Variational principles in evolution

For a one-locus selection model, Svirezhev introduced an integral variational principle by defining a Lagrangian which remained stationary on the trajectory followed by the population undergoing selection. It is shown here (i) that this principle can be extended to multiple loci in some simple cases and (ii) that the Lagrangian is defined by a straightforward generalization of the one-locus case, but (iii) that in two-locus or more general models there is no straightforward extension of this principle if linkage and epistasis are present. The population trajectories can be constructed as trajectories of steepest ascent in a Riemannian metric space. A general method is formulated to find the metric tensor and the surface-in the metric space on which the trajectories, which characterize the variations in the gene structure of the population, lie. The local optimality principle holds good in such a space. In the special case when all possible linkage disequilibria are zero, the phase point of the n-locus genetic system moves on the surface of the product space of n higher dimensional unit spheres in a certain Riemannian metric space of gene frequencies so that the rate of change of mean fitness is maximum along the trajectory. In the two-locus case the corresponding surface is a hyper-torus.

Free convection in power-law fluids near a three-dimensional stagnation point

Numerical results are presented for the free-convection boundary-layer equations of the Ostwald de-Waele non-Newtonian power-law type fluids near a three-dimensional (3-D) stagnation point of attachment on an isothermal surface. The existence of dual solutions that are three-dimensional in nature have been verified by means of a numerical procedure. An asymptotic solution for very large Prandtl numbers has also been derived. Solutions are presented for a range of values of the geometric curvature parameter c, the power-law index n, and the Prandtl number Pr.

Structure of sesbania mosaic virus at 3 å resolution

Background: Sobemoviruses are a group of RNA plant viruses that have a narrow host range. They are characterized in vitro by their stability, high thermal inactivation point and longevity. The three-dimensional structure of only one virus belonging to this group, southern bean mosaic virus (SBMV), is known. Structural studies on sesbania mosaic virus (SMV), which is closely related to SBMV, will provide details of the molecular interactions that are likely to be important in the stability and assembly of sobemoviruses. Results: We have determined the three-dimensional structure of SMV at 3 Angstrom resolution. The polypeptide fold and quaternary organization are very similar to those of SBMV. The capsid consists of sixty icosahedral asymmetric units, each comprising three copies of a chemically identical coat protein subunit, which are designated as A, B and C and are in structurally different environments. Four cation-binding sites have been located in the icosahedral asymmetric unit. Of these, the site at the quasi-threefold axis is not found in SBMV. Structural differences are observed in loops and regions close to this cation-binding site. Preliminary studies on ethylene diamine tetra acetic acid (EDTA) treated crystals suggest asymmetry in removal of the quasi-equivalent cations at the AB, BC, and AC subunit interfaces. Conclusions: Despite the overall similarity between SMV and SBMV in the nature of the polypeptide fold, these viruses show a number of differences in intermolecular interactions. The polar interactions at the quasi-threefold axis are substantially less in SMV and positively charged residues on the RNA-facing side of the protein and in the N-terminal arm are not particularly well conserved. This suggests that protein-RNA interactions are likely to be different between the two viruses.

On Walkup's class K (d) and a minimal triangulation of (S-3 (sic) S-1)(#3)

For d >= 2, Walkup's class K (d) consists of the d-dimensional simplicial complexes all whose vertex-links are stacked (d - 1)-spheres. Kalai showed that for d >= 4, all connected members of K (d) are obtained from stacked d-spheres by finitely many elementary handle additions. According to a result of Walkup, the face vector of any triangulated 4-manifold X with Euler characteristic chi satisfies f(1) >= 5f(0) - 15/2 chi, with equality only for X is an element of K(4). Kuhnel observed that this implies f(0)(f(0) - 11) >= -15 chi, with equality only for 2-neighborly members of K(4). Kuhnel also asked if there is a triangulated 4-manifold with f(0) = 15, chi = -4 (attaining equality in his lower bound). In this paper, guided by Kalai's theorem, we show that indeed there is such a triangulation. It triangulates the connected sum of three copies of the twisted sphere product S-3 (sic) S-1. Because of Kuhnel's inequality, the given triangulation of this manifold is a vertex-minimal triangulation. By a recent result of Effenberger, the triangulation constructed here is tight. Apart from the neighborly 2-manifolds and the infinite family of (2d + 3)-vertex sphere products Sd-1 X S-1 (twisted for d odd), only fourteen tight triangulated manifolds were known so far. The present construction yields a new member of this sporadic family. We also present a self-contained proof of Kalai's result. (C) 2011 Elsevier B.V. All rights reserved.

Hot deformation and microstructural evolution in an alpha(2)/O titanium aluminide alloy Ti-25Al-15Nb

Deformation processing and microstructural development of an alpha(2)/O aluminide alloy Ti-25Al-15Nb (at.%) was studied in the temperature range of 950 to 1200 degrees C and strain rate range of 10(-3) to 100 s(-1). Regions of processing and instability were identified using dynamic materials model. Dynamic recrystallization (DRX) of alpha(2)/O phase and p phase were seen to occur in the region of 950 to 1050 degrees C/0.001 to 0.05 s(-1) and 1125 to 1175 degrees C/0.001 to 0.1 s(-1), respectively. Unstable flow was seen to occur in the region of 1050 to 1190 degrees C/10 to 100 s(-1). Thermal activation analysis showed that DRX of alpha(2)/O and beta was controlled by cross-slip.

RPS: Repeats in Protein Sequences

Repeats are two or more contiguous segments of amino acid residues that are believed to have arisen as a result of intragenic duplication, recombination and mutation events. These repeats can be utilized for protein structure prediction and can provide insights into the protein evolution and phylogenetic relationship. Therefore, to aid structural biologists and phylogeneticists in their research, a computing resource (a web server and a database), Repeats in Protein Sequences (RPS), has been created. Using RPS, users can obtain useful information regarding identical, similar and distant repeats (of varying lengths) in protein sequences. In addition, users can check the frequency of occurrence of the repeats in sequence databases such as the Genome Database, PIR and SWISS-PROT and among the protein sequences available in the Protein Data Bank archive. Furthermore, users can view the three-dimensional structure of the repeats using the Java visualization plug-in Jmol. The proposed computing resource can be accessed over the World Wide Web at http://bioserver1.physics.iisc.ernet.in/rps/.

Real-time Computer Simulation of Three Dimensional Elastostatics using the Finite Point Method

Real-time simulation of deformable solids is essential for some applications such as biological organ simulations for surgical simulators. In this work, deformable solids are approximated to be linear elastic, and an easy and straight forward numerical technique, the Finite Point Method (FPM), is used to model three dimensional linear elastostatics. Graphics Processing Unit (GPU) is used to accelerate computations. Results show that the Finite Point Method, together with GPU, can compute three dimensional linear elastostatic responses of solids at rates suitable for real-time graphics, for solids represented by reasonable number of points.

Microstructure evolution during solidification of DRMMCs (discontinuously reinforced metal matrix composites): State of art

Distribution of particle reinforcements in cast composites is determined by the morphology of the solidification front. Interestingly, during solidification, the morphology of the interface is intrinsically affected by the presence of dispersed reinforcements. Thus the dispersoid distribution and length scale of matrix microstructure is a result of the interplay between these two. A proper combination of material and process parameters can be used to obtain composites with tailored microstructures. This requires the generation of a broad data base and optimization of the complete solidification process. The length scale of soldification microtructure has a large influence on the mechanical properties of the composites. This presentation addresses the concept of a particle distribution map which can help in predicting particle distribution under different solidification conditions Future research directions have also been indicated.

Bis{2-4-(methylsulfanyl)phenyl]-1H-benzimidazol-3-ium} tetrabromidocuprate(II) dihydrate

The asymmetric unit of the title compound, (C14H13N2S)(2)CuBr4]center dot 2H(2)O, contains two cations, one anion and two solvent water molecules that are connected via O-H center dot center dot center dot Br, N-H center dot center dot center dot Br and N-H center dot center dot center dot O hydrogen bonds into a two-dimensional polymeric structure. The cations are arranged in a head-to-tail fashion and form stacks along 100]. The central Cu-II atom of the anion is in a distorted tetrahedral environment.

Spin distributions in antiferromagnetically coupled Mn2+Cu2+ systems: from the pair to the infinite chain

Probably the most informative description of the ground slate of a magnetic molecular species is provided by the spin density map. Such a map may be experimentally obtained from polarized neutron diffraction (PND) data or theoretically calculated using quantum chemical approaches. Density functional theory (DFT) methods have been proved to be well-adapted for this. Spin distributions in one-dimensional compounds may also be computed using the density matrix renormalization group (DMRG) formalism. These three approaches, PND, DFT, and DMRG, have been utilized to obtain new insights on the ground state of two antiferromagnetically coupled Mn2+Cu2+ compounds, namely [Mn(Me-6-[14]ane-N-4)Cu(oxpn)](CF3SO3)(2) and MnCu(pba)(H2O)(3) . 2H(2)O, with Me-6-[14]ane-N-4 = (+/-)-5,7,7,12,14,14-hexamethyl-1,4,8,11-tetraazacyclotetradecane, oxpn = N,N'-bis(3-aminopropyl)oxamido and pba = 1,3-propylenebis(oxamato). Three problems in particular have been investigated: the spin distribution in the mononuclear precursors [Cu(oxpn)] and [Cu(pba)](2-), the spin density maps in the two Mn2+Cu2+ compounds, and the evolution of the spin distributions on the Mn2+ and Cu2+ sites when passing from a pair to a one-dimensional ferrimagnet.

The algebra and geometry of SU(3) matrices

We give an elementary treatment of the defining representation and Lie algebra of the three-dimensional unitary unimodular group SU(3). The geometrical properties of the Lie algebra, which is an eight dimensional real Linear vector space, are developed in an SU(3) covariant manner. The f and d symbols of SU(3) lead to two ways of 'multiplying' two vectors to produce a third, and several useful geometric and algebraic identities are derived. The axis-angle parametrization of SU(3) is developed as a generalization of that for SU(2), and the specifically new features are brought out. Application to the dynamics of three-level systems is outlined.

Stochastic dynamics modeling of the protein sequence length distribution in genomes: implications for microbial evolution

In this paper, we report an analysis of the protein sequence length distribution for 13 bacteria, four archaea and one eukaryote whose genomes have been completely sequenced, The frequency distribution of protein sequence length for all the 18 organisms are remarkably similar, independent of genome size and can be described in terms of a lognormal probability distribution function. A simple stochastic model based on multiplicative processes has been proposed to explain the sequence length distribution. The stochastic model supports the random-origin hypothesis of protein sequences in genomes. Distributions of large proteins deviate from the overall lognormal behavior. Their cumulative distribution follows a power-law analogous to Pareto's law used to describe the income distribution of the wealthy. The protein sequence length distribution in genomes of organisms has important implications for microbial evolution and applications. (C) 1999 Elsevier Science B.V. All rights reserved.

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.

Hydrothermal synthesis and structure of organically templated one-dimensional and three-dimensional iron fluorophosphate

Two new open-framework iron fluorophosphates, [C(4)N(2)H(12)](0.5) [FeF(HPO(4))(H(2)PO(4))] (I) and [C(4)N(2)H(12)][Fe(4)F(2)(H(2)O)(4)(PO(4))(4)]. 0.5H(2)O (II), were synthesized hydrothermally using piperazine as a templating agent. The structures were determined by single-crystal X-ray diffraction. Compound I crystallizes in the orthorhombic space group Pbca, a = 7.2126(2) Angstrom, b = 14.2071(4) Angstrom, c = 17.1338(2) Angstrom, Z = 8. The structure is composed of infinite anionic chains of [FeF(HPO(4))(H(2)PO(4))](n)(-) built by trans-fluorine sharing FeF(2)O(4) octahedra. These chains are similar to those found in tancoite-type minerals. Compound II crystallizes in the monoclinic space group P2(1)/n, a = 9.9045(3) Angstrom, b = 12.3011(3) Angstrom, c = 17.3220(4) Angstrom, beta = 103.7010(10)degrees, Z = 4. The structure of compound II has a three-dimensional (3D) architecture with an eight-membered channel along the b axis, in which protonoted piperazine molecules reside. The complex framework is built from two types of secondary building unit (SBU): one hexamer [Fe(3)F(2)(H(2)O)(2)(PO(4))(3)] (SBU6), and one dimer [FeO(4)(H(2)O)(2)PO(4)] (SBU2). The vertex sharing between these SBUs create the 3D structure.