MS08 - CDEV-07

Modeling cell migration at multiple scales (Part 2)

Friday, July 18 at 10:20am

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Note: this minisymposia has multiple sessions. The other session is: and Part-1.

Jared Barber (Indiana University Indianapolis), Luoding Zhu

Description:

Cell migration is inarguably an important process as it plays a major role in embryo development, inflammation, cancer metastasis, wound healing, and other processes. It is an inherently complex multi-scale process. While most molecular parts and corresponding processes involved in cell migration are well-characterized, it is not yet clear how such parts and processes connect and interact in order to produce the migratory motion that we typically see. For this reason, research on cell migration has continued with mathematical modeling yielding major contributions on the way. To explore how part/process interactions affect migration at multiple scales, we have invited speakers to share their work with talks that use mathematical models to explore important factors for cell migration including factors on the subcellular, cellular, and collective migration scales.

Anotida Madzvamuse

University of British Columbia

"A geometric bulk-surface PDE approach for modelling single and collective cell migration"

In this talk, I will present a geometric bulk-surface PDE approach for modelling single cell migration. First, I will discuss a geometric-surface PDE approach where cell migration is described by a force balance equation posed only on the cell plasma membrane, under a sharp interface formulation. The evolution law for the cell plasma membrane is discribed through forces acting at each material point, in the normal direction. These forces include (but are not limited to): actomyosin forces for cell polarisation, driven by molecular species resident on the plasma membrane and these obey a surface reaction-diffusion system; forces describing the energetic nature of the plasma membrane (e.g. surface tension, bending energy, etc); forces associated with volume constraint and external forces (including cell-to-cell interactions, cell-to-obstacle interactions), and so forth. By introducing bulk dynamics associated with the bulk-surface wave-pinning model, we will demonstrate the generalisation to a geometric bulk-surface modelling approach. To support the modelling approach, numerical examples will be exhibited based on evolving bulk-surface finite elements to model single and collective cell migration through stationary and deformable extracellular matrices as well as cell migration through confined spaces, reminiscent of microfluidic devices.

Jared Barber

Indiana University Indianapolis

"Admissible behaviors for a model of actin filaments pushing the cell forward"

During cell migration across a 2D surface, cells develop a flat protrusive structure called a lamellipodium (“sheet-like foot”). Actin (protein) filaments form inside of this structure and push at the leading edge of the cell in order to propel the cell forward. While there are various complexities associated in this process, in this talk, we explore a simple version of the “Filament-Based Lamellipodium Model (FBLM)”. In this version, filaments are represented by multiple line segments that are relatively short, parallel to each other, and perpendicular to the front of the cell/lamellipodium. The model includes frictional forces as well as forces that tend to keep the filaments approximately equally spaced from each other, the front of the cell, and the side of the lamellipodium. Such forces are derived by defining corresponding energies and then using variational techniques. We study this system near equilibrium to better understand what solutions are admissible and share numerical representations of such solutions. Such information informs us about the variation that may arise when actin filament networks act to push forward the lamellipodium during cell migration.

Jianda Du

University of Florida

"Effect of Curvature in a Cell Migration Model"

Cell migration is essential for processes such as tissue development, wound healing, and cancer metastasis. For instance, during gastrulation—an early stage of embryonic development—cell migration is crucial for the formation of germ layers that eventually develop into tissues and organs. We extend a previously established continuum mechanical model of cell migration by introducing curvature as a key factor. We investigate how curvature influences cell migration in spreading embryonic tissues of two species: the aquatic frog Xenopus laevis and the axolotl salamander Ambystoma mexicanum. Simulations are conducted with various initial tissue shapes to assess the impact of curvature. Sensitivity analysis and approximate Bayesian computation with sequential Monte Carlo (ABC-SMC) are used to evaluate the importance of incorporating curvature and to additionally determine the form of curvature dependence that best reflects the experimental data.

David Odde

University of Minnesota

"Modeling the mechanics of glioblastoma progression and treatment."

Effector CD8+ T cells must make cell-to-cell contacts (TCR-MHC-antigenic-peptide-complex) to identify and eliminate cancer cells selectively. This requirement could become a make-or-break factor in the clearance of solid tumors such as glioma, which we focus on in this study, where T cells have to actively search for the cancer cells in the tissue. Several immunotherapies, such as checkpoint blockade and adoptive T cell therapy, have been proposed; however, all of these essentially aim to make T cells better killers, not migrators. In this study, we recognize an equally important factor crucial for their success, i.e., their migration in the tissue. T cells have been assumed to be optimal navigators based on evolutionary reasons, an idea we challenge in this study. Using a combination of ex vivo brain tissue and in vitro assays, we found that T cells, on average, migrated slower than reported in the literature (0.5-2 μm/min, 0.1-1 μm/min vs 6-10 μm/min, 10-30 μm/min) and only modestly faster than cancer cells in a similar setting (0.1-0.2 μm/min), suggesting the need for improvement for effective immune response and immunotherapy. Strikingly, for T cells, the best description was not a single, homogeneous population of superdiffusive walks as previously found but a mix of comparable numbers of sub, normal, and superdiffusive walks, especially at longer time scales. This heterogeneity is advantageous for finding targets of a range of sizes but worse than the single superdiffusive population for finding a fixed target such as a glioma. We investigated the reason for such slow migration. Our T cells, consistent with previous studies, showed evidence of a 'stop-and-go' pattern. We found that hyper adhesive interactions with the perivascular space of blood vessels, the entry point of T cells into the brain, microglia, a major antigen-presenting cell in the brain, and hyaluronic acid, a major ECM protein in the brain, all could explain many, but not all, of the 'stops”. Reducing these 'stops' could increase net T cell migration, potentially an improvement enough to stop the inevitable GBM recurrence under current standard therapy regimens. Next, we used drug-perturbation experiments and high-resolution imaging to unravel the biomechanics of CD8+ T cell migration. We discovered that these T cells are capable of using multiple modes, highlighting their adaptive nature, but often use the familiar motor-clutch mode of cell migration usually reported for cancer cells, but with altered, faster protrusion and focal-adhesion dynamics. To capture these dynamics we developed a momentum-conserving model for hybrid bleb-adhesion-based rapid T cell migration. Together, these results advance our fundamental understanding of T cell migration in the brain, which may inspire better immunotherapies in the future that are focused on making T cells both powerful killers and adept at rapidly locating target cancer cells.

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Annual Meeting for the Society for Mathematical Biology, 2025.