Collective Signal Processing in Cluster Chemotaxis: Roles of Adaptation, Amplification, and Co-attraction in Collective Guidance

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.

Decoding complex transport patterns in flow-induced autologous chemotaxis of multicellular systems

Cell migration via autologous chemotaxis in the presence of interstitial fluid flow is important in cancer metastasis and embryonic development. Despite significant recent progress, our understanding of flow-induced autologous chemotaxis of multicellular systems remains poor. The literature presents inconsistent findings regarding the effectiveness of collective autologous chemotaxis of densely packed cells under interstitial fluid flow. Here, we present a high-fidelity computational model to analyze the migration of multicellular systems performing autologous chemotaxis in the presence of interstitial fluid flow. Our simulations show that the details of the complex transport dynamics of the chemoattractant and fluid flow patterns that occur in the extracellular space, previously overlooked, are essential to understand this cell migration mechanism. We find that, although flow-induced autologous chemotaxis is a robust migration mechanism for individual cells, the cell-cell interactions that occur in multicellular systems render autologous chemotaxis an inefficient mechanism of collective cell migration. Our results offer new perspectives on the potential role of autologous chemotaxis in the tumor microenvironment, where fluid flow is an important modulator of transport.

The cellular Potts model on disordered lattices

The cellular Potts model, also known as the Glazier-Graner-Hogeweg model, is a lattice-based approach by which biological tissues at the level of individual cells can be numerically studied. Traditionally, a square or hexagonal underlying lattice structure is assumed for two-dimensional systems, and this is known to introduce artifacts in the structure and dynamics of the model tissues. That is, on regular lattices, cells can assume shapes that are dictated by the symmetries of the underlying lattice. Here, we developed a variant of this method that can be applied to a broad class of (ir)regular lattices. We show that on an irregular lattice deriving from a fluid-like configuration, two types of artifacts can be removed. We further report on the transition between a fluid-like disordered and a solid-like hexagonally ordered phase present for monodisperse confluent cells as a function of their surface tension. This transition shows the hallmarks of a first-order phase transition and is different from the glass/jamming transitions commonly reported for the vertex and active Voronoi models. We emphasize this by analyzing the distribution of shape parameters found in our state space. Our analysis provides a useful reference for the future study of epithelia using the (ir)regular cellular Potts model.

Trade-offs in concentration sensing in dynamic environments

When cells measure concentrations of chemical signals, they may average multiple measurements over time in order to reduce noise in their measurements. However, when cells are in an environment that changes over time, past measurements may not reflect current conditions-creating a new source of error that trades off against noise in chemical sensing. What statistics in the cell's environment control this trade-off? What properties of the environment make it variable enough that this trade-off is relevant? We model a single eukaryotic cell sensing a chemical secreted from bacteria (e.g., folic acid). In this case, the environment changes because the bacteria swim-leading to changes in the true concentration at the cell. We develop analytical calculations and stochastic simulations of sensing in this environment. We find that cells can have a huge variety of optimal sensing strategies ranging from not time averaging at all to averaging over an arbitrarily long time or having a finite optimal averaging time. The factors that primarily control the ideal averaging are the ratio of sensing noise to environmental variation and the ratio of timescales of sensing to the timescale of environmental variation. Sensing noise depends on the receptor-ligand kinetics, while environmental variation depends on the density of bacteria and the degradation and diffusion properties of the secreted chemoattractant. Our results suggest that fluctuating environmental concentrations may be a relevant source of noise even in a relatively static environment.

Collective effects in flow-driven cell migration

Autologous chemotaxis is the process in which cells secrete and detect molecules to determine the direction of fluid flow. Experiments and theory suggest that autologous chemotaxis fails at high cell densities because molecules from other cells interfere with a given cell's signal. We investigate autologous chemotaxis using a three-dimensional Monte Carlo-based motility simulation that couples spatial and temporal gradient sensing with cell-cell repulsion. Surprisingly, we find that when temporal gradient sensing dominates, high-density clusters chemotax faster than individual cells. To explain this observation, we propose a mechanism by which temporal gradient sensing allows cells to form a collective sensory unit. We demonstrate using computational fluid mechanics that that this mechanism indeed allows a cluster of cells to outperform single cells in terms of the detected anisotropy of the signal, a finding that we demonstrate with analytic scaling arguments. Our work suggests that collective autologous chemotaxis at high cell densities is possible and requires only known, ubiquitous cell capabilities.

Thermotaxis in an apolar, non-neuronal animal

Neuronal circuits are hallmarks of complex decision-making processes in the animal world. How animals without neurons process information and respond to environmental cues promises a new window into studying precursors of neuronal control and origin of the nervous system as we know it today. Robust decision making in animals, such as in chemotaxis or thermotaxis, often requires internal symmetry breaking (such as anterior-posterior (AP) axis) provided naturally by a given body plan of an animal. Here we report the discovery of robust thermotaxis behaviour in Trichoplax adhaerens, an early-divergent, enigmatic animal with no anterior-posterior symmetry breaking (apolar) and no known neurons or muscles. We present a quantitative and robust behavioural response assay in Placozoa, which presents an apolar flat geometry. By exposing T. adhaerens to a thermal gradient under a long-term imaging set-up, we observe robust thermotaxis that occurs over timescale of hours, independent of any circadian rhythms. We quantify that T. adhaerens can detect thermal gradients of at least 0.1°C cm-1. Positive thermotaxis is observed for a range of baseline temperatures from 17°C to 22.5°C, and distributions of momentary speeds for both thermotaxis and control conditions are well described by single exponential fits. Interestingly, the organism does not maintain a fixed orientation while performing thermotaxis. Using natural diversity in size of adult organisms (100 µm to a few millimetres), we find no apparent size-dependence in thermotaxis behaviour across an order of magnitude of organism size. Several transient receptor potential (TRP) family homologues have been previously reported to be conserved in metazoans, including in T. adhaerens. We discover naringenin, a known TRPM3 antagonist, inhibits thermotaxis in T. adhaerens. The discovery of robust thermotaxis in T. adhaerens provides a tractable handle to interrogate information processing in a brainless animal. Understanding how divergent marine animals process thermal cues is also critical due to rapid temperature rise in our oceans.

Single-cell directional sensing from just a few receptor binding events

Identifying the directionality of signaling sources from noisy input to membrane receptors is an essential task performed by many cell types. A variety of models have been proposed to explain directional sensing in cells. However, many of these require significant computational and memory capacities for the cell. We propose and analyze a simple mechanism in which a cell adopts the direction associated with the first few membrane binding events. This model yields an accurate angular estimate to the source long before steady state is reached in biologically relevant scenarios. Our proposed mechanism allows for reliable estimates of the directionality of external signals using temporal information and assumes minimal computational capacities of the cell.

Coupling cell shape and velocity leads to oscillation and circling in keratocyte galvanotaxis

During wound healing, fish keratocyte cells undergo galvanotaxis where they follow a wound-induced electric field. In addition to their stereotypical persistent motion, keratocytes can develop circular motion without a field or oscillate while crawling in the field direction. We developed a coarse-grained phenomenological model that captures these keratocyte behaviors. We fit this model to experimental data on keratocyte response to an electric field being turned on. A critical element of our model is a tendency for cells to turn toward their long axis, arising from a coupling between cell shape and velocity, which gives rise to oscillatory and circular motion. Galvanotaxis is influenced not only by the field-dependent responses, but also cell speed and cell shape relaxation rate. When the cell reacts to an electric field being turned on, our model predicts that stiff, slow cells react slowly but follow the signal reliably. Cells that polarize and align to the field at a faster rate react more quickly and follow the signal more reliably. When cells are exposed to a field that switches direction rapidly, cells follow the average of field directions, while if the field is switched more slowly, cells follow a "staircase" pattern. Our study indicated that a simple phenomenological model coupling cell speed and shape is sufficient to reproduce a broad variety of different keratocyte behaviors, ranging from circling to oscillation to galvanotactic response, by only varying a few parameters.

Network Analysis Identifies Phase Transitions for Tumor With Interacting Cells

Metastasis is the process by which cancer cells acquire the capability to leave the primary tumor and travel to distant sites. Recent experiments have suggested that the epithelial–mesenchymal transition can regulate invasion and metastasis. Another possible scenario is the collective motion of cells. Recent studies have also proposed a jamming–unjamming transition for epithelial cells based on physical forces. Here, we assume that there exists a short-range chemical attraction between cancer cells and employ the Brownian dynamics to simulate tumor growth. Applying the network analysis, we suggest three possible phases for a given tumor and study the transition between these phases by adjusting the attraction strength.

Collective gradient sensing with limited positional information

Eukaryotic cells sense chemical gradients to decide where and when to move. Clusters of cells can sense gradients more accurately than individual cells by integrating measurements of the concentration made across the cluster. Is this gradient-sensing accuracy impeded when cells have limited knowledge of their position within the cluster, i.e., limited positional information? We apply maximum likelihood estimation to study gradient-sensing accuracy of a cluster of cells with finite positional information. If cells must estimate their location within the cluster, this lowers the accuracy of collective gradient sensing. We compare our results with a tug-of-war model where cells respond to the gradient by polarizing away from their neighbors without relying on their positional information. As the cell positional uncertainty increases, there is a trade-off where the tug-of-war model responds more accurately to the chemical gradient. However, for sufficiently large cell clusters or sufficiently shallow chemical gradients, the tug-of-war model will always be suboptimal to one that integrates information from all cells, even if positional uncertainty is high.

The role of cell geometry and cell-cell communication in gradient sensing

Cells can measure shallow gradients of external signals to initiate and accomplish a migration or a morphogenetic process. Recently, starting from mathematical models like the local-excitation global-inhibition (LEGI) model and with the support of empirical evidence, it has been proposed that cellular communication improves the measurement of an external gradient. However, the mathematical models that have been used have over-simplified geometries (e.g., they are uni-dimensional) or assumptions about cellular communication, which limit the possibility to analyze the gradient sensing ability of more complex cellular systems. Here, we generalize the existing models to study the effects on gradient sensing of cell number, geometry and of long- versus short-range cellular communication in 2D systems representing epithelial tissues. We find that increasing the cell number can be detrimental for gradient sensing when the communication is weak and limited to nearest neighbour cells, while it is beneficial when there is long-range communication. We also find that, with long-range communication, the gradient sensing ability improves for tissues with more disordered geometries; on the other hand, an ordered structure with mostly hexagonal cells is advantageous with nearest neighbour communication. Our results considerably extend the current models of gradient sensing by epithelial tissues, making a step further toward predicting the mechanism of communication and its putative mediator in many biological processes.

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.

Topological data analysis of collective and individual epithelial cells using persistent homology of loops

Interacting, self-propelled particles such as epithelial cells can dynamically self-organize into complex multicellular patterns, which are challenging to classify without a priori information. Classically, different phases and phase transitions have been described based on local ordering, which may not capture structural features at larger length scales. Instead, topological data analysis (TDA) determines the stability of spatial connectivity at varying length scales (i.e. persistent homology), and can compare different particle configurations based on the "cost" of reorganizing one configuration into another. Here, we demonstrate a topology-based machine learning approach for unsupervised profiling of individual and collective phases based on large-scale loops. We show that these topological loops (i.e. dimension 1 homology) are robust to variations in particle number and density, particularly in comparison to connected components (i.e. dimension 0 homology). We use TDA to map out phase diagrams for simulated particles with varying adhesion and propulsion, at constant population size as well as when proliferation is permitted. Next, we use this approach to profile our recent experiments on the clustering of epithelial cells in varying growth factor conditions, which are compared to our simulations. Finally, we characterize the robustness of this approach at varying length scales, with sparse sampling, and over time. Overall, we envision TDA will be broadly applicable as a model-agnostic approach to analyze active systems with varying population size, from cytoskeletal motors to motile cells to flocking or swarming animals.

Intermediate adhesion maximizes migration velocity of multicellular clusters

Collections of cells exhibit coherent migration during morphogenesis, cancer metastasis, and wound healing. In many cases, bigger clusters split, smaller subclusters collide and reassemble, and gaps continually emerge. The connections between cell-level adhesion and cluster-level dynamics, as well as the resulting consequences for cluster properties such as migration velocity, remain poorly understood. Here we investigate collective migration of one- and two-dimensional cell clusters that collectively track chemical gradients using a mechanism based on contact inhibition of locomotion. We develop both a minimal description based on the lattice gas model of statistical physics and a more realistic framework based on the cellular Potts model which captures cell shape changes and cluster rearrangement. In both cases, we find that cells have an optimal adhesion strength that maximizes cluster migration speed. The optimum negotiates a tradeoff between maintaining cell-cell contact and maintaining configurational freedom, and we identify maximal variability in the cluster aspect ratio as a revealing signature. Our results suggest a collective benefit for intermediate cell-cell adhesion.

Gradient sensing via cell communication

Experimental evidence lends support to the conjecture that cell-to-cell communication plays a role in the gradient sensing of chemical species by certain chains of cells. Models have been formulated to explore this idea. For cells with no identifiable sensing structure, Mugler et al. [Proc. Natl. Acad. Sci. (U.S.A.) 113, E689 (2016)10.1073/pnas.1509597112] have defined a particular local excitation, global inhibition (LEGI) model that pits nearest-neighbor communication against local reactions in a noisy environment to suggest how this sensing capability might arise in a physical system. In this study, we generalize the nearest-neighbor communication mechanism in the aforementioned LEGI model in order to explore the extent to which the gradient sensing characteristics depend on the parametrization of the communication itself, as well as on the cell size, the radius of influence of neighboring cells, and the influence of the background noise. Using our generalization and a collection of particular candidate communication models, we find that the precision of gradient sensing is indeed sensitive to the particular communication model, and we derive physical and analytic explanations for these results. The framework established and the associated results should prove useful in understanding the appropriateness of particular cell-to-cell communication models in gradient sensing studies.

Tools for computational analysis of moving boundary problems in cellular mechanobiology

A cell's ability to change shape is one of the most fundamental biological processes and is essential for maintaining healthy organisms. When the ability to control shape goes awry, it often results in a diseased system. As such, it is important to understand the mechanisms that allow a cell to sense and respond to its environment so as to maintain cellular shape homeostasis. Because of the inherent complexity of the system, computational models that are based on sound theoretical understanding of the biochemistry and biomechanics and that use experimentally measured parameters are an essential tool. These models involve an inherent feedback, whereby shape is determined by the action of regulatory signals whose spatial distribution depends on the shape. To carry out computational simulations of these moving boundary problems requires special computational techniques. A variety of alternative approaches, depending on the type and scale of question being asked, have been used to simulate various biological processes, including cell motility, division, mechanosensation, and cell engulfment. In general, these models consider the forces that act on the system (both internally generated, or externally imposed) and the mechanical properties of the cell that resist these forces. Moving forward, making these techniques more accessible to the non-expert will help improve interdisciplinary research thereby providing new insight into important biological processes that affect human health. This article is categorized under: Cancer > Cancer>Computational Models Cancer > Cancer>Molecular and Cellular Physiology.

Collective chemotaxis of active nematic droplets

Collective chemotaxis plays a key role in the navigation of cell clusters in, e.g., embryogenesis and cancer metastasis. Using the active nematic continuum equations, coupled to a chemical field that regulates activity, we demonstrate and explain a physical mechanism that results in collective chemotaxis. The activity naturally leads to cell polarization at the cluster interface which induces outward flows. The chemical gradient then breaks the symmetry of the flow field, leading to a net motion. The velocity is independent of the cluster size, in agreement with experiment.

Collective behaviors of Drosophila-derived retinal progenitors in controlled microenvironments

Collective behaviors of retinal progenitor cells (RPCs) are critical to the development of neural networks needed for vision. Signaling cues and pathways governing retinal cell fate, migration, and functional organization are remarkably conserved across species, and have been well-studied using Drosophila melanogaster. However, the collective migration of heterogeneous groups of RPCs in response to dynamic signaling fields of development remains incompletely understood. This is in large part because the genetic advances of seminal invertebrate models have been poorly complemented by in vitro cell study of its visual development. Tunable microfluidic assays able to replicate the miniature cellular microenvironments of the developing visual system provide newfound opportunities to probe and expand our knowledge of collective chemotactic responses essential to visual development. Our project used a controlled, microfluidic assay to produce dynamic signaling fields of Fibroblast Growth Factor (FGF) that stimulated the chemotactic migration of primary RPCs extracted from Drosophila. Results illustrated collective RPC chemotaxis dependent on average size of clustered cells, in contrast to the non-directional movement of individually-motile RPCs. Quantitative study of these diverse collective responses will advance our understanding of retina developmental processes, and aid study/treatment of inherited eye disease. Lastly, our unique coupling of defined invertebrate models with tunable microfluidic assays provides advantages for future quantitative and mechanistic study of varied RPC migratory responses.

Invertebrate Retinal Progenitors as Regenerative Models in a Microfluidic System

Regenerative retinal therapies have introduced progenitor cells to replace dysfunctional or injured neurons and regain visual function. While contemporary cell replacement therapies have delivered retinal progenitor cells (RPCs) within customized biomaterials to promote viability and enable transplantation, outcomes have been severely limited by the misdirected and/or insufficient migration of transplanted cells. RPCs must achieve appropriate spatial and functional positioning in host retina, collectively, to restore vision, whereas movement of clustered cells differs substantially from the single cell migration studied in classical chemotaxis models. Defining how RPCs interact with each other, neighboring cell types and surrounding extracellular matrixes are critical to our understanding of retinogenesis and the development of effective, cell-based approaches to retinal replacement. The current article describes a new bio-engineering approach to investigate the migratory responses of innate collections of RPCs upon extracellular substrates by combining microfluidics with the well-established invertebrate model of Drosophila melanogaster. Experiments utilized microfluidics to investigate how the composition, size, and adhesion of RPC clusters on defined extracellular substrates affected migration to exogenous chemotactic signaling. Results demonstrated that retinal cluster size and composition influenced RPC clustering upon extracellular substrates of concanavalin (Con-A), Laminin (LM), and poly-L-lysine (PLL), and that RPC cluster size greatly altered collective migratory responses to signaling from Fibroblast Growth Factor (FGF), a primary chemotactic agent in Drosophila. These results highlight the significance of examining collective cell-biomaterial interactions on bio-substrates of emerging biomaterials to aid directional migration of transplanted cells. Our approach further introduces the benefits of pairing genetically controlled models with experimentally controlled microenvironments to advance cell replacement therapies.

Minimal Network Topologies for Signal Processing during Collective Cell Chemotaxis

Cell-cell communication plays an important role in collective cell migration. However, it remains unclear how cells in a group cooperatively process external signals to determine the group's direction of motion. Although the topology of signaling pathways is vitally important in single-cell chemotaxis, the signaling topology for collective chemotaxis has not been systematically studied. Here, we combine mathematical analysis and simulations to find minimal network topologies for multicellular signal processing in collective chemotaxis. We focus on border cell cluster chemotaxis in the Drosophila egg chamber, in which responses to several experimental perturbations of the signaling network are known. Our minimal signaling network includes only four elements: a chemoattractant, the protein Rac (indicating cell activation), cell protrusion, and a hypothesized global factor responsible for cell-cell interaction. Experimental data on cell protrusion statistics allows us to systematically narrow the number of possible topologies from more than 40,000,000 to only six minimal topologies with six interactions between the four elements. This analysis does not require a specific functional form of the interactions, and only qualitative features are needed; it is thus robust to many modeling choices. Simulations of a stochastic biochemical model of border cell chemotaxis show that the qualitative selection procedure accurately determines which topologies are consistent with the experiment. We fit our model for all six proposed topologies; each produces results that are consistent with all experimentally available data. Finally, we suggest experiments to further discriminate possible pathway topologies.

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.

Hybrid epithelial/mesenchymal phenotype(s): The 'fittest' for metastasis?

Metastasis is the leading cause of mortality among cancer patients. Dissemination enabled by an epithelial-to-mesenchymal transition (EMT) of carcinoma cells has long been considered to be the predominant mechanism for carcinoma metastasis, based on overexpression studies of many EMT-inducing transcription factors. Individual CTCs - and a binary framework of EMT - have been long considered to be sufficient and necessary condition for metastasis. However, recent studies have shown that collective migration and invasion through tumor buds and clusters of Circulating Tumor Cells (CTCs) as possibly being the prevalent mode of metastasis, although individual CTCs may still contribute to metastasis. These strands and clusters have been proposed to often exhibit a hybrid epithelial/mesenchymal (E/M) phenotype where cells retain epithelial traits of cell-cell adhesion and simultaneously gain mesenchymal characteristics of migration and invasion. To highlight the crucial questions regarding metastasis, we define EMT in a non-binary and context-specific manner, suggest that it can be viewed as a trans-differentiation process, and illustrate the implications of hybrid E/M phenotype(s) and cluster-based dissemination in metastasis.

Analysis of Hierarchical Organization in Gene Expression Networks Reveals Underlying Principles of Collective Tumor Cell Dissemination and Metastatic Aggressiveness of Inflammatory Breast Cancer

Clusters of circulating tumor cells (CTCs), despite being rare, may account for more than 90% of metastases. Cells in these clusters do not undergo a complete epithelial-to-mesenchymal transition (EMT), but retain some epithelial traits as compared to individually disseminating tumor cells. Determinants of single cell dissemination versus collective dissemination remain elusive. Inflammatory breast cancer (IBC), a highly aggressive breast cancer subtype that chiefly metastasizes via CTC clusters, is a promising model for studying mechanisms of collective tumor cell dissemination. Previous studies, motivated by a theory that suggests physical systems with hierarchical organization tend to be more adaptable, have found that the expression of metastasis-associated genes is more hierarchically organized in cases of successful metastases. Here, we used the cophenetic correlation coefficient (CCC) to quantify the hierarchical organization in the expression of two distinct gene sets, collective dissemination-associated genes and IBC-associated genes, in cancer cell lines and in tumor samples from breast cancer patients. Hypothesizing that a higher CCC for collective dissemination-associated genes and for IBC-associated genes would be associated with retention of epithelial traits enabling collective dissemination and with worse disease progression in breast cancer patients, we evaluated the correlation of CCC with different phenotypic groups. The CCC of both the abovementioned gene sets, the collective dissemination-associated genes and the IBC-associated genes, was higher in (a) epithelial cell lines as compared to mesenchymal cell lines and (b) tumor samples from IBC patients as compared to samples from non-IBC breast cancer patients. A higher CCC of both gene sets was also correlated with a higher rate of metastatic relapse in breast cancer patients. In contrast, neither the levels of CDH1 gene expression nor gene set enrichment analysis (GSEA) of the abovementioned gene sets could provide similar insights. These results suggest that retention of some epithelial traits in disseminating tumor cells as IBC progresses promotes successful breast cancer metastasis. The CCC provides additional information regarding the organizational complexity of gene expression in comparison to GSEA. We have shown that the CCC may be a useful metric for investigating the collective dissemination phenotype and a prognostic factor for IBC.

Collective gradient sensing and chemotaxis: modeling and recent developments

Cells measure a vast variety of signals, from their environment's stiffness to chemical concentrations and gradients; physical principles strongly limit how accurately they can do this. However, when many cells work together, they can cooperate to exceed the accuracy of any single cell. In this topical review, I will discuss the experimental evidence showing that cells collectively sense gradients of many signal types, and the models and physical principles involved. I also propose new routes by which experiments and theory can expand our understanding of these problems.

Cell-to-cell variation sets a tissue-rheology-dependent bound on collective gradient sensing

When a single cell senses a chemical gradient and chemotaxes, stochastic receptor-ligand binding can be a fundamental limit to the cell's accuracy. For clusters of cells responding to gradients, however, there is a critical difference: Even genetically identical cells have differing responses to chemical signals. With theory and simulation, we show collective chemotaxis is limited by cell-to-cell variation in signaling. We find that when different cells cooperate, the resulting bias can be much larger than the effects of ligand-receptor binding. Specifically, when a strongly responding cell is at one end of a cell cluster, cluster motion is biased toward that cell. These errors are mitigated if clusters average measurements over times long enough for cells to rearrange. In consequence, fluid clusters are better able to sense gradients: We derive a link between cluster accuracy, cell-to-cell variation, and the cluster rheology. Because of this connection, increasing the noisiness of individual cell motion can actually increase the collective accuracy of a cluster by improving fluidity.

Modelling the collective response of heterogeneous cell populations to stationary gradients and chemical signal relay

The directed motion of cell aggregates toward a chemical source occurs in many relevant biological processes. Understanding the mechanisms that control this complex behavior is of great relevance for our understanding of developmental biological processes and many diseases. In this paper, we consider a self-propelled particle model for the movement of heterogeneous subpopulations of chemically interacting cells towards an imposed stable chemical gradient. Our simulations show explicitly how self-organisation of cell populations (which could lead to engulfment or complete cell segregation) can arise from the heterogeneity of chemotactic responses alone. This new result complements current theoretical and experimental studies that emphasise the role of differential cell-cell adhesion on self-organisation and spatial structure of cellular aggregates. We also investigate how the speed of individual cell aggregations increases with the chemotactic sensitivity of the cells, and decreases with the number of cells inside the aggregates.

Emergent versus Individual-Based Multicellular Chemotaxis

Multicellular chemotaxis can occur via individually chemotaxing cells that are mechanically coupled. Alternatively, it can emerge collectively, from cells chemotaxing differently in a group than they would individually. Here we consider collective movement that emerges from cells on the exterior of the collective responding to chemotactic signals, whereas bulk cells remain uninvolved in sensing and directing the collective. We find that the precision of this type of emergent chemotaxis is higher than that of individual-based chemotaxis for one-dimensional cell chains and two-dimensional cell sheets, but not three-dimensional cell clusters. We describe the physical origins of these results, discuss their biological implications, and show how they can be tested using common experimental measures such as the chemotactic index.

Collective cell migration: a physics perspective

Cells have traditionally been viewed either as independently moving entities or as somewhat static parts of tissues. However, it is now clear that in many cases, multiple cells coordinate their motions and move as collective entities. Well-studied examples comprise development events, as well as physiological and pathological situations. Different ex vivo model systems have also been investigated. Several recent advances have taken place at the interface between biology and physics, and have benefitted from progress in imaging and microscopy, from the use of microfabrication techniques, as well as from the introduction of quantitative tools and models. We review these interesting developments in quantitative cell biology that also provide rich examples of collective out-of-equilibrium motion.

Collective Chemotaxis through Noisy Multicellular Gradient Sensing

Collective cell migration in response to a chemical cue occurs in many biological processes such as morphogenesis and cancer metastasis. Clusters of migratory cells in these systems are capable of responding to gradients of <1% difference in chemical concentration across a cell length. Multicellular systems are extremely sensitive to their environment, and although the limits to multicellular sensing are becoming known, how this information leads to coherent migration remains poorly understood. We develop a computational model of multicellular sensing and migration in which groups of cells collectively measure noisy chemical gradients. The output of the sensing process is coupled to the polarization of individual cells to model migratory behavior. Through the use of numerical simulations, we find that larger clusters of cells detect the gradient direction with higher precision and thus achieve stronger polarization bias, but larger clusters also induce more drag on collective motion. The trade-off between these two effects leads to an optimal cluster size for most efficient migration. We discuss how our model could be validated using simple, phenomenological experiments.

Inflammatory breast cancer: a model for investigating cluster-based dissemination

Metastases claim more than 90% of cancer-related patient deaths and are usually seeded by a subset of circulating tumor cells shed off from the primary tumor. In circulation, circulating tumor cells are found both as single cells and as clusters of cells. The clusters of circulating tumor cells, although many fewer in number, possess much higher metastatic potential as compared to that of individual circulating tumor cells. In this review, we highlight recent insights into molecular mechanisms that can enable the formation of these clusters—(a) hybrid epithelial/mesenchymal phenotype of cells that couples their ability to migrate and adhere, and (b) intercellular communication that can spatially coordinate the cluster formation and provide survival signals to cancer cells. Building upon these molecular mechanisms, we also offer a possible mechanistic understanding of why clusters are endowed with a higher metastatic potential. Finally, we discuss the highly aggressive Inflammatory Breast Cancer as an example of a carcinoma that can metastasize via clusters and corroborates the proposed molecular mechanisms.

Mechanisms of Cell Polarization

Cell polarization is a key step in the migration, development, and organization of eukaryotic cells, both at the single cell and multicellular level. Research on the mechanisms that give rise to polarization of a given cell, and organization of polarity within a tissue has led to new understanding across cellular and developmental biology. In this review, we describe some of the history of theoretical and experimental aspects of the field, as well as some interesting questions and challenges for the future.

Physical models of collective cell motility: from cell to tissue

In this article, we review physics-based models of collective cell motility. We discuss a range of techniques at different scales, ranging from models that represent cells as simple self-propelled particles to phase field models that can represent a cell's shape and dynamics in great detail. We also extensively review the ways in which cells within a tissue choose their direction, the statistics of cell motion, and some simple examples of how cell-cell signaling can interact with collective cell motility. This review also covers in more detail selected recent works on collective cell motion of small numbers of cells on micropatterns, in wound healing, and the chemotaxis of clusters of cells.

Modeling Contact Inhibition of Locomotion of Colliding Cells Migrating on Micropatterned Substrates

In cancer metastasis, embryonic development, and wound healing, cells can coordinate their motion, leading to collective motility. To characterize these cell-cell interactions, which include contact inhibition of locomotion (CIL), micropatterned substrates are often used to restrict cell migration to linear, quasi-one-dimensional paths. In these assays, collisions between polarized cells occur frequently with only a few possible outcomes, such as cells reversing direction, sticking to one another, or walking past one another. Using a computational phase field model of collective cell motility that includes the mechanics of cell shape and a minimal chemical model for CIL, we are able to reproduce all cases seen in two-cell collisions. A subtle balance between the internal cell polarization, CIL and cell-cell adhesion governs the collision outcome. We identify the parameters that control transitions between the different cases, including cell-cell adhesion, propulsion strength, and the rates of CIL. These parameters suggest hypotheses for why different cell types have different collision behavior and the effect of interventions that modulate collision outcomes. To reproduce the heterogeneity in cell-cell collision outcomes observed experimentally in neural crest cells, we must either carefully tune our parameters or assume that there is significant cell-to-cell variation in key parameters like cell-cell adhesion.

Many cells cooperate with their neighbors to move as a group. However, the mechanisms of these cell-cell interactions are not well understood. One experimental tool to analyze interactions is to allow cells to collide with one another, and see what happens. In order to better understand what features these experiments measure, we develop a computational model of cell-cell collisions, and identify the biochemical and mechanical parameters that lead to different outcomes of collisions. We can recreate all known types of collisions seen in experiments, including cells reversing on contact, sticking, or walking past each other. Our model suggests that what happens in a collision may depend strongly on the mechanical forces between the two cells.

Contact inhibition of locomotion determines cell-cell and cell-substrate forces in tissues

Cells organized in tissues exert forces on their neighbors and their environment. Those cellular forces determine tissue homeostasis as well as reorganization during embryonic development and wound healing. To understand how cellular forces are generated and how they can influence the tissue state, we develop a particle-based simulation model for adhesive cell clusters and monolayers. Cells are contractile, exert forces on their substrate and on each other, and interact through contact inhibition of locomotion (CIL), meaning that cell-cell contacts suppress force transduction to the substrate and propulsion forces align away from neighbors. Our model captures the traction force patterns of small clusters of nonmotile cells and larger sheets of motile Madin-Darby canine kidney (MDCK) cells. In agreement with observations in a spreading MDCK colony, the cell density in the center increases as cells divide and the tissue grows. A feedback between cell density, CIL, and cell-cell adhesion gives rise to a linear relationship between cell density and intercellular tensile stress and forces the tissue into a nonmotile state characterized by a broad distribution of traction forces. Our model also captures the experimentally observed tissue flow around circular obstacles, and CIL accounts for traction forces at the edge.