CAREER: Entanglement of Active Polymers

NONTECHNICAL SUMMARY

This award supports theoretical, mathematical, and computational research, and education on active polymers which can drive biological function by exerting forces and changing their shape. Biological cells contain active polymers - long filamentous molecules - that can consume energy and change connectivity and architecture during the cell cycle. The PI aims to develop a method that can provide insight into the dynamic reorganization of such systems.

The PI aims to investigate whether the many-chain geometry and topology of these filaments in combination with active interconnections among polymers alone can describe key elements that account for the mechanics of active matter filaments in many contexts. This research examines this hypothesis using an approach that involves mathematical ideas from the field of topology and computer simulation to obtain results that can be compared to experiments.

The PI aims to use rigorous methods from mathematics to understand, model, and eventually control how polymer filaments entangle in active physical systems with biological applications. This project will lead to a better understanding of living matter and will advance the smart manufacturing of new soft glassy materials.

This project also supports outreach activities, including public talks, university outreach programs, and the Challenger STEM Center, which can present aspects of the research to a potentially wide audience. Software and simulation techniques developed through this project will be shared broadly with the community. Results will be presented by the PI and her students at interdisciplinary conferences, including those organized by the PI.

Additionally, the PI is strongly committed to broadening participation of underrepresented minorities and women in STEM; new courses will be developed to train interdisciplinary scientists in 21st-century mathematical tools. TECHNICAL SUMMARY

Active matter is used to classify a range of physical systems that are driven out of equilibrium by the presence of ''active'' constituents that exert forces by dissipating energy. Conventional polymer physics arguments provide limited understanding of the dynamic reorganization of such systems. A challenge in the field is to connect properties of isolated filaments to properties of a collection of filaments.

This relates to a big challenge in the field of entangled polymers, which is how to measure entanglement of open curves in 3-space. This project will use topology, modeling, and simulation to measure topological entanglement in active matter filaments and provide a new model for its mechanics. This research advances knowledge and breaks existing technical barriers (1) in topology by defining and studying the Jones polynomial of a collection of open curves in 3-space and in systems employing Periodic Boundary Conditions and (2) in understanding entanglement effects in materials science and biology, by providing a new model for the viscoelastic response of active matter filaments.

This work is aimed to lead to predictive modeling of the behavior of such systems with the possibility of controlling their functions by judicious selection of their chemical compositions and structures, for example, by changing the number of active cross-links or the type of cross-linking motifs.

This award is jointly funded through the Condensed Matter and Materials Theory Program in the Division of Materials Research, and the Topology and Mathematical Biology Programs in the Division of Mathematical Sciences.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.