Autonomous mathematical models: constructing theories of metabolic control

This paper considers how the relationship between mathematical models and theories in biology may change over time, on the basis of a historical analysis of the development of a mathematical model of metabolism, metabolic control analysis, and its relationship to theories of metabolic control. I argue that one can distinguish two ways of characterising the relationship between models and theories, depending on the stage of model and/or theory development that one is considering: partial independence and autonomy. Partial independence describes a model's relationship with existing theory, thus referring to relationships that have already been established between model and theory during model construction. By contrast, autonomy is a feature of relationships which may become established between model and theory in the future, and is expressed by a model's open ended role in constructing emerging theory. These characteristics have often been conflated by existing philosophical accounts, partly because they can only be identified and analysed when adopting a historical perspective on scientific research. Adopting a clear distinction between partial independence and autonomy improves philosophical insight into the changing relationship between models and theories.