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

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.

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.

Mechanical regulation of the early stages of angiogenesis

Favouring or thwarting the development of a vascular network is essential in fields as diverse as oncology, cardiovascular disease or tissue engineering. As a result, understanding and controlling angiogenesis has become a major scientific challenge. Mechanical factors play a fundamental role in angiogenesis and can potentially be exploited for optimizing the architecture of the resulting vascular network. Largely focusing on in vitro systems but also supported by some in vivo evidence, the aim of this Highlight Review is dual. First, we describe the current knowledge with particular focus on the effects of fluid and solid mechanical stimuli on the early stages of the angiogenic process, most notably the destabilization of existing vessels and the initiation and elongation of new vessels. Second, we explore inherent difficulties in the field and propose future perspectives on the use of in vitro and physics-based modelling to overcome these difficulties.

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 role of viscoelasticity in long time cell rearrangement

Cell rearrangement caused by collective cell migration (CCM) during free expansion of epithelial monolayers has become a landmark in our current understanding of fundamental biological processes such as tissue development, regeneration, wound healing or cancer invasion. Cell spreading causes formation of mechanical waves which has a feedback effect on cell rearrangement and can lead to the cell jamming state. The mechanical waves describe oscillatory changes in cell velocity, as well as, the rheological parameters that affect them. The velocity oscillations, obtained at a time scale of hours, are in the form of forward and backward flows. Collision of forward and backward flows can induce an increase in the cell compressive stress accompanied with cell packing density which have a feedback impact on cell mobility, tissue viscoelasticity and alters the tissue stiffness. The tissue stiffness depends on the cell packing density and the active/passive (i.e. migrating/resting) state of single cells and can be used as an indicator of cell jamming state transition. Since cell stiffness can be measured it may directly show in which state the multicellular system is. In this work a review of existing modeling approaches is given along with assortment of published experimental findings, in order to invite experimentalists to test given theoretical considerations in multicellular systems.

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.

Mathematical and computational models in spheroid-based biofabrication

Ubiquitous in embryonic development, tissue fusion is of interest to tissue engineers who use tissue spheroids or organoids as building blocks of three-dimensional (3D) multicellular constructs. This review presents mathematical models and computer simulations of the fusion of tissue spheroids. The motivation of this study stems from the need to predict the post-printing evolution of 3D bioprinted constructs. First, we provide a brief overview of differential adhesion, the main morphogenetic mechanism involved in post-printing structure formation. It will be shown that clusters of cohesive cells behave as an incompressible viscous fluid on the time scale of hours. The discussion turns then to mathematical models based on the continuum hydrodynamics of highly viscous liquids and on statistical mechanics. Next, we analyze the validity and practical use of computational models of multicellular self-assembly in live constructs created by tissue spheroid bioprinting. Finally, we discuss the perspectives of the field as machine learning starts to reshape experimental design, and modular robotic workstations tend to alleviate the burden of repetitive tasks in biofabrication. STATEMENT OF SIGNIFICANCE: Bioprinted constructs are living systems, which evolve via morphogenetic mechanisms known from developmental biology. This review presents mathematical and computational tools devised for modeling post-printing structure formation. They help achieving a desirable outcome without expensive optimization experiments. While previous reviews mainly focused on assumptions, technical details, strengths, and limitations of computational models of multicellular self-assembly, this article discusses their validity and practical use in biofabrication. It also presents an overview of mathematical models that proved to be useful in the evaluation of experimental data on tissue spheroid fusion, and in the calibration of computational models. Finally, the perspectives of the field are discussed in the advent of robotic biofabrication platforms and bioprinting process optimization by machine learning.

Analysis of a viscoelastic phase separation model

A new model for viscoelastic phase separation is proposed, based on a systematically derived conservative two-fluid model. Dissipative effects are included by phenomenological viscoelastic terms. By construction, the model is consistent with the second law of thermodynamics. We study well-posedness of the model in two space dimensions, i.e., existence of weak solutions, a weak-strong uniqueness principle, and stability with respect to perturbations, which are proven by means of relative energy estimates. Our numerical simulations based on the new viscoelastic phase separation model are in good agreement with physical experiments. Furthermore, a good qualitative agreement with mesoscopic simulations is observed.

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.

Collective cell migration and residual stress accumulation: Rheological consideration

Stress generation during collective cell migration represents one of the key factors which influence the configuration of migrating cells, viscoelasticity of multicellular systems and their inter-relation. Local generation of stress (normal and shear) is significant even in 2D. Normal stress is primarily accumulated within a core region of migrating cell clusters during their movement through the dense environment and during the collisions of migrating cell clusters caused by uncorrelated motility. Shear stress can be significant within perturbed boundary layers around migrating clusters. Cells are more sensitive to the action of shear stress compared with normal stress. Shear stress of a few Pa significantly influences cell state. Prior studies have shown that collectively migrating cells move in such a way to minimize this stress, but it has not yet been determined how cells effectively minimize it. Deeper insight into possible cell mechanisms for minimizing undesirable shear stress would be of great importance because it may help to direct morphogenesis, accelerate wound healing or prevent cancer invasion. In the proposed model three primary mechanisms in which cells may reduce shear are given: decreasing speed, tissue thickening, and/or reducing slip effects. Suggestions obtained from the proposed model indicate a need for further experimental studies that will reveal whether the heterogeneity in the cell-cell adhesion types correlates well with the stiffness inhomogeneity, or changes in the adhesion clustering, cytoskeletal linkage or some other modification to the adhesion complex (adherens junctions or tight junctions) are occurring to influence overall adhesive strength.