Derivation and Use of Mathematical Models in Systems Biology

Systems Biology has brought together researchers from biology, mathe-matics, physics and computer science to illuminate our understanding of biologicalmechanisms. In this chapter, we provide an overview of numerical techniques andconsiderations required to construct useful models describing natural phenomena.Initially, we show how the dynamics of single molecules up to the developmentof tissues can be described mathematically over both temporal and spatial scales.Importantly, we discuss the issue of model selection whereby multiple models candescribe the same phenomena. We then illustrate how reaction rates can be estimatedfrom datasets and experimental observations as well as highlighting the “parameteridentifiability problem”. Finally, we suggest ways in which mathematical modelscan be used to generate new hypothesesand aid researchers in uncoveringthe designprinciples regulating specific biological mechanisms. We hope that this chapter willprovide an introduction to the ideas of mathematical modelling for those that wishto incorporate it into their research