A Grobner basis for certain affine monomial curves

Let K be a field and let m(0),...,m(e-1) be a sequence of positive integers. Let W be a monomial curve in the affine e-space A(K)(e), defined parametrically by X-0 = T-m0,...,Xe-1 = Tme-1 and let p be the defining ideal of W. In this article, we assume that some e-1 terms of m(0), m(e-1) form an arithmetic sequence and produce a Grobner basis for p.

Conformational basis for substrate recognition and regulation of catalytic activity in Staphylococcus aureus nucleoside di-phosphate kinase

Nucleoside diphosphate kinases (NDK) are characterized by high catalytic turnover rates and diverse substrate specificity. These features make this enzyme an effective activator of a pro-drug an application that has been actively pursued for a variety of therapeutic strategies. The catalytic mechanism of this enzyme is governed by a conserved histidine that coordinates a magnesium ion at the active site. Despite substantial structural and biochemical information on NDK, the mechanistic feature of the phospho-transfer that leads to auto-phosphorylation remains unclear. While the role of the histidine residue is well documented, the other active site residues, in particular the conserved serine remains poorly characterized. Studies on some homologues suggest no role for the serine residue at the active site, while others suggest a crucial role for this serine in the regulation and quaternary association of this enzyme in some species. Here we report the biochemical features of the Staphylococcus aureus NDK and the mutant enzymes. We also describe the crystal structures of the apo-NDK, as a transition state mimic with vanadate and in complex with different nucleotide substrates. These structures formed the basis for molecular dynamics simulations to understand the broad substrate specificity of this enzyme and the role of active site residues in the phospho-transfer mechanism and oligomerization. Put together, these data suggest that concerted changes in the conformation of specific residues facilitate the stabilization of nucleotide complexes thereby enabling the steps involved in the ping-pong reaction mechanism without large changes to the overall structure of this enzyme. (C) 2011 Elsevier B.V. All rights reserved.

Structural basis for the functional and inhibitory mechanisms of beta-hydroxyacyl-acyl carrier protein dehydratase (FabZ) of Plasmodium falciparum

The beta-hydroxyacyl-acyl carrier protein dehydratase of Plasmodium falciparum (PfFabZ) catalyzes the third and important reaction of the fatty acid elongation cycle. The crystal structure of PfFabZ is available in hexameric (active) and dimeric (inactive) forms. However, PfFabZ has not been crystallized with any bound inhibitors until now. We have designed a new condition to crystallize PfFabZ with its inhibitors bound in the active site, and determined the crystal structures of four of these complexes. This is the first report on any FabZ enzyme with active site inhibitors that interact directly with the catalytic residues. Inhibitor binding not only stabilized the substrate binding loop but also revealed that the substrate binding tunnel has an overall shape of ``U''. In the crystal structures, residue Phe169 located in the middle of the tunnel was found to be in two different conformations, open and closed. Thus, Phe169, merely by changing its side chain conformation, appears to be controlling the length of the tunnel to make it suitable for accommodating longer substrates. The volume of the substrate binding tunnel is determined by the sequence as well as by the conformation of the substrate binding loop region and varies between organisms for accommodating fatty acids of different chain lengths. This report on the crystal structures of the complexes of PfFabZ provides the structural basis of the inhibitory mechanism of the enzyme that could be used to improve the potency of inhibitors against an important component of fatty acid synthesis common to many infectious organisms. (C) 2011 Elsevier Inc. All rights reserved.

Conformational Basis for Substrate Recruitment in Protein Tyrosine Phosphatase 10D

The coordinated activity of protein tyrosine phosphatases (PTPs) is crucial for the initiation, modulation, and termination of diverse cellular processes. The catalytic activity of this protein depends on a nucleophilic cysteine at the active site that mediates the hydrolysis of the incoming phosphotyrosine substrate. While the role of conserved residues in the catalytic mechanism of PTPs has been extensively examined, the diversity in the mechanisms of substrate recognition and modulation of catalytic activity suggests that other, less conserved sequence and structural features could contribute to this process. Here we describe the crystal structures of Drosophila melanogaster PTP10D in the apo form as well as in a complex with a substrate peptide and an inhibitor. These studies reveal the role of aromatic ring stacking interactions at the boundary of the active site of PTPs in mediating substrate recruitment. We note that phenylalanine 76, of the so-called KNRY loop, is crucial for orienting the phosphotyrosine residue toward the nucleophilic cysteine. Mutation of phenylalanine 76 to leucine results in a 60-fold decrease in the catalytic efficiency of the enzyme. Fluorescence measurements with a competitive inhibitor, p-nitrocatechol sulfate, suggest that Phe76 also influences the formation of the enzyme-substrate intermediate. The structural and biochemical data for PTP10D thus highlight the role of relatively less conserved residues in PTP domains in both substrate recruitment and modulation of reaction kinetics.

Composite instantaneous comparators basis for design and their transient performance

Principles of design of composite instantaneous comparators (a combination of amplitude- and phase- comparison techniques) are laid out to provide directional, directional-reactance, nonoffset-resistance and conductance characteristices. The respective signals provided by the voltage transformer and the current transformer are directly used as relaying signals without resorting to any form of mixing. Phase shifts required, are obtained by using magnetic ferrite cores in a novel manner. Sampling units employing a combination of ferrite cores and semiconductor devices provide highly reliable designs. Special attention is paid to the choice of relaying signals, to eliminate the need for any synchronisation or modification and to avoid `image¿ characteristics. These factors have resulted in a considerable simplification of the practical circuitry. A thyristor AND circuit is employed in dual comparator units to provide the final tripping, and leads to a circuit which is much less sensitive to extraneous signals than a single-thyristor unit.

An (O)over-bar(m(2)n) randomized algorithm to compute a minimum cycle basis of a directed graph

We consider the problem of computing a minimum cycle basis in a directed graph G. The input to this problem is a directed graph whose arcs have positive weights. In this problem a {- 1, 0, 1} incidence vector is associated with each cycle and the vector space over Q generated by these vectors is the cycle space of G. A set of cycles is called a cycle basis of G if it forms a basis for its cycle space. A cycle basis where the sum of weights of the cycles is minimum is called a minimum cycle basis of G. The current fastest algorithm for computing a minimum cycle basis in a directed graph with m arcs and n vertices runs in O(m(w+1)n) time (where w < 2.376 is the exponent of matrix multiplication). If one allows randomization, then an (O) over tilde (m(3)n) algorithm is known for this problem. In this paper we present a simple (O) over tilde (m(2)n) randomized algorithm for this problem. The problem of computing a minimum cycle basis in an undirected graph has been well-studied. In this problem a {0, 1} incidence vector is associated with each cycle and the vector space over F-2 generated by these vectors is the cycle space of the graph. The fastest known algorithm for computing a minimum cycle basis in an undirected graph runs in O(m(2)n + mn(2) logn) time and our randomized algorithm for directed graphs almost matches this running time.

On maximum entropy and minimum KL-divergence optimization by Grobner basis methods

In this paper we study constrained maximum entropy and minimum divergence optimization problems, in the cases where integer valued sufficient statistics exists, using tools from computational commutative algebra. We show that the estimation of parametric statistical models in this case can be transformed to solving a system of polynomial equations. We give an implicit description of maximum entropy models by embedding them in algebraic varieties for which we give a Grobner basis method to compute it. In the cases of minimum KL-divergence models we show that implicitization preserves specialization of prior distribution. This result leads us to a Grobner basis method to embed minimum KL-divergence models in algebraic varieties. (C) 2012 Elsevier Inc. All rights reserved.

Sequence and structural basis for chromosomal fragility during translocations in cancer

Chromosomal aberration is considered to be one of the major characteristic features in many cancers. Chromosomal translocation, one type of genomic abnormality, can lead to deregulation of critical genes involved in regulating important physiological functions such as cell proliferation and DNA repair. Although chromosomal translocations were thought to be random events, recent findings suggest that certain regions in the human genome are more susceptible to breakage than others. The possibility of deviation from the usual B-DNA conformation in such fragile regions has been an active area of investigation. This review summarizes the factors that contribute towards the fragility of these regions in the chromosomes, such as DNA sequences and the role of different forms of DNA structures. Proteins responsible for chromosomal fragility, and their mechanism of action are also discussed. The effect of positioning of chromosomes within the nucleus favoring chromosomal translocations and the role of repair mechanisms are also addressed.

Structural and molecular basis of interaction of HCV non-structural protein 5A with human casein kinase 1 alpha and PKR

Background: Interaction of non-structural protein 5A (NS5A) of Hepatitis C virus (HCV) with human kinases namely, casein kinase 1 alpha (ck1 alpha) and protein kinase R (PKR) have different functional implications such as regulation of viral replication and evasion of interferon induced immune response respectively. Understanding the structural and molecular basis of interactions of the viral protein with two different human kinases can be useful in developing strategies for treatment against HCV. Results: Serine 232 of NS5A is known to be phosphorylated by human ck1 alpha. A structural model of NS5A peptide containing phosphoacceptor residue Serine 232 bound to ck1 alpha has been generated using the known 3-D structures of kinase-peptide complexes. The substrate interacting residues in ck1 alpha has been identified from the model and these are found to be conserved well in the ck1 family. ck1 alpha - substrate peptide complex has also been used to understand the structural basis of association between ck1 alpha and its other viral stress induced substrate, tumour suppressor p53 transactivation domain which has a crystal structure available. Interaction of NS5A with another human kinase PKR is primarily genotype specific. NS5A from genotype 1b has been shown to interact and inhibit PKR whereas NS5A from genotype 2a/3a are unable to bind and inhibit PKR efficiently. This is one of the main reasons for the varied response to interferon therapy in HCV patients across different genotypes. Using PKR crystal structure, sequence alignment and evolutionary trace analysis some of the critical residues responsible for the interaction of NS5A 1b with PKR have been identified. Conclusions: The substrate interacting residues in ck1 alpha have been identified using the structural model of kinase substrate peptide. The PKR interacting NS5A 1b residues have also been predicted using PKR crystal structure, NS5A sequence analysis along with known experimental results. Functional significance and nature of interaction of interferon sensitivity determining region and variable region 3 of NS5A in different genotypes with PKR which was experimentally shown are also supported by the findings of evolutionary trace analysis. Designing inhibitors to prevent this interaction could enable the HCV genotype 1 infected patients respond well to interferon therapy.

Border basis detection is NP-complete

Border basis detection (BBD) is described as follows: given a set of generators of an ideal, decide whether that set of generators is a border basis of the ideal with respect to some order ideal. The motivation for this problem comes from a similar problem related to Grobner bases termed as Grobner basis detection (GBD) which was proposed by Gritzmann and Sturmfels (1993). GBD was shown to be NP-hard by Sturmfels and Wiegelmann (1996). In this paper, we investigate the computational complexity of BBD and show that it is NP-complete.

Crystal structures and binding studies of atovaquone and its derivatives with cytochrome bc(1): a molecular basis for drug design

Crystal structure of trans-atovaquone (antimalarial drug), its polymorph and its stereoisomer (cis) along with five other derivatives with different functional groups have been analyzed. Based on the conformational features of these compounds and the characteristics of the nature of intermolecular interactions, valuable insights into the atomistic details of protein-inhibitor interactions have been derived by docking studies. Atovaquone and its derivatives pack in the crystal lattice using intermolecular O-H center dot center dot center dot O hydrogen bond dimer motifs supported by surrogate weak interactions including C-H center dot center dot center dot O and C-H center dot center dot center dot Cl hydrogen bonds. The docking results of these molecules with cytochrome bc(1) show preferences to form N-H center dot center dot center dot O, O-H center dot center dot center dot O and O-H center dot center dot center dot Cl hydrogen bonds. The involvement of halogen atoms in the binding pocket appears to be significant and is contrary to the theoretically predicted mechanism of protein-ligand docking reported earlier based on mimicking experimental binding results of stigmatellin with cytochrome bc(1). The significance of subtle energy factors controlled by weak intermolecular interactions appears to play a major role in drug binding.

Estimation of design basis earthquake using region-specific M-max, for the NPP site at Kalpakkam, Tamil Nadu, India

The objective of the paper is to estimate Safe Shutdown Earthquake (SSE) and Operating/Design Basis Earthquake (OBE/DBE) for the Nuclear Power Plant (NPP) site located at Kalpakkam, Tamil Nadu, India. The NPP is located at 12.558 degrees N, 80.175 degrees E and a 500 km circular area around NPP site is considered as `seismic study area' based on past regional earthquake damage distribution. The geology, seismicity and seismotectonics of the study area are studied and the seismotectonic map is prepared showing the seismic sources and the past earthquakes. Earthquake data gathered from many literatures are homogenized and declustered to form a complete earthquake catalogue for the seismic study area. The conventional maximum magnitude of each source is estimated considering the maximum observed magnitude (M-max(obs)) and/or the addition of 0.3 to 0.5 to M-max(obs). In this study maximum earthquake magnitude has been estimated by establishing a region's rupture character based on source length and associated M-max(obs). A final source-specific M-max is selected from the three M-max values by following the logical criteria. To estimate hazard at the NPP site, ten Ground-Motion Prediction Equations (GMPEs) valid for the study area are considered. These GMPEs are ranked based on Log-Likelihood (LLH) values. Top five GMPEs are considered to estimate the peak ground acceleration (PGA) for the site. Maximum PGA is obtained from three faults and named as vulnerable sources to decide the magnitudes of OBE and SSE. The average and normalized site specific response spectrum is prepared considering three vulnerable sources and further used to establish site-specific design spectrum at NPP site.