Large-scale simulations of biological cell sorting driven by differential adhesion follow diffusion-limited domain coalescence regime

Cell sorting by active forces in a phase-field model of cell monolayers

Cell sorting, the segregation of cells with different properties into distinct domains, is a key phenomenon in biological processes such as embryogenesis. We use a phase-field model of a confluent cell layer to study the role of activity in cell sorting. We find that a mixture of cells with extensile or contractile dipolar activity, and which are identical apart from their activity, quickly sort into small, elongated patches which then grow slowly in time. We interpret the sorting as driven by the different diffusivity of the extensile and contractile cells, mirroring the ordering of Brownian particles connected to different hot and cold thermostats. We check that the free energy is not changed by either partial or complete sorting, thus confirming that activity can be responsible for the ordering even in the absence of thermodynamic mechanisms.

Phase Separation Driven by Active Flows

We extend the continuum theories of active nematohydrodynamics to model a two-fluid mixture with separate velocity fields for each fluid component, coupled through a viscous drag. The model is used to study an active nematic fluid mixed with an isotropic fluid. We find microphase separation, and argue that this results from an interplay between active anchoring and active flows driven by concentration gradients. The results may be relevant to cell sorting and the formation of lipid rafts in cell membranes.

Biophysical models of early mammalian embryogenesis

Embryo development is a critical and fascinating stage in the life cycle of many organisms. Despite decades of research, the earliest stages of mammalian embryogenesis are still poorly understood, caused by a scarcity of high-resolution spatial and temporal data, the use of only a few model organisms, and a paucity of truly multidisciplinary approaches that combine biological research with biophysical modeling and computational simulation. Here, we explain the theoretical frameworks and biophysical processes that are best suited to modeling the early mammalian embryo, review a comprehensive list of previous models, and discuss the most promising avenues for future work.

Is cell segregation like oil and water: Asymptotic versus transitory regime

Understanding the segregation of cells is crucial to answer questions about tissue formation in embryos or tumor progression. Steinberg proposed that separation of cells can be compared to the separation of two liquids. Such a separation is well described by the Cahn-Hilliard (CH) equations and the segregation indices exhibit an algebraic decay with exponent 1/3 with respect to time. Similar exponents are also observed in cell-based models. However, the scaling behavior in these numerical models is usually only examined in the asymptotic regime and these models have not been directly applied to actual cell segregation data. In contrast, experimental data also reveals other scaling exponents and even slow logarithmic scaling laws. These discrepancies are commonly attributed to the effects of collective motion or velocity-dependent interactions. By calibrating a 2D cellular automaton (CA) model which efficiently implements a dynamic variant of the differential adhesion hypothesis to 2D experimental data from Méhes et al., we reproduce the biological cell segregation experiments with just adhesive forces. The segregation in the cellular automaton model follows a logarithmic scaling initially, which is in contrast to the proposed algebraic scaling with exponent 1/3. However, within the less than two orders of magnitudes in time which are observable in the experiments, a logarithmic scaling may appear as a pseudo-algebraic scaling. In particular, we demonstrate that the cellular automaton model can exhibit a range of exponents ≤1/3 for such a pseudo-algebraic scaling. Moreover, the time span of the experiment falls into the transitory regime of the cellular automaton rather than the asymptotic one. We additionally develop a method for the calibration of the 2D Cahn-Hilliard model and find a match with experimental data within the transitory regime of the Cahn-Hilliard model with exponent 1/4. On the one hand this demonstrates that the transitory behavior is relevant for the experiment rather than the asymptotic one. On the other hand this corroborates the ambiguity of the scaling behavior, when segregation processes can be only observed on short time spans.

Segregation of different cell types is a crucial process for the pattern formation in tissues, in particular during embryogenesis. Since the involved cell interactions are complex and difficult to measure individually in experiments, mathematical modelling plays an increasingly important role to unravel the mechanisms governing segregation. The analysis of these theoretical models focuses mainly on the asymptotic behavior at large times, in a steady regime and for large numbers of cells. Most famously, cell-segregation models based on the minimization of the total surface energy, a mechanism also driving the demixing of immiscible fluids, are known to exhibit asymptotically a particular algebraic scaling behavior. However, it is not clear, whether the asymptotic regime of the numerical models is relevant at the spatio-temporal scales of actual biological processes and in-vitro experiments. By developing a mapping between 2D cell-based models and experimental settings, we are able to directly compare previous experimental data to numerical simulations of cell segregation quantitatively. We demonstrate that the experiments are reproduced by the transitory regime of the models rather than the asymptotic one. Our work puts a new perspective on previous model-driven conclusions on cell segregation mechanisms.

Application of aptamers in regenerative medicine

Regenerative medicine is a discipline that studies how to use biological and engineering principles and operation methods to repair and regenerate damaged tissues and organs. Until now, regenerative medicine has focused mainly on the in-depth study of the pathological mechanism of diseases, the further development and application of new drugs, and tissue engineering technology strategies. The emergence of aptamers has supplemented the development methods and types of new drugs and enriched the application elements of tissue engineering technology, injecting new vitality into regenerative medicine. The role and application status of aptamers screened in recent years in various tissue regeneration and repair are reviewed, and the prospects and challenges of aptamer technology are discussed, providing a basis for the design and application of aptamers in long-term transformation.

Role of senescent cells in the motile behavior of active, non-senescent cells in confluent populations

Characteristics of cell migration in a confluent population depend on the nature of cell-to-cell interactions as well as cell-intrinsic properties such as the directional persistence in crawling. In addition, biological tissues (or cell cultures) almost always carry anisotropies and they too can significantly affect cell motility. In the light of this viewpoint, the emergence of cellular senescences in a confluent population of active cells raises an interesting question. Cellular senescence is a process through which a cell enters a permanent growth-arrest state and generally exhibits a dramatic body expansion. Therefore, randomly emerging senescent cells transform an initially homogeneous cell population to a “binary mixture” of two distinct cell types. Here, using in vitro cultures of MDA-MB-231 cells we investigate how spatially localized cellular senescence affect the motility of active cells within a confluent population. Importantly, we estimate the intercellular surface energy of the interface between non-senescent and senescent MDA-MB-231 cells by combining the analysis on the motile behaviors of non-senescent cells encircling senescent cells and the result of extensive numerical simulations of a cellular Potts model. We find that the adhesion of normal cells to senescent cells is much weaker than that among normal cells and that the ‘arclength’ traveled by a normal cell along the boundary of a senescent cell, on average, is several times greater than the persistence length of normal cell in a densely packed homogeneous population. The directional persistent time of normal cell during its contact with a senescent cell also increases significantly. We speculate that the phenomenon could be a general feature associated with senescent cells as the enormous expansion of senescent cell’s membrane would inevitably decrease the density of cell adhesion molecules.

Cluster size distribution of cells disseminating from a primary tumor

The first stage of the metastatic cascade often involves motile cells emerging from a primary tumor either as single cells or as clusters. These cells enter the circulation, transit to other parts of the body and finally are responsible for growth of secondary tumors in distant organs. The mode of dissemination is believed to depend on the EMT nature (epithelial, hybrid or mesenchymal) of the cells. Here, we calculate the cluster size distribution of these migrating cells, using a mechanistic computational model, in presence of different degree of EMT-ness of the cells; EMT is treated as given rise to changes in their active motile forces (μ) and cell-medium surface tension (Γ). We find that, for (μ > μ_min, Γ > 1), when the cells are hybrid in nature, the mean cluster size, N¯∼Γ2.0/μ2.8, where μ_min increases with increase in Γ. For Γ ≤ 0, N¯=1, the cells behave as completely mesenchymal. In presence of spectrum of hybrid states with different degree of EMT-ness (motility) in primary tumor, the cells which are relatively more mesenchymal (higher μ) in nature, form larger clusters, whereas the smaller clusters are relatively more epithelial (lower μ). Moreover, the heterogeneity in μ is comparatively higher for smaller clusters with respect to that for larger clusters. We also observe that more extended cell shapes promote the formation of smaller clusters. Overall, this study establishes a framework which connects the nature and size of migrating clusters disseminating from a primary tumor with the phenotypic composition of the tumor, and can lead to the better understanding of metastasis.

In the process of metastasis, tumor cells disseminate from the primary tumor either as single cells or multicellular clusters. These clusters are potential contributor to the initiation of secondary tumor in distant organs. Our computational model captures the size distribution of migrating clusters depending on the adhesion and motility of the cells (which determine the degree of their EMT nature). Furthermore, we investigate the effect of heterogeneity of cell types in the primary tumor on the resultant heterogeneity of cell types in clusters of different sizes. We believe that the understanding the formation and nature of these clusters, dangerous actors in the deadly aspect of cancer progression, will be useful for improving prognostic methods and eventually better treatments.