Abstract

In this talk I use applied mathematics to understand two emergent phenomena related to fundamental biophysical problems. They are linked to one another via the multiscale techniques I use to understand them.

In the first part, I discuss an overarching question in developmental biology: how is it that cells are able to decode spatio-temporally varying signals into functionally robust patterns in the presence of confounding effects caused by unpredictable or heterogeneous environments? This is linked to the general idea first explored by Alan Turing in the 1950s. Through multiscale analysis, I present a general theory of pattern formation in the presence of spatio-temporal input variations, and show how biological systems can generate non-standard dynamic robustness for ‘free’ over physiologically relevant timescales.

In the second part, I investigate how the rapid spinning of 3D microswimmers affects their emergent (observed) trajectories in shear flow. This is an active version of the classic fluid mechanics result of Jeffery’s orbits for inert spheroids, first explored by George Jeffery in the 1920s. I show that the short-scale rapid 3D spinning exhibited by many microswimmers can have a significant effect on longer-scale trajectories, despite the common neglect of this spinning in some mathematical models, and how this can be systematically incorporated into modified versions of Jeffery’s original equations.