Definitions and nomenclature of nucleic acid structure parameters

At an EMBO Workshop on DNA Curvature and Bending, held at Churchill College, Cambridge, on 10-15 September 1988, two sessions were scheduled on definitions of parameters used to describe the geometry of nucleic acid chains and helices, and a common nomenclature for these parameters. The most widely used library of helix analysis programs, HELIB (Fratini et al., 1982; Dickerson, 1985) suffers from the fact that the translations and rotations as defined are not fully independent and depend to a certain extent upon the choice of overall helix axis. Several research groups have been engaged independently in developing alternative programs for the geometrical analysis of polynucleotide chains, but with different definitions of quantities calculated and with widely different nomenclature even when the same parameter was involved.

Behaviour of the curve of critical exponents near and away from a double critical point

To investigate the nature of the curve of critical exponents (as a function of the distance from a double critical point), we have combined our measurements of the osmotic compressibility with all published data for quasibinary liquid mixtures. This curve has a parabolic shape. An explanation of this result is advanced in terms of the geometry of the coexistence dome, which is contained in a triangular prism.

Crystal structures, spectral and magnetic properties of (µ-hydroxo)(µ-acetato)dicopper(II) complexes containing chelating amines

The reaction of [Cu2(O2CMe)4(H2O)2] with N, N, N′, N′-tetramethylethane- 1,2-diamine (tmen) in ethanol yielded the dicopper(II) complex [Cu2(OH)(O2CMe)(tmen)2][ClO4]21. A similar reaction with N, N- dimethylethane- 1,2-diamine (dmen) afforded a crystalline product 2 in which two dicopper(II) complexes, [Cu2(OH)(O2CMe)(dmen)2][ClO4]22a and [Cu2(OH)(O2CMe)(H2O)2(dmen)2][ClO4]22b, are cocrystallized in a 1 : 1 molar ratio along with 2NaClO4. The crystal structures of 1 and 2 have been determined. The complexes have an asymmetrically dibridged [Cu2(µ-OH)(µ-O2CMe)]2+ core. The co-ordination geometry of the metal is square planar (CuO2N2). The copper atoms in 2b have a square-pyramidal CuO3N2 co-ordination sphere. The Cu Cu distances and Cu–O–Cu angles in 1, 2a and 2b are 3.339(2), 3.368(3), 3.395(7)Å, 120.1(2), 116.4(1) and 123.6(2)°, respectively. Complex 1 exhibits an axial ESR spectrum in a methanol glass giving g∥= 2.26 (A∥= 164 × 10–4 cm–1) and g⊥= 2.04. The ESR spectra obtained from the bulk material of the dmen product are indicative of the presence of two dimers, viz. complex 2a(g∥= 2.25, A∥= 165 × 10–4 cm–1; g⊥= 2.03) and 2b(g∥= 2.19, A∥= 184 × 10–4 cm–1; g⊥= 2.0). Variable-temperature magnetic susceptibility measurements on these complexes show an intramolecular antiferromagnetic coupling in the dimeric core. The fitting parameters are J=–27.8 cm–1, g= 2.1 for complex 1 and J=–10.1 cm–1, g= 2.0 for 2. The magnetostructural properties of the complexes are discussed. There is a linear correlation of the –2J values with the Cu Cu distances among dibridged complexes having square-planar copper(II) centres.

Conformation of polymerizable diacetylenic lecithin, DC8,9PC, by 1H-NMR spectroscopy

Diacetylenic phospholipid, 1,2 bis-(tricosa-10,12-diynoyl)-sn-glycero-3-phosphocholine (DC8,9PC), forms helices and tubules in addition to liposomes. The diacetylenic moiety responsible for the transformation is probed by 2-D NMR correlated spectroscopy. Chemical shift assignments and the analysis of 2D-COSY measurements were done on the lipid in chloroform-d solution. Based on this analysis, a model for the lipid is proposed. The geometry of the headgroup, glycerol backbone and acyl chains up to three methylenes from glycerol backbone [-(CH2)(3)-] is similar to that of dipalmitoyl phosphatidylcholine. The estimated torsional angle for methylene groups adjacent to diacetylenic moieties suggested an overall tilt of the diacetylenic lipid molecule from the bilayer axis of 25-30 degrees. This tilt could be negative or positive depending on the handedness of the resultant microstructures.

Thermodynamic and structural consequences of changing a sulfur atom to a methylene group in the M13Nle mutation in ribonuclease-S

Two fragments of pancreatic ribonuclease A, a truncated version of S-peptide (residues 1-15) and S-protein (residues 21-124), combine to give a catalytically active complex. We have substituted the wild-type residue at position 13, methionine (Met), with norleucine (Nle), where the only covalent change is the replacement of the sulfur atom with a methylene group. The thermodynamic parameters associated with the binding of this variant to S-protein, determined by titration calorimetry in the temperature range 10-40 degrees C, are reported and compared to values previously reported [Varadarajan, R., Connelly, P. R., Sturtevant, J. M., & Richards, F. M. (1992) Biochemistry 31, 1421-1426] for other position 13 analogs. The differences in the free energy and enthalpy of binding between the Met and Nle peptides are 0.6 and 7.9 kcal/mol at 25 degrees C, respectively. These differences are slightly larger than, but comparable to, the differences in the values for the Met/Ile and Met/Leu pairs. The structure of the mutant complex was determined to 1.85 Angstrom resolution and refined to an R-factor of 17.4% The structures of mutant and wild-type complexes are practically identical although the Nle side chain has a significantly higher average B-factor than the corresponding Met side chain. In contrast, the B-factors of the atoms of the cage of residues surrounding position 13 are all somewhat lower in the Nle variant than in the Met wild-type. Thus, the large differences in the binding enthalpy appear to reside entirely in the difference in chemical properties or dynamic behavior of the -S- and -CH2- groups and not in differences in the geometry of the side chains or the internal cavity surface. In addition, a novel method of obtaining protein stability data by means of isothermal titration calorimetry is introduced.

Density-matrix renormalization-group study of low-lying excitations of polyacene within a Pariser-Parr-Pople model

We have carried out symmetrized density-matrix renormalization-group calculations to study the nature of excited states of long polyacene oligomers within a Pariser-Parr-Pople Hamiltonian. We have used the C-2 symmetry, the electron-hole symmetry, and the spin parity of the system in our calculations. We find that there is a crossover in the lowest dipole forbidden two-photon state and the lowest dipole allowed excited state with size of the oligomer. In the long system limit, the two-photon state lies below the lowest dipole allowed excited state. The triplet state lies well below the two-photon state and energetically does not correspond to its description as being made up of two triplets. These results are in agreement with the general trends in linear conjugated polymers. However, unlike in linear polyenes wherein the two-photon state is a localized excitation, we find that in polyacenes, the two-photon excitation is spread out over the system. We have doped the systems with a hole and an electron and have calculated the charge excitation gap. Using the charge gap and the optical gap, we estimate the binding energy of the 1(1)B(-) exciton to be 2.09 eV. We have also studied doubly doped polyacenes and find that the bipolaron in these systems, to be composed of two separated polarons, as indicated by the calculated charge-density profile and charge-charge correlation function. We have studied bond orders in various states in order to get an idea of the excited state geometry of the system. We find that the ground state, the triplet state, the dipole allowed state, and the polaron excitations correspond to lengthening of the rung bonds in the interior of the oligomer while the two-photon excitation corresponds to the rung bond lengths having two maxima in the system.

Surfaces of Bounded Mean Curvature In Riemannian Manifolds

Consider a sequence of closed, orientable surfaces of fixed genus g in a Riemannian manifold M with uniform upper bounds on the norm of mean curvature and area. We show that on passing to a subsequence, we can choose parametrisations of the surfaces by inclusion maps from a fixed surface of the same genus so that the distance functions corresponding to the pullback metrics converge to a pseudo-metric and the inclusion maps converge to a Lipschitz map. We show further that the limiting pseudo-metric has fractal dimension two. As a corollary, we obtain a purely geometric result. Namely, we show that bounds on the mean curvature, area and genus of a surface F subset of M, together with bounds on the geometry of M, give an upper bound on the diameter of F. Our proof is modelled on Gromov's compactness theorem for J-holomorphic curves.

Reconstructing Solid Model from 2D Scanned Images of Biological Organs for Finite Element Simulation

This work presents a methodology to reconstruct 3D biological organs from image sequences or other scan data using readily available free softwares with the final goal of using the organs (3D solids) for finite element analysis. The methodology deals with issues such as segmentation, conversion to polygonal surface meshes, and finally conversion of these meshes to 3D solids. The user is able to control the detail or the level of complexity of the solid constructed. The methodology is illustrated using 3D reconstruction of a porcine liver as an example. Finally, the reconstructed liver is imported into the commercial software ANSYS, and together with a cyst inside the liver, a nonlinear analysis performed. The results confirm that the methodology can be used for obtaining 3D geometry of biological organs. The results also demonstrate that the geometry obtained by following this methodology can be used for the nonlinear finite element analysis of organs. The methodology (or the procedure) would be of use in surgery planning and surgery simulation since both of these extensively use finite elements for numerical simulations and it is better if these simulations are carried out on patient specific organ geometries. Instead of following the present methodology, it would cost a lot to buy a commercial software which can reconstruct 3D biological organs from scanned image sequences.

Variational Asymptotic Analysis of a Self-healing SMA Composite

A Shape Memory Alloy (SMA) wire reinforced composite shell structure is analyzed for self-healing characteristic using Variational Asymptotic Method (VAM). SMA behavior is modeled using a onedimensional constitutive model. A pre-notched specimen is loaded longitudinally to simulate crack propagation. The loading process is accompanied by martensitic phase transformation in pre-strained SMA wires, bridging the crack. To heal the composite, uniform heating is required to initiate reverse transformation in the wires and bringing the crack faces back into contact. The pre-strain in the SMA wires used for reinforcement, causes a closure force across the crack during reverse transformation of the wires under heating. The simulation can be useful in design of self-healing composite structures using SMA. Effect of various parameters, like composite and SMA material properties and the geometry of the specimen, on the cracking and self-healing can also be studied.

Topology Optimization of Micromachined Structures with the Manufacturing Constraints of KOH Etching of (110) Silicon

The focus of this paper is on designing useful compliant micro-mechanisms of high-aspect-ratio which can be microfabricated by the cost-effective wet etching of (110) orientation silicon (Si) wafers. Wet etching of (110) Si imposes constraints on the geometry of the realized mechanisms because it allows only etch-through in the form of slots parallel to the wafer's flat with a certain minimum length. In this paper, we incorporate this constraint in the topology optimization and obtain compliant designs that meet the specifications on the desired motion for given input forces. Using this design technique and wet etching, we show that we can realize high-aspect-ratio compliant micro-mechanisms. For a (110) Si wafer of 250 µm thickness, the minimum length of the etch opening to get a slot is found to be 866 µm. The minimum achievable width of the slot is limited by the resolution of the lithography process and this can be a very small value. This is studied by conducting trials with different mask layouts on a (110) Si wafer. These constraints are taken care of by using a suitable design parameterization rather than by imposing the constraints explicitly. Topology optimization, as is well known, gives designs using only the essential design specifications. In this work, we show that our technique also gives manufacturable mechanism designs along with lithography mask layouts. Some designs obtained are transferred to lithography masks and mechanisms are fabricated on (110) Si wafers.

CFD Based Design Optimizations of the Diffuser of a Gas Dynamically Driver Laser Cavity

Based on the an earlier CFD analysis of the performance of the gas-dynamically controlled laser cavity [1]it was found that there is possibility of optimizing the geometry of the diffuser that can bring about reductions in both size and cost of the system by examining the critical dimensional requirements of the diffuser. Consequently,an extensive CFD analysis has been carried out for a range of diffuser configurations by simulating the supersonic flow through the arrangement including the laser cavity driven by a bank of converging – diverging nozzles and the diffuser. The numerical investigations with 3D-RANS code are carried out to capture the flow patterns through diffusers past the cavity that has multiple supersonic jet interactions with shocks leading to complex flow pattern. Varying length of the diffuser plates is made to be the basic parameter of the study. The analysis reveals that the pressure recovery pattern during the flow through the diffuser from the simulation, being critical for the performance of the laser device shows its dependence on the diffuser length is weaker beyond a critical lower limit and this evaluation of this limit would provide a design guideline for a more efficient system configuration.The observation based on the parametric study shows that the pressure recovery transients in the near vicinity of the cavity is not affected for the reduction in the length of the diffuser plates up to its 10% of the initial size, indicating the design in the first configuration that was tested experimentally has a large factor of margin. The flow stability in the laser cavity is found to be unaffected since a strong and stable shock is located at the leading edge of the diffuser plates while the downstream shock and flow patterns are changed, as one would expect. Results of the study for the different lengths of diffusers in the range of 10% to its full length are presented, keeping the experimentally tested configuration used in the earlier study [1] as the reference length. The conclusions drawn from the analysis is found to be of significance since it provides new design considerations based on the understanding of the intricacies of the flow, allowing for a hardware optimization that can lead to substantial size reduction of the device with no loss of performance.

Optimal location of centre of gravity for swashplateless helicopter UAV and MAV

To investigate the use of centre of gravity location on reducing cyclic pitch control for helicopter UAV's (unmanned air vehicles) and MAV's (micro air vehicles). Low cyclic pitch is a necessity to implement the swashplateless rotor concept using trailing edge flaps or active twist using current generation low authority piezoceramic actuators. Design/methodology/approach – An aeroelastic analysis of the helicopter rotor with elastic blades is used to perform parametric and sensitivity studies of the effects of longitudinal and lateral center of gravity (cg) movements on the main rotor cyclic pitch. An optimization approach is then used to find cg locations which reduce the cyclic pitch at a given forward speed. Findings – It is found that the longitudinal cyclic pitch and lateral cyclic pitch can be driven to zero at a given forward speed by shifting the cg forward and to the port side, respectively. There also exist pairs of numbers for the longitudinal and lateral cg locations which drive both the cyclic pitch components to zero at a given forward speed. Based on these results, a compromise optimal cg location is obtained such that the cyclic pitch is bounded within ±5° for a BO105 helicopter rotor. Originality/value – The reduction in the cyclic pitch due to helicopter cg location is found to significantly reduce the maximum magnitudes of the control angles in flight, facilitating the swashplateless rotor concept. In addition, the existence of cg locations which drive the cyclic pitches to zero allows for the use of active cg movement as a way to replace the cyclic pitch control for helicopter MAV's.

Parallel Computation of 2D Morse-Smale Complexes

The Morse-Smale complex is a useful topological data structure for the analysis and visualization of scalar data. This paper describes an algorithm that processes all mesh elements of the domain in parallel to compute the Morse-Smale complex of large two-dimensional data sets at interactive speeds. We employ a reformulation of the Morse-Smale complex using Forman's Discrete Morse Theory and achieve scalability by computing the discrete gradient using local accesses only. We also introduce a novel approach to merge gradient paths that ensures accurate geometry of the computed complex. We demonstrate that our algorithm performs well on both multicore environments and on massively parallel architectures such as the GPU.

A Numerical Scheme for Three-Dimensional Front Propagation and Control of Jordan Mode

As an example of a front propagation, we study the propagation of a three-dimensional nonlinear wavefront into a polytropic gas in a uniform state and at rest. The successive positions and geometry of the wavefront are obtained by solving the conservation form of equations of a weakly nonlinear ray theory. The proposed set of equations forms a weakly hyperbolic system of seven conservation laws with an additional vector constraint, each of whose components is a divergence-free condition. This constraint is an involution for the system of conservation laws, and it is termed a geometric solenoidal constraint. The analysis of a Cauchy problem for the linearized system shows that when this constraint is satisfied initially, the solution does not exhibit any Jordan mode. For the numerical simulation of the conservation laws we employ a high resolution central scheme. The second order accuracy of the scheme is achieved by using MUSCL-type reconstructions and Runge-Kutta time discretizations. A constrained transport-type technique is used to enforce the geometric solenoidal constraint. The results of several numerical experiments are presented, which confirm the efficiency and robustness of the proposed numerical method and the control of the Jordan mode.

Influence of anion on the quadratic nonlinearity and depolarization ratios of scattered second harmonic light from cation-pi complexes

We have investigated quadratic nonlinearity (beta(HRS)) and linear and circular depolarization ratios (D and D', respectively) of a series of 1:1 complexes of tropyliumtetrafluoroborate as a cation and methyl-substituted benzenes as pi-donors by making polarization resolved hyper-Rayleigh scattering measurements in solution. The measured D and D' values are much lower than the values expected from a typical sandwich or a T-shaped geometry of a complex. In the cation-pi complexes studied here, the D value varies from 1.36 to 1.46 and D' from 1.62 to 1.72 depending on the number of methyl substitutions on the benzene ring. In order to probe it further, beta, D and D' were computed using the Zerner intermediate neglect of differential overlap-correction vector self-consistent reaction field technique including single and double configuration interactions in the absence and presence of BF4- anion. In the absence of the anion, the calculated value of D varies from 4.20 to 4.60 and that of D' from 2.45 to 2.72 which disagree with experimental values. However, by arranging three cation-pi BF4- complexes in a trigonal symmetry, the computed values are brought to agreement with experiments. When such an arrangement was not considered, the calculated beta values were lower than the experimental values by more than a factor of two. This unprecedented influence of the otherwise ``unimportant'' anion in solution on the beta value and depolarization ratios of these cation-pi complexes is highlighted and emphasized in this paper. (C) 2012 American Institute of Physics. http://dx.doi.org/10.1063/1.4716020]