Categorical systems biology : an appreciation of categorical arguments in cellular modelling.

Abstract

With big science projects like the human genome project, [2], and preliminary attempts to seriously study brain activity, e.g. [9], mathematical biology has come of age, employing formalisms and tools from most branches of mathematics. Recent results, [51] and [53], have extended the relational (or categorical) approach of Rosen [44], to demonstrate that (in a very general class of systems) cellular self-organization/self-replication is implicit in metabolism and repair/stability. This is a powerful philosophical statement and removes the need of teleological argument. However, the result carries a technical limitation to Cartesian closed categories, which excludes many mathematical languages. We review the relevant literature on metabolic-repair pathways, category theory and systems theory, before performing a critique of this work. We find that the restriction to Cartesian closed categories is purely for simplicity, and describe how equivalent arguments may be built for monoidal closed categories. Moreover, any symmetric monoidal category may be "embedded" in a closed one. We discuss how these constructions/techniques provide the formal structure to treat self-organization/self-replication in most contemporary mathematical (modelling) languages. These results signicantly soften the impact on current modelling paradigms while extending the philosophical implications.