Mathematical Biology

Listed on this page are current research projects being offered for the Vacation Scholarship Program.

For more information on this research group see: Mathematical Biology



Fluid mechanics of active granular systems

Dense arrays of microorganisms exhibit striking collective motions, jamming and turbulent-like properties, and their behaviour underpins a range of processes in biology. However, the physical principles giving rise to their collective properties are not well understood.

Co-supervised by Dr Douglas Brumley and Professor Antoinette Tordesillas, this project will investigate the bulk properties of active suspensions, and develop simplified models to predict the flow of nearly-jammed arrays of microorganisms. Some background in fluid dynamics and computational work would be beneficial. No biological background necessary.

Contact: Douglas Brumley d.brumley@unimelb.edu.au, Antoinette Tordesillas atordesi@unimelb.edu.au

Statistical analysis of emerging biological data

Technological improvements have allowed for the collection of data from different types of molecules (e.g. genes, proteins, metabolites, microorganisms) resulting in multiple ‘omics data (e.g. transcriptomics, proteomics, metabolomics, microbiome) measured from the same set N of biospecimens, individuals, or cells. Our group is interested in developing computational and statistical methods for the analysis of such data, and tackle problems such as data integration, feature selection, and mathematical modelling. Integrating data include numerous challenges – data are complex and large, each with few samples (N < 50) and many molecules (P > 10,000), and generated using different technologies.

More details on our research can be found on our webiste and examples of methods we have developed for data mining and integration. Projects range from methods development, computational implementation in R and applications to case studies we have available through our collaborators.

Contact: Kim-Anh le Cao kimanh.lecao@unimelb.edu.au

Mathematical models of nanoparticle-cell interactions

Nanoparticles are a promising tool for the targeted delivery of medicine. However, the complex biological and physical processes that influence nanoparticle-cell interactions are not well understood. This project will develop mathematical models of nanoparticle transport (differential equations) and cell behaviour (differential equations or agent-based models). These models will help us understand which biological and physical processes dictate whether the targeted delivery of medicine via nanoparticles will be successful.

Contact: Stuart Johnston stuart.johnston@unimelb.edu.au