Possible cooperation of differential adhesion and chemotaxis in mound formation of Dictyostelium

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.

Tissue self-organization based on collective cell migration by contact activation of locomotion and chemotaxis

Despite their central role in multicellular organization, navigation rules that dictate cell rearrangement remain largely undefined. Contact between neighboring cells and diffusive attractant molecules are two of the major determinants of tissue-level patterning; however, in most cases, molecular and developmental complexity hinders one from decoding the exact governing rules of individual cell movement. A primordial example of tissue patterning by cell rearrangement is found in the social amoeba Dictyostelium discoideum where the organizing center or the "tip" self-organizes as a result of sorting of differentiating prestalk and prespore cells. By employing microfluidics and microsphere-based manipulation of navigational cues at the single-cell level, here we uncovered a previously overlooked mode of Dictyostelium cell migration that is strictly directed by cell-cell contact. The cell-cell contact signal is mediated by E-set Ig-like domain-containing heterophilic adhesion molecules TgrB1/TgrC1 that act in trans to induce plasma membrane recruitment of the SCAR complex and formation of dendritic actin networks, and the resulting cell protrusion competes with those induced by chemoattractant cAMP. Furthermore, we demonstrate that both prestalk and prespore cells can protrude toward the contact signal as well as to chemotax toward cAMP; however, when given both signals, prestalk cells orient toward the chemoattractant, whereas prespore cells choose the contact signal. These data suggest a model of cell sorting by competing juxtacrine and diffusive cues, each with potential to drive its own mode of collective cell migration.

Intelligent Micro/nanomotors with Taxis

Micro/nanomotors (MNMs) are micro/nanoscale devices that can convert energy from their surroundings into autonomous motion. With this unique ability, they may revolutionize application fields ranging from active drug delivery to biological surgeries, environmental remediation, and micro/nanoengineering. To complete these applications, MNMs are required to have a vital capability to reach their destinations. Employing external fields to guide MNMs to the targets is common and effective way. However, in application scenarios where targets are generally unknown or dynamically change, MNMs must possess the capability of self-navigation or self-targeting. Taking advantage of tactic movements toward or away from signal sources, numerous intelligent MNMs with self-navigation or self-targeting have been demonstrated and attracted much attention during the past few years. In this Account, we elucidate the intelligent response mechanisms of such tactic MNMs, which are summarized as two main models. One is that local vector fields, including those of chemical concentration gradients, gravity, flows, and magnetic fields existing in systems, achieve the overall alignment of asymmetric MNMs via aligning torques, directing the MNMs to swim toward or away from the signal sources. Another is that isotropic MNMs may produce propulsion forces with direction solely determined by the local vector field regardless of their Brownian rotations. Then we discuss and highlight the recent progress in tactic MNMs, including chemotactic, phototactic, rheotactic, gravitactic, and magnetotactic motors. Artificial chemotactic MNMs can be designed with different morphologies and compositions if asymmetric reactions are associated with chemical concentration gradients. In these systems, asymmetric phoretic slip flows are induced, leading to torques that enable the anisotropic particles to align and exhibit chemotaxis. For phototactic MNMs, light irradiation establishes asymmetric fields surrounding the motors via light-induced chemical reactions or physical effects to generate phototactic motion. Shape-asymmetric MNMs reorient in natural fluid flows because of torques applied by the flows, inducing rheotactic movements. MNMs with either the centroid or magnetic components distributed asymmetrically maintain orientation under the torque triggered by gravity or magnetic forces, generating tactic motions. In the end, we envision the future development of synthetic tactic MNMs, including enhancement of the sensitivity of motors to target signals, increasing the diversity of chemical motor systems, and combining multiple mechanisms to endow the tactic motors with multiple functionality. By highlighting the current achievements and offering our perspective on tactic MNMs, we look forward to inspiring the emergence of the next generation of intelligent MNMs with taxis.

A multiscale model for heterogeneous tumor spheroid in vitro

In this paper, a novel multiscale method is proposed for the study of heterogeneous tumor spheroid growth in vitro. The entire tumor spheroid is described by an ellipsoid-based model while nutrient and other environmental factors are treated as continua. The ellipsoid-based discrete component is capable of incorporating mechanical effects and deformability, while keeping a minimum set of free variables to describe complex shape variations. Moreover, our purely cell-based description of tumor avoids the complex mutual conversion between a cell-based model and continuum model within a tumor, such as force and mass transformation. This advantage makes it highly suitable for the study of tumor spheroids in vitro whose size are normally less than 800 μm in diameter. In addition, our numerical scheme provides two computational options depending on tumor size. For a small or medium tumor spheroid, a three-dimensional (3D) numerical model can be directly applied. For a large spheroid, we suggest the use of a 3D-adapted 2D cross section configuration, which has not yet been explored in the literature, as an alternative for the theoretical investigation to bridge the gap between the 2D and 3D models. Our model and its implementations have been validated and applied to various studies given in the paper. The simulation results fit corresponding in vitro experimental observations very well.

The evolution of adhesiveness as a social adaptation

Cellular adhesion is a key ingredient to sustain collective functions of microbial aggregates. Here, we investigate the evolutionary origins of adhesion and the emergence of groups of genealogically unrelated cells with a game-theoretical model. The considered adhesiveness trait is costly, continuous and affects both group formation and group-derived benefits. The formalism of adaptive dynamics reveals two evolutionary stable strategies, at each extreme on the axis of adhesiveness. We show that cohesive groups can evolve by small mutational steps, provided the population is already endowed with a minimum adhesiveness level. Assortment between more adhesive types, and in particular differential propensities to leave a fraction of individuals ungrouped at the end of the aggregation process, can compensate for the cost of increased adhesiveness. We also discuss the change in the social nature of more adhesive mutations along evolutionary trajectories, and find that altruism arises before directly beneficial behavior, despite being the most challenging form of cooperation.

Genetic control of morphogenesis in Dictyostelium

Cells grow, move, expand, shrink and die in the process of generating the characteristic shapes of organisms. Although the structures generated during development of the social amoeba Dictyostelium discoideum look nothing like the structures seen in metazoan embryogenesis, some of the morphogenetic processes used in their making are surprisingly similar. Recent advances in understanding the molecular basis for directed cell migration, cell type specific sorting, differential adhesion, secretion of matrix components, pattern formation, regulation and terminal differentiation are reviewed. Genes involved in Dictyostelium aggregation, slug formation, and culmination of fruiting bodies are discussed.

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.

Differential adhesion between moving particles as a mechanism for the evolution of social groups

The evolutionary stability of cooperative traits, that are beneficial to other individuals but costly to their carrier, is considered possible only through the establishment of a sufficient degree of assortment between cooperators. Chimeric microbial populations, characterized by simple interactions between unrelated individuals, restrain the applicability of standard mechanisms generating such assortment, in particular when cells disperse between successive reproductive events such as happens in Dicyostelids and Myxobacteria. In this paper, we address the evolutionary dynamics of a costly trait that enhances attachment to others as well as group cohesion. By modeling cells as self-propelled particles moving on a plane according to local interaction forces and undergoing cycles of aggregation, reproduction and dispersal, we show that blind differential adhesion provides a basis for assortment in the process of group formation. When reproductive performance depends on the social context of players, evolution by natural selection can lead to the success of the social trait, and to the concomitant emergence of sizeable groups. We point out the conditions on the microscopic properties of motion and interaction that make such evolutionary outcome possible, stressing that the advent of sociality by differential adhesion is restricted to specific ecological contexts. Moreover, we show that the aggregation process naturally implies the existence of non-aggregated particles, and highlight their crucial evolutionary role despite being largely neglected in theoretical models for the evolution of sociality.

Although pervasive in the living world, collective behavior is a puzzle for evolutionary biology. The genetic traits that sustain it are costly for their carriers and make them vulnerable to the exploitation of asocial “free-riders” that benefit from the group without contributing to its cohesion. This paradox has spawned an extensive literature mainly concerned with elaborate cooperative behaviors that might be inoperant for simple biological entities such as microbes. We model successive life cycles of aggregation, reproduction and dispersal in a biological population combining a statistical physics approach to mimic the group formation process and an evolutionary game theory approach to account for the conflict between individual competition and collective success. Our results show a parsimonious way to the advent of sociality based on differential physical adhesion in organisms deprived of complex cognitive abilities. We also stress the key role of ungrouped individuals and specify the conditions on motion properties that make sociality possible. In detailing a mechanism akin to promote social behavior in microbes in the absence of genealogical relatedness, our work might shed light on both the maintenance of facultative multicellular lifestyles and the evolutionary origins of multicellularity.

Role of differential adhesion in cell cluster evolution: from vasculogenesis to cancer metastasis

Cell-cell and cell-matrix adhesions are fundamental to numerous physiological processes, including angiogenesis, tumourigenesis, metastatic spreading and wound healing. We use cellular potts model to computationally predict the organisation of cells within a 3D matrix. The energy potentials regulating cell-cell (JCC) and cell-matrix (JMC) adhesive interactions are systematically varied to represent different, biologically relevant adhesive conditions. Chemotactically induced cell migration is also addressed. Starting from a cluster of cells, variations in relative cell adhesion alone lead to different cellular patterns such as spreading of metastatic tumours and angiogenesis. The combination of low cell-cell adhesion (high JCC) and high heterotypic adhesion (low JMC) favours the fragmentation of the original cluster into multiple, smaller cell clusters (metastasis). Conversely, cellular systems exhibiting high-homotypic affinity (low JCC) preserve their original configuration, avoiding fragmentation (organogenesis). For intermediate values of JCC and JMC (i.e. JCC/JMC ∼ 1), tubular and corrugated structures form. Fully developed vascular trees are assembled only in systems in which contact-inhibited chemotaxis is activated upon cell contact. Also, the rate of secretion, diffusion and sequestration of chemotactic factors, cell deformability and motility do not significantly affect these trends. Further developments of this computational model will predict the efficacy of therapeutic interventions to modulate the diseased microenvironment by directly altering cell cohesion.

The green tea catechin epigallocatechin gallate (EGCG) blocks cell motility, chemotaxis and development in Dictyostelium discoideum

Catechins, flavanols found at high levels in green tea, have received significant attention due to their potential health benefits related to cancer, autoimmunity and metabolic disease, but little is known about the mechanisms by which these compounds affect cellular behavior. Here, we assess whether the model organism Dictyostelium discoideum is a useful tool with which to characterize the effects of catechins. Epigallocatechin gallate (EGCG), the most abundant and potent catechin in green tea, has significant effects on the Dictyostelium life cycle. In the presence of EGCG aggregation is delayed, cells do not stream and development is typically stalled at the loose aggregate stage. The developmental effects very likely result from defects in motility, as EGCG reduces both random movement and chemotaxis of Dictyostelium amoebae. These results suggest that catechins and their derivatives may be useful tools with which to better understand cell motility and development in Dictyostelium and that this organism is a useful model to further characterize the activities of catechins.

The cell adhesion molecule DdCAD-1 regulates morphogenesis through differential spatiotemporal expression in Dictyostelium discoideum

During development of Dictyostelium, multiple cell types are formed and undergo a coordinated series of morphogenetic movements guided by their adhesive properties and other cellular factors. DdCAD-1 is a unique homophilic cell adhesion molecule encoded by the cadA gene. It is synthesized in the cytoplasm and transported to the plasma membrane by contractile vacuoles. In chimeras developed on soil plates, DdCAD-1-expressing cells showed greater propensity to develop into spores than did cadA-null cells. When development was performed on non-nutrient agar, wild-type cells sorted from the cadA-null cells and moved to the anterior zone. They differentiated mostly into stalk cells and eventually died, whereas the cadA-null cells survived as spores. To assess the role of DdCAD-1 in this novel behavior of wild-type and mutant cells, cadA-null cells were rescued by the ectopic expression of DdCAD-1-GFP. Morphological studies have revealed major spatiotemporal changes in the subcellular distribution of DdCAD-1 during development. Whereas DdCAD-1 became internalized in most cells in the post-aggregation stages, it was prominent in the contact regions of anterior cells. Cell sorting was also restored in cadA(-) slugs by exogenous recombinant DdCAD-1. Remarkably, DdCAD-1 remained on the surface of anterior cells, whereas it was internalized in the posterior cells. Additionally, DdCAD-1-expressing cells migrated slower than cadA(-) cells and sorted to the anterior region of chimeric slugs. These results show that DdCAD-1 influences the sorting behavior of cells in slugs by its differential distribution on the prestalk and prespore cells.

Cell type-specific filamin complex regulation by a novel class of HECT ubiquitin ligase is required for normal cell motility and patterning

Differential cell motility, which plays a key role in many developmental processes, is perhaps most evident in examples of pattern formation in which the different cell types arise intermingled before sorting out into discrete tissues. This is thought to require heterogeneities in responsiveness to differentiation-inducing signals that result in the activation of cell type-specific genes and 'salt and pepper' patterning. How differential gene expression results in cell sorting is poorly defined. Here we describe a novel gene (hfnA) that provides the first mechanistic link between cell signalling, differential gene expression and cell type-specific sorting in Dictyostelium. HfnA defines a novel group of evolutionarily conserved HECT ubiquitin ligases with an N-terminal filamin domain (HFNs). HfnA expression is induced by the stalk differentiation-inducing factor DIF-1 and is restricted to a subset of prestalk cells (pstO). hfnA(-) pstO cells differentiate but their sorting out is delayed. Genetic interactions suggest that this is due to misregulation of filamin complex activity. Overexpression of filamin complex members phenocopies the hfnA(-) pstO cell sorting defect, whereas disruption of filamin complex function in a wild-type background results in pstO cells sorting more strongly. Filamin disruption in an hfnA(-) background rescues pstO cell localisation. hfnA(-) cells exhibit altered slug phototaxis phenotypes consistent with filamin complex hyperactivity. We propose that HfnA regulates filamin complex activity and cell type-specific motility through the breakdown of filamin complexes. These findings provide a novel mechanism for filamin regulation and demonstrate that filamin is a crucial mechanistic link between responses to differentiation signals and cell movement in patterning based on 'salt and pepper' differentiation and sorting out.

Phospholipase D controls Dictyostelium development by regulating G protein signaling

Dictyostelium discoideum cells normally exist as individual amoebae, but will enter a period of multicellular development upon starvation. The initial stages of development involve the aggregation of individual cells, using cAMP as a chemoattractant. Chemotaxis is initiated when cAMP binds to its receptor, cAR1, and activates the associated G protein, Gα2βγ. However, chemotaxis will not occur unless there is a high density of starving cells present, as measured by high levels of the secreted quorum sensing molecule, CMF. We previously demonstrated that cells lacking PldB bypass the need for CMF and can aggregate at low cell density, whereas cells overexpressing pldB do not aggregate even at high cell density. Here, we found that PldB controlled both cAMP chemotaxis and cell sorting. PldB was also required by CMF to regulate G protein signaling. Specifically, CMF used PldB, to regulate the dissociation of Gα2 from Gβγ. Using fluorescence resonance energy transfer (FRET), we found that along with cAMP, CMF increased the dissociation of the G protein. In fact, CMF augmented the dissociation induced by cAMP. This augmentation was lost in cells lacking PldB. PldB appears to mediate the CMF signal through the production of phosphatidic acid, as exogenously added phosphatidic acid phenocopies overexpression of pldB. These results suggest that phospholipase D activity is required for CMF to alter the kinetics of cAMP-induced G protein signaling.

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.

Stochastic collective movement of cells and fingering morphology: no maverick cells

The classical approach to model collective biological cell movement is through coupled nonlinear reaction-diffusion equations for biological cells and diffusive chemicals that interact with the biological cells. This approach takes into account the diffusion of cells, proliferation, death of cells, and chemotaxis. Whereas the classical approach has many advantages, it fails to consider many factors that affect multicell movement. In this work, a multiscale approach, the Glazier-Graner-Hogeweg model, is used. This model is implemented for biological cells coupled with the finite element method for a diffusive chemical. The Glazier-Graner-Hogeweg model takes the biological cell state as discrete and allows it to include cohesive forces between biological cells, deformation of cells, following the path of a single cell, and stochastic behavior of the cells. Where the continuity of the tissue at the epidermis is violated, biological cells regenerate skin to heal the wound. We assume that the cells secrete a diffusive chemical when they feel a wounded region and that the cells are attracted by the chemical they release (chemotaxis). Under certain parameters, the front encounters a fingering morphology, and two fronts progressing against each other are attracted and correlated. Cell flow exhibits interesting patterns, and a drift effect on the chemical may influence the cells' motion. The effects of a polarized substrate are also discussed.

Multiscale modeling of cell mechanics and tissue organization

Nowadays, experimental biology gathers a large number of molecular and genetic data to understand the processes in living systems. Many of these data are evaluated on the level of cells, resulting in a changed phenotype of cells. Tools are required to translate the information on the cellular scale to the whole tissue, where multiple interacting cell types are involved. Agent-based modeling allows the investigation of properties emerging from the collective behavior of individual units. A typical agent in biology is a single cell that transports information from the intracellular level to larger scales. Mainly, two scales are relevant: changes in the dynamics of the cell, e.g. surface properties, and secreted molecules that can have effects at a distance larger than the cell diameter.

Multicell simulations of development and disease using the CompuCell3D simulation environment

Mathematical modeling and computer simulation have become crucial to biological fields from genomics to ecology. However, multicell, tissue-level simulations of development and disease have lagged behind other areas because they are mathematically more complex and lack easy-to-use software tools that allow building and running in silico experiments without requiring in-depth knowledge of programming. This tutorial introduces Glazier-Graner-Hogeweg (GGH) multicell simulations and CompuCell3D, a simulation framework that allows users to build, test, and run GGH simulations.

Growth based morphogenesis of vertebrate limb bud

Many genes and their regulatory relationships are involved in developmental phenomena. However, by chemical information alone, we cannot fully understand changing organ morphologies through tissue growth because deformation and growth of the organ are essentially mechanical processes. Here, we develop a mathematical model to describe the change of organ morphologies through cell proliferation. Our basic idea is that the proper specification of localized volume source (e.g., cell proliferation) is able to guide organ morphogenesis, and that the specification is given by chemical gradients. We call this idea "growth-based morphogenesis." We find that this morphogenetic mechanism works if the tissue is elastic for small deformation and plastic for large deformation. To illustrate our concept, we study the development of vertebrate limb buds, in which a limb bud protrudes from a flat lateral plate and extends distally in a self-organized manner. We show how the proportion of limb bud shape depends on different parameters and also show the conditions needed for normal morphogenesis, which can explain abnormal morphology of some mutants. We believe that the ideas shown in the present paper are useful for the morphogenesis of other organs.

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 unified theory for osteonal and hemi-osteonal remodeling

The process of bone remodeling is carried out by 'basic multicellular units' of osteoclasts and osteoblasts. Osteoclasts excavate a resorption space that is subsequently filled with new bone by osteoblasts. In cortical bone osteoclasts dig tunnels through solid bone, in cancellous bone they dig trenches across the trabecular surface. Osteoblasts fill these tunnels and trenches, creating osteons and hemi-osteons, respectively. Both the osteons of cortical bone and the trabeculae of cancellous bone are aligned to the dominant loading direction, indicating that BMU's are mechanically regulated. How mechanical forces guide these cells is still uncertain. We hypothesize that strain-induced osteocyte signals inhibit osteoclast activity and stimulate osteoblast activity. This hypothesis was implemented in a finite element-based bone adaptation model, that was extended with a cell simulation model. This allowed us to examine tunneling and trenching by osteoclasts. We found that our simulations capture key features of BMU-based remodeling: (1) cortical BMU's create load-aligned osteons; (2) cancellous BMU's move across the surface of trabeculae instead of piercing them; (3) resorption-formation coupling occurs in response to strains around resorption sites; and (4) resorbing osteoclasts target nearby regions of osteocyte death, thus providing a mechanism for bone repair.

Modeling emergent tissue organization involving high-speed migrating cells in a flow equilibrium

There is increasing interest in the analysis of biological tissue, its organization and its dynamics with the help of mathematical models. In the ideal case emergent properties on the tissue scale can be derived from the cellular scale. However, this has been achieved in rare examples only, in particular, when involving high-speed migration of cells. One major difficulty is the lack of a suitable multiscale simulation platform, which embeds reaction diffusion of soluble substances, fast cell migration and mechanics, and, being of great importance in several tissue types, cell flow homeostasis. In this paper a step into this direction is presented by developing an agent-based mathematical model specifically designed to incorporate these features with special emphasis on high-speed cell migration. Cells are represented as elastic spheres migrating on a substrate in lattice-free space. Their movement is regulated and guided by chemoattractants that can be derived from the substrate. The diffusion of chemoattractants is considered to be slower than cell migration and, thus, to be far from equilibrium. Tissue homeostasis is not achieved by the balance of growth and death but by a flow equilibrium of cells migrating in and out of the tissue under consideration. In this sense the number and the distribution of the cells in the tissue is a result of the model and not part of the assumptions. For the purposes of demonstration of the model properties and functioning, the model is applied to a prominent example of tissue in a cellular flow equilibrium, the secondary lymphoid tissue. The experimental data on cell speed distributions in these tissues can be reproduced using reasonable mechanical parameters for the simulated cell migration in dense tissue.

Propagation and refraction of chemical waves generated by local periodic forcing in a reaction-diffusion model

We study wave propagation, interaction, and transmission across the boundary between two chemical media in a model of an oscillatory reaction-diffusion medium subjected to local periodic forcing. The forced waves can be either outwardly (OP) or inwardly propagating (IP), depending on the dispersion of the medium. Competition among forced waves, spontaneous spiral waves, and bulk oscillations is studied for both cases. We demonstrate development of a negatively refracted wave train when forced waves traverse the boundary between the OP medium and the IP medium.

A cell-based model exhibiting branching and anastomosis during tumor-induced angiogenesis

This work describes the first cell-based model of tumor-induced angiogenesis. At the extracellular level, the model describes diffusion, uptake, and decay of tumor-secreted pro-angiogenic factor. At the cellular level, the model uses the cellular Potts model based on system-energy reduction to describe endothelial cell migration, growth, division, cellular adhesion, and the evolving structure of the stroma. Numerical simulations show: 1), different tumor-secreted pro-angiogenic factor gradient profiles dramatically affect capillary sprout morphology; 2), average sprout extension speeds depend on the proximity of the proliferating region to the sprout tip, and the coordination of cellular functions; and 3), inhomogeneities in the extravascular tissue lead to sprout branching and anastomosis, phenomena that emerge without any prescribed rules. This model provides a quantitative framework to test hypotheses on the biochemical and biomechanical mechanisms that control tumor-induced angiogenesis.

Directed cell migration in the presence of obstacles

Background

Chemotactic movement is a common feature of many cells and microscopic organisms. In vivo, chemotactic cells have to follow a chemotactic gradient and simultaneously avoid the numerous obstacles present in their migratory path towards the chemotactic source. It is not clear how cells detect and avoid obstacles, in particular whether they need a specialized biological mechanism to do so.

Results

We propose that cells can sense the presence of obstacles and avoid them because obstacles interfere with the chemical field. We build a model to test this hypothesis and find that this naturally enables efficient at-a-distance sensing to be achieved with no need for a specific and active obstacle-sensing mechanism. We find that (i) the efficiency of obstacle avoidance depends strongly on whether the chemotactic chemical reacts or remains unabsorbed at the obstacle surface. In particular, it is found that chemotactic cells generally avoid absorbing barriers much more easily than non-absorbing ones. (ii) The typically low noise in a cell's motion hinders the ability to avoid obstacles. We also derive an expression estimating the typical distance traveled by chemotactic cells in a 3D random distribution of obstacles before capture; this is a measure of the distance over which chemotaxis is viable as a means of directing cells from one point to another in vivo.

Conclusion

Chemotactic cells, in many cases, can avoid obstacles by simply following the spatially perturbed chemical gradients around obstacles. It is thus unlikely that they have developed specialized mechanisms to cope with environments having low to moderate concentrations of obstacles.

On multiscale approaches to three-dimensional modelling of morphogenesis

In this paper we present the foundation of a unified, object-oriented, three-dimensional biomodelling environment, which allows us to integrate multiple submodels at scales from subcellular to those of tissues and organs. Our current implementation combines a modified discrete model from statistical mechanics, the Cellular Potts Model, with a continuum reaction-diffusion model and a state automaton with well-defined conditions for cell differentiation transitions to model genetic regulation. This environment allows us to rapidly and compactly create computational models of a class of complex-developmental phenomena. To illustrate model development, we simulate a simplified version of the formation of the skeletal pattern in a growing embryonic vertebrate limb.

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.

A framework for three-dimensional simulation of morphogenesis

We present COMPUCELL3D, a software framework for three-dimensional simulation of morphogenesis in different organisms. COMPUCELL3D employs biologically relevant models for cell clustering, growth, and interaction with chemical fields. COMPUCELL3D uses design patterns for speed, efficient memory management, extensibility, and flexibility to allow an almost unlimited variety of simulations. We have verified COMPUCELL3D by building a model of growth and skeletal pattern formation in the avian (chicken) limb bud. Binaries and source code are available, along with documentation and input files for sample simulations, at http:// compucell.sourceforge.net.

A multiscale model for avascular tumor growth

The desire to understand tumor complexity has given rise to mathematical models to describe the tumor microenvironment. We present a new mathematical model for avascular tumor growth and development that spans three distinct scales. At the cellular level, a lattice Monte Carlo model describes cellular dynamics (proliferation, adhesion, and viability). At the subcellular level, a Boolean network regulates the expression of proteins that control the cell cycle. At the extracellular level, reaction-diffusion equations describe the chemical dynamics (nutrient, waste, growth promoter, and inhibitor concentrations). Data from experiments with multicellular spheroids were used to determine the parameters of the simulations. Starting with a single tumor cell, this model produces an avascular tumor that quantitatively mimics experimental measurements in multicellular spheroids. Based on the simulations, we predict: 1), the microenvironmental conditions required for tumor cell survival; and 2), growth promoters and inhibitors have diffusion coefficients in the range between 10(-6) and 10(-7) cm2/h, corresponding to molecules of size 80-90 kDa. Using the same parameters, the model also accurately predicts spheroid growth curves under different external nutrient supply conditions.

Strong-coupling dynamics of a multicellular chemotactic system

Chemical signaling is one of the ubiquitous mechanisms by which intercellular communication takes place at the microscopic level, particularly via chemotaxis. Such multicellular systems are popularly studied using continuum, mean-field equations. In this Letter we study a stochastic model of chemotactic signaling. The Langevin formalism of the model makes it amenable to calculation via nonperturbative analysis, which enables a quantification of the effect of fluctuations on both the weak and the strongly coupled biological dynamics. In particular, we show that the (i) self-localization due to autochemotaxis is impossible. (ii) When aggregation occurs, the aggregate performs a random walk with a renormalized diffusion coefficient D(R) proportiuonal to epsilon-2N-3. (iii) The stochastic model exhibits sharp transitions in cell motile behavior for negative chemotaxis, behavior that has no parallel in the mean-field Keller-Segel equations.

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

In the slug stage of the cellular slime mold Dictyostelium discoideum, prespore cells and four types of prestalk cells show a well-defined spatial distribution in a migrating slug. We have developed a continuous mathematical model for the distribution pattern of these cell types based on the balance of force in individual cells. In the model, cell types are assumed to have different properties in cell motility, i.e. different motive force, the rate of resistance against cell movement, and diffusion coefficient. Analysis of the stationary solution of the model shows that combination of these parameters and slug speed determines the three-dimensional shape of a slug and cell distribution pattern within it. Based on experimental data of slug motive force and velocity measurements, appropriate sets of parameters were chosen so that the cell-type distribution at stationary state matches the distribution in real slugs. With these parameters, we performed numerical calculation of the model in two-dimensional space using a moving particle method. The results reproduced many of the basic features of slug morphogenesis, i.e. cell sorting, translocation of the prestalk region, elongation of the slug, and its steady migration.

A spatial model of germinal center reactions: cellular adhesion based sorting of B cells results in efficient affinity maturation

Affinity maturation of humoral responses to T-cell-dependent antigens occurs in germinal centers (GC). In GCs antigen-specific B cells undergo rounds of somatic mutations that alter their affinity. High-affinity mutants take over GCs very soon after they appear; the replacement rate is as high as 4 per day (Radmacher et al., Immunol. Cell Biol. 76 (1998) 373). To gain more insight into this selection process, we present a spatial model of GC reactions, where B cells compete for survival signals from follicular dendritic cells (FDC). Assuming that high-affinity B cells have increased cellular adhesion to FDCs, we obtain an affinity-based sorting of B cells on the FDC. This sorting imposes a very strong selection and therefore results in a winner-takes-all behavior. By comparing our sorting model with "affinity-proportional selection models", we show that this winner-takes-all selection is in fact required to account for the fast rates at which high affinity mutants take over GCs. Another important feature of in vivo GC reactions is that they are non-mixed, i.e. GCs contain either no high-affinity cells at all or they are dominated by high-affinity cells. We here show that this all-or-none behavior can be obtained if B cells are sorted based on their affinity on the FDC surface. Affinity-proportional selection models, in contrast, always produce mixed GCs.

Disruption of the gene encoding the cell adhesion molecule DdCAD-1 leads to aberrant cell sorting and cell-type proportioning during Dictyostelium development

The cadA gene in Dictyostelium encodes the Ca2+-dependent cell adhesion molecule DdCAD-1, which is expressed soon after the initiation of development. To investigate the biological role of DdCAD-1, the cadA gene was disrupted by homologous recombination. The cadA-null cells showed a 50% reduction in EDTA-sensitive cell adhesion. The remaining EDTA-sensitive adhesion sites were resistant to dissociation by anti-DdCAD-1 antibody, suggesting that they were distinct adhesion sites. Cells that lacked DdCAD-1 were able to complete development and form fruiting bodies. However, they displayed abnormal slug morphology and culmination was delayed by ∼6 hours. The yield of spores was reduced by ∼50%. The proportion of prestalk cells in cadA– slugs showed a 2.5-fold increase over the parental strain. When cadA– cells were transfected with pcotB::GFP to label prespore cells, aberrant cell-sorting patterns in slugs became apparent. When mutant prestalk cells were mixed with wild-type prespore cells, mutant prestalk cells were unable to return to the anterior position of chimeric slugs, suggesting defects in the sorting mechanism. The wild-type phenotype was restored when cadA– cells were transfected with a cadA-expression vector. These results indicate that, in addition to cell-cell adhesion, DdCAD-1 plays a role in cell type proportioning and pattern formation.

Spontaneous symmetry breaking turing-type pattern formation in a confined Dictyostelium cell mass

We have discovered a new type of patterning which occurs in a two-dimensionally confined cell mass of the cellular slime mold Dictyostelium discoideum. Besides the longitudinal structure reported earlier, we observed a spontaneous symmetry breaking spot pattern whose wavelength shows similar strain dependency to that of the longitudinal pattern. We propose that these structures are due to a reaction-diffusion Turing instability similar to the one which has been exemplified by CIMA (chlorite-iodide-malonic acid) reaction. The present finding may exhibit the first biochemical Turing structure in a developmental system with a controllable boundary condition.

Evolving mechanisms of morphogenesis: on the interplay between differential adhesion and cell differentiation

Differential cell adhesion, mediated by e.g. integrin and cadherins/catenines, plays an important role in morphogenesis and it has been shown that there is intimate cross-talk between their expression and modification, and inter-cellular signalling, cell differentiation, cell growth and apoptosis. In this paper, we introduce and use a formal model to explore the morphogenetic potential of the interplay between these processes. We demonstrate the formation of interesting morphologies. Initiated by cell differentiation, differential cell adhesion leads to a long transient of cell migrations, e.g. engulfing and intercalation of cells and cell layers. This transient can be sustained dynamically by further cell differentiation, and by cell growth/division and cell death which are triggered by the (also long range) forces (stretching and squeezing) generated by the cell adhesion. We study the interrelation between modes of cell differentiation and modes of morphogenesis. We use an evolutionary process to zoom in on gene-regulation networks which lead to cell differentiation. Morphogenesis is not selected for but appears as a side-effect. The evolutionary dynamics shows the hallmarks of evolution on a rugged landscape, including long neutral paths. We show that a combinatorially large set of morphologies occurs in the vicinity of a neutral path which sustains cell differentiation. Thus, an almost linear molecular phylogeny gives rise to mosaic evolution on the morphological level.

Morphogenetic cell movement in Dictyostelium

Dictyostelium morphogenesis starts with the chemotactic aggregation of starving individual cells. The cells move in response to propagating waves of the chemoattractant cyclic AMP initiated by cells in the aggregation centre. During aggregation the cells begin to differentiate into several types with different signalling and chemotactic properties. These cell types sort out from each other to form an axial pattern in the slug. There is now good evidence that periodic chemotactic signals not only control aggregation, but also later stages of morphogenesis. These signals take the form of target patterns, spirals, multi-armed spirals and scroll waves. I will discuss their role in the control of cell movement during mound and slug formation and in the formation of the fruiting body.