Spanning Trees on Hypercubic Lattices and Non-orientable Surfaces

We consider the problem of enumerating spanning trees on lattices. Closed-form expressions are obtained for the spanning tree generating function for a hypercubic lattice of size N_1 x N_2 x...x N_d in d dimensions under free, periodic, and a combination of free and periodic boundary conditions. Results are also obtained for a simple quartic net embedded on two non-orientable surfaces, a Moebius strip and the Klein bottle. Our results are based on the use of a formula expressing the spanning tree generating function in terms of the eigenvalues of an associated tree matrix. An elementary derivation of this formula is given.Comment: latex, 9 pages, no figures, to appear in Lett. Appl. Mat

Local and remote controls on observed Arctic warming

Copyright © 2012 American Geophysical UnionThe Arctic is warming two to four times faster than the global average. Debate continues on the relative roles of local factors, such as sea ice reductions, versus remote factors in driving, or amplifying, Arctic warming. This study examines the vertical profile and seasonality of observed tropospheric warming, and addresses its causes using atmospheric general circulation model simulations. The simulations enable the isolation and quantification of the role of three controlling factors of Arctic warming: 1) observed Arctic sea ice concentration (SIC) and sea surface temperature (SST) changes; 2) observed remote SST changes; and 3) direct radiative forcing (DRF) due to observed changes in greenhouse gases, ozone, aerosols, and solar output. Local SIC and SST changes explain a large portion of the observed Arctic near-surface warming, whereas remote SST changes explain the majority of observed warming aloft. DRF has primarily contributed to Arctic tropospheric warming in summer

Conformational transitions of poly(dA-dT)poly(dA-dT) in ethanolic solutions.

Examination of circular dichroic and phosphorus nuclear magnetic resonance spectra showed that poly(dA-dT)-poly(dA-dT) exhibited an ethanol-induced transition to the A form in an Na+ containing medium like natural DNAs. A mere replacement of the Na+ by Cs+ counterions meant that the polynucleotide was with a little cooperativity transformed into a novel conformation displaying a deep negative band in the long wavelength part of the CD spectrum. The presence of very low concentration of Cs2+ shifted the midpoint of the transition to a lower content of ethanol

Cleavage of Vimentin by Different Retroviral Proteases

Proteases (PRs) of retroviruses cleave viral polyproteins into their mature structural proteins and replication enzymes. Besides this essential role in the replication cycle of retroviruses, PRs also cleave a variety of host cell proteins. We have analyzed the in vitro cleavage of mouse vimentin by proteases of human immunodeficiency virus type 1 (HIV-1) and type 2 (HIV-2), bovine leukemia virus (BLV), Mason-Pfizer monkey virus (M-PMV), myeloblastosis-associated virus (MAV), and two active-site mutants of MAV PR. Retroviral proteases display significant differences in specificity requirements. Here, we show a comparison of substrate specificities of several retroviral proteases on vimentin as a substrate. Vimentin was cleaved by all the proteases at different sites and with different rates. The results show that the physiologically important cellular protein vimentin can be degraded by different retroviral proteases

An engineered retroviral proteinase from myeloblastosis associated virus acquires pH dependence and substrate specificity of the HIV-1 proteinase

In an attempt to understand the structural reasons for differences in specificity and activity of proteinases from two retroviruses encoded by human immunodeficiency virus (HIV) and myeloblastosis associated virus (MAV), we mutated five key residues predicted to form part of the enzyme subsites S1, S2 and S3 in the substrate binding cleft of the wild-type MAV proteinase wMAV PR. These were changed to the residues occupying a similar or identical position in the HIV-1 enzyme. The resultant mutated MAV proteinase (mMAV PR) exhibits increased enzymatic activity, altered substrate specificity, a substantially changed pH activity profile and a higher pH stability close to that observed in the HIV-1 PR. This dramatic alteration of MAV PR activity achieved by site-directed mutagenesis suggests that we have identified the amino acid residues contributing substantially to the differences between MAV and HIV-1 proteinases

Genomic structure of Hstx2 modifier of Prdm9-dependent hybrid male sterility in mice

F1 hybrids between mouse inbred strains PWD and C57BL/6 represent the most thoroughly genetically defined model of hybrid sterility in vertebrates. Hybrid male sterility can be fully reconstituted from three components of this model, namely the Prdm9 hybrid sterility gene, intersubspecific homeology of Mus musculus musculus and Mus musculus domesticus autosomes, and the X-linked Hstx2 locus. Hstx2 modulates the extent of Prdm9-dependent meiotic arrest and harbors two additional genetic factors responsible for intersubspecific introgression-induced oligospermia (Hstx1) and reduced global meiotic recombination rate (Meir1). To facilitate positional cloning and to overcome the recombination suppression within the 4.3 Mb genomicDob interval encompassing the Hstx2 locus we designed Hstx2-CRISPR and SPO11/Cas9 transgenes aimed to induce DNA double-strand breaks specifically within the Hstx2 locus. The resulting recombinant reduced the Hstx2 locus to 2.70 Mb (Chr X:66.51-69.21 Mb). The newly defined Hstx2 still operates as the major X-linked factor of the F1 hybrid sterility, controls meiotic chromosome synapsis, and modifies meiotic recombination rate. Despite extensive further crosses, the 2.70 Mb Hstx2 interval behaved as a recombination cold spot with reduced PRDM9-mediated H3K4 hotspots and absence of DMC1-defined DNA DSB hotspots. To search for structural anomalies as a possible cause of recombination suppression we used optical mapping of the Hstx2 interval and observed high incidence of subspecies-specific structural variants along the X chromosome, with a striking copy number polymorphism of the microRNA Mir465 cluster. Finally, we analyzed the role of one of the Hstx2 candidate genes, the Fmr1 neighbor (Fmr1nb) gene in male fertility.Article summary Early meiotic arrest of mouse intersubspecific hybrids depends on the interaction between the Prdm9 gene and Hybrid sterility X2 (Hstx2) locus on chromosome X. Lustyk et al. conducted high-resolution genetic and physical mapping of the Hstx2 locus, reduced it to 2.7 Mb interval within a constitutive recombination cold spot and found that the newly defined Hstx2 still operates as the X-linked hybrid sterility factor, controls meiotic chromosome synapsis, and modifies recombination rate. Optical mapping of the Hstx2 genomic region excluded inversion as a cause of recombination suppression and revealed a striking copy number polymorphism of the microRNA Mir465 cluster