arXiv subjects

Matej Krajnc

Publications and source records attributed to Matej Krajnc.

11 recordsLinked to original sources

arXiv2026

Tissue-Intrinsic Shape Mechanics in Growing Pre-Migratory Tumor Spheroids

One of the hallmarks of pre-migratory tumors is the progressive loss of compact morphology. To investigate how tumors may intrinsically regulate their shape during growth, we employ a three-dimensional (3D) vertex model of multicellular aggregates that incorporates key structural features of tumor spheroids, including its surface, a proliferative rim, and a necrotic core. Focusing exclusively on tumor-intrinsic mechanical interactions, we examine how their collective effects guide morphological evolution en route to metastasis. We show that spheroids acquire lobulated morphologies through an interplay between differential tensions at the spheroid surface and the living-necrotic interface (LNI), together with differential growth within the proliferative rim. In addition, spheroid shapes can be substantially modulated by tissue rheological properties emerging from active, cell-scale forces. Our cell- and tissue-scale simulations of tumor morphologies are enabled by a computational framework that overcomes a major limitation of 3D vertex models - the lack of cell-division - by introducing a graph-based polyhedral-division algorithm within the Graph Vertex Model (GVM).

cond-mat.soft↗

arXiv2025

Reentrant Rigidity Transition in Planar Epithelia with Volume- and Area Elasticity

We find a reentrant columnar-to-squamous rigidity transition in 3D epithelia, governed by volume- and area elasticity. Our framework maps onto the classic 2D Area- and Perimeter-Elasticity model but, unlike its 2D counterpart, exhibits both softening and stiffening depending on the initial state. The phase diagram reveals floppy states with vanishing shear and in-plane bulk moduli, alongside a lateral-tension-driven discontinuous columnar-to-squamous transition. The critical behavior underlying the emergence of the reentrant transition belongs to the mean-field universality class.

cond-mat.soft↗

arXiv2025

Emergent epithelial elasticity governed by interfacial surface mechanics and substrate interaction

During the life of animals, epithelial tissues undergo extensive deformations--first to form organs during embryogensis and later to preserve integrity and function in adulthood. To what extent these deformations resemble that of non-living elastic materials is not well understood. We derive an elasticity theory of epithelia, supported by a thin layer of extracellular material and the stroma, in which the mechanics of individual cells are dominated by differential interfacial tensions stemming from cell cortical tension and adhesion. Upon coarse-graining a discrete single-cell-level mechanics model, we obtain a harmonic deformation energy and derive the critical conditions for the elastic instability, where an initially flat tissue either buckles out of plane or forms wrinkles. Due to the distinct origin of elasticity, the scaling of the critical load to induce an instability and the wrinkling wavelength with layer thickness is fundamentally different than in solid plates. The theory also naturally describes reversal of the groove-to-crest thickness-modulation phase--a recently observed epithelial shape feature which cannot be explained by the classical elasticity theory. Our work provides a guideline for understanding the relative role of cell surface tensions and the interaction of tissues with substrates during epithelial morphogenesis.

cond-mat.soft↗

arXiv2024

Graph topological transformations in space-filling cell aggregates

Cell rearrangements are fundamental mechanisms driving large-scale deformations of living tissues. In three-dimensional (3D) space-filling cell aggregates, cells rearrange through local topological transitions of the network of cell-cell interfaces, which is most conveniently described by the vertex model. Since these transitions are not yet mathematically properly formulated, the 3D vertex model is generally difficult to implement. The few existing implementations rely on highly customized and complex software-engineering solutions, which cannot be transparently delineated and are thus mostly non-reproducible. To solve this outstanding problem, we propose a reformulation of the vertex model. Our approach, called Graph Vertex Model (GVM), is based on storing the topology of the cell network into a knowledge graph with a particular data structure that allows performing cell-rearrangement events by simple graph transformations. Importantly, when these same transformations are applied to a two-dimensional (2D) polygonal cell aggregate, they reduce to a well-known T1 transition, thereby generalizing cell-rearrangements in 2D and 3D space-filling packings. This result suggests that the GVM's graph data structure may be the most natural representation of cell aggregates and tissues. We also develop a Python package that implements GVM, relying on a graph-database-management framework Neo4j. We use this package to characterize an order-disorder transition in 3D cell aggregates, driven by active noise and we find aggregates undergoing efficient ordering close to the transition point. In all, our work showcases knowledge graphs as particularly suitable data models for structured storage, analysis, and manipulation of tissue data.

cond-mat.soft↗

arXiv2024

Basolateral mechanics prevents rigidity transition in epithelial monolayers

The mechanics of epithelial tissues, which is governed by forces generated in various cell domains, is often investigated using two-dimensional models that account for the apically-positioned actomyosin structures but neglect basolateral mechanics. We employ a more detailed three-dimensional model to study how lateral surface tensions affect the structure and rigidity of such tissues. We find that cells are apicobasally asymmetric, with one side appearing more ordered than the other depending on cell target perimeter. In contrast to the 2D model, which predicts a rigidity transition at large target perimeters, tissues in the 3D model remain solid-like across all parameter space.

cond-mat.soft↗

arXiv2023

Wrinkling instability in unsupported epithelial sheets

We investigate the elasticity of unsupported epithelial monolayer and we discover that unlike a thin solid plate, which wrinkles if geometrically incompatible with the underlying substrate, the epithelium may do so even in absence of the substrate. From a cell-based model, we derive an exact elasticity theory and discover wrinkling driven by the differential apico-basal surface tension. Our theory can be mapped onto that for solid plates by introducing a phantom substrate whose stiffness is finite beyond a critical differential tension. This suggests a new mechanism for an autonomous control of tissues over the length scale of their surface patterns.

cond-mat.soft↗

arXiv2021

Active instability and nonlinear dynamics of cell-cell junctions

Active cell-junction remodeling is important for tissue morphogenesis, yet its underlying physics is not understood. We study a mechanical model that describes junctions as dynamic active force dipoles. Their instability can trigger cell intercalations by a critical collapse. Nonlinearities in tissue's elastic response can stabilize the collapse either by a limit cycle or condensation of junction lengths at cusps of the energy landscape. Furthermore, active junction networks undergo collective instability to drive active in-plane ordering or develop a limit cycle of collective oscillations, which extends over regions of the energy landscape corresponding to distinct network topologies.

cond-mat.soft↗

arXiv2021

Morphologies of compressed active epithelial monolayers

Using a three-dimensional active vertex model, we numerically study the shapes of strained unsupported epithelial monolayers subject to active junctional noise due to stochastic binding and unbinding of myosin. We find that while uniaxial, biaxial, and isotropic in-plane compressive strains do lead to the formation of longitudinal, herringbone-pattern, and labyrinthine folds, respectively, the villus morphology characteristic of, e.g., the small intestine appears only if junctional tension fluctuations are strong enough to fluidize the tissue. Moreover, the fluidized epithelium features villi even in absence of compressive strain provided that the apico-basal differential tension is large enough. We analyze several details of the different epithelial forms including the role of strain rate and the modulation of tissue thickness across folds. Our results show that nontrivial morphologies can form even in unsupported, non-patterned epithelia.

cond-mat.soft↗

arXiv2020

Elasticity, stability, and quasi-oscillations of cell-cell junctions in solid confluent epithelia

Macroscopic properties and shapes of biological tissues depend on the remodelling of cell-cell junctions at the microscopic scale. We propose a theoretical framework that couples a vertex model of solid confluent tissues with the dynamics describing generation of local force dipoles in the junctional actomyosin. Depending on the myosin-turnover rate, junctions either preserve stable length or collapse to initiate cell rearrangements. We find that noise can amplify and sustain transient oscillations to the fixed point, giving rise to quasi-periodic junctional dynamics. We also discover that junctional stability is affected by cell arrangements and junctional rest tensions, which may explain junctional collapse during convergence and extension in embryos.

cond-mat.soft↗

arXiv2020

Collective Cell Mechanics of Small-Organoid Morphologies

The study of organoids, artificially grown cell aggregates with the functionality and small-scale anatomy of real organs, is one of the most active areas of research in biology and biophysics, yet the basic physical origins of their different morphologies remain poorly understood. Here we propose a mechanistic theory of small-organoid morphologies. Using a 3D surface-tension-based vertex model, we reproduce the characteristic shapes, ranging from branched and budded structures to invaginated shapes. We find that the formation of branched morphologies relies strongly on junctional activity, enabling temporary aggregations of topological defects in cell packing. To elucidate our numerical results, we develop an effective elasticity theory, which allows one to estimate the apico-basal polarity from the organoid-scale modulation of cell height. Our work provides a generic interpretation of the observed small-organoid morphologies, highlighting the role of physical factors such as the differential surface tension, cell rearrangements, and tissue growth.

physics.bio-ph↗

arXiv2018

Fluidization of epithelial sheets by active cell rearrangements

We theoretically explore fluidization of epithelial tissues by active T1 neighbor exchanges. We show that the geometry of cell-cell junctions encodes important information about the local features of the energy landscape, which we support by an elastic theory of T1 transformations. Using a 3D vertex model, we show that the degree of active noise driving forced cell rearrangements governs the stress-relaxation time-scale of the tissue. We study tissue response to in-plane shear at different time scales. At short time, the tissue behaves as a solid, whereas its long-time fluid behavior can be associated with an effective viscosity which scales with the rate of active T1 transformations. Furthermore, we develop a coarse-grained theory, where we treat the tissue as an active fluid and confirm the results of the vertex model. The impact of cell rearrangements on tissue shape is illustrated by studying axial compression of an epithelial tube.

cond-mat.soft↗