Connecting individual to collective cell migration

CO2-Free On-Stage Incubator for Live Cell Imaging of Cholangiocarcinoma Cell Migration on Microfluidic Device

Long-term live cell imaging requires sophisticated and fully automated commercial-stage incubators equipped with specified inverted microscopes to regulate temperature, CO2 content, and humidity. In this study, we present a CO2-free on-stage incubator specifically designed for use across various cell culture platforms, enabling live cell imaging applications. A simple and transparent incubator was fabricated from acrylic sheets to be easily placed on the stages of most inverted microscopes. We successfully performed live-cell imaging of cholangiocarcinoma (CCA) cells and HeLa cell dynamics in both 2D and 3D microenvironments over three days. We also analyzed directed cell migration under high serum induction within a microfluidic device. Interesting phenomena such as "whole-colony migration", "novel type of collective cell migration" and "colony formation during cell and colony migration" are reported here for the first time, to the best of our knowledge. These phenomena may improve our understanding of the nature of cell migration and cancer metastasis.

Maximum likelihood phylogeographic inference of cell motility and cell division from spatial lineage tracing data

MOTIVATION

Recently developed spatial lineage tracing technologies induce somatic mutations at specific genomic loci in a population of growing cells and then measure these mutations in the sampled cells along with the physical locations of the cells. These technologies enable high-throughput studies of developmental processes over space and time. However, these applications rely on accurate reconstruction of a spatial cell lineage tree describing both past cell divisions and cell locations. Spatial lineage trees are related to phylogeographic models that have been well-studied in the phylogenetics literature. We demonstrate that standard phylogeographic models based on Brownian motion are inadequate to describe the spatial symmetric displacement (SD) of cells during cell division.

RESULTS

We introduce a new model-the SD model for cell motility that includes symmetric displacements of daughter cells from the parental cell followed by independent diffusion of daughter cells. We show that this model more accurately describes the locations of cells in a real spatial lineage tracing of mouse embryonic stem cells. Combining the spatial SD model with an evolutionary model of DNA mutations, we obtain a phylogeographic model for spatial lineage tracing. Using this model, we devise a maximum likelihood framework-MOLLUSC (Maximum Likelihood Estimation Of Lineage and Location Using Single-Cell Spatial Lineage tracing Data)-to co-estimate time-resolved branch lengths, spatial diffusion rate, and mutation rate. On both simulated and real data, we show that MOLLUSC accurately estimates all parameters. In contrast, the Brownian motion model overestimates spatial diffusion rate in all test cases. In addition, the inclusion of spatial information improves accuracy of branch length estimation compared to sequence data alone. On real data, we show that spatial information has more signal than sequence data for branch length estimation, suggesting augmenting lineage tracing technologies with spatial information is useful to overcome the limitations of genome-editing in developmental systems.

AVAILABILITY AND IMPLEMENTATION

The python implementation of MOLLUSC is available at https://github.com/raphael-group/MOLLUSC.

Dynamics of multicellular swirling on micropatterned substrates

Chirality plays a crucial role in biology, as it is highly conserved and fundamentally important in the developmental process. To better understand the relationship between the chirality of individual cells and that of tissues and organisms, we develop a generalized mechanics model of chiral polarized particles to investigate the swirling dynamics of cell populations on substrates. Our analysis reveals that cells with the same chirality can form distinct chiral patterns on ring-shaped or rectangular substrates. Interestingly, our studies indicate that an excessively strong or weak individual cellular chirality hinders the formation of such chiral patterns. Our studies also indicate that there exists the influence distance of substrate boundaries in chiral patterns. Smaller influence distances are observed when cell-cell interactions are weaker. Conversely, when cell-cell interactions are too strong, multiple cells tend to be stacked together, preventing the formation of chiral patterns on substrates in our analysis. Additionally, we demonstrate that the interaction between cells and substrate boundaries effectively controls the chiral distribution of cellular orientations on ring-shaped substrates. This research highlights the significance of coordinating boundary features, individual cellular chirality, and cell-cell interactions in governing the chiral movement of cell populations and provides valuable mechanics insights into comprehending the intricate connection between the chirality of single cells and that of tissues and organisms.

Computational modeling of angiogenesis: The importance of cell rearrangements during vascular growth

Angiogenesis is the process wherein endothelial cells (ECs) form sprouts that elongate from the pre-existing vasculature to create new vascular networks. In addition to its essential role in normal development, angiogenesis plays a vital role in pathologies such as cancer, diabetes and atherosclerosis. Mathematical and computational modeling has contributed to unraveling its complexity. Many existing theoretical models of angiogenic sprouting are based on the "snail-trail" hypothesis. This framework assumes that leading ECs positioned at sprout tips migrate toward low-oxygen regions while other ECs in the sprout passively follow the leaders' trails and proliferate to maintain sprout integrity. However, experimental results indicate that, contrary to the snail-trail assumption, ECs exchange positions within developing vessels, and the elongation of sprouts is primarily driven by directed migration of ECs. The functional role of cell rearrangements remains unclear. This review of the theoretical modeling of angiogenesis is the first to focus on the phenomenon of cell mixing during early sprouting. We start by describing the biological processes that occur during early angiogenesis, such as phenotype specification, cell rearrangements and cell interactions with the microenvironment. Next, we provide an overview of various theoretical approaches that have been employed to model angiogenesis, with particular emphasis on recent in silico models that account for the phenomenon of cell mixing. Finally, we discuss when cell mixing should be incorporated into theoretical models and what essential modeling components such models should include in order to investigate its functional role. This article is categorized under: Cardiovascular Diseases > Computational Models Cancer > Computational Models.

Pulling the strings on solid-to-liquid phase transitions in cell collectives

Cell collectives must dynamically adapt to different biological contexts. For instance, in homeostatic conditions, epithelia must establish a barrier between body compartments and resist external stresses, while during development, wound healing or cancer invasion, these tissues undergo extensive remodeling. Using analogies from inert, passive materials, changes in cellular density, shape, rearrangements and/or migration were shown to result in collective transitions between solid and fluid states. However, what biological mechanisms govern these transitions remains an open question. In particular, the upstream signaling pathways and molecular effectors controlling the key physical axes determining tissue rheology and dynamics remain poorly understood. In this perspective, we focus on emerging evidence identifying the first biological signals determining the collective state of living tissues, with an emphasis on how these mechanisms are exploited for functionality across biological contexts.

A deep learning-based pipeline for analyzing the influences of interfacial mechanochemical microenvironments on spheroid invasion using differential interference contrast microscopic images

Metastasis is the leading cause of cancer-related deaths. During this process, cancer cells are likely to navigate discrete tissue-tissue interfaces, enabling them to infiltrate and spread throughout the body. Three-dimensional (3D) spheroid modeling is receiving more attention due to its strengths in studying the invasive behavior of metastatic cancer cells. While microscopy is a conventional approach for investigating 3D invasion, post-invasion image analysis, which is a time-consuming process, remains a significant challenge for researchers. In this study, we presented an image processing pipeline that utilized a deep learning (DL) solution, with an encoder-decoder architecture, to assess and characterize the invasion dynamics of tumor spheroids. The developed models, equipped with feature extraction and measurement capabilities, could be successfully utilized for the automated segmentation of the invasive protrusions as well as the core region of spheroids situated within interfacial microenvironments with distinct mechanochemical factors. Our findings suggest that a combination of the spheroid culture and DL-based image analysis enable identification of time-lapse migratory patterns for tumor spheroids above matrix-substrate interfaces, thus paving the foundation for delineating the mechanism of local invasion during cancer metastasis.

Large Coherent States Formed from Disordered k-Regular Random Graphs

The present work is motivated by the need for robust, large-scale coherent states that can play possible roles as quantum resources. A challenge is that large, complex systems tend to be fragile. However, emergent phenomena in classical systems tend to become more robust with scale. Do these classical systems inspire ways to think about robust quantum networks? This question is studied by characterizing the complex quantum states produced by mapping interactions between a set of qubits from structure in graphs. We focus on maps based on k-regular random graphs where many edges were randomly deleted. We ask how many edge deletions can be tolerated. Surprisingly, it was found that the emergent coherent state characteristic of these graphs was robust to a substantial number of edge deletions. The analysis considers the possible role of the expander property of k-regular random graphs.

Engineering tools for quantifying and manipulating forces in epithelia

The integrity of epithelia is maintained within dynamic mechanical environments during tissue development and homeostasis. Understanding how epithelial cells mechanosignal and respond collectively or individually is critical to providing insight into developmental and (patho)physiological processes. Yet, inferring or mimicking mechanical forces and downstream mechanical signaling as they occur in epithelia presents unique challenges. A variety of in vitro approaches have been used to dissect the role of mechanics in regulating epithelia organization. Here, we review approaches and results from research into how epithelial cells communicate through mechanical cues to maintain tissue organization and integrity. We summarize the unique advantages and disadvantages of various reduced-order model systems to guide researchers in choosing appropriate experimental systems. These model systems include 3D, 2D, and 1D micromanipulation methods, single cell studies, and noninvasive force inference and measurement techniques. We also highlight a number of in silico biophysical models that are informed by in vitro and in vivo observations. Together, a combination of theoretical and experimental models will aid future experiment designs and provide predictive insight into mechanically driven behaviors of epithelial dynamics.

Mathematical model of mechano-sensing and mechanically induced collective motility of cells on planar elastic substrates

Cells mechanically interact with their environment to sense, for example, topography, elasticity and mechanical cues from other cells. Mechano-sensing has profound effects on cellular behaviour, including motility. The current study aims to develop a mathematical model of cellular mechano-sensing on planar elastic substrates and demonstrate the model's predictive capabilities for the motility of individual cells in a colony. In the model, a cell is assumed to transmit an adhesion force, derived from a dynamic focal adhesion integrin density, that locally deforms a substrate, and to sense substrate deformation originating from neighbouring cells. The substrate deformation from multiple cells is expressed as total strain energy density with a spatially varying gradient. The magnitude and direction of the gradient at the cell location define the cell motion. Cell-substrate friction, partial motion randomness, and cell death and division are included. The substrate deformation by a single cell and the motility of two cells are presented for several substrate elasticities and thicknesses. The collective motility of 25 cells on a uniform substrate mimicking the closure of a circular wound of 200 µm is predicted for deterministic and random motion. Cell motility on substrates with varying elasticity and thickness is explored for four cells and 15 cells, the latter again mimicking wound closure. Wound closure by 45 cells is used to demonstrate the simulation of cell death and division during migration. The mathematical model can adequately simulate the mechanically induced collective cell motility on planar elastic substrates. The model is suitable for extension to other cell and substrates shapes and the inclusion of chemotactic cues, offering the potential to complement in vitro and in vivo studies.

Accelerated epithelial layer healing induced by tactile anisotropy in surface topography

Mammalian cells respond to tactile cues from topographic elements presented by the substrate. Among these, anisotropic features distributed in an ordered manner give directionality. In the extracellular matrix, this ordering is embedded in a noisy environment altering the contact guidance effect. To date, it is unclear how cells respond to topographical signals in a noisy environment. Here, using rationally designed substrates, we report morphotaxis, a guidance mechanism enabling fibroblasts and epithelial cells to move along gradients of topographic order distortion. Isolated cells and cell ensembles perform morphotaxis in response to gradients of different strength and directionality, with mature epithelia integrating variations of topographic order over hundreds of micrometers. The level of topographic order controls cell cycle progression, locally delaying or promoting cell proliferation. In mature epithelia, the combination of morphotaxis and noise-dependent distributed proliferation provides a strategy to enhance wound healing as confirmed by a mathematical model capturing key elements of the process.

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.

Disentangling cadherin-mediated cell-cell interactions in collective cancer cell migration

Cell dispersion from a confined area is fundamental in a number of biological processes, including cancer metastasis. To date, a quantitative understanding of the interplay of single-cell motility, cell proliferation, and intercellular contacts remains elusive. In particular, the role of E- and N-cadherin junctions, central components of intercellular contacts, is still controversial. Combining theoretical modeling with in vitro observations, we investigate the collective spreading behavior of colonies of human cancer cells (T24). The spreading of these colonies is driven by stochastic single-cell migration with frequent transient cell-cell contacts. We find that inhibition of E- and N-cadherin junctions decreases colony spreading and average spreading velocities, without affecting the strength of correlations in spreading velocities of neighboring cells. Based on a biophysical simulation model for cell migration, we show that the behavioral changes upon disruption of these junctions can be explained by reduced repulsive excluded volume interactions between cells. This suggests that in cancer cell migration, cadherin-based intercellular contacts sharpen cell boundaries leading to repulsive rather than cohesive interactions between cells, thereby promoting efficient cell spreading during collective migration.

Tunable 3D Hydrogel Microchannel Networks to Study Confined Mammalian Cell Migration

Cells adapt and move due to chemical, physical, and mechanical cues from their microenvironment. It is therefore important to create materials that mimic human tissue physiology by surface chemistry, architecture, and dimensionality to control cells in biomedical settings. The impact of the environmental architecture is particularly relevant in the context of cancer cell metastasis, where cells migrate through small constrictions in their microenvironment to invade surrounding tissues. Here, a synthetic hydrogel scaffold with an interconnected, random, 3D microchannel network is presented that is functionalized with collagen to promote cell adhesion. It is shown that cancer cells can invade such scaffolds within days, and both the microarchitecture and stiffness of the hydrogel modulate cell invasion and nuclear dynamics of the cells. Specifically, it is found that cell migration through the microchannels is a function of hydrogel stiffness. In addition to this, it is shown that the hydrogel stiffness and confinement, influence the occurrence of nuclear envelope ruptures of cells. The tunable hydrogel microarchitecture and stiffness thus provide a novel tool to investigate cancer cell invasion as a function of the 3D microenvironment. Furthermore, the material provides a promising strategy to control cell positioning, migration, and cellular function in biological applications, such as tissue engineering.

Paxillin Promotes Breast Tumor Collective Cell Invasion through Maintenance of Adherens Junction Integrity

Distant organ metastasis is linked to poor prognosis during cancer progression. The expression level of the focal adhesion adapter protein paxillin varies among different human cancers, but its role in tumor progression is unclear. Herein, we utilize a newly generated PyMT mammary tumor mouse model with conditional paxillin ablation in breast tumor epithelial cells, combined with in vitro 3D tumor organoids invasion analysis and 2D calcium switch assays, to assess the roles for paxillin in breast tumor cell invasion. Paxillin had little effect on primary tumor initiation and growth but is critical for the formation of distant lung metastasis. In paxillin-depleted 3D tumor organoids, collective cell invasion was substantially perturbed. Two-dimensional cell culture revealed paxillin-dependent stabilization of adherens junctions (AJ). Mechanistically, paxillin is required for AJ assembly through facilitating E-cadherin endocytosis and recycling and HDAC6-mediated microtubule acetylation. Furthermore, Rho GTPase activity analysis and rescue experiments with a RhoA activator or Rac1 inhibitor suggest paxillin is potentially regulating the E-cadherin-dependent junction integrity and contractility through control of the balance of RhoA and Rac1 activities. Together, these data highlight new roles for paxillin in the regulation of cell-cell adhesion and collective tumor cell migration to promote the formation of distance organ metastases. [Media: see text] [Media: see text] [Media: see text] [Media: see text] [Media: see text] [Media: see text] [Media: see text] [Media: see text].

Synthetic Cell as a Platform for Understanding Membrane-Membrane Interactions

In the pursuit of understanding life, model membranes made of phospholipids were envisaged decades ago as a platform for the bottom-up study of biological processes. Micron-sized lipid vesicles have gained great acceptance as their bilayer membrane resembles the natural cell membrane. Important biological events involving membranes, such as membrane protein insertion, membrane fusion, and intercellular communication, will be highlighted in this review with recent research updates. We will first review different lipid bilayer platforms used for incorporation of integral membrane proteins and challenges associated with their functional reconstitution. We next discuss different methods for reconstitution of membrane fusion and compare their fusion efficiency. Lastly, we will highlight the importance and challenges of intercellular communication between synthetic cells and synthetic cells-to-natural cells. We will summarize the review by highlighting the challenges and opportunities associated with studying membrane-membrane interactions and possible future research directions.

Born to Run? Diverse Modes of Epithelial Migration

Bundled with various kinds of adhesion molecules and anchored to the basement membrane, the epithelium has historically been considered as an immotile tissue and, to migrate, it first needs to undergo epithelial-mesenchymal transition (EMT). Since its initial description more than half a century ago, the EMT process has fascinated generations of developmental biologists and, more recently, cancer biologists as it is believed to be essential for not only embryonic development, organ formation, but cancer metastasis. However, recent progress shows that epithelium is much more motile than previously realized. Here, we examine the emerging themes in epithelial collective migration and how this has impacted our understanding of EMT.

Roles of leader and follower cells in collective cell migration

Collective cell migration is a widely observed phenomenon during animal development, tissue repair, and cancer metastasis. Considering its broad involvement in biological processes, it is essential to understand the basics behind the collective movement. Based on the topology of migrating populations, tissue-scale kinetics, called the “leader–follower” model, has been proposed for persistent directional collective movement. Extensive in vivo and in vitro studies reveal the characteristics of leader cells, as well as the special mechanisms leader cells employ for maintaining their positions in collective migration. However, follower cells have attracted increasing attention recently due to their important contributions to collective movement. In this Perspective, the current understanding of the molecular mechanisms behind the “leader–follower” model is reviewed with a special focus on the force transmission and diverse roles of leaders and followers during collective cell movement.

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.

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.

Evolution of multicellularity by collective integration of spatial information

At the origin of multicellularity, cells may have evolved aggregation in response to predation, for functional specialisation or to allow large-scale integration of environmental cues. These group-level properties emerged from the interactions between cells in a group, and determined the selection pressures experienced by these cells. We investigate the evolution of multicellularity with an evolutionary model where cells search for resources by chemotaxis in a shallow, noisy gradient. Cells can evolve their adhesion to others in a periodically changing environment, where a cell's fitness solely depends on its distance from the gradient source. We show that multicellular aggregates evolve because they perform chemotaxis more efficiently than single cells. Only when the environment changes too frequently, a unicellular state evolves which relies on cell dispersal. Both strategies prevent the invasion of the other through interference competition, creating evolutionary bi-stability. Therefore, collective behaviour can be an emergent selective driver for undifferentiated multicellularity.

Disease-associated keratin mutations reduce traction forces and compromise adhesion and collective migration

Keratin intermediate filament (IF) proteins constitute the major cytoskeletal components in epithelial cells. Missense mutations in keratin 5 (K5; also known as KRT5) or keratin 14 (K14; also known as KRT14), highly expressed in the basal epidermis, cause the severe skin blistering disease epidermolysis bullosa simplex (EBS). EBS-associated mutations disrupt keratin networks and change keratinocyte mechanics; however, molecular mechanisms by which mutations shape EBS pathology remain incompletely understood. Here, we demonstrate that, in contrast to keratin-deficient keratinocytes, cells expressing K14R125C, a mutation that causes severe EBS, generate lower traction forces, accompanied by immature focal adhesions with an altered cellular distribution. Furthermore, mutant keratinocytes display reduced directionality during collective migration. Notably, RhoA activity is downregulated in human EBS keratinocytes, and Rho activation rescues stiffness-dependent cell-extracellular matrix (ECM) adhesion formation of EBS keratinocytes. Collectively, our results strongly suggest that intact keratin IF networks regulate mechanotransduction through a Rho signaling pathway upstream of cell-ECM adhesion formation and organized cell migration. Our findings provide insights into the underlying pathophysiology of EBS.This article has an associated First Person interview with the first author of the paper.

Tethering, evagination, and vesiculation via cell-cell interactions in microvascular flow

Vesiculation is a ubiquitous process undergone by most cell types and serves a variety of vital cell functions; vesiculation from erythrocytes, in particular, is a well-known example and constitutes a self-protection mechanism against premature clearance, inter alia. Herein, we explore a paradigm that red blood cell derived vesicles may form within the microvascular, in intense shear flow, where cells become adhered to either other cells or the extracellular matrix, by forming tethers or an evagination. Adherence may be enhanced, or caused, by diseased states or chemical anomalies as are discussed herein. The mechanisms for such processes are detailed via numerical simulations that are patterned directly from video-recorded cell microflow within the splenic venous sinus (MacDonald et al. 1987), as included, e.g., as Supplementary Material. The mechanisms uncovered highlight the necessity of accounting for remodeling of the erythrocyte's membrane skeleton and, specifically, for the time scales associated with that process that is an integral part of cell deformation. In this way, the analysis provides pointed, and vital, insights into the notion of what the, often used phrase, cell deformability actually entails in a more holistic manner. The analysis also details what data are required to make further quantitative descriptions possible and suggests experimental pathways for acquiring such.

Decoding collective communications using information theory tools

Organisms have evolved sensory mechanisms to extract pertinent information from their environment, enabling them to assess their situation and act accordingly. For social organisms travelling in groups, like the fish in a school or the birds in a flock, sharing information can further improve their situational awareness and reaction times. Data on the benefits and costs of social coordination, however, have largely allowed our understanding of why collective behaviours have evolved to outpace our mechanistic knowledge of how they arise. Recent studies have begun to correct this imbalance through fine-scale analyses of group movement data. One approach that has received renewed attention is the use of information theoretic (IT) tools like mutual information, transfer entropy and causation entropy, which can help identify causal interactions in the type of complex, dynamical patterns often on display when organisms act collectively. Yet, there is a communications gap between studies focused on the ecological constraints and solutions of collective action with those demonstrating the promise of IT tools in this arena. We attempt to bridge this divide through a series of ecologically motivated examples designed to illustrate the benefits and challenges of using IT tools to extract deeper insights into the interaction patterns governing group-level dynamics. We summarize some of the approaches taken thus far to circumvent existing challenges in this area and we conclude with an optimistic, yet cautionary perspective.

Continuum descriptions of spatial spreading for heterogeneous cell populations: Theory and experiment

Variability in cell populations is frequently observed in both in vitro and in vivo settings. Intrinsic differences within populations of cells, such as differences in cell sizes or differences in rates of cell motility, can be present even within a population of cells from the same cell line. We refer to this variability as cell heterogeneity. Mathematical models of cell migration, for example, in the context of tumour growth and metastatic invasion, often account for both undirected (random) migration and directed migration that is mediated by cell-to-cell contacts and cell-to-cell adhesion. A key feature of standard models is that they often assume that the population is composed of identical cells with constant properties. This leads to relatively simple single-species homogeneous models that neglect the role of heterogeneity. In this work, we use a continuum modelling approach to explore the role of heterogeneity in spatial spreading of cell populations. We employ a three-species heterogeneous model of cell motility that explicitly incorporates different types of experimentally-motivated heterogeneity in cell sizes: (i) monotonically decreasing; (ii) uniform; (iii) non-monotonic; and (iv) monotonically increasing distributions of cell size. Comparing the density profiles generated by the three-species heterogeneous model with density profiles predicted by a more standard single-species homogeneous model reveals that when we are dealing with monotonically decreasing and uniform distributions a simple and computationally efficient single-species homogeneous model can be remarkably accurate in describing the evolution of a heterogeneous cell population. In contrast, we find that the simpler single-species homogeneous model performs relatively poorly when applied to non-monotonic and monotonically increasing distributions of cell sizes. Additional results for heterogeneity in parameters describing both undirected and directed cell migration are also considered, and we find that similar results apply.

A DISCRETE MATHEMATICAL MODEL FOR SINGLE AND COLLECTIVE MOVEMENT IN AMOEBOID CELLS

In this paper, we develop a new discrete mathematical model for individual and collective cell motility. We introduce a mechanical model for the movement of a cell on a two-dimensional rigid surface to describe and investigate the cell–cell and cell–substrate interactions. The cell cytoskeleton is modeled as a series of springs and dashpots connected in parallel. The cell–substrate attachments and the cell protrusions are also included. In particular, this model is used to describe the directed movement of endothelial cells on a Matrigel plate. We compare the results from our model with experimental data. We show that cell density and substrate rigidity play an important role in network formation.

Dancing Styles of Collective Cell Migration: Image-Based Computational Analysis of JRAB/MICAL-L2

Collective cell migration is observed during morphogenesis, angiogenesis, and wound healing, and this type of cell migration also contributes to efficient metastasis in some kinds of cancers. Because collectively migrating cells are much better organized than a random assemblage of individual cells, there seems to be a kind of order in migrating clusters. Extensive research has identified a large number of molecules involved in collective cell migration, and these factors have been analyzed using dramatic advances in imaging technology. To date, however, it remains unclear how myriad cells are integrated as a single unit. Recently, we observed unbalanced collective cell migrations that can be likened to either precision dancing or awa-odori, Japanese traditional dancing similar to the style at Rio Carnival, caused by the impairment of the conformational change of JRAB/MICAL-L2. This review begins with a brief history of image-based computational analyses on cell migration, explains why quantitative analysis of the stylization of collective cell behavior is difficult, and finally introduces our recent work on JRAB/MICAL-L2 as a successful example of the multidisciplinary approach combining cell biology, live imaging, and computational biology. In combination, these methods have enabled quantitative evaluations of the “dancing style” of collective cell migration.