Tensor method for optimal control problems constrained by fractional three-dimensional elliptic operator with variable coefficients

We introduce the tensor numerical method for solving optimal control problems that are constrained by fractional two- (2D) and three-dimensional (3D) elliptic operators with variable coefficients. We solve the governing equation for the control function which includes a sum of the fractional operator and its inverse, both discretized over large 3D $n\times n\times n$ spacial grids. Using the diagonalization of the arising matrix-valued functions in the eigenbasis of the one-dimensional Sturm–Liouville operators, we construct the rank-structured tensor approximation with controllable precision for the discretized fractional elliptic operators and the respective preconditioner. The right-hand side in the constraining equation (the optimal design function) is supposed to be represented in a form of a low-rank canonical tensor. Then the equation for the control function is solved in a tensor structured format by using preconditioned CG iteration with the adaptive rank truncation procedure that also ensures the accuracy of calculations, given an $\epsilon$-threshold. This method reduces the numerical cost for solving the control problem to $O(n\log n)$ (plus the quadratic term $O(n^2)$ with a small weight), which outperforms traditional approaches with $O(n^3\log n)$ complexity in the 3D case. The storage for the representation of all 3D nonlocal operators and functions involved is also estimated by $O(n\log n)$. This essentially outperforms the traditional methods operating with fully populated $n^3\times n^3$ matrices and vectors in ${?}^{n^3}$. Numerical tests for 2D/3D control problems indicate the almost linear complexity scaling of the rank truncated preconditioned conjugate gradient iteration in the univariate grid size n.     

Two‐Color Valence‐to‐Core X‐ray Emission Spectroscopy Tracks Cofactor Protonation State in a Class I Ribonucleotide Reductase

Proton transfer reactions are of central importance to a wide variety of biochemical processes, though determining proton location and monitoring proton transfers in biological systems is often extremely challenging. Herein, we use two‐color valence‐to‐core X‐ray emission spectroscopy (VtC XES) to identify protonation events across three oxidation states of the O₂‐activating, radical‐initiating manganese–iron heterodinuclear cofactor in a class I‐c ribonucleotide reductase. This is the first application of VtC XES to an enzyme intermediate and the first simultaneous measurement of two‐color VtC spectra. In contrast to more conventional methods of assessing protonation state, VtC XES is a more direct probe applicable to a wide range of metalloenzyme systems. These data, coupled to insight provided by DFT calculations, allow the inorganic cores of the Mn^IVFe^IV and Mn^IVFe^III states of the enzyme to be assigned as Mn^IV(μ‐O)₂Fe^IV and Mn^IV(μ‐O)(μ‐OH)Fe^III, respectively.     

Cubic phases in biosensing systems

Incorporation of membrane proteins with retained activity in artificial membranes for use in membrane-based sensors has attracted scientists for decades. This review briefly summarises general concepts on relevant cubic phases with and without incorporated proteins and provides some insight into the development of biosensors where bicontinuous cubic phases are used for incorporation of an enzyme. Some new data on impedance characterisation of a supported cubic phase are also shown. An efficient membrane-based electrochemical biosensor requires that the analyte has free access to the immobilised membrane protein and that regeneration of the catalysing enzyme is fast. Long-term stability of the system is also necessary for the biosensor to find applications outside the research laboratory. These basic concepts are discussed in the review along with presentation of those biosensing systems based on cubic phases that are reported in the literature.     

Zinc and Cobalt Complexes Derived from Tetradentate Tripodal Ligands with N2O2 Donorset as Model Compounds for Phosphatases

Starting from the tripodal tetradentate ligands ‐(3,5‐dibromo‐2‐hydroxybenzyl)(2‐hydroxybenzyl)(2‐pyridyl)methylamine (H₂L1), (3,5‐dibromo‐2‐hydroxybenzyl)(2‐hydroxy‐5‐nitrobenzyl)(2‐pyridyl)methylamine (H₂L2), and (3,5‐dichloro2‐hydroxybenzyl)(2‐hydroxy‐5‐nitrobenzyl)(2‐pyridyl)methylamine (H₂L3) the new isostructural dinuclear zinc compounds [Zn₂(L1)₂]·N(CH₂CH₃)₃ ( 1 ), [Zn₂(L2)₂]·2CH₃OH ( 2 ) and [Zn₂(L3)₂]·C₄H₁₀O ( 3 ) were synthesized. Due to their enzyme‐like trigonal bipyramidal N₂O₃ coordination environment of the zinc ions and the similar Zn···Zn distances the complexes can be considered to be structural models for the active sites in phospholipase C and nuclease P1. With H₂L3 also the dinuclear complex [Co₂(L2)₂(CH₃OH)]·2CH₃OH·0.5C₄H₁₀O ( 4 ) could be prepared. The new compounds were isolated and characterized by single crystal X‐ray crystallography as well as infrared spectroscopy. The cobalt compound 4 was additionally characterized by UV‐Vis spectroscopy and magnetic measurements. 1 crystallizes in the monoclinic space group P2₁/n with a = 11.2814(2), b = 28.6154(2), c = 13.1866(3) Å, β = 96.995(1)°, V = 4225.2(2) ų, Z = 4. 2 and 3 are monoclinic, space group C2/c with a = 23.084(5), b = 9.232(2), c = 21.849(4) Å, &β; = 96.83(3)°, V = 4623(2) ų, Z = 4, and a = 22.7834(3), b = 9.2463(1), c = 21.6351(3) Å, &β; = 97.592(1)°, V = 4517.7(2) ų, Z = 4, respectively. 4 crystallizes in the monoclinic space group I2/a with a = 22.4680(4), b = 20.5517(4), c = 22.8910(6) Å, &β; = 111.938(1)°, V = 9804.7(4) ų, Z = 8. 4 shows an effective magnetic moment of 6.72 μ_B at 300 K which clearly indicates the presence of two cobalt(II) high spin ions with Curie‐Weiss behaviour above 80 K. At lower temperatures a decrease of the effective magnetic moment was observed.     

Digital Microfluidics and Magnetic Bead-Based Intact Proteoform Elution for Quantitative Top-down Nanoproteomics of Single C. elegans Nematodes

While most nanoproteomics approaches for the analysis of low-input samples are based on bottom-up proteomics workflows, top-down approaches enabling proteoform characterization are still underrepresented. Using mammalian cell proteomes, we established a facile one-pot sample preparation protocol based on protein aggregation on magnetic beads and intact proteoform elution using 40 % formic acid. Performed on a digital microfluidics device, the workflow enabled sensitive analyses of single Caenorhabditis elegans nematodes, thereby increasing the number of proteoform identifications compared to in-tube sample preparation by 46 %. Label-free quantification of single nematodes grown under different conditions allowed to identify changes in the abundance of proteoforms not distinguishable by bottom-up proteomics. The presented workflow will facilitate proteoform-directed analysis on samples of limited availability.     

An electrochemical study into the interaction between complement-derived peptides and DOPC mono- and bilayers

Electrochemical methods employing the hanging mercury drop electrode were used to study the interaction between variants of the complement-derived antimicrobial peptide CNY21 (CNYITELRRQH ARASHLGLAR) and dioleoyl phosphatidylcholine (DOPC) monolayers. Capacitance potential and impedance measurements showed that the CNY21 analogues investigated interact with DOPC monolayers coating the mercury drop. Increasing the peptide hydrophobicity by substituting the two histidine residues with leucine resulted in a deeper peptide penetration into the hydrophobic region of the DOPC monolayer, indicated by an increase in the dielectric constant of the lipid monolayer (Deltaepsilon = 2.0 after 15 min interaction). Increasing the peptide net charge from +3 to +5 by replacing the histidines by lysines, on the other hand, arrests the peptide in the lipid head group region. Reduction of electroactive ions (Tl+, Pb2+, Cd2+, and Eu3+) at the monolayer-coated electrode was employed to further characterize the types of defects induced by the peptides. All peptides studied permeabilize the monolayer to Tl+ to an appreciable extent, but this effect is more pronounced for the more hydrophobic peptide (CNY21L), which also allows penetration of larger ions and ions of higher valency. The results for the various ions indicate that charge repulsion rather than ion size is the determining factor for cation penetration through peptide-induced defects in the DOPC monolayer. The effects obtained for monolayers were compared to results obtained with bilayers from liposome leakage and circular dichroism studies for unilamellar DOPC vesicles, and in situ ellipsometry for supported DOPC bilayers. Trends in peptide-induced liposome leakage were similar to peptide effects on electrochemical impedance and permeability of electroactive ions for the monolayer system, demonstrating that formation of transmembrane pores alone does not constitute the mechanism of action for the peptides investigated. Instead, our results point to the importance of local packing defects in the lipid membrane in close proximity to the adsorbed peptide molecules.     

Spectroscopic and computational evaluation of the structure of the high-spin Fe(IV)-oxo intermediates in taurine: alpha-ketoglutarate dioxygenase from Escherichia coli and its His99Ala ligand variant

The Fe(II)- and alpha-ketoglutarate (alphaKG)-dependent dioxygenases activate O2 for cleavage of unactivated C-H bonds in their substrates. The key intermediate that abstracts hydrogen in the reaction of taurine:alphaKG dioxygenase (TauD), a member of this enzyme family, was recently characterized. The intermediate, denoted J, was shown to contain an iron(IV)-oxo unit. Other important structural features of J, such as the number, identity, and disposition of ligands in the Fe(IV) coordination sphere, are not yet understood. To probe these important structural features, a series of models for J with the Fe(IV) ion coordinated by the expected two imidazole (from His99 and His255), two carboxylate (succinate and Asp101), and oxo ligands have been generated by density functional theory (DFT) calculations, and spectroscopic parameters (M?ssbauer isomer shift, quadrupole splitting, and asymmetry parameter, 57Fe hyperfine coupling tensor, and zero field splitting parameters, D and E/D) have been calculated for each model. The calculated parameters of distorted octahedral models for J, in which one of the carboxylates serves as a monodentate ligand and the other as a bidentate ligand, and a trigonal bipyramidal model, in which both carboxylates serve as monodentate ligands, agree well with the experimental parameters, whereas the calculated parameters of a square pyramidal model, in which the oxo ligand is in the equatorial plane, are inconsistent with the data. Similar analysis of the Fe(IV) complex generated in the variant protein with His99, the residue that contributes the imidazole ligand cis to the oxo group, replaced by alanine suggests that the deleted imidazole is replaced by a water ligand. This work lends credence to the idea that the combination of M?ssbauer spectroscopy and DFT calculations can provide detailed structural information for reactive intermediates in the catalytic cycles of iron enzymes.     

CD and MCD of CytC3 and taurine dioxygenase: role of the facial triad in alpha-KG-dependent oxygenases

The alpha-ketoglutarate (alpha-KG)-dependent oxygenases are a large and diverse class of mononuclear non-heme iron enzymes that require FeII, alpha-KG, and dioxygen for catalysis with the alpha-KG cosubstrate supplying the additional reducing equivalents for oxygen activation. While these systems exhibit a diverse array of reactivities (i.e., hydroxylation, desaturation, ring closure, etc.), they all share a common structural motif at the FeII active site, termed the 2-His-1-carboxylate facial triad. Recently, a new subclass of alpha-KG-dependent oxygenases has been identified that exhibits novel reactivity, the oxidative halogenation of unactivated carbon centers. These enzymes are also structurally unique in that they do not contain the standard facial triad, as a Cl- ligand is coordinated in place of the carboxylate. An FeII methodology involving CD, MCD, and VTVH MCD spectroscopies was applied to CytC3 to elucidate the active-site structural effects of this perturbation of the coordination sphere. A significant decrease in the affinity of FeII for apo-CytC3 was observed, supporting the necessity of the facial triad for iron coordination to form the resting site. In addition, interesting differences observed in the FeII/alpha-KG complex relative to the cognate complex in other alpha-KG-dependent oxygenases indicate the presence of a distorted 6C site with a weak water ligand. Combined with parallel studies of taurine dioxygenase and past studies of clavaminate synthase, these results define a role of the carboxylate ligand of the facial triad in stabilizing water coordination via a H-bonding interaction between the noncoordinating oxygen of the carboxylate and the coordinated water. These studies provide initial insight into the active-site features that favor chlorination by CytC3 over the hydroxylation reactions occurring in related enzymes.