Multiplicity of solutions for semilinear subelliptic Dirichlet problem

In this paper, we study the semilinear subelliptic equation \left\{ \begin{array}{cc} -\triangle_{X} u=f(x,u)+g(x,u) & \mbox{in}~\Omega, \\[2mm] u=0\hfill & \mbox{on}~\partial\Omega, \end{array} \right. where $\triangle_{X}=-\sum_{i=1}^{m}X_{i}^{*}X_{i}$ is the self-adjoint H\"{o}rmander operator associated with vector fields $X=(X_{1},X_{2},\ldots,X_{m})$ satisfying the H\"{o}rmander condition, $f(x,u)\in C(\overline{\Omega}\times \mathbb{R})$, $g(x,u)$ is a Carath\'{e}odory function on $\Omega\times \mathbb{R}$, and $\Omega$ is an open bounded domain in $\mathbb{R}^n$ with smooth boundary. Combining the perturbation from symmetry method with the approaches involving eigenvalue estimate and Morse index in estimating the min-max values, we obtain two kinds of existence results for multiple weak solutions to the problem above. Furthermore, we discuss the difference between the eigenvalue estimate approach and the Morse index approach in degenerate situations. Compared with the classical elliptic cases, both approaches here have their own strengths in the degenerate cases. This new phenomenon implies the results in general degenerate cases would be quite different from the situations in classical elliptic cases.Comment: This paper has been accepted for publication in SCIENCE CHINA Mathematic

Characterization of Host-Cell Line Specific Glycosylation Profiles of Early Transmitted/Founder HIV-1 gp120 Envelope Proteins

Glycosylation plays an essential role in regulating protein function by modulating biological, structural, and therapeutic properties. However, due to its inherent heterogeneity and diversity, the comprehensive analysis of protein glycosylation remains a challenge. As part of our continuing effort in the analysis of glycosylation profiles of recombinant HIV-1 envelope-based immunogens, we evaluated and compared the host-cell specific glycosylation pattern of recombinant HIV-1 surface glycoprotein, gp120, derived from clade C transmitted/founder virus 1086.C expressed in Chinese hamster ovary (CHO) and human embryonic kidney containing T antigen (293T) cell lines. We used an integrated glycopeptide-based mass mapping workflow that includes a partial deglycosylation step described in our previous study1 with the inclusion of the fragmentation technique, electron transfer dissociation (ETD), to complement collision induced dissociation (CID). The inclusion of ETD facilitated the analysis by providing additional validation for glycopeptide identification and expanding the identified glycopeptides to include coverage of O-linked glycosylation. The site-specific glycosylation analysis shows that the transmitted/founder 1086.C gp120 expressed in CHO and 293T displayed distinct similarities and differences. For N-linked glycosylation, two sites (N386 and N392), in the V4 region were populated with high mannose glycans in the CHO cell-derived 1086.C gp120, while these sites had a mixture of high mannose and processed glycans in the 293T cell-derived 1086.C gp120. Compositional analysis of O-linked glycans revealed that 293T cell-derived 1086.C gp120 consisted of cores 1, 2, and 4 type O-linked glycans while CHO cell-derived 1086.C exclusively consisted of core 1 type O-linked glycans. Overall, glycosylation site occupancy of the CHO and 293T cell-derived 1086.C gp120 show high degree of similarity except for one site at N88 in the C1 region. This site was partially occupied in 293T-gp120 but fully occupied in CHO-gp120. Site-specific glycopeptide analysis of transmitted/founder 1086.C gp120 expressed in CHO cells revealed the presence of phosphorylated glycans while 293T cell produced 1086.C gp120 glycans were not phosphorylated. While the influence of phosphorylated glycans on immunogenicity is unclear, distinguishing host-cell specific variations in glycosylation profiles provides insights into the similarity (or difference) in recombinant vaccine products. While these differences had minimal effect on envelope antigenicity, they may be important in considering immunogenicity and functional capacities of recombinant envelope proteins produced in different expression systems

4-(1-Cyclo­propyl-6-fluoro-4-oxo-1,4-dihydro­quinolin-7-yl)piperazin-1-ium 2,4,5-tricarb­oxy­benzene-1-carboxyl­ate monohydrate

In the crystal of title compound, C16H19FN3O+·C10H5O8 −·H2O, the water mol­ecule and the ions are connected by inter­molecular N—H⋯O and O—H⋯O hydrogen bonds and π–π stacking [centroid–centroid separation = 3.602 (1) Å] between the benzene ring and the pyridine ring, generating a three-dimensional supra­molecular structure

Methods development for Analysis of Partially Deglycosylated Proteins and Application to an HIV Envelope Protein Vaccine Candidate

The work presented herein describes the first comprehensive analysis of a partially deglycosylated HIV vaccine candidate envelope protein (Env). The Env, JRFL gp140 ΔCF, with 27 potential glycosylation sites, was partially deglycosylated with PNGase F as part of a strategy to generate a more immunogenic HIV vaccine, and the resulting protein’s glycosylation was characterized in a unique workflow using two different glycosidases, Endo H and Endo F3. This unique analysis protocol provided for coverage on 26 of the 27 glycosylation sites, and the data showed that the biochemical treatment with PNGase F resulted in a highly heterogeneous glycoprotein product that had been partially deglycosylated at most of the glycosylation sites. The protocols described in this work could be useful for characterizing the glycosylation site occupancy of other native or biochemically deglycosylated proteins

Study on the synergistic effect of foreign trade, technological progress, and carbon emissions

A primary development plan for a country is to attain carbon neutrality and high-quality international commerce development. This study uses panel data from 30 provinces in mainland China to analyze the dynamic interplay between international trade, technological innovation, and carbon emissions. The findings show that foreign trade, technological progress, and carbon emissions all have their own “economic inertia” that can be self-motivated and self-reinforcing. Foreign commerce and carbon emissions are mutually inhibiting, but technical progress and carbon emissions are mutually reinforcing. This illustrates that achieving a positive cycle of international trade, technological improvement, and carbon emissions necessitates a significant baseline need. Overcoming carbon trade barriers is currently the most difficult challenge for Chinese enterprises involved in foreign commerce. Low-carbon technology advancements are a critical part in this process. Our research strengthens the positive connections between international trade and carbon emissions as a result of technological improvement and proposes a feasible plan for international trade to achieve carbon peaking and carbon neutrality

Comparison of ocular trauma between normalized and the COVID-19 epidemic periods in China: a multi-center cross-sectional study

AIM: To compare the feature of ocular trauma between normalized period and the COVID-19 epidemic period in China, and to provide a profile for eye injuries in special times in future. METHODS: This is a multi-center cross-sectional study with 30 participated hospitals involving the China Ocular Trauma Society members. All hospitalized cases who visited the Ophthalmology Department in participated hospitals with eye injuries during the normalized period (2019) and the COVID-19 epidemic period (2020) were included in this study. Demographic characteristic of cases, date of injury, sites and types of injury were collected. RESULTS: This study involved 13 525 (61 cases with both eyes) injured cases. There were 7269 (53.74%) eye-injured cases and 6256 (46.26%) eye-injured cases in 2019 and 2020 separately. Compared with 2019, the incidence of ocular trauma in retirees, housewives and unemployed increased with year-on-year of 4.96%, 102.67%, and 11.64% among all occupations. In 2020, the incidence of eye injuries decreased in all injury sites except for an increase in home (30.29% year-on-year). The incidence of mechanical eye injuries decreased, while that of non-mechanical eye injuries (chemical/thermal/radiation) increased (47.45% year-on-year). There were 255 (3.51%, 255/7269) and 376 (6.01%, 376/6256) non-mechanical injured cases in 2019 and 2020 (Pearson Chi2=47.33, P<0.001) separately. CONCLUSION: During the COVID-19 epidemic period, the total cases of ocular trauma decrease but the proportion of non-mechanical ocular trauma increase. Penetrating is still the highest proportion among all types of mechanical ocular trauma. From a preventive point of view, protection for retired persons, housewives and unemployed persons should be improved during public health events period

Glycosylation Site-Specific Analysis of Clade C HIV-1 Envelope Proteins

The extensive glycosylation of HIV-1 envelope proteins (Env), gp120/gp41, is known to play an important role in evasion of host immune response by masking key neutralization epitopes and presenting the Env glycosylation as “self” to the host immune system. The Env glycosylation is mostly conserved but continues to evolve to modulate viral infectivity. Thus, profiling Env glycosylation and distinguishing interclade and intraclade glycosylation variations are necessary components in unraveling the effects of glycosylation on Env’s immunogenicity. Here, we describe a mass spectrometry-based approach to characterize the glycosylation profiles of two rVV-expressed clade C Envs by identifying the glycan motifs on each glycosylation site and determining the degree of glycosylation site occupancy. One Env is a wild-type Env, while the other is a synthetic “consensus” sequence (C.CON). The observed differences in the glycosylation profiles between the two clade C Envs show that C.CON has more unutilized sites and high levels of high mannose glycans; these features mimic the glycosylation profile of a Group M consensus immunogen, CONS. Our results also reveal a clade-specific glycosylation pattern. Discerning interclade and intraclade glycosylation variations could provide valuable information in understanding the molecular differences among the different HIV-1 clades and in designing new Env-based immunogens