An Orthogonal Multi-input Integration System to Control Gene Expression in Escherichia coli
TL;DR: This work implements a system that compares the concentration of two signal molecules, and tunes GFP expression proportionally to their relative abundance, performed via molecular titration between an orthogonal σ factor and its cognate anti-σ factor.
Abstract: In many biotechnological applications, it is useful for gene expression to be regulated by multiple signals, as this allows the programming of complex behavior. Here we implement, in Escherichia coli, a system that compares the concentration of two signal molecules, and tunes GFP expression proportionally to their relative abundance. The computation is performed via molecular titration between an orthogonal σ factor and its cognate anti-σ factor. We use mathematical modeling and experiments to show that the computation system is predictable and able to adapt GFP expression dynamically to a wide range of combinations of the two signals, and our model qualitatively captures most of these behaviors. We also demonstrate in silico the practical applicability of the system as a reference-comparator, which compares an intrinsic signal (reflecting the state of the system) with an extrinsic signal (reflecting the desired reference state) in a multicellular feedback control strategy.
Citations
More filters
TL;DR: It is proved mathematically that there is a single fundamental biomolecular controller topology that realizes integral feedback and achieves robust perfect adaptation in arbitrary intracellular networks with noisy dynamics.
Abstract: Homeostasis is a recurring theme in biology that ensures that regulated variables robustly—and in some systems, completely—adapt to environmental perturbations. This robust perfect adaptation feature is achieved in natural circuits by using integral control, a negative feedback strategy that performs mathematical integration to achieve structurally robust regulation1,2. Despite its benefits, the synthetic realization of integral feedback in living cells has remained elusive owing to the complexity of the required biological computations. Here we prove mathematically that there is a single fundamental biomolecular controller topology3 that realizes integral feedback and achieves robust perfect adaptation in arbitrary intracellular networks with noisy dynamics. This adaptation property is guaranteed both for the population-average and for the time-average of single cells. On the basis of this concept, we genetically engineer a synthetic integral feedback controller in living cells4 and demonstrate its tunability and adaptation properties. A growth-rate control application in Escherichia coli shows the intrinsic capacity of our integral controller to deliver robustness and highlights its potential use as a versatile controller for regulation of biological variables in uncertain networks. Our results provide conceptual and practical tools in the area of cybergenetics3,5, for engineering synthetic controllers that steer the dynamics of living systems3–9. A synthetic gene circuit implementing an integral feedback topology is shown to achieve robust perfect adaptation in living cells--mathematical analysis proves this topology is necessary for adaptation in networks with noisy dynamics.
251 citations
TL;DR: The potential of well-characterized basal expression and regulatory elements in synthetic biology applications, where they may ensure orthogonal, predictable and tunable expression of (heterologous) target genes and pathways, aims at a minimal burden for the host.
Abstract: Gene expression occurs in two essential steps: transcription and translation. In bacteria, the two processes are tightly coupled in time and space, and highly regulated. Tight regulation of gene expression is crucial. It limits wasteful consumption of resources and energy, prevents accumulation of potentially growth inhibiting reaction intermediates, and sustains the fitness and potential virulence of the organism in a fluctuating, competitive and frequently stressful environment. Since the onset of studies on regulation of enzyme synthesis, numerous distinct regulatory mechanisms modulating transcription and/or translation have been discovered. Mostly, various regulatory mechanisms operating at different levels in the flow of genetic information are used in combination to control and modulate the expression of a single gene or operon. Here, we provide an extensive overview of the very diverse and versatile bacterial gene regulatory mechanisms with major emphasis on their combined occurrence, intricate intertwinement and versatility. Furthermore, we discuss the potential of well-characterized basal expression and regulatory elements in synthetic biology applications, where they may ensure orthogonal, predictable and tunable expression of (heterologous) target genes and pathways, aiming at a minimal burden for the host.
102 citations
TL;DR: This work modelled, built and validated two synthetic negative feedback circuits that use rationally-designed sRNAs for the first time, and analysis of the noise profiles of both circuits showed that the use of s RNAs did not result in large increases in noise.
Abstract: Negative feedback is known to enable biological and man-made systems to perform reliably in the face of uncertainties and disturbances. To date, synthetic biological feedback circuits have primarily relied upon protein-based, transcriptional regulation to control circuit output. Small RNAs (sRNAs) are non-coding RNA molecules that can inhibit translation of target messenger RNAs (mRNAs). In this work, we modelled, built and validated two synthetic negative feedback circuits that use rationally-designed sRNAs for the first time. The first circuit builds upon the well characterised tet-based autorepressor, incorporating an externally-inducible sRNA to tune the effective feedback strength. This allows more precise fine-tuning of the circuit output in contrast to the sigmoidal, steep input-output response of the autorepressor alone. In the second circuit, the output is a transcription factor that induces expression of an sRNA, which inhibits translation of the mRNA encoding the output, creating direct, closed-loop, negative feedback. Analysis of the noise profiles of both circuits showed that the use of sRNAs did not result in large increases in noise. Stochastic and deterministic modelling of both circuits agreed well with experimental data. Finally, simulations using fitted parameters allowed dynamic attributes of each circuit such as response time and disturbance rejection to be investigated.
69 citations
Cites background from "An Orthogonal Multi-input Integrati..."
...In vivo feedback has been employed in many synthetic gene circuits, including circuits such as the toggle switch (28,29), the repressilator (30), sustained and tunable oscillators (31), a concentration tracker (32) and a reference comparator (33,34)....
[...]
TL;DR: Using a tailored moment closure method, approximate expressions for the stationary variance for the controlled network are derived that demonstrate that increasing the strength of the negative feedback can indeed decrease the variance, sometimes even below its constitutive level.
Abstract: The ability of a cell to regulate and adapt its internal state in response to unpredictable environmental changes is called homeostasis and this ability is crucial for the cell's survival and proper functioning. Understanding how cells can achieve homeostasis, despite the intrinsic noise or randomness in their dynamics, is fundamentally important for both systems and synthetic biology. In this context, a significant development is the proposed antithetic integral feedback (AIF) motif, which is found in natural systems, and is known to ensure robust perfect adaptation for the mean dynamics of a given molecular species involved in a complex stochastic biomolecular reaction network. From the standpoint of applications, one drawback of this motif is that it often leads to an increased cell-to-cell heterogeneity or variance when compared to a constitutive (i.e. open-loop) control strategy. Our goal in this paper is to show that this performance deterioration can be countered by combining the AIF motif and a negative feedback strategy. Using a tailored moment closure method, we derive approximate expressions for the stationary variance for the controlled network that demonstrate that increasing the strength of the negative feedback can indeed decrease the variance, sometimes even below its constitutive level. Numerical results verify the accuracy of these results and we illustrate them by considering three biomolecular networks with two types of negative feedback strategies. Our computational analysis indicates that there is a trade-off between the speed of the settling-time of the mean trajectories and the stationary variance of the controlled species; i.e. smaller variance is associated with larger settling-time.
67 citations
TL;DR: This work develops an analytic framework for understanding the hard limits, performance tradeoffs, and architectural properties of this simple model of biological feedback control, called antithetic integral feedback, which can be implemented using the binding of two molecules.
Abstract: Feedback regulation is pervasive in biology at both the organismal and cellular level. In this article, we explore the properties of a particular biomolecular feedback mechanism called antithetic integral feedback, which can be implemented using the binding of two molecules. Our work develops an analytic framework for understanding the hard limits, performance tradeoffs, and architectural properties of this simple model of biological feedback control. Using tools from control theory, we show that there are simple parametric relationships that determine both the stability and the performance of these systems in terms of speed, robustness, steady-state error, and leakiness. These findings yield a holistic understanding of the behavior of antithetic integral feedback and contribute to a more general theory of biological control systems.
55 citations
References
More filters
TL;DR: This work used three transcriptional repressor systems that are not part of any natural biological clock to build an oscillating network, termed the repressilator, in Escherichia coli, which periodically induces the synthesis of green fluorescent protein as a readout of its state in individual cells.
Abstract: Networks of interacting biomolecules carry out many essential functions in living cells, but the 'design principles' underlying the functioning of such intracellular networks remain poorly understood, despite intensive efforts including quantitative analysis of relatively simple systems Here we present a complementary approach to this problem: the design and construction of a synthetic network to implement a particular function We used three transcriptional repressor systems that are not part of any natural biological clock to build an oscillating network, termed the repressilator, in Escherichia coli The network periodically induces the synthesis of green fluorescent protein as a readout of its state in individual cells The resulting oscillations, with typical periods of hours, are slower than the cell-division cycle, so the state of the oscillator has to be transmitted from generation to generation This artificial clock displays noisy behaviour, possibly because of stochastic fluctuations of its components Such 'rational network design may lead both to the engineering of new cellular behaviours and to an improved understanding of naturally occurring networks
4,488 citations
4,255 citations
Book•
05 Sep 2011
TL;DR: The present article is a commencement at attempting to remedy this deficiency of scientific correlation, and the meaning and working of the various formulæ have been explained sufficiently, it is hoped, to render them readily usable even by those whose knowledge of mathematics is elementary.
Abstract: All knowledge—beyond that of bare isolated occurrence—deals with uniformities. Of the latter, some few have a claim to be considered absolute, such as mathematical implications and mechanical laws. But the vast majority are only partial; medicine does not teach that smallpox is inevitably escaped by vaccination, but that it is so generally; biology has not shown that all animals require organic food, but that nearly all do so; in daily life, a dark sky is no proof that it will rain, but merely a warning; even in morality, the sole categorical imperative alleged by Kant was the sinfulness of telling a lie, and few thinkers since have admitted so much as this to be valid universally. In psychology, more perhaps than in any other science, it is hard to find absolutely inflexible coincidences; occasionally, indeed, there appear uniformities sufficiently regular to be practically treated as laws, but infinitely the greater part of the observations hitherto recorded concern only more or less pronounced tendencies of one event or attribute to accompany another. Under these circumstances, one might well have expected that the evidential evaluation and precise mensuration of tendencies had long been the subject of exhaustive investigation and now formed one of the earliest sections in a beginner’s psychological course. Instead, we find only a general naı̈ve ignorance that there is anything about it requiring to be learnt. One after another, laborious series of experiments are executed and published with the purpose of demonstrating some connection between two events, wherein the otherwise learned psychologist reveals that his art of proving and measuring correspondence has not advanced beyond that of lay persons. The consequence has been that the significance of the experiments is not at all rightly understood, nor have any definite facts been elicited that may be either confirmed or refuted. The present article is a commencement at attempting to remedy this deficiency of scientific correlation. With this view, it will be strictly confined to the needs of practical workers, and all theoretical mathematical demonstrations will be omitted; it may, however, be said that the relations stated have already received a large amount of empirical verification. Great thanks are due from me to Professor Haussdorff and to Dr. G. Lipps, each of whom have supplied a useful theorem in polynomial probability; the former has also very kindly given valuable advice concerning the proof of the important formulæ for elimination of ‘‘systematic deviations.’’ At the same time, and for the same reason, the meaning and working of the various formulæ have been explained sufficiently, it is hoped, to render them readily usable even by those whose knowledge of mathematics is elementary. The fundamental procedure is accompanied by simple imaginary examples, while the more advanced parts are illustrated by cases that have actually occurred in my personal experience. For more abundant and positive exemplification, the reader is requested to refer to the under cited research, which is entirely built upon the principles and mathematical relations here laid down. In conclusion, the general value of the methodics recommended is emphasized by a brief criticism of the best correlational work hitherto made public, and also the important question is discussed as to the number of ‘‘cases’’ required for an experimental series.
3,687 citations
Journal Article•
2,321 citations
TL;DR: An engineered genetic oscillator in Escherichia coli is described that is fast, robust and persistent, with tunable oscillatory periods as fast as 13 min, and Computational modelling demonstrates that the key design principle for constructing a robust oscillator is a time delay in the negative feedback loop.
Abstract: One defining goal of synthetic biology is the development of engineering-based approaches that enable the construction of gene-regulatory networks according to 'design specifications' generated from computational modelling. This approach provides a systematic framework for exploring how a given regulatory network generates a particular phenotypic behaviour. Several fundamental gene circuits have been developed using this approach, including toggle switches and oscillators, and these have been applied in new contexts such as triggered biofilm development and cellular population control. Here we describe an engineered genetic oscillator in Escherichia coli that is fast, robust and persistent, with tunable oscillatory periods as fast as 13 min. The oscillator was designed using a previously modelled network architecture comprising linked positive and negative feedback loops. Using a microfluidic platform tailored for single-cell microscopy, we precisely control environmental conditions and monitor oscillations in individual cells through multiple cycles. Experiments reveal remarkable robustness and persistence of oscillations in the designed circuit; almost every cell exhibited large-amplitude fluorescence oscillations throughout observation runs. The oscillatory period can be tuned by altering inducer levels, temperature and the media source. Computational modelling demonstrates that the key design principle for constructing a robust oscillator is a time delay in the negative feedback loop, which can mechanistically arise from the cascade of cellular processes involved in forming a functional transcription factor. The positive feedback loop increases the robustness of the oscillations and allows for greater tunability. Examination of our refined model suggested the existence of a simplified oscillator design without positive feedback, and we construct an oscillator strain confirming this computational prediction.
1,154 citations