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Dabrowski‐Tumanski P, Goundaroulis D, Stasiak A, Rawdon EJ, Sulkowska JI. Theta-curves in proteins. Protein Sci 2024; 33:e5133. [PMID: 39167036 PMCID: PMC11337915 DOI: 10.1002/pro.5133] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/20/2024] [Revised: 06/22/2024] [Accepted: 07/10/2024] [Indexed: 08/23/2024]
Abstract
We study and characterize the topology of connectivity circuits observed in natively folded protein structures whose coordinates are deposited in the Protein Data Bank (PDB). Polypeptide chains of some proteins naturally fold into unique knotted configurations. Another kind of nontrivial topology of polypeptide chains is observed when, in addition to covalent bonds connecting consecutive amino acids in polypeptide chains, one also considers disulfide and ionic bonds between non-consecutive amino acids. Bonds between non-consecutive amino acids introduce bifurcation points into connectivity circuits defined by bonds between consecutive and nonconsecutive amino acids in analyzed proteins. Circuits with bifurcation points can form θ-curves with various topologies. We catalog here the observed topologies of θ-curves passing through bridges between consecutive and non-consecutive amino acids in studied proteins.
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Affiliation(s)
| | - Dimos Goundaroulis
- Center for Genome Architecture, Department of Molecular and Human GeneticsBaylor College of MedicineHoustonTexasUSA
- Center for Theoretical Biological PhysicsRice UniversityHoustonTexasUSA
| | - Andrzej Stasiak
- Center for Integrative GenomicsUniversity of LausanneLausanneSwitzerland
- Swiss Institute of BioinformaticsLausanneSwitzerland
| | - Eric J. Rawdon
- Department of MathematicsUniversity of St. ThomasSt. PaulMinnesotaUSA
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2
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Truong DT, Ho K, Pham DQH, Chwastyk M, Nguyen-Minh T, Nguyen MT. Treatment of flexibility of protein backbone in simulations of protein-ligand interactions using steered molecular dynamics. Sci Rep 2024; 14:10475. [PMID: 38714683 PMCID: PMC11076533 DOI: 10.1038/s41598-024-59899-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/11/2024] [Accepted: 04/16/2024] [Indexed: 05/10/2024] Open
Abstract
To ensure that an external force can break the interaction between a protein and a ligand, the steered molecular dynamics simulation requires a harmonic restrained potential applied to the protein backbone. A usual practice is that all or a certain number of protein's heavy atoms or Cα atoms are fixed, being restrained by a small force. This present study reveals that while fixing both either all heavy atoms and or all Cα atoms is not a good approach, while fixing a too small number of few atoms sometimes cannot prevent the protein from rotating under the influence of the bulk water layer, and the pulled molecule may smack into the wall of the active site. We found that restraining the Cα atoms under certain conditions is more relevant. Thus, we would propose an alternative solution in which only the Cα atoms of the protein at a distance larger than 1.2 nm from the ligand are restrained. A more flexible, but not too flexible, protein will be expected to lead to a more natural release of the ligand.
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Affiliation(s)
- Duc Toan Truong
- Laboratory for Chemical Computation and Modeling, Institute for Computational Science and Artificial Intelligence, Van Lang University, Ho Chi Minh City, 70000, Vietnam
- Faculty of Applied Technology, School of Technology, Van Lang University, Ho Chi Minh City, 70000, Vietnam
| | - Kiet Ho
- Institute for Computational Science and Technology (ICST), Quang Trung Software City, Ho Chi Minh City, 70000, Vietnam
| | | | - Mateusz Chwastyk
- Institute of Physics, Polish Academy of Sciences, Warsaw, Poland
| | - Thai Nguyen-Minh
- University of Medicine and Pharmacy at Ho Chi Minh City, Ho Chi Minh City, 70000, Vietnam
| | - Minh Tho Nguyen
- Laboratory for Chemical Computation and Modeling, Institute for Computational Science and Artificial Intelligence, Van Lang University, Ho Chi Minh City, 70000, Vietnam.
- Faculty of Applied Technology, School of Technology, Van Lang University, Ho Chi Minh City, 70000, Vietnam.
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3
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Hou Y, Xie T, He L, Tao L, Huang J. Topological links in predicted protein complex structures reveal limitations of AlphaFold. Commun Biol 2023; 6:1098. [PMID: 37898666 PMCID: PMC10613300 DOI: 10.1038/s42003-023-05489-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/21/2023] [Accepted: 10/19/2023] [Indexed: 10/30/2023] Open
Abstract
AlphaFold is making great progress in protein structure prediction, not only for single-chain proteins but also for multi-chain protein complexes. When using AlphaFold-Multimer to predict protein‒protein complexes, we observed some unusual structures in which chains are looped around each other to form topologically intertwining links at the interface. Based on physical principles, such topological links should generally not exist in native protein complex structures unless covalent modifications of residues are involved. Although it is well known and has been well studied that protein structures may have topologically complex shapes such as knots and links, existing methods are hampered by the chain closure problem and show poor performance in identifying topologically linked structures in protein‒protein complexes. Therefore, we address the chain closure problem by using sliding windows from a local perspective and propose an algorithm to measure the topological-geometric features that can be used to identify topologically linked structures. An application of the method to AlphaFold-Multimer-predicted protein complex structures finds that approximately 1.72% of the predicted structures contain topological links. The method presented in this work will facilitate the computational study of protein‒protein interactions and help further improve the structural prediction of multi-chain protein complexes.
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Affiliation(s)
- Yingnan Hou
- Key Laboratory of Structural Biology of Zhejiang Province, School of Life Sciences, Westlake University, 18 Shilongshan Road, Hangzhou, 310024, Zhejiang, China
- Westlake AI Therapeutics Lab, Westlake Laboratory of Life Sciences and Biomedicine, 18 Shilongshan Road, Hangzhou, 310024, Zhejiang, China
| | - Tengyu Xie
- Key Laboratory of Structural Biology of Zhejiang Province, School of Life Sciences, Westlake University, 18 Shilongshan Road, Hangzhou, 310024, Zhejiang, China
- Westlake AI Therapeutics Lab, Westlake Laboratory of Life Sciences and Biomedicine, 18 Shilongshan Road, Hangzhou, 310024, Zhejiang, China
| | - Liuqing He
- Key Laboratory of Structural Biology of Zhejiang Province, School of Life Sciences, Westlake University, 18 Shilongshan Road, Hangzhou, 310024, Zhejiang, China
- Center for Infectious Disease Research, Westlake Laboratory of Life Sciences and Biomedicine, 18 Shilongshan Road, Hangzhou, 310024, Zhejiang, China
| | - Liang Tao
- Key Laboratory of Structural Biology of Zhejiang Province, School of Life Sciences, Westlake University, 18 Shilongshan Road, Hangzhou, 310024, Zhejiang, China
- Center for Infectious Disease Research, Westlake Laboratory of Life Sciences and Biomedicine, 18 Shilongshan Road, Hangzhou, 310024, Zhejiang, China
| | - Jing Huang
- Key Laboratory of Structural Biology of Zhejiang Province, School of Life Sciences, Westlake University, 18 Shilongshan Road, Hangzhou, 310024, Zhejiang, China.
- Westlake AI Therapeutics Lab, Westlake Laboratory of Life Sciences and Biomedicine, 18 Shilongshan Road, Hangzhou, 310024, Zhejiang, China.
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4
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Pham DQH, Chwastyk M, Cieplak M. The coexistence region in the Van der Waals fluid and the liquid-liquid phase transitions. Front Chem 2023; 10:1106599. [PMID: 36760519 PMCID: PMC9905123 DOI: 10.3389/fchem.2022.1106599] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/23/2022] [Accepted: 12/29/2022] [Indexed: 01/26/2023] Open
Abstract
Cellular membraneless organelles are thought to be droplets formed within the two-phase region corresponding to proteinaceous systems endowed with the liquid-liquid transition. However, their metastability requires an additional constraint-they arise in a certain region of density and temperature between the spinodal and binodal lines. Here, we consider the well-studied van der Waals fluid as a test model to work out criteria to determine the location of the spinodal line for situations in which the equation of state is not known. Our molecular dynamics studies indicate that this task can be accomplished by considering the specific heat, the surface tension and characteristics of the molecular clusters, such as the number of component chains and radius of gyration.
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Dabrowski-Tumanski P, Rubach P, Niemyska W, Gren BA, Sulkowska JI. Topoly: Python package to analyze topology of polymers. Brief Bioinform 2021; 22:bbaa196. [PMID: 32935829 PMCID: PMC8138882 DOI: 10.1093/bib/bbaa196] [Citation(s) in RCA: 28] [Impact Index Per Article: 9.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/14/2020] [Revised: 07/15/2020] [Accepted: 07/29/2020] [Indexed: 12/27/2022] Open
Abstract
The increasing role of topology in (bio)physical properties of matter creates a need for an efficient method of detecting the topology of a (bio)polymer. However, the existing tools allow one to classify only the simplest knots and cannot be used in automated sample analysis. To answer this need, we created the Topoly Python package. This package enables the distinguishing of knots, slipknots, links and spatial graphs through the calculation of different topological polynomial invariants. It also enables one to create the minimal spanning surface on a given loop, e.g. to detect a lasso motif or to generate random closed polymers. It is capable of reading various file formats, including PDB. The extensive documentation along with test cases and the simplicity of the Python programming language make it a very simple to use yet powerful tool, suitable even for inexperienced users. Topoly can be obtained from https://topoly.cent.uw.edu.pl.
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Affiliation(s)
| | | | | | | | - Joanna Ida Sulkowska
- Corresponding author: Joanna Ida Sulkowska, Centre of New Technologies, University of Warsaw, Warsaw, 02-097, Poland; Faculty of Chemistry, University of Warsaw, 02-093, Warsaw, Poland. Tel.: +48-22-55-43678 E-mail:
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Gierut AM, Dabrowski-Tumanski P, Niemyska W, Millett KC, Sulkowska JI. PyLink: a PyMOL plugin to identify links. Bioinformatics 2020; 35:3166-3168. [PMID: 30649182 DOI: 10.1093/bioinformatics/bty1038] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/14/2018] [Revised: 10/28/2018] [Accepted: 12/22/2018] [Indexed: 11/13/2022] Open
Abstract
SUMMARY Links are generalization of knots, that consist of several components. They appear in proteins, peptides and other biopolymers with disulfide bonds or ions interactions giving rise to the exceptional stability. Moreover because of this stability such biopolymers are the target of commercial and medical use (including anti-bacterial and insecticidal activity). Therefore, topological characterization of such biopolymers, not only provides explanation of their thermodynamical or mechanical properties, but paves the way to design templates in pharmaceutical applications. However, distinction between links and trivial topology is not an easy task. Here, we present PyLink-a PyMOL plugin suited to identify three types of links and perform comprehensive topological analysis of proteins rich in disulfide or ion bonds. PyLink can scan for the links automatically, or the user may specify their own components, including closed loops with several bridges and ion interactions. This creates the possibility of designing new biopolymers with desired properties. AVAILABILITY AND IMPLEMENTATION The PyLink plugin, manual and tutorial videos are available at http://pylink.cent.uw.edu.pl.
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Affiliation(s)
- Aleksandra M Gierut
- Centre of New Technologies, University of Warsaw, Warsaw, Poland.,Faculty of Physics, Astronomy and Applied Computer Science, Jagiellonian University, Cracow, Poland
| | - Pawel Dabrowski-Tumanski
- Centre of New Technologies, University of Warsaw, Warsaw, Poland.,Faculty of Chemistry, University of Warsaw, Warsaw, Poland
| | - Wanda Niemyska
- Centre of New Technologies, University of Warsaw, Warsaw, Poland
| | - Kenneth C Millett
- Department of Mathematics, University of California, Santa Barbara, CA, USA
| | - Joanna I Sulkowska
- Centre of New Technologies, University of Warsaw, Warsaw, Poland.,Faculty of Chemistry, University of Warsaw, Warsaw, Poland
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Transient knots in intrinsically disordered proteins and neurodegeneration. PROGRESS IN MOLECULAR BIOLOGY AND TRANSLATIONAL SCIENCE 2020; 174:79-103. [PMID: 32828471 DOI: 10.1016/bs.pmbts.2020.03.003] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/08/2023]
Abstract
We provide a brief overview of the topological features found in structured proteins and of the dynamical processes that involve knots. We then discuss the knotted states that arise in the intrinsically disordered polyglutamine and α-synuclein. We argue that the existence of the knotted conformations stalls degradation by proteases and thus enhances aggregation. This mechanism works if the length of a peptide chain exceeds a threshold, as in the Huntington disease. We also study the cavities that form within the conformations of the disordered proteins. The volume of the cavities varies in time in a way that is different than that of the radius of gyration or the end-to-end distance. In addition, we study the traffic between the conformational basins and identify patterns associated with the deep and shallow knots. The results are obtained by molecular dynamics simulations that use coarse-grained and all-atom models (with and without the explicit solvent).
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Perego C, Potestio R. Computational methods in the study of self-entangled proteins: a critical appraisal. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2019; 31:443001. [PMID: 31269476 DOI: 10.1088/1361-648x/ab2f19] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
The existence of self-entangled proteins, the native structure of which features a complex topology, unveils puzzling, and thus fascinating, aspects of protein biology and evolution. The discovery that a polypeptide chain can encode the capability to self-entangle in an efficient and reproducible way during folding, has raised many questions, regarding the possible function of these knots, their conservation along evolution, and their role in the folding paradigm. Understanding the function and origin of these entanglements would lead to deep implications in protein science, and this has stimulated the scientific community to investigate self-entangled proteins for decades by now. In this endeavour, advanced experimental techniques are more and more supported by computational approaches, that can provide theoretical guidelines for the interpretation of experimental results, and for the effective design of new experiments. In this review we provide an introduction to the computational study of self-entangled proteins, focusing in particular on the methodological developments related to this research field. A comprehensive collection of techniques is gathered, ranging from knot theory algorithms, that allow detection and classification of protein topology, to Monte Carlo or molecular dynamics strategies, that constitute crucial instruments for investigating thermodynamics and kinetics of this class of proteins.
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Affiliation(s)
- Claudio Perego
- Max Panck Institute for Polymer Research, Ackermannweg 10, Mainz 55128, Germany
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9
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Xu Y, Li S, Yan Z, Luo Z, Ren H, Ge B, Huang F, Yue T. Stabilizing Effect of Inherent Knots on Proteins Revealed by Molecular Dynamics Simulations. Biophys J 2018; 115:1681-1689. [PMID: 30314655 PMCID: PMC6225051 DOI: 10.1016/j.bpj.2018.09.015] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/04/2018] [Revised: 09/11/2018] [Accepted: 09/18/2018] [Indexed: 10/28/2022] Open
Abstract
A growing number of proteins have been identified as knotted in their native structures, with such entangled topological features being expected to play stabilizing roles maintaining both the global fold and the nature of proteins. However, the molecular mechanism underlying the stabilizing effect is ambiguous. Here, we combine unbiased and mechanical atomistic molecular dynamics simulations to investigate how a protein is stabilized by an inherent knot by directly comparing chemical, thermal, and mechanical denaturing properties of two proteins having the same sequence and secondary structures but differing in the presence or absence of an inherent knot. One protein is YbeA from Escherichia coli, containing a deep trefoil knot within the sequence, and the other is the modified protein with the knot of YbeA being removed. Under certain chemical denaturing conditions, the unknotted protein fully unfolds whereas the knotted protein does not, suggesting a higher intrinsic stability for the protein having a knot. Both proteins unfold under enhanced thermal fluctuations but at different rates and with distinct pathways. Opening the hydrophobic core via separation between two α-helices is identified as a crucial step initiating the protein unfolding, which, however, is restrained for the knotted protein by topological and geometrical frustrations. Energy barriers for denaturing the protein are reduced by removing the knot, as evidenced by mechanical unfolding simulations. Finally, yet importantly, no obvious change in size or location of the knot was observed during denaturing processes, indicating that YbeA may remain knotted for a relatively long time during and after denaturation.
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Affiliation(s)
- Yan Xu
- State Key Laboratory of Heavy Oil Processing, College of Chemical Engineering, China University of Petroleum (East China), Qingdao, China
| | - Shixin Li
- Center for Bioengineering and Biotechnology, College of Chemical Engineering, China University of Petroleum (East China), Qingdao, China
| | - Zengshuai Yan
- Center for Bioengineering and Biotechnology, College of Chemical Engineering, China University of Petroleum (East China), Qingdao, China
| | - Zhen Luo
- Center for Bioengineering and Biotechnology, College of Chemical Engineering, China University of Petroleum (East China), Qingdao, China
| | - Hao Ren
- Center for Bioengineering and Biotechnology, College of Chemical Engineering, China University of Petroleum (East China), Qingdao, China
| | - Baosheng Ge
- Center for Bioengineering and Biotechnology, College of Chemical Engineering, China University of Petroleum (East China), Qingdao, China
| | - Fang Huang
- State Key Laboratory of Heavy Oil Processing, College of Chemical Engineering, China University of Petroleum (East China), Qingdao, China
| | - Tongtao Yue
- State Key Laboratory of Heavy Oil Processing, College of Chemical Engineering, China University of Petroleum (East China), Qingdao, China; Center for Bioengineering and Biotechnology, College of Chemical Engineering, China University of Petroleum (East China), Qingdao, China.
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10
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Zhao Y, Cieplak M. Stability of structurally entangled protein dimers. Proteins 2018; 86:945-955. [DOI: 10.1002/prot.25526] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/19/2018] [Revised: 04/23/2018] [Accepted: 05/14/2018] [Indexed: 12/12/2022]
Affiliation(s)
- Yani Zhao
- Institute of Physics, Polish Academy of Sciences; Aleja Lotników 32/46, Warsaw 02668 Poland
| | - Marek Cieplak
- Institute of Physics, Polish Academy of Sciences; Aleja Lotników 32/46, Warsaw 02668 Poland
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11
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Dabrowski-Tumanski P, Sulkowska JI. To Tie or Not to Tie? That Is the Question. Polymers (Basel) 2017; 9:E454. [PMID: 30965758 PMCID: PMC6418553 DOI: 10.3390/polym9090454] [Citation(s) in RCA: 37] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/26/2017] [Revised: 09/11/2017] [Accepted: 09/12/2017] [Indexed: 12/18/2022] Open
Abstract
In this review, we provide an overview of entangled proteins. Around 6% of protein structures deposited in the PBD are entangled, forming knots, slipknots, lassos and links. We present theoretical methods and tools that enabled discovering and classifying such structures. We discuss the advantages and disadvantages of the non-trivial topology in proteins, based on available data about folding, stability, biological properties and evolutionary conservation. We also formulate intriguing and challenging questions on the border of biophysics, bioinformatics, biology and mathematics, which arise from the discovery of an entanglement in proteins. Finally, we discuss possible applications of entangled proteins in medicine and nanotechnology, such as the chance to design super stable proteins, whose stability could be controlled by chemical potential.
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Affiliation(s)
- Pawel Dabrowski-Tumanski
- Centre of New Technologies, University of Warsaw, Warsaw 02-097, Poland.
- Faculty of Chemistry, University of Warsaw, Warsaw 02-093, Poland.
| | - Joanna I Sulkowska
- Centre of New Technologies, University of Warsaw, Warsaw 02-097, Poland.
- Faculty of Chemistry, University of Warsaw, Warsaw 02-093, Poland.
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12
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Mechanical Pulling of Linked Ring Polymers: Elastic Response and Link Localisation. Polymers (Basel) 2017; 9:polym9080327. [PMID: 30971003 PMCID: PMC6418824 DOI: 10.3390/polym9080327] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/30/2017] [Revised: 07/26/2017] [Accepted: 07/27/2017] [Indexed: 12/28/2022] Open
Abstract
By using Langevin dynamics simulations, we study how semiflexible rings that are topologically linked respond to mechanical stretching. We use both constant-force and constant-velocity pulling protocols and map out how the mechanical tension affects observables related to metric quantities such as the longitudinal extension or span, and topology-related ones such as the length of the linked portion. We find that the average extension of linked rings, once divided by that of a single equivalent ring, is nonmonotonic in the applied force. We show that this remarkable feature becomes more prominent as the link complexity is increased, and originates from the different stretching compliance of the linked portion and the rest of the rings’ contour. By comparing the results of different pulling protocols, we also establish the best one for telling apart different types of links from their tensile response.
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