Graph Theory

Al-Taie, Mohammed Zuhair; Kadry, Seifedine

doi:10.1007/978-3-319-53004-8_3

Cited by 3 publications

(3 citation statements)

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“…The Arabidopsis ortholog PPIs were subsequently processed using R to fit the input format of the MONET toolbox (Arenas et al, 2008; Tomasoni et al, 2020). According to the graph theory (Al-Taie and Kadry, 2017), the two interacting proteins and the connection between the two proteins of a PPI were defined as nodes and an edge (or called a link), respectively. The number of connections on a protein node was defined as protein degree.…”

Section: Star Methodsmentioning

confidence: 99%

Capturing the Hierarchically Assorted Modules of Protein Interaction in the Organized Nucleome

Dai

Liu

Zhou

et al. 2022

Preprint

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Nuclear proteins are major constituents and key regulators of the topological organization of nucleome. To elucidate the global connectivity of nucleomic proteins and to decipher the hierarchically organized modules of protein interaction that are involved in nucleomic organization and nuclear events, both formaldehyde and CBDPS crosslinkers were applied sequentially on the in vivo prefixed nuclei to perform a double chemical crosslinking with mass spectrometry (XL-MS) analysis. The integration of dimethyl-labelling with XL-MS generated a quantitative XL-MS workflow (qXL-MS) that consequently identified 5,340 cross-linked peptides (crosslinks) from nucleome. These crosslinks were construed into 1,297 nuclear protein-protein interactions (PPIs), from which discovered were 250 and 26 novel interactors of histones and nucleolar box C/D snoRNP complex, respectively. MONET-based modulomic analysis of their Arabidopsis orthoglous PPIs constructed 27 and 24 master nuclear protein interaction modules (NPIMs) that contain the condensate-forming protein(s) and the intrinsically disordered region (IDR)-containing proteins, respectively. These NPIMs successfully captured the previously reported nuclear protein complexes and nuclear bodies in nucleome. Surprisingly, modulomic analysis showed that these NPIMs were hierarchically assorted into four communities of NPIMs in nucleome including Genome Community and Nucleolus Community. The qXL-MS-based quantitative interactomics finally revealed 17 Hormone-specific module variants participating in a broad range of nuclear events. Thus, this integrated pipeline of qXL-MS and MONET modulomics, named as CHAMPION, is capable of capturing both nuclear protein complexes and nuclear bodies, constructing the topological architecture of protein interaction modules and module variants in nucleome and probably of mapping the protein compositions of condensates.

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Section: Star Methodsmentioning

confidence: 99%

Capturing the Hierarchically Assorted Modules of Protein Interaction in the Organized Nucleome

Dai

Liu

Zhou

et al. 2022

Preprint

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“…Here, we recall the definitions central to our discussions, along with some of the characterizations that our results rely upon. We restrict our attention to finite, simple, undirected graphs and use the standard graph theory notation . The following paragraphs are based on the comprehensive discussion of the layout parameters as given in the literature…”

Section: Methodsmentioning

confidence: 99%

On the Role of Half-Catalan Numbers and Pathwidth in Hyperbranched Polymers Synthesized by AB_m Step Polymerization

et al. 2021

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Topological features of polymer chains have been used as the key controlling mechanism for the physicochemical properties of hyperbranched polymers (HPs) and, therefore, provide a significant impetus to determine their branching characteristics. Single monomer methodology (SMM) involving AB m step polymerization has been one of the routes to synthesize both compact and segmented HPs. Here, we explore Catalan and half-Catalan numbers in the context of AB m step polymerization to deduce the structural information of HPs. Our approach harnesses the concepts of combinatorics and graph theory to calculate the exact numbers of isomeric, branched and linear, structures of polymer chains. We also demonstrate that the extent of branching of a polymer chain can be measured via pathwidth and establish its bounds as a function of its length. We believe that our findings can be leveraged to design and control the architecture of HPs synthesized via SMM or any other chemistries in a straightforward manner.

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“…A graph is formally defined as a pair of sets = ( , ), where is a set of vertices and is a set of edges [50], [51]. Each edge connects to at least two vertices described by { , } pairs denoting originating and terminating vertices, x,y respectively.…”

Section: A Graph Network Backgroundmentioning

confidence: 99%

Review of Graph-Based Hazardous Event Detection Methods for Autonomous Driving Systems

Xiao

Dianati

Geiger

et al. 2023

IEEE Trans. Intell. Transport. Syst.

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Graph Theory

Cited by 3 publications

References 0 publications

Capturing the Hierarchically Assorted Modules of Protein Interaction in the Organized Nucleome

Capturing the Hierarchically Assorted Modules of Protein Interaction in the Organized Nucleome

On the Role of Half-Catalan Numbers and Pathwidth in Hyperbranched Polymers Synthesized by AB_m Step Polymerization

Review of Graph-Based Hazardous Event Detection Methods for Autonomous Driving Systems

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Graph Theory

Cited by 3 publications

References 0 publications

Capturing the Hierarchically Assorted Modules of Protein Interaction in the Organized Nucleome

Capturing the Hierarchically Assorted Modules of Protein Interaction in the Organized Nucleome

On the Role of Half-Catalan Numbers and Pathwidth in Hyperbranched Polymers Synthesized by ABm Step Polymerization

Review of Graph-Based Hazardous Event Detection Methods for Autonomous Driving Systems

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On the Role of Half-Catalan Numbers and Pathwidth in Hyperbranched Polymers Synthesized by AB_m Step Polymerization