Modelling molecular interaction pathways using a two-stage identification algorithm

In systems biology, molecular interactions are typically modelled using white-box methods, usually based on mass action kinetics. Unfortunately, problems with dimensionality can arise when the number of molecular species in the system is very large, which makes the system modelling and behavior simulation extremely difficult or computationally too expensive. As an alternative, this paper investigates the identification of two molecular interaction pathways using a black-box approach. This type of method creates a simple linear-in-the-parameters model using regression of data, where the output of the model at any time is a function of previous system states of interest. One of the main objectives in building black-box models is to produce an optimal sparse nonlinear one to effectively represent the system behavior. In this paper, it is achieved by applying an efficient iterative approach, where the terms in the regression model are selected and refined using a forward and backward subset selection algorithm. The method is applied to model identification for the MAPK signal transduction pathway and the Brusselator using noisy data of different sizes. Simulation results confirm the efficacy of the black-box modelling method which offers an alternative to the computationally expensive conventional approach.