By incorporating feedback around systems we wish to manipulate, it is possible to improve their performance and robustness properties to meet pre-specified design objectives. For decades control engineers have been successfully implementing feedback controllers for complex mechanical and electrical systems such as aircraft and sports cars. Natural biological systems use feedback extensively for regulation and adaptation but apart from the most basic designs, there is no systematic framework for designing feedback controllers in Synthetic Biology. In this paper we describe how classical approaches from linear control theory can be used to close the loop. This includes the design of genetic circuits using feedback control and the presentation of a biological phase lag controller.
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.
Negative feedback is known to endow biological and man-made systems with robust performance in the face of uncertainties and disturbances. To date, synthetic biological feedback circuits have relied upon protein-based, transcriptional regulation to control circuit output. Small RNAs (sRNAs) are non-coding RNA molecules which can inhibit translation of target messenger RNAs (mRNAs). In this paper, we designed, modelled and built 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 input-output response of the autorepressor alone. In the second circuit, the output is a transcription factor that induces expression of an sRNA which negatively regulates the translation of the mRNA encoding this 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.
Small non-coding RNAs (sRNA) are a key bacterial regulatory mechanism that has yet to be fully exploited in synthetic gene regulatory networks. In this paper a linear design methodology for gene regulatory networks presented previously is extended for application to sRNAs. Standard models of both sRNA inhibition and activation are presented, linearised and transformed into the frequency domain. We demonstrate how these mechanisms can emulate subtraction and minimum comparator functions in specific parameter regimes. Finally, the design of a genetic feedback circuit is included, illustrating that sRNAs can be used to improve the performance of a range of synthetic biological systems.
We propose a method for bounding state functionals of a class of nonlinear stochastic differential equations. Given a class of state functionals of a stochastic system, the Feynman-Kac Lemma presents a backward in time partial differential equation that describes the evolution of the state functional. We bound these state functionals based on a method which uses barrier functionals. We show that, under the assumption of polynomial data, the bounds can be obtained by semi-definite programming. The proposed method is then applied to the case study of noise in genetic negative autoregulation to bound a functional of the second moment, which is of specific interest to experimental assays. The bound yielded, using biological parameters, is found to be in good agreement with experimental results in the literature.
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