Three-dimensional hydrogen-bonded structures in the 1:1 proton-transfer compounds of L-tartaric acid with the associative-group monosubstituted pyridines 3-minopyridine, 3-carboxypyridine (nicotinic acid) and 2-carboxypyridine (picolinic acid).

The 1:1 proton-transfer compounds of L-tartaric acid with 3-aminopyridine [3-aminopyridinium hydrogen (2R,3R)-tartrate dihydrate, C5H7N2+·C4H5O6-·2H2O, (I)], pyridine-3-carboxylic acid (nicotinic acid) [anhydrous 3-carboxypyridinium hydrogen (2R,3R)-tartrate, C6H6NO2+·C4H5O6-, (II)] and pyridine-2-carboxylic acid [2-carboxypyridinium hydrogen (2R,3R)-tartrate monohydrate, C6H6NO2+·C4H5O6-·H2O, (III)] have been determined. In (I) and (II), there is a direct pyridinium-carboxyl N+-HO hydrogen-bonding interaction, four-centred in (II), giving conjoint cyclic R12(5) associations. In contrast, the N-HO association in (III) is with a water O-atom acceptor, which provides links to separate tartrate anions through Ohydroxy acceptors. All three compounds have the head-to-tail C(7) hydrogen-bonded chain substructures commonly associated with 1:1 proton-transfer hydrogen tartrate salts. These chains are extended into two-dimensional sheets which, in hydrates (I) and (III) additionally involve the solvent water molecules. Three-dimensional hydrogen-bonded structures are generated via crosslinking through the associative functional groups of the substituted pyridinium cations. In the sheet struture of (I), both water molecules act as donors and acceptors in interactions with separate carboxyl and hydroxy O-atom acceptors of the primary tartrate chains, closing conjoint cyclic R44(8), R34(11) and R33(12) associations. Also, in (II) and (III) there are strong cation carboxyl-carboxyl O-HO hydrogen bonds [OO = 2.5387 (17) Å in (II) and 2.441 (3) Å in (III)], which in (II) form part of a cyclic R22(6) inter-sheet association. This series of heteroaromatic Lewis base-hydrogen L-tartrate salts provides further examples of molecular assembly facilitated by the presence of the classical two-dimensional hydrogen-bonded hydrogen tartrate or hydrogen tartrate-water sheet substructures which are expanded into three-dimensional frameworks via peripheral cation bifunctional substituent-group crosslinking interactions.

Hydrate stabilization in the three-dimensional hydrogen-bonded structure of the brucinium compound, bis(2,3-dimethoxy-10-oxostrychnidinium) biphenyl-4,4'-disulfonate hexahydrate

The crystal structure of the 2:1 proton-transfer compound of brucine with biphenyl-4,4’-disulfonate, bis(2,3-dimethoxy-10-oxostrychnidinium) biphenyl-4,4'-disulfonate hexahydrate (1) has been determined at 173 K. Crystals are monoclinic, space group P21 with Z = 2 in a cell with a = 8.0314(2), b = 29.3062(9), c = 12.2625(3) Å, β = 101.331(2)o. The crystallographic asymmetric unit comprises two brucinium cations, a biphenyl-4,4'-disulfonate dianion and six water molecules of solvation. The brucinium cations form a variant of the common undulating and overlapping head-to-tail sheet sub-structure. The sulfonate dianions are also linked head-to-tail by hydrogen bonds into parallel zig-zag chains through clusters of six water molecules of which five are inter-associated, featuring conjoint cyclic eight-membered hydrogen-bonded rings [graph sets R33(8) and R34(8)], comprising four of the water molecules and closed by sulfonate O-acceptors. These chain structures occupy the cavities between the brucinium cation sheets and are linked to them peripherally through both brucine N+-H...Osulfonate and Ocarbonyl…H-Owater to sulfonate O bridging hydrogen bonds, forming an overall three-dimensional framework structure. This structure determination confirms the importance of water in the stabilization of certain brucine compounds which have inherent crystal instability.

A new class of three dimensional D-pi-A trigonal cryptand derivatives for second-order nonlinear optics

Synthesis, crystal structures, linear and nonlinear optical properties of tris D-pi-A cryptand derivatives with C-3 symmetry are reported. Three fold symmetry inherent in the cryptand molecules has been utilized for designing these molecules. Molecular nonlinearities have been measured by hyper-Rayleigh scattering (HRS) experiments. Among the compounds studied, L-1 adopts non-centrosymmetric crystal structure. Compounds L-1, L-2, L-3 and L-4 show a measurable SHG powder signal. These molecules are more isotropic and have significantly higher melting points than the classical p-nitroaniline based dipolar NLO compounds, making them useful for further device applications. Besides, different acceptor groups can be attached to the cryptand molecules to modulate their NLO properties.

Structural and mechanistic motifs in membrane proteins: the three-dimensional modelling of rhodopsin, band 3, and the nicotinic acetylcholine receptor

Because so little is known about the structure of membrane proteins, an attempt has been made in this work to develop techniques by which to model them in three dimensions. The procedures devised rely heavily upon the availability of several sequences of a given protein. The modelling procedure is composed of two parts. The first identifies transmembrane regions within the protein sequence on the basis of hydrophobicity, β-turn potential, and the presence of certain amino acid types, specifically, proline and basic residues. The second part of the procedure arranges these transmembrane helices within the bilayer based upon the evolutionary conservation of their residues. Conserved residues are oriented toward other helices and variable residues are positioned to face the surrounding lipids. Available structural information concerning the protein's helical arrangement, including the lengths of interhelical loops, is also taken into account. Rhodopsin, band 3, and the nicotinic acetylcholine receptor have all been modelled using this methodology, and mechanisms of action could be proposed based upon the resulting structures.

Specific residues in the rhodopsin and iodopsin sequences were identified, which may regulate the proteins' wavelength selectivities. A hinge-like motion of helices M3, M4, and M5 with respect to the rest of the protein was proposed to result in the activation of transducin, the G-protein associated with rhodopsin. A similar mechanism is also proposed for signal transduction by the muscarinic acetylcholine and β-adrenergic receptors.

The nicotinic acetylcholine receptor was modelled with four trans-membrane helices per subunit and with the five homologous M2 helices forming the cation channel. Putative channel-lining residues were identified and a mechanism of channel-opening based upon the concerted, tangential rotation of the M2 helices was proposed.

Band 3, the anion exchange protein found in the erythrocyte membrane, was modelled with 14 transmembrane helices. In general the pathway of anion transport can be viewed as a channel composed of six helices that contains a single hydrophobic restriction. This hydrophobic region will not allow the passage of charged species, unless they are part of an ion-pair. An arginine residue located near this restriction is proposed to be responsible for anion transport. When ion-paired with a transportable anion it rotates across the barrier and releases the anion on the other side of the membrane. A similar process returns it to its original position. This proposed mechanism, based on the three-dimensional model, can account for the passive, electroneutral, anion exchange observed for band 3. Dianions can be transported through a similar mechanism with the additional participation of a histidine residue. Both residues are located on M10.

Three-dimensional graphene-Co3O4 cathodes for rechargeable Li-O2 batteries

A three-dimensional (3D) graphene-Co₃O₄ electrode was prepared by a two-step method in which graphene was initially deposited on a Ni foam with Co₃O₄ then grown on the resulting graphene structure. Cross-linked Co₃O₄ nanosheets with an open pore structure were fully and vertically distributed throughout the graphene skeleton. The free-standing and binder-free monolithic electrode was used directly as a cathode in a Li-O₂ battery. This composite structure exhibited enhanced performance with a specific capacity of 2453 mA h g^-1 at 0.1 mA cm^-2 and 62 stable cycles with 583 mA h g^-1 (1000 mA h g_carbon^-1). The excellent electrochemical performance is associated with the unique architecture and superior catalytic activity of the 3D electrode. 

Modeling corneal surfaces with three-dimensional basis functions

Purpose: To ascertain the effectiveness of object-centered three-dimensional representations for the modeling of corneal surfaces. Methods: Three-dimensional (3D) surface decomposition into series of basis functions including: (i) spherical harmonics, (ii) hemispherical harmonics, and (iii) 3D Zernike polynomials were considered and compared to the traditional viewer-centered representation of two-dimensional (2D) Zernike polynomial expansion for a range of retrospective videokeratoscopic height data from three clinical groups. The data were collected using the Medmont E300 videokeratoscope. The groups included 10 normal corneas with corneal astigmatism less than −0.75 D, 10 astigmatic corneas with corneal astigmatism between −1.07 D and 3.34 D (Mean = −1.83 D, SD = ±0.75 D), and 10 keratoconic corneas. Only data from the right eyes of the subjects were considered. Results: All object-centered decompositions led to significantly better fits to corneal surfaces (in terms of the RMS error values) than the corresponding 2D Zernike polynomial expansions with the same number of coefficients, for all considered corneal surfaces, corneal diameters (2, 4, 6, and 8 mm), and model orders (4th to 10th radial orders) The best results (smallest RMS fit error) were obtained with spherical harmonics decomposition which lead to about 22% reduction in the RMS fit error, as compared to the traditional 2D Zernike polynomials. Hemispherical harmonics and the 3D Zernike polynomials reduced the RMS fit error by about 15% and 12%, respectively. Larger reduction in RMS fit error was achieved for smaller corneral diameters and lower order fits. Conclusions: Object-centered 3D decompositions provide viable alternatives to traditional viewer-centered 2D Zernike polynomial expansion of a corneal surface. They achieve better fits to videokeratoscopic height data and could be particularly suited to the analysis of multiple corneal measurements, where there can be slight variations in the position of the cornea from one map acquisition to the next.

Three-dimensional hydrogen-bonded structures in the guanidinium salts of the monocyclic dicarboxylic acids rac-trans-cyclohexane-1,2-dicarboxylic acid (2:1, anhydrous), isophthalic acid (1:1, monohydrate) and terephthalic acid (2:1, trihydrate).

The structures of bis(guanidinium)rac-trans-cyclohexane-1,2-dicarboxylate, 2(CH6N3+) C8H10O4- (I), guanidinium 3-carboxybenzoate monohydrate CH6N3+ C8H5O4- . H2O (II) and bis(guanidinium) benzene-1,4-dicarboxylate trihydrate, 2(CH6N3+) C8H4O4^2- . 3H2O (III) have been determined and the hydrogen bonding in each examined. All three compounds form three-dimensional hydrogen-bonded framework structures. In anhydrous (I), both guanidinium cations give classic cyclic R2/2(8) N--H...O,O'(carboxyl) and asymmetric cyclic R1/2(6) hydrogen-bonding interactions while one cation gives an unusual enlarged cyclic interaction with O acceptors of separate ortho-related carboxyl groups [graph set R2/2(11)]. Cations and anions also associate across inversion centres giving cyclic R2/4(8) motifs. In the 1:1 guanidinium salt (II), the cation gives two separate cyclic R1/2(6) interactions, one with a carboxyl O-acceptor, the other with the water molecule of solvation. The structure is unusual in that both carboxyl groups give short inter-anion O...H...O contacts, one across a crystallographic inversion centre [2.483(2)\%A], the other about a two-fold axis of rotation [2.462(2)\%A] with a half-occupancy hydrogen delocalized on the symmetry element in each. The water molecule links the cation--anion ribbon structures into a three-dimensional framework. In (III), the repeating molecular unit comprises a benzene-1,4-dicarboxylate dianion which lies across a crystallographic inversion centre, two guanidinium cations and two water molecules of solvation (each set related by two-fold rotational symmetry), and a single water molecule which lies on a two-fold axis. Each guanidinium cation gives three types of cyclic interactions with the dianions: one R^1^~2~(6), the others R2/3(8) and R3/3(10) (both of these involving the water molecules), giving a three-dimensional structure through bridges down the b cell direction. The water molecule at the general site also forms an unusual cyclic R2/2(4) homodimeric association across an inversion centre [O--H...O, 2.875(2)\%A]. The work described here provides further examples of the common cyclic guanidinium cation...carboxylate anion hydrogen-bonding associations as well as featuring other less common cyclic motifs.

Investigating the change in three dimensional deformity for idiopathic scoliosis using axially loaded MRI

Background: Adolescent idiopathic scoliosis is a complex three-dimensional deformity, involving a lateral deformity in the coronal plane and axial rotation of the vertebrae in the transverse plane. Gravitational loading plays an important biomechanical role in governing the coronal deformity, however, less is known about how they influence the axial deformity. This study investigates the change in three-dimensional deformity of a series of scoliosis patients due to compressive axial loading. Methods: Magnetic resonance imaging scans were obtained and coronal deformity (measured using the coronal Cobb angle) and axial rotations measured for a group of 18 scoliosis patients (Mean major Cobb angle was 43.4 o). Each patient was scanned in an unloaded and loaded condition while compressive loads equivalent to 50% body mass were applied using a custom developed compressive device. Findings: The mean increase in major Cobb angle due to compressive loading was 7.4 o (SD 3.5 o). The most axially rotated vertebra was observed at the apex of the structural curve and the largest average intravertebral rotations were observed toward the limits of the coronal deformity. A level-wise comparison showed no significant difference between the average loaded and unloaded vertebral axial rotations (intra-observer error = 2.56 o) or intravertebral rotations at each spinal level. Interpretation: This study suggests that the biomechanical effects of axial loading primarily influence the coronal deformity, with no significant change in vertebral axial rotation or intravertebral rotation observed between the unloaded and loaded condition. However, the magnitude of changes in vertebral rotation with compressive loading may have been too small to detect given the resolution of the current technique.

Alternating direction implicit numerical method for the space and time fractional Bloch-Torrey equation in 3-D

Recently, some authors have considered a new diffusion model–space and time fractional Bloch-Torrey equation (ST-FBTE). Magin et al. (2008) have derived analytical solutions with fractional order dynamics in space (i.e., _ = 1, β an arbitrary real number, 1 < β ≤ 2) and time (i.e., 0 < α < 1, and β = 2), respectively. Yu et al. (2011) have derived an analytical solution and an effective implicit numerical method for solving ST-FBTEs, and also discussed the stability and convergence of the implicit numerical method. However, due to the computational overheads necessary to perform the simulations for nuclear magnetic resonance (NMR) in three dimensions, they present a study based on a two-dimensional example to confirm their theoretical analysis. Alternating direction implicit (ADI) schemes have been proposed for the numerical simulations of classic differential equations. The ADI schemes will reduce a multidimensional problem to a series of independent one-dimensional problems and are thus computationally efficient. In this paper, we consider the numerical solution of a ST-FBTE on a finite domain. The time and space derivatives in the ST-FBTE are replaced by the Caputo and the sequential Riesz fractional derivatives, respectively. A fractional alternating direction implicit scheme (FADIS) for the ST-FBTE in 3-D is proposed. Stability and convergence properties of the FADIS are discussed. Finally, some numerical results for ST-FBTE are given.

Collective dynamics and control of a 3-D small-world network with time delays

The paper presents a detailed analysis on the collective dynamics and delayed state feedback control of a three-dimensional delayed small-world network. The trivial equilibrium of the model is first investigated, showing that the uncontrolled model exhibits complicated unbounded behavior. Then three control strategies, namely a position feedback control, a velocity feedback control, and a hybrid control combined velocity with acceleration feedback, are then introduced to stabilize this unstable system. It is shown in these three control schemes that only the hybrid control can easily stabilize the 3-D network system. And with properly chosen delay and gain in the delayed feedback path, the hybrid controlled model may have stable equilibrium, or periodic solutions resulting from the Hopf bifurcation, or complex stranger attractor from the period-doubling bifurcation. Moreover, the direction of Hopf bifurcation and stability of the bifurcation periodic solutions are analyzed. The results are further extended to any "d" dimensional network. It shows that to stabilize a "d" dimensional delayed small-world network, at least a "d – 1" order completed differential feedback is needed. This work provides a constructive suggestion for the high dimensional delayed systems.

A simple method for fabricating 3-D multilayered composite scaffolds

One limitation of electrospinning stems from the charge build-up that occurs during processing, preventing further fibre deposition and limiting the scaffold overall thickness and hence their end-use in tissue engineering applications targeting large tissue defect repair. To overcome this, we have developed a technique in which thermally induced phase separation (TIPS) and electrospinning are combined. Thick three-dimensional, multilayered composite scaffolds were produced by simply stacking individual polycaprolactone (PCL) microfibrous electrospun discs into a cylindrical holder that was filled with a 3% poly(lactic-co-glycolic acid) (PLGA) solution in dimethylsulfoxide (a good solvent for PLGA but a poor one for PCL). The construct was quenched in liquid nitrogen and the solvent removed by leaching out in cold water. This technique enables the fabrication of scaffolds composed principally of electrospun membranes that have no limit to their thickness. The mechanical properties of these scaffolds were assessed under both quasi-static and dynamic conditions. The multilayered composite scaffolds had similar compressive properties to 5% PCL scaffolds fabricated solely by the TIPS methodology. However, tensile tests demonstrated that the multilayered construct outperformed a scaffold made purely by TIPS, highlighting the contribution of the electrospun component of the composite scaffold to enhancing the overall mechanical property slate. Cell studies revealed cell infiltration principally from the scaffold edges under static seeding conditions. This fabrication methodology permits the rapid construction of thick, strong scaffolds from a range of biodegradable polymers often used in tissue engineering, and will be particularly useful when large dimension electrospun scaffolds are required.

Hydrogen-bonded two- and three-dimensional polymeric structures in the ammonium salts of 3,5-dinitrobenzoic acid, 4-nitrobenzoic acid and 2,4-dichlorobenzoic acid

The structures of the ammonium salts of 3,5-dinitrobenzoic acid, NH4+ C7H3N2O6- (I), 4-nitrobenzoic acid, NH4+ C7H4N2O4- . 2H2O (II) and 2,4-dichlorobenzoic acid, NH4+ C7H3Cl2O2- . 0.5H2O (III), have been determined and their hydrogen-bonded structures are described. All salts form hydrogen-bonded polymeric structures, three-dimensional in (I) and two-dimensional in (II) and (III). With (I), a primary cation-anion cyclic association is formed [graph set R3/4(10)] through N-H...O hydrogen bonds, involving a carboxyl O,O' group on one side and a single carboxyl O-atom on the other. Structure extension involves both N-H...O hydrogen bonds to both carboxyl and nitro O-atom acceptors. With structure (II), the primary inter-species interactions and structure extension into layers lying parallel to (0 0 1) are through conjoined cyclic hydrogen-bonding motifs: R3/4(10) [one cation, a carboxyl (O,O') group and two water molecules] and centrosymmetric R2/4(8) [two cations and two water molecules]. The structure of (III) also has conjoined R3/4(10) and centrosymmetric R2/4(8) motifs in the layered structure but these differ in that he first involves one cation, a carboxyl (O,O') as well as a carboxyl (O) group and one water molecule, the second, two cations and two carboxyl O-groups. The layers lie parallel to (1 0 0). The structures of the salt hydrates (II) and (III) reported in this work, giving two-dimensional layered arrays through conjoined hydrogen-bonded nets provide further illustrations of a previously indicated trend among ammonium salts of carboxylic acids, but the anhydrous three-dimensional structure of (I) is inconsistent.

Automated fit quantification of tibial nail designs during the insertion using computer three-dimensional modelling

Intramedullary nailing is the standard fixation method for displaced diaphyseal fractures of the tibia. An optimal nail design should both facilitate insertion and anatomically fit the bone geometry at its final position in order to reduce the risk of stress fractures and malalignments. Due to the nonexistence of suitable commercial software, we developed a software tool for the automated fit assessment of nail designs. Furthermore, we demonstrated that an optimised nail, which fits better at the final position, is also easier to insert. Three-dimensional models of two nail designs and 20 tibiae were used. The fitting was quantified in terms of surface area, maximum distance, sum of surface areas and sum of maximum distances by which the nail was protruding into the cortex. The software was programmed to insert the nail into the bone model and to quantify the fit at defined increment levels. On average, the misfit during the insertion in terms of the four fitting parameters was smaller for the Expert Tibial Nail Proximal bend (476.3 mm2, 1.5 mm, 2029.8 mm2, 6.5 mm) than the Expert Tibial Nail (736.7 mm2, 2.2 mm, 2491.4 mm2, 8.0 mm). The differences were statistically significant (p ≤ 0.05). The software could be used by nail implant manufacturers for the purpose of implant design validation.

Strategies for three dimensional deployment of tethered satellites

Tethered satellites deployed from the Space Shuttle have been proposed for diverse applications. A funda- mental issue in the utilization of tethers is quick deployment and retrieval of the attached payload. Inordinate librations of the tether during deployment and retrieval is undesirable. The structural damping present in the system is too low to contain the librations. Rupp [1] proposed to control the tether reel located in the parent spacecraft to alter the tension in the tether, which in turn changes the stiffness and the damping of the system. Baker[2] applied the tension control law to a model which included out of plane motion. Modi et al.[3] proposed a control law that included nonlinear feedback of the out-of plane tether angular rate. More recently, nonlinear feedback control laws based on Liapunov functions have been proposed. Two control laws are derived in [4]. The first is based on partial decomposition of the equations of motion and utilization of a two dimensional control law developed in [5]. The other is based on a Liapunov function that takes into consideration out-of-plane motion. It is shown[4] that the control laws are effective when used in conjunction with out-of-plane thrusting. Fujii et al.,[6] used the mission function control approach to study the control law including aerodynamic drag effect explicitly into the control algorithm.

Three-dimensional 3d-4f heterometallic polymers containing both azide and carboxylate as co-ligands

The hydrothermal reaction of Ln(NO3)(3), Ni(NO3)(2), NaN3, and isonicotinic acid (L) yielded two novel 3-D coordination frameworks (1 and 2) of general formula [Ni(2)Ln(L)(5)(N-3)(2)(H2O)(3)] center dot 2H(2)O (Ln = Pr(III) for 1 and Nd(III) for 2), containing Ni-Pr or Ni-Nd hybrid extended three-dimensional networks containing both azido and carboxylate as co-ligands. Both the compounds are found to be isostructural and crystallize in monoclinic system having P2(1)/n space group. Here the lanthanide ions are found to be nonacoordinated. Both bidentate and monodentate modes of binding of the carboxylate with the lanthanides have been observed in the above complexes. Variable temperature magnetic studies of the above two complexes have been investigated in the temperature range 2-300 K which showed dominant antiferromagnetic interaction in both the cases and these experimental results are analyzed with the theoretical models. (c) 2008 Elsevier B.V. All rights reserved.