Multiphase field models for collective cell migration

Cellular elasticity in cancer: a review of altered biomechanical features

A large number of studies have shown that changes in biomechanical characteristics are an important indicator of tumor transformation in normal cells. Elastic deformation is one of the more studied biomechanical features of tumor cells, which plays an important role in tumourigenesis and development. Altered cell elasticity often brings many indications. This manuscript reviews the effects of altered cellular elasticity on cell characteristics, including adhesion viscosity, migration, proliferation, and differentiation elasticity and stiffness. Also, the physical factors that may affect cell elasticity, such as temperature, cell height, cell-viscosity, and aging, are summarized. Then, the effects of cell-matrix, cytoskeleton, in vitro culture medium, and cell-substrate with different three-dimensional structures on cell elasticity during cell tumorigenesis are outlined. Importantly, we summarize the current signaling pathways that may affect cellular elasticity, as well as tests for cellular elastic deformation. Finally, we summarize current hybrid materials: polymer-polymer, protein-protein, and protein-polymer hybrids, also, nano-delivery strategies that target cellular resilience and cases that are at least in clinical phase 1 trials. Overall, the behavior of cancer cell elasticity is modulated by biological, chemical, and physical changes, which in turn have the potential to alter cellular elasticity, and this may be an encouraging prediction for the future discovery of cancer therapies.

Coordinated Motion of Epithelial Layers on Curved Surfaces

Coordinated cellular movements are key processes in tissue morphogenesis. Using a cell-based modeling approach we study the dynamics of epithelial layers lining surfaces with constant and varying curvature. We demonstrate that extrinsic curvature effects can explain the alignment of cell elongation with the principal directions of curvature. Together with specific self-propulsion mechanisms and cell-cell interactions this effect gets enhanced and can explain observed large-scale, persistent, and circumferential rotation on cylindrical surfaces. On toroidal surfaces the resulting curvature coupling is an interplay of intrinsic and extrinsic curvature effects. These findings unveil the role of curvature and postulate its importance for tissue morphogenesis.

Robust statistical properties of T1 transitions in a multi-phase field model of cell monolayers

Large-scale tissue deformation which is fundamental to tissue development hinges on local cellular rearrangements, such as T1 transitions. In the realm of the multi-phase field model, we analyse the statistical and dynamical properties of T1 transitions in a confluent monolayer. We identify an energy profile that is robust to changes in several model parameters. It is characterized by an asymmetric profile with a fast increase in energy before the T1 transition and a sudden drop after the T1 transition, followed by a slow relaxation. The latter being a signature of the fluidity of the cell monolayer. We show that T1 transitions are sources of localised large deformation of the cells undergoing the neighbour exchange, and they induce other T1 transitions in the nearby cells leading to a chaining of events that propagate local cell deformation to large scale tissue flows.

Mechanical basis and topological routes to cell elimination

Cell layers eliminate unwanted cells through the extrusion process, which underlines healthy versus flawed tissue behaviors. Although several biochemical pathways have been identified, the underlying mechanical basis including the forces involved in cellular extrusion remains largely unexplored. Utilizing a phase-field model of a three-dimensional cell layer, we study the interplay of cell extrusion with cell-cell and cell-substrate interactions in a flat monolayer. Independent tuning of cell-cell versus cell-substrate adhesion forces reveals that extrusion events can be distinctly linked to defects in nematic and hexatic orders associated with cellular arrangements. Specifically, we show that by increasing relative cell-cell adhesion forces the cell monolayer can switch between the collective tendency towards fivefold, hexatic, disclinations relative to half-integer, nematic, defects for extruding a cell. We unify our findings by accessing three-dimensional mechanical stress fields to show that an extrusion event acts as a mechanism to relieve localized stress concentration.

MorphoSim: an efficient and scalable phase-field framework for accurately simulating multicellular morphologies

The phase field model can accurately simulate the evolution of microstructures with complex morphologies, and it has been widely used for cell modeling in the last two decades. However, compared to other cellular models such as the coarse-grained model and the vertex model, its high computational cost caused by three-dimensional spatial discretization hampered its application and scalability, especially for multicellular organisms. Recently, we built a phase field model coupled with in vivo imaging data to accurately reconstruct the embryonic morphogenesis of Caenorhabditis elegans from 1- to 8-cell stages. In this work, we propose an improved phase field model by using the stabilized numerical scheme and modified volume constriction. Then we present a scalable phase-field framework, MorphoSim, which is 100 times more efficient than the previous one and can simulate over 100 mechanically interacting cells. Finally, we demonstrate how MorphoSim can be successfully applied to reproduce the assembly, self-repairing, and dissociation of a synthetic artificial multicellular system - the synNotch system.

Emergence of macroscopic directional motion of deformable active cells in confined structures

There is now growing evidence of collective turbulentlike motion of cells in dense tissues. However, how to control and harness this collective motion is an open question. We investigate the transport of deformable active cells in a periodically asymmetric channel by using a phase-field model. We demonstrate that collective turbulent-like motion of cells can power and steer the macroscopic directional motion through the ratchet channel. The active intercellular forces proportional to the deformation of cells can break thermodynamical equilibrium and induce the directional motion. This directional motion is caused by the ratchet effect rather than the spontaneous symmetry breaking. The motion direction is determined by the asymmetry of the channel. Remarkably, there exits an optimal nonequilibrium driving (depending on the active strength, the elasticity, and the packing fraction) at which the average velocity reaches the maximum. In addition, the optimized packing fraction and the optimized minimum width of the channel can facilitate the directional motion of cells. Our findings are relevant to understanding how macroscopic directional motion relates to the local force transmission mediated by cell-cell contacts in cellular monolayers.

Local Yield and Compliance in Active Cell Monolayers

The rheology of biological tissue plays an important role in many processes, from organ formation to cancer invasion. Here, we use a multiphase field model of motile cells to simulate active microrheology within a tissue monolayer. When unperturbed, the tissue exhibits a transition between a solidlike state and a fluidlike state tuned by cell motility and deformability-the ratio of the energetic costs of steric cell-cell repulsion and cell-edge tension. When perturbed, solid tissues exhibit local yield-stress behavior, with a threshold force for the onset of motion of a probe particle that vanishes upon approaching the solid-to-liquid transition. This onset of motion is qualitatively different in the low and high deformability regimes. At high deformability, the tissue is amorphous when solid, it responds compliantly to deformations, and the probe transition to motion is smooth. At low deformability, the monolayer is more ordered translationally and stiffer, and the onset of motion appears discontinuous. Our results suggest that cellular or nanoparticle transport in different types of tissues can be fundamentally different and point to ways in which it can be controlled.

Bridging microscopic cell dynamics to nematohydrodynamics of cell monolayers

It is increasingly being realized that liquid-crystalline features can play an important role in the properties and dynamics of cell monolayers. Here, we present a cell-based model of cell layers, based on the phase-field formulation, that connects cell-cell interactions specified at the single cell level to large-scale nematic and hydrodynamic properties of the tissue. In particular, we present a minimal formulation that reproduces the well-known bend and splay hydrodynamic instabilities of the continuum nemato-hydrodynamic formulation of active matter, together with an analytical description of the instability threshold in terms of activity and elasticity of the cells. Furthermore, we provide a quantitative characterisation and comparison of flows and topological defects for extensile and contractile stress generation mechanisms, and demonstrate activity-induced heterogeneity and spontaneous formation of gaps within a confluent monolayer. Together, these results contribute to bridging the gap between cell-scale dynamics and tissue-scale collective cellular organisation.

Impact of contact inhibition on collective cell migration and proliferation

Contact inhibition limits migration and proliferation of cells in cell colonies. We consider a multiphase field model to investigate the growth dynamics of a cell colony, composed of proliferating cells. The model takes into account the mechanism of contact inhibition of proliferation by local mechanical interactions. We compare nonmigrating and migrating cells, in order to provide a quantitative characterization of the dynamics and analyze the velocity of the colony boundary for both cases. Additionally, we measure single cell velocities, number of neighbor distributions, as well as the influence of stress and age on positions of the cells and with respect to each other.

Deformable active nematic particles and emerging edge currents in circular confinements

We consider a microscopic field theoretical approach for interacting active nematic particles. With only steric interactions the self-propulsion strength in such systems can lead to different collective behaviour, e.g. synchronized self-spinning and collective translation. The different behaviour results from the delicate interplay between internal nematic structure, particle shape deformation and particle-particle interaction. For intermediate active strength an asymmetric particle shape emerges and leads to chirality and self-spinning crystals. For larger active strength the shape is symmetric and translational collective motion emerges. Within circular confinements, depending on the packing fraction, the self-spinning regime either stabilizes positional and orientational order or can lead to edge currents and global rotation which destroys the synchronized self-spinning crystalline structure.