CROSS-SECTIONAL ANALYSIS OF PRE-TWISTED THICK BEAMS USING VARIATIONAL ASYMPTOTIC METHOD

An asymptotically-exact methodology is presented for obtaining the cross-sectional stiffness matrix of a pre-twisted moderately-thick beam having rectangular cross sections and made of transversely isotropic materials. The anisotropic beam is modeled from 3-D elasticity, without any further assumptions. The beam is allowed to have large displacements and rotations, but small strain is assumed. The strain energy of the beam is computed making use of the constitutive law and the kinematical relations derived with the inclusion of geometrical nonlinearities and initial twist. Large displacements and rotations are allowed, but small strain is assumed. The Variational Asymptotic Method is used to minimize the energy functional, thereby reducing the cross section to a point on the reference line with appropriate properties, yielding a 1-D constitutive law. In this method as applied herein, the 2-D cross-sectional analysis is performed asymptotically by taking advantage of a material small parameter and two geometric small parameters. 3-D strain components are derived using kinematics and arranged as orders of the small parameters. Warping functions are obtained by the minimization of strain energy subject to certain set of constraints that renders the 1-D strain measures well-defined. Closed-form expressions are derived for the 3-D non-linear warping and stress fields. The model is capable of predicting interlaminar and transverse shear stresses accurately up to first order.

Analysis of Transverse Shear Strains in Pre-Twisted Thick Beams using Variational Asymptotic Method

The cross-sectional stiffness matrix is derived for a pre-twisted, moderately thick beam made of transversely isotropic materials and having rectangular cross sections. An asymptotically-exact methodology is used to model the anisotropic beam from 3-D elasticity, without any further assumptions. The beam is allowed to have large displacements and rotations, but small strain is assumed. The strain energy is computed making use of the beam constitutive law and kinematical relations derived with the inclusion of geometrical nonlinearities and an initial twist. The energy functional is minimized making use of the Variational Asymptotic Method (VAM), thereby reducing the cross section to a point on the beam reference line with appropriate properties, forming a 1-D constitutive law. VAM is a mathematical technique employed in the current problem to rigorously split the 3-D analysis of beams into two: a 2-D analysis over the beam cross-sectional domain, which provides a compact semi-analytical form of the properties of the cross sections, and a nonlinear 1-D analysis of the beam reference curve. In this method, as applied herein, the cross-sectional analysis is performed asymptotically by taking advantage of a material small parameter and two geometric small parameters. 3-D strain components are derived using kinematics and arranged in orders of the small parameters. Closed-form expressions are derived for the 3-D non-linear warping and stress fields. Warping functions are obtained by the minimization of strain energy subject to certain set of constraints that render the 1-D strain measures well-defined. The zeroth-order 3-D warping field thus yielded is then used to integrate the 3-D strain energy density over the cross section, resulting in the 1-D strain energy density, which in turn helps identify the corresponding cross-sectional stiffness matrix. The model is capable of predicting interlaminar and transverse shear stresses accurately up to first order.

Structure-Based Phylogenetic Analysis of the Lipocalin Superfamily

Lipocalins constitute a superfamily of extracellular proteins that are found in all three kingdoms of life. Although very divergent in their sequences and functions, they show remarkable similarity in 3-D structures. Lipocalins bind and transport small hydrophobic molecules. Earlier sequence-based phylogenetic studies of lipocalins highlighted that they have a long evolutionary history. However the molecular and structural basis of their functional diversity is not completely understood. The main objective of the present study is to understand functional diversity of the lipocalins using a structure-based phylogenetic approach. The present study with 39 protein domains from the lipocalin superfamily suggests that the clusters of lipocalins obtained by structure-based phylogeny correspond well with the functional diversity. The detailed analysis on each of the clusters and sub-clusters reveals that the 39 lipocalin domains cluster based on their mode of ligand binding though the clustering was performed on the basis of gross domain structure. The outliers in the phylogenetic tree are often from single member families. Also structure-based phylogenetic approach has provided pointers to assign putative function for the domains of unknown function in lipocalin family. The approach employed in the present study can be used in the future for the functional identification of new lipocalin proteins and may be extended to other protein families where members show poor sequence similarity but high structural similarity.

Probing the role of highly conserved residues in triosephosphate isomerase-analysis of site specific mutants at positions 64 and 75 in the Plasmodial enzyme

Highly conserved residues in enzymes are often found to be clustered close to active sites, suggesting that functional constraints dictate the nature of amino acid residues accommodated at these sites. Using the Plasmodiumfalciparum triosephosphate isomerase (PfTIM) enzyme () as a template, we have examined the effects of mutations at positions 64 and 75, which are not directly involved in the proton transfer cycle. Thr (T) occurring at position 75 is completely conserved, whereas only Gln (Q) and Glu (E) are accommodated at position 64. Biophysical and kinetic data are reported for four T75 (T75S/V/C/N) and two Q64 (Q64N/E) mutants. The dimeric structure is weakened in the Q64E and Q64N mutants, whereas dimer integrity is unimpaired in all four T75 mutants. Measurement of the concentration dependence of enzyme activity permits an estimate of K-d values for dimer dissociation (Q64N=73.79.2nm and Q64E=44.6 +/- 8.4nm). The T75S/V/C mutants have activities comparable to the wild-type enzyme, whereas a fourfold drop is observed for T75N. All four T75 mutants show a dramatic fall in activity between 35 degrees C and 45 degrees C. Crystal structure determination of the T75S/V/N mutants provides insights into the variations in local interactions, with the T75N mutant showing the largest changes. Hydrogen-bond interactions determine dimer stability restricting the choice of residues at position 64 to Gln (Q) and Glu (E). At position 75, the overwhelming preference for Thr (T) may be dictated by the imperative of maintaining temperature stability of enzyme activity.

A FRAMEWORK FOR THE ERROR ANALYSIS OF DISCONTINUOUS FINITE ELEMENT METHODS FOR ELLIPTIC OPTIMAL CONTROL PROBLEMS AND APPLICATIONS TO C-0 IP METHODS

In this article, an abstract framework for the error analysis of discontinuous Galerkin methods for control constrained optimal control problems is developed. The analysis establishes the best approximation result from a priori analysis point of view and delivers a reliable and efficient a posteriori error estimator. The results are applicable to a variety of problems just under the minimal regularity possessed by the well-posedness of the problem. Subsequently, the applications of C-0 interior penalty methods for a boundary control problem as well as a distributed control problem governed by the biharmonic equation subject to simply supported boundary conditions are discussed through the abstract analysis. Numerical experiments illustrate the theoretical findings.

Functional expression and purification of Anabaena PCC 7120 XisA protein

Anabaena PCC 7120 xisA gene product mediates the site-specific excision of 11,278 bp nifD element in heterocysts formed under nitrogen starvation conditions. Although XisA protein possesses both site-specific recombinase and endonuclease activities, till date neither xisA transcript nor XisA protein has been detected. Gene encoding XisA protein was isolated from plasmid pMX25 and overexpressed in Escherichia coli BL21 DE3 yielding 7.7 mg enzyme per L of growth culture in soluble fraction. His-tagged XisA was purified using Ni-NTA affinity chromatography with 95% recovery. The purified XisA showed a single band on SDS-PAGE with molecular mass of 52 kDa. Identity of XisA was confirmed by MALDI-TOF analysis and functionality of enzyme was confirmed using restriction digestion. A PCR based method was developed to monitor excision by XisA, which displayed near 100% activity in E. coli within 1 h at 37 degrees C on LB under static condition. (C) 2015 Elsevier Inc. All rights reserved.