Mathematical Biology and Ecology Seminar

Advances in spatial profiling technologies are providing insights into how molecular programs are influenced by local signalling and environmental cues. However, cell fate specification and tissue patterning involve the interplay of biochemical and mechanical feedback. Here, we propose a new computational framework that enables the joint statistical analysis of transcriptional and mechanical signals in the context of spatial transcriptomics. To illustrate the application and utility of the approach, we use spatial transcriptomics data from the developing mouse embryo to infer the forces acting on individual cells, and use these results to identify mechanical, morphometric, and gene expression signatures that are predictive of tissue compartment boundaries. In addition, we use geoadditive structural equation modelling to identify gene modules that predict the mechanical behaviour of cells in an unbiased manner. This computational framework is easily generalized to other spatial profiling contexts, providing a generic scheme for exploring the interplay of biomolecular and mechanical cues in tissues.

How do mobile organisms situate themselves in space?  This is a fundamental question in both ecology and cell biology but, since space use is an emergent feature of movement processes operating on small spatio-temporal scales, it requires a mathematical approach to answer.  In recent years, increasing empirical research has shown that non-locality is a key aspect of movement processes, whilst mathematical models have demonstrated its importance for understanding emergent space use patterns.  In this talk, I will describe a broad class of models for modelling the space use of interacting populations, whereby directed movement is in the form of non-local advection.  I will detail various methods for ascertaining pattern formation properties of these models, fundamental for answering the question of how organisms situate themselves in space, and describe some of the rich variety of patterns that emerge. I will also explain how to connect these models to data on animal and cellular movement.