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Exploring the Dynamics of Nonlinear Biochemical Systems using Control-Based Continuation

Gomes, Brandon; de Cesare, Irene; Guarino, Agostino; di Bernardo, Mario; Renson, Ludovic; Marucci, Lucia


Mathematical modelling is routinely used in Systems Biology to understand the mechanisms causing nonlinear phenomena in gene expression, such as switch-like behaviours and temporal oscillations. The reliability of model predictions and bifurcation analysis depend on modelling assumptions and specific choices of model parameters; however, the identification of models is highly challenging due to the complexity of biochemical interactions and noise in experimental data.

This paper numerically investigates the use of control-based continuation (CBC) for tracking dynamical features of biochemical systems and, in particular, the bistable dynamics of a gene regulating pluripotency in embryonic stem cells.

CBC is a method that exploits feedback control and path following algorithms to explore the dynamic features of a nonlinear physical system directly during experimental tests. CBC applications have so far been limited to non-living (i.e. electro-mechanical) systems. Our numerical simulations show that, in principle, CBC could also be applied to biological experiments to characterise the switch-like dynamics of genes that are important for cell decision making.

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