Let G = （V, E） be a connected graph. X belong to V（G） is a vertex set. X is a 3-restricted cut of G, if G- X is not connected and every component of G- X has at least three vertices. The 3-restricted connectivity ...Let G = （V, E） be a connected graph. X belong to V（G） is a vertex set. X is a 3-restricted cut of G, if G- X is not connected and every component of G- X has at least three vertices. The 3-restricted connectivity κ3（G） （in short κ3） of G is the cardinality of a minimum 3-restricted cut of G. X is called κ3-cut, if ｜X｜ = κ3. A graph G is κ3-connected, if a 3-restricted cut exists. Let G be a graph girth g ≥ 4, κ3（G） is min{d（x） ＋ d（y） ＋ d（z） - 4 ： xyz is a 2-path of G}. It will be shown that κ3（G） = ξ3（G） under the condition of girth.展开更多
The high polymorphism of histocompatibility complex class Ⅱ(MHC-Ⅱ)alleles and limited immunopeptidomic data hinder pan-species epitope prediction.In this study,leveraging the predictive power of AlphaFold(AF)and the...The high polymorphism of histocompatibility complex class Ⅱ(MHC-Ⅱ)alleles and limited immunopeptidomic data hinder pan-species epitope prediction.In this study,leveraging the predictive power of AlphaFold(AF)and the conserved structural features of the core region of MHC-Ⅱ-binding peptides,derived from a comprehensive analysis of MHC-Ⅱ structure data in the PDB database,we developed a new tool,AF-prediction(AF-pred),with explicit quantitative criteria for MHC-Ⅱ-restricted epitope prediction.We validated AF-pred across human,porcine,bovine,and bat MHC-Ⅱ molecules through large-scale in silico analyses using known immunopeptidome datasets(1000 positive and 1000 negative antigenic peptides),together with in vitro binding assays and crystallographic characterization of newly predicted epitopes.Using uncharacterized bat MHC-Ⅱ structures,we demonstrated that AF-pred’s amino-acid interaction prediction underpins its pan-prediction capability and the underlying rationale of the method.Conversely,this characteristic limits the prediction of atypical MHC-Ⅱ peptide-binding modes.Compared with sequence-based tools,AF-pred demonstrates enhanced cross-species MHC-Ⅱ binding prediction,with higher accuracy and interpretability,and further reveals that iterative AF updates improve AF-pred performance.AF-pred has the potential to facilitate the development of novel T-cell epitope vaccines and advance the“One Health”initiative.展开更多
Let G be a k-regular connected graph of order at least six. If G has girth three, its 3-restricted edge connectivity λ3(G) ≤3k-6. The equality holds when G is a cubic or 4-regular connected vertex-transitive graph w...Let G be a k-regular connected graph of order at least six. If G has girth three, its 3-restricted edge connectivity λ3(G) ≤3k-6. The equality holds when G is a cubic or 4-regular connected vertex-transitive graph with the only exception that G is a 4-regular graph with λ3(G) = 4. Furthermore, λ3(G) = 4 if and only if G contains K4 as its subgraph.展开更多
基金the National Natural Science Foundation of China (10671165)Specialized Research Fund for the Doctoral Program of Higher Education of China (20050755001)
文摘Let G = （V, E） be a connected graph. X belong to V（G） is a vertex set. X is a 3-restricted cut of G, if G- X is not connected and every component of G- X has at least three vertices. The 3-restricted connectivity κ3（G） （in short κ3） of G is the cardinality of a minimum 3-restricted cut of G. X is called κ3-cut, if ｜X｜ = κ3. A graph G is κ3-connected, if a 3-restricted cut exists. Let G be a graph girth g ≥ 4, κ3（G） is min{d（x） ＋ d（y） ＋ d（z） - 4 ： xyz is a 2-path of G}. It will be shown that κ3（G） = ξ3（G） under the condition of girth.
基金supported by the National Key Research and Development Program of China(grant number 2021YFD1800100 to N.Z.)the National Natural Science Foundation of China(grant number 32172871 to N.Z.)the 2115 Talent Development Program of China Agricultural University to N.Z.This study was supported by High-performance Computing Platform of China Agricultural University.
文摘The high polymorphism of histocompatibility complex class Ⅱ(MHC-Ⅱ)alleles and limited immunopeptidomic data hinder pan-species epitope prediction.In this study,leveraging the predictive power of AlphaFold(AF)and the conserved structural features of the core region of MHC-Ⅱ-binding peptides,derived from a comprehensive analysis of MHC-Ⅱ structure data in the PDB database,we developed a new tool,AF-prediction(AF-pred),with explicit quantitative criteria for MHC-Ⅱ-restricted epitope prediction.We validated AF-pred across human,porcine,bovine,and bat MHC-Ⅱ molecules through large-scale in silico analyses using known immunopeptidome datasets(1000 positive and 1000 negative antigenic peptides),together with in vitro binding assays and crystallographic characterization of newly predicted epitopes.Using uncharacterized bat MHC-Ⅱ structures,we demonstrated that AF-pred’s amino-acid interaction prediction underpins its pan-prediction capability and the underlying rationale of the method.Conversely,this characteristic limits the prediction of atypical MHC-Ⅱ peptide-binding modes.Compared with sequence-based tools,AF-pred demonstrates enhanced cross-species MHC-Ⅱ binding prediction,with higher accuracy and interpretability,and further reveals that iterative AF updates improve AF-pred performance.AF-pred has the potential to facilitate the development of novel T-cell epitope vaccines and advance the“One Health”initiative.
文摘Let G be a k-regular connected graph of order at least six. If G has girth three, its 3-restricted edge connectivity λ3(G) ≤3k-6. The equality holds when G is a cubic or 4-regular connected vertex-transitive graph with the only exception that G is a 4-regular graph with λ3(G) = 4. Furthermore, λ3(G) = 4 if and only if G contains K4 as its subgraph.
