Dynamics of nearly parallel interacting vortex filaments

The dynamics of interacting vortex filaments in an incompressible fluid, which are nearly parallel, have been approximated in the Klein–Majda–Damodaran model. The regime considers the deflection of each filament from a central axis; that is to say, the vortex filaments are assumed to be roughly parallel and centred along parallel lines. While this model has attracted a fair amount of mathematical interest in the recent literature, particularly concerning the existence of certain specific vortex filament structures, our aim is to generalise several known interesting filament solutions, found in the self-induced motion of a single vortex filament, to the case of pairwise interactions between multiple vortex filaments under the Klein–Majda–Damodaran model by means of asymptotic and numerical methods. In particular, we obtain asymptotic solutions for counter-rotating and co-rotating vortex filament pairs that are separated by a distance, so that the vortex filaments always remain sufficiently far apart, as well as intertwined vortex filaments that are in close proximity, exhibiting overlapping orbits. For each scenario, we consider both co- and counter-rotating pairwise interactions, and the specific kinds of solutions obtained for each case consist of planar filaments, for which motion is purely rotational, as well as travelling wave and self-similar solutions, both of which change their form as they evolve in time. We choose travelling waves, planar filaments and self-similar solutions for the initial filament configurations, as these are common vortex filament structures in the literature, and we use the dynamics under the Klein–Majda–Damodaran model to see how these structures are modified in time under pairwise interaction dynamics. Numerical simulations for each case demonstrate the validity of the asymptotic solutions. Furthermore, we develop equations to study a co-rotating hierarchy of many satellite vortices orbiting around a central filament. We numerically show that such configurations are unstable for plane-wave solutions, which lead to collapse of the hierarchy. We also consider more general travelling wave and self-similar solutions for co-rotating hierarchies, and these give what appears to be chaotic dynamics.

Non-respiratory blood vessels in Latimeria gill filaments

A study of the blood pathways within the gills of Latimeria has been carried out using light and transmission electron microscopy. Clear evidence has been found for the presence of a secondary non–respiratory circulation in addition to the well–established respiratory pathway through the gill lamellae. All essential components of this system have been observed and have the same relationships and basic structure as comparable secondary systems in actinopterygian and elasmobranch fishes. These include a central venous sinus (CVS), arterio–venous anastomoses (AVAs) and central filament arteries (CFAs). AVAs connect both arterial vessels of the primary circulation and CFAs of the secondary circulation to the CVS. The latter contained many red blood cells. The presence of this secondary circulation in Latimeria gills contrasts with the situation in the gills of the three living genera of lungfishes where a system possessing the essential features of the tetrapod lymphatic vessel system has been recognized. No suggestions of a true lymphatic vessel system were observed in Latimeria . Other features of gill and vascular anatomy in Latimeria show its closer relationship to dipnoans than other groups of living fishes but evidence derived from this study of the secondary circulation clearly supports the view that the Dipnoi rather than Latimeria represent the living fishes most closely related to the tetrapods.

Filensin and phakinin form a novel type of beaded intermediate filaments and coassemble de novo in cultured cells.

The fiber cells of the eye lens possess a unique cytoskeletal system known as the "beaded-chain filaments" (BFs). BFs consist of filensin and phakinin, two recently characterized intermediate filament (IF) proteins. To examine the organization and the assembly of these heteropolymeric IFs, we have performed a series of in vitro polymerization studies and transfection experiments. Filaments assembled from purified filensin and phakinin exhibit the characteristic 19-21-nm periodicity seen in many types of IFs upon low angle rotary shadowing. However, quantitative mass-per-length (MPL) measurements indicate that filensin/phakinin filaments comprise two distinct and dissociable components: a core filament and a peripheral filament moiety. Consistent with a nonuniform organization, visualization of unfixed and unstained specimens by scanning transmission electron microscopy (STEM) reveals the the existence of a central filament which is decorated by regularly spaced 12-15-nm-diam beads. Our data suggest that the filamentous core is composed of phakinin, which exhibits a tendency to self-assemble into filament bundles, whereas the beads contain filensin/phakinin hetero-oligomers. Filensin and phakinin copolymerize and form filamentous structures when expressed transiently in cultured cells. Experiments in IF-free SW13 cells reveal that coassembly of the lens-specific proteins in vivo does not require a preexisting IF system. In epithelial MCF-7 cells de novo forming filaments appear to grow from distinct foci and organize as thick, fibrous laminae which line the plasma membrane and the nuclear envelope. However, filament assembly in CHO and SV40-transformed lens-epithelial cells (both of which are fibroblast-like) yields radial networks which codistribute with the endogenous vimentin IFs. These observations document that the filaments formed by lens-specific IF proteins are structurally distinct from ordinary cytoplasmic IFs. Furthermore, the results suggest that the spatial arrangement of filensin/phakinin filaments in vivo is subject to regulation by host-specific factors. These factors may involve cytoskeletal networks (e.g., vimentin IFs) and/or specific sites associated with the cellular membranes.

Evidence of a defined spatial arrangement of hyaluronate in the central filament of cartilage proteoglycan aggregates

Aggregates of proteoglycans from the Swarm rat chondrosarcoma reassembled in vitro have been studied by rotary-shadowing electron microscopy, and shown to be similar to native structures that have never been dissociated [Mörgelin, Engel, Heinegård and Paulsson (1992) J. Biol. Chem. 267, 14275-14284]. A hyaluronate with defined chain length (HAshort) has now been prepared by autoclaving high-Mr hyaluronate and fractionation to a narrow size distribution by gel filtration. Proteoglycan monomers, core protein, hyaluronate-binding region and link protein were combined with HAshort. Free chains of HAshort and reconstituted complexes with proteoglycan, link protein and aggrecan fragments were examined by electron microscopy after rotary shadowing. Length measurements showed that the hyaluronate was condensed to about half of its original length on binding intact aggrecan monomers, any aggrecan fragment or link protein alone. This strongly implies that hyaluronate adopts a defined spatial arrangement within the central filament of the aggregate, probably different from its secondary structure in solution. No differences in length were observed between link-free and link-stabilized aggregates.

Cartilage proteoglycan aggregates. Electronmicroscopic studies of native and fragmented molecules

1. Proteoglycan aggregates from bovine nasal cartilage were studied by using electron microscopy of proteoglycan/cytochrome c monolayers. 2. The aggregates contained a variably long central filament of hyaluronic acid with an average length of 1037nm. The proteoglycan monomers attached to the hyaluronic acid appeared as side chain filaments varying in length (averaging 249nm). They were distributed along the central filament at an average distance of about 36nm. 3. Chondroitin sulphate side chains were removed from the proteoglycan monomers of the aggregates by partial chondroitinase digestion. The molecules obtained had the same general appearance as intact aggregates. 4. Proteoglycan aggregates were treated with trypsin and the largest fragment, which contains the hyaluronic acid, link protein and hyaluronic acid-binding region, was recovered and studied with electron microscopy. Filaments that lacked the side chain extensions and had the same length as the central filament in the intact aggregate were observed. 5. Hyaluronic acid isolated after papain digestion of cartilage extracts gave filaments with similar length and size distribution as observed for the central filament both in the intact aggregate and in the trypsin digests. 6. Umbilical-cord hyaluronic acid was also studied and gave electron micrographs similar to those described for hyaluronic acid from cartilage. However, the length of the filament was somewhat shorter. 7. The electron micrographs of both intact and selectively degraded proteoglycans corroborate the current model of cartilage proteoglycan structure.

A comparison of spermiogenesis and spermatozoal ultrastructure in Megascolecid and Lumbricid earthworms (Oligochaeta : Annelida)

Spermiogenesis of six species of megascolecid earthworms has been investigated by electron microscopy. Numerous spermatids are joined to a central anucleate mass, forming a morula. Connection is made by a filament-clothed bridge, the zonula collaris. At least nine mitochondria are observed in a young spermatid but in all cases only six persist, with their juxtaposed surfaces radiating from a central axis, in the middle piece. A stack of golgi cisternae is present distally and is associated with the immature acrosome, which is subsequently transported proximally and interposed between nucleus and zonula collaris. Microtubules of the manchette ensheath the acrosome nucleus and incipient middle piece and, subsequently, all cytoplasm peripheral to the manchette with the exception of the plasma membrane is eliminated. Cytomorphogenetic changes, including great elongation and condensation of the nucleus, result in a free filamentous spermatozoon with a tapering tubular acrosome, an extremely elongate nucleus (total length 10 �m, cf. 20-30 �m in Lumbricus) a small but elongate middle piece (0.5 - 1.4 �m long) and long flagellum. Close agreement thus exists with spermiogenesis in the Lumbricidae, and the acrosome, which is among the most complex in the animal kingdom, shows general homology with that of Lumbricus. Significant differences from Lumbricus include the domed proximal end of the nucleus, the less discrete basal compartment, the conspicuous limen and greater separation of the outer wall of the acrosomal vesicle from the acrosome wall. A centriole with nine satellites peripheral to nine microtubules is demonstrable. A tetragon configuration in which two central fibres are added to the usual nine doublet+two central singlet microtubules is demonstrated in the proximal flagellum after a short region with a single central filament, but further distally the two fibres cease, giving the normal 9+2. Terminally the doublets are replaced by singlets and the number of microtubules is reduced. Glycogen granules are conspicuous, peripheral to the microtubules through much of the proximal axoneme as in lumbricids. A species of Cryptodrilus shows an asymmetrical 3+2 arrangement of satellites in a peripheral circlet, which exemplifies the taxonomic value of spermatozoal ultrastructure. It is confirmed that oligochaete spermatozoa are fundamentally different from those of polychaetes and archiannelids.

Proteoglycans of hyaline cartilage: Electron-microscopic studies on isolated molecules

Proteoglycan monomers from guinea-pig costal cartilage, bovine nasal and bovine tracheal cartilage were observed in the electron microscope after being spread in a monomolecular layer with cytochrome c. The proteoglycan molecule appeared as an extended central core filament to which side-chain filaments were attached at various intervals. The molecules from the three sources displayed great ultrastructural similarities. On average, the core filament was about 290 nm long, there were about 25 side-chain filaments per core filament, the side-chain filaments were about 45 nm long, and the distance between the attachment points of the side-chain filaments to the core filament was about 11 nm. With regard to the overall size of the molecules, no evidence of distinct subpopulations was obtained. Good correlation was found between ultrastructural data for the proteoglycan molecules and chemical data obtained by enzyme digestions and gel chromatography. Together these data strongly support the interpretation of the electron-microscopic pictures as indicating a central filament corresponding to the protein core and side-chain filaments corresponding to the chondroitin sulphate chain clusters of the proteoglycan monomers.

POROUS SUBSTRUCTURE OF THE GLOMERULAR SLIT DIAPHRAGM IN THE RAT AND MOUSE

The highly ordered, isoporous substructure of the glomerular slit diaphragm was revealed in rat and mouse kidneys fixed by perfusion with tannic acid and glutaraldehyde. The slit diaphragm was similar in both animal species and appeared as a continuous junctional band, 300–450 Å wide, consistently present within all slits formed by the epithelial foot processes. The diaphragm exhibited a zipper-like substructure with alternating, periodic cross bridges extending from the podocyte plasma membranes to a central filament which ran parallel to and equidistant from the cell membranes. The dimensions and spacing of the cross bridges defined a uniform population of rectangular pores approximately 40 by 140 Å in cross section and 70 Å in length. The total area of the pores was calculated to be about 2–3% of the total surface area of the glomerular capillaries. Physiological data indicate that the glomerular filter functions as if it were an isoporous membrane which excludes proteins larger than serum albumin. The similarity between the dimensions of the pores in the slit diaphragm and estimates for the size and shape of serum albumin supports the conclusion from tracer experiments that the slit diaphragm may serve as the principal filtration barrier to plasma proteins in the kidney.