Segregation of co-cultured multicellular systems: review and modeling consideration.

Cell segregation caused by collective cell migration (CCM) is crucial for morphogenesis, functional development of tissue parts, and is an important aspect in other diseases such as cancer and its metastasis process. Efficiency of the cell segregation depends on the interplay between: (1) biochemical processes such as cell signaling and gene expression and (2) physical interactions between cells. Despite extensive research devoted to study the segregation of various co-cultured systems, we still do not understand the role of physical interactions in cell segregation. Cumulative effects of these physical interactions appear in the form of physical parameters such as: (1) tissue surface tension, (2) viscoelasticity caused by CCM, and (3) solid stress accumulated in multicellular systems. These parameters primarily depend on the interplay between the state of cell-cell adhesion contacts and cell contractility. The role of these physical parameters on the segregation efficiency is discussed on model systems such as co-cultured breast cell spheroids consisting of two subpopulations that are in contact. This review study aims to: (1) summarize biological aspects related to cell segregation, mechanical properties of cell collectives, effects along the biointerface between cell subpopulations and (2) describe from a biophysical/mathematical perspective the same biological aspects summarized before. So that overall it can illustrate the complexity of the biological systems that translate into very complex biophysical/mathematical equations. Moreover, by presenting in parallel these two seemingly different parts (biology vs. equations), this review aims to emphasize the need for experiments to estimate the variety of parameters entering the resulting complex biophysical/mathematical models.

The rearrangement of co-cultured cellular model systems via collective cell migration.

Cancer invasion through the surrounding epithelium and extracellular matrix (ECM) is the one of the main characteristics of cancer progression. While significant effort has been made to predict cancer cells response under various drug therapies, much less attention has been paid to understand the physical interactions between cancer cells and their microenvironment, which are essential for cancer invasion. Considering these physical interactions on various co-cultured in vitro model systems by emphasizing the role of viscoelasticity, the tissue surface tension, solid stress, and their inter-relations is a prerequisite for establishing the main factors that influence cancer cell spread and develop an efficient strategy to suppress it. This review focuses on the role of viscoelasticity caused by collective cell migration (CCM) in the context of mono-cultured and co-cultured cancer systems, and on the modeling approaches aimed at reproducing and understanding these biological systems. In this context, we do not only review previously-published biophysics models for collective cell migration, but also propose new extensions of those models to include solid stress accumulated within the spheroid core region and cell residual stress accumulation caused by CCM.

The dynamics along the biointerface between the epithelial and cancer mesenchymal cells: Modeling consideration.

Epithelial cancer is the one of most lethal cancer type worldwide. Targeting the early stage of disease would allow dramatic improvements in the survival of cancer patients. The early stage of the disease is related to cancer cell spreading across surrounding healthy epithelium. Consequently, deeper insight into cell dynamics along the biointerface between epithelial and cancer (mesenchymal) cells is necessary in order to control the disease as soon as possible. Cell dynamics along this epithelial-cancer biointerface is the result of the interplay between various biological and physical mechanisms. Despite extensive research devoted to study cancer cell spreading across the epithelium, we still do not understand the physical mechanisms which influences the dynamics along the biointerface. These physical mechanisms are related to the interplay between physical parameters such as: (1) interfacial tension between cancer and epithelial subpopulations, (2) established interfacial tension gradients, (3) the bending rigidity of the biointerface and its impact on the interfacial tension, (4) surface tension of the subpopulations, (5) viscoelasticity caused by collective cell migration, and (6) cell residual stress accumulation. The main goal of this study is to review some of these physical parameters in the context of the epithelial/cancer biointerface elaborated on the model system such as the biointerface between breast epithelial MCF-10A cells and cancer MDA-MB-231 cells and then to incorporate these parameters into a new biophysical model that could describe the dynamics of the biointerface. We conclude by discussing three biophysical scenarios for cell dynamics along the biointerface, which can occur depending on the magnitude of the generated shear stress: a smooth biointerface, a slightly-perturbed biointerface and an intensively-perturbed biointerface in the context of the Kelvin-Helmholtz instability. These scenarios are related to the probability of cancer invasion.

Response of cells and tissues to shear stress.

Shear stress is essential for normal physiology and malignancy. Common physiological processes - such as blood flow, particle flow in the gut, or contact between migratory cell clusters and their substrate - produce shear stress that can have an impact on the behavior of different tissues. In addition, shear stress has roles in processes of biomedical interest, such as wound healing, cancer and fibrosis induced by soft implants. Thus, understanding how cells react and adapt to shear stress is important. In this Review, we discuss in vivo and in vitro data obtained from vascular and epithelial models; highlight the insights these have afforded regarding the general mechanisms through which cells sense, transduce and respond to shear stress at the cellular levels; and outline how the changes cells experience in response to shear stress impact tissue organization. Finally, we discuss the role of shear stress in collective cell migration, which is only starting to be appreciated. We review our current understanding of the effects of shear stress in the context of embryo development, cancer and fibrosis, and invite the scientific community to further investigate the role of shear stress in these scenarios.

Physical aspects of epithelial cell-cell interactions: hidden system complexities.

The maintenance of homeostasis and the retention of ordered epithelial cell self-organization are essential for morphogenesis, wound healing, and the spread of cancer across the epithelium. However, cell-cell interactions in an overcrowded environment introduce a diversity of complications. Such interactions arise from an interplay between the cell compressive and shear stress components that accompany increased cell packing density. They can lead to various kinds of cell rearrangement such as: the epithelial-to-mesenchymal cell state transition; live cell extrusion; and cell jamming. All of these scenarios of cell rearrangement under mechanical stress relate to changes in the strengths of the cell-cell and cell-matrix adhesion contacts. The objective of this review study is twofold: first, to provide a comprehensive summary of the biological and physical factors influencing the effects of cell mechanical stress on cell-cell interactions, and the consequences of these interactions for the status of cell-cell and cell-matrix adhesion contacts; and secondly, to offer a bio-physical/mathematical analysis of the aforementioned biological aspects. By presenting these two approaches in conjunction, we seek to highlight the intricate nature of biological systems, which manifests in the form of complex bio-physical/mathematical equations. Furthermore, the juxtaposition of these apparently disparate approaches underscores the importance of conducting experiments to determine the multitude of parameters that contribute to the development of these intricate bio-physical/mathematical models.

Hemoglobin Binding to the Red Blood Cell (RBC) Membrane Is Associated with Decreased Cell Deformability.

The deformability of red blood cells (RBCs), expressing their ability to change their shape as a function of flow-induced shear stress, allows them to optimize oxygen delivery to the tissues and minimize their resistance to flow, especially in microcirculation. During physiological aging and blood storage, or under external stimulations, RBCs undergo metabolic and structural alterations, one of which is hemoglobin (Hb) redistribution between the cytosol and the membrane. Consequently, part of the Hb may attach to the cell membrane, and although this process is reversible, the increase in membrane-bound Hb (MBHb) can affect the cell's mechanical properties and deformability in particular. In the present study, we examined the correlation between the MBHb levels, determined by mass spectroscopy, and the cell deformability, determined by image analysis. Six hemoglobin subunits were found attached to the RBC membranes. The cell deformability was negatively correlated with the level of four subunits, with a highly significant inter-correlation between them. These data suggest that the decrease in RBC deformability results from Hb redistribution between the cytosol and the cell membrane and the respective Hb interaction with the cell membrane.

Physics of collective cell migration.

Movement of cell clusters along extracellular matrices (ECM) during tissue development, wound healing, and early stage of cancer invasion involve various inter-connected migration modes such as: (1) cell movement within clusters, (2) cluster extension (wetting) and compression (de-wetting), and (3) directional cluster movement. It has become increasingly evident that dilational and volumetric viscoelasticity of cell clusters and their surrounding substrate significantly influence these migration modes through physical parameters such as: tissue and matrix surface tensions, interfacial tension between cells and substrate, gradients of surface and interfacial tensions, as well as, the accumulation of cell and matrix residual stresses. Inhomogeneous distribution of tissue surface tension along the cell-matrix biointerface can appear as a consequence of different contractility of various cluster regions. While the directional cell migration caused by the matrix stiffness gradient (i.e., durotaxis) has been widely elaborated, the structural changes of matrix surface caused by cell tractions which lead to the generation of the matrix surface tension gradient has not been considered yet. The main goal of this theoretical consideration is to clarify the roles of various physical parameters in collective cell migration based on the formulation of a biophysical model. This complex phenomenon is discussed with the help of model systems such as the movement of cell clusters on a collagen I gel matrix, simultaneously reviewing various experimental data with and without cells.

Active wetting of epithelial tissues: modeling considerations.

Morphogenesis, tissue regeneration, and cancer invasion involve transitions in tissue morphology. These transitions, caused by collective cell migration (CCM), have been interpreted as active wetting/de-wetting transitions. This phenomenon is considered based on a model system as wetting of a cell aggregate on a rigid substrate, which includes cell aggregate movement and isotropic/anisotropic spreading of a cell monolayer around the aggregate depending on the substrate rigidity and aggregate size. This model system accounts for the transition between 3D epithelial aggregate and 2D cell monolayer as a product of: (1) tissue surface tension, (2) surface tension of substrate matrix, (3) cell-matrix interfacial tension, (4) interfacial tension gradient, (5) viscoelasticity caused by CCM, and (6) viscoelasticity of substrate matrix. These physical parameters depend on the cell contractility and state of cell-cell and cell-matrix adhesion contacts, as well as the stretching/compression of cellular systems caused by CCM. Despite extensive research devoted to study cell wetting, we still do not understand the interplay among these physical parameters which induces an oscillatory trend of cell rearrangement. This review focuses on these physical parameters in governing the cell rearrangement in the context of epithelial aggregate wetting/de-wetting, and on modeling approaches aimed at reproducing and understanding these biological systems. In this context, we not only review previously published biophysical models for cell rearrangement caused by CCM, but also propose new extensions of those models to point out the interrelation between cell-matrix interfacial tension and epithelial viscoelasticity and the role of the interfacial tension gradient in cell spreading.

Red Blood Cell Deformability Is Expressed by a Set of Interrelated Membrane Proteins.

Red blood cell (RBC) deformability, expressing their ability to change their shape, allows them to minimize their resistance to flow and optimize oxygen delivery to the tissues. RBC with reduced deformability may lead to increased vascular resistance, capillary occlusion, and impaired perfusion and oxygen delivery. A reduction in deformability, as occurs during RBC physiological aging and under blood storage, is implicated in the pathophysiology of diverse conditions with circulatory disorders and anemias. The change in RBC deformability is associated with metabolic and structural alterations, mostly uncharacterized. To bridge this gap, we analyzed the membrane protein levels, using mass spectroscopy, of RBC with varying deformability determined by image analysis. In total, 752 membrane proteins were identified. However, deformability was positively correlated with the level of only fourteen proteins, with a highly significant inter-correlation between them. These proteins are involved in membrane rafting and/or the membrane-cytoskeleton linkage. These findings suggest that the reduction of deformability is a programmed (not arbitrary) process of remodeling and shedding of membrane fragments, possibly mirroring the formation of extracellular vesicles. The highly significant inter-correlation between the deformability-expressing proteins infers that the cell deformability can be assessed by determining the level of a few, possibly one, of them.

Marangoni effect and cell spreading.

Cells are very sensitive to the shear stress (SS). However, undesirable SS is generated during physiological process such as collective cell migration (CCM) and influences the biological processes such as morphogenesis, wound healing and cancer invasion. Despite extensive research devoted to study the SS generation caused by CCM, we still do not fully understand the main cause of SS appearance. An attempt is made here to offer some answers to these questions by considering the rearrangement of cell monolayers. The SS generation represents a consequence of natural and forced convection. While forced convection is dependent on cell speed, the natural convection is induced by the gradient of tissue surface tension. The phenomenon is known as the Marangoni effect. The gradient of tissue surface tension induces directed cell spreading from the regions of lower tissue surface tension to the regions of higher tissue surface tension and leads to the cell sorting. This directional cell migration is described by the Marangoni flux. The phenomenon has been recognized during the rearrangement of (1) epithelial cell monolayers and (2) mixed cell monolayers made by epithelial and mesenchymal cells. The consequence of the Marangoni effect is an intensive spreading of cancer cells through an epithelium. In this work, a review of existing literature about SS generation caused by CCM is given along with the assortment of published experimental findings, to invite experimentalists to test given theoretical considerations in multicellular systems.

Mechanical waves caused by collective cell migration: generation.

Long-timescale viscoelasticity caused by collective cell migration (CCM) significantly influences cell rearrangement and induces generation of mechanical waves. The phenomenon represents a product of the active turbulence occurring at low Reynolds number. The generation of mechanical waves has been a subject of intensive research primarily in 2D multicellular systems, while 3D systems have not been considered in this context. The aim of this contribution is to discuss the generation of mechanical waves during 3D CCM in two model systems: (1) the fusion of two-cell aggregates and (2) cell aggregate rounding after uni-axial compression, pointing out that mechanical waves represent a characteristic of CCM in general. Such perturbations are also involved in various biological processes, such as embryogenesis, wound healing and cancer invasion. The inter-relation between the viscoelasticity and the appearance of active turbulence remains poorly understood even in 2D. The phenomenon represents a consequence of the competition between the viscoelastic force and the surface tension force which induces successive stiffening and softening of parts of multicellular systems. The viscoelastic force is a product of the residual cell stress accumulation and its inhomogeneous distribution caused by CCM. This modeling consideration represents a powerful tool to address the generation of mechanical waves in CCM towards an understanding of this important but still controversial topic.

Long-time viscoelasticity of multicellular surfaces caused by collective cell migration - Multi-scale modeling considerations.

Long-time viscoelasticity of multicellular surfaces caused by collective cell migration depends on: (1) the volume fraction and configuration of migrating cells and the rate of its change, (2) the viscoelasticity of migrating cell groups, and (3) the viscoelasticity of surrounding resting cells. The key parameter that influences the viscoelasticity is the size, shape, and thickness of the biointerface between migrating and resting cell sub-populations. The multi-scale nature of the biointerface dynamics represents the product of: (1) the local changes of the size and shape of migrating cell groups, (2) the local accumulation of resistance stress within the core regions of migrating cell groups (internal effects), (3) the collision of the velocity fronts (external effects). The local changes of the size and shape of migrating cell groups induces additional energy dissipation. The accumulated stress could induce disordering of migrating cell groups and consequently migrating-to-resting cell state transition. The collision of the velocity fronts could lead to stagnant zone formation and local increase of the volume fraction of resting cells. Herein, an attempt is made to discuss and connect various modeling approaches from the stand point of thermodynamics and rheology obtained at: (1) cellular level, (2) biointerface between migrating cell group and surrounding resting cells, and (3) a part of multicellular surfaces. These complex phenomena are discussed on the model system such as cell aggregate rounding after uni-axial compression under in vitro conditions at characteristic times such as: (1) cell shape relaxation time under stretching/compression, (2) contact time between migrating cell group and surrounding resting cells, (3) cell persistence time, (4) the lifetime of migrating cell groups, (5) cell rearrangement time (i.e. the process time), and (6) the stress and strain relaxation times of perturbed multicellular surface parts. The results of this theoretical analysis point to the relationship between interfacial size, mechanical coupling mode and rheological behavior of multicellular surfaces. Multi scale dynamics at the biointerface is a key parameter which influences mechanical behavior of multicellular surfaces. Consequently, the shape of migrating cell groups and their distribution are not random characteristics of the multicellular surface but rather influenced by cause-consequence relations between biochemical processes at the cellular level and surface stiffness distribution at the mesoscopic level.

Multiscale nature of cell rearrangement caused by collective cell migration.

Collective cell migration (CCM), a highly coordinated and fine-tuned migratory mode, is involved in a plethora of biological processes, such as embryogenesis, tissue repair and cancer invasion. Although a good comprehension of how cells collectively migrate by following molecular rules has been generated, the impact of cellular rearrangements on collective migration remains less understood. Thus, considering CCM from a multi-scale quantitative approach could result in a powerful tool to address the contribution of cellular rearrangements in CCM and help to understand this important but still controversial topic. In this work, a review of existing literature in CCM modeling at different scales is given along with assortment of published experimental findings, to invite experimentalists to test given theoretical considerations in multicellular systems. In addition, three different time and space scales (free or weakly connected cells, cluster of cells and collision fronts of different cells clusters) are considered and the multi-scale nature of those processes was discussed with special emphasis of jamming and unjamming states.

Viscoelasticity of multicellular systems caused by collective cell migration: dynamics at the biointerface.

Viscoelasticity of multicellular systems caused by collective cell migration depends on (1) viscoelasticity of migrating clusters, (2) viscoelasticity of surrounding resting cells and (3) the size, slip effects and thickness of the biointerface. A previously developed model for a sharp biointerface is expanded for the case of a finite biointerface based on thermodynamic and rheological considerations to estimate the influence of the biointerface properties on viscoelasticity. These properties of the interface layer are one of the key factors which influence the overall properties of the mixture, such as its viscoelasticity. Sliding of cell clusters through dense surroundings induces generation of significant shear stress, within the biointerface, which influences (1) the active (contractile) or passive state of single cells and (2) the state of cell-cell adhesion contacts. Cells retain collectivity in migration patterns even upon a reduction of cell-cell adhesion caused by stress generation. A greater size to the biointerface leads to the weakening of multicellular systems for the same volume fraction of migrating cells due to energy dissipation. Various factors such as (1) increase of the interface size, (2) reduction in slip effects under the constant thickness of the biointerface and (3) decrease in the biointerface thickness under constant slip effects induce an increase of the shear rate as well as the overall energy dissipation and can lead to circular cell movement within the biointerface layer. Additional experiments at subcellular and cellular levels are needed to determine the influence of mechanical factors on collective cell migration.

Essential Oils as Feed Additives-Future Perspectives.

The inconsistency of phytogenic feed additives' (PFA) effects on the livestock industry poses a risk for their use as a replacement for antibiotic growth promoters. The livestock market is being encouraged to use natural growth promotors, but information is limited about the PFA mode of action. The aim of this paper is to present the complexity of compounds present in essential oils (EOs) and factors that influence biological effects of PFA. In this paper, we highlight various controls and optimization parameters that influence the processes for the standardization of these products. The chemical composition of EOs depends on plant genetics, growth conditions, development stage at harvest, and processes of extracting active compounds. Their biological effects are further influenced by the interaction of phytochemicals and their bioavailability in the gastrointestinal tract of animals. PFA effects on animal health and production are also complex due to various EO antibiotic, antioxidant, anti-quorum sensing, anti-inflammatory, and digestive fluids stimulating activities. Research must focus on reliable methods to identify and control the quality and effects of EOs. In this study, we focused on available microencapsulation techniques of EOs to increase the bioavailability of active compounds, as well as their application in the animal feed additive industry.

Modeling of the metabolic energy dissipation for restricted tumor growth.

Energy dissipation mostly represents unwanted outcome but in the biochemical processes it may alter the biochemical pathways. However, it is rarely considered in the literature although energy dissipation and its alteration due to the changes in cell microenvironment may improve methods for guiding chemical and biochemical processes in the desired directions. Deeper insight into the changes of metabolic activity of tumor cells exposed to osmotic stress or irradiation may offer the possibility of tumor growth reduction. In this work effects of the osmotic stress and irradiation on the thermodynamical affinity of tumor cells and their damping effects on metabolic energy dissipation were investigated and modeled. Although many various models were applied to consider the tumor restrictive growth they have not considered the metabolic energy dissipation. In this work a pseudo rheological model in the form of "the metabolic spring-pot element" is formulated to describe theoretically the metabolic susceptibility of tumor spheroid. This analog model relates the thermodynamical affinity of cell growth with the volume expansion of tumor spheroid under isotropic loading conditions. Spheroid relaxation induces anomalous nature of the metabolic energy dissipation which causes the damping effects on cell growth. The proposed model can be used for determining the metabolic energy "structure" in the context of restrictive cell growth as well as for predicting optimal doses for cancer curing in order to tailor the clinical treatment for each person and each type of cancer.

Successive relaxation cycles during long-time cell aggregate rounding after uni-axial compression.

The mean features of cell surface rearrangement during cell aggregate rounding after uni-axial compression between parallel plates are considered. This is based on long-time rheological modeling approaches in order to shed further light on collective cell migration. Many aspects of cell migration at the supra-cellular level, such as the coordination between surrounding migrating cell groups that leads to uncorrelated motility, have remained unclear. Aggregate shape changes during rounding are considered depending on the size and homogeneity of 2-D and 3-D cell aggregates. Cell aggregate shape changes that are taking place during successive relaxation cycles have various relaxation rates per cycle. Every relaxation rate is related to the corresponding cell migrating state. If most of the cells migrate per cycle, the relaxation rate is maximal. If most of the cells are in a resting state per cycle, the relaxation rate is nearing zero. If some cell groups migrate while the others, at the same time, stay in a resting state, the relaxation rate is lower than that obtained for the migrating cells. The relaxation rates per cycles are not random, but they have a tendency to gather around two or three values indicating an organized cell migrating pattern. Such behavior suggests that uncorrelated motility during collective cell migration in one cycle induces a decrease of the relaxation rate in the next cycle caused by an accumulation of cells in the resting state. However, cells have the ability to overcome these perturbations and re-establish an ordered migrating trend in the next cycle. These perturbations of the cell migrating state are more pronounced for: (1) more mobile cells, (2) a heterogeneous cell population, and (3) a larger cell population under the same experimental conditions.

Actin cortex rearrangement caused by coupling with the lipid bilayer-modeling considerations.

Studies of cell membrane fluctuations under micro rheological measurements suggest that coupling between the lipid bilayer and the actin cortex can affects viscoelastic behavior of the single cell membranes. Coupling induces anomalous nature of energy dissipation during rearrangement of both: the actin cortex and the lipid bilayer. The actin cortex ability to rearrange for various cell types: erythrocytes, Jurkat cells, fibroblasts, epithelial lung cells, and muscle cells based on experimental data for storage and loss moduli versus angular velocity are considered. The cortex of softer cells such as erythrocytes, Jurkat cells, and fibroblasts has the ability to rearrange at low angular velocities which is quantified by their rearrangement time and the average size of the cortex micro domains. The rearrangement time of the cortex for Jurkat cells and fibroblasts is at the order of magnitude higher than that for erythrocytes, i.e., 2.70-7.53 s. The average size of the cortex micro domains for erythrocytes varied from 3.0 to 5.3 µm, for Jurkat cells is ~0.20-0.22 µm and for fibroblasts is ~36 nm. Lower size of the micro domains and higher rearrangement time indicate the stiffer cortex structure. The cortex rearrangement for stiffer cells such as epithelial lung cells and muscle cells has never been observed.

Role of band 3 in the erythrocyte membrane structural changes under thermal fluctuations -multi scale modeling considerations.

An attempt was made to discuss and connect various modeling approaches on various time and space scales which have been proposed in the literature in order to shed further light on the erythrocyte membrane rearrangement caused by the cortex-lipid bilayer coupling under thermal fluctuations. Roles of the main membrane constituents: (1) the actin-spectrin cortex, (2) the lipid bilayer, and (3) the trans membrane protein band 3 and their course-consequence relations were considered in the context of the cortex non linear stiffening and corresponding anomalous nature of energy dissipation. The fluctuations induce alternating expansion and compression of the membrane parts in order to ensure surface and volume conservation. The membrane structural changes were considered within two time regimes. The results indicate that the cortex non linear stiffening and corresponding anomalous nature of energy dissipation are related to the spectrin flexibility distribution and the rate of its changes. The spectrin flexibility varies from purely flexible to semi flexible. It is influenced by: (1) the number of band 3 molecules attached to single spectrin filaments, and (2) phosphorylation of the actin-junctions. The rate of spectrin flexibility changes depends on the band 3 molecules rearrangement.