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In this paper, we study the uniqueness of nodal radial solutions to nonlinear elliptic equations in the unit ball in ℝ3$$ {\mathrm{\mathbb{R}}}^3 $$. Under suitable conditions, we prove that, for any given positive integer k$$ k $$, the problem we considered has at most one solution possessing exactly k−1$$ k-1 $$ nodes. Together with the results presented by Nagasaki [J. Fac. Sci. Univ. Tokyo Sect. IA Math. 36 (2): 211–232, 1989] and Tanaka [Proc. Roy. Soc. Edinburgh Sect. A. 138 (6): 1331–1343, 2008], we can prove that more types of nonlinear elliptic equations have the uniqueness of nodal radial solutions. [ABSTRACT FROM AUTHOR]

This study introduces a novel approach for synthesizing Benzoxazine‐centered Polychiral Polyheterocycles (BPCPHCs) via an innovative asymmetric carbene‐alkyne metathesis‐triggered cascade. Overcoming challenges associated with intricate stereochemistry and multiple chiral centers, the catalytic asymmetric Carbene Alkyne Metathesis‐mediated Cascade (CAMC) is employed using dirhodium catalyst/Brønsted acid co‐catalysis, ensuring precise stereo control as validated by X‐ray crystallography. Systematic substrate scope evaluation establishes exceptional diastereo‐ and enantioselectivities, creating a unique library of BPCPHCs. Pharmacological exploration identifies twelve BPCPHCs as potent Nav ion channel blockers, notably compound 8 g. In vivo studies demonstrate that intrathecal injection of 8 g effectively reverses mechanical hyperalgesia associated with chemotherapy‐induced peripheral neuropathy (CIPN), suggesting a promising therapeutic avenue. Electrophysiological investigations unveil the inhibitory effects of 8 g on Nav1.7 currents. Molecular docking, dynamics simulations and surface plasmon resonance (SPR) assay provide insights into the stable complex formation and favorable binding free energy of 8 g with C5aR1. This research represents a significant advancement in asymmetric CAMC for BPCPHCs and unveils BPCPHC 8 g as a promising, uniquely acting pain blocker, establishing a C5aR1‐Nav1.7 connection in the context of CIPN. [ABSTRACT FROM AUTHOR]

Graph similarity learning is a significant and fundamental issue in the theory and analysis of graphs, which has been applied in a variety of fields, including object tracking, recommender systems, similarity search, and so on. Recent methods for graph similarity learning that utilize deep learning typically share two deficiencies: (1) they leverage graph neural networks as backbones for learning graph representations but have not well captured the complex information inside data, and (2) they employ a cross-graph attention mechanism for graph similarity learning, which is computationally expensive. Taking these limitations into consideration, a method for graph similarity learning is devised in this study, namely, Contrastive Graph Similarity Network (CGSim). To enhance graph similarity learning, CGSim makes use of the complementary information of two input graphs and captures pairwise relations in a contrastive learning framework. By developing a dual contrastive learning module with a node-graph matching and a graph-graph matching mechanism, our method significantly reduces the quadratic time complexity for cross-graph interaction modeling to linear time complexity. Jointly learning in an end-to-end framework, the graph representation embedding module and the well-designed contrastive learning module can be beneficial to one another. A comprehensive series of experiments indicate that CGSim outperforms state-of-the-art baselines on six datasets and significantly reduces the computational cost, which demonstrates our CGSim model's superiority over other baselines. [ABSTRACT FROM AUTHOR]

In this paper, the nonlinear Schrödinger‐type equation −(∇+iA)2u+u+λIα∗K|u|2Ku=af(|u|)|u|uinℝ3$$ -{\left(\nabla + iA\right)}^2u+u+\lambda \left[{I}_{\alpha}\ast \left(K{\left|u\right|}^2\right)\right] Ku=a\frac{f\left(|u|\right)}{\mid u\mid }u\kern.5em \mathrm{in}\kern.5em {\mathrm{\mathbb{R}}}^3 $$is considered in the presence of magnetic field, where A∈C1(ℝ3,ℝ3)$$ A\in {C}^1\left({\mathrm{\mathbb{R}}}^3,{\mathrm{\mathbb{R}}}^3\right) $$, α∈(0,3)$$ \alpha \in \left(0,3\right) $$, Iα$$ {I}_{\alpha } $$ denotes the Riesz potential, K∈Lp(ℝ3)$$ K\in {L}^p\left({\mathrm{\mathbb{R}}}^3\right) $$ is a positive potential for some p∈(6/(1+α),∞]$$ p\in \left(6/\left(1+\alpha \right),\infty \right] $$, a∈Lq(ℝ3)\{0}$$ a\in {L}^q\left({\mathrm{\mathbb{R}}}^3\right)\backslash \left\{0\right\} $$ is a nonnegative potential for some q∈(3/2,∞]$$ q\in \left(3/2,\infty \right] $$, and f∈C(ℝ,[0,∞))$$ f\in C\left(\mathrm{\mathbb{R}},\right[0,\infty \left)\right) $$ is assumed to be asymptotically linear at infinity. Under suitable assumptions regarding A$$ A $$, K$$ K $$, a$$ a $$, and f$$ f $$, variational methods are used to establish the existence of ground‐state solutions of the above equation for sufficiently small values of the parameter λ$$ \lambda $$. [ABSTRACT FROM AUTHOR]

Proteases contribute to a broad spectrum of cellular functions. Given a relatively limited amount of experimental data, developing accurate sequence-based predictors of substrate cleavage sites facilitates a better understanding of protease functions and substrate specificity. While many protease-specific predictors of substrate cleavage sites were developed, these efforts are outpaced by the growth of the protease substrate cleavage data. In particular, since data for 100+ protease types are available and this number continues to grow, it becomes impractical to publish predictors for new protease types, and instead it might be better to provide a computational platform that helps users to quickly and efficiently build predictors that address their specific needs. To this end, we conceptualized, developed, tested and released a versatile bioinformatics platform, ProsperousPlus , that empowers users, even those with no programming or little bioinformatics background, to build fast and accurate predictors of substrate cleavage sites. ProsperousPlus facilitates the use of the rapidly accumulating substrate cleavage data to train, empirically assess and deploy predictive models for user-selected substrate types. Benchmarking tests on test datasets show that our platform produces predictors that on average exceed the predictive performance of current state-of-the-art approaches. ProsperousPlus is available as a webserver and a stand-alone software package at http://prosperousplus.unimelb-biotools.cloud.edu.au/. [ABSTRACT FROM AUTHOR]

This paper is concerned with the existence of solutions to the Kirchhoff-type equation − a + b ∫ R 3 | ∇ u | 2 Δ u + (V + λ) u = | u | p − 2 u + μ | u | q − 2 u i n R 3 under the normalized constraint ∫ R 3 u 2 = ρ 2 , where a, b, ρ > 0, 14/3 < q < p ⩽ 6, μ > 0 is a constant, and λ ∈ R appears as a Lagrange multiplier. Under an explicit assumption on V, we can prove the existence of positive ground state solutions to the above equation. A new concentration compactness type result is established to recover compactness in the Sobolev critical case. [ABSTRACT FROM AUTHOR]

Antimicrobial peptides (AMPs) are short peptides that play crucial roles in diverse biological processes and have various functional activities against target organisms. Due to the abuse of chemical antibiotics and microbial pathogens' increasing resistance to antibiotics, AMPs have the potential to be alternatives to antibiotics. As such, the identification of AMPs has become a widely discussed topic. A variety of computational approaches have been developed to identify AMPs based on machine learning algorithms. However, most of them are not capable of predicting the functional activities of AMPs, and those predictors that can specify activities only focus on a few of them. In this study, we first surveyed 10 predictors that can identify AMPs and their functional activities in terms of the features they employed and the algorithms they utilized. Then, we constructed comprehensive AMP datasets and proposed a new deep learning-based framework, iAMPCN (identification of AMPs based on CNNs), to identify AMPs and their related 22 functional activities. Our experiments demonstrate that iAMPCN significantly improved the prediction performance of AMPs and their corresponding functional activities based on four types of sequence features. Benchmarking experiments on the independent test datasets showed that iAMPCN outperformed a number of state-of-the-art approaches for predicting AMPs and their functional activities. Furthermore, we analyzed the amino acid preferences of different AMP activities and evaluated the model on datasets of varying sequence redundancy thresholds. To facilitate the community-wide identification of AMPs and their corresponding functional types, we have made the source codes of iAMPCN publicly available at https://github.com/joy50706/iAMPCN/tree/master. We anticipate that iAMPCN can be explored as a valuable tool for identifying potential AMPs with specific functional activities for further experimental validation. [ABSTRACT FROM AUTHOR]

Background Promoters are DNA regions that initiate the transcription of specific genes near the transcription start sites. In bacteria, promoters are recognized by RNA polymerases and associated sigma factors. Effective promoter recognition is essential for synthesizing the gene-encoded products by bacteria to grow and adapt to different environmental conditions. A variety of machine learning-based predictors for bacterial promoters have been developed; however, most of them were designed specifically for a particular species. To date, only a few predictors are available for identifying general bacterial promoters with limited predictive performance. Results In this study, we developed TIMER, a Siamese neural network-based approach for identifying both general and species-specific bacterial promoters. Specifically, TIMER uses DNA sequences as the input and employs three Siamese neural networks with the attention layers to train and optimize the models for a total of 13 species-specific and general bacterial promoters. Extensive 10-fold cross-validation and independent tests demonstrated that TIMER achieves a competitive performance and outperforms several existing methods on both general and species-specific promoter prediction. As an implementation of the proposed method, the web server of TIMER is publicly accessible at http://web.unimelb-bioinfortools.cloud.edu.au/TIMER/. [ABSTRACT FROM AUTHOR]

A-to-I editing is the most prevalent RNA editing event, which refers to the change of adenosine (A) bases to inosine (I) bases in double-stranded RNAs. Several studies have revealed that A-to-I editing can regulate cellular processes and is associated with various human diseases. Therefore, accurate identification of A-to-I editing sites is crucial for understanding RNA-level (i.e. transcriptional) modifications and their potential roles in molecular functions. To date, various computational approaches for A-to-I editing site identification have been developed; however, their performance is still unsatisfactory and needs further improvement. In this study, we developed a novel stacked-ensemble learning model, ATTIC (A-To-I ediTing predICtor), to accurately identify A-to-I editing sites across three species, including Homo sapiens , Mus musculus and Drosophila melanogaster. We first comprehensively evaluated 37 RNA sequence-derived features combined with 14 popular machine learning algorithms. Then, we selected the optimal base models to build a series of stacked ensemble models. The final ATTIC framework was developed based on the optimal models improved by the feature selection strategy for specific species. Extensive cross-validation and independent tests illustrate that ATTIC outperforms state-of-the-art tools for predicting A-to-I editing sites. We also developed a web server for ATTIC, which is publicly available at http://web.unimelb-bioinfortools.cloud.edu.au/ATTIC/. We anticipate that ATTIC can be utilized as a useful tool to accelerate the identification of A-to-I RNA editing events and help characterize their roles in post-transcriptional regulation. [ABSTRACT FROM AUTHOR]

Antiviral defenses are one of the significant roles of RNA interference (RNAi) in plants. It has been reported that the host RNAi mechanism machinery can target viral RNAs for destruction because virus-derived small interfering RNAs (vsiRNAs) are found in infected host cells. Therefore, the recognition of plant vsiRNAs is the key to understanding the functional mechanisms of vsiRNAs and developing antiviral plants. In this work, we introduce a deep learning-based stacking ensemble approach, named computational prediction of plant exclusive virus-derived small interfering RNAs (COPPER), for plant vsiRNA prediction. COPPER used word2vec and fastText to generate sequence features and a hybrid deep learning framework, including a convolutional neural network, multiscale residual network and bidirectional long short-term memory network with a self-attention mechanism to enable precise predictions of plant vsiRNAs. Extensive benchmarking experiments with different sequence homology thresholds and ablation studies illustrated the comparative predictive performance of COPPER. In addition, the performance comparison with PVsiRNAPred conducted on an independent test dataset showed that COPPER significantly improved the predictive performance for plant vsiRNAs compared with other state-of-the-art methods. The datasets and source codes are publicly available at https://github.com/yuanyuanbu/COPPER. [ABSTRACT FROM AUTHOR]

Lysine 2-hydroxyisobutylation (Khib), which was first reported in 2014, has been shown to play vital roles in a myriad of biological processes including gene transcription, regulation of chromatin functions, purine metabolism, pentose phosphate pathway and glycolysis/gluconeogenesis. Identification of Khib sites in protein substrates represents an initial but crucial step in elucidating the molecular mechanisms underlying protein 2-hydroxyisobutylation. Experimental identification of Khib sites mainly depends on the combination of liquid chromatography and mass spectrometry. However, experimental approaches for identifying Khib sites are often time-consuming and expensive compared with computational approaches. Previous studies have shown that Khib sites may have distinct characteristics for different cell types of the same species. Several tools have been developed to identify Khib sites, which exhibit high diversity in their algorithms, encoding schemes and feature selection techniques. However, to date, there are no tools designed for predicting cell type-specific Khib sites. Therefore, it is highly desirable to develop an effective predictor for cell type-specific Khib site prediction. Inspired by the residual connection of ResNet, we develop a deep learning-based approach, termed ResNetKhib, which leverages both the one-dimensional convolution and transfer learning to enable and improve the prediction of cell type-specific 2-hydroxyisobutylation sites. ResNetKhib is capable of predicting Khib sites for four human cell types, mouse liver cell and three rice cell types. Its performance is benchmarked against the commonly used random forest (RF) predictor on both 10-fold cross-validation and independent tests. The results show that ResNetKhib achieves the area under the receiver operating characteristic curve values ranging from 0.807 to 0.901, depending on the cell type and species, which performs better than RF-based predictors and other currently available Khib site prediction tools. We also implement an online web server of the proposed ResNetKhib algorithm together with all the curated datasets and trained model for the wider research community to use, which is publicly accessible at https://resnetkhib.erc.monash.edu/. [ABSTRACT FROM AUTHOR]

Determining the pathogenicity and functional impact (i.e. gain-of-function; GOF or loss-of-function; LOF) of a variant is vital for unraveling the genetic level mechanisms of human diseases. To provide a 'one-stop' framework for the accurate identification of pathogenicity and functional impact of variants, we developed a two-stage deep-learning-based computational solution, termed VPatho, which was trained using a total of 9619 pathogenic GOF/LOF and 138 026 neutral variants curated from various databases. A total number of 138 variant-level, 262 protein-level and 103 genome-level features were extracted for constructing the models of VPatho. The development of VPatho consists of two stages: (i) a random under-sampling multi-scale residual neural network (ResNet) with a newly defined weighted-loss function (RUS-Wg-MSResNet) was proposed to predict variants' pathogenicity on the gnomAD_NV + GOF/LOF dataset; and (ii) an XGBOD model was constructed to predict the functional impact of the given variants. Benchmarking experiments demonstrated that RUS-Wg-MSResNet achieved the highest prediction performance with the weights calculated based on the ratios of neutral versus pathogenic variants. Independent tests showed that both RUS-Wg-MSResNet and XGBOD achieved outstanding performance. Moreover, assessed using variants from the CAGI6 competition, RUS-Wg-MSResNet achieved superior performance compared to state-of-the-art predictors. The fine-trained XGBOD models were further used to blind test the whole LOF data downloaded from gnomAD and accordingly, we identified 31 nonLOF variants that were previously labeled as LOF/uncertain variants. As an implementation of the developed approach, a webserver of VPatho is made publicly available at http://csbio.njust.edu.cn/bioinf/vpatho/ to facilitate community-wide efforts for profiling and prioritizing the query variants with respect to their pathogenicity and functional impact. [ABSTRACT FROM AUTHOR]

Neuropathic pain is a refractory chronic disease affecting millions of people worldwide. Given that present painkillers have poor efficacy or severe side effects, developing novel analgesics is badly needed. The multiplex structure of active ingredients isolated from natural products provides a new source for phytochemical compound synthesis. Here, we identified a natural product, Narirutin, a flavonoid compound isolated from the Citrus unshiu, showing antinociceptive effects in rodent models of neuropathic pain. Using calcium imaging, whole-cell electrophysiology, western blotting, and immunofluorescence, we uncovered a molecular target for Narirutin's antinociceptive actions. We found that Narirutin (i) inhibits Veratridine-triggered nociceptor activities in L4-L6 rat dorsal root ganglion (DRG) neurons, (ii) blocks voltage-gated sodium (NaV) channels subtype 1.7 in both small-diameter DRG nociceptive neurons and human embryonic kidney (HEK) 293 cell line, (iii) does not affect tetrodotoxin-resistant (TTX-R) NaV channels, and (iv) blunts the upregulation of Nav1.7 in calcitonin gene-related peptide (CGRP)-labeled DRG sensory neurons after spared nerve injury (SNI) surgery. Identifying Nav1.7 as a molecular target of Narirutin may further clarify the analgesic mechanism of natural flavonoid compounds and provide an optimal idea to produce novel selective and efficient analgesic drugs. [ABSTRACT FROM AUTHOR]

Subcellular localization of messenger RNAs (mRNAs) plays a key role in the spatial regulation of gene activity. The functions of mRNAs have been shown to be closely linked with their localizations. As such, understanding of the subcellular localizations of mRNAs can help elucidate gene regulatory networks. Despite several computational methods that have been developed to predict mRNA localizations within cells, there is still much room for improvement in predictive performance, especially for the multiple-location prediction. In this study, we proposed a novel multi-label multi-class predictor, termed Clarion, for mRNA subcellular localization prediction. Clarion was developed based on a manually curated benchmark dataset and leveraged the weighted series method for multi-label transformation. Extensive benchmarking tests demonstrated Clarion achieved competitive predictive performance and the weighted series method plays a crucial role in securing superior performance of Clarion. In addition, the independent test results indicate that Clarion outperformed the state-of-the-art methods and can secure accuracy of 81.47, 91.29, 79.77, 92.10, 89.15, 83.74, 80.74, 79.23 and 84.74% for chromatin, cytoplasm, cytosol, exosome, membrane, nucleolus, nucleoplasm, nucleus and ribosome, respectively. The webserver and local stand-alone tool of Clarion is freely available at http://monash.bioweb.cloud.edu.au/Clarion/. [ABSTRACT FROM AUTHOR]