An Adaptive Moving Mesh Method for Forced Curve Shortening Flow.

We propose a novel adaptive moving mesh method for the numerical solution of a forced curve shortening geometric evolution equation. Control of the mesh quality is obtained using a tangential mesh velocity derived from a mesh equidistribution principle, where a positive adaptivity measure or monitor function is approximately equidistributed along the evolving curve. Central finite differences are used to discretize in space the governing evolution equation for the position vector, and a second-order implicit scheme is used for the temporal integration. Simulations are presented indicating the generation of meshes which resolve areas of high curvature and are of second-order accuracy. Furthermore, the new method delivers improved solution accuracy compared to the use of uniform arc-length meshes.

Local modulation of chemoattractant concentrations by single cells: dissection using a bulk-surface computational model.

Chemoattractant gradients are usually considered in terms of sources and sinks that are independent of the chemotactic cell. However, recent interest has focused on 'self-generated' gradients, in which cell populations create their own local gradients as they move. Here, we consider the interplay between chemoattractants and single cells. To achieve this, we extend a recently developed computational model to incorporate breakdown of extracellular attractants by membrane-bound enzymes. Model equations are parametrized, using the published estimates from Dictyostelium cells chemotaxing towards cyclic AMP. We find that individual cells can substantially modulate their local attractant field under physiologically appropriate conditions of attractant and enzymes. This means the attractant concentration perceived by receptors can be a small fraction of the ambient concentration. This allows efficient chemotaxis in chemoattractant concentrations that would be saturating without local breakdown. Similar interactions in which cells locally mould a stimulus could function in many types of directed cell motility, including haptotaxis, durotaxis and even electrotaxis.

A computational method for the coupled solution of reaction-diffusion equations on evolving domains and manifolds: Application to a model of cell migration and chemotaxis.

In this paper, we devise a moving mesh finite element method for the approximate solution of coupled bulk-surface reaction-diffusion equations on an evolving two dimensional domain. Fundamental to the success of the method is the robust generation of bulk and surface meshes. For this purpose, we use a novel moving mesh partial differential equation (MMPDE) approach. The developed method is applied to model problems with known analytical solutions; these experiments indicate second-order spatial and temporal accuracy. Coupled bulk-surface problems occur frequently in many areas; in particular, in the modelling of eukaryotic cell migration and chemotaxis. We apply the method to a model of the two-way interaction of a migrating cell in a chemotactic field, where the bulk region corresponds to the extracellular region and the surface to the cell membrane.

A major role for Scar/WAVE-1 downstream of GPVI in platelets.

BACKGROUND: The small GTPase Rac1 plays a critical role in lamellipodia assembly in platelets on matrix proteins in the absence or presence of G protein-coupled receptor (GPCR) agonists. Rac mediates actin assembly via Scar/WAVE, a family of scaffolding proteins that direct actin reorganization by relaying signals from Rac to the Arp2/3 complex. OBJECTIVE: To evaluate the role of Scar/WAVE-1 in mediating platelet activation and cytoskeletal reorganization. METHODS AND RESULTS: Using specific antibodies, we demonstrate that murine platelets, like human platelets, express Scar/WAVE-1 and Scar/WAVE-2. Lamellipodia formation in Scar/WAVE-1(-/-) platelets is markedly inhibited on immobilized collagen-related peptide (CRP) and on laminin, both of which signal through the collagen receptor GPVI. In contrast, lamellipodia formation on collagen, which requires release of the GPCR agonists ADP and thromboxane A(2), is not altered. Immobilized fibrinogen supports limited formation of lamellipodia in murine platelets, which is not altered in Scar/WAVE-1(-/-) platelets. As with Rac1(-/-) platelets, Scar/WAVE-1(-/-) platelets exhibit a marked inhibition of aggregation in response to CRP, whereas the response to the GPCR agonist thrombin is not altered. Platelet aggregation on immobilized collagen under shear, which is dependent on signaling by matrix and GPCR agonists, was unaltered in the absence of Scar/WAVE-1. CONCLUSION: This study demonstrates a major role for Scar/WAVE-1 in mediating platelet cytoskeletal reorganization and aggregate formation downstream of activation by GPVI but not by GPCR agonists.

Regulation of actin assembly by SCAR/WAVE proteins.

Actin reorganization is a tightly regulated process that co-ordinates complex cellular events, such as cell migration, chemotaxis, phagocytosis and adhesion, but the molecular mechanisms that underlie these processes are not well understood. SCAR (suppressor of cAMP receptor)/WAVE [WASP (Wiskott-Aldrich syndrome protein)-family verprolin homology protein] proteins are members of the conserved WASP family of cytoskeletal regulators, which play a critical role in actin dynamics by triggering Arp2/3 (actin-related protein 2/3)-dependent actin nucleation. SCAR/WAVEs are thought to be regulated by a pentameric complex which also contains Abi (Abl-interactor), Nap (Nck-associated protein), PIR121 (p53-inducible mRNA 121) and HSPC300 (haematopoietic stem progenitor cell 300), but the structural organization of the complex and the contribution of its individual components to the regulation of SCAR/WAVE function remain unclear. Additional features of SCAR/WAVE regulation are highlighted by the discovery of other interactors and distinct complexes. It is likely that the combinatorial assembly of different components of SCAR/WAVE complexes will prove to be vital for their roles at the centre of dynamic actin reorganization.

Control of SCAR activity in Dictyostelium discoideum.

The WASP (Wiskott-Aldrich syndrome protein)/SCAR (suppressor of cAMP receptor) family of adaptor proteins regulate actin polymerization by coupling Rho-family GTPases to the activation of the Arp2/3 complex. SCAR exists within a complex of proteins, including Nap1 (Nck-associated protein 1), PIR121 (p53-inducible mRNA 121), Abi2 (Abl-interactor 2) and HSPC300. This complex was first reported to inhibit SCAR activity, but there is now some controversy over whether the complex is inhibitory or activatory. This complex is currently being studied in a wide range of different systems, and model organisms such as the amoeba Dictyostelium discoideum have been used to remove genetically SCAR complex members to ascertain their specific roles.

PIP3, PIP2, and cell movement--similar messages, different meanings?

The inositol lipids PI(4,5)P(2) and PI(3,4,5)P(3) are important regulators of actin polymerization, but their different temporal and spatial dynamics suggest that they perform separate roles. PI(3,4,5)P(3) seems to act as an instructive second messenger, inducing local actin polymerization. PI(4,5)P(2) appears to be present at too high a concentration and homogeneous a distribution to fulfil a similar role. Instead, we suggest that PI(4,5)P(2) acts permissively, restricting new actin polymerization to the region of the plasma membrane.

Dictyostelium: an ideal organism for genetic dissection of Ras signalling networks.

Signalling pathways based on the small GTPase Ras regulate a multitude of cellular events in eukaryotic cells. Dictyostelium expresses a large and varied family of Ras proteins. It also uses a range of known Ras regulators, in particular RasGEFs, and effectors. The genetic tractability of Dictyostelium, together with the wide range of Ras proteins and regulators, make it an ideal model for the genetic dissection of Ras pathways. This review highlights the recent advances in our understanding of Ras function in Dictyostelium, and considers the implications of these findings for our understanding of eukaryotic signal transduction.

Small GTPases in Dictyostelium: lessons from a social amoeba.

Although the process of sequencing the Dictyostelium genome is not complete, it is already producing surprises, including an unexpectedly large number of Ras- and Rho-subfamily GTPases. Members of these families control a wide variety of cellular processes in eukaryotes, including proliferation, differentiation, cell motility and cell polarity. Comparison of small GTPases from Dictyostelium with those from higher eukaryotes provides an intriguing view of their cellular and evolutionary roles. In particular, although mammalian Ras proteins interact with several signalling pathways, the Dictyostelium pathways appear more linear, with each Ras apparently performing a specific cellular function.

A novel Dictyostelium RasGEF is required for normal endocytosis, cell motility and multicellular development.

BACKGROUND: Dictyostelium possesses a surprisingly large number of Ras proteins and little is known about their activators, the guanine nucleotide exchange factors (GEFs). It is also unclear, in Dictyostelium or in higher eukaryotes, whether Ras pathways are linear, with each Ras controlled by its own GEF, or networked, with multiple GEFs acting on multiple Ras proteins. RESULTS: We have identified the Dictyostelium gene that encodes RasGEFB, a protein with homology to known RasGEFs such as the Son-of-sevenless (Sos) protein. Dictyostelium cells in which the gene for RasGEFB was disrupted moved unusually rapidly, but lost the ability to perform macropinocytosis and therefore to grow in liquid medium. Crowns, the sites of macropinocytosis, were replaced by polarised lamellipodia. Mutant cells were also profoundly defective in early development, although they eventually formed tiny but normally proportioned fruiting bodies. This defect correlated with loss of discoidin Igamma mRNA, a starvation-induced gene, although other genes required for development were expressed normally or even precociously. RasGEFB was able to rescue a Saccharomyces CDC25 mutant, indicating that it is a genuine GEF for Ras proteins. CONCLUSIONS: RasGEFB appears to be the principal activator of the RasS protein, which regulates macropinocytosis and cell speed, but it also appears to regulate one or more other Ras proteins.

Ca(2+) signalling is not required for chemotaxis in Dictyostelium.

Dictyostelium cells can move rapidly towards a source of cyclic-AMP (cAMP). This chemoattractant is detected by G-protein-linked receptors, which trigger a signalling cascade including a rapid influx of Ca(2+). We have disrupted an inositol 1,4,5-trisphosphate (InsP(3)) receptor-like gene, iplA, to produce null cells in which Ca(2+) entry in response to chemoattractants is abolished, as is the normal increase in free cytosolic Ca(2+) ([Ca(2+)](c)) that follows chemotactic stimulation. However, the resting [Ca(2+)](c) is similar to wild type. This mutant provides a test for the role of Ca(2+) influx in both chemotaxis and the signalling cascade that controls it. The production of cyclic-GMP and cAMP, and the activation of the MAP kinase, DdERK2, triggered from the cAMP receptor, are little perturbed in the mutant; mobilization of actin into the cytoskeleton also follows similar kinetics to wild type. Mutant cells chemotax efficiently towards cAMP or folic acid and their sensitivity to cAMP is similar to wild type. Finally, they move at similar speeds to wild-type cells, with or without chemoattractant. We conclude that Ca(2+) signalling is not necessary for chemotaxis to cAMP.

Dictyostelium RasD is required for normal phototaxis, but not differentiation.

RasD, a Dictyostelium homolog of mammalian Ras, is maximally expressed during the multicellular stage of development. Normal Dictyostelium aggregates are phototactic and thermotactic, moving towards sources of light and heat with great sensitivity. We show that disruption of the gene for rasD causes a near-total loss of phototaxis and thermotaxis in mutant aggregates, without obvious effects on undirected movement. Previous experiments had suggested important roles for RasD in development and cell-type determination. Surprisingly, rasD(-) cells show no obvious changes in these processes. These cells represent a novel class of phototaxis mutant, and indicate a role for a Ras pathway in the connections between stimuli and coordinated cell movement.

Phosphatidylinositol 4,5-bisphosphate induces actin-based movement of raft-enriched vesicles through WASP-Arp2/3.

BACKGROUND: Phosphatidylinositol 4,5-bisphosphate (PIP(2)) has been implicated in the regulation of the actin cytoskeleton and vesicle trafficking. It stimulates de novo actin polymerization by activating the pathway involving the Wiskott-Aldrich syndrome protein (WASP) and the actin-related protein complex Arp2/3. Other studies show that actin polymerizes from cholesterol-sphingolipid-rich membrane microdomains called 'rafts', in a manner dependent on tyrosine phosphorylation. Although actin has been implicated in vesicle trafficking, and rafts are sites of active phosphoinositide and tyrosine kinase signaling that mediate apically directed vesicle trafficking, it is not known whether phosphoinositide regulation of actin dynamics occurs in rafts, or if it is linked to vesicle movements. RESULTS: Overexpression of type I phosphatidylinositol phosphate 5-kinase (PIP5KI), which synthesizes PIP(2), promoted actin polymerization from membrane-bound vesicles to form motile actin comets. Pervanadate (PV), a tyrosine phosphatase inhibitor, induced comets even in the absence of PIP5KI overexpression. PV increased PIP(2) levels, suggesting that it induces comets by changing PIP(2) homeostasis and by increasing tyrosine phosphorylation. Platelet-derived growth factor (PDGF) enhanced PV-induced comet formation, and these stimuli together potentiated the PIP5KI effect. The vesicles at the heads of comets were enriched in PIP5KIs and tyrosine phosphoproteins. WASP-Arp2/3 involvement was established using dominant-negative WASP constructs. Endocytic and exocytic markers identified vesicles enriched in lipid rafts as preferential sites of comet generation. Extraction of cholesterol with methyl-beta-cyclodextrin reduced comets, establishing that rafts promote comet formation. CONCLUSIONS: Sphingolipid-cholesterol rafts are preferred platforms for membrane-linked actin polymerization. This is mediated by in situ PIP(2) synthesis and tyrosine kinase signaling through the WASP-Arp2/3 pathway. Actin comets may provide a novel mechanism for raft-dependent vesicle transport and apical membrane trafficking.

The Dictyostelium RasS protein is required for macropinocytosis, phagocytosis and the control of cell movement.

Endocytosis and cell migration both require transient localised remodelling of the cell cortex. Several lines of evidence suggest a key regulatory role in these activities for members of the Ras family of small GTPases. We have generated Dictyostelium cells lacking one member of this family, RasS, and the mutant cells are perturbed in endocytosis and cell migration. Mutant amoebae are defective in phagocytosis and fluid-phase endocytosis and are impaired in growth. Conversely, the rasS(-)cells show an enhanced rate of cell migration, moving three times faster than wild-type controls. The mutant cells display an aberrant morphology, are highly polarised, carry many elongated actin protrusions and show a concomitant decrease in formation of pinocytic crowns on the cell surface. These morphological aberrations are paralleled by changes in the actin cytoskeleton, with a significant proportion of the cortical F-actin relocalised to prominent pseudopodia. Rapid migration and endocytosis appear to be mutually incompatible and it is likely that RasS protein is required to maintain the normal balance between these two actin-dependent processes.

The helC gene encodes a putative DEAD-box RNA helicase required for development in Dictyostelium discoideum.

DEAD-box RNA helicases, defined by the sequence Asp-Glu-Ala-Asp (DEAD, in single-letter amino-acid code), regulate RNA unwinding and secondary structure in an ATP-dependent manner in vitro [1] and control mRNA stability and protein translation. Both yeast and mammals have large families of DEAD-box proteins, many of unknown function. We have disrupted a Dictyostelium discoideum gene, helC, which encodes helicase C, a member of the DEAD-box family of RNA helicases that shows strong homology to the product of the essential Saccharomyces cerevisiae gene dbp5 [2] and to related helicases in mouse and Schizosaccharomyces pombe. The HelC protein also shows weaker homology to the translation initiation factor elF-4a. Other DEAD-box-containing proteins, which are less closely related to HelC, have been implicated in developmental roles in Drosophila [3] and Xenopus laevis; one example is the Xenopus Vasa-like protein (XVLP) [4-6]. In Drosophila and Xenopus, Vasa and XVLP, respectively, are required for the establishment of tissue polarity during development. In yeast, DEAD-box helicases such as Prp8 [7] are components of the spliceosome and connect pre-mRNA splicing with the cell cycle. Disruption of the helC gene in D. discoideum led to developmental asynchrony, failure to differentiate and aberrant morphogenesis. We postulate that one reason for the existence of large families of homologous DEAD-box proteins in yeast, mammals and Dictyostelium could be that some DEAD-box proteins have developmentally specific roles regulating protein translation or mRNA stability.

Scar1 and the related Wiskott-Aldrich syndrome protein, WASP, regulate the actin cytoskeleton through the Arp2/3 complex.

BACKGROUND: The actin-related proteins Arp2 and Arp3 are part of a seven-protein complex which is localized in the lamellipodia of a variety of cell types, and in actin-rich spots of unknown function. The Arp2/3 complex enhances actin nucleation and causes branching and crosslinking of actin filaments in vitro; in vivo it is thought to drive the formation of lamellipodia and to be a control center for actin-based motility. The Wiskott-Aldrich syndrome protein, WASP, is an adaptor protein implicated in the transmission of signals from tyrosine kinase receptors and small GTPases to the actin cytoskeleton. Scar1 is a member of a new family of proteins related to WASP, and it may also have a role in regulating the actin cytoskeleton. Scar1 is the human homologue of Dictyostelium Scar1, which is thought to connect G-protein-coupled receptors to the actin cytoskeleton. The mammalian Scar family contains at least four members. We have examined the relationships between WASP, Scar1, and the Arp2/3 complex. RESULTS: We have identified WASP and its relative Scar1 as proteins that interact with the Arp2/3 complex. We have used deletion analysis to show that both WASP and Scar1 interact with the p21 subunit of the Arp2/3 complex through their carboxyl termini. Overexpression of carboxy-terminal fragments of Scar1 or WASP in cells caused a disruption in the localization of the Arp2/3 complex and, concomitantly, induced a complete loss of lamellipodia and actin spots. The induction of lamellipodia by platelet-derived growth factor was also suppressed by overexpression of the fragment of Scar1 that binds to the Arp2/3 complex. CONCLUSIONS: We have identified a conserved sequence domain in proteins of the WASP family that binds to the Arp2/3 complex. Overexpression of this domain in cells disrupts the localization of the Arp2/3 complex and inhibits lamellipodia formation. Our data suggest that WASP-related proteins may regulate the actin cytoskeleton through the Arp2/3 complex.

Dictyostelium RasG is required for normal motility and cytokinesis, but not growth.

RasG is the most abundant Ras protein in growing Dictyostelium cells and the closest relative of mammalian Ras proteins. We have generated null mutants in which expression of RasG is completely abolished. Unexpectedly, RasG- cells are able to grow at nearly wild-type rates. However, they exhibit defective cell movement and a wide range of defects in the control of the actin cytoskeleton, including a loss of cell polarity, absence of normal lamellipodia, formation of unusual small, punctate polymerized actin structures, and a large number of abnormally long filopodia. Despite their lack of polarity and abnormal cytoskeleton, mutant cells perform normal chemotaxis. However, rasG- cells are unable to perform normal cytokinesis, becoming multinucleate when grown in suspension culture. Taken together, these data suggest a principal role for RasG in coordination of cell movement and control of the cytoskeleton.