Exploring the nonlinear dynamic behaviour of synthetic biological systems using nonlinear feedback control

Synthetic Biology aims at redesigning living organisms so that they produce a useful substance (medicine) or gain a new functionality (switching, oscillations). Mathematical modelling is widely used within Synthetic Biology's design cycle to indicate the region of parameter space where the desired behaviours are present. The derivation of biochemical models can however be challenging, both in terms of model structure (which depend on underlying hypothesis), and parameter identification. Experimental data is often generated in an ad hoc manner, incomplete and (very) noisy. Resulting model uncertainties inevitably lead to misleading conclusions regarding the relationship between physical parameters variations and the key nonlinear phenomena (bifurcations) that create the desired biological functions. Consequently, the design of synthetic biochemical circuits that perform as intended is extremely difficult and requires numerous design-build-test iterations.

Control-based Continuation (CBC) is a general and systematic testing method that can circumvent these issues and has the potential to profoundly change the approach to circuit design in synthetic biology. Without the need for a model, CBC uses sensors and actuators to intelligently probe physical systems. Combining feedback control and numerical algorithms, CBC targets the dynamic responses of interest, tracks their evolution as controllable parameters are changed and detects boundaries between qualitatively different types of behaviours (bifurcations) directly during experimental tests. CBC could therefore be exploited to collect more informative data, thereby improving models of biochemical systems, or even used to adjust inputs and parameters to optimize cell behaviour and function directly during tests.

While CBC shows great promises and has been applied to a wide range of non-living (i.e. electro-mechanical) systems, it cannot currently be applied to living organisms. The feedback control algorithms currently used in CBC cannot deal with the noise and different time scales typically present in biochemical reactions, and traditional algorithms available in the control literature cannot be used directly due to the close interactions that exist between the control and the numerical methods used in CBC.

The objective of this PhD project is to develop the control algorithms necessary to apply CBC to living cell systems. The project will look at the development of control algorithms that can exploit basic mathematical models (Model-predictive-control) but that are also robust to modelling inaccuracies. The importance of noise will require the use of stochastic control theory and sophisticated filters (such as adaptive particle filters). Biochemical experiments often consider many cells which can individually settle to different states (bistability) and form different populations. The rigorous analysis and exploration of the dynamic behaviour of such systems will require us to extend CBC to the control of population ratios.