Edward J. Hancock

Tuning the dials of Synthetic Biology.

Synthetic Biology is the ‘Engineering of Biology’ – it aims to use a forward-engineering design cycle based on specifications, modelling, analysis, experimental implementation, testing and validation to modify natural or design new, synthetic biology systems so that they behave in a predictable fashion. Motivated by the need for truly plug-and-play synthetic biological components, we present a comprehensive review of ways in which the various parts of a biological system can be modified systematically. In particular, we review the list of ‘dials’ that are available to the designer and discuss how they can be modelled, tuned and implemented. The dials are categorized according to whether they operate at the global, transcriptional, translational or post-translational level and the resolution that they operate at. We end this review with a discussion on the relative advantages and disadvantages of some dials over others.

Simplified mechanistic models of gene regulation for analysis and design

Simplified mechanistic models of gene regulation are fundamental to systems biology and essential for synthetic biology. However, conventional simplified models typically have outputs that are not directly measurable and are based on assumptions that do not often hold under experimental conditions. To resolve these issues, we propose a ‘model reduction’ methodology and simplified kinetic models of total mRNA and total protein concentration, which link measurements, models and biochemical mechanisms. The proposed approach is based on assumptions that hold generally and include typical cases in systems and synthetic biology where conventional models do not hold. We use novel assumptions regarding the ‘speed of reactions’, which are required for the methodology to be consistent with experimental data. We also apply the methodology to propose simplified models of gene regulation in the presence of multiple protein binding sites, providing both biological insights and an illustration of the generality of the methodology. Lastly, we show that modelling total protein concentration allows us to address key questions on gene regulation, such as efficiency, burden, competition and modularity.

Structured sum of squares for networked systems analysis

In this paper we introduce a structured Sum of Squares technique that enables Sum of Squares programming to be applied to networked systems analysis. By taking the structure of the network into account, we limit the size and number of decision variables in the LMI representation of the Sum of Squares, which improves the scalability of the technique for networked systems beyond taking advantage of symmetry and sparsity. We apply the technique to test non-negativity of fourth order structured polynomials in many variables and show that for these problems the technique has improved scalability over existing Sum of Squares techniques.

Synthetic negative feedback circuits using engineered small RNAs

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.

The Interplay Between Feedback and Buffering in Homeostasis

This SI section analyzes a minimal model of a buffering-feedback system. This analysis includes deriving a minimal model for analysis (S1.1-S1.2), followed by analyzing the effect of reactions on different time scales (S1.3), the effect of disturbances (S1.4-S1.8), stability (S1.9), noise (S1.10), the comparison with technological controllers (S1.11), disturbances acting on the buffering species (S1.12), and feedback occurring from the buffering species (S1.13).

Engineering a Genetic Oscillator Using Delayed Feedback

Oscillators are one of the best studied synthetic genetic circuits and a focus of the emerging field of Synthetic Biology. A number of different feedback arrangements that can produce oscillations have been proposed; the two most important constructs involve a single gene with negative feedback including delay and three genes in negative feedback forming a structure called a repressilator. Each of these has a different range of performance characteristics and different design rules. In this book chapter we discuss how oscillators of the first type can be designed to meet frequency and amplitude requirements. We also discuss how coupling heterogeneous populations of delayed oscillators can produce oscillations with robust amplitude and frequency. The analysis and design is rooted in techniques from control theory and dynamical systems.

An invariance principle for time-varying systems

In this paper we propose an invariance principle for time-varying dynamical systems. We first present a novel proof of the Krasovskii-Lasalle invariance principle for forward time using invariance properties of regions of attraction, rather than the invariance property of the limit set. We then propose an invariance principle for bounded time-varying systems, in the spirit of the classical result, by using the Lasalle-Yoshizawa theorem and a uniformity condition. The simple, practical use of the theorem is shown using an example of a pendulum with time-varying parameters.