Rastko Sknepnek

The mammalian cornea constantly regenerates its outer epithelial layer. Cells lost by abrasion are replaced by division of both corneal epithelial cells and stem cell populations around the corneal periphery, the limbus. Limbal-derived epithelial cells migrate into the cornea, maintaining equal rates of cell loss and replacement (the ‘XYZ hypothesis’). This process produces a striking stable spiral cell motion pattern across the corneal surface, with a central vortex. Here, we show that this spiral pattern can be explained by the interplay of limbus position, cell division, extrusion, and collective cell migration along the curved corneal surface. Using dissected LacZ mosaic murine corneas, we inferred the surface flow field by following stripe edges, revealing a tightening spiral. To explain these flow fields, we developed a cell-level in silico model treating corneal epithelial cells as soft, self-propelled particles with density-dependent proliferation and extrusion rates, and noisy alignment of migration direction. Even without global guidance cues, the model predicted stripes and spirals closely recapitulating experiment. A complementary continuum description generalised the XYZ hypothesis. Spiral formation was robust to curvature changes, but not topology, and sensitive to limbal stem cells and flocking alignment, showing how swarm physics on curved surfaces can explain tissue-scale biological processes.

Curvature plays a central role in the proper function of many biological processes. With active matter being a standard framework for understanding many aspects of the physics of life, it is natural to ask what effect curvature has on the collective behavior of active matter. In this paper, we use the classical theory of surfaces to explore the active motion of self-propelled agents confined to move on a smooth curved two-dimensional surface embedded in Euclidean space. Even without interactions and alignment, the motion is nontrivially affected by the presence of curvature, leading to effects akin, e.g., to gravitational lensing and tidal forces. Such effects can lead to intermittent trapping of particles and profoundly affect their flocking behavior. We show that these effects are governed by a geometric torque that, in the absence of noise and interactions, compels particles to move along geodesics.

The apicomedial actomyosin network is crucial for generating mechanical forces in cells. Oscillatory behavior of this contractile network is commonly observed before or during significant morphogenetic events. For instance, during the development of the Drosophila adult abdominal epidermis, larval epithelial cells (LECs) undergo pulsed contractions before being replaced by histoblasts. These contractions involve the formation of contracted regions of concentrated actin and myosin. The emergence and control of pulsed contractions are not fully understood. Here, we combined in vivo 4D microscopy with numerical simulations of an active elastomer model applied to realistic cell geometries and boundary conditions informed by cell polarity to study in vivo subcellular spatial patterns of LEC actomyosin dynamics. The active elastomer model quantitatively reproduced in vivo observations. When compared to rectangular domains, simulations on realistic cell geometries showed systematically better agreement with experiments. We found that cell shape, cell polarity, and organization of the cell’s actomyosin network codetermine spatiotemporal network dynamics both in vivo and in simulations. Furthermore, the model predicted changes to LEC contractile activity under genetic perturbation of the actomyosin network. Our results show that cell geometry, accompanied by boundary conditions which reflect the cells’ polarity, is important to understanding the dynamics of the apicomedial actomyosin network. Moreover, our findings support the notion that spatiotemporal oscillatory behavior of the actomyosin network is an emergent property of the actomyosin network, rather than driven by upstream signaling.

P -atic liquid crystal theories offer new perspectives on how cells self-organize and respond to mechanical cues. Understanding and quantifying the underlying orientational orders is, therefore, essential for unraveling the physical mechanisms that govern tissue dynamics. Due to the deformability of cells this requires quantifying their shape. We introduce rigorous mathematical tools and a reliable framework for such shape analysis. Applying this to segmented cells in MDCK monolayers and computational approaches for active vertex models and multiphase field models allows to demonstrate independence of shape measures and the presence of various p -atic orders at the same time. This challenges previous findings and opens new pathways for understanding the role of orientational symmetries and p -atic liquid crystal theories in tissue mechanics and development.

Curvature-guided organization of active filaments. Increasing geometrical constraints modulate curvature distribution, driving a transition from geodesic alignment and rotating bands to curvature-induced trapping in high-curvature necks.

P-atic liquid crystal theories offer new perspectives on how cells self-organize and respond to mechanical cues. Understanding and quantifying the underlying orientational orders is therefore essential for unraveling the physical mechanisms that govern tissue dynamics. Due to the deformability of cells this requires quantifying their shape. We introduce rigorous mathematical tools and a reliable framework for such shape analysis. Applying this to segmented cells in MDCK monolayers and computational approaches for active vertex models and multiphase field models allows to demonstrate independence of shape measures and the presence of various p-atic orders at the same time. This challenges previous findings and opens new pathways for understanding the role of orientational symmetries and p-atic liquid crystal theories in tissue mechanics and development.

Curvature plays a central organizational role in active polymer dynamics. Using large-scale Langevin-dynamics simulations, we study active semiflexible filaments confined to smooth curved surfaces and map how curvature, bending rigidity, and activity interact. We find geodesic alignment, curvature lensing, and curvature-induced trapping. In particular, regions of negative Gaussian curvature localize filaments and hinder global surface exploration. These results show how surface geometry can be used to control the organization and transport of active matter on curved substrates

Machine learning (ML) strategies are opening the door to faster computer simulations, allowing us to simulate more realistic colloidal systems. Since the interactions in colloidal systems are often highly many-body, stemming from, e.g., depletion and steric interactions, one of the challenges for these algorithms is capturing the many-body nature of these interactions. In this paper, we introduce a new ML-based strategy for fitting many-body interactions in colloidal systems where the many-body interaction is highly local. To this end, we develop Voronoi-based descriptors for capturing the local environment and fit the effective potential using a simple neural network. To test this algorithm, we consider a simple two-dimensional model for a colloid-polymer mixture, where the colloid–colloid interactions and colloid–polymer interactions are hard-disk like, while the polymers themselves interact as ideal gas particles. We find that a Voronoi-based description is sufficient to accurately capture the many-body nature of this system. Moreover, we find that the Pearson correlation function alone is insufficient to determine the predictive power of the network emphasizing the importance of additional metrics when assessing the quality of ML-based potentials.

Curvature plays a central role in the proper function of many biological processes. With active matter being a standard framework for understanding many aspects of the physics of life, it is natural to ask what effect curvature has on the collective behaviour of active matter. In this paper, we use the classical theory of surfaces to explore the active motion of self-propelled agents confined to move on a smooth curved two-dimensional surface embedded in Euclidean space. Even without interactions and alignment, the motion is non-trivially affected by the presence of curvature, leading to effects akin, e.g.\ to gravitational lensing and tidal forces. Such effects can lead to intermittent trapping of particles and profoundly affect their flocking behaviour.