Polymer Topology
Polymeric systems often exhibit complex internal architectures, where the physical or chemical contacts between monomeric sites define their functional properties. Polymer topology focuses on the entanglement of these chains, which can range from simple loops to intricate knots and multi-chain braids. Familiar examples include the folding of proteins into functional shapes, the packaging of DNA within a cell nucleus, or the development of high-strength synthetic fibers. My research involves using low-dimensional topology (knot theory, circuit topology) characterize the universal principles of entanglement. I investigate how topological constraints influence structural phase transitions, chirality, and the collective behavior of polymeric bundles.
Projects
An overview of my research projects, including the systems I study and the analytical and computational approaches I use. Colored links will send you to the corresponding publications.
Circuit Topology
Circuit topology (CT) has emerged as a counterpart for knot theory, which decomposes closed chains into prime knots, whereas CT describes open chains in terms of fundamental topological 'motifs' that can be formed by contacts (chemical bonds) between monomers or residues. My work focuses on merging CT with braid theory, which describes entanglement between chains rather than any bonded interaction. This can be used to study structural phase transitions in semiflexible polymer bundles as well as coil-to-globule transitions in LCST homopolymers with explicit solvents, and to determine chirality in these systems.
Active polymers
Analysis of interacting run-and-tumble particles to characterize deviations from Gaussian motion. Combines an exactly solvable polymer model with lattice simulations to study anomalous diffusion and non-Gaussian displacement distributions arising from the dynamically evolving particle environment
Energetics of pulled knots
When a polymer is stretched by exerting a force, it transitions between two non-equilibrium steady states, and its energetics can be naturally described by the fluctuation relations of Jarzynski and Crooks. My work studies such pulled polymers with embedded knots and how their energetics differ when a solvent is present.