Absolute Differentiation in Metric Spaces

In this article, we introduce a new notion of (strong) absolute derivative, for functions derived between metric spaces, and we investigate various properties and uses of this concept, especially regarding the geometry of abstract metric spaces carrying no other structure

Loss of strumpellin in the melanocytic lineage impairs the WASH Complex but does not affect coat colour

The five-subunit WASH complex generates actin networks that participate in endocytic trafficking, migration and invasion in various cell types. Loss of one of the two subunits WASH or strumpellin in mice is lethal, but little is known about their role in mammals in vivo. We explored the role of strumpellin, which has previously been linked to hereditary spastic paraplegia, in the mouse melanocytic lineage. Strumpellin knockout in melanocytes revealed abnormal endocytic vesicle morphology but no impairment of migration in vitro or in vivo and no change in coat colour. Unexpectedly, WASH and filamentous actin could still localize to vesicles in the absence of strumpellin, although the shape and size of vesicles was altered. Blue native PAGE revealed the presence of two distinct WASH complexes, even in strumpellin knockout cells, revealing that the WASH complex can assemble and localize to endocytic compartments in cells in the absence of strumpellin

Replacement of the essential Dictyostelium Arp2 gene by its Entamoeba homologue using parasexual genetics

Background: Cell motility is an essential feature of the pathogenesis and morbidity of amoebiasis caused by Entamoeba histolytica. As motility depends on cytoskeletal organisation and regulation, a study of the molecular components involved is key to a better understanding of amoebic pathogenesis. However, little is known about the physiological roles, interactions and regulation of the proteins of the Entamoeba cytoskeleton. Results: We have established a genetic strategy that uses parasexual genetics to allow essential Dictyostelium discoideum genes to be manipulated and replaced with modified or tagged homologues. Our results show that actin related protein 2 (Arp2) is essential for survival, but that the Dictyostelium protein can be complemented by E. histolytica Arp2, despite the presence of an insertion of 16 amino acids in an otherwise highly conserved protein. Replacement of endogenous Arp2 with myc-tagged Entamoeba or Dictyostelium Arp2 has no obvious effects on growth and the protein incorporates effectively into the Arp2/3 complex. Conclusion: We have established an effective two-step method for replacing genes that are required for survival. Our protocol will allow such genes to be studied far more easily, and also allows an unambiguous demonstration that particular genes are truly essential. In addition, cells in which the Dictyostelium Arp2 has been replaced by the Entamoeba protein are potential targets for drug screens

p21-activated kinase (PAK) regulates cytoskeletal reorganization and directional migration in human neutrophils

Neutrophils serve as a first line of defense in innate immunity owing in part to their ability to rapidly migrate towards chemotactic factors derived from invading pathogens. As a migratory function, neutrophil chemotaxis is regulated by the Rho family of small GTPases. However, the mechanisms by which Rho GTPases orchestrate cytoskeletal dynamics in migrating neutrophils remain ill-defined. In this study, we characterized the role of p21-activated kinase (PAK) downstream of Rho GTPases in cytoskeletal remodeling and chemotactic processes of human neutrophils. We found that PAK activation occurred upon stimulation of neutrophils with f-Met-Leu-Phe (fMLP), and PAK accumulated at the actin-rich leading edge of stimulated neutrophils, suggesting a role for PAK in Rac-dependent actin remodeling. Treatment with the pharmacological PAK inhibitor, PF3758309, abrogated the integrity of RhoA-mediated actomyosin contractility and surface adhesion. Moreover, inhibition of PAK activity impaired neutrophil morphological polarization and directional migration under a gradient of fMLP, and was associated with dysregulated Ca2+ signaling. These results suggest that PAK serves as an important effector of Rho-family GTPases in neutrophil cytoskeletal reorganization, and plays a key role in driving efficient directional migration of human neutrophils

LPP3 mediates self-generation of chemotactic LPA gradients by melanoma cells

Melanoma cells steer out of tumours using self-generated lysophosphatidic acid (LPA) gradients. The cells break down LPA, which is present at high levels around the tumours, creating a dynamic gradient that is low in the tumour and high outside. They then also migrate up this gradient, creating a complex and evolving outward chemotactic stimulus. Here we introduce a new assay for self-generated chemotaxis, and show that raising LPA levels causes a delay in migration rather than loss of chemotactic efficiency. Knockdown of the lipid phosphatase LPP3 - but not its homologues LPP1 or LPP2 - diminishes the cell's ability to break down LPA. This is specific for chemotactically active LPAs, such as the 18:1 and 20:4 species. Inhibition of autotaxin-mediated LPA production does not diminish outward chemotaxis, but loss of LPP3-mediated LPA breakdown blocks it. Similarly, in both 2D and 3D invasion assays, knockdown of LPP3 diminishes melanoma cells' ability to invade. Our results demonstrate that LPP3 is the key enzyme in melanoma cells' breakdown of LPA, and confirm the importance of attractant breakdown in LPA-mediated cell steering

WASP family proteins and formins compete in pseudopod- and bleb-based migration

Actin pseudopods induced by SCAR/WAVE drive normal migration and chemotaxis in eukaryotic cells. Cells can also migrate using blebs, in which the edge is driven forward by hydrostatic pressure instead of actin. In Dictyostelium discoideum, loss of SCAR is compensated by WASP moving to the leading edge to generate morphologically normal pseudopods. Here we use an inducible double knockout to show that cells lacking both SCAR and WASP are unable to grow, make pseudopods or, unexpectedly, migrate using blebs. Remarkably, amounts and dynamics of actin polymerization are normal. Pseudopods are replaced in double SCAR/WASP mutants by aberrant filopods, induced by the formin dDia2. Further disruption of the gene for dDia2 restores cells’ ability to initiate blebs and thus migrate, though pseudopods are still lost. Triple knockout cells still contain near-normal F-actin levels. This work shows that SCAR, WASP, and dDia2 compete for actin. Loss of SCAR and WASP causes excessive dDia2 activity, maintaining F-actin levels but blocking pseudopod and bleb formation and migration

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 chemoattractant

SILAC-based proteomic quantification of chemoattractant-induced cytoskeleton dynamics on a second to minute timescale

Cytoskeletal dynamics during cell behaviours ranging from endocytosis and exocytosis to cell division and movement is controlled by a complex network of signalling pathways, the full details of which are as yet unresolved. Here we show that SILAC-based proteomic methods can be used to characterize the rapid chemoattractant-induced dynamic changes in the actin–myosin cytoskeleton and regulatory elements on a proteome-wide scale with a second to minute timescale resolution. This approach provides novel insights in the ensemble kinetics of key cytoskeletal constituents and association of known and novel identified binding proteins. We validate the proteomic data by detailed microscopy-based analysis of in vivo translocation dynamics for key signalling factors. This rapid large-scale proteomic approach may be applied to other situations where highly dynamic changes in complex cellular compartments are expected to play a key role

The wear of fixed and mobile bearing unicompartmental knee replacements

Unicompartmental knee replacements (UKR) are an option for surgical intervention for the treatment of single-compartment osteoarthritis. The aim of this study was to compare the wear of a low-conformity fixed-bearing UKR with a conforming mobile bearing UKR under two kinematic conditions, to investigate the effect of implant design and kinematics on wear performance in a physiological knee wear simulator. Under both sets of kinematic conditions, the relatively low-conforming fixed UKR showed lower wear, compared with the more conforming anterior-posterior sliding mobile bearing. However, it should be noted that differences in materials between the two designs also contribute to the relative wear performance of the bearings. The combined wear of the medial and lateral bearings of the fixed-bearing UKR as a ‘total knee’ were significantly reduced compared with a fixed-bearing total knee replacement studied under the same kinematic condition

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 discretise 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