All publications by Gawthrop in 2023

Intermittent control combines open-loop trajectories with feedback at discrete time instances determined by events. Among other applications, it has recently been used to model quiet standing in humans where the system was assumed to be time-invariant. This article expands this work to the time-variant case by introducing an adaptive intermittent controller that exploits the well-known self-tuning architecture of adaptive control with a Kalman filter to perform online state and parameter estimation. Simulation and experimental results using a rotational inverted pendulum show advantages of the intermittent controllers compared to continuous feedback control since the former can provide persistent excitation due to their internal triggering mechanism, even when no external reference changes or disturbances are applied. Moreover, the results show that the event thresholds of intermittent control can be used to adjust the degree of responsiveness of the adaptation in the system, becoming a tool to balance the trade-off between steady-state performance and flexibility against parametric changes, addressing the stability–plasticity dilemma of adaptation and learning in control.

The sensitivity of systems biology models to parameter variation can give insights into which parameters are most important for physiological function, and also direct efforts to estimate parameters. However, in general, kinetic models of biochemical systems do not remain thermodynamically consistent after perturbing parameters. To address this issue, we analyse the sensitivity of biological reaction networks in the context of a bond graph representation. We find that the parameter sensitivities can themselves be represented as bond graph components, mirroring potential mechanisms for controlling biochemistry. In particular, a sensitivity system is derived which re-expresses parameter variation as additional system inputs. The sensitivity system is then linearized with respect to these new inputs to derive a linear system which can be used to give local sensitivity to parameters in terms of linear system properties such as gain and time constant. This linear system can also be used to find so-called sloppy parameters in biological models. We verify our approach using a model of the Pentose Phosphate Pathway, confirming the reactions and metabolites most essential to maintaining the function of the pathway.

Synthetic biology aims to engineer novel functionalities into biological systems. While the approach has been widely applied to single cells, the scale of synthetic circuits designed in this way is limited by factors such as resource competition and retroactivity. Synthetic biology of cell populations has the potential to overcome some of these limitations by physically isolating synthetic genes from each other. To rationally design cell populations, we require mathematical models that link between intracellular biochemistry and intercellular interactions. The interfacing of agent-based models with systems biology models is particularly important in understanding the effects of cell heterogeneity and cell-to-cell interactions. In this study, we develop a model of gene expression that is suitable for incorporation into agent-based models of cell populations. To be scalable to large cell populations, models of gene expression should be both computationally efficient and compliant with the laws of physics. We satisfy the first requirement by applying a model reduction scheme to translation, and the second requirement by formulating models using bond graphs. We show that the reduced model of translation faithfully reproduces the behaviour of the full model at steady state. The reduced model is benchmarked against the full model, and we find a substantial speedup at realistic protein lengths. Using the modularity of the bond graph approach, we couple separate models of gene expression to build models of the toggle switch and repressilator. With these models, we explore the effects of resource availability and cell-to-cell heterogeneity on circuit behaviour. The modelling approaches developed in this study are a bridge towards rationally designing collective cell behaviours such as synchronisation and division of labour.Competing Interest StatementThe authors have declared no competing interest.