MS08 - CDEV-07 Part 2 of 2

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.

Shubhadeep Sadhukhan

Weizmann Institute of Science

"Modelling how lamellipodia-driven cells maintain persistent migration and interact with external barriers"

Cell motility is fundamental to many biological processes, and cells exhibit a variety of migration patterns. Many motile cell types follow a universal law that connects their speed and persistency, a property that can originate from the intracellular transport of polarity cues due to the global actin retrograde flow. This mechanism was termed the ``Universal Coupling between cell Speed and Persistency'(UCSP). Here we implemented a simplified version of the UCSP mechanism in a coarse-grained ``minimal-cell' model, which is composed of a three-dimensional vesicle that contains curved active proteins. This model spontaneously forms a lamellipodia-like motile cell shape, which is however sensitive and can depolarize into a non-motile form due to random fluctuations or when interacting with external obstacles. The UCSP implementation introduces long-range inhibition, which stabilizes the motile phenotype. This allows our model to describe the robust polarity observed in cells and explain a large variety of cellular dynamics, such as the relation between cell speed and aspect ratio, cell-barrier scattering, and cellular oscillations in different types of geometric confinements.

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Annual Meeting for the Society for Mathematical Biology, 2025.