The effect of conspecific attraction on metapopulation dynamics

Random dispersal direction is assumed in all current metapopulation models. This assumption is called into question by recent experiments demonstrating that some species disperse preferentially to sites occupied by conspecifies. We incorporate conspecific attraction into two metapopulation models which differ in type of dispersal, the Levins model and a two-dimensional stepping-stone model. In both models, conspecific attraction lowers the proportion of occupied habitat patches within a metapopulation at equilibrium.     

Computational Modeling Reveals that a Combination of Chemotaxis and Differential Adhesion Leads to Robust Cell Sorting during Tissue Patterning

Robust tissue patterning is crucial to many processes during development. The "French Flag" model of patterning, whereby naïve cells in a gradient of diffusible morphogen signal adopt different fates due to exposure to different amounts of morphogen concentration, has been the most widely proposed model for tissue patterning. However, recently, using time-lapse experiments, cell sorting has been found to be an alternative model for tissue patterning in the zebrafish neural tube. But it remains unclear what the sorting mechanism is. In this article, we used computational modeling to show that two mechanisms, chemotaxis and differential adhesion, are needed for robust cell sorting. We assessed the performance of each of the two mechanisms by quantifying the fraction of correct sorting, the fraction of stable clusters formed after correct sorting, the time needed to achieve correct sorting, and the size variations of the cells having different fates. We found that chemotaxis and differential adhesion confer different advantages to the sorting process. Chemotaxis leads to high fraction of correct sorting as individual cells will either migrate towards or away from the source depending on its cell type. However after the cells have sorted correctly, there is no interaction among cells of the same type to stabilize the sorted boundaries, leading to cell clusters that are unstable. On the other hand, differential adhesion results in low fraction of correct clusters that are more stable. In the absence of morphogen gradient noise, a combination of both chemotaxis and differential adhesion yields cell sorting that is both accurate and robust. However, in the presence of gradient noise, the simple combination of chemotaxis and differential adhesion is insufficient for cell sorting; instead, chemotaxis coupled with delayed differential adhesion is required to yield optimal sorting.     

A Mechanistic Collective Cell Model for Epithelial Colony Growth and Contact Inhibition

We present a mechanistic hybrid continuum-discrete model to simulate the dynamics of epithelial cell colonies. Collective cell dynamics are modeled using continuum equations that capture plastic, viscoelastic, and elastic deformations in the clusters while providing single-cell resolution. The continuum equations can be viewed as a coarse-grained version of previously developed discrete models that treat epithelial clusters as a two-dimensional network of vertices or stochastic interacting particles and follow the framework of dynamic density functional theory appropriately modified to account for cell size and shape variability. The discrete component of the model implements cell division and thus influences cell size and shape that couple to the continuum component. The model is validated against recent in vitro studies of epithelial cell colonies using Madin-Darby canine kidney cells. In good agreement with experiments, we find that mechanical interactions and constraints on the local expansion of cell size cause inhibition of cell motion and reductive cell division. This leads to successively smaller cells and a transition from exponential to quadratic growth of the colony that is associated with a constant-thickness rim of growing cells at the cluster edge, as well as the emergence of short-range ordering and solid-like behavior. A detailed analysis of the model reveals a scale invariance of the growth and provides insight into the generation of stresses and their influence on the dynamics of the colonies. Compared to previous models, our approach has several advantages: it is independent of dimension, it can be parameterized using classical elastic properties (Poisson’s ratio and Young’s modulus), and it can easily be extended to incorporate multiple cell types and general substrate geometries.     

Multiparameter analysis and sorting of mammalian cells

An improved multisensor cell sorting instrument for quantitative analysis and sorting of cells has been developed. Cells stained with fluorescent dyes enter a flow chamber where cell volume, fluorescence, and light scatter sensors simultaneously measure multiple cellular properties. Cells then emerge in a liquid jet that is broken into uniform liquid droplets. Sensor signals are electronically processed in one of several ways for optimum cell discrimination and are displayed as pulse-amplitude distributions using a multichannel pulse-height analyzer. Processed signals activate cell sorting according to preselected parametric criteria by electrically charging droplets containing cells and electrostatically deflecting them into collection vessels. Illustrative examples of multiparameter cell analysis and sorting experiments using a model mouse tumor cell system, human and animal leukocytes, and cultured mammalian cells are presented.     

The mechanics of cell sorting and envelopment

Aggregates of embryonic cells undergo a variety of intriguing processes including sorting by histological type and envelopment of cell masses of one type by another. It has long been held that these processes were driven by differential adhesions, as embodied in the famous differential adhesion hypothesis (DAH). Here, we use analytical mechanics to investigate the forces that are generated by various sub-cellular structures including microfilaments, cell membranes and their associated proteins, and by sources of cell-cell adhesions. We consider how these forces cause the triple junctions between cells to move, and how these motions ultimately give rise to phenomena such as cell sorting and tissue envelopment. The analyses show that, contrary to the widely accepted DAH, differential adhesions alone are unable to drive sorting and envelopment. They show, instead, that these phenomena are driven by the combined effect of several force generators, as embodied in an equivalent surface or interfacial tension. These unconventional findings follow directly from the relevant surface physics and mechanics, and are consistent with well-known cell sorting and envelopment experiments, and with recent computer simulations.     

The cellular basis of cell sorting kinetics

Cell sorting is a dynamical cooperative phenomenon that is fundamental for tissue morphogenesis and tissue homeostasis. According to Steinberg's differential adhesion hypothesis, the structure of sorted cell aggregates is determined by physical characteristics of the respective tissues, the tissue surface tensions. Steinberg postulated that tissue surface tensions result from quantitative differences in intercellular adhesion. Several experiments in cell cultures as well as in developing organisms support this hypothesis.The question of how tissue surface tension might result from differential adhesion was addressed in some theoretical models. These models describe the cellular interdependence structure once the temporal evolution has stabilized. In general, these models are capable of reproducing sorted patterns. However, the model dynamics at the cellular scale are defined implicitly and are not well-justified. The precise mechanism describing how differential adhesion generates the observed sorting kinetics at the tissue level is still unclear.It is necessary to formulate the concepts of cell level kinetics explicitly. Only then it is possible to understand the temporal development at the cellular and tissue scales. Here we argue that individual cell mobility is reduced the more the cells stick to their neighbors. We translate this assumption into a precise mathematical model which belongs to the class of stochastic interacting particle systems. Analyzing this model, we are able to predict the emergent sorting behavior at the population level. We describe qualitatively the geometry of cell segregation depending on the intercellular adhesion parameters. Furthermore, we derive a functional relationship between intercellular adhesion and surface tension and highlight the role of cell mobility in the process of sorting. We show that the interaction between the cells and the boundary of a confining vessel has a major impact on the sorting geometry.     

Bayesian estimation of recent migration rates after a spatial expansion

Approximate Bayesian computation (ABC) is a highly flexible technique that allows the estimation of parameters under demographic models that are too complex to be handled by full-likelihood methods. We assess the utility of this method to estimate the parameters of range expansion in a two-dimensional stepping-stone model, using samples from either a single deme or multiple demes. A minor modification to the ABC procedure is introduced, which leads to an improvement in the accuracy of estimation. The method is then used to estimate the expansion time and migration rates for five natural common vole populations in Switzerland typed for a sex-linked marker and a nuclear marker. Estimates based on both markers suggest that expansion occurred <10,000 years ago, after the most recent glaciation, and that migration rates are strongly male biased.     

A Validated Mathematical Model of Tumor Growth Including Tumor–Host Interaction,Cell-Mediated Immune Response and Chemotherapy

We consider a dynamical model of cancer growth including three interacting cell populations of tumor cells, healthy host cells and immune effector cells. The tumor–immune and the tumor–host interactions are characterized to reproduce experimental results. A thorough dynamical analysis of the model is carried out, showing its capability to explain theoretical and empirical knowledge about tumor development. A chemotherapy treatment reproducing different experiments is also introduced. We believe that this simple model can serve as a foundation for the development of more complicated and specific cancer models.     

Computational cell model based on autonomous cell movement regulated by cell-cell signalling successfully recapitulates the "inside and outside" pattern of cell sorting

Background

Development of multicellular organisms proceeds from a single fertilized egg as the combined effect of countless numbers of cellular interactions among highly dynamic cells. Since at least a reminiscent pattern of morphogenesis can be recapitulated in a reproducible manner in reaggregation cultures of dissociated embryonic cells, which is known as cell sorting, the cells themselves must possess some autonomous cell behaviors that assure specific and reproducible self-organization. Understanding of this self-organized dynamics of heterogeneous cell population seems to require some novel approaches so that the approaches bridge a gap between molecular events and morphogenesis in developmental and cell biology. A conceptual cell model in a computer may answer that purpose. We constructed a dynamical cell model based on autonomous cell behaviors, including cell shape, growth, division, adhesion, transformation, and motility as well as cell-cell signaling. The model gives some insights about what cellular behaviors make an appropriate global pattern of the cell population.

Results

We applied the model to "inside and outside" pattern of cell-sorting, in which two different embryonic cell types within a randomly mixed aggregate are sorted so that one cell type tends to gather in the central region of the aggregate and the other cell type surrounds the first cell type. Our model can modify the above cell behaviors by varying parameters related to them. We explored various parameter sets with which the "inside and outside" pattern could be achieved. The simulation results suggested that direction of cell movement responding to its neighborhood and the cell's mobility are important for this specific rearrangement.

Conclusion

We constructed an in silico cell model that mimics autonomous cell behaviors and applied it to cell sorting, which is a simple and appropriate phenomenon exhibiting self-organization of cell population. The model could predict directional cell movement and its mobility are important in the "inside and outside" pattern of cell sorting. Those behaviors are altered by signal molecules and consequently affect the global pattern of the cell sorting. Our model is also applicable to other developmental processes beyond cell sorting.     

A new cell-based FE model for the mechanics of embryonic epithelia

In order to overcome a significant stiffening artefact associated with current finite element (FE) models for the mechanics of embryonic epithelia, two new FE formulations were developed. Cell–cell interfacial tensions γ are represented by constant-force rod elements as in previous models. However, the viscosity of the cytoplasm with its embedded organelles and filament networks is modeled using viscous triangular elements, it is modeled using either radial and circumferential dashpots or an orthogonal dashpot system rather than the viscous triangular elements typical of previous two-dimensional FE models. The models are tested against tissue (epithelium) stretching because it gives rise to significant changes in cell shape and against cell sorting because it involves high rates of cell rearrangement. The orthogonal dashpot system is found to capture cell size and shape effects well, give the model cells characteristics that are consistent with those of real cells, provide high computational efficiency and hold promise for future three-dimensional analyses.     

A new cell-based FE model for the mechanics of embryonic epithelia

In order to overcome a significant stiffening artefact associated with current finite element (FE) models for the mechanics of embryonic epithelia, two new FE formulations were developed. Cell-cell interfacial tensions gamma are represented by constant-force rod elements as in previous models. However, the viscosity of the cytoplasm with its embedded organelles and filament networks is modeled using viscous triangular elements, it is modeled using either radial and circumferential dashpots or an orthogonal dashpot system rather than the viscous triangular elements typical of previous two-dimensional FE models. The models are tested against tissue (epithelium) stretching because it gives rise to significant changes in cell shape and against cell sorting because it involves high rates of cell rearrangement. The orthogonal dashpot system is found to capture cell size and shape effects well, give the model cells characteristics that are consistent with those of real cells, provide high computational efficiency and hold promise for future three-dimensional analyses.     

Non-straight cell edges are important to invasion and engulfment as demonstrated by cell mechanics model

Computational models of cell–cell mechanical interactions typically simulate sorting and certain other motions well, but as demands on these models continue to grow, discrepancies between the cell shapes, contact angles and behaviours they predict and those that occur in real cells have come under increased scrutiny. To investigate whether these discrepancies are a direct result of the straight cell–cell edges generally assumed in these models, we developed a finite element model that approximates cell boundaries using polylines with an arbitrary number of segments. We then compared the predictions of otherwise identical polyline and monoline (straight-edge) models in a variety of scenarios, including annealing, single- and multi-cell engulfment, sorting, and two forms of mixing—invasion and checkerboard pattern formation. Keeping cell–cell edges straight influences cell motion, cell shape, contact angle, and boundary length, especially in cases where one cell type is pulled between or around cells of a different type, as in engulfment or invasion. These differences arise because monoline cells have restricted deformation modes. Polyline cells do not face these restrictions, and with as few as three segments per edge yielded realistic edge shapes and contact angle errors one-tenth of those produced by monoline models, making them considerably more suitable for situations where angles and shapes matter, such as validation of cellular force–inference techniques. The findings suggest that non-straight cell edges are important both in modelling and in nature.     

Is cell sorting caused by differences in the work of intercellular adhesion? A critique of the steinberg hypothesis

The differential adhesion hypothesis, developed by Malcolm Steinberg, proposes that the histotypic sorting out behavior of aggregated cells is mechanistically equivalent to certain aspects of liquid surface tension, specifically the spontaneous separation of immiscible liquids of differing surface tension. According to Steinberg's hypothesis, the adhesive forces between aggregated cells play essentially the same role in cell sorting as are played by intermolecular attractive forces in liquid surface tension.In this paper I discuss a number of crucial distinctions between intermolecular attraction (in liquids) and intercellular adhesion (in aggregates). First, liquid drops are closed systems thermodynamically whereas aggregates of living cells can generate an indeterminate amount of metabolic energy capable of altering cell positions and adhesions. Secondly, intercellular adhesions are more than just close range attractions since cells can be held together by forces in addition to those which originally pulled them together. Third, the breakage of intercellular adhesions need not be simply the reverse, thermodynamically, of the formation of those adhesions. And fourthly, because intercellular adhesion is generally concentrated at relatively small foci such as desmosomes, a maximization of intercellular adhesion does not necessarily require a maximization of intercellular contact area, or vice versa.In addition, several alternative hypotheses are proposed, each of which is theoretically capable of explaining cell sorting and the other surface tension-like aspects of cell aggregate behavior which Steinberg has sought to explain as consequences of differential adhesion. In particular, a differential surface contraction hypothesis is proposed, according to which cell sorting and related phenomena are the results of cell surface contractions induced to occur over those portions of the cell surface which are exposed to the surrounding culture medium. Because of the evidence that various invagination type movements of embryonic epithelia are caused by cell surface contractions, it is suggested that differential surface contraction is the most likely explanation of histotypic cell sorting. A number of experiments are suggested by which these various hypotheses might be tested.     

A 3-D model used to explore how cell adhesion and stiffness affect cell sorting and movement in multicellular systems

A three-dimensional mathematical model is used to determine the effects of adhesion and cell signalling on cell movements during the aggregation and slug stages of Dictyostelium discoideum (Dd) and to visualize cell sorting. The building blocks of the model are individual deformable ellipsoidal cells, where movement depends on internal parameter state (cell size and stiffness) and on external cues from the neighboring cells, extracellular matrix, and chemical signals. Cell movement and deformation are calculated from equations of motion using the total force acting on each cell, ensuring that forces are balanced. The simulations show that the sorting patterns of prestalk and prespore cells, emerging during the slug stage, depend critically on the type of cell adhesion and not just on chemotactic differences between cells. This occurs because cell size and stiffness can prevent the otherwise faster cells from passing the slower cells. The patterns are distinctively different when the prestalk cells are more or less adhesive than the prespore cells. These simulations suggest that sorting is not solely due to differential chemotaxis, and that differences in both adhesion strength and type between different cell types play a very significant role, both in Dictyostelium and other systems.     

A simple model can unify a broad range of phenomena in retinotectal map development

A paradigm model system for studying the development of patterned connections in the nervous system is the topographic map formed by retinal axons in the optic tectum/superior colliculus. Starting in the 1970s, a series of computational models have been proposed to explain map development in both normal conditions, and perturbed conditions where the retina and/or tectum/superior colliculus are altered. This stands in contrast to more recent models that have often been simpler than older ones, and tend to address more limited data sets, but include more recent genetic manipulations. The original exploration of many of the early models was one-dimensional and limited by the computational resources of the time. This leaves open the ability of these early models to explain both map development in two dimensions, and the genetic manipulation data that have only appeared more recently. In this article, we show that a two-dimensional and updated version of the XBAM model (eXtended Branch Arrow Model), first proposed in 1982, reproduces a range of surgical map manipulations not yet demonstrated by more modern models. A systematic exploration of the parameter space of this model in two dimensions also reveals richer behavior than that apparent from the original one-dimensional versions. Furthermore, we show that including a specific type of axon?Caxon interaction can account for the map collapse recently observed when particular receptor levels are genetically manipulated in a subset of retinal ganglion cells. Together these results demonstrate that balancing multiple influences on map development seems to be necessary to explain many biological phenomena in retinotectal map formation, and suggest important constraints on the underlying biological variables.     

Cloning of Plasmodium falciparum by single-cell sorting

Malaria parasite cloning is traditionally carried out mainly by using the limiting dilution method, which is laborious, imprecise, and unable to distinguish multiply-infected RBCs. In this study, we used a parasite engineered to express green fluorescent protein (GFP) to evaluate a single-cell sorting method for rapidly cloning Plasmodium falciparum. By dividing a two-dimensional scattergram from a cell sorter into 17 gates, we determined the parameters for isolating singly-infected erythrocytes and sorted them into individual cultures. Pre-gating of the engineered parasites for GFP allowed the isolation of almost 100% GFP-positive clones. Compared with the limiting dilution method, the number of parasite clones obtained by single-cell sorting was much higher. Molecular analyses showed that parasite isolates obtained by single-cell sorting were highly homogenous. This highly efficient single-cell sorting method should prove very useful for cloning both P. falciparum laboratory populations from genetic manipulation experiments and clinical samples.     

Study on multicellular systems using a phase field model

A model of multicellular systems with several types of cells is developed from the phase field model. The model is presented as a set of partial differential equations of the field variables, each of which expresses the shape of one cell. The dynamics of each cell is based on the criteria for minimizing the surface area and retaining a certain volume. The effects of cell adhesion and excluded volume are also taken into account. The proposed model can be used to find the position of the membrane and/or the cortex of each cell without the need to adopt extra variables. This model is suitable for numerical simulations of a system having a large number of cells. The two-dimensional results of cell division, cell adhesion, rearrangement of a cell cluster, chemotaxis, and cell sorting as well as the three-dimensional results of cell clusters on the substrate are presented.     

Turing Pattern Formation with Two Kinds of Cells and a Diffusive Chemical

We study a three-variable Turing system with two kinds of cells and a diffusive chemical, considering the formation and maintenance of fish skin patterns with multiple pigment cells. The two types of cells are produced from undifferentiated cells. They inhibit the supply rate of the other cell type, forming local clusters of the same cell type. In addition, the cells of one type can be maintained only in the presence of a diffusive chemical produced by the other cell type, resulting in the coexistence of two cell types in heterogeneous spatial patterns. We assume linear interaction among cells and the chemical, and cell supply rates constrained to be positive or zero. We derive the condition for diffusion-driven instability. In one-dimensional model, we examine how the wavelength of the periodic pattern depends on parameters. In the two-dimensional model, we study the condition for spot, stripe or reversed spot pattern to emerge (pattern selection). We discuss heuristic criteria for the pattern selection.     

炭疽疫苗及治疗药物筛选和评价模型研究进展

炭疽疫苗和治疗药物的研究是近年来国际上研究热点之一,由于对它们的有效性研究不能在人体进行,因此实验模型的选择就特别重要.目前常用的细胞模型主要包括CHO细胞和J774A.1细胞.动物模型种类较多,包括小鼠、大鼠、豚鼠、兔和猴等都被作为炭疽的动物模型加以研究.由于模型选择的差异,实验结果常出现较大差异,甚至得到相反的结果.回顾了以往在细胞和动物模型上进行的炭疽实验,分析选择炭疽研究模型的原则和依据.同时,为探讨不同模型之间产生实验结果差异的原因,简要介绍了炭疽杆菌的致病机理,以及炭疽疫苗和治疗药物的研究进展.