Mathematics of Life

This theme employs techniques from data science, AI, and mathematics to provide insight into the biological mechanisms underpinning health and disease. By constructing, calibrating, and analysing theoretical models, we generate testable predictions to quantify the contribution of such mechanisms to observed phenomena in a range of systems across neuroscience, neuroendocrinology, evolutionary biology, protein and molecular dynamics, and cell motility. We work hand-in-hand with experimental and clinical collaborators to ensure that our theoretical models and analysis techniques are directly translated into novel bioscientific understanding.

The research falls into three streams:

1) Data analysis: We use cutting-edge data science and AI techniques from -omics analysis, time series analysis, and topological data analysis to identify relationships between biological variables in complex systems. We further investigate these relationships using a range of techniques across machine learning and network science to quantify the relative importance of particular interactions for understanding specific phenotypes or behaviour.

2) Model construction: We construct data-driven theoretical models to provide tools to interrogate the dynamical behaviour of biological systems. These models range from simple agent-based and differential equation models to large systems of equations posed across multiple spatial and temporal scales. Data science techniques from parameter optimisation and uncertainty quantification are used to fit these models to data to ensure that they accurately reflect real-world biological systems.

3) Model analysis: We use techniques from dynamical systems and control theory to analyse the constructed theoretical models. We develop and apply tools for high-throughput numerical simulation of our models and use bifurcation analysis to predict transitions, such as the acquisition of genotypes during development, in the dynamical behaviour of the biological system being modelled. The analysed models are then used to generate hypotheses of the role of specific biological mechanisms and to optimise experimental design to test these hypotheses.