Computational and Theoretical Modeling of Active Nematics in 3D and Under Confinement

Brandeis University, Waltham MA

Investigators

Abstract

NONTECHNICAL SUMMARY This award supports theoretical and computational modeling of active materials and related educational activities. Active materials are made from components that can use energy from their local environment to propel themselves. This capability enables active materials to have properties which are not possible in traditional materials. Examples of naturally occurring active materials are found within biological cells, and these materials enable cells to perform functions such as moving, replicating themselves, and healing of wounds. Recent experimental advances are now making it possible to construct artificial active materials, that potentially could have similar capabilities. However, the current theoretical understanding of active materials is incomplete. Improving this theory will guide the design of novel artificial materials, and will help to understand biological processes such as organismal development, cell motility, and cancer growth. This award will support research aimed at making progress towards such a theory. The PI will develop theoretical and computational models for a recently developed experimental artificial active material made from biological filaments and molecular motor proteins. The models will describe how the system behaves when it is confined in a variety of geometries, such as within channels or spherical droplets. The accuracy of the theoretical and computational models will be assessed by testing model predictions against data from experiments in the same confinement geometries. Goals of the research include understanding how the individual components of an active material work collectively to enable behaviors such as large-scale motions, and how propulsion affects the structural order of the system. The supported research will provide valuable science, technology, engineering, and mathematical (STEM) training for undergraduate and graduate students at the interface between mathematical methods and theoretical and experimental soft matter physics. Research activities include training programs that are designed to engage diverse students in computational research, and to provide instruction in scientific communication to specialized and non-specialized audiences. The award also supports public outreach programs that use the spectacular visual effects that arise in active matter simulations and experiments to excite the interest of lay audiences in scientific research. TECHNICAL SUMMARY This award supports theoretical and computational modeling of active materials and related educational activities. Active matter describes intrinsically non-equilibrium materials whose constituent elements consume energy to generate forces and motion. For example, the consumption of ATP by molecules within a biological cell enables it to perform diverse functions such as motion, replication, and self-healing. It is now possible to construct artificial active materials from biomolecules or synthetic colloids which have a similar capability to convert energy to motion. These building blocks could enable a new class of soft materials, with functionalities currently found only in biological organisms. However, the current theoretical understanding of active matter is far from complete. Developing such a theory is crucial to enable rational design of novel artificial active materials, and would elucidate biological processes such as organismal development, cell motility, and cancer growth, and would enable rational design of novel artificial active materials. This award will support research aimed at progressing toward such a theory, by developing theoretical and computational models motivated by a model active material developed by experimental collaborators - a three-dimensional (3D) "active nematic" constructed from a suspension of microtubules and motor proteins. The PI will develop continuum hydrodynamic models of 3D active nematics, and use recently developed numerical methods to solve them in a variety of confinement geometries. The continuum models will be linked to particle-based simulations that probe how energy generated at the particle scale dissipates into larger scale modes. A particular focus of the research will be elucidating the structure of topological defects in 3D, and how they power emergent dynamics. Model predictions will be extensively tested against the experimental 3D active nematics system. The research will build on the current theoretical understanding of active matter by overcoming the following limitations: (1) Most real-world applications require 3D materials, but to date almost all controllable experimental active systems have been 2D or quasi-2D. Thus, the current theoretical understanding of active matter is largely limited to 2D. (2) While boundaries can usually be neglected in an equilibrium theory, they have profound, long-ranged effects on active matter. Thus, models for active matter must treat boundaries explicitly and with appropriate boundary conditions. (3) Energy input at the particle scale in an active system cascades continuously to larger scales, making it difficult to identify a separation of scales that can be exploited to simplify theoretical descriptions. Thus, models that link the microscale force generation units to large-scale descriptions of collective behaviors are needed. The supported research will provide valuable science, technology, engineering, and mathematical (STEM) training for undergraduate and graduate students at the interface between mathematical methods and theoretical and experimental soft matter physics. Research activities include training programs that are designed to engage diverse students in computational research, and to provide instruction in scientific communication to specialized and non-specialized audiences. The award also supports public outreach programs that use the spectacular visual effects that arise in active matter simulations and experiments to excite the interest of lay audiences in scientific research. 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.