The European Physical Journal E

Mechanical properties of epithelial tissues play essential roles in morphogenesis and physiological function. In this study, we analytically derived the in-plane bulk modulus, shear modulus, and Poissons ratio of a three-dimensional cell vertex model of epithelial monolayers. We showed that the model can robustly reproduce a near-zero in-plane Poissons ratio, a mechanical feature reported in cultured epithelial tissues. Numerical simulations further confirmed that the theoretically predicted Poissons ratio accurately describes the response of the model under finite, biologically relevant strains. In addition, the model exhibits not only morphological bistability between squamous-like and columnar-like states, but also mechanical bistability characterized by distinct elastic responses. Together, these results provide a minimal three-dimensional framework that links cell-scale mechanical interactions and epithelial morphology to tissue-scale elastic properties.

Understanding how cells migrate through confined environments is crucial for elucidating fundamental biological processes, including cancer invasion, immune surveillance, and tissue morphogenesis. The nucleus, as the largest and stiffest cellular organelle, often limits cellular deformability, making it a key factor in migration through narrow pores or highly constrained spaces. In this work, we introduce a geometric surface partial differential equation (GS-PDE) model in which the cell plasma membrane and nuclear envelope are described as evolving energetic closed surfaces governed by force-balance equations. We replicate the results of a biophysical experiment, in which a microfluidic device is used to impose compressive stresses on cells by driving them through narrow microchannels under a controlled pressure gradient. The model is validated by reproducing cell entry into the microchannels. A parametric sensitivity analysis highlights the dominant influence of specific parameters, whose accurate estimation is essential to faithfully capture the experimental setup. We found that surface tension and confinement geometry emerge as key determinants of translocation efficiency. Although tailored to this specific setup for validation purposes, the framework is sufficiently general to be applied to a broad range of cell mechanics scenarios, providing a robust and flexible tool for investigating the interplay between cell mechanics and confinement. It also offers a solid foundation for future extensions integrating more complex biochemical processes such as active confined migration. Author summaryCells often migrate through very narrow spaces in tissues, a process critical for cancer invasion, immune surveillance, and tissue development. In particular, the stiffness of the nucleus, the largest and most rigid organelle, can limit migration through tight pores. In this study, we present a mathematical model describing the motion of a cell and its nucleus through a microchannel during cell translocation, using a geometric formulation based on surface partial differential equations. The model is general and applicable to a variety of scenarios involving confined cell transport. The model is validated by reproducing key experiments on cell translocation through narrow microchannels. The framework incorporates essential surface features, including mechanical responses, bending rigidity, and surface tension. Sensitivity analysis highlights surface tension and channel geometry as the parameters that most strongly influence translocation. Overall, the model provides new insights into the mechanics of confined cell transport, grants access to cellular quantities that are difficult to measure experimentally, such as cell and nucleus areas, perimeters, and stresses, and establishes a foundation for future extensions incorporating more complex biochemical processes.

Colorectal cancer (CRC) is the second most common cause of cancer-related mortality. At the molecular level, CRC is associated with genetic mutations and epigenetic modifications that dysregulate various signaling networks. From the biophysical viewpoint, invasive and metastatic cell migration need to be empowered by mechanical forces. In this study, we analyze the dynamic deformation of patient-derived CRC organoids in Fourier space and demonstrate how organoids with protooncogene BRAF mutation exhibit deformation phenotypes at an early stage. The organoids with BRAFmut have significantly lower elasticity and higher viscosity than those with BRAFWT, which mathematically indicated as the weakening of cell-cell adhesion. Immunohistochemical images, qRT-PCR, and TCGA data analysis confirm the downregulation of E-cadherin (CDH1) in BRAFmut organoids as well as in BRAFmut CRC, suggesting that the decrease in cell-cell adhesion in BRAFmut CRC facilitates invasive and metastatic migration. Notably, the recovery of CDH1 expression by pharmacological inhibition of DNA methylation can quantitatively be detected as the change in mechanical properties, suggesting that the complementary combination of dynamic phenotyping, mathematical modelling, and molecular-level analyses has a potential to unravel the mechanistic causality of the critical gene mutation and CRCs prognosis and the response to therapeutic interventions.

Methods to visualize and quantify the molecular responses of cells to local forces exerted at adhesions are crucial to elucidate how physical forces control cellular behavior. Of the many proteins involved in focal adhesions, vinculin plays a key role in mediating force-sensitive processes. Here, we combined optical tweezers and Forster resonance energy transfer (FRET) microscopy to measure the intensity and FRET efficiency of the vinculin tension sensor, VinTS, in response to a force. Fibroblasts expressing VinTS formed adhesions on fibronectin-coated, 3m-diameter, polystyrene beads. As the beads were displaced by the cell, we applied an optical trap to counteract this movement and increase the traction force required by the cell to maintain the bead displacement. The optical trap stiffness varied from zero (no laser) up to 0.26 pN/nm. In this range, the median bead displacement after 5 min was ~200nm in all trapping conditions inducing counteracting forces in the 10-100pN range. To maintain this displacement, vinculin recruitment increased (up to 35% in relative intensity at high stiffness) while tension increased but more moderately (1-2% decrease in absolute FRET efficiency). For higher trap stiffness, the main response was an increase in vinculin recruitment, while the tension did not increase significantly. The increase in vinculin intensity was correlated with the decrease in FRET efficiency at 0.26 pN/nm but not at lower stiffness. Thus, the presence of the high stiffness optical trap over 5 min appears to induce a positive correlation between vinculin recruitment and vinculin tension. In a few instances, vinculin puncta migrated a few microns away from the bead exceeding the bead movement speed while experiencing an increase in both vinculin intensity and tension. Taken together, the results suggest that combining an optical trap with vinculin tension measurements uncovers novel vinculin dynamics in the presence of a force.

It is an essential element of mechanobiology to measure the forces of biological cells. In microparticle traction force microscopy, they are inferred from the deformation of elastic microparticles. Two complementary variants have been introduced before: the volume method, which reconstructs surface stresses from the displacements of fiducial markers embedded inside the particles, and the surface method, which infers stresses directly from the deformation of the particle surface. However, a systematic comparison of the two methods has been lacking. Here, we quantitatively compare both approaches using simulated traction fields representing biologically relevant loading scenarios. We find that the surface method consistently reconstructs traction profiles with substantially lower errors than the volume method, which suffers from displacement tracking and stress calculation at the surface. At high noise levels, however, the performance gap becomes smaller. To compare the performance of the two methods in a realistic experimental setting, we developed DNA-based hydrogel microparticles equipped with both fluorescent surface labels and embedded fluorescent nanoparticles, enabling the direct comparison of the two methods within the same system. Compression experiments produced traction profiles consistent with Hertzian contact mechanics and confirmed the trends observed in the simulations. While our computational workflow establishes a framework to apply both methods, our experimental workflow establishes DNA microparticles as versatile and biocompatible probes for measuring cellular forces.

Cells are mechanosensitive, responding to external mechanical stimulation. Nanovibrational stimulation has been shown to enhance cell contractility and actin stress fibre formation. These changes in morphology occur quickly, alongside associated mechanical changes. Here, the relationship between acute morphological and mechanical changes in NIH 3T3 fibroblastic cells in response to nanovibrational stimulation is presented. A 1 kHz, 30 nm vibration is applied continuously for 72 hours. Atomic force microscopy (AFM) quantifies mechanical properties of the nucleus and cytoplasm at multiple timepoints, while immunofluorescence tracks morphological changes. Within 3 hours of stimulation, both nuclear and cytoplasmic stiffness increase significantly, accompanied by a decrease in the cellular fluid exponent, suggesting a shift of the cell towards more solid-like behaviour. These changes correlate with increased nuclear area. Actin polymerisation also increases within 24 hours, although variably. To understand the role of the cytoskeleton, actin polymerisation and contraction are inhibited using cytochalasin D and blebbistatin. Results show that inhibition prevents stiffness increases and results in a higher fluid exponent, indicating a more fluid-like state. These findings demonstrate that actin-myosin dynamics mediate cell stiffening under nanovibrational stimulation. Interestingly, prolonged stimulation appears to reverse this effect, suggesting that temporal optimisation of stimulation may enhance long-term mechanotransducive responses.

1Nuclear envelope stretch and rupture are common to cell spreading and migration in a variety of microenvironments, leading to marked changes in nucleocytoplasmic transport. Predicting cell response to different mechanochemical cues that are transmitted to the nucleus remains an open problem in the field of mechanomedicine. We developed a predictive modeling framework to examine how nuclear deformation on substrates with different nanotopographies influences nucleocytoplasmic transport and rearrangement of the nuclear lamina. Using the finite element method, we simulated nuclear compression by the perinuclear actin cap on substrates with arrays of nanopillars, modeling the nuclear envelope as a nonlinear elastic structure and coupling deformations to a biochemical model of lamin remodeling and nucleocytoplasmic transport. These simulations predicted regions of high nuclear envelope stretch adjacent to cell-nanopillar contacts, leading to maximized nuclear envelope tension on small nanopillars spaced by 4-5 microns. We then considered the effects on nuclear transport of YAP and TAZ and found that increased nuclear compression led to YAP/TAZ nuclear localization in agreement with previous experiments. Furthermore, the simulated force load per lamin was maximized on nanopillar substrates with high nuclear stretch. The magnitude of this load was modulated by the rate of actin cap assembly and the overall expression level of lamin A/C - decreasing lamin content in the nuclear envelope led to a higher likelihood of rupture. We validated this prediction in subsequent experiments with lamin-depleted U2OS cells, establishing the central importance of lamin transport and microenvironment nanotopography to nuclear mechanotransduction. 2 SignificanceCell nuclei commonly experience large strains, but existing computational models do not explain the coupling between such deformations and molecular transport. Here, we present a modeling framework that includes the mechanics of nuclear deformations and the reaction-transport of molecules within the cytoplasm, nuclear envelope, and nuclear interior. As a well-controlled setup for comparing experiments and simulations, we consider nuclear indentations exhibited by cells on nanopillar substrates. Our simulations recapitulate measurements of nuclear YAP/TAZ localization from the literature and predict that low-lamin cells experience higher force loads at the nuclear envelope. We validate this prediction experimentally, showing that lamin-depleted cells are more likely to exhibit nuclear rupture. Overall, our framework presents opportunities to predict nuclear mechanoadaptation to different microenvironments.

Cytoplasmic mechanical properties are often treated as constant background parameters, yet whether they change systematically during development remains unclear. Here, we directly measured cytoplasmic mechanics during early embryogenesis of Caenorhabditis elegans by establishing active microrheology using micrometer-sized magnetic droplets. Active microrheology revealed a progressive decrease in creep compliance from the 1-cell to the 8-cell stage, indicating a progressive stiffening of the local cytoplasmic environment during development. This decrease persisted even when cytokinesis was inhibited, demonstrating that it cannot be explained solely by geometric changes associated with cell division. Passive microrheology using 40-nm fluorescent beads showed a consistent decrease in probe mobility over development. Together, these results demonstrate that cytoplasmic mechanical properties undergo a gradual, developmentally programmed change during embryogenesis that cannot be explained by cell division-associated geometry alone.

Nucleus shape is a sensitive indicator of cell state, influenced by numerous bio-chemical and physiological factors. While prior work has cataloged how perturbations alter nucleus morphology, we address the inverse: inferring underlying molecular changes from nucleus shape alone. We previously developed a mechanical model yielding two nondimensional parameters: flatness index and scale factor, which are surrogate measures for cortical actin tension and nuclear envelope compliance respectively. In this study, we apply these parameters to investigate the dynamics in cellular mechanics during confined migration. We fabricated polydimethylsiloxane (PDMS) microchannels with widths of 3 {micro}m (high confinement) and 10 {micro}m (low confinement) and tracked cells migrating through them. We captured high-frequency 3D nucleus shapes via double fluorescence exclusion microscopy and custom image analysis. Fitting the model and estimating flatness index and scale factor to time-resolved shapes revealed dynamic regulation in 3 {micro}m channels: actin tension decreased and nucleus compliance increased immediately before nucleus entry into the constriction, with rapid restoration to baseline upon exit. No such changes occurred in 10 {micro}m channels, indicating active, confinement-dependent cytoskeletal adaptation. Immunostaining for YAP and lamin-A,C confirmed these model inferences. Our results uncover mechanostasis, active mechanical homeostasis, during confined migration and establish the combination of double fluorescence exclusion microscopy and nondimensional nucleus shape parameters as a powerful, non-invasive tool for single-cell mechanobiology studies.

Vertex models are widely used within the field of developmental biology to study tissue morphogenesis. These models are well-suited for modeling deformation at the cellular level where movement is driven by local forces. However, understanding how these microscopic movements coordinate to yield macroscopic phenomena such as the shapes of entire tissues remains a challenge. Here we study a top-down approach using differentiable programming on a simplified vertex model of a laminar tissue, and investigate whether the attributes of individual cells can be tuned to make the mesh as a whole acquire a predefined shape. We let the mesh evolve according to simple rules defined by the input to each polygon, and evaluate the resulting shape against a target boundary. Additionally, we show how the high degeneracy of the output can be reduced by constraining the polygon distributions: first, by adding simple penalties on tissue-wide attributes; and second, by dividing the tissue into regions, within which we bias the attributes toward characteristic values. Our study shows how a simple vertex model can be combined with differentiable programming to model developing tissues, and provides insight into the way individual cells must coordinate to yield macroscopic phenomena such as pre-programmed shapes.

Understanding how biological shape and movement interact with surrounding fluids represents a fundamental challenge at the intersection of biology, physics, and engineering. Fish locomotion exemplifies this challenge: body morphology and swimming kinematics together determine the hydrodynamic forces and flow structures that enable efficient propulsion and maneuverability. Whereas biologists have long sought to connect morphological variation to swimming performance, traditional morphometric approaches provide limited insight into the fluid mechanical consequences of shape differences. Similarly, although computational fluid dynamics can reveal detailed flow physics, simulating hydrodynamics across diverse and dynamic morphologies remains prohibitively expensive for systematic investigation. To bridge this gap, we introduce a data-driven framework that connects fish body shape dynamics to hydro-dynamic performance through compact morphospace parameterization and reduced-order modeling. Using CFD simulations of 15 fish species from the Digital Life Project database (www.digitallife3d.org/3d-model), we generate hydrodynamic datasets capturing the shape-flow relationship. Principal Component Analysis (PCA) extracts four dominant shape parameters from dorsal body profiles, which are then integrated into an Inverse-Design with Dynamic Mode Decomposition (ID-DMD) framework to model the resulting fluid dynamics. The resulting modal analysis suggests that locomotion strategies emerge from specific shape-flow interactions. We further demonstrate the frameworks utility through single- and multi-objective shape optimization, showing how it enables efficient exploration of the morphology-hydrodynamics relationship. This approach offers a novel analysis and design tool for understanding how biological form and motion interact with fluid mechanics, with applications ranging from bio-inspired vehicle development to evolutionary biomechanics.

With the development of microfluidics, it has now become possible to assess the susceptibility of bacteria to antibiotics at the single-cell level instead of relying on population measurements. Such studies are particularly relevant when the growth of bacterial population in the presence of antibiotics is heterogeneous. Here, we build a model to describe such a case, and apply it to experimental measurements on a small population of E. Coli exposed to ciprofloxacin, a drug which is well known for triggering a bistable response.

Background/ObjectivesThe unprecedented structural and binding data for antibodies to the SARS-COV2 virus taken together with the mutations for the spike protein allows for a broad simulation study of antibody-spike protein binding. This provides an understanding of the co-evolution of human immunity and viral immunity escape. MethodsWe utilized the YASARA molecular dynamics program to generate initial antibody-spike structures and simulate to equilibration for six SARS-COV2 variants and 10 different antibodies sampling two different binding regions to the receptor binding domain of the spike (especially for the Class I antibodies in the same part of the spike which attaches to the ACE2 receptor protein) and one to the N-terminal of the spike. Starting structures for antibody binding to variant spike proteins are perturbatively achieved through point mutations and insertions/deletions in the YASARA program. We employed YASARA to measure interfacial hydrogen bound counts between antibodies and variant spike proteins, and the HawkDock MMGBSA program to characterize trends in binding energies with mutation for four of the antibodies. We utilized the VMD program to analyze the time course of hydrogen bond populations. ResultsAs seen in previous studies, interfacial hydrogen bond counts serve as an excellent proxy for binding energies without the large systematic error inherent in the latter. We find that there is generally a decline in antibody binding strength, as measured by interfacial hydrogen bond counts, with viral evolution, but that a modest re-entrance of binding strength is present for most antibodies studied. Generically, the antibody heavy chain binds more strongly to the spike protein, through for approximately half the antibodies the light chain binding strength converges to the heavy chain strength with viral evolution. ConclusionsThe key conclusion is that the identified re-entrant immunity, speculatively arising from a balancing of maintenance of ACE2-spike binding while escaping antibodies through mutation, allows for some maintenance and even strengthening of immunity for later viral strains from early infection or vaccination.

Functional spinal cord repair in zebrafish is governed by regeneration-favorable biochemical and mechanical cues within the lesion microenvironment. Alterations in extracellular matrix composition and stiffness are closely associated with axon regeneration. However, experimentally dissecting the interplay between mechanical signals and axonal regrowth in vivo remains technically challenging. Here, we present an agent-based modeling framework to simulate stiffness-mediated axonal growth trajectories across the lesion. We use this model to explore potential mechanisms underlying the characteristic growth patterns observed during zebrafish spinal cord regeneration. Computational predictions were qualitatively compared with confocal imaging data obtained from larval zebrafish. These phenomenological comparisons revealed a close agreement between simulated and experimentally observed axon growth, indicating that experimentally observed patterns could be governed by transient changes in the stiffness profile of the spinal cord and lesion microenvironment. Hence, our computational framework provides an in silico platform for investigating the role of mechanical cues in axon regeneration in the injured spinal cord.

Take-off is a fast and energy-efficient strategy for bipedal animals, such as birds, to achieve rapid movement; however, how muscle physiology scales to govern this universal behavior remains unresolved. Research in other species physiologies is not readily applicable. As a result, important questions, whether theropod dinosaurs such as Tyrannosaurus rex were capable of jumping, remain unanswered. In this article, we coupled Lagrangian dynamics with Hills muscle equations and developed new experimental methods to quantify joint rotational stiffness and damping, thereby enabling a systematic description of lower-limb mechanics. The approach establishes a novel kinetic framework that links muscle contractile properties to lower-limb performance without invoking control optimization. Animal observations and tabletop mechanisms validate the framework. The mechanics model reveals that the take-off time of about 0.1 s across body masses of 0.003 to 90 kg is achievable, as heavier birds generate proportionally higher reaction forces. Additionally, Tyrannosaurus rex should be capable of jumping, based on the available physiology data. Beyond evolutionary insights, our framework provides a new methodology for analyzing the mechanical properties of biological joints and informing the design of scalable bio-inspired robots.

Quantitative histological analysis of skeletal muscle morphometry provides critical insights into muscle physiology but remains labor-intensive and technically demanding. While recent developments in machine-learning-based image segmentation techniques have facilitated large-scale tissue analysis, existing tools that automate muscle morphometry analysis are largely tailored to mammalian models, with limited applicability to teleosts. Moreover, there is a lack of effective tools for visualizing spatial organization and morphometric variability of teleost muscle fibers, a feature that is important for understanding hyperplastic muscle growth dynamics in teleosts. In this study, we show that cytoplasmic staining combined with deep learning-based cell segmentation offers a robust and accurate approach for automated muscle morphometry analysis in developing zebrafish. We also introduce a FIJI2 plugin, implemented in Jython, that streamlines both morphometric analysis and visualization. This tool accommodates shallow and deep learning-based segmentation techniques and incorporates novel quantification and visualization methods suited to teleost-specific muscle features, including mosaic hyperplasia dynamics. The plugin features an intuitive graphical user interface and is designed for flexibility, with minimal constraints regarding species, image quality, or staining protocol. Its modular architecture allows it to be used as a baseline for automated muscle morphometry analysis, while permitting integration with other tools and workflows.

Biological tissues grow at rates that depend on the geometry of the supporting tissue substrate. In this study, we present a novel discrete mathematical model for simulating biological tissue growth in a range of geometries. The discrete model is deterministic and tracks the evolution of the tissue interface by representing it as a chain of individual cells that interact mechanically and simultaneously generate new tissue material. To describe the collective behaviour of cells, we derive a continuum limit description of the discrete model leading to a reaction-diffusion partial differential equation governing the evolution of cell density along the evolving interface. In the continuum limit, the mechanical properties of discrete cells are directly linked to their collective diffusivity, and spatial constraints introduce curvature dependence that is not explicitly incorporated in the discrete model. Numerical simulations of both the discrete and continuum models reproduce the smoothing behaviour observed experimentally with minimal discrepancies between the models. The discrete model offers further individual-level details, including cell trajectory data, for any restoring force law and initial geometry. Where applicable, we discuss how the discrete model and its continuum description can be used to interpret existing experimental observations.

The epithelial-mesenchymal transition (EMT) alters cell-cell interactions to facilitate collective or individual migration during embryonic development, wound repair, or tumor invasion. Epithelial cells are typically cohesive and stationary while mesenchymal cells are individually dispersed and motile. Additional "partial" EMT states are thought to occur with distinct adhesive and migratory behaviors, but these functional phenotypes are poorly understood. Here, we show that cells treated with moderate TGF-{beta} concentration exhibit collective migration that is fast and directionally persistent despite heterogeneity in epithelial, partial, and mesenchymal states. We find cells coordinate their motility by reorienting in similar directions after transient contacts, a distinct "collision guidance" mechanism that differs from epithelial arrest or mesenchymal repulsion. Moreover, partial EMT cells sustain collision guidance when interacting with epithelial or mesenchymal cells, which otherwise have increased tendency to repel. We corroborate these experimental observations with a computational model using self-propelled interacting particles that align their motion or repel upon contact. Finally, we show that partial EMT enables tissue monolayer fronts to overwhelm and displace monolayers of other cell types after collision. Overall, these results reveal that partial EMT promotes coherent and emergent behaviors that bridge from cell to tissue length scales, with potential implications for shaping epithelial tissue formation, regeneration, or disorganization.

The structural integrity of spinal cord tissue and the transmission of mechanical stimuli across the different levels of tissue microarchitecture and varying spatial scales of mechanical loading challenge experimental and computational efforts to accurately model, simulate and interpret tissue mechanics, leading to conflicting findings in existing literature. Here, we demonstrate that the bead size used in spherical indentation tests significantly affects the stiffness ratio of spinal cord gray to white matter, a dependence which we only observe on the transverse plane and not the coronal plane of the tissue. Our study reveals a shift in stiffness ratio such that for smaller spherical indenters gray matter is stiffer than white matter, while for larger indenters, white matter is stiffer than gray matter. The mean relative change from the 100 {micro}m bead to the 500 {micro}m bead differed between anatomical planes, with transverse sections showing a decrease in gray matter (-13.3%) and an increase in white matter stiffness (+26.9%), accompanied by a reduction in the gray-to-white matter stiffness ratio from 1.07 to 0.76, whereas coronal sections exhibited increases in both gray (+21.0%) and white matter (+33.8%), along with a change in the ratio from 0.99 to 1.14. These findings contribute to explaining previously contradictory results in the literature and underscore the relevance of spatial scales in mechanical characterization studies.

Saturated fatty acids such as stearic acid (SA) can exhibit both antimicrobial and growth-promoting effects on bacteria, depending on their concentration and chemical structure. However, the physical properties of the bacterial cell envelope in response to such molecules remain under-explored compared to their biochemical pathways. In this study, a comprehensive investigation is presented on the interaction of SA with the Gram-positive bacterium, Staphylococcus epider-midis (S. epi). SA alters bacterial growth, reflected in a higher maximum specific growth rate, a shorter lag phase, and an extended exponential phase, consistent with a prebiotic effect. Using fluorescence correlation spectroscopy and fluorescence lifetime imaging microscopy, we show that SA incorporation leads to significant fluidization of the lipid membrane, characterized by enhanced lateral diffusion and reduced membrane viscosity. Coarse-grained molecular dynamics (CG-MD) simulations demonstrate spontaneous insertion of SA into the membrane and a significant increase in mean-square displacement after insertion, supporting our experimental observations. Importantly, atomic force microscopy measurements show an increase in cell-envelope stiffness, reflected by a higher Youngs modulus which can be attributed to modulations in the glycan-peptide linkage density based on earlier studies that correlate stiffness changes to peptidoglycan (PG) crosslinking in Gram-positive strains [1]. These results provide direct evidence linking membrane fluidization induced by SA and increased cell wall stiffness due to transport modifications in the membrane mediated PG synthesis pathways to enhance bacterial cell viability.