Derivation and use of mathematical models in systems biology

Abstract

Systems Biology has brought together researchers from biology, mathematics, physics and computer science to illuminate our understanding of biological mechanisms. In this chapter, we provide an overview of numerical techniques and considerations required to construct useful models describing natural phenomena. Initially, we show how the dynamics of single molecules up to the development of tissues can be described mathematically over both temporal and spatial scales. Importantly, we discuss the issue of model selection whereby multiple models can describe the same phenomena. We then illustrate how reaction rates can be estimated from datasets and experimental observations as well as highlighting the "parameter identifiability problem". Finally, we suggest ways in which mathematical models can be used to generate new hypotheses and aid researchers in uncovering the design principles regulating specific biological mechanisms. We hope that this chapter will provide an introduction to the ideas of mathematical modelling for those that wish to incorporate it into their research.