This paper discusses the scientific rationale behind the e-Science project, Integrative Biology, which is developing mathematical modelling tools, HPC-enabled simulations and an underpinning Grid infrastructure to provide an integrative approach to the modelling of complex biological systems. The project is focusing on two key applications to validate the approach: the modelling of heart disease and cancer, which together are responsible for over 60% of deaths in the United Kingdom. This paper provides an overview of the project, describes the initial prototype architecture and discusses the long-term scientific aims.