Componentwise linearity of ideals arising from graphs

Let $G$ be a simple undirected graph on $n$ vertices. Francisco and Van Tuyl have shown that if $G$ is chordal, then $\bigcap_{\{x_i,x_j\}\in E_G} < x_i,x_j>$ is componentwise linear. A natural question that arises is for which $t_{ij}>1$ the ideal $\bigcap_{\{x_i,x_j\}\in E_G}^{t_{ij}}$ is componentwise linear, if $G$ is chordal. In this report we show that $\bigcap_{\{x_i,x_j\}\in E_G} ^{t}$ is componentwise linear for all $n\geq 3$ and positive $t$, if $G$ is a complete graph. We give also an example where $G$ is chordal, but the intersection ideal is not componentwise linear for any $t>1$.Comment: 5 page

Just the Financial Facts Please! A Secret Survey of Financial Services in San Francisco's Mission District

Examines the costs and dynamics of borrowing $1,000 from various financial service providers in a historic immigrant community. Proposes Financial Facts labels and a Responsible Lending and Borrowing Checklist to increase residents' financial capability

The delayed rectifier potassium conductance in the sarcolemma and the transverse tubular system membranes of mammalian skeletal muscle fibers.

A two-microelectrode voltage clamp and optical measurements of membrane potential changes at the transverse tubular system (TTS) were used to characterize delayed rectifier K currents (IK(V)) in murine muscle fibers stained with the potentiometric dye di-8-ANEPPS. In intact fibers, IK(V) displays the canonical hallmarks of K(V) channels: voltage-dependent delayed activation and decay in time. The voltage dependence of the peak conductance (gK(V)) was only accounted for by double Boltzmann fits, suggesting at least two channel contributions to IK(V). Osmotically treated fibers showed significant disconnection of the TTS and displayed smaller IK(V), but with similar voltage dependence and time decays to intact fibers. This suggests that inactivation may be responsible for most of the decay in IK(V) records. A two-channel model that faithfully simulates IK(V) records in osmotically treated fibers comprises a low threshold and steeply voltage-dependent channel (channel A), which contributes ∼31% of gK(V), and a more abundant high threshold channel (channel B), with shallower voltage dependence. Significant expression of the IK(V)1.4 and IK(V)3.4 channels was demonstrated by immunoblotting. Rectangular depolarizing pulses elicited step-like di-8-ANEPPS transients in intact fibers rendered electrically passive. In contrast, activation of IK(V) resulted in time- and voltage-dependent attenuations in optical transients that coincided in time with the peaks of IK(V) records. Normalized peak attenuations showed the same voltage dependence as peak IK(V) plots. A radial cable model including channels A and B and K diffusion in the TTS was used to simulate IK(V) and average TTS voltage changes. Model predictions and experimental data were compared to determine what fraction of gK(V) in the TTS accounted simultaneously for the electrical and optical data. Best predictions suggest that K(V) channels are approximately equally distributed in the sarcolemma and TTS membranes; under these conditions, &gt;70% of IK(V) arises from the TTS

Novel Inhibitors for Isocitrate Lyase as a Potent Antitubercular Agent for Mycobacterium Tuberculosis

Introduction: Mycobacterium tuberculosis (Mtb) is the causative agent of tuberculosis (TB). TB claimed 1.4 million lives in 2019. It is estimated that one-quarter of the world’s population is infected with latent TB. Current first- and second-line drugs used to treat TB require adherence to an extended period of therapy (at least six months) and do not target latent TB. It has been shown that the enzyme isocitrate lyase (ICL) is essential for the survival and persistence of Mtb in latent TB. ICL plays an important role in two metabolic pathways required during TB latency, the glyoxylate and methylcitrate cycle. ICL is absent in humans, and therefore, it is considered a promising drug target. Herein, is reported a novel family of ICL inhibitors that is effective in vitro against both the enzyme and Mtb. Methods: The His-tagged ICL1 enzyme was expressed using E. coli as a host and purified by Ni-NTA chromatography. The recombinant enzyme was used to set up crystallisation trials and in vitro enzymatic assay was performed on ICL1 inhibitors. The synthesis of D/L-threo-2-methylisocitrate and the methylation of five other drug candidates were described. Both co-crystallisation and soaking techniques were performed to obtain an ICL1:CL-54-04 complex crystal, whose structure was solved. The CL-54 drug family was tested against Mtb. A checkerboard assay was utilised to test the combinatory effect of CL-54-04 with rifampicin or bedaquiline in both glycerol and propionate media. To investigate the role of acetate metabolism in drug tolerance, ΔpckA, ICL knock-down and ΔprpD Mtb mutants were assessed. Results: Seven new conditions to crystallise ICL1 were identified, and eleven drugs were tested against the isolated enzyme. A promising new family of drugs have been identified as the most potent ICL1 inhibitors reported to date. One of the analogues, CL-54-04, had a bacteriostatic effect at 10 μM and a bactericidal effect at 100 μM against Mtb in vitro. A drug combination screening of CL-54-04 with rifampicin or bedaquiline led to an additive effect in the checkerboard assay and a significant impact in the colony-forming unit assay. The role of fatty acid metabolism in drug tolerance was investigated by testing three central carbon metabolism mutant strains against isoniazid. Discussion: From the three CL-54 analogues tested, only CL-54-04 caused a bactericidal effect against Mtb. A solved ICL1:CL-54-04 complex crystal structure showed that the catalytic loop had a distinctive move of 13.8 Å, suggesting that the binding of ICL with CL-54-04 leads to a close conformation of the active site. A superimposition of the solved ICL1:CL-54-04 complex and the ICL1 structure alignment with 3-nitropropionate demonstrates that CL-54-04 inhibitor binds and causes the same conformational changes as 3-nitropropionate. Using metabolomics analysis, the combination of rifampicin and CL-54-04 causes an accumulation of the methylcitrate cycle metabolites in propionate media, suggesting that the ICL has been inhibited. Fatty acid as a sole carbon source showed to increase the drug tolerance of all three Mtb mutants against isoniazid. Conclusion: A new drug family has been identified as lead compounds against ICL. The estimated IC50 of CL-54-01 is approximately half of the 3-nitropropionamide, and it causes the exact conformational change to the enzyme as 3-nitropropionate (the analogue of 3-nitropropionamide). These findings suggest that this drug family are the most promising ICL1 inhibitors reported to date

Stac3 enhances expression of human CaV1.1 in Xenopus oocytes and reveals gating pore currents in HypoPP mutant channels.

Mutations of CaV1.1, the pore-forming subunit of the L-type Ca2+ channel in skeletal muscle, are an established cause of hypokalemic periodic paralysis (HypoPP). However, functional assessment of HypoPP mutant channels has been hampered by difficulties in achieving sufficient plasma membrane expression in cells that are not of muscle origin. In this study, we show that coexpression of Stac3 dramatically increases the expression of human CaV1.1 (plus α2-δ1b and β1a subunits) at the plasma membrane of Xenopus laevis oocytes. In voltage-clamp studies with the cut-open oocyte clamp, we observe ionic currents on the order of 1 μA and gating charge displacements of ∼0.5-1 nC. Importantly, this high expression level is sufficient to ascertain whether HypoPP mutant channels are leaky because of missense mutations at arginine residues in S4 segments of the voltage sensor domains. We show that R528H and R528G in S4 of domain II both support gating pore currents, but unlike other R/H HypoPP mutations, R528H does not conduct protons. Stac3-enhanced membrane expression of CaV1.1 in oocytes increases the throughput for functional studies of disease-associated mutations and is a new platform for investigating the voltage-dependent properties of CaV1.1 without the complexity of the transverse tubule network in skeletal muscle

Spanish-English Code-Switching in American Mainstream TV Series

This study examines how English-Spanish code-switching (CS) has evolved throughout time in American mainstream TV shows. More specifically, it looks at the frequency of CS in shows from the past, 20th century, versus shows from the present time, 21st century. Furthermore, it also investigates which gender (males or females) is employing CS more frequently in both time periods. The study focuses on four American TV shows that include English-Spanish bilingual speakers and that are representative of both the past and the present time. The purpose of this study is to observe if the presence of English-Spanish CS is growing or declining in American mainstream TV shows overtime and how gender is playing a role in CS frequency. Results indicated that on average, based on the shows observed only, CS usage has decreased in 21st century TV shows in comparison to their 20th century counterparts, and that males are employing CS more frequently than females on average. The first outcome could have been influenced by the number of shows observed being small, therefore, only serve as a representation of CS patterns overtime. Lastly, the second outcome could be attributed to the fact that research (e.g. Fischer 1958, Lavob 1966, Trudgill, 1972) has demonstrated that males tend to utilize more non-standard forms of language than females