Brownian dynamics simulation of the diffusion of rods and wormlike chains in a gel modeled as a cubic lattice: application to DNA

The translational diffusion constant of a particle, D, in a congested medium or a gel can be written as the product of two terms that account for long-range hydrodynamic interaction between the gel or congested medium and the particle, DEM, and a short-range "steric" term, S. For particles of arbitrary shape, DEM has been examined previously within the framework of the effective medium, EM, model (S. Allison et al., J. Phys. Chem. B 2008, 112, 5858-5866). In the present work, we examine S for rod- and wormlike chain models of duplex DNA in the size range of 100 to over 2000 base pairs. The gel is modeled explicitly as a cubic lattice, and Brownian dynamics simulation is used to examine S for a wide range of rod/wormlike chain and gel parameters. For wormlike chains with P = 50 nm, an empirical formula is derived for S that should be valid over a wide range of wormlike chain/gel parameters. For duplex DNA in the size of several hundred to several thousand base pairs in an agarose gel of 2% or less, fair agreement between modeling and experiment is obtained. However, modeling overestimates the length dependence of D observed experimentally. Finally, the reduction of D of DNA (100 to over 1000 base pairs in length) in cytoplasm relative to water can be accounted for quite well using the effective medium plus steric correction approach.     

The Duffin–Schaeffer Conjecture with extra divergence

Given a nonnegative function \({\psi\mathbb{N} \to \mathbb{R}}\), let W(ψ) denote the set of real numbers x such that |nx ? a| < ψ(n) for infinitely many reduced rationals a/n (n > 0). A consequence of our main result is that W(ψ) is of full Lebesgue measure if there exists an \({\epsilon > 0}\) such that

$ \textstyle \sum_{n\in\mathbb{N}}\left(\frac{\psi(n)}{n}\right)^{1+\epsilon}\varphi (n)=\infty. $

The Duffin–Schaeffer Conjecture is the corresponding statement with \({\epsilon = 0}\) and represents a fundamental unsolved problem in metric number theory. Another consequence is that W(ψ) is of full Hausdorff dimension if the above sum with \({\epsilon = 0}\) diverges; i.e. the dimension analogue of the Duffin–Schaeffer Conjecture is true.

     

Porous salts based on the pamoate ion

A number of porous salts based on the pamoate anion in combination with lutidinium or picolinium cations have been characterised. One salt undergoes single-crystal to single-crystal solvent exchange, while another isostructural series of salts contain channels that can be partly evacuated without collapse of the framework.     

Assessment of functional changes in nanoparticle-exposed neuroendocrine cells with amperometry: exploring the generalizability of nanoparticle-vesicle matrix interactions

Using two of the most commonly synthesized noble metal nanoparticle preparations, citrate-reduced Au and Ag, the impacts of short-term accidental nanoparticle exposure are examined in primary culture murine adrenal medullary chromaffin cells. Transmission electron microscopy (TEM), inductively coupled plasma atomic emission spectroscopy (ICP-AES) and Alamar Blue viability studies revealed that nanoparticles are taken up by cells but do not decrease cell viability within 48 hours of exposure. Carbon-fiber microelectrode amperometry (CFMA) examination of exocytosis in nanoparticle-exposed cells revealed that nanoparticle exposure does lead to decreased secretion of chemical messenger molecules, of up to 32.5% at 48 hours of Au exposure. The kinetics of intravesicular species liberation also slows after nanoparticle exposure, between 30 and 50% for Au and Ag, respectively. Repeated stimulation of exocytosis demonstrated that these effects persisted during subsequent stimulations, meaning that nanoparticles do not interfere directly with the vesicle recycling machinery but also that cellular function is unable to recover following vesicle content expulsion. By comparing these trends with parallel studies done using mast cells, it is clear that similar exocytosis perturbations occur across cell types following noble metal nanoparticle exposure, supporting a generalizable effect of nanoparticle-vesicle interactions.     

Changing and unchanging domination: a classification

The six classes of graphs resulting from the changing or unchanging of the domination number of a graph when a vertex is deleted, or an edge is deleted or added are considered. Each of these classes has been studied individually in the literature. We consider relationships among the classes, which are illustrated in a Venn diagram. We show that no subset of the Venn diagram is empty for arbitrary graphs, and prove that some of the subsets are empty for connected graphs. Our main result is a characterization of trees in each subset of the Venn diagram.     

Characterization of LaRhO3 perovskites for dry (CO2) reforming of methane (DRM)

This work reports on the characterization of LaRhO₃ perovskite as a catalyst for dry reforming of methane. The catalyst was studied using CH₄-temperature programmed reduction (TPR), H₂-TPR, and temperature programmed surface reaction (TPSR), and the changes in the crystal structure of the catalyst due to these treatments were studied by X-ray diffraction (XRD). XRD pattern of the freshly calcined perovskites showed the formation of highly crystalline LaRhO₃ and La₂O₃ phases. H₂-TPR of the fresh calcined catalyst showed a shoulder at 342°C and a broad peak at 448°C, suggesting that the reduction of Rh in perovskite occurs in multiple steps. XRD pattern of the reduced catalyst suggests complete reduction of the LaRhO₃ phase and the formation of metallic Rh and minor amounts of La(OH)₃. The CH4-TPR data show qualitatively similar results as H₂-TPR, with a shoulder and a broad peak in the same temperature range. Following the H₂-TPR up to 950°C, the same batch of catalyst was oxidized by flowing 5 vol. % O₂/He up to 500°C and a second H₂-TPR (also up to 950°C) was conducted. This second H₂-TPR differed significantly from that of the fresh calcined catalyst. The single sharp peak at 163°C in the second H₂-TPR suggests a significant change in the catalyst, probably causedby the transformation of about 90 % of the perovskite into Rh/La₂O₃. This was confirmed by the XRD studies of the catalyst reduced after the oxidation at 500°C. TPSR of the dry reforming reaction on the fresh calcined catalyst showed CO and H₂ formation starting at 400°C, with complete consumption of the reactants at 650°C. The uneven consumption of reactants between 400°C and 650°C suggests that reactions other than DRM occur, including reverse water gas shift (RWGS) and the Boudouard reaction (BR), probably as a result of in-situ changes in the catalyst, consistent with the H₂-TPR results. TPSR, after a H₂-TPR up to 950°C, showed that the dry reforming reaction did not light off until 570°C, which is much higher temperature than the one observed using fresh calcined catalyst. This shows that the uniform sites produced during the 950°C H₂-TPR are catalytically less active than those of the fresh calcined catalyst, and that no significant side reactions such as RWGS or the Boudouard reaction occur. This suggests that reduction leads to the formation of a single type of sites which do not catalyze simultaneous side reactions.     

Locating and total dominating sets in trees

A set S of vertices in a graph G=(V,E) is a total dominating set of G if every vertex of V is adjacent to a vertex in S. We consider total dominating sets of minimum cardinality which have the additional property that distinct vertices of V are totally dominated by distinct subsets of the total dominating set.