Algebraic Perspectives in Biology

Once you start looking for them, algebraic structures are everywhere in biology. Networks and hypergraphs are perhaps the most obvious examples but we are finding that abstraction is an enormously helpful tool to make sense of aspects of the living world. We are working on new algebraic approaches to understand the organisation of living systems. The aim is to find commonalities and fundamental organising principles.

The right level of abstraction can make a mathematical (and biological) problem much more tractable and we are translating concepts and tools from algebra and algebraic geometry (but also a host of other concepts from “pure” mathematics) for use in biology and the analysis of complex high-dimensional systems.

We have used this for model selection, for model comparison, but also to study how the organisation of sub-cellular structures affects a cell’s information processing capability.