A Branch and Bound Algorithm for a Transportation Type Problem with Piecewise Linear Convex Objective Function

A branch and bound type algorithm is presented in this paper to the problem of finding a transportation schedule which minimises the total transportation cost, where the transportation cost over each route is assumed to be a piecewice linear continuous convex function with increasing slopes. The algorithm is an extension of the work done by Balachandran and Perry, in which the transportation cost over each route is assumed to beapiecewise linear discontinuous function with decreasing slopes. A numerical example is solved illustrating the algorithm.

Free-to-bound and bound exciton transitions at isoelectronic impurities: GaP(Zn,O)

We show, for sufficiently high temperatures and sufficiently weak majority-carrier binding energies, that the dominant radiative transition at an isoelectronic acceptor (donor) in p-type (n-type) material consists of the recombination of singly trapped minority carriers (bound by central-cell forces) with free majority carriers attracted by a Coulomb interaction. There are two reasons why the radiative recombination rate of the free-to-bound process is greater than the bound exciton process, which dominates at lower temperatures: (i) The population of free majority-carrier states greatly exceeds that of exciton states at higher temperatures, and (ii) the oscillator strength of the free-to-bound transition is greatly enhanced by the Coulomb attraction between the free carrier and the charged isoelectronic impurity. This enhancement is important for isoelectronic centers and is easily calculable from existing exciton models. We show that the free carrier attracted by a Coulomb interaction can be viewed as a continuum excited state of the bound exciton. When we apply the results of our calculations to the GaP(Zn, O) system, we find that the major part of the room-temperature luminescence from nearest-neighbor isoelectronic Zn-O complexes results from free-to-bound recombination and not exciton recombination as has been thought previously. Recent experiments on impulse excitation of luminescence in GaP(Zn, O) are reevaluated in the light of our calculations and are shown to be consistent with a strong free-to-bound transition. For deep isoelectronic centers with weakly bound majority carriers, we predict an overwhelming dominance of the free-to-bound process at 300°K.

Bottleneck assignment problems under categorization

This paper considers two special cases of bottleneck grouped assignment problems when n jobs belong to m distinct categories (m < n). Solving these special problems through the available branch and bound algorithms will result in a heavy computational burden. Sequentially identifying nonopitmal variables, this paper provides more efficient methods for those cases. Propositions leading to the algorithms have been established. Numerical examples illustrate the respective algorithms.

A time minimising transportation problem with quality dependent time

The usual assumption made in time minimising transportation problem is that the time for transporting a positive amount in a route is independent of the actual amount transported in that route. In this paper we make a more general and natural assumption that the time depends on the actual amount transported. We assume that the time function for each route is an increasing piecewise constant function. Four algorithms - (1) a threshold algorithm, (2) an upper bounding technique, (3) a primal dual approach, and (4) a branch and bound algorithm - are presented to solve the given problem. A method is also given to compute the minimum bottle-neck shipment corresponding to the optimal time. A numerical example is solved illustrating the algorithms presented in this paper.

Importance of non-conserved distal carboxyl terminal amino acids in two peptidases belonging to the M1 family: Thermoplasma acidophilum Tricorn interacting factor F2 and Escherichia coli Peptidase N

Enzymes belonging to the M1 family play important cellular roles and the key amino acids (aa) in the catalytic domain are conserved. However, C-terminal domain aa are highly variable and demonstrate distinct differences in organization. To address a functional role for the C-terminal domain, progressive deletions were generated in Tricorn interacting factor F2 from Thermoplasma acidophilum (F2) and Peptidase N from Escherichia coli (PepN). Catalytic activity was partially reduced in PepN lacking 4 C-terminal residues (PepNΔC4) whereas it was greatly reduced in F2 lacking 10 C-terminal residues (F2ΔC10) or PepN lacking eleven C-terminal residues (PepNΔC11). Notably, expression of PepNΔC4, but not PepNΔC11, in E. coliΔpepN increased its ability to resist nutritional and high temperature stress, demonstrating physiological significance. Purified C-terminal deleted proteins demonstrated greater sensitivity to trypsin and bound stronger to 8-amino 1-napthalene sulphonic acid (ANS), revealing greater numbers of surface exposed hydrophobic aa. Also, F2 or PepN containing large aa deletions in the C-termini, but not smaller deletions, were present in high amounts in the insoluble fraction of cell extracts probably due to reduced protein solubility. Modeling studies, using the crystal structure of E. coli PepN, demonstrated increase in hydrophobic surface area and change in accessibility of several aa from buried to exposed upon deletion of C-terminal aa. Together, these studies revealed that non-conserved distal C-terminal aa repress the surface exposure of apolar aa, enhance protein solubility, and catalytic activity in two soluble and distinct members of the M1 family.

Crystal structure of Salmonella typhimurium 2-methylcitrate synthase: Insights on domain movement and substrate specificity

2-Methylcitric acid (2-MCA) cycle is one of the well studied pathways for the utilization of propionate as a source of carbon and energy in bacteria such as Salmonella typhimurium and Escherichia coli. 2-Methylcitrate synthase (2-MCS) catalyzes the conversion of oxaloacetate and propionyl-CoA to 2-methylcitrate and CoA in the second step of 2-MCA cycle. Here, we report the X-ray crystal structure of S. typhimurium 2-MCS (StPrpC) at 2.4 A resolution and its functional characterization. StPrpC was found to utilize propionyl-CoA more efficiently than acetyl-CoA or butyryl-CoA. The polypeptide fold and the catalytic residues of StPrpC are conserved in citrate synthases (CSs) suggesting similarities in their functional mechanisms. In the triclinic P1 cell, StPrpC molecules were organized as decamers composed of five identical dimer units. In solution, StPrpC was in a dimeric form at low concentrations and was converted to larger oligomers at higher concentrations. CSs are usually dimeric proteins. In Gram-negative bacteria, a hexameric form, believed to be important for regulation of activity by NADH, is also observed. Structural comparisons with hexameric E. coil CS suggested that the key residues involved in NADH binding are not conserved in StPrpC. Structural comparison with the ligand free and bound states of CSs showed that StPrpC is in a nearly closed conformation despite the absence of bound ligands. It was found that the Tyr197 and Leu324 of StPrpC are structurally equivalent to the ligand binding residues His and Val, respectively, of CSs. These substitutions might determine the specificities for acyl-CoAs of these enzymes. (C) 2010 Elsevier Inc. All rights reserved.

Smart polymer mediated purification and recovery of active proteins from inclusion bodies

Obtaining correctly folded proteins from inclusion bodies of recombinant proteins expressed in bacterial hosts requires solubilization with denaturants and a refolding step. Aggregation competes with the second step. Refolding of eight different proteins was carried out by precipitation with smart polymers. These proteins have different molecular weights, different number of disulfide bridges and some of these are known to be highly prone to aggregation. A high throughput refolding screen based upon fluorescence emission maximum around 340 nm (for correctly folded proteins) was developed to identify the suitable smart polymer. The proteins could be dissociated and recovered after the refolding step. The refolding could be scaled up and high refolding yields in the range of 8 mg L-1 (for CD4D12, the first two domains of human CD4) to 58 mg L-1 (for malETrx, thioredoxin fused with signal peptide of maltose binding protein) were obtained. Dynamic light scattering (DLS) showed that polymer if chosen correctly acted as a pseuclochaperonin and bound to the proteins. It also showed that the time for maximum binding was about 50 min which coincided with the time required for incubation (with the polymer) before precipitation for maximum recovery of folded proteins. The refolded proteins were characterized by fluorescence emission spectra, circular dichroism (CD) spectroscopy, melting temperature (T-m), and surface hydrophobicity measurement by ANS (8-anilinol-naphthalene sulfonic acid) fluorescence. Biological activity assay for thioredoxin and fluorescence based assay in case of maltose binding protein (MBP) were also carried out to confirm correct refolding. (C) 2012 Elsevier B.V. All rights reserved.

The interaction of N-trifluoroacetylgalactosamine and its derivatives with winged bean (Psophocarpus tetragonolobus) basic agglutinin reveals differential mechanism of their recognition: a fluorine-19 nuclear magnetic resonance study

Here, we show the binding results of a leguminosae lectin, winged bean basic agglutinin (WBA I) to N-trifluoroacetylgalactosamine (NTFAGalN), methyl-alpha-N-trifluoroacetylgalactosamine (Me alpha NTFAGalN) and methyl-beta-tifluoroacetylgalactosamine (Me beta NTFAGalN) using (19) F NMR spectroscopy. No chemical shift difference between the free and bound states for NTFAGalN and Me beta NTFAGalN, and 0.01-ppm chemical shift change for Me alpha NTFAGalN, demonstrate that the Me alpha NTFAGalN has a sufficiently long residence time on the protein binding site as compared to Me beta NTFAGalN and the free anomers of NTFAGalN. The sugar anomers were found in slow exchange with the binding site of agglutinin. Consequently, we obtained their binding parameters to the protein using line shape analyses. Aforementioned analyses of the activation parameters for the interactions of these saccharides indicate that the binding of alpha and beta anomers of NTFAGalN and Me alpha NTFAGalN is controlled enthalpically, while that of Me beta NTFAGalN is controlled entropically. This asserts the sterically constrained nature of the interaction of the Me beta NTFAGalN with WBA I. These studies thus highlight a significant role of the conformation of the monosaccharide ligands for their recognition by WBA I.

Characterization of single-stranded DNA-binding proteins from Mycobacteria. The carboxyl-terminal of domain of SSB is essential for stable association with its cognate RecA protein

Single-stranded DNA-binding proteins (SSB) play an important role in most aspects of DNA metabolism including DNA replication, repair, and recombination. We report here the identification and characterization of SSB proteins of Mycobacterium smegmatis and Mycobacterium tuberculosis. Sequence comparison of M. smegmatis SSB revealed that it is homologous to M. tuberculosis SSB, except for a small spacer connecting the larger amino-terminal domain with the extreme carboxyl-terminal tail. The purified SSB proteins of mycobacteria bound single-stranded DNA with high affinity, and the association and dissociation constants were similar to that of the prototype SSB. The proteolytic signatures of free and bound forms of SSB proteins disclosed that DNA binding was associated with structural changes at the carboxyl-terminal domain. Significantly, SSB proteins from mycobacteria displayed high affinity for cognate RecA, whereas Escherichia coli SSB did not under comparable experimental conditions. Accordingly, SSB and RecA were coimmunoprecipitated from cell lysates, further supporting an interaction between these proteins in vivo. The carboxyl-terminal domain of M. smegmatis SSB, which is not essential for interaction with ssDNA, is the site of binding of its cognate RecA. These studies provide the first evidence for stable association of eubacterial SSB proteins with their cognate RecA, suggesting that these two proteins might function together during DNA repair and/or recombination.

Facile synthesis of large area porous Cu2O as super hydrophobic yellow-red phosphors

By employing a thermal oxidation strategy, we have grown large area porous Cu2O from Cu foil. CuO nanorods are grown by heating Cu which were in turn heated in an argon atmosphere to obtain a porous Cu2O layer. The porous Cu2O layer is superhydrophobic and exhibits red luminescence. In contrast, Cu2O obtained by direct heating, is hydrophobic and exhibits yellow luminescence. Two more luminescence bands are observed in addition to red and yellow luminescence, corresponding to the recombination of free and bound excitons. Over all, the porous Cu2O obtained from Cu via CuO nanorods, can serve as a superhydrophobic luminescence/phosphor material.

Comparison of tertiary structures of proteins in protein-protein complexes with unbound forms suggests prevalence of allostery in signalling proteins

Abstract: Background: Most signalling and regulatory proteins participate in transient protein-protein interactions during biological processes. They usually serve as key regulators of various cellular processes and are often stable in both protein-bound and unbound forms. Availability of high-resolution structures of their unbound and bound forms provides an opportunity to understand the molecular mechanisms involved. In this work, we have addressed the question "What is the nature, extent, location and functional significance of structural changes which are associated with formation of protein-protein complexes?" Results: A database of 76 non-redundant sets of high resolution 3-D structures of protein-protein complexes, representing diverse functions, and corresponding unbound forms, has been used in this analysis. Structural changes associated with protein-protein complexation have been investigated using structural measures and Protein Blocks description. Our study highlights that significant structural rearrangement occurs on binding at the interface as well as at regions away from the interface to form a highly specific, stable and functional complex. Notably, predominantly unaltered interfaces interact mainly with interfaces undergoing substantial structural alterations, revealing the presence of at least one structural regulatory component in every complex. Interestingly, about one-half of the number of complexes, comprising largely of signalling proteins, show substantial localized structural change at surfaces away from the interface. Normal mode analysis and available information on functions on some of these complexes suggests that many of these changes are allosteric. This change is largely manifest in the proteins whose interfaces are altered upon binding, implicating structural change as the possible trigger of allosteric effect. Although large-scale studies of allostery induced by small-molecule effectors are available in literature, this is, to our knowledge, the first study indicating the prevalence of allostery induced by protein effectors. Conclusions: The enrichment of allosteric sites in signalling proteins, whose mutations commonly lead to diseases such as cancer, provides support for the usage of allosteric modulators in combating these diseases.

Thermodynamics of higher spin black holes in 3D

We examine the thermodynamic properties of recently constructed black hole solutions in SL(3, R) x SL(3, R) Chern-Simons theory in the presence of a chemical potential for spin-3 charge, which acts as an irrelevant deformation of the dual CFT with W-3 X W-3 symmetry. The smoothness or holonomy conditions admit four branches of solutions describing a flow between two AdS(3) backgrounds corresponding to two different CFTs. The dominant branch at low temperatures, connected to the BTZ black hole, merges smoothly with a thermodynamically unstable branch and disappears at higher temperatures. We confirm that the UV region of the flow satisfies the Ward identities of a CFT with W-3((2)) x W-3((2)) symmetry deformed by a spin-3/2 current. This allows to identify the precise map between UV and HI thermodynamic variables. We find that the high temperature regime is dominated by a black hole branch whose thermodynamics can only be consistently inferred with reference to this W-3((2)) x W-3((2)) CFT.

Nature and Properties of a Repulsive Fermi Gas in the Upper Branch of the Energy Spectrum

We generalize the Nozieres-Schmitt-Rink method to study the repulsive Fermi gas in the absence of molecule formation, i.e., in the so-called ``upper branch.'' We find that the system remains stable except close to resonance at sufficiently low temperatures. With increasing scattering length, the energy density of the system attains a maximum at a positive scattering length before resonance. This is shown to arise from Pauli blocking which causes the bound states of fermion pairs of different momenta to disappear at different scattering lengths. At the point of maximum energy, the compressibility of the system is substantially reduced, leading to a sizable uniform density core in a trapped gas. The change in spin susceptibility with increasing scattering length is moderate and does not indicate any magnetic instability. These features should also manifest in Fermi gases with unequal masses and/or spin populations.

Structures of mannose-6-phosphate isomerase from Salmonella typhimurium bound to metal atoms and substrate: implications for catalytic mechanism

Mannose-6-phosphate isomerase (MPI) catalyzes the inter-conversion of mannose 6-phosphate and fructose 6-phosphate. X-ray crystal structures of MPI from Salmonella typhimurium in the apo form (with no metal bound) and in the holo form (with bound Zn2+) and two other structures with yttrium bound at an inhibitory site and complexed with Zn2+ and fructose 6-phosphate (F6P) were determined in order to gain insights into the structure and the isomerization mechanism. Isomerization involves acid/base catalysis with proton transfer between the C1 and C2 atoms of the substrate. His99, Lys132, His131 and Asp270 are close to the substrate and are likely to be the residues involved in proton transfer. The interactions observed at the active site suggest that the ring-opening step is probably catalyzed by His99 and Asp270. An active-site loop consisting of residues 130-133 undergoes conformational changes upon substrate binding. Zn2+ binding induces structural order in the loop consisting of residues 50-54. The metal atom appears to play a role in substrate binding and is probably also important for maintaining the architecture of the active site. Isomerization probably follows the previously suggested cis-enediol mechanism.