A Rho-GTPase based model explains spontaneous collective migration of neural crest cell clusters

A biased random walk approach for modeling the collective chemotaxis of neural crest cells

Collective cell migration is a multicellular phenomenon that arises in various biological contexts, including cancer and embryo development. 'Collectiveness' can be promoted by cell-cell interactions such as co-attraction and contact inhibition of locomotion. These mechanisms act on cell polarity, pivotal for directed cell motility, through influencing the intracellular dynamics of small GTPases such as Rac1. To model these dynamics we introduce a biased random walk model, where the bias depends on the internal state of Rac1, and the Rac1 state is influenced by cell-cell interactions and chemoattractive cues. In an extensive simulation study we demonstrate and explain the scope and applicability of the introduced model in various scenarios. The use of a biased random walk model allows for the derivation of a corresponding partial differential equation for the cell density while still maintaining a certain level of intracellular detail from the individual based setting.

A multiscale theory for spreading and migration of adhesion-reinforced mesenchymal cells

We present a chemomechanical whole-cell theory for the spreading and migration dynamics of mesenchymal cells that can actively reinforce their adhesion to an underlying viscoelastic substrate as a function of its stiffness. Our multiscale model couples the adhesion reinforcement effect at the subcellular scale with the nonlinear mechanics of the nucleus-cytoskeletal network complex at the cellular scale to explain the concurrent monotonic area-stiffness and non-monotonic speed-stiffness relationships observed in experiments: we consider that large cell spreading on stiff substrates flattens the nucleus, increasing the viscous drag force on it. The resulting force balance dictates a reduction in the migration speed on stiff substrates. We also reproduce the experimental influence of the substrate viscosity on the cell spreading area and migration speed by elucidating how the viscosity may either maintain adhesion reinforcement or prevent it depending on the substrate stiffness. Additionally, our model captures the experimental directed migration behaviour of the adhesion-reinforced cells along a stiffness gradient, known as durotaxis, as well as up or down a viscosity gradient (viscotaxis or anti-viscotaxis), the cell moving towards an optimal viscosity in either case. Overall, our theory explains the intertwined mechanics of the cell spreading, migration speed and direction in the presence of the molecular adhesion reinforcement mechanism.

Colec12 and Trail signaling confine cranial neural crest cell trajectories and promote collective cell migration

BACKGROUND

Collective and discrete neural crest cell (NCC) migratory streams are crucial to vertebrate head patterning. However, the factors that confine NCC trajectories and promote collective cell migration remain unclear.

RESULTS

Computational simulations predicted that confinement is required only along the initial one-third of the cranial NCC migratory pathway. This guided our study of Colec12 (Collectin-12, a transmembrane scavenger receptor C-type lectin) and Trail (tumor necrosis factor-related apoptosis-inducing ligand, CD253) which we show expressed in chick cranial NCC-free zones. NCC trajectories are confined by Colec12 or Trail protein stripes in vitro and show significant and distinct changes in cell morphology and dynamic migratory characteristics when cocultured with either protein. Gain- or loss-of-function of either factor or in combination enhanced NCC confinement or diverted cell trajectories as observed in vivo with three-dimensional confocal microscopy, respectively, resulting in disrupted collective migration.

CONCLUSIONS

These data provide evidence for Colec12 and Trail as novel NCC microenvironmental factors playing a role to confine cranial NCC trajectories and promote collective cell migration.

A multiscale whole-cell theory for mechanosensitive migration on viscoelastic substrates

Increasing experimental evidence validates that both the elastic stiffness and viscosity of the extracellular matrix regulate mesenchymal cell behavior, such as the rational switch between durotaxis (cell migration to stiffer regions), anti-durotaxis (migration to softer regions), and adurotaxis (stiffness-insensitive migration). To reveal the mechanisms underlying the crossover between these motility regimes, we have developed a multiscale chemomechanical whole-cell theory for mesenchymal migration. Our framework couples the subcellular focal adhesion dynamics at the cell-substrate interface with the cellular cytoskeletal mechanics and the chemical signaling pathways involving Rho GTPase proteins. Upon polarization by the Rho GTPase gradients, our simulated cell migrates by concerted peripheral protrusions and contractions, a hallmark of the mesenchymal mode. The resulting cell dynamics quantitatively reproduces the experimental migration speed as a function of the uniform substrate stiffness and explains the influence of viscosity on the migration efficiency. In the presence of stiffness gradients and absence of chemical polarization, our simulated cell can exhibit durotaxis, anti-durotaxis, and adurotaxis respectively with increasing substrate stiffness or viscosity. The cell moves toward an optimally stiff region from softer regions during durotaxis and from stiffer regions during anti-durotaxis. We show that cell polarization through steep Rho GTPase gradients can reverse the migration direction dictated by the mechanical cues. Overall, our theory demonstrates that opposing durotactic behaviors emerge via the interplay between intracellular signaling and cell-medium mechanical interactions in agreement with experiments, thereby elucidating complex mechanosensing at the single-cell level.

Picking winners in cell-cell collisions: Wetting, speed, and contact

Groups of eukaryotic cells can coordinate their crawling motion to follow cues more effectively, stay together, or invade new areas. This collective cell migration depends on cell-cell interactions, which are often studied by colliding pairs of cells together. Can the outcome of these collisions be predicted? Recent experiments on trains of colliding epithelial cells suggest that cells with a smaller contact angle to the surface or larger speeds are more likely to maintain their direction ("win") upon collision. When should we expect shape or speed to correlate with the outcome of a collision? To investigate this question, we build a model for two-cell collisions within the phase field framework, which allows for cell shape changes. We can reproduce the observation that cells with high speed and small contact angles are more likely to win with two different assumptions for how cells interact: (1) velocity aligning, in which we hypothesize that cells sense their own velocity and align to it over a finite timescale, and (2) front-front contact repolarization, where cells polarize away from cell-cell contact, akin to contact inhibition of locomotion. Surprisingly, though we simulate collisions between cells with widely varying properties, in each case, the probability of a cell winning is completely captured by a single summary variable: its relative speed (in the velocity-aligning model) or its relative contact angle (in the contact repolarization model). Both models are currently consistent with reported experimental results, but they can be distinguished by varying cell contact angle and speed through orthogonal perturbations.

Two Complementary Signaling Pathways Depict Eukaryotic Chemotaxis: A Mechanochemical Coupling Model

Many eukaryotic cells, including neutrophils and Dictyostelium cells, are able to undergo correlated random migration in the absence of directional cues while reacting to shallow gradients of chemoattractants with exquisite precision. Although progress has been made with regard to molecular identities, it remains elusive how molecular mechanics are integrated with cell mechanics to initiate and manipulate cell motility. Here, we propose a two dimensional (2D) cell migration model wherein a multilayered dynamic seesaw mechanism is accompanied by a mechanical strain-based inhibition mechanism. In biology, these two mechanisms can be mapped onto the biochemical feedback between phosphoinositides (PIs) and Rho GTPase and the mechanical interplay between filamin A (FLNa) and FilGAP. Cell migration and the accompanying morphological changes are demonstrated in numerical simulations using a particle-spring model, and the diffusion in the cell membrane are simulations using a one dimensional (1D) finite differences method (FDM). The fine balance established between endogenous signaling and a mechanically governed inactivation scheme ensures the endogenous cycle of self-organizing pseudopods, accounting for the correlated random migration. Furthermore, this model cell manifests directional and adaptable responses to shallow graded signaling, depending on the overwhelming effect of the graded stimuli guidance on strain-based inhibition. Finally, the model cell becomes trapped within an obstacle-ridden spatial region, manifesting a shuttle run for local explorations and can chemotactically “escape”, illustrating again the balance required in the complementary signaling pathways.

Contact inhibition of locomotion generates collective cell migration without chemoattractants in an open domain

Neural crest cells are embryonic stem cells that migrate throughout embryos and, at different target locations, give rise to the formation of a variety of tissues and organs. The directional migration of the neural crest cells is experimentally described using a process referred to as contact inhibition of locomotion, by which cells redirect their movement upon the cell-cell contacts. However, it is unclear how the migration alignment is affected by the motility properties of the cells. Here, we theoretically model the migration alignment as a function of the motility dynamics and interaction of the cells in an open domain with a channel geometry. The results indicate that by increasing the influx rate of the cells into the domain a transition takes place from random movement to an organized collective migration, where the migration alignment is maximized and the migration time is minimized. This phase transition demonstrates that the cells can migrate efficiently over long distances without any external chemoattractant information about the direction of migration just based on local interactions with each other. The analysis of the dependence of this transition on the characteristic properties of cellular motility shows that the cell density determines the coordination of collective migration whether the migration domain is open or closed. In the open domain, this density is determined by a feedback mechanism between the flux and order parameter, which characterises the alignment of collective migration. The model also demonstrates that the coattraction mechanism proposed earlier is not necessary for collective migration and a constant flux of cells moving into the channel is sufficient to produce directed movement over arbitrary long distances.

Rules of contact inhibition of locomotion for cells on suspended nanofibers

Contact inhibition of locomotion (CIL), in which cells repolarize and move away from contact, is now established as a fundamental driving force in development, repair, and disease biology. Much of what we know of CIL stems from studies on two-dimensional (2D) substrates that do not provide an essential biophysical cue-the curvature of extracellular matrix fibers. We discover rules controlling outcomes of cell-cell collisions on suspended nanofibers and show them to be profoundly different from the stereotyped CIL behavior on 2D substrates. Two approaching cells attached to a single fiber do not repolarize upon contact but rather usually migrate past one another. Fiber geometry modulates this behavior; when cells attach to two fibers, reducing their freedom to reorient, only one cell repolarizes on contact, leading to the cell pair migrating as a single unit. CIL outcomes also change when one cell has recently divided and moves with high speed-cells more frequently walk past each other. Our computational model of CIL in fiber geometries reproduces the core qualitative results of the experiments robustly to model parameters. Our model shows that the increased speed of postdivision cells may be sufficient to explain their increased walk-past rate. We also identify cell-cell adhesion as a key mediator of collision outcomes. Our results suggest that characterizing cell-cell interactions on flat substrates, channels, or micropatterns is not sufficient to predict interactions in a matrix-the geometry of the fiber can generate entirely new behaviors.

Modelling Cell Invasion: A Review of What JD Murray and the Embryo Can Teach Us

Cell invasion and cell plasticity are critical to human development but are also striking features of cancer metastasis. By distributing a multipotent cell type from a place of birth to distal locations, the vertebrate embryo builds organs. In comparison, metastatic tumor cells often acquire a de-differentiated phenotype and migrate away from a primary site to inhabit new microenvironments, disrupting normal organ function. Countless observations of both embryonic cell migration and tumor metastasis have demonstrated complex cell signaling and interactive behaviors that have long confounded scientist and clinician alike. James D. Murray realized the important role of mathematics in biology and developed a unique strategy to address complex biological questions such as these. His work offers a practical template for constructing clear, logical, direct and verifiable models that help to explain complex cell behaviors and direct new experiments. His pioneering work at the interface of development and cancer made significant contributions to glioblastoma cancer and embryonic pattern formation using often simple models with tremendous predictive potential. Here, we provide a brief overview of advances in cell invasion and cell plasticity using the embryonic neural crest and its ancestral relationship to aggressive cancers that put into current context the timeless aspects of his work.

Bridging from single to collective cell migration: A review of models and links to experiments

Mathematical and computational models can assist in gaining an understanding of cell behavior at many levels of organization. Here, we review models in the literature that focus on eukaryotic cell motility at 3 size scales: intracellular signaling that regulates cell shape and movement, single cell motility, and collective cell behavior from a few cells to tissues. We survey recent literature to summarize distinct computational methods (phase-field, polygonal, Cellular Potts, and spherical cells). We discuss models that bridge between levels of organization, and describe levels of detail, both biochemical and geometric, included in the models. We also highlight links between models and experiments. We find that models that span the 3 levels are still in the minority.

Cell-substrate mechanics guide collective cell migration through intercellular adhesion: a dynamic finite element cellular model

During the process of tissue formation and regeneration, cells migrate collectively while remaining connected through intercellular adhesions. However, the roles of cell-substrate and cell-cell mechanical interactions in regulating collective cell migration are still unclear. In this study, we employ a newly developed finite element cellular model to study collective cell migration by exploring the effects of mechanical feedback between cell and substrate and mechanical signal transmission between adjacent cells. Our viscoelastic model of cells consists many triangular elements and is of high resolution. Cadherin adhesion between cells is modeled explicitly as linear springs at subcellular level. In addition, we incorporate a mechano-chemical feedback loop between cell-substrate mechanics and Rac-mediated cell protrusion. Our model can reproduce a number of experimentally observed patterns of collective cell migration during wound healing, including cell migration persistence, separation distance between cell pairs and migration direction. Moreover, we demonstrate that cell protrusion determined by the cell-substrate mechanics plays an important role in guiding persistent and oriented collective cell migration. Furthermore, this guidance cue can be maintained and transmitted to submarginal cells of long distance through intercellular adhesions. Our study illustrates that our finite element cellular model can be employed to study broad problems of complex tissue in dynamic changes at subcellular level.

Active gel segment behaving as an active particle

We reduce a one-dimensional model of an active segment (AS), which is used, for instance, in the description of contraction-driven cell motility, to a zero-dimensional model of an active particle (AP) characterized by two internal degrees of freedom: position and polarity. Both models give rise to hysteretic force-velocity relations showing that an active agent can support two opposite polarities under the same external force and that it can maintain the same polarity while being dragged by external forces with opposite orientations. This double bistability results in a rich dynamic repertoire which we illustrate by studying static, stalled, motile, and periodically repolarizing regimes displayed by an active agent confined in a viscoelastic environment. We show that the AS and AP models can be calibrated to generate quantitatively similar dynamic responses.

Modelling chase-and-run migration in heterogeneous populations

Cell migration is crucial for many physiological and pathological processes. During embryogenesis, neural crest cells undergo coordinated epithelial to mesenchymal transformations and migrate towards various forming organs. Here we develop a computational model to understand how mutual interactions between migrating neural crest cells (NCs) and the surrounding population of placode cells (PCs) generate coordinated migration. According to experimental findings, we implement a minimal set of hypotheses, based on a coupling between chemotactic movement of NCs in response to a placode-secreted chemoattractant (Sdf1) and repulsion induced from contact inhibition of locomotion (CIL), triggered by heterotypic NC–PC contacts. This basic set of assumptions is able to semi-quantitatively recapitulate experimental observations of the characteristic multispecies phenomenon of “chase-and-run”, where the colony of NCs chases an evasive PC aggregate. The model further reproduces a number of in vitro manipulations, including full or partial disruption of NC chemotactic migration and selected mechanisms coordinating the CIL phenomenon. Finally, we provide various predictions based on altering other key components of the model mechanisms.

Tissue mechanics, an important regulator of development and disease

A growing body of work describes how physical forces in and around cells affect their growth, proliferation, migration, function and differentiation into specialized types. How cells receive and respond biochemically to mechanical signals is a process termed mechanotransduction. Disease may arise if a disruption occurs within this mechanism of sensing and interpreting mechanics. Cancer, cardiovascular diseases and developmental defects, such as during the process of neural tube formation, are linked to changes in cell and tissue mechanics. A breakdown in normal tissue and cellular forces activates mechanosignalling pathways that affect their function and can promote disease progression. The recent advent of high-resolution techniques enables quantitative measurements of mechanical properties of the cell and its extracellular matrix, providing insight into how mechanotransduction is regulated. In this review, we will address the standard methods and new technologies available to properly measure mechanical properties, highlighting the challenges and limitations of probing different length-scales. We will focus on the unique environment present throughout the development and maintenance of the central nervous system and discuss cases where disease, such as brain cancer, arises in response to changes in the mechanical properties of the microenvironment that disrupt homeostasis. This article is part of a discussion meeting issue 'Forces in cancer: interdisciplinary approaches in tumour mechanobiology'.

Mechanochemical Coupling and Junctional Forces during Collective Cell Migration

Cell migration, a fundamental physiological process in which cells sense and move through their surrounding physical environment, plays a critical role in development and tissue formation, as well as pathological processes, such as cancer metastasis and wound healing. During cell migration, dynamics are governed by the bidirectional interplay between cell-generated mechanical forces and the activity of Rho GTPases, a family of small GTP-binding proteins that regulate actin cytoskeleton assembly and cellular contractility. These interactions are inherently more complex during the collective migration of mechanically coupled cells because of the additional regulation of cell-cell junctional forces. In this study, we adapted a recent minimal modeling framework to simulate the interactions between mechanochemical signaling in individual cells and interactions with cell-cell junctional forces during collective cell migration. We find that migration of individual cells depends on the feedback between mechanical tension and Rho GTPase activity in a biphasic manner. During collective cell migration, waves of Rho GTPase activity mediate mechanical contraction/extension and thus synchronization throughout the tissue. Further, cell-cell junctional forces exhibit distinct spatial patterns during collective cell migration, with larger forces near the leading edge. Larger junctional force magnitudes are associated with faster collective cell migration and larger tissue size. Simulations of heterogeneous tissue migration exhibit a complex dependence on the properties of both leading and trailing cells. Computational predictions demonstrate that collective cell migration depends on both the emergent dynamics and interactions between cellular-level Rho GTPase activity and contractility and multicellular-level junctional forces.