Exploring the electronic structure of knotted proteins: the case of two ornithine transcarbamylase family.

CONTEXT: Geometrical knots are rare structural arrangements in proteins in which the polypeptide chain ties itself into a knot, which is very intriguing due to the uncertainty of their impact on the protein properties. Presently, classical molecular dynamics is the most employed technique in the few studies found on this topic, so any information on how the presence of knots affects the reactivity and electronic properties of proteins is even scarcer. Using the electronic structure methods and quantum chemical descriptors analysis, we found that the same amino-acid residues in the knot core have statistically larger values for the unknotted protein, for both hard-hard and soft-soft interaction descriptors. In addition, we present a computationally feasible protocol, where we show it is possible to separate the contribution of the geometrical knot to the reactivity and other electronic structure properties. METHODS: In order to investigate these systems, we used PRIMoRDiA, a new software developed by our research group, to explore the electronic structure of biological macromolecules. We evaluated several local quantum chemical descriptors to unveil relevant patterns potentially originating from the presence of the geometrical knot in two proteins, belonging to the ornithine transcarbamylase family. We compared several sampled structures from these two enzymes that are highly similar in both tertiary structure and function, but one of them has a knot whereas the other does not. The sampling was carried out through molecular dynamics simulations using ff14SB force field along 50 ns, and the semiempirical convergence was performed with PM7 Hamiltonian.

Exploring the antiviral activity of α-ketoamides compounds through electronic structure calculations: a structure-activity relationship study.

In recent years, the scientific community has worked intensively in the search and development of new drugs to suppress viral infections, such as COVID-19. In fact, a number of active compounds have been tested; however, the absence of significant structure-activity relationships hinders the production of optimized drugs. In this study, molecular modeling techniques were employed to investigate the electronic, structural and chemical reactivity properties of a set α-ketoamides whose antiviral activities have been reported in the literature, aiming to propose new promising derivatives. The local reactivity of the compounds was evaluated via condensed-to-atoms Fukui indexes and molecular electrostatic potential. Multivariate data analysis and random forests machine learning techniques were employed to correlate the antiviral properties and electronic and structural descriptors and identify relevant variables. A series of new derivatives were then proposed and evaluated via density functional theory-based calculations, and docking/molecular dynamics with the target protein of the virus. The results suggest that active derivatives present reduced reactivity towards electrophilic agents on the central core of the molecules and high reactivity on R1 ligands. Derivatives with higher predicted antiviral activities were proposed based on simple electronic descriptors, and their efficacies are reinforced by docking and molecular dynamics simulations.Communicated by Ramaswamy H. Sarma.

Relativistic adapted Gaussian basis sets free of variational prolapse of small and medium size for cesium through radon.

Relativistic adapted Gaussian basis sets of small and medium sizes are presented in this study for all elements from cesium to radon, including some alternative electron configurations. Both basis sets are made free of variational prolapse, being developed by means of a polynomial version of the generator coordinate Dirac-Fock method. In addition, these sets were designed to be promptly used with two popular finite nuclear models, uniform sphere and Gaussian nuclei. The largest basis set errors found with the uniform sphere nucleus are 27.3 and 10.6 mHartree, respectively, for the small- and medium-size sets. The largest basis set errors obtained with the Gaussian nuclear model are smaller, reaching 23.2 and 7.1 mHartree for the small- and medium-size sets, respectively. Soon, these basis sets will be augmented with polarization functions to be properly used in molecular calculations.

On the structural, electronic, and optical properties of L-histidine crystal: a DFT study.

CONTEXT: The monoclinic L-histidine crystal is critical for protein structure and function and is also found in the myelin of brain nerve cells. This study numerically examines its structural, electronic, and optical properties. Our findings indicate that the L-histidine crystal has an insulating band gap of approximately 4.38 eV. Additionally, electron and hole effective masses range between 3.92[Formula: see text]-15.33[Formula: see text] and 4.16[Formula: see text]-7.53[Formula: see text], respectively. Furthermore, our investigation suggests that the L-histidine crystal is an excellent UV collector due to its strong optical absorption activity for photon energies exceeding 3.5 eV. METHODS: To investigate the structural, electronic, and optical properties of L-histidine crystals, we used the Biovia Materials Studio software to conduct Density Functional Theory (DFT) simulations as implemented in the CASTEP code. Our DFT calculations were performed using the generalized gradient approximation (GGA) as parameterized by the Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional, with an additional dispersion energy correction (PBE [Formula: see text] TS) based on the model proposed by Tkatchenko and Scheffler to describe van der Waals interactions. Additionally, we employed the norm-conserving pseudopotential to treat core electrons.

The role of ETFS amino acids on the stability and inhibition of p53-MDM2 complex of anticancer p53-derivatives peptides: Density functional theory and molecular docking studies.

Cancer is one of the leading causes of mortality in the world. Despite the existence of diverse antineoplastic treatments, these do not possess the expected efficacy in many cases. Knowledge of the molecular mechanisms involved in tumor processes allows the identification of a greater number of therapeutic targets employed in the study of new anticancer drugs. In the last decades, peptide-based therapy design using computational chemistry has gained importance in the field of oncology therapeutics. This work aims to evaluate the electronic structure, physicochemical properties, stability, and inhibition of ETFS amino acids and peptides derived from the p53-MDM2 binding domain with action in cancer cells; by means of chemical descriptors at the DFT-BHandHLYP level in an aqueous solution, and its intermolecular interactions through molecular docking studies. The results show that The ETFS fragment plays a critical role in the intermolecular interactions. Thus, the amino acids E17, T18 and S20 increase intermolecular interactions through hydrogen bonds and enhance structural stability. F19, W23 and V25 enhance the formation of the alpha-helix. The hydrogen bonds formed by the backbone atoms for PNC-27, PNC-27-B and PNC-28 stabilize the α-helices more than hydrogen bonds formed by the side chains atoms. Also, molecular docking indicated that the PNC27B-MDM2, PNC28B-MDM2, PNC27-MDM2 and PNC28A-MDM2 complexes show the best binding energy. Therefore, DFT and molecular docking studies showed that the proposed peptides: PNC-28B, PNC-27B and PNC-28A could inhibit the binding of MDM2 to the p53 protein, decreasing the translocation and degradation of p53 native protein.

Molecular and Therapeutic Insights of Alpha-Lipoic Acid as a Potential Molecule for Disease Prevention.

Alpha-lipoic acid is an organic, sulfate-based compound produced by plants, humans, and animals. As a potent antioxidant and a natural dithiol compound, it performs a crucial role in mitochondrial bioenergetic reactions. A healthy human body, on the other hand, can synthesize enough α-lipoic acid to scavenge reactive oxygen species and increase endogenous antioxidants; however, the amount of α-lipoic acid inside the body decreases significantly with age, resulting in endothelial dysfunction. Molecular orbital energy and spin density analysis indicate that the sulfhydryl (-SH) group of molecules has the greatest electron donating activity, which would be responsible for the antioxidant potential and free radical scavenging activity. α-Lipoic acid acts as a chelating agent for metal ions, a quenching agent for reactive oxygen species, and a reducing agent for the oxidized form of glutathione and vitamins C and E. α-Lipoic acid enantiomers and its reduced form have antioxidant, cognitive, cardiovascular, detoxifying, anti-aging, dietary supplement, anti-cancer, neuroprotective, antimicrobial, and anti-inflammatory properties. α-Lipoic acid has cytotoxic and antiproliferative effects on several cancers, including polycystic ovarian syndrome. It also has usefulness in the context of female and male infertility. Although α-lipoic acid has numerous clinical applications, the majority of them stem from its antioxidant properties; however, its bioavailability in its pure form is low (approximately 30%). However, nanoformulations have shown promise in this regard. The proton affinity and electron donating activity, as a redox-active agent, would be responsible for the antioxidant potential and free radical scavenging activity of the molecule. This review discusses the most recent clinical data on α-lipoic acid in the prevention, management, and treatment of a variety of diseases, including coronavirus disease 2019. Based on current evidence, the preclinical and clinical potential of this molecule is discussed. Supplementary Information: The online version contains supplementary material available at 10.1007/s43450-023-00370-1.

Reaction mechanisms of flavins and flavoproteins from an electronic-structure perspective / Mecanismos de reação de flavinas e flavoproteínas por uma perspectiva de estrutura eletrônica

Proteins equipped with flavin adenine dinucleotides (FAD) or flavin mononucleotides (FMN) are named flavoproteins and constitute about 1% of all existing proteins. They catalyze redox, acid-base and photochemical reactions in a variety of biochemical phenomena that goes from energy metabolism to DNA repair and light sensing. The versatility observed in flavoproteins is ultimately a balance of flavin intrinsic properties modulated by a protein environment. This thesis aims to investigate how flavoproteins work by systematic evaluating flavin properties and reactivity. In particular, the mechanism of fumarate reduction by the flavoenzyme fumarate reductase Fcc3 was determined. Electronic-structure calculations were used for this task based on rigorous calibration with experimental data and error assessment. Flavin properties at chemical accuracy were obtained with single reference coupled-cluster CCSD(T) calculations at the complete basis set limit. Density functional theory was demonstrated an excellent alternative with lower computational costs and slightly less accuracy. Flavin protonation and tautomerism were shown to be important modulators of flavin properties and reactivity, with the possibility of various tautomers existing at neutral pH. Regarding flavin redox properties, an analysis based on multiconfigurational wave function weights was proposed for categorizing flavin redox reactions as hydride or hydrogen-atom transfers. This analysis is an upgrade over traditional partial charges methods and can be applied not only to flavin reactions but to any protoncoupled electron transfer. In the investigation of the enzymatic mechanism of fumarate reduction, the reaction was determined as a nucleophilic addition by hydride transfer with carbanion formation. Fumarate reductase employs electrostatic catalysis in contrast to previous proposals of substrate straining and general-acid catalysis. Also, hydride transfer was shown to be vibronically adiabatic with low tunneling contribution. These findings give new insights into the mechanisms of fumarate reductases and provide a framework for future computational studies of flavoproteins in general. The analyses and benchmark studies presented can be used to build better models of properties and reactivity of flavins and flavoproteins

Proteínas equipadas com dinucleotídeos de flavina-adenina (FAD) e mononucleotídeos de flavina (FMN) são chamadas flavoproteínas e constituem cerca de 1% de todas as proteínas existentes. Elas catalisam reações redox, ácido-base e fotoquímicas numa variedade de fenômenos bioquímicos que vão desde o metabolismo energético até reparo de DNA e captação de luz. A versatilidade observada em flavoproteínas é em última instância um balanço das propriedades intrínsecas de flavinas moduladas por um ambiente proteico. Esta tese busca investigar como flavoproteínas funcionam através de avaliações sistemáticas de propriedades e reatividade de flavinas. Em particular, o mecanismo de redução de fumarato pela flavoenzima fumarato redutase Fcc3 foi determinado. Cálculos de estrutura eletrônica foram usados para esta tarefa com base em rigorosa calibração com dados experimentais e avaliação de erros. As propriedades de flavinas foram determinadas com acurácia química com cálculos monoconfiguracionais de coupled-cluster CCSD(T) no limite de conjunto base completo. A teoria do funcional da densidade mostrou-se uma alternativa excelente com menor custo computacional e um pouco menos de acurácia. Protonação e tautomerismo de flavinas mostraram-se moduladores importantes de suas propriedades e reatividade, com a possibilidade de vários tautômeros existirem em pH neutro. Em relação às propriedades redox de flavinas, uma análise baseada nos pesos de funções de onda multiconfiguracionais foi proposta para categorizar as reações redox de flavinas como transferências de hidreto ou hidrogênio. Esta análise é uma melhoria em relação aos métodos tradicionais de cargas parciais e pode ser aplicada não apenas para reações de flavinas mas para qualquer transferência de próton acoplada a elétrons. Na investigação do mecanismo enzimático de redução de fumarato, a reação foi designada como uma adição nucleofílica por transferência de hidreto e formação de carbânion. A fumarato redutase usa catálise eletrostática diferentemente de prospostas anteriores envolvendo distorção do substrato e catálise ácida geral. Além disso, a transferência de hidreto mostrou-se vibronicamente adiabática com pouca contribuição de tunelamento. Estas descobertas abrem novas perspectivas sobre os mecanismos de fumarato redutases e fornecem uma base para estudos computacionais futuros sobre flavoproteínas em geral. As análises e estudos comparativos apresentados podem ser usados para construir melhores modelos para propriedades e reatividade de flavinas e flavoproteínas

Relativistic adapted Gaussian basis sets free of variational prolapse of small and medium size for hydrogen through xenon.

Two new relativistic adapted Gaussian basis sets of small and medium size are presented for all elements from Hydrogen through Xenon. These sets are free of variational prolapse and were developed with the polynomial generator coordinate Dirac-Fock method to be used with two finite nuclear models, uniform sphere and Gaussian. The largest basis set errors for electronic configurations from the Aufbau principle are around 10.0 and 4.7 mHartree for the small- and medium-size sets, respectively, which is in accordance with the accuracy level expected in each case. Hence, to our knowledge, these are the smallest prolapse free basis sets developed for these elements.

Kinetic and thermodynamic investigations on the HF elimination reactions from neutral and ionized CF3CH2F.

This work discusses the possible HF formation routes via recombination reactions from CF3CH2F (R-134a) and its cation. The molecular properties of the main reagents were first evaluated at the M06-2X/cc-pVTZ level. Then, changes in energy (ΔE) for all reactions comprising a possible HF formation from the studied systems were evaluated at the CCSD(T)/CBS//M06-2X/cc-pVTZ level. With the aid of Intrinsic Reaction Coordinate (IRC) calculations for each path, it is found that the HF formation reaction takes place majorly through the "1,2" elimination, resulting in an olefin as the secondary product. In turn, the IRC associated with "2,2" reactions allowed to find a post-barrier complex between the carbene :CHCF3 and HF in its exit channel, with dissociation energy of ∼4 kcal mol-1. Similarly, the cationic system exhibits favoritism towards the "1,2" elimination, and an ion-dipole post-barrier complex is found. The ΔE of such a complex production is negative in both directions, indicating this complex (25.5 kcal/mol more stable than CF3CH2F+) should be a minimum on the R-134a cation surface. However, unlike the neutral "2,2" path, there is no F atom migration transition state for the 2,2-HF elimination from CF3CH2F+. Hence, the F migration is expected to occur simultaneously with the rest of the structural changes towards the ion-dipole complex. The rate coefficients computed at the current level of theory, including corrections for anharmonicity and hindered rotations, showed a reasonable agreement with the available experimental data, inspiring confidence in our predictions for the cationic system.

Electronic structure and physicochemical properties of the metal and semimetal oxide nanoclusters.

Clusters are physical entities composed of a few to thousands of atoms with capabilities to develop novel materials, like cluster-assembled materials. In this sense, knowing the electronic structure and physicochemical properties of the isolated clusters can be useful to understand how they interact with other chemical species by intermolecular forces, as free, embedded, and saturated clusters, and by intramolecular forces, acting as support clusters. In this way, in the present work, the electronic structure and physicochemical properties of metal oxide nanoclusters (MgO, Al2O3, SiO2, and TiO2) were studied by highly correlated molecular quantum chemistry methods. Through the electronic state's characterization, a semiconductor aspect was found for the titania oxide nanocluster (Te < 0.8 eV) while the other agglomerates showed a characteristic of insulating material (Te > 3.3 eV). From the stability index, the following stability order can be characterized: (SiO2)4 > (Al2O3)4 > (MgO)4 > (TiO2)3. Initial information of intermolecular and intramolecular forces caused by the studied clusters was calculated through the relative electrophilicity index, which classified the (MgO)4 and (TiO2)3 clusters as the more reactive ones, in which the (MgO)4 cluster was identified as a nucleophilic species, while the (TiO2)3 cluster as an electrophilic molecule.

Accurate rate constants for elementary reactions of molecular hydrogen and carbon monoxide mixtures and the role of the H2 rich environment.

This investigation provides accurate rate constant values for a set of elementary reactions relevant to mixtures between molecular hydrogen (H2) and carbon monoxide (CO) such as syngas. We considered intermediates and products including formaldehyde (H2CO), hydroxymethylene (c-HCOH and t-HCOH) and methanol (CH3OH). The calculations were performed employing the improved canonical variational transition state theory with small-curvature tunneling corrections based on high-level electronic structure results. This study demonstrates for the first time that H2 can act as an effective catalyst to the reaction from t-HCOH to H2CO. In this case, the adiabatic barrier height for the reaction decreases from 30.6 kcal⋅mol- 1 to 18.1 kcal⋅mol- 1 in the presence of H2. The results obtained here can improve the comprehension regarding processes such as the combustion of hydrogen-rich syngas.

Molecular properties and tautomeric equilibria of isolated flavins.

Flavins are employed as redox cofactors and chromophores in a plethora of flavoenzymes. Their versatility is an outcome of intrinsic molecular properties of the isoalloxazine ring modulated by the protein scaffold and surrounding solvent. Thus, an investigation of isolated flavins with high-level electronic-structure methods and with error assessment of the calculated properties will contribute to building better models of flavin reactivity. Here, we benchmarked ground-state properties such as electron affinity, gas-phase basicity, dipole moment, torsion energy, and tautomer stability for lumiflavins in all biologically relevant oxidation and charge states. Overall, multiconfigurational effects are small and chemical accuracy is achieved by coupled-cluster treatments of energetic properties. Augmented basis sets and extrapolations to the complete basis-set limit are necessary for consistent agreement with experimental energetics. Among DFT functionals tested, M06-2X shows the best performance for most properties, except gas-phase basicity, in which M06 and CAM-B3LYP perform better. Moreover, dipole moments of radical flavins show large deviations for all functionals studied. Tautomers with noncanonical protonation states are significantly populated at normal temperatures, adding to the complexity of modeling flavins. These results will guide future computational studies of flavoproteins and flavin chemistry by indicating the limitations of electronic-structure methodologies and the contributions of multiple tautomeric states.

In-situ electronic structure redistribution tuning of single-atom Mn/g-C3N4 catalyst to trap atomic-scale lead(II) for highly stable and accurate electroanalysis.

Constructing catalysts with simple structures, uniform effective sites, and excellent performance is crucial for understanding the reaction mechanism of target pollutants. Herein, the single-atom catalyst of Mn-intercalated graphitic carbon nitride (Mn/g-C3N4) was prepared. It was found that the intercalated Mn atoms acted as strong electron donors to effectively tune the electronic structure distribution of the in-situ N atoms, providing a large number of negative potential atomic-scale sites for catalytic reactions. In the detection, the in-situ N atom established an electron bridge for the transient electrostatic trapping of free Pb(II), which induced Pb-N-Mn coordination bonding. Even in g-C3N4-loaded Mn nanoparticles, the N atom was again confirmed to be the interaction site for coupling with Pb. And the MnII-N4-C/MnIV-N4-C cycle actively participated in the electrocatalysis of Pb(II) was confirmed. Moreover, Mn/g-C3N4 achieved highly stable and accurate detection for Pb(II) with a sensitivity of 2714.47 µA·µM-1·cm-2. And excellent reproducibility and specific detection of real water samples made the electrode practical. This study contributes to understanding the changes in the electronic structure of chemically inert substrates after single-atom intercalation and the interaction between contaminants and the microstructure of sensitive materials, providing a guiding strategy for designing highly active electrocatalytic interfaces for accurate electroanalysis.

Predicting the stability and electronic structure of alkali metal aurides.

Density functional theory calculations of phonon modes predict that some compounds of the alkali metal aurides family, general formulaA2MAu6(A= K, Rb or Cs;M= Ti, Zr, Hf, Sn or Pb), have stable three-dimensional phase with a double perovskite-type structure and cubicFm3¯mspace group (K2PtCl6-type). Bader's charge analysis shows that most electron density is located within the six atoms at the octahedra vertices like double perovskite halides. However, the short spacing between Au anions enables d-orbital interactions between them. Compounds of this family, with group 4 metals only, carry conduction states around the Γ point (k= 0). On the other hand, compounds with group 14 metals possess more conduction states around all the Brillouin zone and have electron pockets in their band structures. These compounds provide further insights into the unusual anionic behavior of gold and present other alternatives for the construction of divergent nanodevices.

Na⋯B bond in NaBH 3 - : An induced spin-polarized bond.

The nature of the Na⋯B bond, in the recently synthesized NaBH 3 - adduct, is analyzed on the light of the Na- propensity to polarize along the bond axis as a consequence of the electric field produced by the BH3 fragment. The observed induced polarization has two consequences: (i) the energetic stabilization of the Na- , and (ii) the split of its valence electrons into two opposite lobes along the bond axis. Additionally, an analysis of the electron localization is presented using the information content of the correlated conditional pair density that reveals a significant delocalization between one lobe of the polarized Na- anion and the BH3 fragment at the equilibrium distance. Our findings reported here complement previous works on this system.

Structural, Electronic and Thermochemical preference for multi-PCET reactivity of Ruthenium(II)-Amine and Ruthenium(IV)-Amido Complexes.

The multiredox reactivity of bioinorganic cofactors is often coupled to proton transfers. Here we investigate the structural, thermochemical, and electronic structure of ruthenium-amino/amido complexes with multi- proton-coupled electron transfer reactivity. The bis(amino)ruthenium(II) and bis(amido)ruthenium(IV) complexes [RuII(bpy)(en*)2]2+ (RuII-H0 ) and [RuIV(bpy)(en*-H2)2]2+ (RuIV-H2 ) interconvert reversibly with the transfer of 2e-/2H+ (bpy = 2,2'-bipyridine, en* = 2,3-diamino-2,3-dimethylbutane). X-ray structures allow correlations between the structural and electronic parameters, and the thermochemical data of the 2e-/2H+ multi-square grid scheme. Redox potentials, acidity constants and DFT calculations reveal potential intermediates implicated in 2e-/2H+ reactivity with organic reagents in non-protic solvents, which shows a strong inverted redox potential favouring 2e-/2H+ transfer. This is suggested to be an attractive system for potential one-step (concerted) transfer of 2e-and 2H+ due to the small changes of the pseudo-octahedral geometries and the absence of charge change, indicating a relatively small overall reorganization energy.

Electronic structure of molecular hydrogen in MoS2nanopores.

Atom controlled sub-nanometer MoS2pores have been recently fabricated with promising applications, such gas sensing, hydrogen storage and DNA translocation. In this work we carried out first-principles calculations of hydrogen adsorption in tiny MoS2nanopores. Some of the pores show metallic behaviour whereas others have a sizeable band gap. Whereas adsorption of molecular hydrogen on bare pores are dominated by physisorption, adsorption in the nanopores show chemisorption behaviour with high selectivity depending on the pore inner termination. Finally, we show that functionalization with copper atoms leads to does not improve dignificantly the adsorption energies of selected pores.

Effects of Temperature on Enantiomerization Energy and Distribution of Isomers in the Chiral Cu13 Cluster.

In this study, we report the lowest energy structure of bare Cu13 nanoclusters as a pair of enantiomers at room temperature. Moreover, we compute the enantiomerization energy for the interconversion from minus to plus structures in the chiral putative global minimum for temperatures ranging from 20 to 1300 K. Additionally, employing nanothermodynamics, we compute the probabilities of occurrence for each particular isomer as a function of temperature. To achieve that, we explore the free energy surface of the Cu13 cluster, employing a genetic algorithm coupled with density functional theory. Moreover, we discuss the energetic ordering of isomers computed with various density functionals. Based on the computed thermal population, our results show that the chiral putative global minimum strongly dominates at room temperature.

The influence of the environment in chemical reactivity: the HCOOH formation from the H2O + CO reaction.

The reaction between carbon monoxide and water was studied occurring in an aerosol medium rich in methanol. This environment is plausible for the primitive and prebiotic Earth atmosphere. The chemical environment is expressed in terms of dielectric constant (ε) and the chemical system was modeled employing the polarizable continuum model (PCM). The main results were acquired from calculations employing the M06-2X density functional for the electronic structure calculations and the canonical variational theory with small curvature tunneling for the chemical kinetic calculations. The rise of ε affects both the thermochemistry and the kinetics of the reaction, increasing the barrier height and decreasing the rate constant for the reaction occurring at room temperature. For example, the rate constant at 300 K is 5-10× 10- 53 cm3 ⋅molecule- 1 ⋅s- 1 for low dielectric constant (ε < 3) and around 2-4× 10- 53 cm3 ⋅molecule- 1 ⋅s- 1 for ε between 7 and 40. Our results indicate that the ε variation allows a fine tuning to the rate of the reaction.

Self-Consistent Schrödinger-Poisson Study of Electronic Properties of GaAs Quantum Well Wires with Various Cross-Sectional Shapes.

Quantum wires continue to be a subject of novel applications in the fields of electronics and optoelectronics. In this work, we revisit the problem of determining the electron states in semiconductor quantum wires in a self-consistent way. For that purpose, we numerically solve the 2D system of coupled Schrödinger and Poisson equations within the envelope function and effective mass approximations. The calculation method uses the finite-element approach. Circle, square, triangle and pentagon geometries are considered for the wire cross-sectional shape. The features of self-consistent band profiles and confined electron state spectra are discussed, in the latter case, as functions of the transverse wire size and temperature. Particular attention is paid to elucidate the origin of Friedel-like oscillations in the density of carriers at low temperatures.