Our group works on problems where we can make a contribution to both computational mathematics and cell biology.
As the quantitative biologist Wallace Marshall once asked me: “What’s in it for the mathematicians?”
With this in mind, our research has a dual-track focus. In biology, we are determining how the architecture and biochemistry of the cytoskeleton shape macroscopic cell dynamics. On the mathematical side, we are developing new computational tools to simulate cytoskeletal filaments. See the links at left for specific projects.
What biology are we studying?
Our group is interested in the actin cytoskeleton – a dynamic network of filaments, cross linking proteins, and molecular motors that gives the cell its structure and shape. Changes in cytoskeletal organization drive cell division, polarization, and migration, making them important for embryonic development, cancer cell metastasis, and wound healing.
The primary component of the cytoskeleton is actin filaments, which are inextensible fluctuating fibers that organize into linear and branched architectures. The images below provide a sample.
We are interested in how the biochemistry in the cytoskeleton signals the formation of new filamentous architectures, and how those architectures in turn shape the mechanics of the cell. We are working with experimentalists in the Munro, Kovar, and Bement labs to answer these questions.
What “new math” are we developing?
Actin networks present challenges for numerical methods. Filaments are slender and inextensible, cross linkers are stiff, and dynamics occur in a suspending fluid which immerses the filaments and moves them around. Broadly speaking, our numerical methods focus on Brownian motion under constraints (see [1] linked below). Recently, we have become more interested in coupling these kinds of simulations to experimental data through an inverse problem framework. See project links at left for more information.
Representative publications
- Maxian, O., & Donev, A. (2024). A simulation platform for slender, semiflexible, and inextensible fibers with Brownian hydrodynamics and steric repulsion. Physics of Fluids, 36(12).
- Maxian, O., Peláez, R. P., Mogilner, A., & Donev, A. (2021). Simulations of dynamically cross-linked actin networks: morphology, rheology, and hydrodynamic interactions. PLoS computational biology, 17(12), e1009240