Reduced Levels of Tissue Inhibitors of Metalloproteinases in UVB‐Irradiated Corneal Epithelium

Tissue inhibitors of metalloproteinases (TIMPs) are the major endogenous regulators of metalloproteinase activity in tissues. TIMPs are able to inhibit activity of all known matrix metalloproteinases (MMPs) and thus participate in controlling extracellular matrix synthesis and degradation. We showed previously elevated expressions of MMPs in the rabbit corneal epithelium upon UVB exposure and suggested that these enzymes might be involved in corneal destruction caused by excessive proteolysis. The aim of this study was to investigate TIMPs in the corneal epithelium after UV irradiation using immunohistochemical and biochemical methods. We found that as compared to control rabbit corneas where relatively high levels of TIMPs were present in the epithelium, repeated irradiation of the cornea with UVB rays (not with UVA rays of similar doses) significantly decreased TIMPs in corneal epithelial cells. The results of this study point to the suggestion that the decrease in TIMPs in the corneal epithelium after UVB irradiation contributes to increased proteolytic activity of MMPs in UVB‐irradiated corneal epithelium found previously.     

Prediction of iron K-edge absorption spectra using time-dependent density functional theory

Iron K-edge X-ray absorption pre-edge features have been calculated using a time-dependent density functional approach. The influence of functional, solvation, and relativistic effects on the calculated energies and intensities has been examined by correlation of the calculated parameters to experimental data on a series of 10 iron model complexes, which span a range of high-spin and low-spin ferrous and ferric complexes in O(h) to T(d) geometries. Both quadrupole and dipole contributions to the spectra have been calculated. We find that good agreement between theory and experiment is obtained by using the BP86 functional with the CP(PPP) basis set on the Fe and TZVP one of the remaining atoms. Inclusion of solvation yields a small improvement in the calculated energies. However, the inclusion of scalar relativistic effects did not yield any improved correlation with experiment. The use of these methods to uniquely assign individual spectral transitions and to examine experimental contributions to backbonding is discussed.     

Properties of the singular, inverse and generalized inverse partitioned Wishart distributions

In this paper we discuss the distributions and independency properties of several generalizations of the Wishart distribution. First, an analog to Muirhead [R.J. Muirhead, Aspects of Multivariate Statistical Theory, Wiley, New York, 1982] Theorem 3.2.10 for the partitioned matrix is established in the case of arbitrary partitioning for singular and inverse Wishart distributions. Second, the density of is derived in the case of singular, non-central singular, inverse and generalized inverse Wishart distributions. The importance of the derived results is illustrated with an example from portfolio theory.     

Characterization of a genuine iron(V)-nitrido species by nuclear resonant vibrational spectroscopy coupled to density functional calculations

The characterization of high-valent iron species is of interest due to their relevance to biological reaction mechanisms. Recently, we have synthesized and characterized an [Fe(V)-nitrido-cyclam-acetato]+ complex, which has been characterized by M?ssbauer, magnetic susceptibility data, and XAS spectroscopies combined with DFT calculations (Aliaga-Alcade, N.; DeBeer George, S.; Bill, E.; Wieghardt, K.; Neese, F. Angew. Chem., Int. Ed. 2005, 44, 2908-2912). The results of this study indicated that the [Fe(V)-nitrido-cyclam-acetato]+ complex is an unusual d3 system with a nearly orbitally degenerate S=1/2 ground state. Although the calculations predicted fairly different Fe-N stretching frequencies for the S=1/2 and the competing S=3/2 ground states, a direct experimental determination of this important fingerprint quantity was missing. Here we apply synchrotron-based nuclear resonance vibrational scattering (NRVS) to characterize the Fe-N stretching frequency of an Fe(V)-nitrido complex and its Fe(III)-azide precursor. The NRVS data show a new isolated band at 864 cm(-1) in the Fe(V)-nitrido complex that is absent in the precursor. The NRVS spectra are fit and simulated using a DFT approach, and the new feature is unambiguously assigned to a Fe(V)-N stretch. The calculated Fe-N stretching frequency is too high by approximately 75 cm(-1). Anharmonic contributions to the Fe-N stretching frequency have been evaluated and have been found to be small (-5.5 cm(-1)). The NRVS data provided a unique opportunity to obtain this vibrational information, which had eluded characterization by more traditional vibrational spectroscopies.     

Single-molecule dynamic triangulation.

A proposal for using single molecules as nanoprobes capable of detecting the trajectory of an elementary charge is discussed in detail. Presented numerical simulations prove that this single-molecule technique allows determination of a three-dimensional single-electron displacement within a few seconds with an accuracy better than 0.006 nm. Surprisingly, this significantly exceeds the accuracy with which the probe molecule itself can be localized (given the same measuring time) by means of single-molecule microscopy. It is also shown that the optimal concentration of probe molecules in the vicinity of the electron (i.e. the concentration which provides the best accuracy of the inferred electron displacement) is of the order of 10(-5) m.     

Reactions of 4,5‐Dihydro‐1,4‐Benzothiazepin‐3(2H)‐one 1,1‐Dioxide and 1,5‐Dihydro‐4,1‐Benzothiazepin‐2(3H)‐one 4,4‐Dioxide Derivatives with Vilsmeier Reagent and DMFDMA

The regioselectivity of the interaction between isomeric 4,5‐dihydro‐1,4‐benzothiazepin‐3(2H)‐one 1,1‐dioxide and 1,5‐dihydro‐4,1‐benzothiazepin‐2(3H)‐one 4,4‐dioxide derivatives with the Vilsmeier reagent and DMFDMA (N,N‐dimethylformamide dimethylacetal) has been investigated. The structures of synthesized compounds are confirmed by ¹H, ¹³C NMR, elemental analysis, and X‐ray data.     

Efficient time-dependent density functional theory approximations for hybrid density functionals: analytical gradients and parallelization

In this paper, we present the implementation of efficient approximations to time-dependent density functional theory (TDDFT) within the Tamm-Dancoff approximation (TDA) for hybrid density functionals. For the calculation of the TDDFT/TDA excitation energies and analytical gradients, we combine the resolution of identity (RI-J) algorithm for the computation of the Coulomb terms and the recently introduced "chain of spheres exchange" (COSX) algorithm for the calculation of the exchange terms. It is shown that for extended basis sets, the RIJCOSX approximation leads to speedups of up to 2 orders of magnitude compared to traditional methods, as demonstrated for hydrocarbon chains. The accuracy of the adiabatic transition energies, excited state structures, and vibrational frequencies is assessed on a set of 27 excited states for 25 molecules with the configuration interaction singles and hybrid TDDFT/TDA methods using various basis sets. Compared to the canonical values, the typical error in transition energies is of the order of 0.01 eV. Similar to the ground-state results, excited state equilibrium geometries differ by less than 0.3 pm in the bond distances and 0.5° in the bond angles from the canonical values. The typical error in the calculated excited state normal coordinate displacements is of the order of 0.01, and relative error in the calculated excited state vibrational frequencies is less than 1%. The errors introduced by the RIJCOSX approximation are, thus, insignificant compared to the errors related to the approximate nature of the TDDFT methods and basis set truncation. For TDDFT/TDA energy and gradient calculations on Ag-TB2-helicate (156 atoms, 2732 basis functions), it is demonstrated that the COSX algorithm parallelizes almost perfectly (speedup ~26-29 for 30 processors). The exchange-correlation terms also parallelize well (speedup ~27-29 for 30 processors). The solution of the Z-vector equations shows a speedup of ~24 on 30 processors. The parallelization efficiency for the Coulomb terms can be somewhat smaller (speedup ~15-25 for 30 processors), but their contribution to the total calculation time is small. Thus, the parallel program completes a Becke3-Lee-Yang-Parr energy and gradient calculation on the Ag-TB2-helicate in less than 4 h on 30 processors. We also present the necessary extension of the Lagrangian formalism, which enables the calculation of the TDDFT excited state properties in the frozen-core approximation. The algorithms described in this work are implemented into the ORCA electronic structure system.     

On the dimension of the space of ℝ-places of certain rational function fields

We prove that for every n ∈ ? the space M(K(x ₁, …, x _n ) of ?-places of the field K(x ₁, …, x _n ) of rational functions of n variables with coefficients in a totally Archimedean field K has the topological covering dimension dimM(K(x ₁, …, x _n )) ≤ n. For n = 2 the space M(K(x ₁, x ₂)) has covering and integral dimensions dimM(K(x ₁, x ₂)) = dim_? M(K(x ₁, x ₂)) = 2 and the cohomological dimension dim _G M(K(x ₁, x ₂)) = 1 for any Abelian 2-divisible coefficient group G.