Information flow in the presence of cell mixing and signaling delays during embryonic development

Beyond stiffness: deciphering the role of viscoelasticity in cancer evolution and treatment response

There is increasing evidence that cancer progression is linked to tissue viscoelasticity, which challenges the commonly accepted notion that stiffness is the main mechanical hallmark of cancer. However, this new insight has not reached widespread clinical use, as most clinical trials focus on the application of tissue elasticity and stiffness in diagnostic, therapeutic, and surgical planning. Therefore, there is a need to advance the fundamental understanding of the effect of viscoelasticity on cancer progression, to develop novel mechanical biomarkers of clinical significance. Tissue viscoelasticity is largely determined by the extracellular matrix (ECM), which can be simulatedin vitrousing hydrogel-based platforms. Since the mechanical properties of hydrogels can be easily adjusted by changing parameters such as molecular weight and crosslinking type, they provide a platform to systematically study the relationship between ECM viscoelasticity and cancer progression. This review begins with an overview of cancer viscoelasticity, describing how tumor cells interact with biophysical signals in their environment, how they contribute to tumor viscoelasticity, and how this translates into cancer progression. Next, an overview of clinical trials focused on measuring biomechanical properties of tumors is presented, highlighting the biomechanical properties utilized for cancer diagnosis and monitoring. Finally, this review examines the use of biofabricated tumor models for studying the impact of ECM viscoelasticity on cancer behavior and progression and it explores potential avenues for future research on the production of more sophisticated and biomimetic tumor models, as well as their mechanical evaluation.

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.

Swarmalators with delayed interactions

We investigate the effects of delayed interactions in a population of "swarmalators," generalizations of phase oscillators that both synchronize in time and swarm through space. We discover two steady collective states: a state in which swarmalators are essentially motionless in a disk arranged in a pseudocrystalline order, and a boiling state in which the swarmalators again form a disk, but now the swarmalators near the boundary perform boiling-like convective motions. These states are reminiscent of the beating clusters seen in photoactivated colloids and the living crystals of starfish embryos.

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.

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.

Stability bounds of a delay visco-elastic rheological model with substrate friction

Cells and tissues exhibit sustained oscillatory deformations during remodelling, migration or embryogenesis. Although it has been shown that these oscillations correlate with intracellular biochemical signalling, the role of these oscillations is as yet unclear, and whether they may trigger drastic cell reorganisation events or instabilities remains unknown. Here, we present a rheological model that incorporates elastic, viscous and frictional components, and that is able to generate oscillatory response through a delay adaptive process of the rest-length. We analyse its stability as a function of the model parameters and deduce analytical bounds of the stable domain. While increasing values of the delay and remodelling rate render the model unstable, we also show that increasing friction with the substrate destabilises the oscillatory response. This fact was unexpected and still needs to be verified experimentally. Furthermore, we numerically verify that the extension of the model with non-linear deformation measures is able to generate sustained oscillations converging towards a limit cycle. We interpret this sustained regime in terms of non-linear time varying stiffness parameters that alternate between stable and unstable regions of the linear model. We also note that this limit cycle is not present in the linear model. We study the phase diagram and the bifurcations of the non-linear model, based on our conclusions on the linear one. Such dynamic analysis of the delay visco-elastic model in the presence of friction is absent in the literature for both linear and non-linear rheologies. Our work also shows how increasing values of some parameters such as delay and friction decrease its stability, while other parameters such as stiffness stabilise the oscillatory response.

Time and space in segmentation

Arthropod segmentation and vertebrate somitogenesis are leading fields in the experimental and theoretical interrogation of developmental patterning. However, despite the sophistication of current research, basic conceptual issues remain unresolved. These include: (i) the mechanistic origins of spatial organization within the segment addition zone (SAZ); (ii) the mechanistic origins of segment polarization; (iii) the mechanistic origins of axial variation; and (iv) the evolutionary origins of simultaneous patterning. Here, I explore these problems using coarse-grained models of cross-regulating dynamical processes. In the morphogenetic framework of a row of cells undergoing axial elongation, I simulate interactions between an 'oscillator', a 'switch' and up to three 'timers', successfully reproducing essential patterning behaviours of segmenting systems. By comparing the output of these largely cell-autonomous models to variants that incorporate positional information, I find that scaling relationships, wave patterns and patterning dynamics all depend on whether the SAZ is regulated by temporal or spatial information. I also identify three mechanisms for polarizing oscillator output, all of which functionally implicate the oscillator frequency profile. Finally, I demonstrate significant dynamical and regulatory continuity between sequential and simultaneous modes of segmentation. I discuss these results in the context of the experimental literature.

Tissue tectonics and the multi-scale regulation of developmental timing

Development encompasses processes that occur at multiple length scales, including gene-regulatory interactions, cell movements and reorganization, cell signalling and growth. It is essential that the timing of events in all of these different processes is coordinated to generate well-patterned tissues and organs. However, how the timing of intrinsic cell state changes is coordinated with events occurring at the multi-tissue and whole-organism level is unknown. Here, we argue that an important mechanism that accounts for the integration of timing across levels of organization is provided by tissue tectonics, i.e. how morphogenetic events driving tissue shape changes result in the relative displacement of signalling and responding tissues and coordinate developmental timing across scales. In doing so, tissue tectonics provides a mechanism by which the cell specification events intrinsic to cells can be modulated by the temporal exposure to extracellular signals. This exposure is in turn regulated by higher-order properties of the embryo, such as their physical properties, rates of growth and the combination of dynamic cell behaviours, impacting tissue morphogenesis. Tissue tectonics creates a downward flow of information from higher to lower levels of biological organization, providing an instance of downward causation in development.

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.

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.