Membrane geometry of “open” prolamellar bodies

Summary The open type of prolamellar body in etiplasts was examined by electron microscopy to characterise its three-dimensional organisation. As in more compact forms of prolamellar body, its basic geometric unit is a tetrahedrally branched tubule. In the open type, these lie smoothly confluent with one another at the vertices of 5- and 6-membered rings which circumscribe the faces of three kinds of polyhedra: pentagonal dodecahedra (with 12 pentagonal faces), 14-hedra (2 opposite hexagonal faces joined by two circlets of six pentagonal faces), and 15-hedra (3 hexagonal and 12 pentagonal faces). These polyhedra join confluently in their turn, sharing faces with one another in at least one recognisable superstructure which accounts for the appearance of open prolamellar bodies in many ultrathin sections. In this organisation, columns of pentagonal dodecahedra are arranged at 120 ° to one another in the x-y-plane of the lattice. They do not fill the plane but intersect so as to delimit voids in the form of hexagonally arranged 14-hedra (with hexagonal rings in the x-y-plane). Strata of this type alternate with strata made of face-sharing 15-hedra (with their hexagonal rings normal to x-y), which also delimit 14-hedra. The 14-hedra thus lie in register in the z-axis in hexagonally arranged columns, normal to the alternating strata. Other possible organisations cannot be excluded and local variations and dislocations certainly occur, but many micrographs that display elements of symmetry in open prolamellar bodies can be matched to thin slices through such a model. Its geometry is like that of the cages of water molecules in type IV (sensu Jeffrey=type IIIsensu O'Keeffe) clathrate-hydrates, point group P6/mmm, but about two orders of magnitude larger.     

Model for a DNA-mediated synaptic complex suggested by crystal packing of gamma delta resolvase subunits.

The packing arrangement of the 12 subunits of intact gamma delta resolvase in the unit cell of a hexagonal crystal form suggests a model for site-specific recombination that involves a DNA-mediated synaptic intermediate. The crystal structure has been determined by molecular replacement and partially refined at 2.8/3.5 A resolution. Although the small DNA-binding domain is disordered in these crystals, packing considerations show that only a small region of space in the crystal could accommodate a domain of its size. A family of related models for a synaptic complex between two DNA duplexes and 12 monomers that are arranged as situated in the crystal is consistent with the known topology of the complex and the distances between the three resolvase dimer-binding sites per DNA; further, these models place the two DNA recombination sites in contact with each other between two resolvase dimers, implying that strand exchange is accomplished through direct DNA-DNA interaction. A major role postulated, then, for the resolvase protein assembly is to stabilize a res DNA structure that is close to the topological transition state of the reaction.     

Increasing Biomass Production on Limited Land Area Through an Optimal Planting Arrangement

Planting density is a primary consideration in silviculture; however, planting arrangement is often ignored. Most, if not all, forest plantations are arranged in rectangular or square lattices (i.e., grids). Using a simple mathematical model, we investigate the potential influence of planting arrangement on planting density, biomass yield, and rotation period by assuming that efficiently arranging trees is similar to packing congruent circles on a plane. The hexagonal lattice achieves the densest circle packing on a plane; therefore, a hexagonal or triangular lattice arrangement of stems provides the highest planting density for a given spacing. Using packing density to quantify arrangement efficiency, tree crowns in a hexagonal lattice fill approximately 90.7% of available area at initial canopy contact, while tree crowns in a square lattice fill approximately 78.5% of available area at initial canopy contact. The hexagonal lattice permits about a 15% higher density than the square lattice, which allows canopy closure to occur earlier without any change in individual tree growth. Short rotation woody crop (SRWC) systems are excellent candidates under the model’s assumptions of level stand with even-age monoculture. If belowground resources are non-limiting, a hexagonal lattice arrangement shortens rotation period and thus optimizes the biomass yield per land area over time. Higher productivity over time is central to sustainable and efficient use of limited area for bioenergy and biomass products.     

Cross-sectional structure of the central mitotic spindle of Diatoma vulgare. Evidence for specific interactions between antiparallel microtubules

During the transition from prometaphase to metaphase, the cross- sectional area of the central spindle of Diatoma decreases by a factor of nearly two, both at the poles and at the region of overlapping microtubules (MTs) near the spindle equator. The density of spindle MT packing stays approximately constant throughout mitosis. Optical diffraction analysis of electron micrographs shows that the packing of the MTs at the poles at all stages of mitosis is similar to that expected for a two-dimensional liquid. Analysis of the region of overlap reveals more packing regularity: during prometaphase, a square packing emerges that displays sufficient organization by late metaphase to generate five orders of diffraction; during anaphase the packing in the overlap region shifts to hexagonal; at telophase, it returns to square. From the data provided by serial section reconstructions of the central spindle, it is possible to identify the polarity of almost every spindle MT, that is, to identify one pole with which the MT is associated. Near neighbor analyses of MTs in cross sections of the overlap region show that MTs prefer antiparallel near neighbors. These near neighbors are most often found at a spacing of approximately 40 nm center-to-center, while parallel near neighbors in the zone of overlap are spaced essentially at random. These results are evidence for a specific interaction between antiparallel MTs. In some sections definite bridges between MTs can be seen. Our findings show that certain necessary conditions for a sliding filament model of anaphase spindle elongation are met.     

Polymorphic forms of 1,2-dipalmitoyl-sn-glycerol: a combined X-ray and electron diffraction study

Quantitative crystallographic structure analyses are carried out for two polymorphic forms of 1,2-dipalmitoyl-sn-glycerol. A single crystal X-ray determination on the higher melting beta'L-form reveals that the hairpin conformer structure is essentially identical to that of the dilauroyl homolog reported earlier (I. Pascher, S. Sundell and H. Hauser (1981) J. Mol. Biol. 153, 791-806) with inclined acyl chain packing in the O perpendicular methylene subcell. Lamellar electron diffraction intensity data from epitaxially crystallized samples were used to determine the structure of the lower melting alpha L-form. The chains pack in the hexagonal subcell and are perpendicular to the lamellar surface. An appropriately oriented molecular model based on the beta'L-polymorph does not lead to a satisfactory structure solution but models based on the conformationally different 1,2-diglyceride moiety of several phospholipid structures does lead to a closer match to the observed diffraction data. In this proposed packing model for the alpha L-form, the hydroxyl oxygens are somewhat farther away from the unit cell origin than in the beta'L-form crystal structure, and, in combination with the different molecular conformation, this might explain the observed stability of this crystal polymorph against acyl shifts.     

Interaction of collagen with hydrophobic protein granules in the egg capsule of the dogfish scyliorhinus canicula

The egg capsule of the dogfish is a composite material containing collagenous fibrils and 2 mum spherical hydrophobic protein granules. The latter appear to owe much of their hydrophobicity to an exceptionally high tyrosine content (approximately 20% of total amino acid residues). The hydrophobic component appears to form as an emulsion in the secretory granules of the D and E zone gland cells of the nidamental gland. Droplets of the hydrophobic material appear to become coated with remarkably regular layers of radially-arranged collagen molecules which form a series of concentric, evenly spaced layers around each hydrophobic granule. Numerous disclinations were seen where the layers around adjacent granules interfered with one another. The layers are thought to represent a lamellar liquid crystalline phase previously described for this collagen (Knight et al., 1993). The fine structural appearance of the concentric layers and evidence for radial arrangement of collagen molecules within them is compatible with the suggestion that the layers are built from a dumbbell-shaped unit approximately 35 nm long with hydrophobic groups concentrated at the ends. This unit may represent a dumbbell-shaped molecule or an oligomer of two or more molecules lying parallel with one another in a head-to-tail arrangement. Such a unit can be readily incorporated into models for the micellar, hexagonal columnar and final fibrillar phases previously described for this collagen (Knight et al., 1993). Evidence from the TEM study of stretched egg capsule wall suggests that there is a mechanical interaction between the hydrophobic granules and the collagen fibrils in the fully formed material. We suggest that the radial, concentric layered arrangement of collagen molecules is established by hydrophobic interactions within the liquid crystalline material and locked into place by oxidative covalent cross-linking to give a 3-dimensional cross-linked meshwork of collagen fibrils and hydrophobic granules. The latter arrangement helps to account for the high tensilestrength and toughness of this material.     

Crystallization and preliminary crystallographic studies of glucosamine-6-phosphate deaminase from Escherichia coli K12.

Hexameric glucosamine-6-phosphate deaminase from Escherichia coli has been crystallized isomorphously with both phosphate and ammonium sulphate as precipitants, over a wide pH range (6.0 to 9.0). The crystals belong to space group R32 and the cell parameters in the hexagonal setting are a = b = 125.9 A and c = 223.2 A. A complete native data set was collected to 2.1 A resolution. Self-rotation function studies suggest that the hexamers sit on the 3-fold axis and have point group symmetry 32, with a non-crystallographic dyad relating two monomers linked by an interchain disulfide bridge. A possible packing for the unit cell is proposed.     

X-ray diffraction studies on crystalline complexes of the gene 5 DNA-unwinding protein with deoxyoligonucleotides

Complexes of the gene 5 protein with a variety of oligodeoxynucleotides, ranging in length from two to eight and having several different sequences, have been formed and crystallized for x-ray diffraction analysis. The crystallographic parameters of four different unit cells, all of which are based on hexagonal packing arrangements, indicate that the fundamental unit of the complex is composed of 12 gene 5 monomers.     

Two-dimensional crystal packing of matrix porin. A channel forming protein in Escherichia coli outer membranes

Two-dimensional crystalline porin sheets were obtained by reconstitution of monodisperse protein trimers and phospholipids (dimyristoylphosphatidylcholine) by detergent dialysis, analogous to the reconstitution method used for functional tests (Schindler & Rosenbusch, 1981). Three different packing arrangements were observed: two were hexagonal (with p3 symmetry and lattice constants of 9.3 nm and 7.9 nm), and one rectangular (a = 7.9 nm, b = 13.9 nm). The different crystals could be correlated to phospholipid-to-protein weight ratios of 0.16 to 0.72. At the higher ratio, large hexagonal lattices predominated. Higher lipid ratios did not reveal other crystal forms. The packing arrangement of the large hexagonal form appears very similar to the hexagonal habit of three-dimensional crystal forms (Garavito et al., 1983). The shape of the stain-penetrated triplet indentations appeared conserved in the crystal forms to a resolution of 2.2 nm. The mass distribution between triplets, however, were significantly different. They are likely to correspond primarily to lipids. Mass determinations of unstained porin by scanning transmission electron microscopy showed that unit cells consisted of single trimers. The mass found (100,000 daltons) is in good agreement with the value obtained by sedimentation equilibrium analysis.     

Preliminary molecular replacement results for a crystalline gene 5 protein–deoxyoligonucleotide complex

Complexes of the gene 5 protein from bacteriophage fd with a variety of oligodeoxynucleotides, ranging in length from two to eight and comprised of several different sequences, have been formed and crystallized for X-ray diffraction analysis. The crystallographic parameters of four different unit cells, all of which are based on hexagonal packing arrangements, indicate that the fundamental unit of the complex is composed of six gene 5 protein dimers. We believe this aggregate has 622 point group symmetry and is a ring formed by end-to-end closure of a linear array of six dimers. From our results we have proposed a double-helix model for the gene 5 protein–DNA complex in which the protein forms a spindle or core around which the DNA is spooled. Currently 5.0-Å X-ray diffraction data from one of the crystalline complexes is being analyzed by molecular replacement techniques to obtain a direct image of the protein–nucleic acid complex.     

The intermolecular space of reconstituted collagen fibrils

The extent, geometry and heterogeneity of the intermolecular space of hydrated, purified and reconstituted steer skin collagen fibrils has been characterized. The extent of the space has been assessed experimentally by an X-ray diffraction method and a new physical chemical technique, and found to be 1.14 ml per gram collagen. A theoretical model relating the intermolecular space to X-ray diffraction parameters has been presented, and this suggests that the geometry of the intermolecular space arises from a near-hexagonal packing of the collagen molecules. On the basis of an assumed microfibrillar packing model and a geometric construction of the shape of a collagen molecule, the distribution of the space within reconstituted collagen fibrils has been characterized as follows: 0.13 ml of the intermolecular space/g collagen can be attributed to the helical groove of the collagen molecules per se and 1.01 ml/g is interstitial; 0.66 ml/g is present in the form of “pores” (hexagonally-closed packed spaces), whereas 0.48 ml/g is present in the form of “holes” (hexagonal volume defects); 0.73 ml/g of the intermolecular space is associated with a region of the collagen fibrils where holes are localized and 0.41 ml/g is attributable to the regions of the fibril in which pores only are present.     

How environment geometry affects grid cell symmetry and what we can learn from it

The mammalian hippocampal formation provides neuronal representations of environmental location but the underlying mechanisms are unclear. The majority of cells in medial entorhinal cortex and parasubiculum show spatially periodic firing patterns. Grid cells exhibit hexagonal symmetry and form an important subset of this more general class. Occasional changes between hexagonal and non-hexagonal firing patterns imply a common underlying mechanism. Importantly, the symmetrical properties are strongly affected by the geometry of the environment. Here, we introduce a field–boundary interaction model where we demonstrate that the grid cell pattern can be formed from competing place-like and boundary inputs. We show that the modelling results can accurately capture our current experimental observations.     

Molecular blending by polymerization of intercalated solvent. Poly(gamma-benzyl-L-glutamate)/benzyl methacrylate as a model system

The aim of the present research is to obtain blending between a polymer and a (polymerized) solvent on the molecular level. Because of its rigid rod structure, poly(gamma-benzyl-L-glutamate) (PBLG) is chosen as the polymer. Benzyl methacrylate (BzMA) has been chosen as the solvent for two reasons. First, the structure of the solvent is very similar to the structure of the side chain of PBLG, favoring interactions between the two materials. Second, the solvent can be polymerized, because of the presence of a C=C bond. In cast films of PBLG and BzMA separate zones of the polymer and solvent are present. Wide-angle X-ray diffraction and Raman results show that upon heating the cast films homogenization occurs and solvent molecules intercalate between the helices of PBLG. At 150 degrees C a hexagonal packing is obtained. The dimensions of the obtained packing depend on the solvent concentration, which confirms that solvent molecules are indeed present within the crystalline lattice. DSC experiments imply that the observed changes upon heating correspond to thermodynamic processes. On cooling the homogeneous samples, disordering of the hexagonal packing occurs. Polymerization of the homogeneous samples results in a disordering of the hexagonal packing and in a contraction of the unit cell. The latter once more confirms that solvent molecules are indeed present within the crystalline lattice. The applied principle of polymerization of a solvent in a molecular homogeneous system can be favorable for many applications, for which morphology control at the molecular level is required.     

LOW RESISTANCE JUNCTIONS IN CRAYFISH : II. Structural Details and Further Evidence for Intercellular Channels by Freeze-Fracture and Negative Staining

Low resistance junctions between axons of crayfish ganglia are studied by freeze-fracture and negative staining. In freeze-fracture, fracture planes that go through a junctional membrane expose two faces, both internal, called face A and face B. Face A belongs to the internal membrane leaflet and faces the gap. Face B belongs to the external membrane leaflet and faces the axoplasm. Face A displays pits, 60–100 Å in diameter, arranged in a hexagonal array with a unit cell of ~200 Å. An ~25 Å bump is frequently seen at the center of each pit. Some pits are occupied by a globule ~125 Å in diameter, which displays a central depression ~25 Å in size. Face B contains globules also arranged in a fairly regular hexagonal pattern. The center-to-center distance between adjacent globules is most frequently ~200 Å; however, occasionally certain globules are seen separated by a distance as short as ~125 Å. The top surface of the globules occasionally displays a starlike profile and seems to contain a central depression ~25 Å in diameter. In negatively stained preparations of membranes from the nerve cord, two types of membranes are seen containing a fairly regular pattern. In one, globules ~95 Å in diameter form a hexagonal close packing with a unit cell of ~95 Å. In the other, globules of the same size are organized in a larger hexagonal array with a unit cell of ~155 Å (swollen arrangement). Some of the globules forming the swollen arrangement are seen containing six subunits. The six subunits form a hexagon which is skewed with respect to the main rows of hexagons in such a way that the subunits lie on rows which make an angle of ~37° with the main rows.     

An algorithmic approach to modelling the retinal receptor topography

Based on published research results on the structure of the human retina and the initial assumption of tight hexagonal packing of cones, the mean cone-distance function is derived. Disorder in the cone lattice is explained as the superposition of increasing topological distortion in the hexagonal lattice (providing a possible explanation for observed systematic lattice distortions) and local jitter of neighbor-toneighbor distances, for which a simple statistical model is provided. These individual results are incorporated into a proposed algorithm for simulating the cone receptors' topography in 3D-space. Finally, possible software and hardware applications of the algorithmically defined retina model are briefly touched.     

Radial packing, order, and disorder in collagen fibrils.

Collagen fibrils resemble smectic, liquid crystals in being highly ordered axially but relatively disordered laterally. In some connective tissues, x-ray diffraction reveals three-dimensional crystallinity in the molecular packing within fibrils, although the continued presence of diffuse scatter indicates significant underlying disorder. In addition, several observations from electron microscopy suggest that the molecular packing is organized concentrically about the fibril core. In the present work, theoretical equatorial x-ray diffraction patterns for a number of models for collagen molecular packing are calculated and compared with the experimental data from tendon fibrils. None of the models suggested previously can account for both the crystalline Bragg peaks and the underlying diffuse scatter. In addition, models in which any of the nearest-neighbor, intermolecular vectors are perpendicular to the radial direction are inconsistent with the observed radial orientation of the principal approximately 4 nm Bragg spacing. Both multiple-start spiral and concentric ring models are devised in which one of the nearest-neighbor vectors is along the radial direction. These models are consistent with the radial orientation of the approximately 4 nm spacing, and energy minimization results in radially oriented crystalline domains separated by disordered grain boundaries. Theoretical x-ray diffraction patterns show a combination of sharp Bragg peaks and underlying diffuse scatter. Close agreement with the observed equatorial diffraction pattern is obtained. The concentric ring model is consistent with the observation that the diameters of collagen fibrils are restricted to discrete values.     

Crystal structure of a tripeptide,L-alanyl-glycyl-glycine and its relevance to the poly(glycine)-II type of conformation

A tripeptide molecule, L -alanyl-glycyl-glycine, crystallizes in the form of a left-handed helix with (?,ψ) = ?83°, 170°. A pseudohexagonal packing arrangement and interchain hydrogen-bonded interactions are reminiscent of the model for the structure of poly(glycine)-II. Observations of certain intermolecular interactions appear to be relevant to the stereochemical assumptions incorporated in the models proposed for poly(glycine)-II and related polypeptides.     

Topological solution for cell proliferation in intestinal crypt. I. Elastic growth without cell loss

The cells of an intestinal crypt are tightly packed and, consequently, cell renewal must proceed in accordance with topological laws implicit in the hexagonal cell patterns. The division wave is proposed as the simplest way of proliferation, satisfying topological requirements in steady state. Six pentagonal cells, persisting by topological necessity in the crypt bottom, are the sources of division waves for the whole crypt. The positions of the six pentagonal cells specify the order of cell division. The division, reciprocally, changes the positions of the pentagons which, in turn, specify the order of division in the new cells, and so on. The resulting order of cell division accounts for maintenance of the crypt structure, cell movement toward the villus and cessation of division. Since the pattern of elastic growth is dictated entirely by topological considerations, it does not depend on the genetic constitution of the organism. This model is different from conventional models in which the crypt is assumed to be composed of fixed longitudinal cell columns, the cells of the bottom contributing collectively to the proliferative potential of the whole crypt.     

Conformational flexibility and crystallization of tandemly linked type III modules of human fibronectin.

Fibronectin is a large cell adhesion molecule that is composed of several functional domains. The cell-binding domain that binds to cell surface integrins consists of repeated homologous type III modules. In this study, recombinant fragments from the cell-binding domain of human fibronectin that participate in a newly characterized fibronectin-fibronectin interaction with FNIII1 were crystallized. In each case, the crystals had more than one fibronectin fragment in the asymmetric unit. Crystals of FNIII10-11 grew in the space group C2 with a = 117.1 A, b = 38.6 A, c = 80.6 A, beta = 97.2 degrees, and two molecules in the asymmetric unit. These crystals diffracted to 2.5 A resolution. Fragment FNIII8-11 and a shorter fragment, FNIII8-10, crystallized in hexagonal space groups with large unit cells and two to four molecules per asymmetric unit. Even very large crystals of these fragments did not diffract beyond 4 A. The crystal packing for this collection of fibronectin fragments suggests conformational flexibility between linked type III modules. The functional relevance of this flexibility for elongated versus compact models of the cell-binding domain of fibronectin is discussed.     

Crystalline fibril structure of type II collagen in lamprey notochord sheath

We report here the existence of a crystalline molecular packing of type II collagen in the fibrils of the lamprey notochord sheath. This is the first finding of a crystalline structure in any collagen other than type I.The lamprey notochord sheath has a composition similar to that of cartilage, with type II collagen, a minor collagen component with 1α, 2α and 3α chains, and cartilage-like proteoglycan. The high degree of orientation of fibrils in the notochord makes it possible to use X-ray diffraction to determine collagen fibril organization in this type II-containing tissue. The low angle equatorial scattering shows the fibrils are all about 17 nm in diameter and have an average center-to-center separation of 31 nm. These results are supported by electron microscope observations. A set of broad equatorial diffraction maxima at higher angles represents the sampling of the collagen molecular transform by a limited crystalline lattice, extending over a lateral dimension close to the diameter of one fibril. This indicates that each 17 nm fibril contains a crystalline array of molecules and, although a unit cell is difficult to determine because of the broad overlapping reflections, it is clear that the quasi-hexagonal triclinic unit cell of type I collagen in rat tail tendon is not consistent with the data. The meridional diffraction pattern showed 26 orders with the characteristic 67 nm periodicity found for tendon. However, the intensities of these reflections differ markedly from those found for tendon and cannot be explained by an unmodified gap/ overlap model within each 67 nm period. Both X-ray diffraction and electron microscope data indicate a low degree of contrast along the fibril axis and are consistent with a periodic binding of a non-collagenous component in such a way as to obscure the gap region.