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.

Reducing surgical outpatient waiting is not the solution to meeting the 2005 colorectal cancer target.

OBJECTIVES: The majority of colorectal cancers (CRC) are not diagnosed through the Rapid access route (RAR) and follow-ups (FU) may prolong outpatient-waiting time for new referrals. The aim of this study was to assess the relative contributions of an efficient colorectal clinic and a stringent colonoscopy booking system on the total journey time for CRC. PATIENTS AND METHODS: We reduced the number of follow-up appointments with the introduction of 'Paper clinics'. The composition of the new clinic was determined by the known cancer yield through RAR and non-RAR route. A prospective analysis of clinics and CRC journey times was undertaken from November 2003 for 13 months, with the new outpatient clinic template introduced in December 2003. This coincided with a stringent policy on referral pattern for colonoscopy. RESULTS: In our hospital, only 4% of RAR yield CRC. Seventy-five percent of our CRC are referred through the non-RAR route. Eighty-one percent of follow-ups in a 'paper clinic' were discharged. A flexible template for the outpatient clinics, introduced a corresponding reduction in follow-up and increased urgent and routine slots. There was a progressive drop in the follow-up to new ratio and the waiting times for routine and urgent category decreased from a median of 15.9 and 3.4 weeks to 6.7 and 0.7 weeks, respectively (P < 0.001). Average waiting times for all categories fell from 13.35 weeks in November 2003 to 3.5 weeks in December 2004, while the number of patients waiting less than 4 weeks rose from 46% to 71%. This was associated with reduction in total journey times from 93 days to 62 days (P < 0.05). DNA rates remained unaffected. CONCLUSION: Modifying outpatient clinic composition with 'paper clinics' reduces the waiting time for all referrals to a surgical clinic with a modest effect on CRC clinic waiting time. Reduction in the total waiting time to first treatment (for CRC) is due to reducing the demand on colonoscopy in favour of barium enema. Redirecting the flow of patients towards barium enema is perhaps one way of improving the existing CRC journey time to first treatment, within existing resources. Achieving the 62 day target for cancer journey time will be difficult unless traditional surgical clinic habits are challenged.

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.

Dynamics of the Dictyostelium Arp2/3 complex in endocytosis, cytokinesis, and chemotaxis.

The Arp2/3 complex is a ubiquitous and important regulator of the actin cytoskeleton. Here we identify this complex from Dictyostelium and investigate its dynamics in live cells. The predicted sequences of the subunits show a strong homology to the members of the mammalian complex, with the larger subunits generally better conserved than the smaller ones. In the highly motile cells of Dictyostelium, the Arp2/3 complex is rapidly re-distributed to the cytoskeleton in response to external stimuli. Fusions of Arp3 and p41-Arc with GFP reveal that in phagocytosis, macropinocytosis, and chemotaxis the complex is recruited within seconds to sites where actin polymerization is induced. In contrast, there is little or no localization to the cleavage furrow during cytokinesis. Rather the Arp2/3 complex is enriched in ruffles at the polar regions of mitotic cells, which suggests a role in actin polymerization in these ruffles.

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.

Purification and cloning of phosphatidylinositol transfer proteins from Dictyostelium discoideum: homologues of both mammalian PITPs and Saccharomyces cerevisiae sec14p are found in the same cell.

Soluble phosphatidylinositol transfer proteins (PITPs) have important roles in lipid-mediated signalling as well as in membrane traffic. Two PITPs (alpha and beta) have been cloned from mammalian cells, which are unrelated in sequence to yeast PITP (the product of the SEC14 gene). However, all three PITPs can perform interchangeably to reconstitute function in mammalian cells. We have now purified the major PITP from the cytoplasm of Dictyostelium discoideum and cloned the gene. This protein, DdPITP1, is homologous with mammalian PITPalpha and PITPbeta. We have also cloned a second gene (DdPITP2) related in sequence to DdPITP1. In addition, an independently cloned cDNA encodes a relative of the SEC14 family of yeast PITPs. DdPITP1, DdPITP2 and DdSec14 proteins were all able to mediate the transfer of PtdIns from one membrane compartment to another; they thus exhibited the hallmark of PITPs. Secondly, all three PITPs were able to rescue phospholipase C-mediated phosphoinositide hydrolysis in PITP-depleted HL60 cells, indicating that all three PITPs were capable of stimulating phosphoinositide synthesis. The identification of PITPs related to both mammalian PITPs and yeast Sec14p in a single organism will provide a unique opportunity to examine the functions of this class of protein with genetic approaches.

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.

Functional overlap of the dictyostelium RasG, RasD and RasB proteins.

Disruption of the rasG gene in Dictyostelium discoideum results in several distinct phenotypes: a defect in cytokinesis, reduced motility and reduced growth. Reintroduction of the rasG gene restores all of the properties of the rasG(-) cells to those of the wild type. To determine whether the defects are due to impaired interactions with a single or multiple downstream effectors, we tested the ability of the highly related but non identical Dictyostelium ras genes, rasD and rasB, to rescue the defects. Introduction of the rasD gene under the control of the rasG promoter into rasG null (rasG(-)) cells corrected all phenotypes except the motility defect, suggesting that motility is regulated by a RasG mediated pathway that is different to those regulating growth or cytokinesis. Western blot analysis of RasD protein levels revealed that vegetative rasG(- )cells contained considerably more protein than the parental AX-3 cells, suggesting that RasD protein levels are negatively regulated in vegetative cells by RasG. The level of RasD was enhanced when the rasD gene was introduced under the control of the rasG promoter, and this increase in protein is presumably responsible for the reversal of the growth and cytokinesis defects of the rasG(- )cells. Thus, RasD protein levels are controlled by the level of RasG, but not by the level of RasD. Introduction of the rasB gene under the control of the rasG promoter into rasG(-) cells produced a complex phenotype. The transformants were extremely small and mononucleate and exhibited enhanced motility. However, the growth of these cells was considerably slower than the growth of the rasG(-) cells, suggesting the possibility that high levels of RasB inhibit an essential process. This was confirmed by expressing rasB in wild-type cells; the resulting transformants exhibited severely impaired growth. When RasB protein levels were determined by western blot analysis, it was found that levels were higher in the rasG(- )cells than they were in the wild-type parental, suggesting that RasG also negatively regulates rasB expression in vegetative cells. Overexpression of rasB in the rasG(- )cells also reduced the level of RasD protein. In view of the fact that alternate Ras proteins correct some, but not all, of the defects exhibited by the rasG(-) cells, we propose that RasG interacts with more than one downstream effector. In addition, it is clear that the levels of the various Ras proteins are tightly regulated in vegetative cells and that overexpression can be deleterious.