Abstract:

Partial differential equation (PDE) models can be a powerful tool for understanding emerging patterns in the life sciences. To mathematically capture these structures, one of the biggest challenges to overcome is the problem of scales: small scale events can result in large scale effects. I will present two projects, which exemplify the synergistic effects of applied mathematics and biology.

In the first part of the talk I will focus on a structure that lies at the heart of many types of cell movement: dynamic networks of branched actin fibres. Using experimental data to inform the models, we investigate how cofilin, a known disassembly agent, creates dynamic networks of fixed lengths. To capture the observed macroscopic fragmentation of the network, we combine PDE-based modelling of the cofilin binding dynamics with a discrete network disassembly model. This allows to predict the equilibrium network length across various control parameters.

In the second part I will discuss modelling, simulation and analysis of travelling waves in collectively moving bacterial swarms. The macroscopic PDEs describing the bacteria are derived from an individual-based description using a biology-focused coarse-graining method. Using the continuous model we can further investigate the unusual phenomena of counter-propagating travelling waves: Two families of interacting travelling waves whose profiles remain unchanged, but whose composition is modified by the oncoming wave.