Modelling of Dictyostelium discoideum slug migration

Viscoelastic cell model of sorting in the dictyostelium discoideum slug

Cell sorting and differential motion are key processes in the life cycle of Dictyostelium discoideum (Dd) and many other organisms. Here we develop a mathematical model and investigate the processes with computer simulations. The slug stage of Dd is modeled with ellipsoidal cells of two types which have viscoelastic properties. Using the force-based model we find that when the two cell types have different strengths of motive forces and or different degrees of directionality one cell type sorts to the front of the slug. These findings are consistent with previously published results using a different model formation. When one cell type is more directed than the other it will consistently sort to the front of the slug. Likewise, but less efficiently, when one cell type exerts greater motive forces than the other it will sort to the front of the slug. The most efficient and robust cell sorting due to differential motion is when both methods are employed.

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.

Second-order agent-based models of emergent behaviour of Dictyostelium discoideum and their inspiration for swarm robotics

By studying and modelling the behaviour of Dictyostelium discoideum, we aim at deriving mechanisms useful for engineering collective artificial intelligence systems. This paper discusses a selection of agent-based models reproducing second-order behaviour of Dictyostelium discoideum, occurring during the migration phase; their corresponding biological illustrations; and how we used them as an inspiration for transposing this behaviour into swarms of Kilobots. For the models, we focus on: (1) the transition phase from first- to second-order emergent behaviour; (2) slugs’ uniform distribution around a light source; and (3) the relationship between slugs’ speed and length occurring during the migration phase of the life cycle of D. discoideum. Results show the impact of the length of the slug on its speed and the effect of ammonia on the distribution of slugs. Our computational results show similar behaviour to our biological experiments, using Ax2(ka) strain. For swarm robotics experiments, we focus on the transition phase, slugs’ chaining, merging and moving away from each other.

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.

Discrete Manhattan and Chebyshev pair correlation functions in k dimensions

Pair correlation functions provide a summary statistic which quantifies the amount of spatial correlation between objects in a spatial domain. While pair correlation functions are commonly used to quantify continuous-space point processes, the on-lattice discrete case is less studied. Recent work has brought attention to the discrete case, wherein on-lattice pair correlation functions are formed by normalizing empirical pair distances against the probability distribution of random pair distances in a lattice with Manhattan and Chebyshev metrics. These distance distributions are typically derived on an ad hoc basis as required for specific applications. Here we present a generalized approach to deriving the probability distributions of pair distances in a lattice with discrete Manhattan and Chebyshev metrics, extending the Manhattan and Chebyshev pair correlation functions to lattices in k dimensions. We also quantify the variability of the Manhattan and Chebyshev pair correlation functions, which is important to understanding the reliability and confidence of the statistic.

Oscillatory cAMP cell-cell signalling persists during multicellular Dictyostelium development

Propagating waves of cAMP, periodically initiated in the aggregation centre, are known to guide the chemotactic aggregation of hundreds of thousands of starving individual Dictyostelium discoideum cells into multicellular aggregates. Propagating optical density waves, reflecting cell periodic movement, have previously been shown to exist in streaming aggregates, mounds and migrating slugs. Using a highly sensitive cAMP-FRET reporter, we have now been able to measure periodically propagating cAMP waves directly in these multicellular structures. In slugs cAMP waves are periodically initiated in the tip and propagate backward through the prespore zone. Altered cAMP signalling dynamics in mutants with developmental defects strongly support a key functional role for cAMP waves in multicellular Dictyostelium morphogenesis. These findings thus show that propagating cAMP not only control the initial aggregation process but continue to be the long range cell-cell communication mechanism guiding cell movement during multicellular Dictyostelium morphogenesis at the mound and slugs stages.

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.

Biological active matter aggregates: Inspiration for smart colloidal materials

Aggregations of social organisms exhibit a remarkable range of properties and functionalities. Multiple examples, such as fire ants or slime mold, show how a population of individuals is able to overcome an existential threat by gathering into a solid-like aggregate with emergent functionality. Surprisingly, these aggregates are driven by simple rules, and their mechanisms show great parallelism among species. At the same time, great effort has been made by the scientific community to develop active colloidal materials, such as microbubbles or Janus particles, which exhibit similar behaviors. However, a direct connection between these two realms is still not evident, and it would greatly benefit future studies. In this review, we first discuss the current understanding of living aggregates, point out the mechanisms in their formation and explore the vast range of emergent properties. Second, we review the current knowledge in aggregated colloidal systems, the methods used to achieve the aggregations and their potential functionalities. Based on this knowledge, we finally identify a set of over-arching principles commonly found in biological aggregations, and further suggest potential future directions for the creation of bio-inspired colloid aggregations.

Evasion of phagotrophic predation by protist hosts and innate immunity of metazoan hosts by Legionella pneumophila

Legionella pneumophila is a ubiquitous environmental bacterium that has evolved to infect and proliferate within amoebae and other protists. It is thought that accidental inhalation of contaminated water particles by humans is what has enabled this pathogen to proliferate within alveolar macrophages and cause pneumonia. However, the highly evolved macrophages are equipped with more sophisticated innate defence mechanisms than are protists, such as the evolution of phagotrophic feeding into phagocytosis with more evolved innate defence processes. Not surprisingly, the majority of proteins involved in phagosome biogenesis (~80%) have origins in the phagotrophy stage of evolution. There are a plethora of highly evolved cellular and innate metazoan processes, not represented in protist biology, that are modulated by L. pneumophila, including TLR2 signalling, NF-κB, apoptotic and inflammatory processes, histone modification, caspases, and the NLRC-Naip5 inflammasomes. Importantly, L. pneumophila infects haemocytes of the invertebrate Galleria mellonella, kill G. mellonella larvae, and proliferate in and kill Drosophila adult flies and Caenorhabditis elegans. Although coevolution with protist hosts has provided a substantial blueprint for L. pneumophila to infect macrophages, we discuss the further evolutionary aspects of coevolution of L. pneumophila and its adaptation to modulate various highly evolved innate metazoan processes prior to becoming a human pathogen.

Modelling Chemotactic Motion of Cells in Biological Tissues

Developmental processes in biology are underlined by proliferation, differentiation and migration of cells. The latter two are interlinked since cellular differentiation is governed by the dynamics of morphogens which, in turn, is affected by the movement of cells. Mutual effects of morphogenetic and cell movement patterns are enhanced when the movement is due to chemotactic response of cells to the morphogens. In this study we introduce a mathematical model to analyse how this interplay can result in a steady movement of cells in a tissue and associated formation of travelling waves in a concentration field of morphogen. Using the model we have identified four chemotactic scenarios for migration of single cell or homogeneous group of cells in a tissue. Such a migration can take place if moving cells are (1) repelled by a chemical produced by themselves or (2) attracted by a chemical produced by the surrounding cells in a tissue. Furthermore, the group of cells can also move if cells in surrounding tissue are (3) repelled by a chemical produced by moving cells or (4) attracted by a chemical produced by surrounding cells themselves. The proposed mechanisms can underlie migration of cells during embryonic development as well as spread of metastatic cells.

Progress and perspectives in signal transduction, actin dynamics, and movement at the cell and tissue level: lessons from Dictyostelium

Movement of cells and tissues is a basic biological process that is used in development, wound repair, the immune response to bacterial invasion, tumour formation and metastasis, and the search for food and mates. While some cell movement is random, directed movement stimulated by extracellular signals is our focus here. This involves a sequence of steps in which cells first detect extracellular chemical and/or mechanical signals via membrane receptors that activate signal transduction cascades and produce intracellular signals. These intracellular signals control the motile machinery of the cell and thereby determine the spatial localization of the sites of force generation needed to produce directed motion. Understanding how force generation within cells and mechanical interactions with their surroundings, including other cells, are controlled in space and time to produce cell-level movement is a major challenge, and involves many issues that are amenable to mathematical modelling.

Distinguishing between mechanisms of cell aggregation using pair-correlation functions

Many cell types form clumps or aggregates when cultured in vitro through a variety of mechanisms including rapid cell proliferation, chemotaxis, or direct cell-to-cell contact. In this paper we develop an agent-based model to explore the formation of aggregates in cultures where cells are initially distributed uniformly, at random, on a two-dimensional substrate. Our model includes unbiased random cell motion, together with two mechanisms which can produce cell aggregates: (i) rapid cell proliferation and (ii) a biased cell motility mechanism where cells can sense other cells within a finite range, and will tend to move towards areas with higher numbers of cells. We then introduce a pair-correlation function which allows us to quantify aspects of the spatial patterns produced by our agent-based model. In particular, these pair-correlation functions are able to detect differences between domains populated uniformly at random (i.e. at the exclusion complete spatial randomness (ECSR) state) and those where the proliferation and biased motion rules have been employed - even when such differences are not obvious to the naked eye. The pair-correlation function can also detect the emergence of a characteristic inter-aggregate distance which occurs when the biased motion mechanism is dominant, and is not observed when cell proliferation is the main mechanism of aggregate formation. This suggests that applying the pair-correlation function to experimental images of cell aggregates may provide information about the mechanism associated with observed aggregates. As a proof of concept, we perform such analysis for images of cancer cell aggregates, which are known to be associated with rapid proliferation. The results of our analysis are consistent with the predictions of the proliferation-based simulations, which supports the potential usefulness of pair correlation functions for providing insight into the mechanisms of aggregate formation.

Dictyostelium: The Mathematician's Organism

This article was to have been written by Kees Weijer, an outstanding pioneer in Dictyostelium research. It was (and is) to celebrate J.T. Bonner’s and Weijer’s contributions to the field and those of the other great pioneers. Unfortunately, Weijer was unable to write his article, due to ill health and since I have some knowledge of this field, I took it over. The article summarises some main results and ideas in Dictyostelium research and their relevance for development of more advanced organisms.

Dislocation is a developmental mechanism in Dictyostelium and vertebrates

The excitable cells of Dictyostelium discoideum show traveling waves of signaling and generate a variety of complex wave forms during their morphogenesis. Important among these wave forms is the 3D spiral or scroll wave, which has been proposed previously to have a twisted variant: the "turbine wave." Herein we argue that a D. discoideum scroll or concentric wave territory containing prespore and prestalk cell types can undergo "dislocation": a wave field that initially controls aggregation of a whole developing population of Dictyostelium cells splits into two. This process leads to discontinuity between two connected domains of wave propagation and to specific phenomena, including high-frequency concentric pacemaker activity by the slime mold's scroll-wave tip. The resulting morphogenetic events reveal a unique mechanism in morphogenesis.

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.

Extracellular calmodulin regulates growth and cAMP-mediated chemotaxis in Dictyostelium discoideum

The existence of extracellular calmodulin (CaM) has had a long and controversial history. CaM is a ubiquitous calcium-binding protein that has been found in every eukaryotic cell system. Calcium-free apo-CaM and Ca(2+)/CaM exert their effects by binding to and regulating the activity of CaM-binding proteins (CaMBPs). Most of the research done to date on CaM and its CaMBPs has focused on their intracellular functions. The presence of extracellular CaM is well established in a number of plants where it functions in proliferation, cell wall regeneration, gene regulation and germination. While CaM has been detected extracellularly in several animal species, including frog, rat, rabbit and human, its extracellular localization and functions are less well established. In contrast the study of extracellular CaM in eukaryotic microbes remains to be done. Here we show that CaM is constitutively expressed and secreted throughout asexual development in Dictyostelium where the presence of extracellular CaM dose-dependently inhibits cell proliferation but increases cAMP mediated chemotaxis. During development, extracellular CaM localizes within the slime sheath where it coexists with at least one CaMBP, the matricellular CaM-binding protein CyrA. Coupled with previous research, this work provides direct evidence for the existence of extracellular CaM in the Dictyostelium and provides insight into its functions in this model amoebozoan.

Coordination of cell differentiation and migration in mathematical models of caudal embryonic axis extension

Vertebrate embryos display a predominant head-to-tail body axis whose formation is associated with the progressive development of post-cranial structures from a pool of caudal undifferentiated cells. This involves the maintenance of active FGF signaling in this caudal region as a consequence of the restricted production of the secreted factor FGF8. FGF8 is transcribed specifically in the caudal precursor region and is down-regulated as cells differentiate and the embryo extends caudally. We are interested in understanding the progressive down-regulation of FGF8 and its coordination with the caudal movement of cells which is also known to be FGF-signaling dependent. Our study is performed using mathematical modeling and computer simulations. We use an individual-based hybrid model as well as a caricature continuous model for the simulation of experimental observations (ours and those known from the literature) in order to examine possible mechanisms that drive differentiation and cell movement during the axis elongation. Using these models we have identified a possible gene regulatory network involving self-repression of a caudal morphogen coupled to directional domain movement that may account for progressive down-regulation of FGF8 and conservation of the FGF8 domain of expression. Furthermore, we have shown that chemotaxis driven by molecules, such as FGF8 secreted in the stem zone, could underlie the migration of the caudal precursor zone and, therefore, embryonic axis extension. These mechanisms may also be at play in other developmental processes displaying a similar mode of axis extension coupled to cell differentiation.

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.

Lighting up developmental mechanisms: how fluorescence imaging heralded a new era

Embryology and genetics have given rise to a mechanistic framework that explains the architecture of a developing organism. Until recently, however, such studies suffered from a lack of quantification and real-time visualization at the subcellular level, limiting their ability to monitor the dynamics of developmental processes. Live imaging using fluorescent proteins has overcome these limitations, uncovering unprecedented insights that call many established models into question. We review how the study of patterning, cell polarization and morphogenesis has benefited from this technology and discuss the possibilities offered by fluorescence imaging and by the contributions of quantitative disciplines.

Collective cell migration in development

Collective cell migration is a key process during the development of most organisms. It can involve either the migration of closely packed mesenchymal cells that make dynamic contacts with frequently changing neighbour cells, or the migration of epithelial sheets that typically display more stable cell-cell interactions and less frequent changes in neighbours. These collective movements can be controlled by short- or long-range dynamic gradients of extracellular signalling molecules, depending on the number of cells involved and their distance of migration. These gradients are sensed by some or all of the migrating cells and translated into directed migration, which in many settings is further modulated by cell-contact-mediated attractive or repulsive interactions that result in contact-following or contact-inhibition of locomotion, respectively. Studies of collective migration of groups of epithelial cells during development indicate that, in some cases, only leader cells sense and migrate up an external signal gradient, and that adjacent cells follow through strong cell-cell contacts. In this Commentary, I review studies of collective cell migration of differently sized cell populations during the development of several model organisms, and discuss our current understanding of the molecular mechanisms that coordinate this migration.

Migration of Dictyostelium slugs: anterior-like cells may provide the motive force for the prespore zone

The collective motion of cells in a biological tissue originates from their individual responses to chemical and mechanical signals. The Dictyostelium slug moves as a collective of up to 100,000 cells with prestalk cells in the anterior 10-30% and prespore cells, intermingled with anterior-like cells (AL cells), in the posterior. We used traction force microscopy to measure the forces exerted by migrating slugs. Wild-type slugs exert frictional forces on their substratum in the direction of motion in their anterior, balanced by motive forces dispersed down their length. StlB- mutants lack the signal molecule DIF-1 and hence a subpopulation of AL cells. They produce little if any motive force in their rear and immediately break up. This argues that AL cells, but not prespore cells, are the motive cells in the posterior zone. Slugs also exert large outward radial forces, which we have analyzed during "looping" movement. Each time the anterior touches down after a loop, the outward forces rapidly develop, approximately normal to the almost stationary contact lines. We postulate that these forces result from the immediate binding of the sheath to the substratum and the subsequent application of outward "pressure," which might be developed in several different ways.

Multi-scale models of cell and tissue dynamics

Cell and tissue movement are essential processes at various stages in the life cycle of most organisms. The early development of multi-cellular organisms involves individual and collective cell movement; leukocytes must migrate towards sites of infection as part of the immune response; and in cancer, directed movement is involved in invasion and metastasis. The forces needed to drive movement arise from actin polymerization, molecular motors and other processes, but understanding the cell- or tissue-level organization of these processes that is needed to produce the forces necessary for directed movement at the appropriate point in the cell or tissue is a major challenge. In this paper, we present three models that deal with the mechanics of cells and tissues: a model of an arbitrarily deformable single cell, a discrete model of the onset of tumour growth in which each cell is treated individually, and a hybrid continuum-discrete model of the later stages of tumour growth. While the models are different in scope, their underlying mechanical and mathematical principles are similar and can be applied to a variety of biological systems.

Using a mathematical model of cadherin-based adhesion to understand the function of the actin cytoskeleton

The actin cytoskeleton plays a role in cell-cell adhesion but its specific function is not clear. Actin might anchor cadherins or drive membrane protrusions in order to facilitate cell-cell adhesion. Using a mathematical model of the forces involved in cadherin-based adhesion, we investigate its possible functions. The immersed boundary method is used to model the cell membrane and cortex with cadherin binding forces added as linear springs. The simulations indicate that cells in suspension can develop normal cell-cell contacts without actin-based cadherin anchoring or membrane protrusions. The cadherins can be fixed in the membrane or free to move, and the end results are similar. For adherent cells, simulations suggest that the actin cytoskeleton must play an active role for the cells to establish cell-cell contact regions similar to those observed in vitro.

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.

Oscillations and waves of cyclic AMP in Dictyostelium: a prototype for spatio-temporal organization and pulsatile intercellular communication

The amoebae Dictyostelium discoideum aggregate after starvation in a wavelike manner in response to periodic pulses of cyclic AMP (cAMP) secreted by cells which behave as aggregation centers. In addition to autonomous oscillations, the cAMP signaling system that controls aggregation is also capable of excitable behavior, which consists in the transient amplification of suprathreshold pulses of extracellular cAMP. Since the first theoretical model for slime mold aggregation proposed by Keller and Segel in 1970, many theoretical studies have addressed various aspects of the mechanism and function of cAMP signaling in Dictyostelium. This paper presents a brief overview of these developments as well as some reminiscences of the author's collaboration with Lee Segel in modeling the dynamics of cAMP relay and oscillations. Considered in turn are models for cAMP signaling in Dictyostelium, the developmental path followed by the cAMP signaling system after starvation, the frequency encoding of cAMP signals, and the origin of concentric or spiral waves of cAMP.

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.

Aerial migration of the Dictyostelium slug

The Dictyostelium slug lays down curved marks in its slime sheath trail as it migrates across an agar substrate. These 'footprints' are caused by elevation of the slug anterior as it initiates a period of aerial migration and can be used as a measure of the slug's propensity for this behavior. A variety of factors have been found to affect the number of footprints created per distance migrated. Smaller slugs produce a higher incidence of footprints than larger slugs. Migration in the light and lower temperatures during migration increase footprint incidence. Activated charcoal reduces, while exogenous addition of ammonia increases, the incidence of footprints. Simulation of the three-dimensional (3D) environment of the soil suggests that aerial migration plays a role in the slug's movement through the cavities of its natural environment. A model proposes that aerial migration is initiated by a small group of continually changing prestalk cells that acts as a pacemaker and is moved around the circumference of the slug tip by the rotation of the prestalk cells. As this pacemaker reaches the upper surface of the slug it can initiate aerial migration.

How cellular movement determines the collective force generated by the Dictyostelium discoideum slug

How the collective motion of cells in a biological tissue originates in the behavior of a collection of individuals, each of which responds to the chemical and mechanical signals it receives from neighbors, is still poorly understood. Here we study this question for a particular system, the slug stage of the cellular slime mold Dictyostelium discoideum (Dd). We investigate how cells in the interior of a migrating slug can effectively transmit stress to the substrate and thereby contribute to the overall motive force. Theoretical analysis suggests necessary conditions on the behavior of individual cells, and computational results shed light on experimental results concerning the total force exerted by a migrating slug. The model predicts that only cells in contact with the substrate contribute to the translational motion of the slug. Since the model is not based specifically on the mechanical properties of Dd cells, the results suggest that this behavior will be found in many developing systems.

Cell movements and mechanical force distribution during the migration of dictyostelium slugs

Migration of Dictyostelium discoideum slugs results from coordinated movement of their constituent cells. It is generally assumed that each cell contributes to the total motive force of the slug. However, the basic mechanisms by which mechanical forces (traction and resistive forces) are transmitted to the substrate, their magnitude and their location, are largely unknown. In this work, we performed detailed observations of cell movements by fluorescence microscopy using two-dimensional (2D) slugs. We show that 2D slugs share most of the properties of 3D ones. In particular, waves of movement propagate in long 2D slugs, and slug speed correlates with slug length as found in 3D slugs. We also present the first measurements of the distribution of forces exerted by 2D and 3D slugs using the elastic substrate method. Traction forces are mainly exerted in the central region of the slug. The large perpendicular forces around slug boundary and the existence of parallel resistive forces in the tip and/or the tail suggest an important role of the sheath in the transmission of forces to the substrate.