Orientation-dependent Function Research Articles

Nonlocal anisotropic model for deformation and fracture using peridynamic operator method

This paper proposes a nonlocal anisotropic model for deformation and fracture based on peridynamic operator method. The classic anisotropic theory is reformulated from its local form into nonlocal form by using peridynamic operator method. The final solution formulation is developed by employing variational principles and Lagrange's equations. In the case of the circular interaction domain, this model can be regarded as a novel anisotropic ordinary state-based peridynamic model. Moreover, we present for the first time the energetic failure criterion for the weak anisotropic fracture. Unlike the existing anisotropic peridynamic models that consider only two fracture toughness constants for orthogonal orientation, the fracture toughness in this criterion is an orientation-dependent function. Additionally, we develop an implicit static solution procedure to investigate corresponding crack propagation problems. Several numerical examples demonstrate the effectiveness and ability of the proposed model in handling the deformation and fracture behaviours of anisotropic materials.

Characterization of anisotropic T2W signals from human knee femoral cartilage: The magic angle effect on a spherical surface.

The aim of the current study was to propose a generalized magic angle effect (gMAE) function for characterizing anisotropic T2W signals of human knee femoral cartilage with a spherical surface in clinical studies. A gMAE model function f(α, ε) was formulated for an orientation-dependent (ε) transverse T2 (i.e., 1/R2 ) relaxation in cartilage assuming an axially symmetric distribution (α) of collagen fibers. T2W sagittal images were acquired on an adult volunteer's healthy knee at 3T, and ROI-based average signals S(ε) were extracted from angularly and radially segmented femoral cartilage. Compared with the standard MAE (sMAE) functions in the deep (DZ, α= 0°) and in the superficial (SZ, α= 90°) zones, a general form of R2 orientation-dependent function f(α, ε) was fitted to S(ε), including an isotropic R2 contribution (internal reference [REF]). Goodness of fit was evaluated by root-mean-square deviations (RMSDs). AnF-test and a paired t-test were respectively used to assess significant differences between the observed variances and means, with statistical significance set to pless than.05. As a symmetric orientation-dependence function with a varying dynamic range, the proposed gMAE model outperformed the previous sMAE functions manifested by significantly reduced RMSDs in the DZ (0.239 ± 0.122 vs. 0.267 ± 0.097, p =.014) and in the SZ (0.183 ± 0.081 vs. 0.254 ± 0.085, p <.001). The fitted average angle α (38.5 ± 34.6° vs. 45.1 ± 30.1°, p <.43) and REF (5.092 ± 0.369 vs. 5.305 ± 0.440, p <.001) were smaller in the DZ than those in SZ, in good agreement with the reported collagen fibril microstructural configurations and the nonbound water contribution to R2 in articular cartilage. In conclusion, a general form of the magic angle effect function was proposed and demonstrated for better characterizing anisotropic T2W signals from human knee femoral cartilage at 3T in clinical studies.

Isotropic-polar phase transitions in an amphiphilic fluid: Density functional theory versus computer simulations

We investigate the critical line separating isotropic from polar phases in an amphiphilic bulk fluid by means of density functional theory (DFT) and Monte Carlo (MC) simulations in the isothermal-isobaric ensemble. The intermolecular interactions are described by a Lennard-Jones potential in which the attractive contribution is modified by an orientation-dependent function. The latter consists of two terms: The first one has the orientation dependence of a classical three-dimensional Heisenberg interaction, whereas, the second one has the orientation dependence of a classical dipole-dipole interaction. However, both contributions are short range. Employing DFT together with a modified mean-field (MMF) approximation for the orientation-dependent pair correlation function, we derive an analytical expression for the critical line separating isotropic from polar liquidlike phases. In parallel MC simulations, we locate the line of critical points through an analysis of Binder's second-order cumulant of the polar-order parameter. Comparison with DFT shows that the dipolelike contribution is irrelevant for the isotropic-polar phase transition. As far as the Heisenberg contribution is concerned, the MC data are in semiquantitative agreement with the DFT predictions for sufficiently strong coupling between molecular orientations. For weaker coupling, the variation in the ratio of critical density and temperature ρ(c)/T(c) with the Heisenberg coupling constant ε(H) is underestimated by the MMF treatment. The MC results suggest that this is because ρ(c) increases with decreasing ε(H) such that the assumption on which the MMF approach rests becomes less applicable in the weaker-coupling limit.

Finite-size scaling analysis of isotropic–polar phase transitions in an amphiphilic fluid

We present Monte Carlo simulations of the isotropic–polar (IP) phase transition in an amphiphilic fluid carried out in the isothermal–isobaric ensemble. Our model consists of Lennard-Jones spheres where the attractive part of the potential is modified by an orientation-dependent function. This function gives rise to an angle dependence of the intermolecular attractions corresponding to that characteristic of point dipoles. Our data show a substantial system-size dependence of the dipolar order parameter. We analyze the system-size dependence in terms of the order-parameter distribution and a cumulant involving its first and second moments. The order parameter, its distribution, and susceptibility observe the scaling behavior characteristic of the 3D Ising universality class. Because of this scaling behavior and because all cumulants have a common intersection irrespective of system size we conclude that the IP phase transition is continuous. Considering pressures 1.3 ≤ P ≤ 3.0 we demonstrate that a line of continuous phase transitions exists which is analogous to the Curie line in systems exhibiting a ferroelectric transition. Our results are qualitatively consistent with Landau’s theory of continuous phase transitions.

A study of isotropic–nematic transition of quadrupolar Gay–Berne fluid using density-functional theory approach

The effects of quadrupole moments on the isotropic–nematic (IN) phase transitions are studied using the density-functional theory (DFT) for a Gay–Berne (GB) fluid for a range of length-to-breadth parameters in the reduced temperature range . The pair-correlation functions of the isotropic phase, which enter into the DFT as input parameters are found by solving the Percus–Yevick integral equation theory. The method used involves an expansion of angle-dependent functions appearing in the integral equations in terms of spherical harmonics and the harmonic coefficients are obtained by an iterative algorithm. All the terms of harmonic coefficients which involve l indices up to less than or equal to 6 are considered. The numerical accuracy of the results depends on the number of spherical harmonic coefficients considered for each orientation-dependent function. As the length-to-breadth ratio of quadrupolar GB molecules is increased, the IN transition is seen to move to lower density (and pressure) at a given temperature. It has been observed that the DFT is good to study the IN transitions in such fluids. The theoretical results have also been compared with the computer simulation results wherever they are available.

Protein side chain modeling with orientation-dependent atomic force fields derived by series expansions.

We describe the development of new force fields for protein side chain modeling called optimized side chain atomic energy (OSCAR). The distance-dependent energy functions (OSCAR-d) and side-chain dihedral angle potential energy functions were represented as power and Fourier series, respectively. The resulting 802 adjustable parameters were optimized by discriminating the native side chain conformations from non-native conformations, using a training set of 12,000 side chains for each residue type. In the course of optimization, for every residue, its side chain was replaced by varying rotamers, whereas conformations for all other residues were kept as they appeared in the crystal structure. Then, the OSCAR-d were multiplied by an orientation-dependent function to yield OSCAR-o. A total of 1087 parameters of the orientation-dependent energy functions (OSCAR-o) were optimized by maximizing the energy gap between the native conformation and subrotamers calculated as low energy by OSCAR-d. When OSCAR-o with optimized parameters were used to model side chain conformations simultaneously for 218 recently released protein structures, the prediction accuracies were 88.8% for χ(1) , 79.7% for χ(1 + 2) , 1.24 Å overall root mean square deviation (RMSD), and 0.62 Å RMSD for core residues, respectively, compared with the next-best performing side-chain modeling program which achieved 86.6% for χ(1) , 75.7% for χ(1 + 2) , 1.40 Å overall RMSD, and 0.86 Å RMSD for core residues, respectively. The continuous energy functions obtained in this study are suitable for gradient-based optimization techniques for protein structure refinement. A program with built-in OSCAR for protein side chain prediction is available for download at http://sysimm.ifrec.osaka-u.ac.jp/OSCAR/.

Orientation-dependent function for properties of polycrystals and its applications

Polycrystals are aggregates of numerous tiny crystallites whose orientation distributions are described by the orientation distribution function (ODF). Since crystal lattices are anisotropic, the properties of polycrystals depend on the ODF. The texture coefficients, which can be measured by X-ray diffraction, are the expanded coefficients of the ODF under the Wigner D-function bases. The texture coefficients contain the information of crystalline orientation distributions and crystal symmetries on polycrystals. Herein an orientation-dependent function is introduced to present the properties of polycrystals. A general expression of the orientation-dependent function for polycrystals is given. The general expression with the texture coefficients can be widely used to determine the properties of polycrystals. As applications of the general expression, the direction-dependent function, the elastic strain energy, and the yield function for anisotropic cubic polycrystals are given in simple and explicit forms.

1P004 方向性を考慮したタンパク質評価関数の改良(蛋白質(構造・構造機能相関),ポスター発表,第45回日本生物物理学会年会)

1P004 方向性を考慮したタンパク質評価関数の改良(蛋白質(構造・構造機能相関),ポスター発表,第45回日本生物物理学会年会)

DNA bending and orientation-dependent function of YY1 in the c-fos promoter.

The assembly of multicomponent complexes at promoters, enhancers, and silencers likely entails perturbations in the path of the DNA helix. We present evidence that YY1, a ubiquitously expressed DNA-binding protein, regulates the activity of the c-fos promoter primarily through an effect on DNA structure. YY1 binds to and induces a phased DNA bend at three sites in this promoter. By use of a truncated c-fos promoter activity containing a single functional YY1 site, we show that YY1 represses promoter activity but that repression does not appear to be an intrinsic property of the protein in this context. Moreover, when the orientation of the YY1 site is reversed, YY1 activates the same promoter. Repression by YY1 is also alleviated by changing the relative phasing of factor-binding sites on either side of YY1. We conclude that the principal function of YY1 in this promoter is to bend DNA to regulate contact between other proteins. Thus, YY1 represents a new class of transcription factors that influences promoter function by affecting promoter structure rather than by directly contacting the transcriptional machinery. We provide evidence that the product of the male sex determination gene SRY may also belong to this class of structural factors.

Orientation-dependent function of a short CYC1 DNA fragment in directing mRNA 3' end formation in yeast.

We have cloned an 82-base-pair region spanning the site of normal 3' end formation of Saccharomyces cerevisiae CYC1 mRNA into an integrative vector carrying the 5' end of the actin gene (including its intron) fused in frame to HIS4ABC sequences. This vector can confer the ability to grow on histidinol if HIS4C (encoding histidinol dehydrogenase) is sufficiently expressed. With the CYC1 fragment cloned in its wild-type (forward) orientation within the actin intron, transformants cannot grow on histidinol, whereas cells transformed with the vector carrying the reverse orientation of this fragment are able to grow well. RNA transfers demonstrate that transformants containing the forward orientation accumulate less than 40% of the control level of full-length mRNA and reveal the presence of a short, stable (approximately equal to 300 nucleotides) poly(A) RNA that represents 60-70% of the transcripts originating from the same promoter. The reverse orientation of the insert allows near-normal levels of full-length mRNA. Mapping of the 3' end of the truncated RNA indicates that poly(A) addition is variable in length but occurs at the same location as in the normal CYC1 transcript. Dominant and recessive suppressor mutations permit growth on histidinol despite the inserted fragment. Genetic analyses indicate that most of the dominant mutants are cis-acting and that the recessive mutants define a minimum of three complementation groups, indicating that defects in several different genes can restore higher levels of HIS4C expression.

Collision-induced rototranslational spectra of H2-Ar from an accurate ab initio dipole-moment surface.

The induced dipole moment of hydrogen- (${\mathrm{H}}_{2}$) argon pairs is obtained with an estimated accuracy of about 2% by treating the collisional complex like a molecule in self-consistent-field (SCF) and coupled-electron-pair calculations. The basis-set superposition error is effectively avoided by the use of nonorthogonal local orbital sets. Based on the four-term, ab initio, orientation-dependent dipole function and a reliable isotropic potential model, the rototranslational absorption spectra of free and bound ${\mathrm{H}}_{2}$-Ar pairs are computed from an exact quantum formalism. Both the spectral profile and absolute intensity of the ab initio spectra are shown to be in agreement with Dore and Birnbaum's recent measurement. The work demonstrates once more what was seen previously for the He-Ar and ${\mathrm{H}}_{2}$-He far-infrared absorption spectra, namely that the precision attainable in such ab initio computations matches or exceeds that of the best available measurements of the same spectra [Meyer and Frommhold, Phys. Rev. A 33, 3807 (1986), and Phys. Rev. A 34, 2771 (1986).