Modelling of spatio-dynamical systems

Complex spatial nonlinear dynamical models offer a wide range of stimulating statistical challenges with interesting and important potential implementations. The motivating application of our novel methodology lies in cell motility. The motion of migrating cells takes many different forms and is affected by a variety of factors; take, for example, the motion of immune cells within the lymphnode, or the migration of dictyostelium cells towards chemokinetically rich regions. Advances in 2p microscopy (see Figure 1 below) allow us to trace the motion of immune cells within the lymphnode of a live mouse.

Efficient immune cell migration is of paramount importance in immune defense, so understanding and characterizing cellular motion is key. We introduce a statistical model for inferring the chemokine fields that guide lymphocyte migration. We assume that cells are well-descibed by a Langevin diffusion process with a force field. Under suitable model assumptions on the underlying force field, and owing to the Markovian structure of the Langevin process, the cell trajectories follow a Gaussian distribution. Our model is consistent with a chemokine guided directive component of the collective cell motion, fitting a potential field through a radial kernel basis regression. The implied force field is then given by the gradient of the potential field. Applying our methods to 2-photon data obtained from observations in murine lymph nodes, we compare the motion of recently emigrated vs established B cells within the B cell follicle. Our Bayesian analysis provides us with estimates for the spatial structure of the potential field (see Figure 2), capturing the corresponding force fields in 3 dimensions.

Work in progress

Papers and Presentations