Mathematical Biology

Research in Mathematical Biology at the University of Minnesota spans a large range of application areas.

Cell locomotion

One area focuses on cell locomotion, which plays an important role in development, the immune response, wound healing, and cancer metastasis.

This involves the development of computational models based on continuum mechanics to understand how interaction of internal and external signals affect the structure of the cytoskeleton, which in turn affects patterns of crawling and swimming observed in nature.

Mathematical models of cancer

Another group focuses on developing and applying mathematical models of cancer initiation, tumor progression, and treatment response. Current research is focused in five main areas:

1. Data-driven techniques for precision medicine
2. Phenotypic plasticity and epigenetics in cancer
3. Understanding the mechanisms of how cancer arises from healthy tissue
4. Understanding the evolution of resistance to anti-cancer drugs and treatment optimization
5. Phylogenetic analysis of evolution and infection dynamics.

Bacteriophage viruses

A third area deals with the study of the structure and function of bacteriophage viruses. These are viruses that infect bacteria and are currently being investigated in the medical community as therapies for antibiotic resistant illnesses caused by bacterial infections.

The viral genome, a long, semiflexible, electrically charged elastic filament, is packaged in a protein capsid by a molecular motor when target bacteria are absent. It is released to infect bacteria when the virus senses them in its environment.

The mathematical work addresses the three stages of the virus life, packaging, storage and ineffective release. The tools involved include:

• Topology
• Partial differential equations
• Dynamical systems
• Stochastic and numerical methods

The group collaborates with experimental biologists who grow and image viruses under different ionic conditions.

Neurons

A fourth area involves the development of tools for the mathematical analyses of networks of neurons and the use of these to probe the function of networks in the brain. This involves development of analytical tools to estimate neuronal connectivity patterns from simultaneous recordings of neuronal activity and development of mathematical tools to study response properties of neurons.

Related methodological research

• Stochastic simulation
• Molecular dynamics
• Parameter estimation
• Machine learning and data science
• Probabilistic analysis
• Network science
• Computational methods for molecular dynamics