Everything you have been taught about Turing patterns is wrong! (Well, not everything, but qualifying statements tend to weaken a punchy first sentence). Turing patterns are universally used to generate and understand patterns across a wide range of biological phenomena. They are wonderful to work with from a theoretical, simulation and application point of view. However, they have a paradoxical problem of being too easy to produce generally, whilst simultaneously being heavily dependent on the details. In this talk I demonstrate how to fix known problems such as small parameter regions and sensitivity, but then highlight a new set of issues that arise from usually overlooked issues, such as boundary conditions, initial conditions, and domain shape. Although we’ve been exploring Turing’s theory for longer than I’ve been alive, there’s still life in the old (spotty) dog yet.

Normal heart function relies of the fine-tuned synchronization of cellular components. In healthy hearts, calcium oscillations and physical contractions are coupled across a synchronised network of 3 billion heart cells. When the process of functional isolation of rogue cells isn’t successful, the network becomes maladapted, resulting in cardiovascular diseases, including heart failure and arrythmia. To advance knowledge on this normal-to-disease transition we must first address the lack of a mechanistic understanding of the plastic readaptation of these networks. In this talk I will explore coupling and loss of synchronisation using a mathematical model of calcium oscillations informed by experimental data. I will show some preliminary results pointing at the heterogeneity hidden behind seemingly uniform cell populations, as a causative mechanism behind disrupted dynamics in maladapted networks.

Certain models of collective dynamics exhibit deceptively simple patterns that are surprisingly difficult to explain. These patterns often arise from phase transitions within the underlying dynamics. However, these phase transitions can be explained only when one derives continuum equations from the corresponding individual-based models. In this talk, I will explore this subtle yet rich phenomenon and discuss advances and open problems.