Quantifying the impact of electric fields on single-cell motility.

Cell motility in response to environmental cues forms the basis of many developmental processes in multicellular organisms. One such environmental cue is an electric field (EF), which induces a form of motility known as electrotaxis. Electrotaxis has evolved in a number of cell types to guide wound healing and has been associated with different cellular processes, suggesting that observed electrotactic behavior is likely a combination of multiple distinct effects arising from the presence of an EF. To determine the different mechanisms by which observed electrotactic behavior emerges, and thus to design EFs that can be applied to direct and control electrotaxis, researchers require accurate quantitative predictions of cellular responses to externally applied fields. Here, we use mathematical modeling to formulate and parameterize a variety of hypothetical descriptions of how cell motility may change in response to an EF. We calibrate our model to observed data using synthetic likelihoods and Bayesian sequential learning techniques and demonstrate that EFs bias cellular motility through only one of a selection of hypothetical mechanisms. We also demonstrate how the model allows us to make predictions about cellular motility under different EFs. The resulting model and calibration methodology will thus form the basis for future data-driven and model-based feedback control strategies based on electric actuation.

Ribo-attenuators: novel elements for reliable and modular riboswitch engineering.

Riboswitches are structural genetic regulatory elements that directly couple the sensing of small molecules to gene expression. They have considerable potential for applications throughout synthetic biology and bio-manufacturing as they are able to sense a wide range of small molecules and regulate gene expression in response. Despite over a decade of research they have yet to reach this considerable potential as they cannot yet be treated as modular components. This is due to several limitations including sensitivity to changes in genetic context, low tunability, and variability in performance. To overcome the associated difficulties with riboswitches, we have designed and introduced a novel genetic element called a ribo-attenuator in Bacteria. This genetic element allows for predictable tuning, insulation from contextual changes, and a reduction in expression variation. Ribo-attenuators allow riboswitches to be treated as truly modular and tunable components, thus increasing their reliability for a wide range of applications.

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.

Designing Conservation Relations in Layered Synthetic Biomolecular Networks.

In Synthetic Biology, biomolecular networks are designed and constructed to perform specified tasks. Design strategies for these networks tend to center on tuning the parameters of mathematical models to achieve a specified behavior, and implementing these parameters experimentally. This design strategy often assumes a fixed network structure that defines the possible behaviors, which may be too restrictive for our purposes. This paper investigates the extent to which the state space of a synthetic network can also be designed and shaped by parametric tuning. We exploit timescale separation to implement new, nonlinear, tunable conservation relations that hold for all times beyond a fast transient. We demonstrate an application of this design strategy by flexibly constraining the possible behaviors of a gene regulatory network through the design of fast protein interactions.

Quantification of Interactions between Dynamic Cellular Network Functionalities by Cascaded Layering.

Large, naturally evolved biomolecular networks typically fulfil multiple functions. When modelling or redesigning such systems, functional subsystems are often analysed independently first, before subsequent integration into larger-scale computational models. In the design and analysis process, it is therefore important to quantitatively analyse and predict the dynamics of the interactions between integrated subsystems; in particular, how the incremental effect of integrating a subsystem into a network depends on the existing dynamics of that network. In this paper we present a framework for simulating the contribution of any given functional subsystem when integrated together with one or more other subsystems. This is achieved through a cascaded layering of a network into functional subsystems, where each layer is defined by an appropriate subset of the reactions. We exploit symmetries in our formulation to exhaustively quantify each subsystem's incremental effects with minimal computational effort. When combining subsystems, their isolated behaviour may be amplified, attenuated, or be subject to more complicated effects. We propose the concept of mutual dynamics to quantify such nonlinear phenomena, thereby defining the incompatibility and cooperativity between all pairs of subsystems when integrated into any larger network. We exemplify our theoretical framework by analysing diverse behaviours in three dynamic models of signalling and metabolic pathways: the effect of crosstalk mechanisms on the dynamics of parallel signal transduction pathways; reciprocal side-effects between several integral feedback mechanisms and the subsystems they stabilise; and consequences of nonlinear interactions between elementary flux modes in glycolysis for metabolic engineering strategies. Our analysis shows that it is not sufficient to just specify subsystems and analyse their pairwise interactions; the environment in which the interaction takes place must also be explicitly defined. Our framework provides a natural representation of nonlinear interaction phenomena, and will therefore be an important tool for modelling large-scale evolved or synthetic biomolecular networks.

Layered decomposition for the model order reduction of timescale separated biochemical reaction networks.

Biochemical reaction networks tend to exhibit behaviour on more than one timescale and they are inevitably modelled by stiff systems of ordinary differential equations. Singular perturbation is a well-established method for approximating stiff systems at a given timescale. Standard applications of singular perturbation partition the state variable into fast and slow modules and assume a quasi-steady state behaviour in the fast module. In biochemical reaction networks, many reactants may take part in both fast and slow reactions; it is not necessarily the case that the reactants themselves are fast or slow. Transformations of the state space are often required in order to create fast and slow modules, which thus no longer model the original species concentrations. This paper introduces a layered decomposition, which is a natural choice when reaction speeds are separated in scale. The new framework ensures that model reduction can be carried out without seeking state space transformations, and that the effect of the fast dynamics on the slow timescale can be described directly in terms of the original species.

Guaranteed error bounds for structured complexity reduction of biochemical networks.

Biological systems are typically modelled by nonlinear differential equations. In an effort to produce high fidelity representations of the underlying phenomena, these models are usually of high dimension and involve multiple temporal and spatial scales. However, this complexity and associated stiffness makes numerical simulation difficult and mathematical analysis impossible. In order to understand the functionality of these systems, these models are usually approximated by lower dimensional descriptions. These can be analysed and simulated more easily, and the reduced description also simplifies the parameter space of the model. This model reduction inevitably introduces error: the accuracy of the conclusions one makes about the system, based on reduced models, depends heavily on the error introduced in the reduction process. In this paper we propose a method to calculate the error associated with a model reduction algorithm, using ideas from dynamical systems. We first define an error system, whose output is the error between observables of the original and reduced systems. We then use convex optimisation techniques in order to find approximations to the error as a function of the initial conditions. In particular, we use the Sum of Squares decomposition of polynomials in order to compute an upper bound on the worst-case error between the original and reduced systems. We give biological examples to illustrate the theory, which leads us to a discussion about how these techniques can be used to model-reduce large, structured models typical of systems biology.