The influence of cell mechanics, cell-cell interactions, and proliferation on epithelial packing

Interface morphodynamics in living tissues

Interfaces between distinct tissues or between tissues and environments are common in multicellular organisms. The evolution and stability of these interfaces are essential for tissue development, and their dysfunction can lead to diseases such as cancer. Mounting efforts, either theoretical or experimental, have been devoted to uncovering the morphodynamics of tissue interfaces. Here, we review the recent progress of studies on interface morphodynamics. The regulatory mechanisms governing interface evolution are dissected, with a focus on adhesion, cortical tension, cell activity, extracellular matrix, and microenvironment. We examine the methodologies used to study morphodynamics, emphasizing the characteristics of experimental techniques and theoretical models. Finally, we explore the broader implications of interface morphodynamics in tissue morphogenesis and diseases, offering a comprehensive perspective on this rapidly developing field.

Mechanobiological mechanism of cyclic stretch-induced cell columnarization

In vivo, epithelial cells maintain structural integrity under dynamic mechanical perturbations. To study this, we treated various epithelial cell lines with long-term cyclic stretch (CS). Surprisingly, cells transitioned from cuboidal to columnar shape (columnarization) in MDCK cells, while others only elongated. This change correlated with actin accumulation at the top and stress fiber realignment at the bottom. Blocking mechanical stimulation via FAK inhibition or reducing vinculin partially prevented columnarization; however, disrupting tight junctions or cellular contractility substantially blocked it. The MK4 cells, derived from MDCK cells with weaker cell-cell junctions, showed less columnarization under CS, whereas overexpressing Caveolin-1 (Cav1) in MK4 cells enhanced junctions and promoted columnar formation. Atomic force microscopy studies revealed increased apical junctional stiffness in both CS-treated MDCK and Cav1-overexpressing MK4 cells. This, combined with a mathematical model, elucidated the physical characteristics and changes in cell tension post-stretch, revealing the mechanobiological foundation of epithelial cell columnarization.

F-actin dynamics regulates collective cell migration by modulating cell shape and stress correlation

As an essential component in generating cell contractility, F-actin plays a pivotal role in collective cell migration. However, the mechanisms by which subcellular F-actin dynamics influence the collective behaviors of cell clusters across scales remain poorly understood. In this study, we developed a mechanical model to investigate how the dynamics of stress fibers and cryptic lamellipodia, prominent F-actin structures generating traction forces, regulate collective cell migration. Our results show that strengthening stress fibers significantly amplifies cell rearrangements and counteracts the high-density-induced inhibition of cell movements in the monolayer. It is attributed to the tension-caused cell elongation, which facilitates the growth of normalized mean-squared displacements in high-density cell monolayers. Moreover, the model shows that stronger stress fibers could effectively guide collaborative cell movements through enhancing the spatial correlation of maximum principal stress. Additionally, we found cryptic lamellipodia exhibit similar influence on collective cell migration. Our results bridge intracellular F-actin dynamics with collective cell migration, offering insights into the underlying mechanisms and their biological significance.

Vertex models capturing subcellular scales in epithelial tissues

Vertex models provide a robust theoretical framework for studying epithelial tissues as a network of cell boundaries. They have been pivotal in exploring properties such as cell packing geometry and rigidity transitions. Recently, extended vertex models have become instrumental in bridging the subcellular scales to the tissue scale. Here, we review extensions of the model aiming to capture experimentally observed subcellular features of epithelial tissues including heterogeneity in myosin activity across the tissue, non-uniform contractility structures, and mechanosensitive feedback loops. We discuss how these extensions change and challenge current perspectives on observables of macroscopic tissue properties. First, we find that extensions to the vertex model can change model properties significantly, impacting the critical threshold and in some cases even the existence of a rigidity transition. Second, we find that packing disorder can be explained by models employing different subcellular mechanisms, indicating a source of stochasticity and gradual local size changes as common mesoscopic motifs in the mechanics of tissue organization. We address complementary models and statistical inference, putting vertex models in a broader methodological context and we give a brief overview of software packages utilized in increasingly complex vertex model studies. Our review emphasizes the need for more comparative, systematic studies that identify specific classes of vertex models which share a set of well-defined properties, as well as a more in-depth discussion of modeling choices and their biological motivations.

A transient contractile seam promotes epithelial sealing and sequential assembly of body segments

In embryos, epithelial sealing proceeds with progressive zipping eventually leading to a scar-free epithelium and ensuring the assembly of body segments in insects and neural tube in mammals. How zipping is mechanically controlled to promote tissue fusion on long distances, remains unclear. Combining physical modeling with genetic and mechanical perturbations, we reveal the existence of a transient contractile seam that generates forces to reduce the zipping angle by force balance, consequently promoting epidermal sealing during Drosophila embryogenesis. The seam is formed by the adhesion of two tissues, the epidermis and amnioserosa, and is stabilized by the tensions generated by the segment boundaries. Once a segment is zipped, the seam disassembles concurrently with the inactivation of the Jun kinase pathway. Thus, we show that epithelial sealing is promoted by a transient actomyosin contractile seam allowing sequential segment assembly.

Junctional force patterning drives both positional order and planar polarity in the auditory epithelia

Tissue function depends on the precise organisation of the constituent cells. In the cochlea, the fidelity of hearing depends on mechanosensory hair cells being consistently surrounded by supporting cells. In addition to this positional order, auditory sensitivity depends crucially on planar cell polarity. This is characterised by the alignment of the orientation of eccentrically placed hair bundles on each hair cell. These two levels of order emerge simultaneously despite the cellular fluxes that occur during cochlear development. However, the link between tissue-scale cellular rearrangements and intrinsic cellular mechanisms remains unknown. By combining experimental and theoretical approaches, we find a precise force patterning underpinning positional order and planar cell polarity. This occurs through the modulation of the levels and phospho-type of the regulatory light chain of non-muscle myosin II at specific cell-cell junctions of the auditory epithelium. We propose that the control of junctional mechanics is vital for the organisation of multi-cell-type epithelia.

Differential Elasticity Affects Lineage Segregation of Embryonic Stem Cells

The question of what guides lineage segregation is central to development, where cellular differentiation leads to segregated cell populations destined for specialized functions. Here, using optical tweezers measurements of mouse embryonic stem cells, we reveal a mechanical mechanism based on differential elasticity in the second lineage segregation of the embryonic inner cell mass into epiblast (EPI) cells, which will develop into the fetus, and primitive endoderm (PrE), which will form extraembryonic structures such as the yolk sac. Remarkably, we find that these mechanical differences already occur during priming, not just after a cell has committed to differentiation. Specifically, we show that PrE-primed cells exhibit significantly higher elasticity than EPI-primed cells, characterized by lower power spectrum scaling exponents, higher Young's modulus, and lower loss tangent. Using a model of two cell types differing only in elasticity, we show that differential elasticity alone is sufficient to lead to segregation between cell types, suggesting that the mechanical attributes of the cells contribute to the segregation process. Importantly, we find that this process relies on cellular activity. Our findings present differential elasticity as a previously unknown mechanical contributor to lineage segregation during embryo morphogenesis.

Apical constriction requires patterned apical surface remodeling to synchronize cellular deformation

Apical constriction is a basic mechanism for epithelial morphogenesis, making columnar cells into wedge shape and bending a flat cell sheet. It has long been thought that an apically localized myosin generates a contractile force and drives the cell deformation. However, when we tested the increased apical surface contractility in a cellular Potts model simulation, the constriction increased pressure inside the cell and pushed its lateral surface outward, making the cells adopt a drop shape instead of the expected wedge shape. To keep the lateral surface straight, we considered an alternative model in which the cell shape was determined by cell membrane elasticity and endocytosis, and the increased pressure is balanced among the cells. The cellular Potts model simulation succeeded in reproducing the apical constriction, and it also suggested that a too strong apical surface tension might prevent the tissue invagination.

EDA Fibronectin Microarchitecture and YAP Translocation during Wound Closure

Fibronectin (Fn) is an extracellular matrix glycoprotein with mechanosensitive structure-function. Extra domain A (EDA) Fn, a Fn isoform, is not present in adult tissue but is required for tissue repair. Curiously, EDA Fn is linked to both regenerative and fibrotic tissue repair. Given that Fn mechanoregulates cell behavior, EDA Fn organization during wound closure might play a role in mediating these differing responses. One mechanism by which cells sense and respond to their microenvironment is by activating a transcriptional coactivator, yes-associated protein (YAP). Interestingly, YAP activity is not only required for wound closure but similarly linked to both regenerative and fibrotic repair. Therefore, this study aims to evaluate how, during normal and fibrotic wound closure, EDA Fn organization might modulate YAP translocation by culturing human dermal fibroblasts on polydimethylsiloxane substrates mimicking normal (soft: 18 kPa) and fibrotic (stiff: 146 kPa) wounded skin. On stiffer substrates mimicking fibrotic wounds, fibroblasts assembled an aligned EDA Fn matrix comprising thinner fibers, suggesting increased microenvironmental tension. To evaluate if cell binding to the EDA domain of Fn was essential to overall matrix organization, fibroblasts were treated with Irigenin, which inhibits binding to the EDA domain within Fn. Blocking adhesion to EDA led to randomly organized EDA Fn matrices with thicker fibers, suggesting reduced microenvironmental tension even during fibrotic wound closure. To evaluate whether YAP signaling plays a role in EDA Fn organization, fibroblasts were treated with CA3, which suppresses YAP activity in a dose-dependent manner. Treatment with CA3 also led to randomly organized EDA Fn matrices with thicker fibers, suggesting a potential connected mechanism of reducing tension during fibrotic wound closure. Next, YAP activity was assessed to evaluate the impact of EDA Fn organization. Interestingly, fibroblasts migrating on softer substrates mimicking normal wounds increased YAP activity, but on stiffer substrates, they decreased YAP activity. When fibroblasts on stiffer substrates were treated with Irigenin or CA3, fibroblasts increased YAP activity. These results suggest that there may be disrupted signaling between EDA Fn organization and YAP translocation during fibrotic wound closure that could be restored when reestablishing normal EDA Fn matrix organization to instead drive regenerative wound repair.

Neighbor cells restrain furrowing during Xenopus epithelial cytokinesis

Cytokinesis challenges epithelial tissue homeostasis by generating forces that pull on neighboring cells. Junction reinforcement at the furrow in Xenopus epithelia regulates the speed of furrowing, suggesting that cytokinesis is subject to resistive forces from epithelial neighbors. We show that contractility factors accumulate near the furrow in neighboring cells, and increasing neighbor cell stiffness slows furrowing. Optogenetically increasing contractility in one or both neighbor cells slows furrowing or induces cytokinetic failure. Uncoupling mechanotransduction between dividing cells and their neighbors increases the furrow ingression rate, alters topological cell packing following cytokinesis, and impairs barrier function at the furrow. Computational modeling validates our findings and provides additional insights about epithelial mechanics during cytokinesis. We conclude that forces from the cytokinetic array must be carefully balanced with restraining forces generated by neighbor cells to regulate the speed and success of cytokinesis and maintain epithelial homeostasis.

Prickle2 regulates apical junction remodeling and tissue fluidity during vertebrate neurulation

The process of folding the flat neuroectoderm into an elongated neural tube depends on tissue fluidity, a property that allows epithelial deformation while preserving tissue integrity. Neural tube folding also requires the planar cell polarity (PCP) pathway. Here, we report that Prickle2 (Pk2), a core PCP component, increases tissue fluidity by promoting the remodeling of apical junctions (AJs) in Xenopus embryos. This Pk2 activity is mediated by the unique evolutionarily conserved Ser/Thr-rich region (STR) in the carboxyterminal half of the protein. Mechanistically, the effects of Pk2 require Rac1 and are accompanied by increased dynamics of C-cadherin and tricellular junctions, the hotspots of AJ remodeling. Notably, Pk2 depletion leads to the accumulation of mediolaterally oriented cells in the neuroectoderm, whereas the overexpression of Pk2 or Pk1 containing the Pk2-derived STR promotes cell elongation along the anteroposterior axis. We propose that Pk2-dependent regulation of tissue fluidity contributes to anteroposterior tissue elongation in response to extrinsic cues.

Origin of yield stress and mechanical plasticity in model biological tissues

During development and under normal physiological conditions, biological tissues are continuously subjected to substantial mechanical stresses. In response to large deformations, cells in a tissue must undergo multicellular rearrangements to maintain integrity and robustness. However, how these events are connected in time and space remains unknown. Here, using theoretical modeling, we study the mechanical plasticity of cell monolayers under large deformations. Our results suggest that the jamming-unjamming (solid-fluid) transition can vary significantly depending on the degree of deformation, implying that tissues are highly unconventional materials. We elucidate the origins of this behavior. We also demonstrate how large deformations are accommodated through a series of cellular rearrangements, similar to avalanches in non-living materials. We find that these 'tissue avalanches' are governed by stress redistribution and the spatial distribution of "soft" or vulnerable spots, which are more prone to undergo rearrangements. Finally, we propose a simple and experimentally accessible framework to infer tissue-level stress and predict avalanches based on static images.

Epithelial Layer Fluidization by Curvature-Induced Unjamming

The transition of an epithelial layer from a stationary, quiescent state to a highly migratory, dynamic state is required for wound healing, development, and regeneration. This transition, known as the unjamming transition (UJT), is responsible for epithelial fluidization and collective migration. Previous theoretical models have primarily focused on the UJT in flat epithelial layers, neglecting the effects of strong surface curvature characteristic of the epithelium in vivo. In this Letter, we investigate the role of surface curvature on tissue plasticity and cellular migration using a vertex model embedded on a spherical surface. Our findings reveal that increasing curvature promotes the UJT by reducing the energy barriers to cellular rearrangements. Higher curvature favors cell intercalation, mobility, and self-diffusivity, resulting in epithelial structures that are malleable and migratory when small, but become more rigid and stationary as they grow. Together, these results provide a conceptual framework to better understand how cell shape, cell propulsion, and tissue geometry contribute to tissue malleability, remodeling, and stabilization.

How does the extracellular matrix affect the rigidity of an embedded spheroid?

Cellularized tissue and polymer networks can both transition from floppy to rigid as a function of their control parameters, and, yet, the two systems often mechanically interact, which could affect their respective rigidities. To study this interaction, we consider a vertex model with surface tension embedded in a spring network in two dimensions. We identify two regimes with different global spheroid shapes and governed by the pressure resulting from competition between surface tension and tension in the network. In the first regime, the tissue remains compact, while in the second, a cavitation-like instability leads to the emergence of gaps at the tissue-network interface. Intriguingly, compression of the tissue promotes fluidization, while tension promotes cellular alignment and rigidification with the mechanisms driving rigidification differing on either side of the instability.

Tissue Active Matter: Integrating Mechanics and Signaling into Dynamical Models

The importance of physical forces in the morphogenesis, homeostatic function, and pathological dysfunction of multicellular tissues is being increasingly characterized, both theoretically and experimentally. Analogies between biological systems and inert materials such as foams, gels, and liquid crystals have provided striking insights into the core design principles underlying multicellular organization. However, these connections can seem surprising given that a key feature of multicellular systems is their ability to constantly consume energy, providing an active origin for the forces that they produce. Key emerging questions are, therefore, to understand whether and how this activity grants tissues novel properties that do not have counterparts in classical materials, as well as their consequences for biological function. Here, we review recent discoveries at the intersection of active matter and tissue biology, with an emphasis on how modeling and experiments can be combined to understand the dynamics of multicellular systems. These approaches suggest that a number of key biological tissue-scale phenomena, such as morphogenetic shape changes, collective migration, or fate decisions, share unifying design principles that can be described by physical models of tissue active matter.

Transitions between cooperative and crowding-dominated collective motion in non-jammed MDCK monolayers

Transitions between solid-like and fluid-like states in living tissues have been found in steps of embryonic development and in stages of disease progression. Our current understanding of these transitions has been guided by experimental and theoretical investigations focused on how motion becomes arrested with increased mechanical coupling between cells, typically as a function of packing density or cell cohesiveness. However, cells actively respond to externally applied forces by contracting after a time delay, so it is possible that at some packing densities or levels of cell cohesiveness, mechanical coupling stimulates cell motion instead of suppressing it. Here we report our findings that at low densities and within multiple ranges of cell cohesiveness, cell migration speeds increase with these measures of mechanical coupling. Our observations run counter to our intuition that cell motion will be suppressed by increasingly packing or sticking cells together and may provide new insight into biological processes involving motion in dense cell populations.

Actin crosslinking is required for force sensing at tricellular junctions

Mechanical forces are essential for tissue morphogenesis, but risk causing ruptures that could compromise tissue function. In epithelial tissues, adherens junctions withstand the forces that drive morphogenesis by recruiting proteins that stabilize cell adhesion and reinforce connections to the actin cytoskeleton under tension. However, how junctional actin networks respond to forces in vivo is not well understood. Here we show that the actin crosslinker Fimbrin is recruited to tricellular junctions under tension and plays a central role in amplifying actomyosin contractility and stabilizing cell adhesion. Loss of Fimbrin results in a failure to reorganize actin under tension and an inability to enhance myosin-II activity and recruit junction-stabilizing proteins in response to force, disrupting cell adhesion. Conversely, increasing Fimbrin activity constitutively activates force-response pathways, aberrantly stabilizing adhesion. These results demonstrate that Fimbrin-mediated actin crosslinking is an essential step in modulating actomyosin dynamics and reinforcing cell adhesion under tension during epithelial remodeling.

Cell-Level Modelling of Homeostasis in Confined Epithelial Monolayers

Tissue homeostasis, the biological process of maintaining a steady state in tissue via control of cell proliferation and death, is essential for the development, growth, maintenance, and proper function of living organisms. Disruptions to this process can lead to serious diseases and even death. In this study, we use the vertex model for the cell-level description of tissue mechanics to investigate the impact of the tissue environment and local mechanical properties of cells on homeostasis in confined epithelial tissues. We find a dynamic steady state, where the balance between cell divisions and removals sustains homeostasis, and characterise the homeostatic state in terms of cell count, tissue area, homeostatic pressure, and the cells' neighbour count distribution. This work, therefore, sheds light on the mechanisms underlying tissue homeostasis and highlights the importance of mechanics in its control.

Mechanical strain focusing at topological defect sites in regenerating Hydra

The formation of a new head during Hydra regeneration involves the establishment of a head organizer that functions as a signaling center and contains an aster-shaped topological defect in the organization of the supracellular actomyosin fibers. Here, we show that the future head region in regenerating tissue fragments undergoes multiple instances of extensive stretching and rupture events from the onset of regeneration. These recurring localized tissue deformations arise due to transient contractions of the supracellular ectodermal actomyosin fibers that focus mechanical strain at defect sites. We further show that stabilization of aster-shaped defects is disrupted by perturbations of the Wnt signaling pathway. We propose a closed-loop feedback mechanism promoting head organizer formation, and develop a biophysical model of regenerating Hydra tissues that incorporates a morphogen source activated by mechanical strain and an alignment interaction directing fibers along morphogen gradients. We suggest that this positive-feedback loop leads to mechanical strain focusing at defect sites, enhancing local morphogen production and promoting robust organizer formation.

Tissue shear as a cue for aligning planar polarity in the developing Drosophila wing

Planar polarity establishment in epithelia requires interpretation of directional tissue-level information at cellular and molecular levels. Mechanical forces exerted during tissue morphogenesis are emerging as crucial tissue-level directional cues, yet the mechanisms by which they regulate planar polarity are poorly understood. Using the Drosophila pupal wing, we confirm that tissue stress promotes proximal-distal (PD) planar polarity alignment. Moreover, high tissue stress anisotropy can reduce the rate of accumulation and lower the stability on cell junctions of the core planar polarity protein Frizzled (Fz). Notably, under high tissue stress anisotropy, we see an increased gradient of cell flow, characterised by differential velocities across adjacent cell rows. This promotes core protein turnover at cell-cell contacts parallel to the flow direction, possibly via dissociation of transmembrane complexes by shear forces. We propose that gradients of cell flow play a critical role in establishing and maintaining PD-oriented polarity alignment in the developing pupal wing.

Detection of Oral Submucous Fibrosis at the Crossroads of Altering Nucleogeometry, Nuclear Spatial Distribution and Nuclear Molecular Abundance

The manuscript concentrates on spatial distribution and various nucleomorphometric parameters of epithelium to diagnose Oral Submucous Fibrosis (OSF). Histologically confirmed OSF and normal submucosa tissue samples were procured and stained with diamidino phenylindole (DAPI) to visualize nuclei. E-cadherins and p63 were also immunohistochemically stained. Microphotographs were analyzed to quantify the spatial distance among the nuclei of the stained tissue samples. Intensity of the DAPI stained nuclei and p63 was quantified. In addition, morphometric analysis of nuclei was done with the help of ImageJ software to quantify the geometric alterations in OSF tissue. Spatial distances among the nuclei of OSF tissue samples were found to be significantly higher than that of normal tissue. We also observed a significant decrease in the mean intensity of DAPI and p63 in OSF tissue samples. In addition, we have found statistically significant alterations of various morphometric quantifications in OSF tissue nuclei. There was a considerable change in the spatial distribution of nuclei, as well as some distinct changes in the nucleogeometry of OSF tissue, which corresponds to histological abnormalities. Decreased intensity of DAPI and p63 advocate disease progression. The biomarkers in this study are the accountable role-players for early detection of oral carcinoma.

Competing mechanisms for the buckling of an epithelial monolayer identified using multicellular simulation

A model using the rigid body multi-cellular framework (RBMCF) is implemented to investigate the mechanisms of buckling of an epithelial monolayer. Specifically, the deformation of a monolayer of epithelial cells which are attached to a basement membrane and the surrounding stromal tissue. The epithelial monolayer, supporting basement membrane and stromal tissue are modelled using two separate vertex dynamics models (one for the epithelial monolayer layer and one for the basement membrane and stromal tissue combined) and interactions between the two are considered using the RBMCF to ensure biologically realistic interactions. Model simulations are used to investigate the effects of cell-stromal attachment and membrane rigidity on buckling behaviour. We demonstrate that there are two competing modes of buckling, stromal deformation and stromal separation.

Theoretical and Experimental Studies of the Dynamic Damage of Endothelial Cellular Networks Under Ultrasound Cavitation

Introduction

The interaction between endothelial cells can regulate hemostasis, vasodilation, as well as immune and inflammatory responses. Excessive loading on the endothelial cells leads to endothelial damage and endothelial barrier dysfunction. Understanding and mastering the dynamic nature of cell-cell rupture plays a crucial role in exploring the practical applications related to tumor destruction, vascular remodeling, and drug delivery by employing cavitation-induced damage to soft tissues.

Methods

To investigate the damage mechanisms of endothelial cellular networks under ultrasound cavitation, we developed a model of junction rupture in cellular networks based on the assumption that the process of intercellular rupture is irreversible when ultrasound-mediated forces exceed the damage threshold, whereas intercellular junctions have reversible behavior before rupture. Simulations using the strain accumulation method show that stress and strain exhibit complex nonlinear dynamic behavior. Ultrasonic cavitation damage was tested and evaluated on human umbilical vein endothelial cells.

Results

The results indicated that the cellular network damage was positively correlated with force amplitude and pulse frequency and was negatively correlated with driving frequency. The time lag and the internal force of cellular junctions have an important influence on the resistance to damage of the cellular network due to external forces. The damage experiment based on ultrasonic cavitation confirmed the effectiveness of the proposed model.

Conclusions

The model provided a platform for understanding the damage mechanism of endothelial tissues and ultimately improving options for their prevention and treatment.

Connecting Anomalous Elasticity and Sub-Arrhenius Structural Dynamics in a Cell-Based Model

Understanding the structural dynamics of many-particle glassy systems remains a key challenge in statistical physics. Over the last decade, glassy dynamics has also been reported in biological tissues, but is far from being understood. It was recently shown that vertex models of dense biological tissue exhibit very atypical, sub-Arrhenius dynamics, and here we ask whether such atypical structural dynamics of vertex models are related to unusual elastic properties. It is known that at zero temperature these models have an elasticity controlled by their underconstrained or isostatic nature, but little is known about how their elasticity varies with temperature. To address this question we investigate the 2D Voronoi model and measure the temperature dependence of the intermediate-time plateau shear modulus and the bulk modulus. We find that unlike in conventional glass formers, these moduli increase monotonically with temperature until the system fluidizes. We further show that the structural relaxation time can be quantitatively linked to the plateau shear modulus G_{p}, i.e. G_{p} modulates the typical energy barrier scale for cell rearrangements. This suggests that the anomalous, structural dynamics of the 2D Voronoi model originates in its unusual elastic properties. Based on our results, we hypothesize that underconstrained systems might more generally give rise to a new class of "ultrastrong" glass formers.

Vertex model with internal dissipation enables sustained flows

Complex tissue flows in epithelia are driven by intra- and inter-cellular processes that generate, maintain, and coordinate mechanical forces. There has been growing evidence that cell shape anisotropy, manifested as nematic order, plays an important role in this process. Here we extend an active nematic vertex model by replacing substrate friction with internal viscous dissipation, dominant in epithelia not supported by a substrate or the extracellular matrix, which are found in many early-stage embryos. When coupled to cell shape anisotropy, the internal viscous dissipation allows for long-range velocity correlations and thus enables the spontaneous emergence of flows with a large degree of spatiotemporal organisation. We demonstrate sustained flow in epithelial sheets confined to a channel, providing a link between the cell-level vertex model of tissue dynamics and continuum active nematics, whose behaviour in a channel is theoretically understood and experimentally realisable. Our findings also show a simple mechanism that could account for collective cell migration correlated over distances large compared to the cell size, as observed during morphogenesis.

A minimal vertex model explains how the amnioserosa avoids fluidization during Drosophila dorsal closure

Dorsal closure is a process that occurs during embryogenesis of Drosophila melanogaster. During dorsal closure, the amnioserosa (AS), a one-cell thick epithelial tissue that fills the dorsal opening, shrinks as the lateral epidermis sheets converge and eventually merge. During this process, both shape index and aspect ratio of amnioserosa cells increase markedly. The standard 2-dimensional vertex model, which successfully describes tissue sheet mechanics in multiple contexts, would in this case predict that the tissue should fluidize via cell neighbor changes. Surprisingly, however, the amnioserosa remains an elastic solid with no such events. We here present a minimal extension to the vertex model that explains how the amnioserosa can achieve this unexpected behavior. We show that continuous shrinkage of the preferred cell perimeter and cell perimeter polydispersity lead to the retention of the solid state of the amnioserosa. Our model accurately captures measured cell shape and orientation changes and predicts nonmonotonic junction tension that we confirm with laser ablation experiments.

Initiation of epithelial wound closure by an active instability at the purse string

The ability of biological systems to withstand and recover from various disruptions, such as spontaneous genetic mutations and environmental damage, largely relies on intricate feedback mechanisms. We theoretically study the mechanical response of an epithelial tissue facing damage in the form of a circular wound. Our model describes a feedback loop between the generation of active forces in the actomyosin and tissue mechanics, described by the vertex model. While the exact dynamics of wound closure may be influenced by several biophysical mechanisms that interplay in a nontrivial way, our findings suggest that the closure may initiate as an active instability, triggered by a reduced myosin turnover rate at the wound's perimeter. We explore the interplay between myosin dynamics and the elastic properties of the tissue, elucidating their collective role in determining a wound's loss of stability, leading to the initiation of the closure process.

Planar polarized force propagation integrates cell behavior with tissue shaping during convergent extension

Convergent extension (CE) is an evolutionarily conserved developmental process that elongates tissues and organs via collective cell movements known as cell intercalation. Here, we sought to understand the mechanisms connecting cell behaviors and tissue shaping. We focus on an often-overlooked aspect of cell intercalation, the resolution of 4-cell vertices. Our data reveal that imbalanced cellular forces are involved in a timely vertex resolution, which, in turn, enables the propagation of such cellular forces, facilitating the propagation of tissue-scale CE. Conversely, delayed vertex resolution leads to a subtle but significant change in tissue-wide cell packing and exerts a profound impact by blocking force propagation, resulting in CE propagation defects. Our findings propose a collaborative nature of local cell intercalations in propagating tissue-wide CE. It unveils a multiscale biomechanical synergy underpinning the cellular mechanisms that orchestrate tissue morphogenesis during CE.

The structure-dynamics feedback mechanism governs the glassy dynamics in epithelial monolayers

The glass-like slow dynamics in confluent epithelial monolayers is crucial for wound healing, embryogenesis, cancer progression, etc. Experiments have indicated several unusual properties in these systems. Unlike ordinary glasses, the glassiness in cellular systems strongly correlates with their static properties and is sub-Arrhenius. These results imply that the slow dynamics in epithelial monolayers is either not glassy or the underlying mechanism is different from ordinary glasses. Combining the analytical mode-coupling theory (MCT), vertex model simulations, and cellular experiments, we show that the slow dynamics is glassy, though the mechanism differs from ordinary glasses. The structure-dynamics feedback mechanism of MCT, and not the barrier-crossing mechanism, dominates the glassy dynamics, where the relaxation time diverges as a power law with a universal exponent 3/2 and naturally explains the sub-Arrhenius relaxation. Our results suggest the possibility of describing various complex biological processes like cell division and apoptosis via the static properties of the systems, such as average cell shape or shape variability.

Deciphering the interplay between biology and physics with a finite element method-implemented vertex organoid model: A tool for the mechanical analysis of cell behavior on a spherical organoid shell

Understanding the interplay between biology and mechanics in tissue architecture is challenging, particularly in terms of 3D tissue organization. Addressing this challenge requires a biological model enabling observations at multiple levels from cell to tissue, as well as theoretical and computational approaches enabling the generation of a synthetic model that is relevant to the biological model and allowing for investigation of the mechanical stresses experienced by the tissue. Using a monolayer human colon epithelium organoid as a biological model, freely available tools (Fiji, Cellpose, Napari, Morphonet, or Tyssue library), and the commercially available Abaqus FEM solver, we combined vertex and FEM approaches to generate a comprehensive viscoelastic finite element model of the human colon organoid and demonstrated its flexibility. We imaged human colon organoid development for 120 hours, following the evolution of the organoids from an immature to a mature morphology. According to the extracted architectural/geometric parameters of human colon organoids at various stages of tissue architecture establishment, we generated organoid active vertex models. However, this approach did not consider the mechanical aspects involved in the organoids' morphological evolution. Therefore, we applied a finite element method considering mechanical loads mimicking osmotic pressure, external solicitation, or active contraction in the vertex model by using the Abaqus FEM solver. Integration of finite element analysis (FEA) into the vertex model achieved a better fit with the biological model. Therefore, the FEM model provides a basis for depicting cell shape, tissue deformation, and cellular-level strain due to imposed stresses. In conclusion, we demonstrated that a combination of vertex and FEM approaches, combining geometrical and mechanical parameters, improves modeling of alterations in organoid morphology over time and enables better assessment of the mechanical cues involved in establishing the architecture of the human colon epithelium.

Topology and Nuclear Size Determine Cell Packing on Growing Lung Spheroids

Within multicellular living systems, cells coordinate their positions with spatiotemporal accuracy to form various tissue structures and control development. These arrangements can be regulated by tissue geometry, biochemical cues, as well as mechanical perturbations. However, how cells pack during dynamic three-dimensional multicellular architectures formation remains unclear. Here, examining a growing spherical multicellular system, human lung alveolospheres, we observe an emergence of hexagonal packing order and a structural transition of cells that comprise the spherical epithelium. Surprisingly, the cell packing behavior on the spherical surface of lung alveolospheres resembles hard-disks packing on spheres, where the less deformable cell nuclei act as effective "hard disks" and prevent cells from getting too close. Nucleus-to-cell size ratio increases during lung spheroids growth; as a result, we find more hexagon-concentrated cellular packing with increasing bond orientational order. Furthermore, by osmotically changing the compactness of cells on alveolospheres, we observe a more ordered packing when nucleus-to-cell size ratio increases, and vice versa. These more ordered cell packing characteristics are consistent with reduced cell dynamics, together suggesting that better cellular packing stabilizes local cell neighborhoods and may regulate more complex biological functions such as cellular maturation and tissue morphogenesis.

Peeking into the future: inferring mechanics in dynamical tissues

Cells exert forces on each other and their environment, shaping the tissue. The resulting mechanical stresses can be determined experimentally or estimated computationally using stress inference methods. Over the years, mechanical stress inference has become a non-invasive, low-cost computational method for estimating the relative intercellular stresses and intracellular pressures of tissues. This mini-review introduces and compares the static and dynamic modalities of stress inference, considering their advantages and limitations. To date, most software has focused on static inference, which requires only a single microscopy image as input. Although applicable in quasi-equilibrium states, this approach neglects the influence that cell rearrangements might have on the inference. In contrast, dynamic stress inference relies on a time series of microscopy images to estimate stresses and pressures. Here, we discuss both static and dynamic mechanical stress inference in terms of their physical, mathematical, and computational foundations and then outline what we believe are promising avenues for in silico inference of the mechanical states of tissues.

The geometric basis of epithelial convergent extension

Shape changes of epithelia during animal development, such as convergent extension, are achieved through the concerted mechanical activity of individual cells. While much is known about the corresponding large-scale tissue flow and its genetic drivers, fundamental questions regarding local control of contractile activity on the cellular scale and its embryo-scale coordination remain open. To address these questions, we develop a quantitative, model-based analysis framework to relate cell geometry to local tension in recently obtained time-lapse imaging data of gastrulating Drosophila embryos. This analysis systematically decomposes cell shape changes and T1 rearrangements into internally driven, active, and externally driven, passive, contributions. Our analysis provides evidence that germ band extension is driven by active T1 processes that self-organize through positive feedback acting on tensions. More generally, our findings suggest that epithelial convergent extension results from the controlled transformation of internal force balance geometry which combines the effects of bottom-up local self-organization with the top-down, embryo-scale regulation by gene expression.

Cell Sorting in an Active Nematic Vertex Model

We study a mixture of extensile and contractile cells using a vertex model extended to include active nematic stresses. The two cell populations phase separate over time. While phase separation strengthens monotonically with an increasing magnitude of contractile activity, the dependence on extensile activity is nonmonotonic, so that sufficiently high values reduce the extent of sorting. We interpret this by showing that extensile activity renders the system motile, enabling cells to undergo neighbor exchanges. Contractile cells that come into contact as a result are then more likely to stay connected due to an effective attraction arising from contractile activity.

Bayesian parameter inference for epithelial mechanics

Cell-based mechanical models, such as the Cell Vertex Model (CVM), have proven useful for studying the mechanical control of epithelial tissue dynamics. We recently developed a statistical method called image-based parameter inference for formulating CVM model functions and estimating their parameters from image data of epithelial tissues. In this study, we employed Bayesian statistics to improve the utility and flexibility of image-based parameter inference. Tests on synthetic data confirmed that both our non-hierarchical and hierarchical Bayesian models provide accurate estimates of model parameters. By applying this method to Drosophila wings, we demonstrated that the reliability of parameter estimation is closely linked to the mechanical anisotropies present in the tissue. Moreover, we revealed that the cortical elasticity term is dispensable for explaining force-shape correlations in vivo. We anticipate that the flexibility of the Bayesian statistical framework will facilitate the integration of various types of information, thereby contributing to the quantitative dissection of the mechanical control of tissue dynamics.

Mechanical forces instruct division plane orientation of cambium stem cells during radial growth in Arabidopsis thaliana

Robust regulation of cell division is central to the formation of complex multi-cellular organisms and is a hallmark of stem cell activity. In plants, due to the absence of cell migration, the correct placement of newly produced cell walls during cell division is of eminent importance for generating functional tissues and organs. In particular, during the radial growth of plant shoots and roots, precise regulation and organization of cell divisions in the cambium are essential to produce adjacent xylem and phloem tissues in a strictly bidirectional manner. Although several intercellular signaling cascades have been identified to instruct tissue organization during radial growth, the role of mechanical forces in guiding cambium stem cell activity has been frequently proposed but, so far, not been functionally investigated on the cellular level. Here, we coupled anatomical analyses with a cell-based vertex model to analyze the role of mechanical stress in radial plant growth at the cell and tissue scale. Simulations based on segmented cellular outlines of radially growing Arabidopsis hypocotyls revealed a distinct stress pattern with circumferential stresses in cambium stem cells, which coincided with the orientation of cortical microtubules. Integrating stress patterns as a cue instructing cell division orientation was sufficient for the emergence of typical cambium-derived cell files and agreed with experimental results for stress-related tissue organization in confining mechanical environments. Our work thus underlines the significance of mechanical forces in tissue organization through self-emerging stress patterns during the growth of plant organs.

Nuclei as mechanical bumpers during epithelial remodeling

The morphogenesis of developing tissues relies on extensive cellular rearrangements in shape, position, and identity. A key process in reshaping tissues is cell intercalation-driven elongation, where epithelial cells align and intercalate along a common axis. Typically, analyses focus on how peripheral cortical forces influence cell shape changes. Less attention is given to how inhomogeneities in internal structures, particularly the nucleus, impact cell shaping. Here, we examine how pulsed contractile and extension dynamics interact with the nucleus in elongating Drosophila embryos. Our data show that tightly packed nuclei in apical layers hinder tissue remodeling/oscillatory behaviors. We identify two mechanisms for resolving internuclear tensions: nuclear deformation and dispersion. Embryos with non-deformable nuclei use nuclear dispersion to maintain near-normal extensile rates, while those with non-dispersible nuclei due to microtubule inhibition exhibit disruptions in contractile behaviors. Disrupting both mechanisms leads to severe tissue extension defects and cell extrusion. These findings highlight the critical role of nuclear shape and positioning in topological remodeling of epithelia.

Modelling the effect of cell motility on mixing and invasion in epithelial monolayers

Collective cell invasion underlies several biological processes such as wound healing, embryonic development, and cancerous invasion. Here, we investigate the impact of cell motility on invasion in epithelial monolayers and its coupling to cellular mechanical properties, such as cell-cell adhesion and cortex contractility. We develop a two-dimensional computational model for cells with active motility based on the cellular Potts model, which predicts that the cellular invasion speed is mainly determined by active cell motility and is independent of the biological and mechanical properties of the cells. We also find that, in general, motile cells out-compete and invade non-motile cells, however, this can be reversed by differential cell proliferation. Stable coexistence of motile and static cell types is also possible for certain parameter regimes.

Regulation of epithelial cell jamming transition by cytoskeleton and cell-cell interactions

Multicellular systems, such as epithelial cell collectives, undergo transitions similar to those in inert physical systems like sand piles and foams. To remodel or maintain tissue organization during development or disease, these collectives transition between fluid-like and solid-like states, undergoing jamming or unjamming transitions. While these transitions share principles with physical systems, understanding their regulation and implications in cell biology is challenging. Although cell jamming and unjamming follow physics principles described by the jamming diagram, they are fundamentally biological processes. In this review, we explore how cellular processes and interactions regulate jamming and unjamming transitions. We begin with an overview of how these transitions control tissue remodeling in epithelial model systems and describe recent findings of the physical principles governing tissue solidification and fluidization. We then explore the mechanistic pathways that modulate the jamming phase diagram axes, focusing on the regulation of cell fluctuations and geometric compatibility. Drawing upon seminal works in cell biology, we discuss the roles of cytoskeleton and cell-cell adhesion in controlling cell motility and geometry. This comprehensive view illustrates the molecular control of cell jamming and unjamming, crucial for tissue remodeling in various biological contexts.

Disease-related non-muscle myosin IIA D1424N rod domain mutation, but not R702C motor domain mutation, disrupts mouse ocular lens fiber cell alignment and hexagonal packing

The mouse ocular lens is an excellent vertebrate model system for studying hexagonal cell packing and shape changes during tissue morphogenesis and differentiation. The lens is composed of two types of cells, epithelial and fiber cells. During the initiation of fiber cell differentiation, lens epithelial cells transform from randomly packed cells to hexagonally shaped and packed cells to form meridional row cells. The meridional row cells further differentiate and elongate into newly formed fiber cells that maintain hexagonal cell shape and ordered packing. In other tissues, actomyosin contractility regulates cell hexagonal packing geometry during epithelial tissue morphogenesis. Here, we use the mouse lens as a model to study the effect of two human disease-related non-muscle myosin IIA (NMIIA) mutations on lens cellular organization during fiber cell morphogenesis and differentiation. We studied genetic knock-in heterozygous mice with NMIIA-R702C motor domain or NMIIA-D1424N rod domain mutations. We observed that while one allele of NMIIA-R702C has no impact on lens meridional row epithelial cell shape and packing, one allele of the NMIIA-D1424N mutation can cause localized defects in cell hexagonal packing. Similarly, one allele of NMIIA-R702C motor domain mutation does not affect lens fiber cell organization while the NMIIA-D1424N mutant proteins disrupt fiber cell organization and packing. Our work demonstrates that disease-related NMIIA rod domain mutations (D1424N or E1841K) disrupt mouse lens fiber cell morphogenesis and differentiation.

A morpho-viscoelasticity theory for growth in proliferating aggregates

Despite significant research efforts in the continuum modeling of biological growth, certain aspects have been overlooked. For instance, numerous investigations have examined the influence of morphogenetic cell behaviors, like division and intercalation, on the mechanical response of passive (non-growing) tissues. Yet, their impact on active growth dynamics remains inadequately explored. A key reason for this inadequacy stems from challenges in the continuum treatment of cell-level processes. While some coarse-grained models have been proposed to address these shortcomings, a focus on cell division and cell expansion has been missing, rendering them unusable when it comes to modeling growth. Moreover, existing studies are limited to two-dimensional tissues and are yet to be formally extended to three-dimensional multicellular systems. To address these limitations, we here present a generalized multiscale model for three-dimensional aggregates that accounts for complex morphogenetic movements that include division, expansion, and intercalation. The proposed continuum theory thus allows for a comprehensive exploration into the growth and dissipation mechanics of proliferating aggregates, such as spheroids and organoids.

Compression theory for inhomogeneous systems

The physics of complex systems stands to greatly benefit from the qualitative changes in data availability and advances in data-driven computational methods. Many of these systems can be represented by interacting degrees of freedom on inhomogeneous graphs. However, the lack of translational invariance presents a fundamental challenge to theoretical tools, such as the renormalization group, which were so successful in characterizing the universal physical behaviour in critical phenomena. Here we show that compression theory allows the extraction of relevant degrees of freedom in arbitrary geometries, and the development of efficient numerical tools to build an effective theory from data. We demonstrate our method by applying it to a strongly correlated system on an Ammann-Beenker quasicrystal, where it discovers an exotic critical point with broken conformal symmetry. We also apply it to an antiferromagnetic system on non-bipartite random graphs, where any periodicity is absent.

Self-organized cell patterning via mechanical feedback in hindbrain neuropore morphogenesis

Cell patterning is essential for organized tissue development, enabling precise geometric arrangement of cells, body axis establishment and developmental timing. Here we investigate the role of physical forces and mechanical cues in organizing and maintaining cell morphological patterns during hindbrain neuropore closure, a critical morphogenetic event in vertebrate development. Through live-imaging in mouse embryos and cell-based biophysical modeling, we demonstrate that active cell crawling and actomyosin purse-string contraction at the neuropore border are insufficient to account for the observed cellular arrangements in space and time. Instead, mechanosensitive feedback between cellular stress, shape, and nematic alignment is required to establish and maintain cell morphological patterns and their spatial order. This feedback-driven model generates persistent shape memory in cells, stalls cell rearrangements, and promotes local tissue solidification to preserve the spatial organization during the closure process. We validate this model experimentally, establishing the critical role of mechanical feedback in guiding tissue-level morphogenesis through active, force-driven patterning.

Assessing mechanical agency during apical apoptotic cell extrusion

Homeostasis is necessary for epithelia to maintain barrier function and prevent the accumulation of defective cells. Unfit, excess, and dying cells in the larval zebrafish tail fin epidermis are removed via controlled cell death and extrusion. Extrusion coincides with oscillations of cell area, both in the extruding cell and its neighbors. Here, we develop a biophysical model of this process to explore the role of autonomous and non-autonomous mechanics. We vary biophysical properties and oscillatory behaviors of extruding cells and their neighbors along with tissue-wide cell density and viscosity. We find that cell autonomous processes are major contributors to the dynamics of extrusion, with the mechanical microenvironment providing a less pronounced contribution. We also find that some cells initially resist extrusion, influencing the duration of the expulsion process. Our model provides insights into the cellular dynamics and mechanics that promote elimination of unwanted cells from epithelia during homeostatic tissue maintenance.

An adaptive numerical method for multi-cellular simulations of tissue development and maintenance

In recent years, multi-cellular models, where cells are represented as individual interacting entities, are becoming ever popular. This has led to a proliferation of novel methods and simulation tools. The first aim of this paper is to review the numerical methods utilised by multi-cellular modelling tools and to demonstrate which numerical methods are appropriate for simulations of tissue and organ development, maintenance, and disease. The second aim is to introduce an adaptive time-stepping algorithm and to demonstrate it's efficiency and accuracy. We focus on off-lattice, mechanics based, models where cell movement is defined by a series of first order ordinary differential equations, derived by assuming over-damped motion and balancing forces. We see that many numerical methods have been used, ranging from simple Forward Euler approaches through to higher order single-step methods like Runge-Kutta 4 and multi-step methods like Adams-Bashforth 2. Through a series of exemplar multi-cellular simulations, we see that if: care is taken to have events (births deaths and re-meshing/re-arrangements) occur on common time-steps; and boundaries are imposed on all sub-steps of numerical methods or implemented using forces, then all numerical methods can converge with the correct order. We introduce an adaptive time-stepping method and demonstrate that the best compromise between L∞ error and run-time is to use Runge-Kutta 4 with an increased time-step and moderate adaptivity. We see that a judicious choice of numerical method can speed the simulation up by a factor of 10-60 from the Forward Euler methods seen in Osborne et al. (2017), and a further speed up by a factor of 4 can be achieved by using an adaptive time-step.

Jamming of nephron-forming niches in the developing mouse kidney creates cyclical mechanical stresses

Urinary collecting tubules form during kidney embryogenesis through the branching of the ureteric bud epithelium. A travelling mesenchyme niche of nephron progenitor cells caps each branching ureteric bud tip. These 'tip domain' niches pack more closely over developmental time and their number relates to nephron endowment at birth. Yet, how the crowded tissue environment impacts niche number and cell decision-making remains unclear. Here, through experiments and mathematical modelling, we show that niche packing conforms to physical limitations imposed by kidney curvature. We relate packing geometries to rigidity theory to predict a stiffening transition starting at embryonic day 15 in the mouse, validated by micromechanical analysis. Using a method to estimate tip domain 'ages' relative to their most recent branch events, we find that new niches overcome mechanical resistance as they branch and displace neighbours. This creates rhythmic mechanical stress in the niche. These findings expand our understanding of kidney development and inform engineering strategies for synthetic regenerative tissues.

Interplay of geometry and mechanics in epithelial wound healing

Wound healing is a complex biological process critical for maintaining an organism's structural integrity and tissue repair following an infection or injury. Recent studies have unveiled the mechanisms involving the coordination of biochemical and mechanical responses in the tissue in wound healing. In this article, we focus on the healing property of an epithelial tissue as a material while the effects of biological mechanisms such as cell proliferation, tissue intercalation, cellular migration, cell crawling, and filopodia protrusion is minimal. We present a mathematical framework that predicts the fate of a wounded tissue based on the wound's geometrical features and the tissue's mechanical properties. Precisely, adapting the vertex model of tissue mechanics, we predict whether a wound of a specific size in an epithelial monolayer characterized by certain levels of actomyosin contractility and cell-cell adhesion will heal (i.e., close), shrink in size, or rupture the tissue further. Moreover, we show how tissue-mediated mechanisms such as purse-string tension at the wound boundary facilitate wound healing. Finally, we validate the predictions of our model by designing an experimental setup that enables us to create wounds of specific sizes in kidney epithelial cells (MDCK) monolayers. Altogether, this work sets up a basis for interpreting the interplay of mechanical and geometrical features of a tissue in the process of wound healing.

A nuclear jamming transition in vertebrate organogenesis

Jamming of cell collectives and associated rigidity transitions have been shown to play a key role in tissue dynamics, structure and morphogenesis. Cellular jamming is controlled by cellular density and the mechanics of cell-cell contacts. However, the contribution of subcellular organelles to the physical state of the emergent tissue is unclear. Here we report a nuclear jamming transition in zebrafish retina and brain tissues, where physical interactions between highly packed nuclei restrict cellular movements and control tissue mechanics and architecture. Computational modelling suggests that the nuclear volume fraction and anisotropy of cells control the emerging tissue physical state. Analysis of tissue architecture, mechanics and nuclear movements during eye development show that retina tissues undergo a nuclear jamming transition as they form, with increasing nuclear packing leading to more ordered cellular arrangements, reminiscent of the crystalline cellular packings in the functional adult eye. Our results reveal an important role of the cell nucleus in tissue mechanics and architecture.

Applying Spatiotemporal Modeling of Cell Dynamics to Accelerate Drug Development

Cells act as physical computational programs that utilize input signals to orchestrate molecule-level protein-protein interactions (PPIs), generating and responding to forces, ultimately shaping all of the physiological and pathophysiological behaviors. Genome editing and molecule drugs targeting PPIs hold great promise for the treatments of diseases. Linking genes and molecular drugs with protein-performed cellular behaviors is a key yet challenging issue due to the wide range of spatial and temporal scales involved. Building predictive spatiotemporal modeling systems that can describe the dynamic behaviors of cells intervened by genome editing and molecular drugs at the intersection of biology, chemistry, physics, and computer science will greatly accelerate pharmaceutical advances. Here, we review the mechanical roles of cytoskeletal proteins in orchestrating cellular behaviors alongside significant advancements in biophysical modeling while also addressing the limitations in these models. Then, by integrating generative artificial intelligence (AI) with spatiotemporal multiscale biophysical modeling, we propose a computational pipeline for developing virtual cells, which can simulate and evaluate the therapeutic effects of drugs and genome editing technologies on various cell dynamic behaviors and could have broad biomedical applications. Such virtual cell modeling systems might revolutionize modern biomedical engineering by moving most of the painstaking wet-laboratory effort to computer simulations, substantially saving time and alleviating the financial burden for pharmaceutical industries.

Rigidity in mechanical biological networks

Multicellular organisms generate complex morphologies required for their function. Organisms control these morphologies by tuning active forces and by altering the emergent 'material properties' of a tissue, i.e. the rheology of the tissue. In many cases, organisms take advantage of dramatic changes in the rheology that occur when the material undergoes a rigidity transition from a fluid-like or floppy state to a solid-like or rigid state. This transition in turn depends on internal parameters at the scale of cells and molecules. This review highlights recent theoretical work identifying the mechanisms that drive such transitions, so that biologists can look for these mechanisms in in vivo or in vitro systems. We discuss two main types of transition: a first-order rigidity transition that depends on the connectivity of small-scale structures, such as the number of contacts between cells or the number of branch points in a biopolymer network; and a second-order rigidity transition that depends on the geometry of small-scale structures, such as the shape of cells or the distance between crosslinks in a polymer network. We provide examples of each type of transition in model organisms and discuss methods for distinguishing between the mechanisms in future experiments.