Cell sorting by differential cell motility: a model for pattern formation in Dictyostelium

Differential cell motion: A mathematical model of anterior posterior sorting

Here, we investigate how a subpopulation of cells can move through an aggregate of cells. Using a stochastic force-based model of Dictyostelium discoideum when the population is forming a slug, we simulate different strategies for prestalk cells to reliably move to the front of the slug while omitting interaction with the substrate thus ignoring the overall motion of the slug. Of the mechanisms that we simulated, prestalk cells being more directed is the best strategy followed by increased asymmetric motive forces for prestalk cells. The lifetime of the cell adhesion molecules, while not enough to produce differential motion, did modulate the results of the strategies employed. Finally, understanding and simulating the appropriate boundary conditions are essential to correctly predict the motion.

Heterogeneous individual motility biases group composition in a model of aggregating cells

Aggregative life cycles are characterized by alternating phases of unicellular growth and multicellular development. Their multiple, independent evolutionary emergence suggests that they may have coopted pervasive properties of single-celled ancestors. Primitive multicellular aggregates, where coordination mechanisms were less efficient than in extant aggregative microbes, must have faced high levels of conflict between different co-aggregating populations. Such conflicts within a multicellular body manifest in the differential reproductive output of cells of different types. Here, we study how heterogeneity in cell motility affects the aggregation process and creates a mismatch between the composition of the population and that of self-organized groups of active adhesive particles. We model cells as self-propelled particles and describe aggregation in a plane starting from a dispersed configuration. Inspired by the life cycle of aggregative model organisms such as Dictyostelium discoideum or Myxococcus xanthus, whose cells interact for a fixed duration before the onset of chimeric multicellular development, we study finite-time configurations for identical particles and in binary mixes. We show that co-aggregation results in three different types of frequency-dependent biases, one of which is associated to evolutionarily stable coexistence of particles with different motility. We propose a heuristic explanation of such observations, based on the competition between delayed aggregation of slower particles and detachment of faster particles. Unexpectedly, despite the complexity and non-linearity of the system, biases can be largely predicted from the behavior of the two corresponding homogenous populations. This model points to differential motility as a possibly important factor in driving the evolutionary emergence of facultatively multicellular life-cycles.

Interplay of mesoscale physics and agent-like behaviors in the parallel evolution of aggregative multicellularity

Myxobacteria and dictyostelids are prokaryotic and eukaryotic multicellular lineages, respectively, that after nutrient depletion aggregate and develop into structures called fruiting bodies. The developmental processes and resulting morphological outcomes resemble one another to a remarkable extent despite their independent origins, the evolutionary distance between them and the lack of traceable homology in molecular mechanisms. We hypothesize that the morphological parallelism between the two lineages arises as the consequence of the interplay within multicellular aggregates between generic processes, physical and physicochemical processes operating similarly in living and non-living matter at the mesoscale (~10^-3-10^-1 m) and agent-like behaviors, unique to living systems and characteristic of the constituent cells, considered as autonomous entities acting according to internal rules in a shared environment. Here, we analyze the contributions of generic and agent-like determinants in myxobacteria and dictyostelid development and their roles in the generation of their common traits. Consequent to aggregation, collective cell-cell contacts mediate the emergence of liquid-like properties, making nascent multicellular masses subject to novel patterning and morphogenetic processes. In both lineages, this leads to behaviors such as streaming, rippling, and rounding-up, as seen in non-living fluids. Later the aggregates solidify, leading them to exhibit additional generic properties and motifs. Computational models suggest that the morphological phenotypes of the multicellular masses deviate from the predictions of generic physics due to the contribution of agent-like behaviors of cells such as directed migration, quiescence, and oscillatory signal transduction mediated by responses to external cues. These employ signaling mechanisms that reflect the evolutionary histories of the respective organisms. We propose that the similar developmental trajectories of myxobacteria and dictyostelids are more due to shared generic physical processes in coordination with analogous agent-type behaviors than to convergent evolution under parallel selection regimes. Insights from the biology of these aggregative forms may enable a unified understanding of developmental evolution, including that of animals and plants.

Cell pelotons: A model of early evolutionary cell sorting, with application to slime mold Dictyostelium discoideum

A theoretical model is presented for early evolutionary cell sorting within cellular aggregates. The model involves an energy-saving mechanism and principles of collective self-organization analogous to those observed in bicycle pelotons (groups of cyclists). The theoretical framework is applied to slime-mold slugs (Dictyostelium discoideum) and incorporated into a computer simulation which demonstrates principally the sorting of cells between the anterior and posterior slug regions. The simulation relies on an existing simulation of bicycle peloton dynamics which is modified to incorporate a limited range of cell metabolic capacities among heterogeneous cells, along with a tunable energy-expenditure parameter, referred to as an "output-level" or "starvation-level" to reflect diminishing energetic supply. Proto-cellular dynamics are modeled for three output phases: "active", "suffering", and "dying or dead." Adjusting the starvation parameter causes cell differentiation and sorting into sub-groups within the cellular aggregate. Tuning of the starvation parameter demonstrates how weak or expired cells shuffle backward within the cellular aggregate.

Statistical Dynamics of Spatial-Order Formation by Communicating Cells

Communicating cells can coordinate their gene expressions to form spatial patterns, generating order from disorder. Ubiquitous "secrete-and-sense cells" secrete and sense the same molecule to do so. Here we present a modeling framework-based on cellular automata and mimicking approaches of statistical mechanics-for understanding how secrete-and-sense cells with bistable gene expression, from disordered beginnings, can become spatially ordered by communicating through rapidly diffusing molecules. Classifying lattices of cells by two "macrostate" variables-"spatial index," measuring degree of order, and average gene-expression level-reveals a conceptual picture: a group of cells behaves as a single particle, in an abstract space, that rolls down on an adhesive "pseudo-energy landscape" whose shape is determined by cell-cell communication and an intracellular gene-regulatory circuit. Particles rolling down the landscape represent cells becoming more spatially ordered. We show how to extend this framework to more complex forms of cellular communication.

Simulating Heterogeneous Tumor Cell Populations

Certain tumor phenomena, like metabolic heterogeneity and local stable regions of chronic hypoxia, signify a tumor's resistance to therapy. Although recent research has shed light on the intracellular mechanisms of cancer metabolic reprogramming, little is known about how tumors become metabolically heterogeneous or chronically hypoxic, namely the initial conditions and spatiotemporal dynamics that drive these cell population conditions. To study these aspects, we developed a minimal, spatially-resolved simulation framework for modeling tissue-scale mixed populations of cells based on diffusible particles the cells consume and release, the concentrations of which determine their behavior in arbitrarily complex ways, and on stochastic reproduction. We simulate cell populations that self-sort to facilitate metabolic symbiosis, that grow according to tumor-stroma signaling patterns, and that give rise to stable local regions of chronic hypoxia near blood vessels. We raise two novel questions in the context of these results: (1) How will two metabolically symbiotic cell subpopulations self-sort in the presence of glucose, oxygen, and lactate gradients? We observe a robust pattern of alternating striations. (2) What is the proper time scale to observe stable local regions of chronic hypoxia? We observe the stability is a function of the balance of three factors related to O2-diffusion rate, local vessel release rate, and viable and hypoxic tumor cell consumption rate. We anticipate our simulation framework will help researchers design better experiments and generate novel hypotheses to better understand dynamic, emergent whole-tumor behavior.

Secreting and sensing the same molecule allows cells to achieve versatile social behaviors

Cells that secrete and sense the same signaling molecule are ubiquitous. To uncover the functional capabilities of the core "secrete-and-sense" circuit motif shared by these cells, we engineered yeast to secrete and sense the mating pheromone. Perturbing each circuit element revealed parameters that control the degree to which the cell communicated with itself versus with its neighbors. This tunable interplay of self-communication and neighbor communication enables cells to span a diverse repertoire of cellular behaviors. These include a cell being asocial by responding only to itself and social through quorum sensing, and an isogenic population of cells splitting into social and asocial subpopulations. A mathematical model explained these behaviors. The versatility of the secrete-and-sense circuit motif may explain its recurrence across species.

Loss of the histidine kinase DhkD results in mobile mounds during development of Dictyostelium discoideum

Background

Histidine kinases are receptors for sensing cellular and environmental signals, and in response to the appropriate cue they initiate phosphorelays that regulate the activity of response regulators. The Dictyostelium discoideum genome encodes 15 histidine kinases that function to regulate several processes during the multicellular developmental program, including the slug to culmination transition, osmoregulation, and spore differentiation. While there are many histidine kinases, there is only a single response regulator, RegA. Not surprisingly given the ubiquitous involvement of cAMP in numerous processes of development in Dictyostelium, RegA is a cAMP phosphodiesterase that is activated upon receiving phosphates through a phosphorelay. Hence, all of the histidine kinases characterized to date regulate developmental processes through modulating cAMP production. Here we investigate the function of the histidine kinase DhkD.

Principal Findings

The dhkD gene was disrupted, and the resulting cells when developed gave a novel phenotype. Upon aggregation, which occurred without streaming, the mounds were motile, a phenotype termed the pollywog stage. The pollywog phenotype was dependent on a functional RegA. After a period of random migration, the pollywogs attempted to form fingers but mostly generated aberrant structures with no tips. While prestalk and prespore cell differentiation occurred with normal timing, proper patterning did not occur. In contrast, wild type mounds are not motile, and the cAMP chemotactic movement of cells within the mound facilitates proper prestalk and prespore patterning, tip formation, and the vertical elongation of the mound into a finger.

Conclusions

We postulate that DhkD functions to ensure the proper cAMP distribution within mounds that in turn results in patterning, tip formation and the transition of mounds to fingers. In the absence of DhkD, aberrant cell movements in response to an altered cAMP distribution result in mound migration, a lack of proper patterning, and an inability to generate normal finger morphology.

A cAMP signaling model explains the benefit of maintaining two forms of phosphodiesterase in Dictyostelium

Starving Dictyostelium cells respond chemotactically to cell-generated waves of cyclic adenosine -3',5'- monophosphate (cAMP) that guide cell aggregation toward a signaling center. In this process, a large number of cells are recruited, resulting in the formation of aggregation territories that are essential for fruiting body formation. The enzyme PdsA phosphodiesterase (PDE), a crucial component of the signaling system, breaks down the external cAMP and can be either membrane-bound or secreted. The existence of two such forms is unusual in cell biology, and it remains to be determined why they have both been maintained through evolution. Here, using a model of the cAMP signaling system, I show that colonies can successfully organize into aggregates over a wider range of initial cell densities when both forms of PDE are present in an appropriately tuned ratio than when only a single form is present. The model indicates that membrane-bound PDE maintains aggregation-territory integrity in colonies with high initial cell density, whereas the secreted form is important for wave propagation at low cell densities. Thus, the ultimate retention of both forms can increase territory size. These findings have implications for other excitable media, including Ca(2+) propagation in cardiac cells and propagation of electrical excitation in nerve axons, since these systems have similar features of spatial nonuniform "release" and "degradation" of the relevant signals.

Forming patterns in development without morphogen gradients: scattered differentiation and sorting out

Few mechanisms provide alternatives to morphogen gradients for producing spatial patterns of cells in development. One possibility is based on the sorting out of cells that initially differentiate in a salt and pepper mixture and then physically move to create coherent tissues. Here, we describe the evidence suggesting this is the major mode of patterning in Dictyostelium. In addition, we discuss whether convergent evolution could have produced a conceptually similar mechanism in other organisms.

Self-organization of engineered epithelial tubules by differential cellular motility

Patterning of developing tissues arises from a number of mechanisms, including cell shape change, cell proliferation, and cell sorting from differential cohesion or tension. Here, we reveal that differences in cell motility can also lead to cell sorting within tissues. Using mosaic engineered mammary epithelial tubules, we found that cells sorted depending on their expression level of the membrane-anchored collagenase matrix metalloproteinase (MMP)-14. These rearrangements were independent of the catalytic activity of MMP14 but absolutely required the hemopexin domain. We describe a signaling cascade downstream of MMP14 through Rho kinase that allows cells to sort within the model tissues. Cell speed and persistence time were enhanced by MMP14 expression, but only the latter motility parameter was required for sorting. These results indicate that differential directional persistence can give rise to patterns within model developing tissues.

Regulation of Dictyostelium morphogenesis by RapGAP3

Rap1 is a key regulator of cell adhesion and cell motility in Dictyostelium. Here, we identify a Rap1-specific GAP protein (RapGAP3) and provide evidence that Rap1 signaling regulates cell-cell adhesion and cell migration within the multicellular organism. RapGAP3 mediates the deactivation of Rap1 at the late mound stage of development and plays an important role in regulating cell sorting during apical tip formation, when the anterior-posterior axis of the organism is formed, by controlling cell-cell adhesion and cell migration. The loss of RapGAP3 results in a severely altered morphogenesis of the multicellular organism at the late mound stage. Direct measurement of cell motility within the mound shows that rapGAP3(-) cells have a reduced speed of movement and, compared to wild-type cells, have a reduced motility towards the apex. rapGAP3(-) cells exhibit some increased EDTA/EGTA sensitive cell-cell adhesion at the late mound stage. RapGAP3 transiently and rapidly translocates to the cell cortex in response to chemoattractant stimulation, which is dependent on F-actin polymerization. We suggest that the altered morphogenesis and the cell-sorting defect of rapGAP3(-) cells may result in reduced directional movement of the mutant cells to the apex of the mound.

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.

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.

Moving forward moving backward: directional sorting of chemotactic cells due to size and adhesion differences

Differential movement of individual cells within tissues is an important yet poorly understood process in biological development. Here we present a computational study of cell sorting caused by a combination of cell adhesion and chemotaxis, where we assume that all cells respond equally to the chemotactic signal. To capture in our model mesoscopic properties of biological cells, such as their size and deformability, we use the Cellular Potts Model, a multiscale, cell-based Monte Carlo model. We demonstrate a rich array of cell-sorting phenomena, which depend on a combination of mescoscopic cell properties and tissue level constraints. Under the conditions studied, cell sorting is a fast process, which scales linearly with tissue size. We demonstrate the occurrence of "absolute negative mobility", which means that cells may move in the direction opposite to the applied force (here chemotaxis). Moreover, during the sorting, cells may even reverse the direction of motion. Another interesting phenomenon is "minority sorting", where the direction of movement does not depend on cell type, but on the frequency of the cell type in the tissue. A special case is the cAMP-wave-driven chemotaxis of Dictyostelium cells, which generates pressure waves that guide the sorting. The mechanisms we describe can easily be overlooked in studies of differential cell movement, hence certain experimental observations may be misinterpreted.

Direct mechanical force measurements during the migration of Dictyostelium slugs using flexible substrata

We use the flexible substrate method to study how and where mechanical forces are exerted during the migration of Dictyostelium slugs. This old and contentious issue has been left poorly understood so far. We are able to identify clearly separate friction forces in the tip and in the tail of the slug, traction forces mostly localized in the inner slug/surface contact area in the prespore region and large perpendicular forces directed in the outward direction at the outline of contact area. Surprisingly, the magnitude of friction and traction forces is decreasing with slug velocity indicating that these quantities are probably related to the dynamics of cell/substrate adhesion complexes. Contrary to what is always assumed in models and simulations, friction is not of fluid type (viscous drag) but rather close to solid friction. We suggest that the slime sheath confining laterally the cell mass of the slug experiences a tension that in turn is pulling out the elastic substrate in the direction tangential to the slug profile where sheath is anchored. In addition, we show in the appendix that the iterative method we developed is well adapted to study forces over large and continuous fields when the experimental error is sufficiently low and when the plane of recorded bead deformations is close enough to the elastomer surface, requirements fulfilled in this experimental study of Dictyostelium slugs.

Dictyostelium morphogenesis

During starvation-induced Dictyostelium development, up to several hundred thousand amoeboid cells aggregate, differentiate and form a fruiting body. The chemotactic movement of the cells is guided by the rising phase of the outward propagating cAMP waves and results in directed periodic movement towards the aggregation centre. In the mound and slug stages of development, cAMP waves continue to play a major role in the coordination of cell movement, cell-type-specific gene expression and morphogenesis; however, in these stages where cells are tightly packed, cell-cell adhesion/contact-dependent signalling mechanisms also play important roles in these processes.

Talin B is required for force transmission in morphogenesis of Dictyostelium

Talin plays a key role in the assembly and stabilisation of focal adhesions, but whether it is directly involved in force transmission during morphogenesis remains to be elucidated. We show that the traction force of Dictyostelium cells mutant for one of its two talin genes talB is considerably smaller than that of wild-type cells, both in isolation and within tissues undergoing morphogenetic movement. The motility of mutant cells in tightly packed tissues in vivo or under strong resistance conditions in vitro was lower than that of wild-type cells, but their motility under low external force conditions was not impaired, indicating inefficient transmission of force in mutant cells. Antibody staining revealed that the talB gene product (talin B) exists as small units subjacent to the cell membrane at adhesion sites without forming large focal adhesion-like assemblies. The total amount of talin B on the cell membrane was larger in prestalk cells, which exert larger force than prespore cells during morphogenesis. We conclude that talin B is involved in force transmission between the cytoskeleton and cell exterior.