Solid mechanics - the modelling of muscle stem cell motion

We propose to construct a mechanical model of muscle stem cell motion combining solid mechanics, stochastic theory and numerical simulations. During healing muscle stem cells adopt an amoeboid form of translocation, known as blebbing, in which cells are round and display highly dynamic plasma membrane extensions and retractions. The model will be a novel testing bed for biological hypotheses of cellular motion and illuminate connections between the multiple scales, as well as provide new mathematical insights into the connection between motion and surface geometry.

The aim is to model this mechanism of cellular motion and characterise the relationship between cell movement and the surrounding environmental geometry e.g. size, shape and topology. This relationship is usually discounted in experiments as extracted cells are placed on flat plates, or gels, which do not match the complicated heterogeneous environments that cells would have to naturally contend with. Mathematical modelling provides us with a way to test these disregarded factors and challenge current biological knowledge as to their importance.

The primary objectives are:

1. develop a general stochastic multiscale framework of cellular motion linking macroscopic migration characteristics to microscopic structural properties of the cell;

2. derive relationships from the framework in point 1 that analytically link probabilistic position distributions of the cell population to the size, shape and topology of the surrounding environment;

3. compare the analytical relationships with known experimental movement data of cells on muscle fibres. These cells have unusual motion characteristics and we seek to account for how much of these effects can be attributed to the domain;

4. predict optimal blebbing motion strategies for moving on, or within, arbitrary spaces;

5. investigate the possibility of modelling multi-blebbing.