MS05 - CDEV-06 Part 1 of 2

Modeling the Role of Geometry and Topology in Shaping Cell Behavior, Function, and Tissue Patterns (Part 1)

Wednesday, July 16 at 10:20am

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Note: this minisymposia has multiple sessions. The other session is: and Part-2.

Fabian Spill (University of Birmingham), Anotida Madzvamuse, University of British Columbia

Description:

Cell and tissue architecture, defined by both geometry and topology, plays a central role in determining cellular behavior and function. From the spatial organization of organelles to large-scale tissue patterns, structural constraints influence intracellular dynamics, mechanical properties, and signaling pathways. This minisymposium will highlight advances in mathematical and computational modeling that reveal how geometric and topological features govern processes such as cell polarization, migration, division, and tissue morphogenesis. Talks will explore approaches including reaction-diffusion systems, mechanical models, and network-based methods to infer functional outcomes from structural properties. By integrating theoretical frameworks with experimental data, this session aims to uncover fundamental principles linking form and function across scales, offering new insights into the physical basis of biological organization.

Alex Grigas

Syracuse University

"Modeling fluidity in stellate mesenchymal tissues"

In many developmental and disease processes, tissues shift from solid-like to fluid-like mechanical behavior to enable large-scale tissue flows. A key unresolved question is how different organisms regulate this transition by controlling cell-scale properties. In both zebrafish and chick, a fluid-to-solid transition occurs in the presomitic mesoderm, the driving force behind posterior body axis elongation. In zebrafish, this transition is well explained by a soft particle model that undergoes a jamming/unjamming transition, driven by small changes in global volume fraction and active fluctuations, without considering cell shape or deformation. However, the tissue architecture in chick is distinct from zebrafish, with large extracellular gaps and stellate cells with distinct arm junctions, indicating that even closely related species may have evolved different mechanisms to cross a fluid/solid transition. Here, we develop a computational model to understand the essential features needed to predict the unique properties of low density, but highly connected, stellate tissues, which tissue rounding experiments demonstrate are fluid-like on long timescale. We compare short-time retraction velocities and tissue relaxation due to laser ablation between experiment and simulation to determine whether the mesenchyme is under tension. Additionally, we propose novel glassy dynamics can be controlled not via density changes but instead by cell-cell adhesion unbinding kinetics coupled with contact inhibition of locomotion, and propose new experiments to test these ideas.

Sharon Minsuk

Indiana U., Bloomington

"The Role of Embryo, Tissue, and Cell Shape in Morphogenesis: Modeling the Cellular Dynamics of Tissue Deformation"

Morphogenesis of embryonic tissues involves complex and extreme deformations in response to intra- and intercellular forces; and is profoundly dependent on the geometry not only of the deforming tissue itself, but of the environment in which that tissue finds itself. Epiboly in zebrafish, the spreading of an epithelial sheet in response to external tension, to cover and engulf the rest of the spherical embryo, requires deformation of a shallow spherical cap into a full sphere, without tearing or buckling, accommodated by cell rearrangement as well as cell shape change. We built a computational model of epiboly. Rearrangement of mechanically coupled model cells is achieved by allowing those couplings to dynamically break and re-form; broken couplings in a tissue under tension risk tearing, which we prevent by adding a constraint on cell packing geometry. The straightening of the leading edge of the expanding tissue, as observed in living embryos, arises emergently and robustly from our model, and is associated with rapid cell rearrangement (tissue fluidization). Changes in cell shape and packing geometry have been implicated in promoting fluidization, suggesting they may play a role in facilitating both tissue deformation and edge straightening. I will briefly describe and demonstrate the model, with special emphasis on the interplay between embryo, tissue, and cell geometry, and the dynamics of morphological transformation.

Margherita De Marzio

Harvard Medical School and Brigham and Women’s Hospital

"Understanding the Role of Surface Curvature on Epithelial Plasticity"

To heal, remodel, or invade, the epithelial tissue transitions from a state that is sedentary and quiescent to one that is strikingly migratory and dynamic. This phenotypic switch is known as the epithelial unjamming transition (UJT). Previous theoretical models have characterized the UJT in flat epithelial layers. By contrast, the epithelium in vivo often resides on highly curved structures like pulmonary alveoli, airways, and intestines. How surface curvature, and the resulting topological defects and out-of-plane forces, impact epithelial plasticity remains poorly understood. In this talk, I will present our recent findings on the role of geometry on the migratory phenotype in vivo. Using a 2D spherical vertex model, we investigated the UJT within physiological ranges of cell density and surface curvature. I will show that increasing curvature promotes tissue fluidization and migration. At higher curvatures, cell rearrangements become energetically advantageous, leading to cellular configurations that are more malleable and migratory. I will demonstrate that this effect is not due to changes in the local mechanism of cell intercalation, which is independent of curvature. Instead, it stems from changes in the global structure of the cell-junction network, which becomes less tensed as curvature increases. Together, these results reveal curvature-induced unjamming as a novel mechanism of epithelial fluidization, offering insights into how surface geometry drives tissue malleability, remodeling, and stabilization.

Padmini Rangamani

UCSD

"Nanoscale curvature of the plasma membrane regulates mechanoadaptation through nuclear deformation and rupture"

Nuclear translocation of the transcription regulatory proteins YAP and TAZ is a critical readout of cellular mechanotransduction. Recent experiments have demonstrated that cells on substrates with well-defined nanotopographies demonstrate mechanoadaptation through a multitude of effects - increased integrin endocytosis as a function of nanopillar curvature, increased local actin assembly on nanopillars but decreased global cytoskeletal stiffness, and enhanced nuclear deformation. How do cells respond to local nanotopo-graphical cues and integrate their responses across multiple length scales? This question is addressed using a biophysical model that incorporates plasma membrane (PM) curvature-dependent endocytosis, PM curvature-sensitive actin assembly, and stretch-induced opening of nuclear pore complexes (NPCs) in the nuclear envelope (NE). This model recapitulates lower levels of global cytoskeletal assembly on nanopillar substrates, which can be partially compensated for by local actin assembly and NE indentation, leading to enhanced YAP/TAZ transport through stretched NPCs. Using cell shapes informed by electron micrographs and fluorescence images, the model predicts lamin A and F-actin localization around nanopillars, in good agreement with experimental measurements. Finally, simulations predict nuclear accumulation of YAP/TAZ following rupture of the NE and this is validated by experiments. Overall, this study indicates that nanotopography tunes mechanoadaptation through both positive and negative feedback on mechanotransduction.

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Annual Meeting for the Society for Mathematical Biology, 2025.