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1. Topology in soft and biological matter

   https://doi.org/10.1016/j.physrep.2024.04.002  

   Tubiana, Luca; Alexander, Gareth P; Barbensi, Agnese; Buck, Dorothy; Cartwright, Julyan HE; Chwastyk, Mateusz; Cieplak, Marek; Coluzza, Ivan; Čopar, Simon; Craik, David J; et al (July 2024, Physics Reports)

   The last years have witnessed remarkable advances in our understanding of the emergence and consequences of topological constraints in biological and soft matter. Examples are abundant in relation to (bio)polymeric systems and range from the characterization of knots in single polymers and proteins to that of whole chromosomes and polymer melts. At the same time, considerable advances have been made in the description of the interplay between topological and physical properties in complex fluids, with the development of techniques that now allow researchers to control the formation of and interaction between defects in diverse classes of liquid crystals. Thanks to technological progress and the integration of experiments with increasingly sophisticated numerical simulations, topological biological and soft matter is a vibrant area of research attracting scientists from a broad range of disciplines. However, owing to the high degree of specialization of modern science, many results have remained confined to their own particular fields, with different jargon making it difficult for researchers to share ideas and work together towards a comprehensive view of the diverse phenomena at play. Compelled by these motivations, here we present a comprehensive overview of topological effects in systems ranging from DNA and genome organization to entangled proteins, polymeric materials, liquid crystals, and theoretical physics, with the intention of reducing the barriers between different fields of soft matter and biophysics. Particular care has been taken in providing a coherent formal introduction to the topological properties of polymers and of continuum materials and in highlighting the underlying common aspects concerning the emergence, characterization, and effects of topological objects in different systems. The second half of the review is dedicated to the presentation of the latest results in selected problems, specifically, the effects of topological constraints on the viscoelastic properties of polymeric materials; their relation with genome organization; a discussion on the emergence and possible effects of knots and other entanglements in proteins; the emergence and effects of topological defects and solitons in complex fluids. This review is dedicated to the memory of Marek Cieplak. 

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2. Could network structures generated with simple rules imposed on a cubic lattice reproduce the structural descriptors of globular proteins?

   https://doi.org/10.1093/comnet/cnab048  

   Burak Okan, Osman; Turgut, Deniz; Atilgan, Canan; Rana Atilgan, Ali; Ozisik, Rahmi (December 2021, Journal of Complex Networks)

   Estrada, Ernesto (Ed.)

   Abstract A direct way to spot structural features that are universally shared among proteins is to find analogues from simpler condensed matter systems. In the current study, the feasibility of creating ensembles of artificial structures that can automatically reproduce a large number of geometrical and topological descriptors of globular proteins is investigated. Towards this aim, a simple cubic (SC) arrangement is shown to provide the best background lattice after a careful analysis of the residue packing trends from 210 globular proteins. It is shown that a minimalistic set of rules imposed on this lattice is sufficient to generate structures that can mimic real proteins. In the proposed method, 210 such structures are generated by randomly removing residues (beads) from clusters that have a SC lattice arrangement such that all the generated structures have single connected components. Two additional sets are prepared from the initial structures via random relaxation and a reverse Monte Carlo simulated annealing algorithm, which targets the average radial distribution function (RDF) of 210 globular proteins. The initial and relaxed structures are compared to real proteins via RDF, bond orientational order parameters and several descriptors of network topology. Based on these features, results indicate that the structures generated with 40% occupancy closely resemble real residue networks. The structure generation mechanism automatically produces networks that are in the same topological class as globular proteins and reproduce small-world characteristics of high clustering and small shortest path lengths. Most notably, the established correspondence rules out icosahedral order as a relevant structural feature for residue networks in contrast to other amorphous systems where it is an inherent characteristic. The close correspondence is also observed in the vibrational characteristics as computed from the Anisotropic Network Model, therefore hinting at a non-superficial link between the proteins and the defect laden cubic crystalline order. 

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3. Protein2Vec: Aligning Multiple PPI Networks with Representation Learning

   Jianliang Gao, Ling Tian (October 2019, IEEE/ACM transactions on computational biology and bioinformatics)

   Research of Protein-Protein Interaction (PPI) Network Alignment is playing an important role in understanding the crucial underlying biological knowledge such as functionally homologous proteins and conserved evolutionary pathways across different species. Existing methods of PPI network alignment often try to improve the coverage ratio of the alignment result by aligning all proteins from different species. However, there is a fundamental biological premise that needs to be considered carefully: not every protein in a species can, nor should, find its homologous proteins in other species. In this work, we propose a novel alignment method to map only those proteins with the most similarity throughout the PPI networks of multiple species. For the similarity features of the protein in the networks, we integrate both topological features with biological characteristics to provide enhanced supports for the alignment procedures. For topological features, we apply a representation learning method on the networks that can generate a low dimensional vector embedding with its surrounding structural features for each protein. The topological similarity of proteins from different PPI networks can thus be transferred as the similarity of their corresponding vector representations, which provides a new way to comprehensively quantify the topological similarities between proteins. We also propose a new measure for the topological evaluation of the alignment results which better uncover the structural quality of the alignment across multiple networks. Both biological and topological evaluations on the alignment results of real datasets demonstrate our approach is promising and preferable against previous multiple alignment methods 

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4. Aligning Multiple PPI Networks with Representation Learning on Networks

   Bo Song, Jianliang Gao (December 2018, 2018 IEEE International Conference on Bioinformatics and Biomedicine (BIBM))

   Protein-protein interaction (PPI) network alignment has been motivating researches for the comprehension of the underlying crucial biological knowledge, such as conserved evolutionary pathways and functionally conserved proteins throughout different species. Existing PPI network alignment methods have tried to improve the coverage ratio by aligning all proteins from different species. However, there is a fundamental biological justification needed to be acknowledged, that not every protein in a species can, nor should, find homologous proteins in other species. In this paper, we propose a novel approach for multiple PPI network alignment that tries to align only those proteins with the most similarities. To provide more comprehensive supports in computing the similarity, we integrate structural features of the networks together with biological characteristics during the alignment. For the structural features, we apply on PPI networks a representation learning method, which creates a low-dimensional vector embedding with the surrounding topologies of each protein in the network. This approach quantifies the structural features, and provides a new way to determine the topological similarity of the networks by transferring which as calculations in vector similarities. We also propose a new metric for the topological evaluation which can better assess the topological quality of the alignment results across different networks. Both biological and topological evaluations demonstrate our approach is promising and preferable against previous multiple alignment methods. 

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5. Aligning Multiple PPI Networks with Representation Learning on Networks

   Bo Song, Jianliang Gao (December 2018, 2018 IEEE BIBM Conference proceeding)

   Abstract—Protein-protein interaction (PPI) network alignment has been motivating researches for the comprehension of the underlying crucial biological knowledge, such as conserved evolutionary pathways and functionally conserved proteins throughout different species. Existing PPI network alignment methods have tried to improve the coverage ratio by aligning all proteins from different species. However, there is a fundamental biological justification needed to be acknowledged, that not every protein in a species can, nor should, find homologous proteins in other species. In this paper, we propose a novel approach for multiple PPI network alignment that tries to align only those proteins with the most similarities. To provide more comprehensive supports in computing the similarity, we integrate structural features of the networks together with biological characteristics during the alignment. For the structural features, we apply on PPI networks a representation learning method, which creates a low-dimensional vector embedding with the surrounding topologies of each protein in the network. This approach quantifies the structural features, and provides a new way to determine the topological similarity of the networks by transferring which as calculations in vector similarities. We also propose a new metric for the topological evaluation which can better assess the topological quality of the alignment results across different networks. Both biological and topological evaluations demonstrate our approach is promising and preferable against previous multiple alignment methods. 

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