now allow us to observe gene expression in real-time at a single-cell level. In a wide variety of biological contexts this new data has revealed that gene expression is highly dynamic and possibly oscillatory. It is thought that periodic gene expression may be useful for keeping track of time and space, as well as transmitting information about signalling cues. Classifying a time series as periodic from single cell data is difficult because it is necessary to distinguish whether peaks and troughs are generated from an underlying oscillator or whether they are aperiodic fluctuations. To this end, we present a novel tool to classify live-cell data as oscillatory or non-oscillatory that accounts for inherent biological noise. We first demonstrate that the method outperforms a competing scheme in classifying computationally simulated single-cell data, and we subsequently analyse live-cell imaging time series. Our method is able to successfully detect oscillations in a known genetic oscillator, but it classifies data from a constitutively expressed gene as aperiodic. The method forms a basis for discovering new gene expression oscillators and quantifying how oscillatory activity alters in response to changes in cell fate and environmental or genetic perturbations.

Robustness of synthetic oscillators in growing and dividing cells

Synthetic biology sets out to implement new functions in cells, and to develop a deeper understanding of biological design principles. Elowitz and Leibler [Nature (London) 403, 335 (2000)NATUAS0028-083610.1038/35002125] showed that by rational design of the reaction network, and using existing biological components, they could create a network that exhibits periodic gene expression, dubbed the repressilator. More recently, Stricker et al. [Nature (London) 456, 516 (2008)NATUAS0028-083610.1038/nature07389] presented another synthetic oscillator, called the dual-feedback oscillator, which is more stable. Detailed studies have been carried out to determine how the stability of these oscillators is affected by the intrinsic noise of the interactions between the components and the stochastic expression of their genes. However, as all biological oscillators reside in growing and dividing cells, an important question is how these oscillators are perturbed by the cell cycle. In previous work we showed that the periodic doubling of the gene copy numbers due to DNA replication can couple not only natural, circadian oscillators to the cell cycle [Paijmans et al., Proc. Natl. Acad. Sci. (USA) 113, 4063 (2016)PNASA60027-842410.1073/pnas.1507291113], but also these synthetic oscillators. Here we expand this study. We find that the strength of the locking between oscillators depends not only on the positions of the genes on the chromosome, but also on the noise in the timing of gene replication: noise tends to weaken the coupling. Yet, even in the limit of high levels of noise in the replication times of the genes, both synthetic oscillators show clear signatures of locking to the cell cycle. This work enhances our understanding of the design of robust biological oscillators inside growing and diving cells.

Design Principles of Biological Oscillators through Optimization: Forward and Reverse Analysis

From cyanobacteria to human, sustained oscillations coordinate important biological functions. Although much has been learned concerning the sophisticated molecular mechanisms underlying biological oscillators, design principles linking structure and functional behavior are not yet fully understood. Here we explore design principles of biological oscillators from a multiobjective optimization perspective, taking into account the trade-offs between conflicting performance goals or demands. We develop a comprehensive tool for automated design of oscillators, based on multicriteria global optimization that allows two modes: (i) the automatic design (forward problem) and (ii) the inference of design principles (reverse analysis problem). From the perspective of synthetic biology, the forward mode allows the solution of design problems that mimic some of the desirable properties appearing in natural oscillators. The reverse analysis mode facilitates a systematic exploration of the design space based on Pareto optimality concepts. The method is illustrated with two case studies: the automatic design of synthetic oscillators from a library of biological parts, and the exploration of design principles in 3-gene oscillatory systems.

A computational method for the investigation of multistable systems and its application to genetic switches

Background

Genetic switches exhibit multistability, form the basis of epigenetic memory, and are found in natural decision making systems, such as cell fate determination in developmental pathways. Synthetic genetic switches can be used for recording the presence of different environmental signals, for changing phenotype using synthetic inputs and as building blocks for higher-level sequential logic circuits. Understanding how multistable switches can be constructed and how they function within larger biological systems is therefore key to synthetic biology.

Results

Here we present a new computational tool, called StabilityFinder, that takes advantage of sequential Monte Carlo methods to identify regions of parameter space capable of producing multistable behaviour, while handling uncertainty in biochemical rate constants and initial conditions. The algorithm works by clustering trajectories in phase space, and iteratively minimizing a distance metric. Here we examine a collection of models of genetic switches, ranging from the deterministic Gardner toggle switch to stochastic models containing different positive feedback connections. We uncover the design principles behind making bistable, tristable and quadristable switches, and find that rate of gene expression is a key parameter. We demonstrate the ability of the framework to examine more complex systems and examine the design principles of a three gene switch. Our framework allows us to relax the assumptions that are often used in genetic switch models and we show that more complex abstractions are still capable of multistable behaviour.

Conclusions

Our results suggest many ways in which genetic switches can be enhanced and offer designs for the construction of novel switches. Our analysis also highlights subtle changes in correlation of experimentally tunable parameters that can lead to bifurcations in deterministic and stochastic systems. Overall we demonstrate that StabilityFinder will be a valuable tool in the future design and construction of novel gene networks.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-016-0375-z) contains supplementary material, which is available to authorized users.