A stochastic model for chemotaxis based on the ordered extension of pseudopods

Many amoeboid cells move by extending pseudopods. Here I present a new stochastic model for chemotaxis that is based on pseudopod extensions by Dictyostelium cells. In the absence of external cues, pseudopod extension is highly ordered with two types of pseudopods: de novo formation of a pseudopod at the cell body in random directions, and alternating right/left splitting of an existing pseudopod that leads to a persistent zig-zag trajectory. We measured the directional probabilities of the extension of splitting and de novo pseudopods in chemoattractant gradients with different steepness. Very shallow cAMP gradients can bias the direction of splitting pseudopods, but the bias is not perfect. Orientation of de novo pseudopods require much steeper cAMP gradients and can be more precise. These measured probabilities of pseudopod directions were used to obtain an analytical model for chemotaxis of cell populations. Measured chemotaxis of wild-type cells and mutants with specific defects in these stochastic pseudopod properties are similar to predictions of the model. These results show that combining splitting and de novo pseudopods is a very effective way for cells to obtain very high sensitivity to stable gradient and still be responsive to changes in the direction of the gradient.     

Chemotaxis in shallow gradients is mediated independently of PtdIns 3-kinase by biased choices between random protrusions

Current models of eukaryotic chemotaxis propose that directional sensing causes localized generation of new pseudopods. However, quantitative analysis of pseudopod generation suggests a fundamentally different mechanism for chemotaxis in shallow gradients: first, pseudopods in multiple cell types are usually generated when existing ones bifurcate and are rarely made de novo; second, in Dictyostelium cells in shallow chemoattractant gradients, pseudopods are made at the same rate whether cells are moving up or down gradients. The location and direction of new pseudopods are random within the range allowed by bifurcation and are not oriented by chemoattractants. Thus, pseudopod generation is controlled independently of chemotactic signalling. Third, directional sensing is mediated by maintaining the most accurate existing pseudopod, rather than through the generation of new ones. Finally, the phosphatidylinositol 3-kinase (PI(3)K) inhibitor LY294002 affects the frequency of pseudopod generation, but not the accuracy of selection, suggesting that PI(3)K regulates the underlying mechanism of cell movement, rather than control of direction.     

Chemotaxis: a feedback-based computational model robustly predicts multiple aspects of real cell behaviour

The mechanism of eukaryotic chemotaxis remains unclear despite intensive study. The most frequently described mechanism acts through attractants causing actin polymerization, in turn leading to pseudopod formation and cell movement. We recently proposed an alternative mechanism, supported by several lines of data, in which pseudopods are made by a self-generated cycle. If chemoattractants are present, they modulate the cycle rather than directly causing actin polymerization. The aim of this work is to test the explanatory and predictive powers of such pseudopod-based models to predict the complex behaviour of cells in chemotaxis. We have now tested the effectiveness of this mechanism using a computational model of cell movement and chemotaxis based on pseudopod autocatalysis. The model reproduces a surprisingly wide range of existing data about cell movement and chemotaxis. It simulates cell polarization and persistence without stimuli and selection of accurate pseudopods when chemoattractant gradients are present. It predicts both bias of pseudopod position in low chemoattractant gradients and--unexpectedly--lateral pseudopod initiation in high gradients. To test the predictive ability of the model, we looked for untested and novel predictions. One prediction from the model is that the angle between successive pseudopods at the front of the cell will increase in proportion to the difference between the cell's direction and the direction of the gradient. We measured the angles between pseudopods in chemotaxing Dictyostelium cells under different conditions and found the results agreed with the model extremely well. Our model and data together suggest that in rapidly moving cells like Dictyostelium and neutrophils an intrinsic pseudopod cycle lies at the heart of cell motility. This implies that the mechanism behind chemotaxis relies on modification of intrinsic pseudopod behaviour, more than generation of new pseudopods or actin polymerization by chemoattractants.     

An excitable cortex and memory model successfully predicts new pseudopod dynamics

Motile eukaryotic cells migrate with directional persistence by alternating left and right turns, even in the absence of external cues. For example, Dictyostelium discoideum cells crawl by extending distinct pseudopods in an alternating right-left pattern. The mechanisms underlying this zig-zag behavior, however, remain unknown. Here we propose a new Excitable Cortex and Memory (EC&M) model for understanding the alternating, zig-zag extension of pseudopods. Incorporating elements of previous models, we consider the cell cortex as an excitable system and include global inhibition of new pseudopods while a pseudopod is active. With the novel hypothesis that pseudopod activity makes the local cortex temporarily more excitable--thus creating a memory of previous pseudopod locations--the model reproduces experimentally observed zig-zag behavior. Furthermore, the EC&M model makes four new predictions concerning pseudopod dynamics. To test these predictions we develop an algorithm that detects pseudopods via hierarchical clustering of individual membrane extensions. Data from cell-tracking experiments agrees with all four predictions of the model, revealing that pseudopod placement is a non-Markovian process affected by the dynamics of previous pseudopods. The model is also compatible with known limits of chemotactic sensitivity. In addition to providing a predictive approach to studying eukaryotic cell motion, the EC&M model provides a general framework for future models, and suggests directions for new research regarding the molecular mechanisms underlying directional persistence.     

Ponticulin plays a role in the positional stabilization of pseudopods

Ponticulin is a 17-kD glycoprotein that represents a major high affinity link between the plasma membrane and the cortical actin network of Dictyostelium. To assess the role of ponticulin in pseudopod extension and retraction, the motile behavior of two independently generated mutants lacking ponticulin was analyzed using computer- assisted two- and three-dimensional motion analysis systems. More than half of the lateral pseudopods formed off the substratum by ponticulin- minus cells slipped relative to the substratum during extension and retraction. In contrast, all pseudopods formed off the substratum by wild-type cells were positionally fixed in relation to the substratum. Ponticulin-minus cells also formed a greater proportion of both anterior and lateral pseudopods off the substratum and absorbed a greater proportion of lateral pseudopods into the uropod than wild-type cells. In a spatial gradient of cAMP, ponticulin-minus cells were less efficient in tracking the source of chemoattractant. Since ponticulin- minus cells extend and retract pseudopods with the same time course as wild-type cells, these behavioral defects in ponticulin-minus cells appear to be the consequence of pseudopod slippage. These results demonstrate that pseudopods formed off the substratum by wild-type cells are positionally fixed in relation to the substratum, that ponticulin is required for positional stabilization, and that the loss of ponticulin and the concomitant loss of positional stability of pseudopods correlate with a decrease in the efficiency of chemotaxis.     

Chemotaxis in Dictyostelium: how to walk straight using parallel pathways

Dictyostelium is one of the most successful and best-studied organisms for research into the mechanisms that drive chemotaxis. In this review, we discuss recent progress in the field. Phosphatidylinositol 3-kinase (PI 3-kinase), previously thought by some to be essential for chemotaxis, has now been proven to be dispensable. However, other pathways are emerging which might connect signalling to migration. In particular, phospholipase A2 homologues appear to play an important role. Other areas of current interest include the fundamental processes by which cells move - pseudopods have been found to be generated in many different ways. Similarly, chemotaxis may be mediated by multiple checks on the number of pseudopods, rather than by simple generation of new pseudopods on demand. Finally, we review several advances in the theory of how cells convert shallow, noisy chemical gradients into overt movement.     

Microfilament reorganization in normal and cytochalasin B treated adherent thrombocytes

Thrombocyte adhesion following activation by a Formvar surface involves a morphologic transition resulting in a fully spread cell. Correlative SEM and whole mount TEM were used to study the cytoskeletal alterations that accompany changes in surface morphology during adhesion. Following initial adhesion, thrombocytes extend slender pseudopods containing longitudinally oriented bundles of filaments that are 13–22 nm in diameter. Concomitant with pseudopod extension, a cytoplasmic hyalomere, consisting of a dense filamentous network, extends between the pseudopods and ultimately results in a fully spread cell. Treatment of thromboyctes with cytochalasin B (10^?5 M) caused clumping of the hyalomere filament network and retraction of the hyalomere. Examination of partially retracted cells revealed that pseudopod filament bundles were continuous with the contracting filamentous network. It is concluded that pseudopod filament bundles and cytoplasmic hyalomere filaments are interconvertible and that their organizational relationship changes in accordance with gross morphologic changes.     

Controlled pseudopod extension of human neutrophils stimulated with different chemoattractants

The formation of pseudopods and lamellae after ligation of chemoattractant sensitive G-protein coupled receptors (GPCRs) is essential for chemotaxis. Here, pseudopod extension was stimulated with chemoattractant delivered from a micropipet. The chemoattractant diffusion and convection mass transport were considered, and it is shown that when the delivery of chemoattractant was limited by diffusion there was a strong chemoattractant gradient along the cell surface. The diffusion-limited delivery of chemoattractant from a micropipet allowed for maintaining an almost constant chemoattractant concentration at the leading edge of single pseudopods during their growth. In these conditions, the rate of pseudopod extension was dependent on the concentration of chemoattractant in the pipet delivering chemoattractant. The pseudopod extension induced using micropipets was oscillatory even in the presence of a constant delivery of chemoattractant. This oscillatory pseudopod extension was controlled by activated RhoA and its downstream effector kinase ROCK and was abolished after the inhibition of RhoA activation with Clostridium botulinium C3 exoenzyme (C3) or the blocking of ROCK activation with Y-27632. The ability of the micropipet assay to establish a well-defined chemoattractant distribution around the activated cell over a wide range of molecular weights of the used chemoattractants allowed for comparison of the effect of chemoattractant stimulation on the dynamics of pseudopod growth. Pseudopod growth was stimulated using N-formylated peptide (N-formyl-methionyl-leucyl-phenylalanine (fMLP)), platelet activating factor (PAF), leukotriene B4 (LTB(4)), C5a anaphylotoxin (C5a), and interleukin-8 (IL-8), which represent the typical ligands for G-protein coupled chemotactic receptors. The dependence of the rate of pseudopod extension on the concentration of these chemoattractants and their equimolar mixture was measured and shown to be similar for all chemoattractants. The inhibition of the activity of phosphoinositide-3 kinase (PI3K) with wortmannin showed that 72%-80% of the rate of pseudopod extension induced with N-formyl-methionyl-leucyl-phenylalanine, platelet activating factor, and leukotriene B4 was phosphoinositide-3 kinase-dependent, in contrast to 55% of the rate of pseudopod extension induced with interleukin-8. The dependence of the rate of pseudopod extension on the concentration of individual chemoattractants and their equimolar mixture suggests that there is a common rate-limiting mechanism for the polymerization of cytoskeletal F-actin in the pseudopod region induced by G-protein coupled chemoattractant receptors.     

PIP3-dependent macropinocytosis is incompatible with chemotaxis

In eukaryotic chemotaxis, the mechanisms connecting external signals to the motile apparatus remain unclear. The role of the lipid phosphatidylinositol 3,4,5-trisphosphate (PIP₃) has been particularly controversial. PIP₃ has many cellular roles, notably in growth control and macropinocytosis as well as cell motility. Here we show that PIP₃ is not only unnecessary for Dictyostelium discoideum to migrate toward folate, but actively inhibits chemotaxis. We find that macropinosomes, but not pseudopods, in growing cells are dependent on PIP₃. PIP₃ patches in these cells show no directional bias, and overall only PIP₃-free pseudopods orient up-gradient. The pseudopod driver suppressor of cAR mutations (SCAR)/WASP and verprolin homologue (WAVE) is not recruited to the center of PIP₃ patches, just the edges, where it causes macropinosome formation. Wild-type cells, unlike the widely used axenic mutants, show little macropinocytosis and few large PIP₃ patches, but migrate more efficiently toward folate. Tellingly, folate chemotaxis in axenic cells is rescued by knocking out phosphatidylinositide 3-kinases (PI 3-kinases). Thus PIP₃ promotes macropinocytosis and interferes with pseudopod orientation during chemotaxis of growing cells.     

Genetic deletion of ABP-120 alters the three-dimensional organization of actin filaments in Dictyostelium pseudopods

This study extends the observations on the defects in pseudopod formation of ABP-120+ and ABP-120- cells by a detailed morphological and biochemical analysis of the actin based cytoskeleton. Both ABP-120+ and ABP-120- cells polymerize the same amount of F-actin in response to stimulation with cAMP. However, unlike ABP-120+ cells, ABP-120- cells do not incorporate actin into the Triton X-100-insoluble cytoskeleton at 30-50 s, the time when ABP-120 is incorporated into the cytoskeleton and when pseudopods are extended after cAMP stimulation in wild-type cells. By confocal and electron microscopy, pseudopods extended by ABP- 120- cells are not as large or thick as those produced by ABP-120+ cells and in the electron microscope, an altered filament network is found in pseudopods of ABP-120- cells when compared to pseudopods of ABP-120+ cells. The actin filaments found in areas of pseudopods in ABP- 120+ cells either before or after stimulation were long, straight, and arranged into space filling orthogonal networks. Protrusions of ABP-120- cells are less three-dimensional, denser, and filled with multiple foci of aggregated filaments consistent with collapse of the filament network due to the absence of ABP-120-mediated cross-linking activity. The different organization of actin filaments may account for the diminished size of protrusions observed in living and fixed ABP-120- cells compared to ABP-120+ cells and is consistent with the role of ABP- 120 in regulating pseudopod extension through its cross-linking of actin filaments.     

Mechanisms of amoeboid chemotaxis: an evaluation of the cortical expansion model

In this work we evaluate the cortical expansion model for amoeboid chemotaxis with regard to new information about molecular events in the cytoskeleton following chemotactic stimulation of Dictyostelium amoebae. A rapid upshift in the concentration of chemoattractant can be used to synchronize the motile behavior of a large population of cells. This synchrony presents an opportunity to study the biochemical basis of morphological changes such as pseudopod extension that are required for amoeboid chemotaxis. Changes in the composition and activity of the cytoskeleton following stimulation can be measured with precision and correlated with important morphological changes. Such studies demonstrate that activation of actin nucleation is one of the first and most crucial events in the actin cytoskeleton following stimulation. This activation is followed by incorporation of specific actin cross-linking proteins into the cytoskeleton, which are implicated in the extension of pseudopods and filopods. These results, as well as those from studies with mutants deficient in myosin, indicate that cortical expansion, driven by focal actin polymerization, cross-linking and gel osmotic swelling, is an important force for pseudopod extension. It is concluded that whereas three forces, frontal sliding, tail contraction, and cortical expansion may cooperate to produce amoeboid movement, the cortical expansion model offers the simplest explanation of how focal stimulation with a chemoattractant causes polarized pseudopod extension.     

Directional budding of human immunodeficiency virus from monocytes.

Time-lapse cinematography revealed that activated human immunodeficiency virus (HIV)-infected monocytes crawl along surfaces, putting forward a leading pseudopod. Scanning electron micrographs showed monocyte pseudopods associated with spherical structures the size of HIV virions, and transmission electron micrographs revealed HIV virions budding from pseudopods. Filamentous actin (F-actin) was localized by electron microscopy in the pseudopod by heavy meromyosin decoration. Colocalization of F-actin and p24 viral antigen by light microscopy immunofluorescence indicated that F-actin and virus were present on the same pseudopod. These observations indicate that monocytes produce virus from a leading pseudopod. We suggest that HIV secretion at the leading edges of donor monocytes/macrophages may be an efficient way for HIV to infect target cells.     

Observations on Iridia diaphana, a Marine Foraminifer

SYNOPSIS. Iridia diaphana , a marine foraminifer, was used as a subject for observations on grano-reticulate pseudopods. The organism readily forms a pseudopod net and its behavior is roughly predictable. Test composition varies with the environment; test shape is more constant. Pseudopod form and structure were observed by transmitted plane and polarized light microscopy, by freeze-drying and scanning electron microscopy, and by thin section studies in the transmission electron microscope. Rigidity is probably due to the numerous 250 A dia. microtubules in the pseudopods. Other organelles observed include mitochondria, vesicles and vacuoles. The plasmalemma may have numerous villous projections. Pseudopod form in I. diaphana does not closely resemble that of Allogromia laticollaris as reported by Wohlfarth-Bottermann (25). A pseudopod may be composed of several membrane-bound units of cytoplasm, or of a single unit of cytoplasm. A reassessment of the theories of the mechanism of cytoplasmic streaming in foraminiferan pseudopods is necessary.     

A Model for a Correlated Random Walk Based on the Ordered Extension of Pseudopodia

Cell migration in the absence of external cues is well described by a correlated random walk. Most single cells move by extending protrusions called pseudopodia. To deduce how cells walk, we have analyzed the formation of pseudopodia by Dictyostelium cells. We have observed that the formation of pseudopodia is highly ordered with two types of pseudopodia: First, de novo formation of pseudopodia at random positions on the cell body, and therefore in random directions. Second, pseudopod splitting near the tip of the current pseudopod in alternating right/left directions, leading to a persistent zig-zag trajectory. Here we analyzed the probability frequency distributions of the angles between pseudopodia and used this information to design a stochastic model for cell movement. Monte Carlo simulations show that the critical elements are the ratio of persistent splitting pseudopodia relative to random de novo pseudopodia, the Left/Right alternation, the angle between pseudopodia and the variance of this angle. Experiments confirm predictions of the model, showing reduced persistence in mutants that are defective in pseudopod splitting and in mutants with an irregular cell surface.     

Quimp3, an automated pseudopod-tracking algorithm

To understand movement of amoeboid cells we have developed an information tool that automatically detects protrusions of moving cells. The algorithm uses digitized cell recordings at a speed of ~1 image per second that are analyzed in three steps. In the first part, the outline of a cell is defined as a polygon of ~150 nodes, using the previously published Quimp2 program. By comparing the position of the nodes in place and time, each node contains information on position, local curvature and speed of movement. The second part uses rules for curvature and movement to define the position and time of start and end of a growing pseudopod. This part of the algorithm produces quantitative data on size, surface area, lifetime, frequency, and direction of pseudopod extension. The third part of the algorithm assigns qualitative properties to each pseudopod. It decides on the origin of a pseudopod as splitting of an existing pseudopod or as extension de novo. It also decides on the fate of each pseudopod as merged with the cell body or retracted. Here we describe the pseudopod tool and present the first data based on the analysis of ~1000 pseudopodia extended by Dictyostelium cells in the absence of external cues.     

Focal exocytosis of VAMP3-containing vesicles at sites of phagosome formation

Phagocytosis involves the receptor-mediated extension of plasmalemmal protrusions, called pseudopods, which fuse at their tip to engulf a particle. Actin polymerizes under the nascent phagosome and may propel the protrusion of pseudopods. Alternatively, membrane extension could result from the localized insertion of intracellular membranes into the plasmalemma next to the particle. Here we show focal accumulation of VAMP3-containing vesicles, likely derived from recycling endosomes, in the vicinity of the nascent phagosome. Using green fluorescent protein (GFP) as both a fluorescent indicator and an exofacial epitope tag, we show that polarized fusion of VAMP3 vesicles precedes phagosome sealing. It is therefore likely that targeted delivery of endomembranes contributes to the elongation of pseudopods. In addition to mediating pseudopod formation, receptor-triggered focal secretion of endosomes may contribute to polarized membrane extension in processes such as lamellipodial elongation or chemotaxis.     

In vitro induction of crawling in the amoeboid sperm of the nematode parasite, Ascaris suum

In a highly synchronous process, the immotile spermatids of Ascaris suum extend pseudopods and become rapidly crawling sperm when treated with an extract from the glandular vas deferens of the male under strict anaerobic conditions. Within 9-12 min, a pseudopod develops, elongates rapidly, and exhibits a continuous flow of membrane specializations, the villipodia, from tip toward base. When attached to acid-washed glass, the pseudopod pulls the cell body along at speeds exceeding 70 microns/min. The pseudopod length remains constant while retrograde flow of villipodia proceeds at the same rate as the sperm's forward movement. Cohorts of about 15 villipodia form at the leading edge, move rearward together, and disappear at the junction of pseudopod and cell body. These are the terminations of branched, refringent fibers, which extend the length of the pseudopod. The latter are the fiber complexes that form its cytoskeleton (Sepsenwol et al.: Journal of Cell Biology 108:55-66, 1989). Locomoting cells sometimes change direction when another crawls by and follow each other. When cells are exposed to air, forward movement ceases in a predictable pattern: the forward extension of the leading edge ceases, the pseudopod shortens from the base, and the cell body continues to be pulled forward. These data contribute to a model for Ascaris sperm amoeboid motility in which independent processes of continuous extension at the leading edge and continuous shortening at the base of the pseudopod act to propel the cell forward.     

Identification of actin nucleation activity and polymerization inhibitor in ameboid cells: their regulation by chemotactic stimulation

Actin polymerization occurs in amebae of Dictyostelium discoideum after chemotactic stimulation (Hall, A. L., A. Schlein, and J. Condeelis. 1988. J. Cell. Biochem. 37:285-299). When cells are lysed with Triton X-100 during stimulation, an actin nucleation activity is detected in lysates by measuring the rate of pyrene-labeled actin polymerization. This stimulated nucleation activity is closely correlated with actin polymerization observed in vivo in its kinetics, developmental regulation, and cytochalasin D sensitivity. Actin polymerization is coordinate with pseudopod extension in synchronized populations of cells and is correlated with the accumulation of F actin in pseudopods. The stimulated actin nucleation activity is present in low-speed pellets from Triton lysates (cytoskeletons) within 3 s of stimulation and is stable compared with the nucleation activity of whole cell lysates. Low-speed supernatants contain a reversible inhibitor of the actin nucleation activity that is itself regulated by chemotactic stimulation. Neither activity requires Ca2+ and both are fully expressed in 10 mM EGTA. Fractions containing the inhibitor do not sever actin filaments but do inhibit actin polymerization that is seeded by fragments of purified F actin. These results indicate that chemotactic stimulation of Dictyostelium discoideum generates both an actin-nucleating activity and an actin-polymerization inhibitor, and suggest that the parallel regulation of these two activities leads to the transient phases of actin polymerization observed in vivo. The different compartmentation of these two activities may account for polarized pseudopod extension in gradients of chemoattractant.     

NADH-synergism of NADPH-dependent o-dealkylation of type II compounds, p-anisidine and p-phenetidine, in rat liver microsomes.

When fresh citrated platelet-rich plasma was stirred at 900 rpm, stopping the stirrer increased the extinction, E (optical density, absorbance), of the plasma by 25%. After the platelets from humans or rabbits had changed shape on the addition of ADP, stopping the stirrer increased E by only about 2%. Assuming the shape of a platelet to approximate an ellipsoid of revolution which is originally flat and becomes more or less spherical after ADP, the effects of stirring on extinction are accounted for with conventional light-scattering theory. The change in extinction caused by stirring is the basis of a proposed nondestructive and remote assay of platelet shape. Extinction changes induced by chlorpromazine, which causes disk-sphere transformation only, are found to agree with theoretical predictions based on the shape change. The effects of ADP, which also produces pseudopods, are systematically smaller. The optical effects of shape and pseudopods can be separated: those of shape are sensitive to stirring, while those of pseudopods are not. ADP evidently produces a 37% increase in extinction of stirred platelets due to disk-sphere transformation plus a 9% decrease due to pseudopod formation (net increase, 28%). With simplified models of pseudopods, light-scattering theory is found to confirm that pseudopod formation should cause a decrease in extinction and total light scattering.     

Underwater locomotion strategy by a benthic pennate diatom Navicula sp.

The mechanism of diatom locomotion has been widely researched but still remains a hypothesis. There are several questionable points on the prevailing model proposed by Edgar, and some of the observed phenomena cannot be completely explained by this model. In this paper, we undertook detailed investigations of cell structures, locomotion, secreted mucilage, and bending deformation for a benthic pennate diatom Navicula species. According to these broad evidences, an updated locomotion model is proposed. For Navicula sp., locomotion is realized via two or more pseudopods or stalks protruded out of the frustules. The adhesion can be produced due to the pull-off of one pseudopod or stalk from the substratum through extracellular polymeric substances. And the positive pressure is generated to balance the adhesion because of the push-down of another pseudopod or stalk onto the substratum. Because of the positive pressure, friction is generated, acting as a driving force of locomotion, and the other pseudopod or stalk can detach from the substratum, resulting in the locomotion. Furthermore, this model is validated by the force evaluation and can better explain observed phenomena. This updated model would provide a novel aspect on underwater locomotion strategy, hence can be useful in terms of artificial underwater locomotion devices.