On Fuglede's conjecture for three intervals

In this paper we prove the "Tiling implies Spectral" part of Fuglede's paper for the case of three intervals. Then we prove the "Spectral implies Tiling" part of the conjecture for the case of three equal intervals as also when the intervals have lengths 1/2, 1/4, 1/4. For the general case we change our approach to get information on the structure of the spectrum for the n-interval case. Finally, we use symbolic computations on Mathematica, and prove this part of the conjecture with an additional assumption on the spectrum.Comment: 21 page

A High Throughput Aqueous Passivation Testing Methodology for Compositionally Complex Alloys using Scanning Droplet Cell

Compositionally complex alloy systems containing more than five principal elements allow exploring a wide range of compositions, processing, and structural variables with the hope for identifying unique properties. Such opportunities also apply to designing materials for improved corrosion resistance, regulated by a self-healing passive film. Such a rich landscape in reactivity and protectivity demands the search for high-throughput experimental testing workflows to uncover key metrics, indicative of superior properties. In this communication, one such methodology is demonstrated for evaluating passivation performance of a combinatorial library of Al0.7-x-yCoxCryFe0.15Ni0.15 thin film alloys in deaerated 0.1 mol/L H2SO4(aq), using a scanning droplet cell

Stochastic kinetics of ribosomes: single motor properties and collective behavior

Synthesis of protein molecules in a cell are carried out by ribosomes. A ribosome can be regarded as a molecular motor which utilizes the input chemical energy to move on a messenger RNA (mRNA) track that also serves as a template for the polymerization of the corresponding protein. The forward movement, however, is characterized by an alternating sequence of translocation and pause. Using a quantitative model, which captures the mechanochemical cycle of an individual ribosome, we derive an {\it exact} analytical expression for the distribution of its dwell times at the successive positions on the mRNA track. Inverse of the average dwell time satisfies a ``Michaelis-Menten-like'' equation and is consistent with the general formula for the average velocity of a molecular motor with an unbranched mechano-chemical cycle. Extending this formula appropriately, we also derive the exact force-velocity relation for a ribosome. Often many ribosomes simultaneously move on the same mRNA track, while each synthesizes a copy of the same protein. We extend the model of a single ribosome by incorporating steric exclusion of different individuals on the same track. We draw the phase diagram of this model of ribosome traffic in 3-dimensional spaces spanned by experimentally controllable parameters. We suggest new experimental tests of our theoretical predictions.Comment: Final published versio

Cluster formation and anomalous fundamental diagram in an ant trail model

A recently proposed stochastic cellular automaton model ({\it J. Phys. A 35, L573 (2002)}), motivated by the motions of ants in a trail, is investigated in detail in this paper. The flux of ants in this model is sensitive to the probability of evaporation of pheromone, and the average speed of the ants varies non-monotonically with their density. This remarkable property is analyzed here using phenomenological and microscopic approximations thereby elucidating the nature of the spatio-temporal organization of the ants. We find that the observations can be understood by the formation of loose clusters, i.e. space regions of enhanced, but not maximal, density.Comment: 11 pages, REVTEX, with 11 embedded EPS file

Flow properties of driven-diffusive lattice gases: theory and computer simulation

We develop n-cluster mean-field theories (0 < n < 5) for calculating the flow properties of the non-equilibrium steady-states of the Katz-Lebowitz-Spohn model of the driven diffusive lattice gas, with attractive and repulsive inter-particle interactions, in both one and two dimensions for arbitrary particle densities, temperature as well as the driving field. We compare our theoretical results with the corresponding numerical data we have obtained from the computer simulations to demonstrate the level of accuracy of our theoretical predictions. We also compare our results with those for some other prototype models, notably particle-hopping models of vehicular traffic, to demonstrate the novel qualitative features we have observed in the Katz-Lebowitz-Spohn model, emphasizing, in particular, the consequences of repulsive inter-particle interactions.Comment: 12 RevTex page

Analysis of Escherichia coli RNase E and RNase III activity in vivo using tiling microarrays

Tiling microarrays have proven to be a valuable tool for gaining insights into the transcriptomes of microbial organisms grown under various nutritional or stress conditions. Here, we describe the use of such an array, constructed at the level of 20 nt resolution for the Escherichia coli MG1655 genome, to observe genome-wide changes in the steady-state RNA levels in mutants defective in either RNase E or RNase III. The array data were validated by comparison to previously published results for a variety of specific transcripts as well as independent northern analysis of additional mRNAs and sRNAs. In the absence of RNase E, 60% of the annotated coding sequences showed either increases or decreases in their steady-state levels. In contrast, only 12% of the coding sequences were affected in the absence of RNase III. Unexpectedly, many coding sequences showed decreased abundance in the RNase E mutant, while more than half of the annotated sRNAs showed changes in abundance. Furthermore, the steady-state levels of many transcripts showed overlapping effects of both ribonucleases. Data are also presented demonstrating how the arrays were used to identify potential new genes, RNase III cleavage sites and the direct or indirect control of specific biological pathways

Intracellular Internalization and Signaling Pathways Triggered by the Large Subunit of HSV-2 Ribonucleotide Reductase (ICP10)

AbstractThe large subunit of the HSV-2 ribonucleotide reductase (RR) (ICP10) is a chimera consisting of a serine threonine (Ser/Thr) protein kinase domain at the amino terminus and the RR domain at the carboxy terminus. Transformed human cells that constitutively express ICP10 (JHLa1) were stained with anti-LA-1 antibody (recognizes ICP10 amino acids 13-26) and immunogold-conjugated goat anti-rabbit IgG and were examined by electron microscopy. ICP10-associated gold particles were observed on the cell surface and in structures with ultrastructural characteristics of endocytic vesicles, multivesicular bodies, and lysosomes, consistent with endocytic internalization. ICP10 was also associated with the cytoskeleton fraction of JHLa1 cells and, at least in part, it colocalized with actin filaments. This was evidenced by immunoprecipitation of [35S]methionine-labeled cell fractions and immunofluorescent staining of Triton-treated cells with anti-LA-1 antibody and phalloidin. Endocytic localization of gold particles was not seen in cells that constitutively express the ICP10 transmembrane (TM)-deleted mutant p139TM (JHL15). p139TM did not associate with the cytoskeleton and was almost entirely localized within the cytoplasm, raf and Erk evidenced decreased mobility consistent with an activated state in JHLa1, but not JHL15, cells, and chloramphenicol acetyl transferase (CAT) expression from a c-fos/cat hybrid construct was significantly increased in JHLa1 but not JHL15 cells. The data indicate that effector molecules downstream of ras are activated in JHLa1 cells and the ICP10 TM segment plays a critical role in ICP10 intracellular localization and its ability to activate signaling pathways. This behavior is analogous to that of an activated growth factor receptor kinase

Notch induces cyclin-D1-dependent proliferation during a specific temporal window of neural differentiation in ES cells

AbstractThe Notch signaling pathway controls cell fate choices at multiple steps during cell lineage progression. To produce the cell fate choice appropriate for a particular stage in the cell lineage, Notch signaling needs to interpret the cell context information for each stage and convert it into the appropriate cell fate instruction. The molecular basis for this temporal context-dependent Notch signaling output is poorly understood, and to study this, we have engineered a mouse embryonic stem (ES) cell line, in which short pulses of activated Notch can be produced at different stages of in vitro neural differentiation. Activation of Notch signaling for 6h specifically at day 3 during neural induction in the ES cells led to significantly enhanced cell proliferation, accompanied by Notch-mediated activation of cyclin D1 expression. A reduction of cyclin-D1-expressing cells in the developing CNS of Notch signaling-deficient mouse embryos was also observed. Expression of a dominant negative form of cyclin D1 in the ES cells abrogated the Notch-induced proliferative response, and, conversely, a constitutively active form of cyclin D1 mimicked the effect of Notch on cell proliferation. In conclusion, the data define a novel temporal context-dependent function of Notch and a critical role for cyclin D1 in the Notch-induced proliferation in ES cells

High Throughput Discovery of Lightweight Corrosion-Resistant Compositionally Complex Alloys

Compositionally complex alloys hold the promise of simultaneously attaining superior combinations of properties such as corrosion resistance, light-weighting, and strength. Achieving this goal is a challenge due in part to a large number of possible compositions and structures in the vast alloy design space. High throughput methods offer a path forward, but a strong connection between the synthesis of a given composition and structure with its properties has not been fully realized to date. Here we present the rapid identification of light weight highly corrosion-resistant alloys based on combinations of Al and Cr in a Cantor-like base alloy (Al-Co-Cr-Fe-Ni). Previously unstudied alloy stoichiometries were identified using a combination of high throughput experimental screening coupled with key metallurgical and electrochemical corrosion tests, identifying alloys with excellent passivation behavior. Importantly, the electrochemical impedance modulus of the exposure-modified, air-formed film at the corrosion potential was found as an accurate non-destructive predictor of corrosion and passivation characteristics. Multi-element EXAFS analyses connected more ordered type chemical short range order in the Ni-Al 1st nn shell to poorer corrosion. This report underscores the utility of high throughput exploration of compositionally complex alloys for the identification and rapid screening of vast stoichiometric space