{"id":41,"date":"2025-04-04T15:38:12","date_gmt":"2025-04-04T19:38:12","guid":{"rendered":"https:\/\/sites.nd.edu\/ondrej-maxian\/?page_id=41"},"modified":"2025-08-29T10:46:00","modified_gmt":"2025-08-29T14:46:00","slug":"research","status":"publish","type":"page","link":"https:\/\/sites.nd.edu\/ondrej-maxian\/research\/","title":{"rendered":"Research"},"content":{"rendered":"\n

Our group works on problems where we can make a contribution to both<\/em> computational mathematics and cell biology.<\/p>\n\n\n\n

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As the quantitative biologist Wallace Marshall once asked me: “What’s in it for the mathematicians?”<\/p>\n<\/blockquote>\n\n\n\n

With this in mind, our research has a dual-track focus. In biology, we are using modeling and simulation to understand self-organization in the actin cytoskeleton.<\/strong> On the mathematical side, we are developing new numerical methods to simulate cytoskeletal mechanics and biochemistry. <\/strong>See the links at left for specific projects.<\/p>\n\n\n\n

What biology are we studying?<\/strong><\/p>\n\n\n\n

Composed of\u00a0actin filaments, cross linkers, and\u00a0myosin motors, the actin cytoskeleton\u00a0generates and sustains mechanical forces capable of dividing, polarizing, and moving the cell, thus shaping\u00a0embryonic development, cancer cell metastasis, and wound healing.\u00a0Regulation of the cytoskeleton\u00a0is often viewed in a \u201clinear\u201d manner, where steps in a signaling cascade yield a network with the organization necessary for the task at hand. Recent\u00a0evidence, however, has\u00a0demonstrated\u00a0that cytoskeletal organization actually emerges from a complex microscopic interplay between actin assembly, myosin-induced contractility, and activator-inhibitor coupling of actin with its regulators.\u00a0A fundamental question is how the cell manipulates these molecular-scale interactions to turn the cytoskeleton into\u00a0a semi-autonomous machine, able to sense and correct mistakes, adapt to new surroundings, and process information from its environment.<\/p>\n\n\n\n

The primary component of the cytoskeleton is actin filaments, inextensible fluctuating fibers which organize into linear and branched architectures. The images below show simulation actin filaments, in vitro<\/em> branched structures, and in vivo<\/em> architectures in the C. elegans<\/em> embryo.<\/p>\n\n\n

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Actin filaments in silico<\/em>, in vitro<\/em> (S. Yde, Kovar lab), and in vivo<\/em> in C. elegans<\/em> (R. Kadzik, Munro lab)<\/figcaption><\/figure>\n<\/div>\n\n\n

<\/p>\n\n\n\n

We are working with experimentalists in the Munro<\/a>, Kovar<\/a>, and Bement<\/a> labs to study how filaments self-organize on the cell scale through interactions on the molecular scale. <\/p>\n\n\n\n

What “new math” are we developing?<\/strong><\/p>\n\n\n\n

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.<\/p>\n\n\n\n

Representative publications<\/strong><\/p>\n\n\n\n

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  1. Maxian O., Dinner A., and Munro E. (2025). Actin network heterogeneity tunes activator-inhibitor dynamics at the cell cortex<\/a>. (Under review). <\/li>\n\n\n\n
  2. Maxian, O., & Donev, A. (2024). A simulation platform for slender, semiflexible, and inextensible fibers with Brownian hydrodynamics and steric repulsion.<\/a> Physics of Fluids<\/em>, 36<\/em>(12).<\/li>\n\n\n\n
  3. Maxian, O., Pel\u00e1ez, R. P., Mogilner, A., & Donev, A. (2021). Simulations of dynamically cross-linked actin networks: morphology, rheology, and hydrodynamic interactions<\/a>. PLoS computational biology<\/em>, 17<\/em>(12), e1009240

    <\/li>\n<\/ol>\n\n\n\n

    <\/p>\n","protected":false},"excerpt":{"rendered":"

    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 using modeling and simulation to understand self-organization in […]<\/p>\n","protected":false},"author":5019,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-41","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/sites.nd.edu\/ondrej-maxian\/wp-json\/wp\/v2\/pages\/41","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sites.nd.edu\/ondrej-maxian\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/sites.nd.edu\/ondrej-maxian\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/sites.nd.edu\/ondrej-maxian\/wp-json\/wp\/v2\/users\/5019"}],"replies":[{"embeddable":true,"href":"https:\/\/sites.nd.edu\/ondrej-maxian\/wp-json\/wp\/v2\/comments?post=41"}],"version-history":[{"count":33,"href":"https:\/\/sites.nd.edu\/ondrej-maxian\/wp-json\/wp\/v2\/pages\/41\/revisions"}],"predecessor-version":[{"id":205,"href":"https:\/\/sites.nd.edu\/ondrej-maxian\/wp-json\/wp\/v2\/pages\/41\/revisions\/205"}],"wp:attachment":[{"href":"https:\/\/sites.nd.edu\/ondrej-maxian\/wp-json\/wp\/v2\/media?parent=41"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}