The Best Linear Approximation of Biomolecular Systems

The dynamical behaviour of biomolecular systems changes between either linear or nonlinear in different parameter regimes. Data-driven techniques used for modelling the biomolecular systems either model the biomolecular systems as the linear time-invariant systems in all parameter regimes or use computationally expensive nonlinear modelling structures to represent their behaviour. Furthermore, these modelling techniques require time-consuming experimental design for data acquisition. Therefore, in this paper, firstly, we utilize the broadband multisine signals to acquire the data in one single experiment. Secondly, we use a novel local polynomial approach to estimate nonparametrically the best linear approximation (BLA) of the biomolecular system in the frequency band of interest. Finally, the usefulness of the technique is demonstrated through simulation case-studies for obtaining the BLA for two biomolecular systems.