Information flow in living matter
I use statistical mechanics, topology, information theory, and dynamical theory to predict emergent function in biological systems.
Projects with my students and collaborators
- Topology supports robust global cycles in stochastic systems. Why are living systems able to exhibit time-scales much longer than those of the underlying components, and how is such robust behavior subserved by stochastic constituents? To address this question, we proposed biologically plausible motifs from which two-dimensional stochastic systems can be constructed. The motifs represent out-of-equilibrium cycles on the microscopic scale, which support macroscopic edge currents in configuration space. These global cycles are a consequence of the Zak topological phase and are accompanied by uniquely non-Hermitian properties such as exceptional points and a non-zero vorticity of the edge states (see above). Our framework enables emergent dynamical phenomena such as a global clock, reminiscent of the biochemical oscillator KaiABC that supports the 24-hour circadian clock. The inclusion of other biologically plausible features supports stochastic growth and degrowth, as well as synchronization, similar to observations prevalent in biology. These diverse behaviors emerge from versatile building blocks where identical motifs can be assembled to drive cycles over widely varying time scales simply by changing the number of constituents involved, directly linking structure to emergent function.
- Learning in complex environments. Our most recent work studies navigation of microswimmers in fluid flows on curved manifolds, which can be described by geodesics in generalizations of general relativity. Previous work analyzed the geometry of neural data from human subjects engaged in value learning, where I found that the most effective learners had more efficient representations. Efficient representations are characterized by both high task dimension and low embedding dimension, evaluated using tools from data science.
- Information in fluid flows. As living systems are governed by goals that are crucial to their survival or constraints unique to their environment, statistical mechanics or thermodynamics often need extensions to capture these factors adequately. I studied the information content carried by a stochastic particle in an arbitrary flow-field, as well as the residence time of this particle. This allows us to understand the relative effects of advection and diffusion, as well as the influence of local flow properties such as strain rate, vorticity, and divergence.
Topology protects robust global cycles in stochastic systems
arXiv: 2010.02845 (2020)
Optimal navigation strategies for microswimmers on curved manifolds
arXiv: 2010.07580 (2020)
Quantifying configurational information for a stochastic particle in a flow-field
New Journal of Physics (2020)