Noise propagation in synthetic gene circuits for metabolic control

Dichotomous feedback: a signal sequestration-based feedback mechanism for biocontroller design

We introduce a new design framework for implementing negative feedback regulation in synthetic biology, which we term ‘dichotomous feedback’. Our approach is different from current methods, in that it sequesters existing fluxes in the process to be controlled, and in this way takes advantage of the process’s architecture to design the control law. This signal sequestration mechanism appears in many natural biological systems and can potentially be easier to realize than ‘molecular sequestration’ and other comparison motifs that are nowadays common in biomolecular feedback control design. The loop is closed by linking the strength of signal sequestration to the process output. Our feedback regulation mechanism is motivated by two-component signalling systems, where a second response regulator could be competing with the natural response regulator thus sequestering kinase activity. Here, dichotomous feedback is established by increasing the concentration of the second response regulator as the level of the output of the natural process increases. Extensive analysis demonstrates how this type of feedback shapes the signal response, attenuates intrinsic noise while increasing robustness and reducing crosstalk.

Stabilization of antithetic control via molecular buffering

A key goal in synthetic biology is the construction of molecular circuits that robustly adapt to perturbations. Although many natural systems display perfect adaptation, whereby stationary molecular concentrations are insensitive to perturbations, its de novo engineering has proven elusive. The discovery of the antithetic control motif was a significant step towards a universal mechanism for engineering perfect adaptation. Antithetic control provides perfect adaptation in a wide range of systems, but it can lead to oscillatory dynamics due to loss of stability; moreover, it can lose perfect adaptation in fast growing cultures. Here, we introduce an extended antithetic control motif that resolves these limitations. We show that molecular buffering, a widely conserved mechanism for homeostatic control in Nature, stabilizes oscillations and allows for near-perfect adaptation during rapid growth. We study multiple buffering topologies and compare their performance in terms of their stability and adaptation properties. We illustrate the benefits of our proposed strategy in exemplar models for biofuel production and growth rate control in bacterial cultures. Our results provide an improved circuit for robust control of biomolecular systems.

Effects of bidirectional phenotype switching on signal noise in a bacterial community

Cells can sense and process various signals. Noise is inevitable in the cell signaling system. In a bacterial community, the mutual conversion between normal cells and persistent cells forms a bidirectional phenotype switching cascade, in which either one can be used as an upstream signal and the other as a downstream signal. In order to quantitatively describe the relationship between noise and signal amplification of each phenotype, the gain-fluctuation relationship is obtained by using the linear noise approximation of the master equation. Through the simulation of these theoretical formulas, it is found that the bidirectional phenotype switching can directly generate interconversion noise which is usually very small and almost negligible. In particular, the bidirectional phenotype switching can provide a global fluctuating environment, which will not only affect the values of noise and covariance, but also generate additional intrinsic noise. The additional intrinsic noise in each phenotype is the main part of the total noise and can be transmitted to the other phenotype. The transmitted noise is also a powerful supplement to the total noise. Therefore, the indirect impact of bidirectional phenotype switching is far greater than its direct impact, which may be one of the reasons why chronic infections caused by persistent cells are refractory to treat.

The switch of DNA states filtering the extrinsic noise in the system of frequency modulation

There is a special node, which the large noise of the upstream element may not always lead to a broad distribution of downstream elements. This node is DNA, with upstream element TF and downstream elements mRNA and proteins. By applying the stochastic simulation algorithm (SSA) on gene circuits inspired by the fim operon in Escherichia coli, we found that cells exchanged the distribution of the upstream transcription factor (TF) for the transitional frequency of DNA. Then cells do an inverse transform, which exchanges the transitional frequency of DNA for the distribution of downstream products. Due to this special feature, DNA in the system of frequency modulation is able to reset the noise. By probability generating function, we know the ranges of parameter values that grant such an interesting phenomenon.

Dynamic control in metabolic engineering: Theories, tools, and applications

Metabolic engineering has allowed the production of a diverse number of valuable chemicals using microbial organisms. Many biological challenges for improving bio-production exist which limit performance and slow the commercialization of metabolically engineered systems. Dynamic metabolic engineering is a rapidly developing field that seeks to address these challenges through the design of genetically encoded metabolic control systems which allow cells to autonomously adjust their flux in response to their external and internal metabolic state. This review first discusses theoretical works which provide mechanistic insights and design choices for dynamic control systems including two-stage, continuous, and population behavior control strategies. Next, we summarize molecular mechanisms for various sensors and actuators which enable dynamic metabolic control in microbial systems. Finally, important applications of dynamic control to the production of several metabolite products are highlighted, including fatty acids, aromatics, and terpene compounds. Altogether, this review provides a comprehensive overview of the progress, advances, and prospects in the design of dynamic control systems for improved titer, rate, and yield metrics in metabolic engineering.

Computation of Single-Cell Metabolite Distributions Using Mixture Models

Metabolic heterogeneity is widely recognized as the next challenge in our understanding of non-genetic variation. A growing body of evidence suggests that metabolic heterogeneity may result from the inherent stochasticity of intracellular events. However, metabolism has been traditionally viewed as a purely deterministic process, on the basis that highly abundant metabolites tend to filter out stochastic phenomena. Here we bridge this gap with a general method for prediction of metabolite distributions across single cells. By exploiting the separation of time scales between enzyme expression and enzyme kinetics, our method produces estimates for metabolite distributions without the lengthy stochastic simulations that would be typically required for large metabolic models. The metabolite distributions take the form of Gaussian mixture models that are directly computable from single-cell expression data and standard deterministic models for metabolic pathways. The proposed mixture models provide a systematic method to predict the impact of biochemical parameters on metabolite distributions. Our method lays the groundwork for identifying the molecular processes that shape metabolic heterogeneity and its functional implications in disease.

Noisy signal propagation and amplification in phenotypic transition cascade of colonic cells

Like genes and proteins, cells can use biochemical networks to sense and process information. The differentiation of the cell state in colonic crypts forms a typical unidirectional phenotypic transitional cascade, in which stem cells differentiate into the transit-amplifying cells (TACs), and TACs continue to differentiate into fully differentiated cells. In order to quantitatively describe the relationship between the noise of each compartment and the amplification of signals, the gain factor is introduced, and the gain-fluctuation relation is obtained by using the linear noise approximation of the master equation. Through the simulation of these theoretical formulas, the characters of noise propagation and amplification are studied. It is found that the transmitted noise is an important part of the total noise in each downstream cell. Therefore, a small number of downstream cells can only cause its small inherent noise, but the total noise may be very large due to the transmitted noise. The influence of the transmitted noise may be the indirect cause of colon cancer. In addition, the total noise of the downstream cells always has a minimum value. As long as a reasonable value of the gain factor is selected, the number of cells in colonic crypts will be controlled within the normal range. This may be a good method to intervene the uncontrollable growth of tumor cells and effectively control the deterioration of colon cancer.

Microbial metabolic noise

From the time a cell was first placed under the microscope, it became apparent that identifying two clonal cells that "look" identical is extremely challenging. Since then, cell-to-cell differences in shape, size, and protein content have been carefully examined, informing us of the ultimate limits that hinder two cells from occupying an identical phenotypic state. Here, we present recent experimental and computational evidence that similar limits emerge also in cellular metabolism. These limits pertain to stochastic metabolic dynamics and, thus, cell-to-cell metabolic variability, including the resulting adapting benefits. We review these phenomena with a focus on microbial metabolism and conclude with a brief outlook on the potential relationship between metabolic noise and adaptive evolution. This article is categorized under: Metabolic Diseases > Computational Models Metabolic Diseases > Biomedical Engineering.

Deciphering noise amplification and reduction in open chemical reaction networks

The impact of fluctuations on the dynamical behaviour of complex biological systems is a longstanding issue, whose understanding would elucidate how evolutionary pressure tends to modulate intrinsic noise. Using the Itō stochastic differential equation formalism, we performed analytic and numerical analyses of model systems containing different molecular species in contact with the environment and interacting with each other through mass-action kinetics. For networks of zero deficiency, which admit a detailed- or complex-balanced steady state, all molecular species are uncorrelated and their Fano factors are Poissonian. Systems of higher deficiency have non-equilibrium steady states and non-zero reaction fluxes flowing between the complexes. When they model homo-oligomerization, the noise on each species is reduced when the flux flows from the oligomers of lowest to highest degree, and amplified otherwise. In the case of hetero-oligomerization systems, only the noise on the highest-degree species shows this behaviour.

Investigation of chemical noise in multisite phosphorylation chain using linear noise approximation

Quantitative and qualitative nature of chemical noise propagation in biochemical reaction networks depend crucially on the topology of the networks. Multisite reversible phosphorylation-dephosphorylation of target proteins is one such recurrently found topology that regulates host of key functions in living cells. Here we analytically calculated the stochasticity in multistep reversible chemical reactions by determining variance of phosphorylated species at the steady state using linear noise approximation to investigate the effect of mass action and Michaelis-Menten kinetics on the noise of phosphorylated species. We probed the dependence of noise on the number of phosphorylation sites and the equilibrium constants of the reaction equilibria to investigate the chemical noise propagation in the multisite phosphorylation chain.

Bounding the stationary distributions of the chemical master equation via mathematical programming

The stochastic dynamics of biochemical networks are usually modeled with the chemical master equation (CME). The stationary distributions of CMEs are seldom solvable analytically, and numerical methods typically produce estimates with uncontrolled errors. Here, we introduce mathematical programming approaches that yield approximations of these distributions with computable error bounds which enable the verification of their accuracy. First, we use semidefinite programming to compute increasingly tighter upper and lower bounds on the moments of the stationary distributions for networks with rational propensities. Second, we use these moment bounds to formulate linear programs that yield convergent upper and lower bounds on the stationary distributions themselves, their marginals, and stationary averages. The bounds obtained also provide a computational test for the uniqueness of the distribution. In the unique case, the bounds form an approximation of the stationary distribution with a computable bound on its error. In the nonunique case, our approach yields converging approximations of the ergodic distributions. We illustrate our methodology through several biochemical examples taken from the literature: Schlögl's model for a chemical bifurcation, a two-dimensional toggle switch, a model for bursty gene expression, and a dimerization model with multiple stationary distributions.

Quantifying Dynamic Regulation in Metabolic Pathways with Nonparametric Flux Inference

One of the central tasks in systems biology is to understand how cells regulate their metabolism. Hierarchical regulation analysis is a powerful tool to study this regulation at the metabolic, gene-expression, and signaling levels. It has been widely applied to study steady-state regulation, but analysis of the metabolic dynamics remains challenging because it is difficult to measure time-dependent metabolic flux. Here, we develop a nonparametric method that uses Gaussian processes to accurately infer the dynamics of a metabolic pathway based only on metabolite measurements; from this, we then go on to obtain a dynamical view of the hierarchical regulation processes invoked over time to control the activity in a pathway. Our approach allows us to use hierarchical regulation analysis in a dynamic setting but without the need for explicitly time-dependent flux measurements.

Extending the linear-noise approximation to biochemical systems influenced by intrinsic noise and slow lognormally distributed extrinsic noise

It is well known that the kinetics of an intracellular biochemical network is stochastic. This is due to intrinsic noise arising from the random timing of biochemical reactions in the network as well as due to extrinsic noise stemming from the interaction of unknown molecular components with the network and from the cell's changing environment. While there are many methods to study the effect of intrinsic noise on the system dynamics, few exist to study the influence of both types of noise. Here we show how one can extend the conventional linear-noise approximation to allow for the rapid evaluation of the molecule numbers statistics of a biochemical network influenced by intrinsic noise and by slow lognormally distributed extrinsic noise. The theory is applied to simple models of gene regulatory networks and its validity confirmed by comparison with exact stochastic simulations. In particular, we consider three important biological examples. First, we investigate how extrinsic noise modifies the dependence of the variance of the molecule number fluctuations on the rate constants. Second, we show how the mutual information between input and output of a network motif is affected by extrinsic noise. And third, we study the robustness of the ubiquitously found feed-forward loop motifs when subjected to extrinsic noise.

Stochastic modelling reveals mechanisms of metabolic heterogeneity

Phenotypic variation is a hallmark of cellular physiology. Metabolic heterogeneity, in particular, underpins single-cell phenomena such as microbial drug tolerance and growth variability. Much research has focussed on transcriptomic and proteomic heterogeneity, yet it remains unclear if such variation permeates to the metabolic state of a cell. Here we propose a stochastic model to show that complex forms of metabolic heterogeneity emerge from fluctuations in enzyme expression and catalysis. The analysis predicts clonal populations to split into two or more metabolically distinct subpopulations. We reveal mechanisms not seen in deterministic models, in which enzymes with unimodal expression distributions lead to metabolites with a bimodal or multimodal distribution across the population. Based on published data, the results suggest that metabolite heterogeneity may be more pervasive than previously thought. Our work casts light on links between gene expression and metabolism, and provides a theory to probe the sources of metabolite heterogeneity.

A Synthetic Close-Loop Controller Circuit for the Regulation of an Extracellular Molecule by Engineered Bacteria

Feedback control is ubiquitous in biological systems. It can also play a crucial role in the design of synthetic circuits implementing novel functions in living systems, to achieve self-regulation of gene expression, noise reduction, rise time decrease, or adaptive pathway control. Despite in vitro, in vivo, and ex vivo implementations have been successfully reported, the design of biological close-loop systems with quantitatively predictable behavior is still a major challenge. In this work, we tested a model-based bottom-up design of a synthetic close-loop controller in engineered Escherichia coli, aimed to automatically regulate the concentration of an extracellular molecule, N-(3-oxohexanoyl)-L-homoserine lactone (HSL), by rewiring the elements of heterologous quorum sensing/quenching networks. The synthetic controller was successfully constructed and experimentally validated. Relying on mathematical model and experimental characterization of individual regulatory parts and enzymes, we evaluated the predictability of the interconnected system behavior in vivo. The culture was able to reach an HSL steady-state level of 72 nM, accurately predicted by the model, and showed superior capabilities in terms of robustness against cell density variation and disturbance rejection, compared with a corresponding open-loop circuit. This engineering-inspired design approach may be adopted for the implementation of other close-loop circuits for different applications and contribute to decreasing trial-and-error steps.

Sources, propagation and consequences of stochasticity in cellular growth

Growth impacts a range of phenotypic responses. Identifying the sources of growth variation and their propagation across the cellular machinery can thus unravel mechanisms that underpin cell decisions. We present a stochastic cell model linking gene expression, metabolism and replication to predict growth dynamics in single bacterial cells. Alongside we provide a theory to analyse stochastic chemical reactions coupled with cell divisions, enabling efficient parameter estimation, sensitivity analysis and hypothesis testing. The cell model recovers population-averaged data on growth-dependence of bacterial physiology and how growth variations in single cells change across conditions. We identify processes responsible for this variation and reconstruct the propagation of initial fluctuations to growth and other processes. Finally, we study drug-nutrient interactions and find that antibiotics can both enhance and suppress growth heterogeneity. Our results provide a predictive framework to integrate heterogeneous data and draw testable predictions with implications for antibiotic tolerance, evolutionary and synthetic biology.

The drivers of growth rate variability in bacteria are yet unknown. Here, the authors present a theory to predict the growth dynamics of individual cells and use a stochastic cell model integrating metabolism, gene expression and replication to identify the processes that underlie growth variation.

Noise propagation in an integrated model of bacterial gene expression and growth

In bacterial cells, gene expression, metabolism, and growth are highly interdependent and tightly coordinated. As a result, stochastic fluctuations in expression levels and instantaneous growth rate show intricate cross-correlations. These correlations are shaped by feedback loops, trade-offs and constraints acting at the cellular level; therefore a quantitative understanding requires an integrated approach. To that end, we here present a mathematical model describing a cell that contains multiple proteins that are each expressed stochastically and jointly limit the growth rate. Conversely, metabolism and growth affect protein synthesis and dilution. Thus, expression noise originating in one gene propagates to metabolism, growth, and the expression of all other genes. Nevertheless, under a small-noise approximation many statistical quantities can be calculated analytically. We identify several routes of noise propagation, illustrate their origins and scaling, and establish important connections between noise propagation and the field of metabolic control analysis. We then present a many-protein model containing >1000 proteins parameterized by previously measured abundance data and demonstrate that the predicted cross-correlations between gene expression and growth rate are in broad agreement with published measurements.

Maintaining maximal metabolic flux by gene expression control

One of the marvels of biology is the phenotypic plasticity of microorganisms. It allows them to maintain high growth rates across conditions. Studies suggest that cells can express metabolic enzymes at tuned concentrations through adjustment of gene expression. The associated transcription factors are often regulated by intracellular metabolites. Here we study metabolite-mediated regulation of metabolic-gene expression that maximises metabolic fluxes across conditions. We developed an adaptive control theory, qORAC (for ‘Specific Flux (q) Optimization by Robust Adaptive Control’), and illustrate it with several examples of metabolic pathways. The key feature of the theory is that it does not require knowledge of the regulatory network, only of the metabolic part. We derive that maximal metabolic flux can be maintained in the face of varying N environmental parameters only if the number of transcription-factor binding metabolites is at least equal to N. The controlling circuits appear to require simple biochemical kinetics. We conclude that microorganisms likely can achieve maximal rates in metabolic pathways, in the face of environmental changes.

To attain high growth rates, microorganisms need to sustain high activities of metabolic reactions. Since the catalysing enzymes are in finite supply, cells need to carefully tune their concentrations. When conditions change, cells need to adjust those concentrations. How cells maintain high metabolism rates across conditions by way of gene regulatory mechanisms and whether they can maximise metabolic activity is far from clear. Here we present a general theory that solves this metabolic control problem, which we have called qORAC for specific flux (q) Optimisation by Robust Adaptive Control. It considers that external changes are sensed by internal “sensor” metabolites that bind to transcription factors in order to regulate enzyme-synthesis rates. We show that such a combined system of metabolism and its gene network can self-optimise its metabolic activity across conditions. We present the mathematical conditions for the required adaptive control for robust system-steering to optimal states across conditions. We provide explicit examples of such self-optimising coupled metabolism and gene network systems. We prove that a cell can be robust to changes in K parameters, e.g. external conditions, if at least K internal metabolite concentrations act transcription-factor binding sensors. We find that the optimal relation of the enzyme synthesis rates of self-optimising systems and the concentration of the sensor metabolites can generally be implemented by basic biochemistry. Our results indicate how cells are able to maintain maximal reaction rates, even in changing conditions.

Flux-dependent graphs for metabolic networks

Cells adapt their metabolic fluxes in response to changes in the environment. We present a framework for the systematic construction of flux-based graphs derived from organism-wide metabolic networks. Our graphs encode the directionality of metabolic flows via edges that represent the flow of metabolites from source to target reactions. The methodology can be applied in the absence of a specific biological context by modelling fluxes probabilistically, or can be tailored to different environmental conditions by incorporating flux distributions computed through constraint-based approaches such as Flux Balance Analysis. We illustrate our approach on the central carbon metabolism of Escherichia coli and on a metabolic model of human hepatocytes. The flux-dependent graphs under various environmental conditions and genetic perturbations exhibit systemic changes in their topological and community structure, which capture the re-routing of metabolic flows and the varying importance of specific reactions and pathways. By integrating constraint-based models and tools from network science, our framework allows the study of context-specific metabolic responses at a system level beyond standard pathway descriptions.

Cellular metabolism is the result of a highly enmeshed set of biochemical reactions that is naturally amenable to graph-based analyses. Yet there are multiple ways to construct a graph representation from any given metabolic model. Here an international research team of UK and Spain scientists presents a principled approach to study metabolic models through the lens of network science. They propose a framework to construct graphs for genome-scale metabolic models that resolve various challenges, such as the incorporation of pool metabolites, the preservation of the directionality of metabolic flows, and the capability to incorporate specific flux information. The method can be integrated into pipelines based on flux balance analysis and provides a systematic framework to explore changes in network connectivity as a result of environmental shifts or genetic perturbations. The framework thus allows to interrogate context-specific metabolic responses beyond standard pathway descriptions. The authors illustrate the approach through the analysis of Escherichia coli's core metabolism in different growth conditions, as well as a rare metabolic disease affecting human hepatocytes.

Making sense of snapshot data: ergodic principle for clonal cell populations

Population growth is often ignored when quantifying gene expression levels across clonal cell populations. We develop a framework for obtaining the molecule number distributions in an exponentially growing cell population taking into account its age structure. In the presence of generation time variability, the average acquired across a population snapshot does not obey the average of a dividing cell over time, apparently contradicting ergodicity between single cells and the population. Instead, we show that the variation observed across snapshots with known cell age is captured by cell histories, a single-cell measure obtained from tracking an arbitrary cell of the population back to the ancestor from which it originated. The correspondence between cells of known age in a population with their histories represents an ergodic principle that provides a new interpretation of population snapshot data. We illustrate the principle using analytical solutions of stochastic gene expression models in cell populations with arbitrary generation time distributions. We further elucidate that the principle breaks down for biochemical reactions that are under selection, such as the expression of genes conveying antibiotic resistance, which gives rise to an experimental criterion with which to probe selection on gene expression fluctuations.

Dynamic metabolic control: towards precision engineering of metabolism

Advances in metabolic engineering have led to the synthesis of a wide variety of valuable chemicals in microorganisms. The key to commercializing these processes is the improvement of titer, productivity, yield, and robustness. Traditional approaches to enhancing production use the “push–pull-block” strategy that modulates enzyme expression under static control. However, strains are often optimized for specific laboratory set-up and are sensitive to environmental fluctuations. Exposure to sub-optimal growth conditions during large-scale fermentation often reduces their production capacity. Moreover, static control of engineered pathways may imbalance cofactors or cause the accumulation of toxic intermediates, which imposes burden on the host and results in decreased production. To overcome these problems, the last decade has witnessed the emergence of a new technology that uses synthetic regulation to control heterologous pathways dynamically, in ways akin to regulatory networks found in nature. Here, we review natural metabolic control strategies and recent developments in how they inspire the engineering of dynamically regulated pathways. We further discuss the challenges of designing and engineering dynamic control and highlight how model-based design can provide a powerful formalism to engineer dynamic control circuits, which together with the tools of synthetic biology, can work to enhance microbial production.

Probing Intercell Variability Using Bulk Measurements

The measurement of noise is critical when assessing the design and function of synthetic biological systems. Cell-to-cell variability can be quantified experimentally using single-cell measurement techniques such as flow cytometry and fluorescent microscopy. However, these approaches are costly and impractical for high-throughput parallelized experiments, which are frequently conducted using plate-reader devices. In this paper we describe reporter systems that allow estimation of the cell-to-cell variability in a biological system's output using only measurements of a cell culture's bulk properties. We analyze one potential implementation of such a system that is based upon a fluorescent protein FRET reporter pair, finding that with typical parameters from the literature it is able to reliably estimate variability. We also briefly describe an alternate implementation based upon an activating sRNA circuit. The feasible region of parameter values for which the reporter system can function is assessed, and the dependence of its performance on both extrinsic and intrinsic noise is investigated. Experimental realization of these constructs can yield novel reporter systems that allow measurement of a synthetic gene circuit's output, as well as the intrapopulation variability of this output, at little added cost.

Impact of negative feedback in metabolic noise propagation

Synthetic biology combines different branches of biology and engineering aimed at designing synthetic biological circuits able to replicate emergent properties useful for the biotechnology industry, human health and environment. The role of negative feedback in noise propagation for a basic enzymatic reaction scheme is investigated. Two feedback control schemes on enzyme expression are considered: one from the final product of the pathway activity, the other from the enzyme accumulation. Both schemes are designed to provide the same steady-state average values of the involved players, in order to evaluate the feedback performances according to the same working mode. Computations are carried out numerically and analytically, the latter allowing to infer information on which model parameter setting leads to a more efficient noise attenuation, according to the chosen scheme. In addition to highlighting the role of the feedback in providing a substantial noise reduction, our investigation concludes that the effect of feedback is enhanced by increasing the promoter sensitivity for both schemes. A further interesting biological insight is that an increase in the promoter sensitivity provides more benefits to the feedback from the product with respect to the feedback from the enzyme, in terms of enlarging the parameter design space.

Dynamic disorder in simple enzymatic reactions induces stochastic amplification of substrate

A growing amount of evidence over the last two decades points to the fact that many enzymes exhibit fluctuations in their catalytic activity, which are associated with conformational changes on a broad range of timescales. The experimental study of this phenomenon, termed dynamic disorder, has become possible thanks to advances in single-molecule enzymology measurement techniques, through which the catalytic activity of individual enzyme molecules can be tracked in time. The biological role and importance of these fluctuations in a system with a small number of enzymes, such as a living cell, have only recently started being explored. In this work, we examine a simple stochastic reaction system consisting of an inflowing substrate and an enzyme with a randomly fluctuating catalytic reaction rate that converts the substrate into an outflowing product. To describe analytically the effect of rate fluctuations on the average substrate abundance at steady state, we derive an explicit formula that connects the relative speed of enzymatic fluctuations with the mean substrate level. Under fairly general modelling assumptions, we demonstrate that the relative speed of rate fluctuations can have a dramatic effect on the mean substrate, and lead to large positive deviations from predictions based on the assumption of deterministic enzyme activity. Our results also establish an interesting connection between the amplification effect and the mixing properties of the Markov process describing the enzymatic activity fluctuations, which can be used to easily predict the fluctuation speed above which such deviations become negligible. As the techniques of single-molecule enzymology continuously evolve, it may soon be possible to study the stochastic phenomena due to enzymatic activity fluctuations within living cells. Our work can be used to formulate experimentally testable hypotheses regarding the nature and magnitude of these fluctuations, as well as their phenotypic consequences.

Perfect Adaptation and Optimal Equilibrium Productivity in a Simple Microbial Biofuel Metabolic Pathway Using Dynamic Integral Control

The production of complex biomolecules by genetically engineered organisms is one of the most promising applications of metabolic engineering and synthetic biology. To obtain processes with high productivity, it is therefore crucial to design and implement efficient dynamic in vivo regulation strategies. We consider here the microbial biofuel production model of Dunlop et al. (2010) for which we demonstrate that an antithetic dynamic integral control strategy can achieve robust perfect adaptation for the intracellular biofuel concentration in the presence of poorly known network parameters and implementation errors in certain rate parameters of the controller. We also show that the maximum equilibrium extracellular biofuel productivity is fully defined by some of the network parameters and, in this respect, it can only be achieved when all the corresponding parameters are perfectly known. Since this optimum is a network property, it cannot be improved by the use of any controller that measures the intracellular biofuel concentration and acts on the production of pump proteins. Additional intrinsic fundamental properties for the process are also unveiled, the most important ones being the existence of a conservation relation between the productivity and the toxicity, a low sensitivity of the optimal productivity with respect to a poor implementation of the set-point for the intracellular biofuel, and a strong intrinsic robustness property of the optimal productivity with respect to poorly known parameters. Taken together, these results demonstrate that a high and robust equilibrium rate of production for the extracellular biofuel can be achieved when the parameters of the model are poorly known and those of the controllers are poorly implemented. Finally, several advantages of the proposed dynamic strategy over a static one are also emphasized.

Design and Selection of a Synthetic Feedback Loop for Optimizing Biofuel Tolerance

Feedback control allows cells to dynamically sense and respond to environmental changes. However, synthetic controller designs can be challenging because of implementation issues, such as determining optimal expression levels for circuit components within a feedback loop. Here, we addressed this by coupling rational design with selection to engineer a synthetic feedback circuit to optimize tolerance of Escherichia coli to the biojet fuel pinene. E. coli can be engineered to produce pinene, but it is toxic to cells. Efflux pumps, such as the AcrAB-TolC pump, can improve tolerance, but pump expression impacts growth. To address this, we used feedback to dynamically regulate pump expression in response to stress. We developed a library with thousands of synthetic circuit variants and subjected it to three types of pinene treatment (none, constant, and varying pinene). We were able to select for strains that were biofuel tolerant without a significant growth cost in the absence of biofuel. Using next-generation sequencing, we found common characteristics in the designs and identified controllers that dramatically improved biofuel tolerance.

Optimization-based synthesis of stochastic biocircuits with statistical specifications

Model-guided design has become a standard approach to engineering biomolecular circuits in synthetic biology. However, the stochastic nature of biomolecular reactions is often overlooked in the design process. As a result, cell-cell heterogeneity causes unexpected deviation of biocircuit behaviours from model predictions and requires additional iterations of design-build-test cycles. To enhance the design process of stochastic biocircuits, this paper presents a computational framework to systematically specify the level of intrinsic noise using well-defined metrics of statistics and design highly heterogeneous biocircuits based on the specifications. Specifically, we use descriptive statistics of population distributions as an intuitive specification language of stochastic biocircuits and develop an optimization-based computational tool that explores parameter configurations satisfying design requirements. Sensitivity analysis methods are also performed to ensure the robustness of a biocircuit design against extrinsic perturbations. These design tools are formulated with convex optimization programs to enable rigorous and efficient quantification of the statistics. We demonstrate these features by designing a stochastic negative feedback biocircuit that satisfies multiple statistical constraints and perform an in-depth study of noise propagation and regulation in negative feedback pathways.

A Synthetic Circuit for Mercury Bioremediation Using Self-Assembling Functional Amyloids

Synthetic biology approaches to bioremediation are a key sustainable strategy to leverage the self-replicating and programmable aspects of biology for environmental stewardship. The increasing spread of anthropogenic mercury pollution into our habitats and food chains is a pressing concern. Here, we explore the use of programmed bacterial biofilms to aid in the sequestration of mercury. We demonstrate that by integrating a mercury-responsive promoter and an operon encoding a mercury-absorbing self-assembling extracellular protein nanofiber, we can engineer bacteria that can detect and sequester toxic Hg²⁺ ions from the environment. This work paves the way for the development of on-demand biofilm living materials that can operate autonomously as heavy-metal absorbents.

Fundamental Design Principles for Transcription-Factor-Based Metabolite Biosensors

Metabolite biosensors are central to current efforts toward precision engineering of metabolism. Although most research has focused on building new biosensors, their tunability remains poorly understood and is fundamental for their broad applicability. Here we asked how genetic modifications shape the dose-response curve of biosensors based on metabolite-responsive transcription factors. Using the lac system in Escherichia coli as a model system, we built promoter libraries with variable operator sites that reveal interdependencies between biosensor dynamic range and response threshold. We developed a phenomenological theory to quantify such design constraints in biosensors with various architectures and tunable parameters. Our theory reveals a maximal achievable dynamic range and exposes tunable parameters for orthogonal control of dynamic range and response threshold. Our work sheds light on fundamental limits of synthetic biology designs and provides quantitative guidelines for biosensor design in applications such as dynamic pathway control, strain optimization, and real-time monitoring of metabolism.

The Interplay between Feedback and Buffering in Cellular Homeostasis

Buffering, the use of reservoirs of molecules to maintain concentrations of key molecular species, and negative feedback are the primary known mechanisms for robust homeostatic regulation. To our knowledge, however, the fundamental principles behind their combined effect have not been elucidated. Here, we study the interplay between buffering and negative feedback in the context of cellular homeostasis. We show that negative feedback counteracts slow-changing disturbances, whereas buffering counteracts fast-changing disturbances. Furthermore, feedback and buffering have limitations that create trade-offs for regulation: instability in the case of feedback and molecular noise in the case of buffering. However, because buffering stabilizes feedback and feedback attenuates noise from slower-acting buffering, their combined effect on homeostasis can be synergistic. These effects can be explained within a traditional control theory framework and are consistent with experimental observations of both ATP homeostasis and pH regulation in vivo. These principles are critical for studying robustness and homeostasis in biology and biotechnology.

A Synthetic Recombinase-Based Feedback Loop Results in Robust Expression

Accurate control of a biological process is essential for many critical functions in biology, from the cell cycle to proteome regulation. To achieve this, negative feedback is frequently employed to provide a highly robust and reliable output. Feedback is found throughout biology and technology, but due to challenges posed by its implementation, it is yet to be widely adopted in synthetic biology. In this paper we design a synthetic feedback network using a class of recombinase proteins called integrases, which can be re-engineered to flip the orientation of DNA segments in a digital manner. This system is highly orthogonal, and demonstrates a strong capability for regulating and reducing the expression variability of genes being transcribed under its control. An excisionase protein provides the negative feedback signal to close the loop in this system, by flipping DNA segments in the reverse direction. Our integrase/excisionase negative feedback system thus provides a modular architecture that can be tuned to suit applications throughout synthetic biology and biomanufacturing that require a highly robust and orthogonally controlled output.

Design of a bistable switch to control cellular uptake

Bistable switches are widely used in synthetic biology to trigger cellular functions in response to environmental signals. All bistable switches developed so far, however, control the expression of target genes without access to other layers of the cellular machinery. Here, we propose a bistable switch to control the rate at which cells take up a metabolite from the environment. An uptake switch provides a new interface to command metabolic activity from the extracellular space and has great potential as a building block in more complex circuits that coordinate pathway activity across cell cultures, allocate metabolic tasks among different strains or require cell-to-cell communication with metabolic signals. Inspired by uptake systems found in nature, we propose to couple metabolite import and utilization with a genetic circuit under feedback regulation. Using mathematical models and analysis, we determined the circuit architectures that produce bistability and obtained their design space for bistability in terms of experimentally tuneable parameters. We found an activation-repression architecture to be the most robust switch because it displays bistability for the largest range of design parameters and requires little fine-tuning of the promoters' response curves. Our analytic results are based on on-off approximations of promoter activity and are in excellent qualitative agreement with simulations of more realistic models. With further analysis and simulation, we established conditions to maximize the parameter design space and to produce bimodal phenotypes via hysteresis and cell-to-cell variability. Our results highlight how mathematical analysis can drive the discovery of new circuits for synthetic biology, as the proposed circuit has all the hallmarks of a toggle switch and stands as a promising design to control metabolic phenotypes across cell cultures.

Control theory meets synthetic biology

The past several years have witnessed an increased presence of control theoretic concepts in synthetic biology. This review presents an organized summary of how these control design concepts have been applied to tackle a variety of problems faced when building synthetic biomolecular circuits in living cells. In particular, we describe success stories that demonstrate how simple or more elaborate control design methods can be used to make the behaviour of synthetic genetic circuits within a single cell or across a cell population more reliable, predictable and robust to perturbations. The description especially highlights technical challenges that uniquely arise from the need to implement control designs within a new hardware setting, along with implemented or proposed solutions. Some engineering solutions employing complex feedback control schemes are also described, which, however, still require a deeper theoretical analysis of stability, performance and robustness properties. Overall, this paper should help synthetic biologists become familiar with feedback control concepts as they can be used in their application area. At the same time, it should provide some domain knowledge to control theorists who wish to enter the rising and exciting field of synthetic biology.

Synthetic biology and regulatory networks: where metabolic systems biology meets control engineering

Metabolic pathways can be engineered to maximize the synthesis of various products of interest. With the advent of computational systems biology, this endeavour is usually carried out through in silico theoretical studies with the aim to guide and complement further in vitro and in vivo experimental efforts. Clearly, what counts is the result in vivo, not only in terms of maximal productivity but also robustness against environmental perturbations. Engineering an organism towards an increased production flux, however, often compromises that robustness. In this contribution, we review and investigate how various analytical approaches used in metabolic engineering and synthetic biology are related to concepts developed by systems and control engineering. While trade-offs between production optimality and cellular robustness have already been studied diagnostically and statically, the dynamics also matter. Integration of the dynamic design aspects of control engineering with the more diagnostic aspects of metabolic, hierarchical control and regulation analysis is leading to the new, conceptual and operational framework required for the design of robust and productive dynamic pathways.

Phenotypic Variability in Synthetic Biology Applications: Dealing with Noise in Microbial Gene Expression

The stochasticity due to the infrequent collisions among low copy-number molecules within the crowded cellular compartment is a feature of living systems. Single cell variability in gene expression within an isogenic population (i.e., biological noise) is usually described as the sum of two independent components: intrinsic and extrinsic stochasticity. Intrinsic stochasticity arises from the random occurrence of events inherent to the gene expression process (e.g., the burst-like synthesis of mRNA and protein molecules). Extrinsic fluctuations reflect the state of the biological system and its interaction with the intra and extracellular environments (e.g., concentration of available polymerases, ribosomes, metabolites, and micro-environmental conditions). A better understanding of cellular noise would help synthetic biologists design gene circuits with well-defined functional properties. In silico modeling has already revealed several aspects of the network topology’s impact on noise properties; this information could drive the selection of biological parts and the design of reliably engineered pathways. Importantly, while optimizing artificial gene circuitry for industrial applications, synthetic biology could also elucidate the natural mechanisms underlying natural phenotypic variability. In this review, we briefly summarize the functional roles of noise in unicellular organisms and address their relevance to synthetic network design. We will also consider how noise might influence the selection of network topologies supporting reliable functions, and how the variability of cellular events might be exploited when designing innovative biotechnology applications.

Multi-objective optimization framework to obtain model-based guidelines for tuning biological synthetic devices: an adaptive network case

Background

Model based design plays a fundamental role in synthetic biology. Exploiting modularity, i.e. using biological parts and interconnecting them to build new and more complex biological circuits is one of the key issues. In this context, mathematical models have been used to generate predictions of the behavior of the designed device. Designers not only want the ability to predict the circuit behavior once all its components have been determined, but also to help on the design and selection of its biological parts, i.e. to provide guidelines for the experimental implementation. This is tantamount to obtaining proper values of the model parameters, for the circuit behavior results from the interplay between model structure and parameters tuning. However, determining crisp values for parameters of the involved parts is not a realistic approach. Uncertainty is ubiquitous to biology, and the characterization of biological parts is not exempt from it. Moreover, the desired dynamical behavior for the designed circuit usually results from a trade-off among several goals to be optimized.

Results

We propose the use of a multi-objective optimization tuning framework to get a model-based set of guidelines for the selection of the kinetic parameters required to build a biological device with desired behavior. The design criteria are encoded in the formulation of the objectives and optimization problem itself. As a result, on the one hand the designer obtains qualitative regions/intervals of values of the circuit parameters giving rise to the predefined circuit behavior; on the other hand, he obtains useful information for its guidance in the implementation process. These parameters are chosen so that they can effectively be tuned at the wet-lab, i.e. they are effective biological tuning knobs. To show the proposed approach, the methodology is applied to the design of a well known biological circuit: a genetic incoherent feed-forward circuit showing adaptive behavior.

Conclusion

The proposed multi-objective optimization design framework is able to provide effective guidelines to tune biological parameters so as to achieve a desired circuit behavior. Moreover, it is easy to analyze the impact of the context on the synthetic device to be designed. That is, one can analyze how the presence of a downstream load influences the performance of the designed circuit, and take it into account.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-016-0269-0) contains supplementary material, which is available to authorized users.

Period doubling induced by thermal noise amplification in genetic circuits

Rhythms of life are dictated by oscillations, which take place in a wide rage of biological scales. In bacteria, for example, oscillations have been proven to control many fundamental processes, ranging from gene expression to cell divisions. In genetic circuits, oscillations originate from elemental block such as autorepressors and toggle switches, which produce robust and noise-free cycles with well defined frequency. In some circumstances, the oscillation period of biological functions may double, thus generating bistable behaviors whose ultimate origin is at the basis of intense investigations. Motivated by brain studies, we here study an “elemental” genetic circuit, where a simple nonlinear process interacts with a noisy environment. In the proposed system, nonlinearity naturally arises from the mechanism of cooperative stability, which regulates the concentration of a protein produced during a transcription process. In this elemental model, bistability results from the coherent amplification of environmental fluctuations due to a stochastic resonance of nonlinear origin. This suggests that the period doubling observed in many biological functions might result from the intrinsic interplay between nonlinearity and thermal noise.