# Mathematical Biology

Stochastic and computational methods applied to biology

### Stochastic Modelling of Biological Systems

Due to recent experimental progress, the field of mathematical biology is rapidly growing. There are plenty of biological systems where mathematical models and analysis are needed. Closely interacting with experimentalists, the PhD candidate would formulate and analyze models of cancer progression, virus dynamics, bacterial evolution, and possibly other systems related to molecular motor motion or the origins of life. The project starts with first building and exploring simple model systems, and continues with their study by computer simulations and analytical methods. Knowledge of the biological background is not necessary at the beginning, but one will eventually learn some biology in order to do relevant research. Informal enquiries can be made to Tibor Antal (Tibor.Antal@ed.ac.uk).

### Probability Models of Cancer Growth

Biology is a fast growing area for applications of probability. Since still in its infancy, there are many unexplored areas and open problems. In particular, there is a great interest in stochastic models of cancers. This PhD project would focus on understanding the most basic and fundamental models of tumor progression. These models include branching processes, other models borrowed from population genetics, or spatial Poisson processes. The work has a light numerical aspect to it, but would focus more on finding exact solutions, and establishing limit theorems. No knowledge of biology is required. Informal enquiries can be made to Tibor Antal (Tibor.Antal@ed.ac.uk).

### Modelling of cellular adhesion in close collaboration with experimental biologists

All the multicellular organisms, including us, humans, are in the end just a pile of cells. But why we are not falling apart? Our team studies cell-cell adhesion from an intracellular perspective. This is a vibrant current area of research, where most labs currently study tissue properties from the macroscopic level (tissue tension, etc), but not from the intracellular level. For cells to stick together, a particular protein must be delivered to its biologically relevant locations along the cell boundary (in order to "glue" nearby cells together) and distributed in such a way that the tissue has desired biological properties. How does this work? Is the outcome robust? We study these processes in close collaboration with the experimental biology lab of Natalia Bulgakova at U. Sheffield, with maths modelling guiding the experiments and vice versa. Maths techniques that we use include PDEs, ODEs, and Stochastic modelling. No previous knowledge of biology is required at the beginning of the project, but the student will learn about the relevant bio processes as the project progresses. The results of this highly interdisciplinary project will be of interest to both maths and bio communities. Informal enquiries can be made to Lyuba Chumakova (Lyuba.Chumakova@ed.ac.uk).