Noncommutative vortices and instantons from generalized Bose operators

Generalized Bose operators correspond to reducible representations of the harmonic oscillator algebra. We demonstrate their relevance in the construction of topologically non-trivial solutions in noncommutative gauge theories, focusing our attention to flux tubes, vortices, and instantons. Our method provides a simple new relation between the topological charge and the number of times the basic irreducible representation occurs in the reducible representation underlying the generalized Bose operator. When used in conjunction with the noncommutative ADHM construction, we find that these new instantons are in general not unitarily equivalent to the ones currently known in literature.

Evolutionary Algorithm for the Determination of Optimal Mode of Bioreactor Operation

Stirred tank bioreactors, employed in the production of a variety of biologically active chemicals, are often operated in batch, fed-batch, and continuous modes of operation. The optimal design of bioreactor is dependent on the kinetics of the biological process, as well as the performance criteria (yield, productivity, etc.) under consideration. In this paper, a general framework is proposed for addressing the two key issues related to the optimal design of a bioreactor, namely, (i) choice of the best operating mode and (ii) the corresponding flow rate trajectories. The optimal bioreactor design problem is formulated with initial conditions and inlet and outlet flow rate trajectories as decision variables to maximize more than one performance criteria (yield, productivity, etc.) as objective functions. A computational methodology based on genetic algorithm approach is developed to solve this challenging multiobjective optimization problem with multiple decision variables. The applicability of the algorithm is illustrated by solving two challenging problems from the bioreactor optimization literature.

Protein-Protein Interactions in Clathrin Vesicular Assembly: Radial Distribution of Evolutionary Constraints in Interfaces

In eukaryotic organisms clathrin-coated vesicles are instrumental in the processes of endocytosis as well as intracellular protein trafficking. Hence, it is important to understand how these vesicles have evolved across eukaryotes, to carry cargo molecules of varied shapes and sizes. The intricate nature and functional diversity of the vesicles are maintained by numerous interacting protein partners of the vesicle system. However, to delineate functionally important residues participating in protein-protein interactions of the assembly is a daunting task as there are no high-resolution structures of the intact assembly available. The two cryoEM structures closely representing intact assembly were determined at very low resolution and provide positions of C alpha atoms alone. In the present study, using the method developed by us earlier, we predict the protein-protein interface residues in clathrin assembly, taking guidance from the available low-resolution structures. The conservation status of these interfaces when investigated across eukaryotes, revealed a radial distribution of evolutionary constraints, i.e., if the members of the clathrin vesicular assembly can be imagined to be arranged in spherical manner, the cargo being at the center and clathrins being at the periphery, the detailed phylogenetic analysis of these members of the assembly indicated high-residue variation in the members of the assembly closer to the cargo while high conservation was noted in clathrins and in other proteins at the periphery of the vesicle. This points to the strategy adopted by the nature to package diverse proteins but transport them through a highly conserved mechanism.

Molecular Epidemiology of HIV-1 Subtypes in India: Origin and Evolutionary History of the Predominant Subtype C

Background: India has the third largest HIV-1 epidemic with 2.4 million infected individuals. Molecular epidemiological analysis has identified the predominance of HIV-1 subtype C (HIV-1C). However, the previous reports have been limited by sample size, and uneven geographical distribution. The introduction of HIV-1C in India remains uncertain due to this lack of structured studies. To fill the gap, we characterised the distribution pattern of HIV-1 subtypes in India based on data collection from nationwide clinical cohorts between 2007 and 2011. We also reconstructed the time to the most recent common ancestor (tMRCA) of the predominant HIV-1C strains. Methodology/Principal Findings: Blood samples were collected from 168 HIV-1 seropositive subjects from 7 different states. HIV-1 subtypes were determined using two or three genes, gag, pol, and env using several methods. Bayesian coalescent-based approach was used to reconstruct the time of introduction and population growth patterns of the Indian HIV-1C. For the first time, a high prevalence (10%) of unique recombinant forms (BC and A1C) was observed when two or three genes were used instead of one gene (p<0.01; p = 0.02, respectively). The tMRCA of Indian HIV-1C was estimated using the three viral genes, ranged from 1967 (gag) to 1974 (env). Pol-gene analysis was considered to provide the most reliable estimate 1971, (95% CI: 1965-1976)]. The population growth pattern revealed an initial slow growth phase in the mid-1970s, an exponential phase through the 1980s, and a stationary phase since the early 1990s. Conclusions/Significance: The Indian HIV-1C epidemic originated around 40 years ago from a single or few genetically related African lineages, and since then largely evolved independently. The effective population size in the country has been broadly stable since the 1990s. The evolving viral epidemic, as indicated by the increase of recombinant strains, warrants a need for continued molecular surveillance to guide efficient disease intervention strategies.

Singlet-state creation and universal quantum computation in NMR using a genetic algorithm

The experimental implementation of a quantum algorithm requires the decomposition of unitary operators. Here we treat unitary-operator decomposition as an optimization problem, and use a genetic algorithm-a global-optimization method inspired by nature's evolutionary process-for operator decomposition. We apply this method to NMR quantum information processing, and find a probabilistic way of performing universal quantum computation using global hard pulses. We also demonstrate the efficient creation of the singlet state (a special type of Bell state) directly from thermal equilibrium, using an optimum sequence of pulses. © 2012 American Physical Society.

Singlet-state creation and universal quantum computation in NMR using a genetic algorithm

The experimental implementation of a quantum algorithm requires the decomposition of unitary operators. Here we treat unitary-operator decomposition as an optimization problem, and use a genetic algorithm-a global-optimization method inspired by nature's evolutionary process-for operator decomposition. We apply this method to NMR quantum information processing, and find a probabilistic way of performing universal quantum computation using global hard pulses. We also demonstrate the efficient creation of the singlet state (a special type of Bell state) directly from thermal equilibrium, using an optimum sequence of pulses.

The origins of the evolutionary signal used to predict protein-protein interactions

Background: The correlation of genetic distances between pairs of protein sequence alignments has been used to infer protein-protein interactions. It has been suggested that these correlations are based on the signal of co-evolution between interacting proteins. However, although mutations in different proteins associated with maintaining an interaction clearly occur (particularly in binding interfaces and neighbourhoods), many other factors contribute to correlated rates of sequence evolution. Proteins in the same genome are usually linked by shared evolutionary history and so it would be expected that there would be topological similarities in their phylogenetic trees, whether they are interacting or not. For this reason the underlying species tree is often corrected for. Moreover processes such as expression level, are known to effect evolutionary rates. However, it has been argued that the correlated rates of evolution used to predict protein interaction explicitly includes shared evolutionary history; here we test this hypothesis. Results: In order to identify the evolutionary mechanisms giving rise to the correlations between interaction proteins, we use phylogenetic methods to distinguish similarities in tree topologies from similarities in genetic distances. We use a range of datasets of interacting and non-interacting proteins from Saccharomyces cerevisiae. We find that the signal of correlated evolution between interacting proteins is predominantly a result of shared evolutionary rates, rather than similarities in tree topology, independent of evolutionary divergence. Conclusions: Since interacting proteins do not have tree topologies that are more similar than the control group of non-interacting proteins, it is likely that coevolution does not contribute much to, if any, of the observed correlations.

A POSSIBLE EVOLUTIONARY SCENARIO OF HIGHLY MAGNETIZED SUPER-CHANDRASEKHAR WHITE DWARFS: PROGENITORS OF PECULIAR TYPE Ia SUPERNOVAE

Several recently discovered peculiar Type Ia supernovae seem to demand an altogether new formation theory that might help explain the puzzling dissimilarities between them and the standard Type Ia supernovae. The most striking aspect of the observational analysis is the necessity of invoking super-Chandrasekhar white dwarfs having masses similar to 2.1-2.8 M-circle dot, M-circle dot being the mass of Sun, as their most probable progenitors. Strongly magnetized white dwarfs having super-Chandrasekhar masses have already been established as potential candidates for the progenitors of peculiar Type Ia supernovae. Owing to the Landau quantization of the underlying electron degenerate gas, theoretical results yielded the observationally inferred mass range. Here, we sketch a possible evolutionary scenario by which super-Chandrasekhar white dwarfs could be formed by accretion on to a commonly observed magnetized white dwarf, invoking the phenomenon of flux freezing. This opens multiple possible evolution scenarios ending in supernova explosions of super-Chandrasekhar white dwarfs having masses within the range stated above. We point out that our proposal has observational support, such as the recent discovery of a large number of magnetized white dwarfs by the Sloan Digital Sky Survey.

Sustaining cooperation on networks: an analytical study based on evolutionary game theory

We analytically study the role played by the network topology in sustaining cooperation in a society of myopic agents in an evolutionary setting. In our model, each agent plays the Prisoner's Dilemma (PD) game with its neighbors, as specified by a network. Cooperation is the incumbent strategy, whereas defectors are the mutants. Starting with a population of cooperators, some agents are switched to defection. The agents then play the PD game with their neighbors and compute their fitness. After this, an evolutionary rule, or imitation dynamic is used to update the agent strategy. A defector switches back to cooperation if it has a cooperator neighbor with higher fitness. The network is said to sustain cooperation if almost all defectors switch to cooperation. Earlier work on the sustenance of cooperation has largely consisted of simulation studies, and we seek to complement this body of work by providing analytical insight for the same. We find that in order to sustain cooperation, a network should satisfy some properties such as small average diameter, densification, and irregularity. Real-world networks have been empirically shown to exhibit these properties, and are thus candidates for the sustenance of cooperation. We also analyze some specific graphs to determine whether or not they sustain cooperation. In particular, we find that scale-free graphs belonging to a certain family sustain cooperation, whereas Erdos-Renyi random graphs do not. To the best of our knowledge, ours is the first analytical attempt to determine which networks sustain cooperation in a population of myopic agents in an evolutionary setting.

Infinitely divisible metrics and curvature inequalities for operators in the Cowen-Douglas class

The curvature (T)(w) of a contraction T in the Cowen-Douglas class B-1() is bounded above by the curvature (S*)(w) of the backward shift operator. However, in general, an operator satisfying the curvature inequality need not be contractive. In this paper, we characterize a slightly smaller class of contractions using a stronger form of the curvature inequality. Along the way, we find conditions on the metric of the holomorphic Hermitian vector bundle E-T corresponding to the operator T in the Cowen-Douglas class B-1() which ensures negative definiteness of the curvature function. We obtain a generalization for commuting tuples of operators in the class B-1() for a bounded domain in C-m.

Correlation between local structural dynamics of proteins inferred from NMR ensembles and evolutionary dynamics of homologues of known structure

Conformational changes in proteins are extremely important for their biochemical functions. Correlation between inherent conformational variations in a protein and conformational differences in its homologues of known structure is still unclear. In this study, we have used a structural alphabet called Protein Blocks (PBs). PBs are used to perform abstraction of protein 3-D structures into a 1-D strings of 16 alphabets (a-p) based on dihedral angles of overlapping pentapeptides. We have analyzed the variations in local conformations in terms of PBs represented in the ensembles of 801 protein structures determined using NMR spectroscopy. In the analysis of concatenated data over all the residues in all the NMR ensembles, we observe that the overall nature of inherent local structural variations in NMR ensembles is similar to the nature of local structural differences in homologous proteins with a high correlation coefficient of .94. High correlation at the alignment positions corresponding to helical and beta-sheet regions is only expected. However, the correlation coefficient by considering only the loop regions is also quite high (.91). Surprisingly, segregated position-wise analysis shows that this high correlation does not hold true to loop regions at the structurally equivalent positions in NMR ensembles and their homologues of known structure. This suggests that the general nature of local structural changes is unique; however most of the local structural variations in loop regions of NMR ensembles do not correlate to their local structural differences at structurally equivalent positions in homologues.

Diffraction tomography from intensity measurements: an evolutionary stochastic search to invert experimental data

We develop iterative diffraction tomography algorithms, which are similar to the distorted Born algorithms, for inverting scattered intensity data. Within the Born approximation, the unknown scattered field is expressed as a multiplicative perturbation to the incident field. With this, the forward equation becomes stable, which helps us compute nearly oscillation-free solutions that have immediate bearing on the accuracy of the Jacobian computed for use in a deterministic Gauss-Newton (GN) reconstruction. However, since the data are inherently noisy and the sensitivity of measurement to refractive index away from the detectors is poor, we report a derivative-free evolutionary stochastic scheme, providing strictly additive updates in order to bridge the measurement-prediction misfit, to arrive at the refractive index distribution from intensity transport data. The superiority of the stochastic algorithm over the GN scheme for similar settings is demonstrated by the reconstruction of the refractive index profile from simulated and experimentally acquired intensity data. (C) 2014 Optical Society of America

Bi-Domain Protein Tyrosine Phosphatases Reveal an Evolutionary Adaptation to Optimize Signal Transduction

Significance: The bi-domain protein tyrosine phosphatases (PTPs) exemplify functional evolution in signaling proteins for optimal spatiotemporal signal transduction. Bi-domain PTPs are products of gene duplication. The catalytic activity, however, is often localized to one PTP domain. The inactive PTP domain adopts multiple functional roles. These include modulation of catalytic activity, substrate specificity, and stability of the bi-domain enzyme. In some cases, the inactive PTP domain is a receptor for redox stimuli. Since multiple bi-domain PTPs are concurrently active in related cellular pathways, a stringent regulatory mechanism and selective cross-talk is essential to ensure fidelity in signal transduction. Recent Advances: The inactive PTP domain is an activator for the catalytic PTP domain in some cases, whereas it reduces catalytic activity in other bi-domain PTPs. The relative orientation of the two domains provides a conformational rationale for this regulatory mechanism. Recent structural and biochemical data reveal that these PTP domains participate in substrate recruitment. The inactive PTP domain has also been demonstrated to undergo substantial conformational rearrangement and oligomerization under oxidative stress. Critical Issues and Future Directions: The role of the inactive PTP domain in coupling environmental stimuli with catalytic activity needs to be further examined. Another aspect that merits attention is the role of this domain in substrate recruitment. These aspects have been poorly characterized in vivo. These lacunae currently restrict our understanding of neo-functionalization of the inactive PTP domain in the bi-domain enzyme. It appears likely that more data from these research themes could form the basis for understanding the fidelity in intracellular signal transduction.

Accurate prediction of interfacial residues in two-domain proteins using evolutionary information: Implications for three-dimensional modeling

With the preponderance of multidomain proteins in eukaryotic genomes, it is essential to recognize the constituent domains and their functions. Often function involves communications across the domain interfaces, and the knowledge of the interacting sites is essential to our understanding of the structure-function relationship. Using evolutionary information extracted from homologous domains in at least two diverse domain architectures (single and multidomain), we predict the interface residues corresponding to domains from the two-domain proteins. We also use information from the three-dimensional structures of individual domains of two-domain proteins to train naive Bayes classifier model to predict the interfacial residues. Our predictions are highly accurate (approximate to 85%) and specific (approximate to 95%) to the domain-domain interfaces. This method is specific to multidomain proteins which contain domains in at least more than one protein architectural context. Using predicted residues to constrain domain-domain interaction, rigid-body docking was able to provide us with accurate full-length protein structures with correct orientation of domains. We believe that these results can be of considerable interest toward rational protein and interaction design, apart from providing us with valuable information on the nature of interactions. Proteins 2014; 82:1219-1234. (c) 2013 Wiley Periodicals, Inc.

Flag structure for operators in the Cowen-Douglas class

The explicit description of homogeneous operators and localization of a Hilbert module naturally leads to the definition of a class of Cowen-Douglas operators possessing a flag structure. These operators are irreducible. We show that the flag structure is rigid in the sense that the unitary equivalence class of the operator and the flag structure determine each other. We obtain a complete set of unitary invariants which are somewhat more tractable than those of an arbitrary operator in the Cowen-Douglas class. (C) 2014 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.