Slow-fast Dynamics in Biological Systems

Many biophysical systems exhibit “slow-fast” dynamics—dynamics with a clear separation of fast and slow timescales. Coupling between fast and slow processes can drive important phenomena, such as marginal stability, but dissecting the coupling between these interactions is often mathematically challenging. Multi-scale analysis is an asymptotic method used in applied mathematics and dynamical systems analysis to attack these types of problems. Our microworking group will explore the application of this technique to a range of biophysical systems, including bioluminescent flashes in firefly swarms, transcriptional bursting, antibody evolution, heart rate dynamics, and visual exploration dynamics, with an aim to provide a dynamical foundation for observed phenomenon.