Temporal decomposition: A strategy for building mathematical models of complex metabolic systems

In 'Discovering complexity' Bechtel and Richardson (1993) highlighted the connection between how biologists investigate the world and the type of explanations they give. This paper extends their account of how we investigate the world by examining the strategies used by researchers to build mathematical models of complex metabolic systems between the 1970s and 1990s. Bechtel and Richardson analysed how researchers decompose complex systems by reducing the number of variables included in the model, thus simplifying them and making them suitable objects for research and understanding. Bechtel and Abrahamsen (2005) later distinguished two types of decomposition: 1) Structural decomposition, starting with the identification of the relevant component parts and 2) functional decomposition, starting with the identification of the relevant component operations. I use my case studies to argue that temporal decomposition should be recognised as an additional strategy for investigating complex metabolic systems. Temporal decomposition involves the identification of the relevant dynamic variables. Existing accounts of decomposition are based on the assumption of a spatial hierarchy which classifies modules according to the frequency of interactions between components. Temporal decomposition is based on the assumption of a time hierarchy which classifies variables as dynamic or constant according to the relative speed with which properties of the system change.