Dynamic heterogeneity influences the leader-follower dynamics during epithelial wound closure

Phenotype structuring in collective cell migration: a tutorial of mathematical models and methods

Populations are heterogeneous, deviating in numerous ways. Phenotypic diversity refers to the range of traits or characteristics across a population, where for cells this could be the levels of signalling, movement and growth activity, etc. Clearly, the phenotypic distribution - and how this changes over time and space - could be a major determinant of population-level dynamics. For instance, across a cancerous population, variations in movement, growth, and ability to evade death may determine its growth trajectory and response to therapy. In this review, we discuss how classical partial differential equation (PDE) approaches for modelling cellular systems and collective cell migration can be extended to include phenotypic structuring. The resulting non-local models - which we refer to as phenotype-structured partial differential equations (PS-PDEs) - form a sophisticated class of models with rich dynamics. We set the scene through a brief history of structured population modelling, and then review the extension of several classic movement models - including the Fisher-KPP and Keller-Segel equations - into a PS-PDE form. We proceed with a tutorial-style section on derivation, analysis, and simulation techniques. First, we show a method to formally derive these models from underlying agent-based models. Second, we recount travelling waves in PDE models of spatial spread dynamics and concentration phenomena in non-local PDE models of evolutionary dynamics, and combine the two to deduce phenotypic structuring across travelling waves in PS-PDE models. Third, we discuss numerical methods to simulate PS-PDEs, illustrating with a simple scheme based on the method of lines and noting the finer points of consideration. We conclude with a discussion of future modelling and mathematical challenges.

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

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

Structural fluctuations in active glasses

The glassy dynamics of dense active matter have recently become a topic of interest due to their importance in biological processes such as wound healing and tissue development. However, while the liquid-state properties of dense active matter have been studied in relation to the glass transition of active matter, the solid-state properties of active glasses have yet to be understood. In this work, we study the structural fluctuations in the active glasses composed of self-propelled particles. We develop a formalism to describe the solid-state properties of active glasses in the harmonic approximation limit and use it to analyze the displacement fields in the active glasses. Our findings reveal that the dynamics of high-frequency normal modes become quasi-static with respect to the active forces, and consequently, excitations of these modes are significantly suppressed. This leads to a violation of the equipartition law, suppression of particle displacements, and the apparent collective motion of active glasses. Overall, our results provide a fundamental understanding of the solid-state properties of active glasses.

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.

Adhesion and Polarity protein distribution-regulates hexagon dominated plasma membrane organization in Drosophila blastoderm embryos

Epithelial cells contain polarity complexes on the lateral membrane and are organized in a hexagon-dominated polygonal array. The mechanisms regulating the organization of polygonal architecture in metazoan embryogenesis are not completely understood. Drosophila embryogenesis enables mechanistic analysis of epithelial polarity formation and its impact on polygonal organization. The plasma membrane (PM) of syncytial Drosophila blastoderm embryos is organized as a polygonal array with pseudocleavage furrow formation during the almost synchronous cortical division cycles. We find that polygonal (PM) organization arises in the metaphase (MP) of division cycle 11, and hexagon dominance occurs with an increase in furrow length in the metaphase of cycle 12. There is a decrease in cell shape index in metaphase from cycles 11 to 13. This coincides with Drosophila E-cad (DE-cadherin) and Bazooka enrichment at the edges and the septin, Peanut at the vertices of the furrow. We further assess the role of polarity and adhesion proteins in pseudocleavage furrow formation and its organization as a polygonal array. We find that DE-cadherin depletion leads to decreased furrow length, loss of hexagon dominance, and increased cell shape index. Bazooka and Peanut depletion lead to decreased furrow length, delay in onset of hexagon dominance from cycle 12 to 13, and increased cell shape index. Hexagon dominance occurs with an increase in furrow length in cycle 13 and increased DE-cadherin, possibly due to the inhibition of endocytosis. We conclude that polarity protein recruitment and regulation of endocytic pathways enable pseudocleavage furrow stability and the formation of a hexagon-dominated polygon array.

Spatiotemporal single-cell tracking analysis in 3D tissues to reveal heterogeneous cellular response to mechanical stimuli

Mechanical stimuli have been recognized as important for tissue maturation, homeostasis and constructing engineered three-dimensional (3D) tissues. However, we know little about the cellular mechanical response in tissues that could be considerably heterogeneous and spatiotemporally dynamic due to the complex structure of tissues. Here, we report a spatiotemporal single-cell tracking analysis of in vitro 3D tissues under mechanical stretch, to reveal the heterogeneous cellular behavior by using a developed stretch and optical live imaging system. The system could affect the cellular orientation and directly measure the distance of cells in in vitro 3D myoblast tissues (3DMTs) at the single-cell level. Moreover, we observed the spatiotemporal heterogeneous cellular locomotion and shape changes under mechanical stretch in 3DMTs. This single-cell tracking analysis can become a principal method to investigate the heterogeneous cellular response in tissues and provide insights that conventional analyses have not yet offered.

Collective heterogeneity of mitochondrial potential in contact inhibition of proliferation

In the epithelium, cell density and cell proliferation are closely connected to each other through contact inhibition of proliferation (CIP). Depending on cell density, CIP proceeds through three distinct stages: the free-growing stage at low density, the pre-epithelial transition stage at medium density, and the post-epithelial transition stage at high density. Previous studies have elucidated how cell morphology, motion, and mechanics vary in these stages. However, it remains unknown whether cellular metabolism also has a density-dependent behavior. By measuring the mitochondrial membrane potential at different cell densities, here we reveal a heterogeneous landscape of metabolism in the epithelium, which appears qualitatively distinct in three stages of CIP and did not follow the trend of other CIP-associated parameters, which increases or decreases monotonically with increasing cell density. Importantly, epithelial cells established a collective metabolic heterogeneity exclusively in the pre-epithelial transition stage, where the multicellular clusters of high- and low-potential cells emerged. However, in the post-epithelial transition stage, the metabolic potential field became relatively homogeneous. Next, to study the underlying dynamics, we constructed a system biology model, which predicted the role of cell proliferation in metabolic potential toward establishing collective heterogeneity. Further experiments indeed revealed that the metabolic pattern spatially correlated with the proliferation capacity of cells, as measured by the nuclear localization of a pro-proliferation protein, YAP. Finally, experiments perturbing the actomyosin contractility revealed that, while metabolic heterogeneity was maintained in the absence of actomyosin contractility, its ab initio emergence depended on the latter. Taken together, our results revealed a density-dependent collective heterogeneity in the metabolic field of a pre-epithelial transition-stage epithelial monolayer, which may have significant implications for epithelial form and function.

Continuum description of confluent tissues with spatial heterogeneous activity

A continuum description is built to characterize the stationary and transient deformations of confluent tissues subject to heterogeneous activities. By defining a coarse-grained texture matrix field to represent the shape and size of cells, we derive the coarse-grained stress tensor for the vertex model. Activity in the tissue takes the form of inhomogeneous apical contractions, which can be modeled as reductions of the vertex model reference areas or perimeters representing activity in the medial and perimeter regions of the cells, respectively. For medial activity, the extra stress is just an isotropic pressure, while for perimeter activity, it also has a deviatoric component, which is aligned with the texture matrix. The predictions of the continuum description are compared with the average spatiotemporal deformations obtained in simulations of the vertex model subject to localized apical contractions, showing an excellent agreement, even if the active patch is as small as one cell. The fluctuations around the average are more prominent when the activity is in the medial region due to the lack of negative active shape feedback, which, coupled with the confluent property, increases cellular shape and size variations.

Dynamical heterogeneity in active glasses is inherently different from its equilibrium behavior

Activity-driven glassy dynamics, while ubiquitous in collective cell migration, intracellular transport, dynamics in bacterial and ant colonies, etc., also extends the scope and extent of the as-yet mysterious physics of glass transition. Active glasses are hitherto assumed to be qualitatively similar to their equilibrium counterparts at an effective temperature, [Formula: see text]. Here, we combine large-scale simulations and an analytical mode-coupling theory (MCT) for such systems and show that, in fact, an active glass is inherently different from an equilibrium glass. Although the relaxation dynamics can be equilibrium-like at a [Formula: see text], effects of activity on the dynamic heterogeneity (DH), which is a hallmark of glassy dynamics, are quite nontrivial and complex. With no preexisting data, we employ four distinct methods for reliable estimates of the DH length scales. Our work shows that active glasses exhibit dramatic growth of DH and systems with similar relaxation times, and thus, [Formula: see text] can have widely varying DH. To theoretically study DH, we extend active MCT and find good qualitative agreement between the theory and simulation results. Our results pave avenues for understanding the role of DH in glassy dynamics and can have fundamental significance even in equilibrium.

Multicellular aligned bands disrupt global collective cell behavior

Mechanical stress patterns emerging from collective cell behavior have been shown to play critical roles in morphogenesis, tissue repair, and cancer metastasis. In our previous work, we constrained valvular interstitial cell (VIC) monolayers on circular protein islands to study emergent behavior in a controlled manner and demonstrated that the general patterns of cell alignment, size, and apoptosis correlate with predicted mechanical stress fields if radially increasing stiffness or contractility are used in the computational models. However, these radially symmetric models did not predict the existence of local regions of dense aligned cells observed in seemingly random locations of individual aggregates. The goal of this study is to determine how the heterogeneities in cell behavior emerge over time and diverge from the predicted collective cell behavior. Cell-cell interactions in circular multicellular aggregates of VICs were studied with time-lapse imaging ranging from hours to days, and migration, proliferation, and traction stresses were measured. Our results indicate that elongated cells create strong local alignment within preconfluent cell populations on the microcontact printed protein islands. These cells influence the alignment of additional cells to create dense, locally aligned bands of cells which disrupt the predicted global behavior. Cells are highly elongated at the endpoints of the bands yet have decreased spread area in the middle and reduced mobility. Although traction stresses at the endpoints of bands are enhanced, even to the point of detaching aggregates from the culture surface, the cells in dense bands exhibit reduced proliferation, less nuclear YAP, and increased apoptotic rates indicating a low stress environment. These findings suggest that strong local cell-cell interactions between primary fibroblastic cells can disrupt the global collective cellular behavior leading to substantial heterogeneity of cell behaviors in constrained monolayers. This local emergent behavior within aggregated fibroblasts may play an important role in development and disease of connective tissues. STATEMENT OF SIGNIFICANCE: Mechanical stress patterns emerging from collective cell behavior play critical roles in morphogenesis, tissue repair, and cancer metastasis. Much has been learned of these collective behaviors by utilizing microcontact printing to constrain cell monolayers (aggregates) into specific shapes. Here we utilize these tools along with long-term video microscopy tracking of individual aggregates to determine how heterogeneous collective behaviors unique to primary fibroblastic cells emerge over time and diverge from computed stress fields. We find that dense multicellular bands form from local collective behavior and disrupt the global collective behavior resulting in heterogeneous patterns of migration, traction stresses, proliferation, and apoptosis. This local emergent behavior within aggregated fibroblasts may play an important role in development and disease of connective tissues.

The Migration and the Fate of Dental Pulp Stem Cells

Human dental pulp stem cells (hDPSCs) are adult mesenchymal stem cells (MSCs) obtained from dental pulp and derived from the neural crest. They can differentiate into odontoblasts, osteoblasts, chondrocytes, adipocytes and nerve cells, and they play a role in tissue repair and regeneration. In fact, DPSCs, depending on the microenvironmental signals, can differentiate into odontoblasts and regenerate dentin or, when transplanted, replace/repair damaged neurons. Cell homing depends on recruitment and migration, and it is more effective and safer than cell transplantation. However, the main limitations of cell homing are the poor cell migration of MSCs and the limited information we have on the regulatory mechanism of the direct differentiation of MSCs. Different isolation methods used to recover DPSCs can yield different cell types. To date, most studies on DPSCs use the enzymatic isolation method, which prevents direct observation of cell migration. Instead, the explant method allows for the observation of single cells that can migrate at two different times and, therefore, could have different fates, for example, differentiation and self-renewal. DPSCs use mesenchymal and amoeboid migration modes with the formation of lamellipodia, filopodia and blebs, depending on the biochemical and biophysical signals of the microenvironment. Here, we present current knowledge on the possible intriguing role of cell migration, with particular attention to microenvironmental cues and mechanosensing properties, in the fate of DPSCs.

Quantification of basal stem cell elongation and stress fiber accumulation in the pseudostratified airway epithelium during the unjamming transition

Under homeostatic conditions, epithelial cells remain non-migratory. However, during embryonic development and pathological conditions, they become migratory. The mechanism underlying the transition of the epithelial layer between non-migratory and migratory phases is a fundamental question in biology. Using well-differentiated primary human bronchial epithelial cells that form a pseudostratified epithelium, we have previously identified that a confluent epithelial layer can transition from a non-migratory to migratory phase through an unjamming transition (UJT). We previously defined collective cellular migration and apical cell elongation as hallmarks of UJT. However, other cell-type-specific changes have not been previously studied in the pseudostratified airway epithelium, which consists of multiple cell types. Here, we focused on the quantifying morphological changes in basal stem cells during the UJT. Our data demonstrate that during the UJT, airway basal stem cells elongated and enlarged, and their stress fibers elongated and aligned. These morphological changes observed in basal stem cells correlated to the previously defined hallmarks of the UJT. Moreover, basal cell and stress fiber elongation were observed prior to apical cell elongation. Together, these morphological changes indicate that basal stem cells in pseudostratified airway epithelium are actively remodeling, presumably through accumulation of stress fibers during the UJT.

Enhanced short time peak in four-point dynamic susceptibility in dense active glass-forming liquids

Active glassy systems are simple model systems that imitate complex biological processes. Sometimes, it becomes crucial to estimate the amount of activity present in such biological systems, such as predicting the progression rate of the cancer cells or the healing time of the wound, etc. In this work, we study a model active glassy system to quantify the degree of activity from the collective, long-wavelength fluctuations in the system. These long-wavelength fluctuations present themselves as an additional peak in the four-point dynamic susceptibility (χ₄(t)) apart from the usual peak at structural relaxation time. We then show how the degree of the activity at such a small timescale can be obtained by measuring the variation in χ₄(t) due to changing activity. A Detailed finite size analysis of the peak height of χ₄(t) suggests the existence of an intrinsic dynamic length scale that grows with increasing activity. Finally, we show that this peak height is a unique function of effective activity across all system sizes, serving as a possible parameter for characterizing the degree of activity in a system.

In primary airway epithelial cells, the unjamming transition is distinct from the epithelial-to-mesenchymal transition

The epithelial-to-mesenchymal transition (EMT) and the unjamming transition (UJT) each comprises a gateway to cellular migration, plasticity and remodeling, but the extent to which these core programs are distinct, overlapping, or identical has remained undefined. Here, we triggered partial EMT (pEMT) or UJT in differentiated primary human bronchial epithelial cells. After triggering UJT, cell-cell junctions, apico-basal polarity, and barrier function remain intact, cells elongate and align into cooperative migratory packs, and mesenchymal markers of EMT remain unapparent. After triggering pEMT these and other metrics of UJT versus pEMT diverge. A computational model attributes effects of pEMT mainly to diminished junctional tension but attributes those of UJT mainly to augmented cellular propulsion. Through the actions of UJT and pEMT working independently, sequentially, or interactively, those tissues that are subject to development, injury, or disease become endowed with rich mechanisms for cellular migration, plasticity, self-repair, and regeneration.

Multi-scale analysis and modelling of collective migration in biological systems

Collective migration has become a paradigm for emergent behaviour in systems of moving and interacting individual units resulting in coherent motion. In biology, these units are cells or organisms. Collective cell migration is important in embryonic development, where it underlies tissue and organ formation, as well as pathological processes, such as cancer invasion and metastasis. In animal groups, collective movements may enhance individuals' decisions and facilitate navigation through complex environments and access to food resources. Mathematical models can extract unifying principles behind the diverse manifestations of collective migration. In biology, with a few exceptions, collective migration typically occurs at a 'mesoscopic scale' where the number of units ranges from only a few dozen to a few thousands, in contrast to the large systems treated by statistical mechanics. Recent developments in multi-scale analysis have allowed linkage of mesoscopic to micro- and macroscopic scales, and for different biological systems. The articles in this theme issue on 'Multi-scale analysis and modelling of collective migration' compile a range of mathematical modelling ideas and multi-scale methods for the analysis of collective migration. These approaches (i) uncover new unifying organization principles of collective behaviour, (ii) shed light on the transition from single to collective migration, and (iii) allow us to define similarities and differences of collective behaviour in groups of cells and organisms. As a common theme, self-organized collective migration is the result of ecological and evolutionary constraints both at the cell and organismic levels. Thereby, the rules governing physiological collective behaviours also underlie pathological processes, albeit with different upstream inputs and consequences for the group. This article is part of the theme issue 'Multi-scale analysis and modelling of collective migration in biological systems'.

Mechanobiology of leader-follower dynamics in epithelial cell migration

Collective cell migration is fundamental to biological form and function. It is also relevant to the formation and repair of organs and to various pathological situations, including metastatic propagation of cancer. Technological, experimental, and computational advancements have allowed the researchers to explore various aspects of collective migration, spanning from biochemical signalling to inter-cellular force transduction. Here, we summarize our current understanding of the mechanobiology of collective cell migration, limiting to epithelial tissues. On the basis of recent studies, we describe how cells sense and respond to guidance signals to orchestrate various modes of migration and identify the determining factors dictating leader-follower interactions. We highlight how the inherent mechanics of dense epithelial monolayers at multicellular length scale might instruct individual cells to behave collectively. On the basis of these findings, we propose that mechanical resilience, obtained by a certain extent of cell jamming, allows the epithelium to perform efficient collective migration during wound healing.