Role of viscoelasticity in the appearance of low-Reynolds turbulence: considerations for modelling.

Inertial effects caused by perturbations of dynamical equilibrium during the flow of soft matter constitute a hallmark of turbulence. Such perturbations are attributable to an imbalance between energy storage and energy dissipation. During the flow of Newtonian fluids, kinetic energy can be both stored and dissipated, while the flow of viscoelastic soft matter systems, such as polymer fluids, induces the accumulation of both kinetic and elastic energies. The accumulation of elastic energy causes local stiffening of stretched polymer chains, which can destabilise the flow. Migrating multicellular systems are hugely complex and are capable of self-regulating their viscoelasticity and mechanical stress generation, as well as controlling their energy storage and energy dissipation. Since the flow perturbation of viscoelastic systems is caused by the inhomogeneous accumulation of elastic energy, rather than of kinetic energy, turbulence can occur at low Reynolds numbers.This theoretical review is focused on clarifying the role of viscoelasticity in the appearance of low-Reynolds turbulence. Three types of system are considered and compared: (1) high-Reynolds turbulent flow of Newtonian fluids, (2) low and moderate-Reynolds flow of polymer solutions, and (3) migration of epithelial collectives, discussed in terms of two model systems. The models considered involve the fusion of two epithelial aggregates, and the free expansion of epithelial monolayers on a substrate matrix.

Collective durotaxis along a self-generated mobile stiffness gradient in vivo.

A crucial aspect of tissue self-organization during morphogenesis, wound healing, and cancer invasion is directed migration of cell collectives. The majority of in vivo directed migration has been guided by chemotaxis, whereby cells follow a chemical gradient. In certain situations, migrating cell collectives can also self-generate the stiffness gradient in the surrounding tissue, which can have a feedback effect on the directionality of the migration. The phenomenon has been observed during collective durotaxis in vivo. Along the biointerface between neighbouring tissues, heterotypic cell-cell interactions are the main cause of this self-generated stiffness gradient. The physical processes in charge of tissue self-organization along the biointerface, which are related to the interplay between cell signalling and the formation of heterotypic cell-cell adhesion contacts, are less well-developed than the biological mechanisms of the cellular interactions. This complex phenomenon is discussed here in the model system, such as collective migration of neural crest cells between ectodermal placode and mesoderm subpopulations within Xenopus embryos by pointing to the role of the dynamics along the biointerface between adjacent cell subpopulations on the subpopulation stiffness.

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.

Cell jamming-to-unjamming transitions and vice versa in development: Physical aspects.

Collective cell migration is essential for a wide range of biological processes such as: morphogenesis, wound healing, and cancer spreading. However, it is well known that migrating epithelial collectives frequently undergo jamming, stay trapped some period of time, and then start migration again. Consequently, only a part of epithelial cells actively contributes to the tissue development. In contrast to epithelial cells, migrating mesenchymal collectives successfully avoid the jamming. It has been confirmed that the epithelial unjamming cannot be treated as the epithelial-to-mesenchymal transition. Some other mechanism is responsible for the epithelial jamming/unjamming. Despite extensive research devoted to study the cell jamming/unjamming, we still do not understand the origin of this phenomenon. The origin is connected to physical factors such as: the cell compressive residual stress accumulation and surface characteristics of migrating (unjamming) and resting (jamming) epithelial clusters which depend primarily on the strength of cell-cell adhesion contacts and cell contractility. The main goal of this theoretical consideration is to clarify these cause-consequence relations.

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.

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.

Alginate Gel-Based Carriers for Encapsulation of Carotenoids: On Challenges and Applications.

Sodium alginate is one of the most interesting and the most investigated and applied biopolymers due to its advantageous properties. Among them, easy, simple, mild, rapid, non-toxic gelation by divalent cations is the most important. In addition, it is abundant, low-cost, eco-friendly, bio-compatible, bio-adhesive, biodegradable, stable, etc. All those properties were systematically considered within this review. Carotenoids are functional components in the human diet with plenty of health benefits. However, their sensitivity to environmental and process stresses, chemical instability, easy oxidation, low water solubility, and bioavailability limit their food and pharmaceutical applications. Encapsulation may help in overcoming these limitations and within this review, the role of alginate-based encapsulation systems in improving the stability and bioavailability of carotenoids is explored. It may be concluded that all alginate-based systems increase carotenoid stability, but only those of micro- and nano-size, as well as emulsion-based, may improve their low bioaccessibility. In addition, the incorporation of other biopolymers may further improve encapsulation system properties. Furthermore, the main techniques for evaluating the encapsulation are briefly considered. This review critically and profoundly explains the role of alginates in improving the encapsulation process of carotenoids, suggesting the best alternatives for those systems. Moreover, it provides a comprehensive cover of recent advances in this field.

Multi-scale nature of the tissue surface tension: Theoretical consideration on tissue model systems.

Tissue surface tension is one of the key parameters that govern tissue rearrangement, shaping, and segregation within various compartments during organogenesis, wound healing, and cancer diseases. Deeper insight into the relationship between tissue surface tension and cell residual stress accumulation caused by collective cell migration can help us to understand the multi-scale nature of cell rearrangement with pronounced oscillatory trend. Oscillatory change of cell velocity that caused strain and generated cell residual stress were discussed in the context of mechanical waves. The tissue surface tension also showed oscillatory behaviour. The main goal of this theoretical consideration is to emphasize an inter-relation between various scenarios of cell rearrangement and tissue surface tension by distinguishing liquid-like and solid-like surfaces. This complex phenomenon is discussed in the context of an artificial tissue model system, namely cell aggregate rounding after uni-axial compression between parallel plates. Experimentally obtained oscillatory changes in the cell aggregate shape during the aggregate rounding, which is accompanied by oscillatory decrease in the aggregate surface area, points to oscillatory changes in the tissue surface tension. Besides long-time oscillations, cell surface tension can perform short time relaxation cycles. This behaviour of the tissue surface tension distinguishes living matter from other soft matter systems. This complex phenomenon is discussed based on dilatational viscoelasticity and thermodynamic approach.

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.

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.

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.

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.

Collective Cell Migration on Collagen-I Networks: The Impact of Matrix Viscoelasticity.

Collective cell migration on extracellular matrix (ECM) networks is a key biological process involved in development, tissue homeostasis and diseases such as metastatic cancer. During invasion of epithelial cancers, cell clusters migrate through the surrounding stroma, which is comprised primarily of networks of collagen-I fibers. There is growing evidence that the rheological and topological properties of collagen networks can impact cell behavior and cell migration dynamics. During migration, cells exert mechanical forces on their substrate, resulting in an active remodeling of ECM networks that depends not only on the forces produced, but also on the molecular mechanisms that dictate network rheology. One aspect of collagen network rheology whose role is emerging as a crucial parameter in dictating cell behavior is network viscoelasticity. Dynamic reorganization of ECM networks can induce local changes in network organization and mechanics, which can further feed back on cell migration dynamics and cell-cell rearrangement. A number of studies, including many recent publications, have investigated the mechanisms underlying structural changes to collagen networks in response to mechanical force as well as the role of collagen rheology and topology in regulating cell behavior. In this mini-review, we explore the cause-consequence relationship between collagen network viscoelasticity and cell rearrangements at various spatiotemporal scales. We focus on structural alterations of collagen-I networks during collective cell migration and discuss the main rheological parameters, and in particular the role of viscoelasticity, which can contribute to local matrix stiffening during cell movement and can elicit changes in cell dynamics.

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.

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.

Preparation and Evaluation of Silymarin-Loaded Solid Eutectic for Enhanced Anti-Inflammatory, Hepatoprotective Effect: In Vitro-In Vivo Prospect.

Solubility of phytochemicals is a major concern for drug delivery, permeability, and their biological response. However, advancements in the novel formulation technologies have been helping to overcome these challenges. The applications of these newer technologies are easy for commercialization and high therapeutic outcomes compared to conventional formulations. Considering these facts, the present study is aimed to prepare a silymarin-loaded eutectic mixture with three different ratios of Polyvinylpyrrolidone K30 (PVP K30) and evaluating their anti-inflammatory, and hepatoprotective effects. The preliminary phytochemical and characterization of silymarin, physical mixture, and solid dispersions suggested and successfully confirmed the formation of solid dispersion of silymarin with PVP K30. It was found that the solubility of silymarin was increased by 5-fold compared to pure silymarin. Moreover, the in vitro dissolution displayed that 83% of silymarin released within 2 h with 2.8-fold increase in dissolution rate compared to pure silymarin. Also, the in vivo study suggested that the formulation significantly reduced the carbon tetrachloride- (0.8620 ± 0.05034∗∗ for 1 : 3 ratio), paracetamol- (0.7300 ± 0.01517∗∗ for 1 : 3 ratio), and ethanol- (0.8100 ± 0.04037∗∗ for 1 : 3 ratio) induced hepatotoxicity in rats. Silymarin solid dispersion was prepared using homogenization methods that have prominent anti-inflammatory effect (0.6520 ± 0.008602∗∗ with 8.33%) in carrageenan-induced rat paw model.

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.

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.

Jamming state transition and collective cell migration.

Jamming state transition has been used in literature to describe migrating-to-resting cell state transition during collective cell migration without proper rheological confirmation. Yield stress often has been used as an indicator of a jamming state. Yield stress points to the liquid-to-solid state transition, but not a priori to jamming state transition. Various solid states such as elastic solid and viscoelastic solids can be considered in the context of their ability to relax. The relaxation time for (1) an elastic solid tends to zero, (2) Kelvin-Voigt viscoelastic solid is finite, and (3) jamming state tends to infinity. In order to clarify the meaning of jamming state from the rheological standpoint we formulated the constitutive model of this state based on following conditions (1) migration of the system constituents is much damped such that the diffusion coefficient tends to zero, (2) relaxation time tends to infinity, (3) storage and loss moduli satisfy the condition G '(ω)/G "(ω) = const > 1. Jamming state represents the non-linear viscoelastic solid state. The main characteristic of this state is that the system cannot relax. Jamming state transition of multicellular systems caused by collective cell migration is discussed on a model system such as cell aggregate rounding after uni-axial compression between parallel plates based on the data from the literature. Cell aggregate rounding occurs via successive relaxation cycles. Every cycle corresponds to a different scenario of cell migration. Three scenarios were established depending on the magnitude of mechanical and biochemical perturbations (1) ordered scenario with reduced perturbations corresponds to the case that most of the cells migrate, (2) disordered scenario corresponds to the case that some cell groups migrate while the others (at the same time) stay in resting state (corresponds to medium perturbations), and (3) highly suppressed cell migration under large perturbations corresponds to the viscoelastic solid under jamming state. If cells reach the jamming state in one cycle, they are able to overcome this undesirable state and start migrating again in the next cycle by achieving the first or second scenarios again.