Understanding and predicting biological networks using linear system identification

This chapter demonstrates how linear systems can be used to model biochemical networks. Such models give predictable power that can be used to generate hypotheses, which in turn can be (in)validated experimentally. The advantages of linear systems are that they are relatively simple, efficient to obtain and simulate, and have been studied in great detail. In spite of inherent nonlinearities in real world applications, linear systems have been successfully used in control theory as a tool to model, analyse and control technological systems. In contrast, although at the molecular level reactions are nonlinear, modelling of key behaviours important to predict new features of a system can in many instances be captured by linear dynamics. Guided by a simple example, this chapter explains step-by-step how to use linear system identification (SId) to obtain causal relationships between different biological species in complex networks. We will cover key aspects of model estimation, validation and selection. The corresponding Matlab™ codes will be also be introduced. The chapter ends with illustrations of practical applications through two case studies, where SId has been used to further our understanding of biological networks