Two complementary molecular energy decomposition schemes: the Mayer and Ziegler-Rauk methods in comparison

In the present paper we discuss and compare two different energy decomposition schemes: Mayer's Hartree-Fock energy decomposition into diatomic and monoatomic contributions [Chem. Phys. Lett. 382, 265 (2003)], and the Ziegler-Rauk dissociation energy decomposition [Inorg. Chem. 18, 1558 (1979)]. The Ziegler-Rauk scheme is based on a separation of a molecule into fragments, while Mayer's scheme can be used in the cases where a fragmentation of the system in clearly separable parts is not possible. In the Mayer scheme, the density of a free atom is deformed to give the one-atom Mulliken density that subsequently interacts to give rise to the diatomic interaction energy. We give a detailed analysis of the diatomic energy contributions in the Mayer scheme and a close look onto the one-atom Mulliken densities. The Mulliken density ρA has a single large maximum around the nuclear position of the atom A, but exhibits slightly negative values in the vicinity of neighboring atoms. The main connecting point between both analysis schemes is the electrostatic energy. Both decomposition schemes utilize the same electrostatic energy expression, but differ in how fragment densities are defined. In the Mayer scheme, the electrostatic component originates from the interaction of the Mulliken densities, while in the Ziegler-Rauk scheme, the undisturbed fragment densities interact. The values of the electrostatic energy resulting from the two schemes differ significantly but typically have the same order of magnitude. Both methods are useful and complementary since Mayer's decomposition focuses on the energy of the finally formed molecule, whereas the Ziegler-Rauk scheme describes the bond formation starting from undeformed fragment densities

Density functional energy decomposition into one- and two-atom contributions

The present work provides a generalization of Mayer's energy decomposition for the density-functional theory (DFT) case. It is shown that one- and two-atom Hartree-Fock energy components in Mayer's approach can be represented as an action of a one-atom potential VA on a one-atom density ρ A or ρ B. To treat the exchange-correlation term in the DFT energy expression in a similar way, the exchange-correlation energy density per electron is expanded into a linear combination of basis functions. Calculations carried out for a number of density functionals demonstrate that the DFT and Hartree-Fock two-atom energies agree to a reasonable extent with each other. The two-atom energies for strong covalent bonds are within the range of typical bond dissociation energies and are therefore a convenient computational tool for assessment of individual bond strength in polyatomic molecules. For nonspecific nonbonding interactions, the two-atom energies are low. They can be either repulsive or slightly attractive, but the DFT results more frequently yield small attractive values compared to the Hartree-Fock case. The hydrogen bond in the water dimer is calculated to be between the strong covalent and nonbonding interactions on the energy scale

Two complementary molecular energy decomposition schemes: the Mayer and Ziegler-Rauk methods in comparison

In the present paper we discuss and compare two different energy decomposition schemes: Mayer's Hartree-Fock energy decomposition into diatomic and monoatomic contributions [Chem. Phys. Lett. 382, 265 (2003)], and the Ziegler-Rauk dissociation energy decomposition [Inorg. Chem. 18, 1558 (1979)]. The Ziegler-Rauk scheme is based on a separation of a molecule into fragments, while Mayer's scheme can be used in the cases where a fragmentation of the system in clearly separable parts is not possible. In the Mayer scheme, the density of a free atom is deformed to give the one-atom Mulliken density that subsequently interacts to give rise to the diatomic interaction energy. We give a detailed analysis of the diatomic energy contributions in the Mayer scheme and a close look onto the one-atom Mulliken densities. The Mulliken density ρA has a single large maximum around the nuclear position of the atom A, but exhibits slightly negative values in the vicinity of neighboring atoms. The main connecting point between both analysis schemes is the electrostatic energy. Both decomposition schemes utilize the same electrostatic energy expression, but differ in how fragment densities are defined. In the Mayer scheme, the electrostatic component originates from the interaction of the Mulliken densities, while in the Ziegler-Rauk scheme, the undisturbed fragment densities interact. The values of the electrostatic energy resulting from the two schemes differ significantly but typically have the same order of magnitude. Both methods are useful and complementary since Mayer's decomposition focuses on the energy of the finally formed molecule, whereas the Ziegler-Rauk scheme describes the bond formation starting from undeformed fragment densities

Density functional energy decomposition into one- and two-atom contributions

The present work provides a generalization of Mayer's energy decomposition for the density-functional theory (DFT) case. It is shown that one- and two-atom Hartree-Fock energy components in Mayer's approach can be represented as an action of a one-atom potential VA on a one-atom density ρ A or ρ B. To treat the exchange-correlation term in the DFT energy expression in a similar way, the exchange-correlation energy density per electron is expanded into a linear combination of basis functions. Calculations carried out for a number of density functionals demonstrate that the DFT and Hartree-Fock two-atom energies agree to a reasonable extent with each other. The two-atom energies for strong covalent bonds are within the range of typical bond dissociation energies and are therefore a convenient computational tool for assessment of individual bond strength in polyatomic molecules. For nonspecific nonbonding interactions, the two-atom energies are low. They can be either repulsive or slightly attractive, but the DFT results more frequently yield small attractive values compared to the Hartree-Fock case. The hydrogen bond in the water dimer is calculated to be between the strong covalent and nonbonding interactions on the energy scale

Theoretical study of the second-order vibrational Stark effect

The behaviour of the harmonic infrared frequency of diatomic molecules subjected to moderate static uniform electric fields is analysed. The potential energy expression has been developed as a function of a static uniform electric field, which brings about a formulation describing the frequency versus field strength curve. With the help of the first and second derivatives of the expressions obtained, which correspond to the first- and second-order Stark effects, it was possible to find the maxima of the frequency versus field strength curves for a series of molecules using a Newton-Raphson search. A method is proposed which requires only the calculation of a few energy derivatives at a particular value of the field strength. At the same time, the expression for the dependence of the interatomic distance on the electric field strength is derived and the minimum of this curve is found for the same species. Derived expressions and numerical results are discussed and compared with other studi

Thirring model with jump defect

The purpose of our work is to extend the formulation of classical affine Toda Models in the presence of jump defects to pure fermionic Thirring model. As a first attempt we construct the Lagrangian of the Grassmanian Thirring model with jump defect (of Backlund type) and present its conserved modified momentum and energy expressions giving a first indication of its integra-bility. Copyright © owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence.

The peroxisome proliferator-activated receptor beta/delta agonist, GW501516, regulates the expression of genes involved in lipid catabolism and energy uncoupling in skeletal muscle cells

Lipid homeostasis is controlled by the peroxisome proliferator-activated receptors (PPARalpha, -beta/delta, and -gamma) that function as fatty acid-dependent DNA-binding proteins that regulate lipid metabolism. In vitro and in vivo genetic and pharmacological studies have demonstrated PPARalpha regulates lipid catabolism. In contrast, PPARgamma regulates the conflicting process of lipid storage. However, relatively little is known about PPARbeta/delta in the context of target tissues, target genes, lipid homeostasis, and functional overlap with PPARalpha and -gamma. PPARbeta/delta, a very low-density lipoprotein sensor, is abundantly expressed in skeletal muscle, a major mass peripheral tissue that accounts for approximately 40% of total body weight. Skeletal muscle is a metabolically active tissue, and a primary site of glucose metabolism, fatty acid oxidation, and cholesterol efflux. Consequently, it has a significant role in insulin sensitivity, the blood-lipid profile, and lipid homeostasis. Surprisingly, the role of PPARbeta/delta in skeletal muscle has not been investigated. We utilize selective PPARalpha, -beta/delta, -gamma, and liver X receptor agonists in skeletal muscle cells to understand the functional role of PPARbeta/delta, and the complementary and/or contrasting roles of PPARs in this major mass peripheral tissue. Activation of PPARbeta/delta by GW501516 in skeletal muscle cells induces the expression of genes involved in preferential lipid utilization, beta-oxidation, cholesterol efflux, and energy uncoupling. Furthermore, we show that treatment of muscle cells with GW501516 increases apolipoprotein-A1 specific efflux of intracellular cholesterol, thus identifying this tissue as an important target of PPARbeta/delta agonists. Interestingly, fenofibrate induces genes involved in fructose uptake, and glycogen formation. In contrast, rosiglitazone-mediated activation of PPARgamma induces gene expression associated with glucose uptake, fatty acid synthesis, and lipid storage. Furthermore, we show that the PPAR-dependent reporter in the muscle carnitine palmitoyltransferase-1 promoter is directly regulated by PPARbeta/delta, and not PPARalpha in skeletal muscle cells in a PPARgamma coactivator-1-dependent manner. This study demonstrates that PPARs have distinct roles in skeletal muscle cells with respect to the regulation of lipid, carbohydrate, and energy homeostasis. Moreover, we surmise that PPARgamma/delta agonists would increase fatty acid catabolism, cholesterol efflux, and energy expenditure in muscle, and speculate selective activators of PPARbeta/delta may have therapeutic utility in the treatment of hyperlipidemia, atherosclerosis, and obesity.

Reprogramming energy metabolism and inducing angiogenesis : co-expression of monocarboxylate transporters with VEGF family members in cervical adenocarcinomas

Reprogramming energy metabolism and inducing angiogenesis: co-expression of monocarboxylate transporters with VEGF family members in cervical adenocarcinomas.

Comparative effects of oleoyl-estrone and a specific b3-adrenergic agonist (CL316, 243) on the expression of genes involved in energy metabolism of rat white adipose tissue

Background: The combination of oleoyl-estrone (OE) and a selective b3-adrenergic agonist (B3A; CL316,243) treatment in rats results in a profound and rapid wasting of body reserves (lipid). Methods: In the present study we investigated the effect of OE (oral gavage) and/or B3A (subcutaneous constant infusion) administration for 10 days to overweight male rats, compared with controls, on three distinct white adipose tissue (WAT) sites: subcutaneous inguinal, retroperitoneal and epididymal. Tissue weight, DNA (and, from these values cellularity), cAMP content and the expression of several key energy handling metabolism and control genes were analyzed and computed in relation to the whole site mass. Results: Both OE and B3A significantly decreased WAT mass, with no loss of DNA (cell numbers). OE decreased and B3A increased cAMP. Gene expression patterns were markedly different for OE and B3A. OE tended to decrease expression of most genes studied, with no changes (versus controls) of lipolytic but decrease of lipogenic enzyme genes. The effects of B3A were widely different, with a generalized increase in the expression of most genes, including the adrenergic receptors, and, especially the uncoupling protein UCP1. Discussion: OE and B3A, elicit widely different responses in WAT gene expression, end producing similar effects, such as shrinking of WAT, loss of fat, maintenance of cell numbers. OE acted essentially on the balance of lipolysislipogenesis and the blocking of the uptake of substrates; its decrease of synthesis favouring lipolysis. B3A induced a shotgun increase in the expression of most regulatory systems in the adipocyte, an effect that in the end favoured again the loss of lipid; this barely selective increase probably produces inefficiency, which coupled with the increase in UCP1 expression may help WAT to waste energy through thermogenesis. Conclusions: There were considerable differences in the responses of the three WAT sites. OE in general lowered gene expression and stealthily induced a substrate imbalance. B3A increasing the expression of most genes enhanced energy waste through inefficiency rather than through specific pathway activation. There was not a synergistic effect between OE and B3A in WAT, but their combined action increased WAT energy waste.

Approximate expression for the energy of a D-dimensional anharmonic oscillator

An approximate expression is constructed for the energy of an anharmonic potential with centrifugal barrier. In order to obtain such an analytical expression, the quasi-exact solvability is used and then a fitting of these exact solutions is done.

Effects of dietary macronutrient content on energy metabolism and uncoupling protein mRNA expression in broiler chickens

The objective of the present study was to investigate the effects of dietary macronutrient ratio on energy metabolism and on skeletal muscle mRNA expression of avian uncoupling protein (UCP), thought to be implicated in thermogenesis in birds. Broiler chickens from 2 to 6 weeks of age received one of three isoenergetic diets containing different macronutrient ratios (low-lipid (LL) 30 v. 77 g lipid/kg-, low-protein (LP) 125 v. 197 g crude protein (N X 6.25)/kg; low-carbohydrate (LC) 440 v. 520 g carbohydrate/kg). LP chickens were characterised by significantly lower body weights and food intakes compared with LL and LC chickens (-47 and -38% respectively) but similar heat production/kg metabolic body weight, as measured by indirect calorimetry, in the three groups. However, heat production/g food ingested was higher in animals receiving the LP diet (+41%, P<0.05). These chickens also deposited 57% less energy as protein (P<0.05) and 33% more as fat. No significant differences in energy and N balances were detected between LL and LC chickens. The diets with the higher fat contents (i.e. The LP and LC diets) induced slightly but significantly higher relative expressions of avian UCP mRNA in gastrocnemius muscle, measured by reverse transcription-polymerase chain reaction, than the LL diet (88 and 90 v. 78% glyceraldehyde-3-phosphate dehydrogenase respectively, P<0.05). Our present results are consistent with the recent view that UCP homologues could be involved in the regulation of lipid utilisation as fuel substrate and provide evidence that the macronutrient content of the diet regulates energy metabolism and especially protein and fat deposition.

The plant energy-dissipating mitochondrial systems: Depicting the genomic structure and the expression profiles of the gene families of uncoupling protein and alternative oxidase in monocots and dicots

The simultaneous existence of alternative oxidases and uncoupling proteins in plants has raised the question as to why plants need two energy-dissipating systems with apparently similar physiological functions. A probably complete plant uncoupling protein gene family is described and the expression profiles of this family compared with the multigene family of alternative oxidases in Arabidopsis thaliana and sugarcane (Saccharum sp.) employed as dicot and monocot models, respectively. In total, six uncoupling protein genes, AtPUMP1-6, were recognized within the Arabidopsis genome and five (SsPUMP1-5) in a sugarcane EST database. The recombinant AtPUMP5 protein displayed similar biochemical properties as AtPUMP1. Sugarcane possessed four Arabidopsis AOx1-type orthologues (SsAOx1a-1d); no sugarcane orthologue corresponding to Arabidopsis AOx2-type genes was identified. Phylogenetic and expression analyses suggested that AtAOx1d does not belong to the AOx1-type family but forms a new (AOx3-type) family. Tissue-enriched expression profiling revealed that uncoupling protein genes were expressed more ubiquitously than the alternative oxidase genes. Distinct expression patterns among gene family members were observed between monocots and dicots and during chilling stress. These findings suggest that the members of each energy-dissipating system are subject to different cell or tissue/organ transcriptional regulation. As a result, plants may respond more flexibly to adverse biotic and abiotic conditions, in which oxidative stress is involved. © The Author [2006]. Published by Oxford University Press [on behalf of the Society for Experimental Biology]. All rights reserved.

Effects of BST and high energy diet on gene expression in mammary parenchyma of dairy heifers

The objective of this study was to determine the effects of dietary energy and recombinant bovine somatotropin (bST) injection to identify genes that might control mammogenesis. Total RNA was extracted from the parenchymal tissue of 32 heifers randomly assigned to one of four treatments: two diets (a standard diet and a high energy, high protein diet), each with or without bST. To perform microarray experiments, RNA samples were pooled (2 animals/pool) before reverse transcription and labeling with Cy3 or Cy5. A 4-node loop design was used to examine the differential gene expression among treatments using a bovine-specific cDNA micro array (National Bovine Functional Genomics Consortium Library, NBFGC) containing 18,263 unique expressed sequence tags (EST). Significance levels of differential gene expression among treatments were assessed using a mixed model approach. Injection of bST altered the expression of 12 % of the genes on NBFGC slide related to tissue development, whereas 6% were altered by diet. Administration of bST increases the expression of genes positively related to cell proliferation and mammary parenchyma to a greater extent than a high energy diet. © 2013 Sociedade Brasileira de Zootecnia.

Search for supersymmetry in hadronic final states with missing transverse energy using the variables αT and b-quark multiplicity in pp collisions at {Mathematical expression}

An inclusive search for supersymmetric processes that produce final states with jets and missing transverse energy is performed in pp collisions at a centre-of-mass energy of 8 TeV. The data sample corresponds to an integrated luminosity of 11.7 fb-1 collected by the CMS experiment at the LHC. In this search, a dimensionless kinematic variable, αT, is used to discriminate between events with genuine and misreconstructed missing transverse energy. The search is based on an examination of the number of reconstructed jets per event, the scalar sum of transverse energies of these jets, and the number of these jets identified as originating from bottom quarks. No significant excess of events over the standard model expectation is found. Exclusion limits are set in the parameter space of simplified models, with a special emphasis on both compressed-spectrum scenarios and direct or gluino-induced production of third-generation squarks. For the case of gluino-mediated squark production, gluino masses up to 950-1125 GeV are excluded depending on the assumed model. For the direct pair-production of squarks, masses up to 450 GeV are excluded for a single light first- or second-generation squark, increasing to 600 GeV for bottom squarks. © 2013 CERN for the benefit of the CMS collaboration.

Energy Signaling in the Regulation of Gene Expression during Stress

Maintenance of homeostasis is pivotal to all forms of life. In the case of plants, homeostasis is constantly threatened by the inability to escape environmental fluctuations, and therefore sensitive mechanisms must have evolved to allow rapid perception of environmental cues and concomitant modification of growth and developmental patterns for adaptation and survival. Re-establishment of homeostasis in response to environmental perturbations requires reprogramming of metabolism and gene expression to shunt energy sources from growth-related biosynthetic processes to defense, acclimation, and, ultimately, adaptation. Failure to mount an initial 'emergency' response may result in nutrient deprivation and irreversible senescence and cell death. Early signaling events largely determine the capacity of plants to orchestrate a successful adaptive response. Early events, on the other hand, are likely to be shared by different conditions through the generation of similar signals and before more specific responses are elaborated. Recent studies lend credence to this hypothesis, underpinning the importance of a shared energy signal in the transcriptional response to various types of stress. Energy deficiency is associated with most environmental perturbations due to their direct or indirect deleterious impact on photosynthesis and/or respiration. Several systems are known to have evolved for monitoring the available resources and triggering metabolic, growth, and developmental decisions accordingly. In doing so, energy-sensing systems regulate gene expression at multiple levels to allow flexibility in the diversity and the kinetics of the stress response.