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Collective cell migration is extensively observed in embryo development and cancer invasion. During these processes, the interactions between cells with distinct identities and fates are of importance for boundary formation and host defense against cancer. In this paper, we explore the collective dynamics of a two-dimensional cell mixing monolayer consisting of non-tumorigenic mammary epithelial cells and breast cancer cells. We show that the epithelial–cancerous cell mixing system displays unique sorting behaviors. The epithelial cells aggregate to form scattered clusters, which perform random motion with simultaneous translation and rotation, strikingly distinct from the classical persistent random walk of individual migratory cells. The motility of cancer cells is markedly promoted by the epithelial clusters, exhibiting remarkable contact enhancement of locomotion. A discrete model based on the Johnson–Kendall–Roberts contact mechanics is proposed to identify the influence of intercellular interactions, active migration forces and cell–substrate friction forces on the collective cell dynamics. These findings could advance our understanding of many biological processes, such as cancer metastasis and tissue morphogenesis. The epithelial–cancerous cell mixing system displays unique collective dynamics. The epithelial cells aggregate to form scattered clusters, which perform random motion with simultaneous translation and rotation, strikingly distinct from the classical persistent random walk of individual migratory cells. The interactions between the two cell types drive the evolution of collective migration dynamics and give rise to a behavior akin to the contact enhancement of locomotion. This study revealed the distinctive dynamic features and the underlying regulatory mechanisms arising from epithelial–cancerous interactions. [ABSTRACT FROM AUTHOR]

During vertebrate somitogenesis an inherent segmentation clock coordinates the spatiotemporal signaling to generate segmented structures that pattern the body axis. Using our experimental and quantitative approach, we study the cell movements and the genetic oscillations of her1 expression level at single-cell resolution simultaneously and scale up to the entire pre-somitic mesoderm (PSM) tissue. From the experimentally determined phases of PSM cellular oscillators, we deduced an in vivo frequency profile gradient along the anterior-posterior PSM axis and inferred precise mathematical relations between spatial cell–level period and tissue-level somitogenesis period. We also confirmed a gradient in the relative velocities of cellular oscillators along the axis. The phase order parameter within an ensemble of oscillators revealed the degree of synchronization in the tailbud and the posterior PSM being only partial, whereas synchronization can be almost complete in the presumptive somite region but with temporal oscillations. Collectively, the degree of synchronization itself, possibly regulated by cell movement and the synchronized temporal phase of the transiently expressed clock protein Her1, can be an additional control mechanism for making precise somite boundaries. • Somite formation in context of moving cellular oscillators being phase synchronized. • Precise mathematical relation between spatial cell periods and somitogenesis period. • Her1 synchronization levels temporally oscillate only in the forming somite. • Low synchronization strength in tailbud/posterior cells. • Clock components are dynamically tuned along the anterior-posterior axis. [ABSTRACT FROM AUTHOR]

Microalgae are a great source of food and supplements as well as a potential source for the production of biofuels. However, the operational cost must be reduced to allow viable productions of bulk chemicals such as biofuels from microalgae. One approach to minimize the cost is to increase the efficiency of the photobioreactor. Photobioreactor efficiency is correlated to hydrodynamic mixing, which promotes single cell exposure to sunlight, keeps algae cells in suspension, and homogenizes the distribution of nutrients. Thus, a possible route to enhance the efficiency of the photobioreactor can be identified through an improved understanding of the mixing phenomenon. Therefore, for the current thin-layer cascade reactor, two aspects of its performance—namely, cell mixing and hydrodynamic characteristics—are evaluated under varying mass flow rates, slope angles, water depths, and aspect ratios of the channel by using computational fluid dynamics. The resulting model is validated with experimental data. Results reveal that limited cell mixing is achieved in the thin-layer cascade reactor with increased water depth and large aspect ratios. However, cell mixing is significantly increased at high mass flow rates. The increase in the mass flow rate and slope angle results in increased flow velocity and power consumption. [ABSTRACT FROM AUTHOR]

In development and disease, cells move as they exchange signals. One example is found in vertebrate development, during which the timing of segment formation is set by a ‘segmentation clock’, in which oscillating gene expression is synchronized across a population of cells by Delta-Notch signaling. Delta-Notch signaling requires local cell-cell contact, but in the zebrafish embryonic tailbud, oscillating cells move rapidly, exchanging neighbors. Previous theoretical studies proposed that this relative movement or cell mixing might alter signaling and thereby enhance synchronization. However, it remains unclear whether the mixing timescale in the tissue is in the right range for this effect, because a framework to reliably measure the mixing timescale and compare it with signaling timescale is lacking. Here, we develop such a framework using a quantitative description of cell mixing without the need for an external reference frame and constructing a physical model of cell movement based on the data. Numerical simulations show that mixing with experimentally observed statistics enhances synchronization of coupled phase oscillators, suggesting that mixing in the tailbud is fast enough to affect the coherence of rhythmic gene expression. Our approach will find general application in analyzing the relative movements of communicating cells during development and disease.

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., (© 2023 Wiley Periodicals LLC.)

Embryonic morphogenesis is organized by an interplay between intercellular signaling and cell movements. Both intercellular signaling and cell movement involve multiple timescales. A key timescale for signaling is the time delay caused by preparation of signaling molecules and integration of received signals into cells' internal state. Movement of cells relative to their neighbors may introduce exchange of positions between cells during signaling. When cells change their relative positions in a tissue, the impact of signaling delays on intercellular signaling increases because the delayed information that cells receive may significantly differ from the present state of the tissue. The time it takes to perform a neighbor exchange sets a timescale of cell mixing that may be important for the outcome of signaling. Here we review recent theoretical work on the interplay of timescales between cell mixing and signaling delays adopting the zebrafish segmentation clock as a model system. We discuss how this interplay can lead to spatial patterns of gene expression that could disrupt the normal formation of segment boundaries in the embryo. The effect of cell mixing and signaling delays highlights the importance of theoretical and experimental frameworks to understand collective cellular behaviors arising from the interplay of multiple timescales in embryonic developmental processes. [ABSTRACT FROM AUTHOR]

Cell populations in multicellular organisms show genetic and non-genetic heterogeneity, even in undifferentiated tissues of multipotent cells during development and tumorigenesis. The heterogeneity causes difference of mechanical properties, such as, cell bond tension or adhesion, at the cell–cell interface, which determine the shape of clonal population boundaries via cell sorting or mixing. The boundary shape could alter the degree of cell–cell contacts and thus influence the physiological consequences of sorting or mixing at the boundary (e.g., tumor suppression or progression), suggesting that the cell mechanics could help clarify the physiology of heterogeneous tissues. While precise inference of mechanical tension loaded at each cell–cell contacts has been extensively developed, there has been little progress on how to distinguish the population-boundary geometry and identify the cause of geometry in heterogeneous tissues. We developed a pipeline by combining multivariate analysis of clone shape with tissue mechanical simulations. We examined clones with four different genotypes within Drosophila wing imaginal discs: wild-type, tartan (trn) overexpression, hibris (hbs) overexpression, and Eph RNAi. Although the clones were previously known to exhibit smoothed or convoluted morphologies, their mechanical properties were unknown. By applying a multivariate analysis to multiple criteria used to quantify the clone shapes based on individual cell shapes, we found the optimal criteria to distinguish not only among the four genotypes, but also non-genetic heterogeneity from genetic one. The efficient segregation of clone shape enabled us to quantitatively compare experimental data with tissue mechanical simulations. As a result, we identified the mechanical basis contributed to clone shape of distinct genotypes. The present pipeline will promote the understanding of the functions of mechanical interactions in heterogeneous tissue in a non-invasive manner.

Microalgae are a great source of food and supplements as well as a potential source for the production of biofuels. However, the operational cost must be reduced to allow viable productions of bulk chemicals such as biofuels from microalgae. One approach to minimize the cost is to increase the efficiency of the photobioreactor. Photobioreactor efficiency is correlated to hydrodynamic mixing, which promotes single cell exposure to sunlight, keeps algae cells in suspension, and homogenizes the distribution of nutrients. Thus, a possible route to enhance the efficiency of the photobioreactor can be identified through an improved understanding of the mixing phenomenon. Therefore, for the current thin-layer cascade reactor, two aspects of its performance—namely, cell mixing and hydrodynamic characteristics—are evaluated under varying mass flow rates, slope angles, water depths, and aspect ratios of the channel by using computational fluid dynamics. The resulting model is validated with experimental data. Results reveal that limited cell mixing is achieved in the thin-layer cascade reactor with increased water depth and large aspect ratios. However, cell mixing is significantly increased at high mass flow rates. The increase in the mass flow rate and slope angle results in increased flow velocity and power consumption.

Computational models of cell-cell mechanical interactions typically simulate sorting and certain other motions well, but as demands on these models continue to grow, discrepancies between the cell shapes, contact angles and behaviours they predict and those that occur in real cells have come under increased scrutiny. To investigate whether these discrepancies are a direct result of the straight cell-cell edges generally assumed in these models, we developed a finite element model that approximates cell boundaries using polylines with an arbitrary number of segments. We then compared the predictions of otherwise identical polyline and monoline (straight-edge) models in a variety of scenarios, including annealing, single- and multi-cell engulfment, sorting, and two forms of mixing-invasion and checkerboard pattern formation. Keeping cell-cell edges straight influences cell motion, cell shape, contact angle, and boundary length, especially in cases where one cell type is pulled between or around cells of a different type, as in engulfment or invasion. These differences arise because monoline cells have restricted deformation modes. Polyline cells do not face these restrictions, and with as few as three segments per edge yielded realistic edge shapes and contact angle errors one-tenth of those produced by monoline models, making them considerably more suitable for situations where angles and shapes matter, such as validation of cellular force-inference techniques. The findings suggest that non-straight cell edges are important both in modelling and in nature. [ABSTRACT FROM AUTHOR]

During animal development, tissues and organs are partitioned into compartments that do not intermix. This organizing principle is essential for correct tissue morphogenesis. Given that cell sorting defects during compartmentalization in humans are thought to cause malignant invasion and congenital defects such as cranio-fronto-nasal syndrome, identifying the molecular and cellular mechanisms that keep cells apart at boundaries between compartments is important. In both vertebrates and invertebrates, transcription factors and short-range signalling pathways, such as EPH/Ephrin, Hedgehog, or Notch signalling, govern compartmental cell sorting. However, the mechanisms that mediate cell sorting downstream of these factors have remained elusive for decades. Here, we review recent data gathered in Drosophila that suggest that the generation of cortical tensile forces at compartmental boundaries by the actomyosin cytoskeleton could be a general mechanism that inhibits cell mixing between compartments. [ABSTRACT FROM AUTHOR]

The TGFβ family member Nodal has been shown to be involved in a variety of processes in development, including early axis formation. Here, we use a conditional gene inactivation strategy to show a specific requirement for Nodal in the epiblast. Complete inactivation of the Nodal locus in the epiblast using the Sox2-Cre deleter strain results in a failure to establish global anterior–posterior patterning, a phenotype that resembles the Nodal null phenotype. By contrast, mosaic inactivation of Nodal in the epiblast using the Mox2-Cre (MORE) deleter strain affects formation of the anterior mesendoderm and subsequent anterior neurectoderm patterning. Furthermore, ES cell chimera experiments indicate that Nodal-deficient ES cells preferentially populate the anterior compartment of the epiblast, suggesting that cell mixing in the epiblast is not random and that Nodal signaling mediates a novel anterior–posterior cell-sorting process within the epiblast before gastrulation. [Copyright &y& Elsevier]

In development and disease, cells move as they exchange signals. One example is found in vertebrate development, during which the timing of segment formation is set by a 'segmentation clock', in which oscillating gene expression is synchronized across a population of cells by Delta-Notch signaling. Delta-Notch signaling requires local cell-cell contact, but in the zebrafish embryonic tailbud, oscillating cells move rapidly, exchanging neighbors. Previous theoretical studies proposed that this relative movement or cell mixing might alter signaling and thereby enhance synchronization. However, it remains unclear whether the mixing timescale in the tissue is in the right range for this effect, because a framework to reliably measure the mixing timescale and compare it with signaling timescale is lacking. Here, we develop such a framework using a quantitative description of cell mixing without the need for an external reference frame and constructing a physical model of cell movement based on the data. Numerical simulations show that mixing with experimentally observed statistics enhances synchronization of coupled phase oscillators, suggesting that mixing in the tailbud is fast enough to affect the coherence of rhythmic gene expression. Our approach will find general application in analyzing the relative movements of communicating cells during development and disease., Competing Interests: Competing interestsThe authors declare no competing or financial interests., (© 2017. Published by The Company of Biologists Ltd.)

Cell populations in multicellular organisms show genetic and non-genetic heterogeneity, even in undifferentiated tissues of multipotent cells during development and tumorigenesis. The heterogeneity causes difference of mechanical properties, such as, cell bond tension or adhesion, at the cell-cell interface, which determine the shape of clonal population boundaries via cell sorting or mixing. The boundary shape could alter the degree of cell-cell contacts and thus influence the physiological consequences of sorting or mixing at the boundary (e.g., tumor suppression or progression), suggesting that the cell mechanics could help clarify the physiology of heterogeneous tissues. While precise inference of mechanical tension loaded at each cell-cell contacts has been extensively developed, there has been little progress on how to distinguish the population-boundary geometry and identify the cause of geometry in heterogeneous tissues. We developed a pipeline by combining multivariate analysis of clone shape with tissue mechanical simulations. We examined clones with four different genotypes within Drosophila wing imaginal discs: wild-type, tartan ( trn ) overexpression, hibris ( hbs ) overexpression, and Eph RNAi. Although the clones were previously known to exhibit smoothed or convoluted morphologies, their mechanical properties were unknown. By applying a multivariate analysis to multiple criteria used to quantify the clone shapes based on individual cell shapes, we found the optimal criteria to distinguish not only among the four genotypes, but also non-genetic heterogeneity from genetic one. The efficient segregation of clone shape enabled us to quantitatively compare experimental data with tissue mechanical simulations. As a result, we identified the mechanical basis contributed to clone shape of distinct genotypes. The present pipeline will promote the understanding of the functions of mechanical interactions in heterogeneous tissue in a non-invasive manner.

RNA-protein complexes are critical for almost all aspects of gene expression. Analysis of RNA-protein interactions can be complicated by the disruption of native complexes and the formation of new, reassorted complexes upon cell lysis. Before concluding that a specific RNA and protein interact in vivo, cell-mixing experiments can be performed to ensure that observed RNA-protein complexes are not formed after lysis of cells., (© 2014 Elsevier Inc. All rights reserved.)