A comparison of energy changes accompanying growth processes by <Emphasis Type="Italic">Saccharomyces cerevisiae</Emphasis>

Calculations are made using the equations Δ_r G = Δ_r H ? TΔ_r S and Δ_r X = Δ_r H ? Δ_r Q where Δ_r X represents the free energy change when the exchange of absorbed thermal energy with the environment is represented by Δ_r Q. The symbol Q has traditionally represented absorbed heat. However, here it is used specifically to represent the enthalpy listed in tabulations of thermodynamic properties as (H _T  ? H ₀) at T = 298.15 K, the reason being that for a given substance TS equals 2.0 Q for solid substances, with the difference being greater for liquids, and especially gases. Since Δ_r H can be measured, and is tangibly the same no matter what thermodynamics are used to describe a reaction equation, a change in the absorbed heat of a biochemical growth process system as represented by either Δ_r Q or TΔ_r S would be expected to result in a different calculated value for the free energy change. Calculations of changes in thermodynamic properties are made which accompany anabolism; the formation of anabolic, organic by-products; catabolism; metabolism; and their respective non-conservative reactions; for the growth of Saccharomyces cerevisiae using four growth process systems. The result is that there is only about a 1% difference in the average quantity of free energy conserved during growth using either Eq. 1 or 2. This is because although values of TΔ_r S and Δ_r Q can be markedly different when compared to one another, these differences are small when compared to the value for Δ_r G or Δ_r X.     

Numerical algorithms for the determinant evaluation of general Hessenberg matrices

Hessenberg matrices frequently arise in many application areas and have been attracted much attention in recent years. In the current paper, we present two numerical algorithms of \(O(n^2)\) for computing the determinant of an n-by-n general Hessenberg matrix. The algorithms are all suited for implementation using Computer Algebra Systems such as MATLAB and MAPLE. Some numerical examples are provided in order to demonstrate the performance of the proposed algorithms.     

Thermodynamic characteristics of complexation between Ho<Superscript>3+</Superscript> and ethylenediamine-<Emphasis Type="Italic">N</Emphasis>,<Emphasis Type="Italic">N</Emphasis>'-disuccinic acid in aqueous solutions at 298.15 K

The thermodynamic characteristics of complexation between ethylenediamine-N,N'-disuccinic acid (H₄Y; EDDA) and Ho³⁺ ion were determined calorimetrically and potentiometrically at 298.15 K and ionic strengths of 0.1, 0.5, 1.0, and 1.5 (KNO₃). The logK, Δ_rG, Δ_rH, and Δ_rS values for the formation of HoY^– and HOHY complexes were calculated at the studied and zero ionic strength values. The changes in thermodynamic parameters of the reactions are discussed.     

Molecular structure of ErCl<Subscript>3</Subscript> and YbCl<Subscript>3</Subscript> according to the data of the simultaneous electron diffraction and mass spectrometric experiment

The saturated vapors of ErCl₃ and YbCl₃ were studied in a simultaneous electron diffraction and mass spectrometric experiment at 1165 K and 1170 K, respectively. In the vapors of these compounds, we found up to 3 mol.% dimers along with the monomers. The parameters of the r _g effective configuration of the monomer molecules were determined. For ErCl₃ and YbCl₃, the internuclear distances r _g(Ln-Cl) were 2.436(5) Å and 2.416(5) Å, and the bond angles ∠_g(Cl-Ln-Cl) were 117.0(10)° and 117.2(10)°, respectively. The equilibrium configurations and vibration frequencies of the monomer and dimer molecules were calculated by the HF, B3LYP, and MP2 methods using the combination of the ECP_D energy-consistent quasirelativistic core potential, including 4f electrons [Kr4d ¹⁰4f ⁿ ], and the contracted [5s4p3d] valence basis set for Er and Yb atoms and the MIDIX [4s3p1d] basis set for Cl atoms. The parameters of the effective r _g configuration of the monomer molecules corresponding to the temperature of the experiment were calculated. The difference between the calculated equilibrium r _e(Ln-Cl) and temperature-averaged r _g(Ln-Cl) distances was found to be 0.001–0.002 Å and did not exceed the error of the r _g(Ln-Cl) parameter determined in the electron diffraction experiment. The experimental parameters of the r _g structure were shown to be consistent with the idea about the planar equilibrium geometrical configuration of ErCl₃ and YbCl₃ molecules.     

Percolation in the model of random successive adhesion of anisotropic particles

Numerical studies of random successive adsorption (the RSA model) of rectangular particles on a flat substrate are performed and the dependences of saturation concentration and the percolation threshold on the parameters of a model are determined. The dependences of saturation concentration φ _j∞ on the particle diameter-to-length ratio r and the parameter of orientational order S are found. Correlations between the ? _j∞(r) function and excluded surface area are discussed. It is revealed that for highly ordered systems (S ≈ 1), the saturation concentration φ _j∞ is equal to 0.557 ± 0.005 and is virtually independent of r. For partially ordered systems, the ? _j∞ value decreases with an increase in r and in the r → ∞, ? _j∞ → 0. Percolation transition and electrical connectivity for the systems studied can take place only under the assumption of the tunnel mechanism of conductivity through gaps with finite thicknesses. The minimum thickness of tunnel gaps, at which percolation can occur, rises with increasing r and decreasing S.     

Crystal structures of a family of layered coordination polymers containing divalent metal ions (Mn<Superscript>2+</Superscript>, Co<Superscript>2+</Superscript>, Ni<Superscript>2+</Superscript> and Zn<Superscript>2+</Superscript>) and the 3-amino 4-methyl benzoate ion

The syntheses and crystal structures of the layered coordination polymers M(C₈H₈NO₂)₂ [M = Mn (1), Co (2), Ni (3) and Zn (4)] are described. These isostructural compounds contain centrosymmetric trans-MN₂O₄ octahedra as parts of infinite sheets; the ligand bonds to three adjacent metal ions in μ³-N,O,O′ mode from both its carboxylate O atoms and its amine N atom. In each case, weak intra-sheet N–H?O and C–H?O hydrogen bonds may help to consolidate the structure. Crystal data: 1, C₁₆H₁₆MnN₂O₄, M _r = 355.25, monoclinic, P2₁/c (No. 14), a = 10.6534(2) Å, b = 4.3990(1) Å, c = 15.5733(5) Å, β = 95.1827(10)°, V = 726.85(3) ų, Z = 2, R(F) = 0.026, wR(F ²) = 0.067. 2, C₁₆H₁₆CoN₂O₄, M _r = 359.24, monoclinic, P2₁/c (No. 14), a = 10.6131(10) Å, b = 4.3374(4) Å, c = 15.3556(17) Å, β = 95.473(4)°, V = 703.65(12) ų, Z = 2, R(F) = 0.041, wR(F ²) = 0.091. 3, C₁₆H₁₆N₂NiO₄, M _r = 359.02, monoclinic, P2₁/c (No. 14), a = 10.6374(4) Å, b = 4.2964(2) Å, c = 15.2827(8) Å, β = 95.9744(14)°, V = 694.66(6) ų, Z = 2, R(F) = 0.028, wR(F ²) = 0.070. 4, C₁₆H₁₆N₂O₄Zn, M _r = 365.68, monoclinic, P2₁/c (No. 14), a = 10.6385(5) Å, b = 4.2967(3) Å, c = 15.2844(8) Å, β = 95.941(3)°, V = 694.89(7) ų, Z = 2, R(F) = 0.038, wR(F ²) = 0.107.     

A novel angle-dependent potential and its exact solution

The quantum mechanics of a diatomic molecule in a noncentral potential of the type V (r) = V _θ (θ)/r ² + V _r (r) are investigated analytically. The θ-dependent part of the relevant potential is suggested for the first time as a novel angle-dependent (NAD) potential \({V_{\theta}(\theta)=\frac{\hbar^2}{2\mu}\left(\frac{\gamma +\beta \sin^2\theta +\alpha \sin^4 \theta}{\sin^2\theta \cos^2\theta}\right)}\) and the radial part is selected as the Coulomb potential or the harmonic oscillator potential, i.e., V _r (r) =  ? H/r or V _r (r) = Kr ², respectively. Exact solutions are obtained in the Schrödinger picture by means of a mathematical method named the Nikiforov–Uvarov (NU). The effect of the angle-dependent part on the solution of the radial part is discussed in several values of the NAD potential’s parameters as well as different values of usual quantum numbers.     

Crystal structures of [Zn(SALIMP)(CH<Subscript>3</Subscript>CO<Subscript>2</Subscript>)]<Subscript>2</Subscript> and [Cu(SALIMP)Cl] with 2-[[(2-pyridinylmethyl) imino]methyl]phenol (HSALIMP) as a ligand

Two complexes [Zn(SALIMP)(CH₃CO₂)]₂ (1) and [Cu(SALIMP)Cl] (2) are obtained by the reactions of zinc(II) and copper(II) salts with a tridentate Schiff base ligand 2-[[(2-pyridinylmethyl) imino]methyl]phenol (HSALIMP). Their structure is determined by single crystal X-ray diffraction. Data for complex 1: C₃₀H₂₈N₄O₆Zn₂, CCDC number: 668213, M _r = 671.3, monoclinic, C2/c, with a = 34.670(5) Å, b = 15.266(2) Å, c = 23.464(4) Å, β = 114.045(2)°, V = 11341(3) ų, Z = 16, F(000) = 5504, GOOF(F ²) = 0.894, the final R = 0.0520 and wR = 0.1272 for 10515 observed reflections with I > 2σ(I); complex 2: C₁₃H₁₂N₂OClCu, CCDC number: 668211, M _r = 311.24, triclinic, P-1, with a = 7.4050(8) Å, b = 10.2369(11) Å, c = 16.2873(17) Å, α = 87.728(2)°, β = 87.818(2)°, γ = 78.279(2)°, V = 1207.4(2) ų, Z = 4, F(000) = 632, GOOF(F ²) = 1.077, the final R = 0.0326 and wR = 0.0381 for 4209 observed reflections with I > 2σ(I).     

3-Hydroxy-2-Nitrobenzoic Acid as a MALDI Matrix for In-Source Decay and Evaluation of the Isomers

In in-source decay (ISD) in matrix-assisted laser desorption/ionization (MALDI)-mass spectrometry (MS), 1,5-diaminonaphthalene (1,5-DAN) is a most frequently used matrix probably due to the highly sensitive detection of fragment ions. 1,5-DAN is a reducing matrix generating c- and z-series ions by N–Cα bond cleavage. However, it is difficult for reducing matrices to distinguish leucine and isoleucine, and generate c_(n-1)-series ions owing to proline (Pro) at residues n. Oxidizing matrices providing a- and x-series ions accompanied by d-series ions by Cα–C bond cleavage solve the problem, but their sensitivity of the ISD fragment ions has been lower than reducing matrices such as 1,5-DAN. Recently, 3-hydroxy-4-nitrobenzoic acid (3H4NBA) had been reported as an oxidizing matrix generating a-series ions with higher intensity compared with conventional oxidizing matrices such as 5-nitrosalicylic acid, but a little lower intensity compared with 1,5-DAN (Anal Chem 88, 8058–8063, 2016). In this study, 3H4NBA isomers (2H3NBA, 2H4NBA, 2H5NBA, 2H6NBA, 3H2NBA, 3H5NBA, 4H2NBA, 4H3NBA, 5H2NBA, and 3H4NBA) were evaluated. All the isomers generated a-series ions accompanied by d-series ions, wherein 3H2NBA, 3H5NBA, 4H2NBA, 4H3NBA, and 5H2NBA were first confirmed as oxidizing matrices for ISD. Among the isomers, 3H2NBA and 4H3NBA generated a-series ions with higher peak intensity compared with 3H4NBA for several peptides. Especially, 3H2NBA generated a-series ions with almost the same or higher intensity, and clearly higher peak resolution compared with c-series ions using 1,5-DAN in several cases. 3H2NBA was expected to contribute to ISD analyses in MALDI-MS as one of the most effective oxidizing matrices.

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Graphical Abstract ?

     

Synthesis and crystal structure of (<Emphasis Type="Italic">o</Emphasis>-Diaminobenzene)<Subscript>2</Subscript> Zn(OAc)<Subscript>2</Subscript>

The treatment of o-diaminobenzene with Zn ( OAc )₂ · 2H₂O in alcohol results in the formation of mononuclear bis(o-diaminobenzene)diacetate Zinc, Zn[C₈H₁₁N₂O₂]₂. Its structure was determined by X-ray diffraction analysis. The complex is also characterized by elemental analysis, ¹H NMR and IR. The crystal is monoclinic space group C2, parameters: a = 16.297(5), b = 4.775(3), c = 11.664(5) Å, β = 97.646(5)°, λ = 1.54184 Å, V = 899.6(7) ų, Z = 2, ρ _c = 1.476 g/cm³, M _r = 399.75, F(000) = 416.0, R ₁ = 0.0594, wR ₂ = 0.1439 for 995 observed reflections with I > 2σ(I).     

Gas electron diffraction and quantum chemical studies of the molecular structure of 2-nitrobenzenesulfonic acid

A combined gas electron diffraction and quantum chemical (B3LYP/6-311+G**, B3LYP/cc-pVTZ) study of the molecular structure of 2-nitrobenzenesulfonic acid (2-NBSA) is performed. Quantum chemical calculations show that the 2-NBSA molecule has five conformers, and the Gibbs energy of one of them is lower by more than 4.5 kcal/mol than the energy of the other conformers. It is found experimentally that the saturated vapor of 2-NBSA at T = 394(5) K contains only the low-energy conformer that has an intramolecular hydrogen bond between the H atom of the hydroxyl group and one of the O atoms of the NO₂ group. The C-C-S-O(H) torsion angle determining the position of the S-O(H) bond is ?72(7)°, while the NO₂ group is substantially turned relative to the benzene ring plane (C1-C2-N-O = 40(5)°). The following experimental values of the internuclear distances are obtained for this conformer (Å): r _h1(C-H)_av = 1.07(2), r _h1(C-C)_av = 1.401(4), r _h1(C-S) = 1.767(6), r _h1(S=O)_av = 1.412(4), r _h1(S-O) = 1.560(6), r _h1(N-O)_av = 1.217(5), r _h1(C-N) = 1.461(8), r _h1(O-H) = 0.99(3).     

A novel metal chalcogenide: HgCd<Subscript>4</Subscript>S<Subscript>5</Subscript>

A novel metal chalcogenide HgCd₄S₅ (1) was synthesized from solid-state reactions and structurally characterized. Compound 1 crystallizes in the space group C222₁ of the orthorhombic system with four formula units in a cell: a = 12.5661(5) Å, b = 7.2551(5) Å, c = 10.7520(7) Å, V = 980.2(1) ų, Cd₄HgS₅, M _r = 810.49, D _c = 5.492 g/cm³, S = 1.010, μ(MoK _α) = 25.128 mm^?1, F(000) = 1408, R = 0.0611 and wR = 0.1495. Compound 1 is characterized by a 3-D cadmium sulfide framework structure with the infinite mercury sulfide chains located in the cavities.     

Molecular structure of SmBr<Subscript>3</Subscript> and DyBr<Subscript>3</Subscript> according to the data of simultaneous electron diffraction and mass spectrometric experiment

The saturated vapors of samarium and dysprosium tribromides were investigated for the first time by electron diffraction with mass spectrometric monitoring at temperatures of 1151(10) K and 1141(10) K. Dimer molecules (up to 2 mole %) were found in vapors along with monomer molecules. The SmBr₃ and DyBr₃ molecules have a pyramidal effective configuration with bond angles ∠_gBr-Sm-Br=115.1(9)° and ∠_gBr-Dy-Br=115.3(7)°. The difference between the internuclear distances of SmBr₃ and DyBr₃ (r _g(Sm-Br) = 2.653(6) Å and r _g(Dy-Br) = 2.609(5) Å) coincides with the difference between the ionic radii of Sm³⁺ and Dy³⁺. The insignificant pyramidality of the r _g configuration and the low deformation vibration frequencies of SmBr₃ and DyBr₃ may be indicative of a planar equilibrium geometry of D _3h symmetry. The equilibrium distances r _e(Sm-Br) and r _e(Dy-Br) have been evaluated and compared with the values obtained by quantum chemical calculations.     

Structure and energetics of β-diketonates. XVI. Molecular structure and vibrational spectrum of zinc acetylacetonate according to gas-phase electron diffraction and quantum-chemical calculations

The molecular structure of zinc acetylacetonate was studied in a simultaneous electron diffraction and mass spectrometric experiment at 376(7) K and by quantum-chemical calculations. The Zn(acac)₂ molecule has a structure of D _2d symmetry with the chelate rings lying in mutually perpendicular planes. The main geometrical parameters of the molecule are r _h1(Zn-O) = 1.942(4) Å, r _h1(C-O) = 1.279(3) Å, r _h1(C-C_r) = 1.398(3) Å, r _h1(C-C _m ) = 1.504(5) Å, ∠(O-Zn-O) = 93.2(7)°, ∠(Zn-O-C) = 125.9(7)°, ∠(C-C_r-C) = 125.8(14)°, ∠(O-C-C _m ) = 115.2(9)°. The effective rotation angle of methyl groups is close to 30°, which is indicative of the free rotation of these groups. The vibration frequencies were obtained by quantumchemical calculations, and the IR spectrum of the Zn(acac)₂ molecule was interpreted.     

A computational approach to linear conjugacy in a class of power law kinetic systems

This paper studies linear conjugacy of PL-RDK systems, which are kinetic systems with power law rate functions whose kinetic orders are identical for branching reactions, i.e. reactions with the same reactant complex. Mass action kinetics (MAK) systems are the best known examples of such systems with reactant-determined kinetic orders (RDK). We specify their kinetics with their rate vector and T matrix. The T matrix is formed from the kinetic order matrix by replacing the reactions with their reactant complexes as row indices (thus compressing identical rows of branching reactions of a reactant complex to one) and taking the transpose of the resulting matrix. The T matrix is hence the kinetic analogue of the network’s matrix of complexes Y with the latter’s columns of non-reactant complexes truncated away. For MAK systems, the T matrix and the truncated Y matrix are identical. We show that, on non-branching networks, a necessary condition for linear conjugacy of MAK systems and, more generally, of PL-FSK (power law factor span surjective kinetics) systems, i.e. those whose T matrix columns are pairwise different, is \(T = T'\), i.e. equality of their T matrices. This motivated our inclusion of the condition \(T = T'\) in exploring extension of results from MAK to PL-RDK systems. We extend the Johnston–Siegel Criterion for linear conjugacy from MAK to PL-RDK systems satisfying the additional assumption of \(T = T'\) and adapt the MILP algorithms of Johnston et al. and Szederkenyi to search for linear conjugates of such systems. We conclude by illustrating the results with several examples and an outlook on further research.     

Gas electron diffraction and quantum chemical study of the structure of a 2-nitrobenzenesulfonyl chloride molecule

A combined gas electron diffraction and quantum chemical (B3LYP/6-311+G**, B3LYP/cc-pVTZ, B3LYP/cc-pVTZ, midix (Cl), and MP2/cc-pVTZ) study of the structure of a 2-NO₂-C₆H₄-SO₂Cl molecule is performed. It is found experimentally that at a temperature of 345(5) K the gas phase contains two conformers of the C ₁ symmetry. Conformer I with a nearly perpendicular arrangement of the S-Cl bond with respect to the benzene ring plane (the C(NO₂)-C-S-Cl torsion angle is 84(3)°) is contained predominantly (69(12)%). In conformer II, the S-Cl bond is located near the benzene ring plane (the C(NO₂)-C-S-Cl angle is 172(3)°). The following experimental internuclear distances (Å) are obtained for conformer I: r _h1(C-H) = 1.064(15), r _h1(C-C)_av = 1.397(3), r _h1(C-S) = 1.761(6), r _h1(S-O)_av = 1.426(4), r _h1(S-Cl) = 2.043(5), r _h1(N-O)_av = 1.222(4), r _h1(C-N) = 1.485(16). In both conformers, the NO₂ group is turned by more than 30° relative to the benzene ring plane.     

The ABC Matrix

The atom-bond connectivity index—abbreviated ABC—has proven to describe the heat of formation of alkanes with an accuracy comparable to that of high-level ab initio and DFT methods. Its physical interpretation in terms of quantum-theory, its generalization, and many of its mathematical properties have been reported. Here, a probabilistic interpretation of the generalized ABC index is provided. It indicates that the terms defining this index represent the probability of visiting a nearest neighbor edge from one side or the other of a given edge in a graph. This interpretation is general enough as to cover the case of polarizing bonds in a molecular context. We then introduce a matrix representation of these probabilities in the form of generalized ABC matrices. Using this representation we study some indices related to the eigenvalues of the ABC matrices, such as the ABC energy and the ABC Estrada index. We provide some bounds for these parameters in general graphs.     

Electron diffraction study of molecular structure of mebicar

The structure of the mebicar molecule has been studied by gas-phase electron-diffractometry using quantum chemical calculations. An eclipsed conformation along the C-C bond (torsion angle ?(H-C-C-H) = 10°) and flattened semi-chair conformations of cyclic fragments have been found. The bond lengths (r _g ) and angles (∠α) show the following average values: r(C-C) 1.576(3) Å, r(C-N) 1.460(3) Å, r(C(O)-N) 1.390(4) Å, r(C=O) 1.211(5) Å, r(C-H) 1.090(5) Å, ∠CCN 103.0(5)°, ∠CNC(O) 112.2(1)°, ∠CNC 122.4(1)°. The dihedral angle between the cyclic fragments is 116.6°.     

Mixed-Ligand Complexation of Zinc and Cobalt(II) Complexonates with Amino Acids in an Aqueous Solution

The formation of mixed-ligand complexes in the M(II)–Nta and Ida–L systems (M = Co, Zn; L = His, Orn, Lys, Gly, Im, en), where Ida and Nta are the residues of iminodiacetic and nitrilotriacetic acids, was studied by pH-metry, calorimetry, and NMR spectroscopy. The thermodynamic parameters (logK, Δ _r G⁰, Δ _r H, Δ _r S) of formation for these complexes were determined at 298.15 K and an ionic strength I = 0.5 (KNO3). The most probable pattern of coordination between a complexone and an amino acid in mixed-ligand complexes was revealed.