Magnetic Coupling in Enantiomerically Pure Trinuclear Helicate‐Type Complexes Formed by Hierarchical Self‐Assembly

Based on chiral, enantiomerically pure 7‐[(S)‐phenylethylurea]‐8‐hydroxyquinoline ( 1 ‐H), trinuclear helicate‐type complexes 2 – 5 are formed with divalent transition‐metal cations. X‐ray structural analyses reveal the connection of two monomeric complex units [M( 1 )₃]^? (M=Zn, Mn, Co, Ni) by a central metal ion to form a “dimer”. Due to the enantiopurity of the ligand, the complexes are obtained as pure enantiomers, resulting in pronounced circular dichroism (CD) spectra. Single‐ion effects and intra‐ and intermolecular coupling are observed with dominating ferromagnetic coupling in the case of the cobalt(II) and nickel(II) and dominating antiferromagnetic coupling in the case of the manganese(II) complex.     

Size-exclusion chromatographic protein refolding: fundamentals, modeling and operation

Size-exclusion chromatography (SEC) has proven its capability to refold a variety of proteins using a range of gel filtration column materials, demonstrated in the growing body of experimental evidence. However, little effort has been allocated to the development of mechanistic models describing size-exclusion chromatographic refolding reactors (SECRR). Mechanistic models are important since they provide a link between process variables like denatured and reduced protein feed concentration (C_f,D&;R), flow rate, column length, etc., and performance indicators like refolding yield (Y_N), thereby opening the possibility for in silico design of SECRRs. A critical step, in the formulation of such models, is the selection of an adequate reaction mechanism, which provides the direct link between the separation and the refolding yield. Therefore, in this work we present a methodology using a SEC refolding reactor model, supported by a library of reaction mechanisms, to estimate a suitable reaction scheme using experimental SEC refolding data. SEC refolding data is used since it provides information about the mass distribution of monomers and aggregates after refolding, information not readily available from batch dilution refolding data alone. Additionally, this work presents (1) a systematic analysis of the reaction mechanisms considered using characteristic time analysis and Damköhler maps, revealing (a) the direct effect of a given reaction mechanism on the shape of the SEC refolding chromatogram (number of peaks and resolution) and (b) the effect that the competition between convection, refolding and aggregation is likely to have on the SEC refolding yield; (2) a comparison between the SECR reactor and the batch dilution refolding reactor based on mechanistic modeling, quantitatively showing the advantages of the former over the latter; and (3) the successful application of the modeling based strategy to study the SEC refolding data of an industrially relevant protein. In principle, the presented modeling strategy can be applied to any protein refolded using any gel filtration material, providing the proper mass balances and activity measurements are available.     

Inequalities for the Eigenvalues of Non-Selfadjoint Jacobi Operators

We prove Lieb-Thirring-type bounds on eigenvalues of non-selfadjoint Jacobi operators, which are nearly as strong as those proven previously for the case of selfadjoint operators by Hundertmark and Simon. We use a method based on determinants of operators and on complex function theory, extending and sharpening earlier work of Borichev, Golinskii and Kupin.     

Dissipative localized States with shieldlike phase structure

A novel type of parametrically excited dissipative solitons is unveiled. It differs from the well-known solitons with constant phase by an intrinsically dynamical evolving shell-type phase front. Analytical and numerical characterizations are proposed, displaying quite a good agreement. In one spatial dimension, the system shows three types of stationary solitons with shell-like structure whereas in two spatial dimensions it displays only one, characterized by a π-phase jump far from the soliton position.     

Optimal branching asymmetry of hydrodynamic pulsatile trees

Most of the studies on optimal transport are done for steady state regime conditions. Yet, there exists numerous examples in living systems where supply tree networks have to deliver products in a limited time due to the pulsatile character of the flow, as it is the case for mammalian respiration. We report here that introducing a systematic branching asymmetry allows the tree to reduce the average delivery time of the products. It simultaneously increases its robustness against the inevitable variability of sizes related to morphogenesis. We then apply this approach to the human tracheobronchial tree. We show that in this case all extremities are supplied with fresh air, provided that the asymmetry is smaller than a critical threshold which happens to match the asymmetry measured in the human lung. This could indicate that the structure is tuned at the maximum asymmetry level that allows the lung to feed all terminal units with fresh air.     

Measurability of semimartingale characteristics with respect to the probability law

Given a càdlàg process X$X$ on a filtered measurable space, we construct a version of its semimartingale characteristics which is measurable with respect to the underlying probability law. More precisely, let _Psem${\mathfrak{P}}_{sem}$ be the set of all probability measures P$P$ under which X$X$ is a semimartingale. We construct processes (B^P,C,ν^P)$(B^P,C,{\nu }^P)$ which are jointly measurable in time, space, and the probability law P$P$, and are versions of the semimartingale characteristics of X$X$ under P$P$ for each P∈_Psem$P\in {\mathfrak{P}}_{sem}$. This result gives a general and unifying answer to measurability questions that arise in the context of quasi-sure analysis and stochastic control under the weak formulation.     

Representation theory of the Yokonuma–Hecke algebra

We develop an inductive approach to the representation theory of the Yokonuma–Hecke algebra _Yd,n(q)${\mathrm{Y}}_{d,n}(q)$, based on the study of the spectrum of its Jucys–Murphy elements which are defined here. We give explicit formulas for the irreducible representations of _Yd,n(q)${\mathrm{Y}}_{d,n}(q)$ in terms of standard d  -tableaux; we then use them to obtain a semisimplicity criterion. Finally, we prove the existence of a canonical symmetrising form on _Yd,n(q)${\mathrm{Y}}_{d,n}(q)$ and calculate the Schur elements with respect to that form.     

Compact groups of positive operators on Banach lattices

In this paper, we study groups of positive operators on Banach lattices. If a certain factorization property holds for the elements of such a group, the group has a homomorphic image in the isometric positive operators which has the same invariant ideals as the original group. If the group is compact in the strong operator topology, it equals a group of isometric positive operators conjugated by a single central lattice automorphism, provided an additional technical assumption is satisfied, for which we have only examples. We obtain a characterization of positive representations of a group with compact image in the strong operator topology, and use this for normalized symmetric Banach sequence spaces to prove an ordered version of the decomposition theorem for unitary representations of compact groups. Applications concerning spaces of continuous functions are also considered.     

Mechanism of multi‐metal(loid) methylation and hydride generation by methylcobalamin and cob(I)alamin: a side reaction of methanogenesis

Metal(loid)s are subject to many transformation processes in the environment, such as oxidation, reduction, methylation and hydride generation, predominantly accomplished by prokaryotes. Since these widespread processes affect the bioavailability and toxicity of metal(loid)s to a large extent, the investigation of their formation is of high relevance. Methanogenic Archaea are capable of methylating and hydrogenating Group 15 and 16 metal(loid)s arsenic, selenium, antimony, tellurium, and bismuth due to side reactions between central methanogenic cofactors, methylcobalamin (CH₃Cob(III)) and cob(I)alamin (Cob(I)). Here, we present systematic mechanistic studies on methylation and hydride generation of Group 15 and 16 metal(loid)s by CH₃Cob(III) and Cob(I). Pentavalent arsenical species showed neither methylation nor reduction as determined by using a newly developed oxidation state specific hydride generation technique, which allows direct determination of tri‐ and pentavalent arsenic species in a single batch. In contrast, efficient methylation of trivalent species without a change in oxidation state indicated that the methyl transfer does not proceed via a Challenger‐like oxidative methylation, but via a non‐oxidative methylation. Our findings also point towards a similar mechanism for antimony, bismuth, selenium, and tellurium. Overall, we suggest that the transfer of a methyl group does not involve a free reactive species, such as a radical, but instead is transferred either in a concerted nucleophilic substitution or in a caged radical mechanism. For hydride generation, we propose the intermediate formation of hydridocobalamin, transferring a hydride ion to the metal(loid)s. Copyright © 2012 John Wiley & Sons, Ltd.