1
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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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Perlinska AP, Sikora M, Sulkowska JI. Everything AlphaFold tells us about protein knots. J Mol Biol 2024; 436:168715. [PMID: 39029890 DOI: 10.1016/j.jmb.2024.168715] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/06/2024] [Revised: 06/29/2024] [Accepted: 07/14/2024] [Indexed: 07/21/2024]
Abstract
Recent advances in Machine Learning methods in structural biology opened up new perspectives for protein analysis. Utilizing these methods allows us to go beyond the limitations of empirical research, and take advantage of the vast amount of generated data. We use a complete set of potentially knotted protein models identified in all high-quality predictions from the AlphaFold Database to search for any common trends that describe them. We show that the vast majority of knotted proteins have 31 knot and that the presence of knots is preferred in neither Bacteria, Eukaryota, or Archaea domains. On the contrary, the percentage of knotted proteins in any given proteome is around 0.4%, regardless of the taxonomical group. We also verified that the organism's living conditions do not impact the number of knotted proteins in its proteome, as previously expected. We did not encounter an organism without a single knotted protein. What is more, we found four universally present families of knotted proteins in Bacteria, consisting of SAM synthase, and TrmD, TrmH, and RsmE methyltransferases.
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Affiliation(s)
- Agata P Perlinska
- Centre of New Technologies, University of Warsaw, Banacha 2c, Warsaw 02-097, Poland
| | - Maciej Sikora
- Centre of New Technologies, University of Warsaw, Banacha 2c, Warsaw 02-097, Poland
| | - Joanna I Sulkowska
- Centre of New Technologies, University of Warsaw, Banacha 2c, Warsaw 02-097, Poland.
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3
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Rubach P, Sikora M, Jarmolinska A, Perlinska A, Sulkowska J. AlphaKnot 2.0: a web server for the visualization of proteins' knotting and a database of knotted AlphaFold-predicted models. Nucleic Acids Res 2024; 52:W187-W193. [PMID: 38842945 PMCID: PMC11223836 DOI: 10.1093/nar/gkae443] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/16/2024] [Revised: 04/29/2024] [Accepted: 05/10/2024] [Indexed: 07/06/2024] Open
Abstract
The availability of 3D protein models is rapidly increasing with the development of structure prediction algorithms. With the expanding availability of data, new ways of analysis, especially topological analysis, of those predictions are becoming necessary. Here, we present the updated version of the AlphaKnot service that provides a straightforward way of analyzing structure topology. It was designed specifically to determine knot types of the predicted structure models, however, it can be used for all structures, including the ones solved experimentally. AlphaKnot 2.0 provides the user's ability to obtain the knowledge necessary to assess the topological correctness of the model. Both probabilistic and deterministic knot detection methods are available, together with various visualizations (including a trajectory of simplification steps to highlight the topological complexities). Moreover, the web server provides a list of proteins similar to the queried model within AlphaKnot's database and returns their knot types for direct comparison. We pre-calculated the topology of high-quality models from the AlphaFold Database (4th version) and there are now more than 680.000 knotted models available in the AlphaKnot database. AlphaKnot 2.0 is available at https://alphaknot.cent.uw.edu.pl/.
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Affiliation(s)
- Pawel Rubach
- Warsaw School of Economics, Al. Niepodleglosci 162, 02-554 Warsaw, Poland
| | - Maciej Sikora
- Centre of New Technologies, University of Warsaw, Banacha 2c, 02-097 Warsaw, Poland
| | | | - Agata P Perlinska
- Centre of New Technologies, University of Warsaw, Banacha 2c, 02-097 Warsaw, Poland
| | - Joanna I Sulkowska
- Centre of New Technologies, University of Warsaw, Banacha 2c, 02-097 Warsaw, Poland
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4
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Sikora M, Klimentova E, Uchal D, Sramkova D, Perlinska AP, Nguyen ML, Korpacz M, Malinowska R, Nowakowski S, Rubach P, Simecek P, Sulkowska JI. Knot or not? Identifying unknotted proteins in knotted families with sequence-based Machine Learning model. Protein Sci 2024; 33:e4998. [PMID: 38888487 PMCID: PMC11184937 DOI: 10.1002/pro.4998] [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: 12/04/2023] [Revised: 03/14/2024] [Accepted: 04/09/2024] [Indexed: 06/20/2024]
Abstract
Knotted proteins, although scarce, are crucial structural components of certain protein families, and their roles continue to be a topic of intense research. Capitalizing on the vast collection of protein structure predictions offered by AlphaFold (AF), this study computationally examines the entire UniProt database to create a robust dataset of knotted and unknotted proteins. Utilizing this dataset, we develop a machine learning (ML) model capable of accurately predicting the presence of knots in protein structures solely from their amino acid sequences. We tested the model's capabilities on 100 proteins whose structures had not yet been predicted by AF and found agreement with our local prediction in 92% cases. From the point of view of structural biology, we found that all potentially knotted proteins predicted by AF can be classified only into 17 families. This allows us to discover the presence of unknotted proteins in families with a highly conserved knot. We found only three new protein families: UCH, DUF4253, and DUF2254, that contain both knotted and unknotted proteins, and demonstrate that deletions within the knot core could potentially account for the observed unknotted (trivial) topology. Finally, we have shown that in the majority of knotted families (11 out of 15), the knotted topology is strictly conserved in functional proteins with very low sequence similarity. We have conclusively demonstrated that proteins AF predicts as unknotted are structurally accurate in their unknotted configurations. However, these proteins often represent nonfunctional fragments, lacking significant portions of the knot core (amino acid sequence).
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Affiliation(s)
- Maciej Sikora
- Centre of New Technologies, University of WarsawWarsawPoland
- Faculty of Mathematics, Informatics and Mechanics, University of WarsawWarsawPoland
| | - Eva Klimentova
- Central European Institute of Technology, Masaryk UniversityBrnoCzech Republic
- National Centre for Biomolecular Research, Faculty of Science, Masaryk UniversityBrnoCzech Republic
| | - Dawid Uchal
- Centre of New Technologies, University of WarsawWarsawPoland
- Faculty of Physics, University of WarsawWarsawPoland
| | - Denisa Sramkova
- Central European Institute of Technology, Masaryk UniversityBrnoCzech Republic
- National Centre for Biomolecular Research, Faculty of Science, Masaryk UniversityBrnoCzech Republic
| | | | - Mai Lan Nguyen
- Centre of New Technologies, University of WarsawWarsawPoland
| | - Marta Korpacz
- Centre of New Technologies, University of WarsawWarsawPoland
- Faculty of Mathematics, Informatics and Mechanics, University of WarsawWarsawPoland
| | - Roksana Malinowska
- Centre of New Technologies, University of WarsawWarsawPoland
- Faculty of Mathematics, Informatics and Mechanics, University of WarsawWarsawPoland
| | - Szymon Nowakowski
- Faculty of Mathematics, Informatics and Mechanics, University of WarsawWarsawPoland
- Faculty of Physics, University of WarsawWarsawPoland
| | - Pawel Rubach
- Centre of New Technologies, University of WarsawWarsawPoland
- Warsaw School of EconomicsWarsawPoland
| | - Petr Simecek
- Central European Institute of Technology, Masaryk UniversityBrnoCzech Republic
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5
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Perlinska AP, Nguyen ML, Pilla SP, Staszor E, Lewandowska I, Bernat A, Purta E, Augustyniak R, Bujnicki JM, Sulkowska JI. Are there double knots in proteins? Prediction and in vitro verification based on TrmD-Tm1570 fusion from C. nitroreducens. Front Mol Biosci 2024; 10:1223830. [PMID: 38903539 PMCID: PMC11187310 DOI: 10.3389/fmolb.2023.1223830] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/16/2023] [Accepted: 10/04/2023] [Indexed: 06/22/2024] Open
Abstract
We have been aware of the existence of knotted proteins for over 30 years-but it is hard to predict what is the most complicated knot that can be formed in proteins. Here, we show new and the most complex knotted topologies recorded to date-double trefoil knots (31 #31). We found five domain arrangements (architectures) that result in a doubly knotted structure in almost a thousand proteins. The double knot topology is found in knotted membrane proteins from the CaCA family, that function as ion transporters, in the group of carbonic anhydrases that catalyze the hydration of carbon dioxide, and in the proteins from the SPOUT superfamily that gathers 31 knotted methyltransferases with the active site-forming knot. For each family, we predict the presence of a double knot using AlphaFold and RoseTTaFold structure prediction. In the case of the TrmD-Tm1570 protein, which is a member of SPOUT superfamily, we show that it folds in vitro and is biologically active. Our results show that this protein forms a homodimeric structure and retains the ability to modify tRNA, which is the function of the single-domain TrmD protein. However, how the protein folds and is degraded remains unknown.
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Affiliation(s)
| | - Mai Lan Nguyen
- Centre of New Technologies, University of Warsaw, Warsaw, Poland
- Polish-Japanese Academy of Information Technology, Warsaw, Poland
| | - Smita P. Pilla
- Centre of New Technologies, University of Warsaw, Warsaw, Poland
| | - Emilia Staszor
- Centre of New Technologies, University of Warsaw, Warsaw, Poland
- Faculty of Chemistry, University of Warsaw, Warsaw, Poland
| | | | - Agata Bernat
- Laboratory of Bioinformatics and Protein Engineering, International Institute of Molecular and Cell Biology in Warsaw, Warsaw, Poland
| | - Elżbieta Purta
- Laboratory of Bioinformatics and Protein Engineering, International Institute of Molecular and Cell Biology in Warsaw, Warsaw, Poland
| | | | - Janusz M. Bujnicki
- Laboratory of Bioinformatics and Protein Engineering, International Institute of Molecular and Cell Biology in Warsaw, Warsaw, Poland
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6
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Sleiman JL, Conforto F, Fosado YAG, Michieletto D. Geometric learning of knot topology. SOFT MATTER 2023; 20:71-78. [PMID: 37877330 PMCID: PMC10732224 DOI: 10.1039/d3sm01199b] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/08/2023] [Accepted: 10/18/2023] [Indexed: 10/26/2023]
Abstract
Knots are deeply entangled with every branch of science. One of the biggest open challenges in knot theory is to formalise a knot invariant that can unambiguously and efficiently distinguish any two knotted curves. Additionally, the conjecture that the geometrical embedding of a curve encodes information on its underlying topology is, albeit physically intuitive, far from proven. Here we attempt to tackle both these outstanding challenges by proposing a neural network (NN) approach that takes as input a geometric representation of a knotted curve and tries to make predictions of the curve's topology. Intriguingly, we discover that NNs trained with a so-called geometrical "local writhe" representation of a knot can distinguish curves that share one or many topological invariants and knot polynomials, such as mutant and composite knots, and can thus classify knotted curves more precisely than some knot polynomials. Additionally, we also show that our approach can be scaled up to classify all prime knots up to 10-crossings with more than 95% accuracy. Finally, we show that our NNs can also be trained to solve knot localisation problems on open and closed curves. Our main discovery is that the pattern of "local writhe" is a potentially unique geometric signature of the underlying topology of a curve. We hope that our results will suggest new methods for quantifying generic entanglements in soft matter and even inform new topological invariants.
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Affiliation(s)
- Joseph Lahoud Sleiman
- School of Physics and Astronomy, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, UK.
| | - Filippo Conforto
- School of Physics and Astronomy, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, UK.
| | | | - Davide Michieletto
- School of Physics and Astronomy, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, UK.
- MRC Human Genetics Unit, Institute of Genetics and Cancer, University of Edinburgh, Edinburgh EH4 2XU, UK
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7
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Zayats V, Sikora M, Perlinska AP, Stasiulewicz A, Gren BA, Sulkowska JI. Conservation of knotted and slipknotted topology in transmembrane transporters. Biophys J 2023; 122:4528-4541. [PMID: 37919904 PMCID: PMC10719070 DOI: 10.1016/j.bpj.2023.10.031] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/21/2023] [Revised: 08/25/2023] [Accepted: 10/30/2023] [Indexed: 11/04/2023] Open
Abstract
The existence of nontrivial topology is well accepted in globular proteins but not in membrane proteins. Our comprehensive topological analysis of the Protein Data Bank structures reveals 18 families of transmembrane proteins with nontrivial topology, showing that they constitute a significant number of membrane proteins. Moreover, we found that they comprise one of the largest groups of secondary active transporters. We classified them based on their knotted fingerprint into four groups: three slipknotted and one knotted. Unexpectedly, we found that the same protein can possess two distinct slipknot motifs that correspond to its outward- and inward-open conformational state. Based on the analysis of structures and knotted fingerprints, we show that slipknot topology is directly involved in the conformational transition and substrate transfer. Therefore, entanglement can be used to classify proteins and to find their structure-function relationship. Furthermore, based on the topological analysis of the transmembrane protein structures predicted by AlphaFold, we identified new potentially slipknotted protein families.
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Affiliation(s)
- Vasilina Zayats
- Centre of New Technologies, University of Warsaw, Warsaw, Poland
| | - Maciej Sikora
- Centre of New Technologies, University of Warsaw, Warsaw, Poland; Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Warsaw, Poland
| | | | - Adam Stasiulewicz
- Centre of New Technologies, University of Warsaw, Warsaw, Poland; Department of Drug Chemistry, Faculty of Pharmacy, Medical University of Warsaw, Warsaw, Poland
| | - Bartosz A Gren
- Centre of New Technologies, University of Warsaw, Warsaw, Poland
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8
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Dabrowski-Tumanski P, Stasiak A. AlphaFold Blindness to Topological Barriers Affects Its Ability to Correctly Predict Proteins' Topology. Molecules 2023; 28:7462. [PMID: 38005184 PMCID: PMC10672856 DOI: 10.3390/molecules28227462] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/22/2023] [Revised: 11/03/2023] [Accepted: 11/04/2023] [Indexed: 11/26/2023] Open
Abstract
AlphaFold is a groundbreaking deep learning tool for protein structure prediction. It achieved remarkable accuracy in modeling many 3D structures while taking as the user input only the known amino acid sequence of proteins in question. Intriguingly though, in the early steps of each individual structure prediction procedure, AlphaFold does not respect topological barriers that, in real proteins, result from the reciprocal impermeability of polypeptide chains. This study aims to investigate how this failure to respect topological barriers affects AlphaFold predictions with respect to the topology of protein chains. We focus on such classes of proteins that, during their natural folding, reproducibly form the same knot type on their linear polypeptide chain, as revealed by their crystallographic analysis. We use partially artificial test constructs in which the mutual non-permeability of polypeptide chains should not permit the formation of complex composite knots during natural protein folding. We find that despite the formal impossibility that the protein folding process could produce such knots, AlphaFold predicts these proteins to form complex composite knots. Our study underscores the necessity for cautious interpretation and further validation of topological features in protein structures predicted by AlphaFold.
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Affiliation(s)
- Pawel Dabrowski-Tumanski
- Faculty of Mathematics and Natural Sciences, School of Exact Sciences, Cardinal Wyszynski University in Warsaw, Wóycickiego 1/3, 01-938 Warsaw, Poland
| | - Andrzej Stasiak
- Center for Integrative Genomics, University of Lausanne, 1015 Lausanne, Switzerland
- SIB Swiss Institute of Bioinformatics, 1015 Lausanne, Switzerland
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9
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Jedrzejewski M, Belza B, Lewandowska I, Sadlej M, Perlinska AP, Augustyniak R, Christian T, Hou YM, Kalek M, Sulkowska JI. Nucleolar Essential Protein 1 (Nep1): Elucidation of enzymatic catalysis mechanism by molecular dynamics simulation and quantum mechanics study. Comput Struct Biotechnol J 2023; 21:3999-4008. [PMID: 37649713 PMCID: PMC10462857 DOI: 10.1016/j.csbj.2023.08.001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/08/2023] [Revised: 08/01/2023] [Accepted: 08/01/2023] [Indexed: 09/01/2023] Open
Abstract
The Nep1 protein is essential for the formation of eukaryotic and archaeal small ribosomal subunits, and it catalyzes the site-directed SAM-dependent methylation of pseudouridine (Ψ) during pre-rRNA processing. It possesses a non-trivial topology, namely, a 31 knot in the active site. Here, we address the issue of seemingly unfeasible deprotonation of Ψ in Nep1 active site by a distant aspartate residue (D101 in S. cerevisiae), using a combination of bioinformatics, computational, and experimental methods. We identified a conserved hydroxyl-containing amino acid (S233 in S. cerevisiae, T198 in A. fulgidus) that may act as a proton-transfer mediator. Molecular dynamics simulations, based on the crystal structure of S. cerevisiae, and on a complex generated by molecular docking in A. fulgidus, confirmed that this amino acid can shuttle protons, however, a water molecule in the active site may also serve this role. Quantum-chemical calculations based on density functional theory and the cluster approach showed that the water-mediated pathway is the most favorable for catalysis. Experimental kinetic and mutational studies reinforce the requirement for the aspartate D101, but not S233. These findings provide insight into the catalytic mechanisms underlying proton transfer over extended distances and comprehensively elucidate the mode of action of Nep1.
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Affiliation(s)
- Mateusz Jedrzejewski
- Centre of New Technologies, University of Warsaw, Banacha 2c, 02-097, Warsaw, Poland
| | - Barbara Belza
- Centre of New Technologies, University of Warsaw, Banacha 2c, 02-097, Warsaw, Poland
| | - Iwona Lewandowska
- Centre of New Technologies, University of Warsaw, Banacha 2c, 02-097, Warsaw, Poland
| | - Marta Sadlej
- Centre of New Technologies, University of Warsaw, Banacha 2c, 02-097, Warsaw, Poland
| | - Agata P. Perlinska
- Centre of New Technologies, University of Warsaw, Banacha 2c, 02-097, Warsaw, Poland
| | - Rafal Augustyniak
- Department of Chemistry, University of Warsaw, Ludwika Pasteura 1, 02-093, Warsaw, Poland
| | - Thomas Christian
- Department of Biochemistry and Molecular Biology, Thomas Jefferson University, 4201 Henry Ave, Philadelphia, PA 19144, USA
| | - Ya-Ming Hou
- Department of Biochemistry and Molecular Biology, Thomas Jefferson University, 4201 Henry Ave, Philadelphia, PA 19144, USA
| | - Marcin Kalek
- Centre of New Technologies, University of Warsaw, Banacha 2c, 02-097, Warsaw, Poland
| | - Joanna I. Sulkowska
- Centre of New Technologies, University of Warsaw, Banacha 2c, 02-097, Warsaw, Poland
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10
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Benjamin K, Mukta L, Moryoussef G, Uren C, Harrington HA, Tillmann U, Barbensi A. Homology of homologous knotted proteins. J R Soc Interface 2023; 20:20220727. [PMID: 37122282 PMCID: PMC10130707 DOI: 10.1098/rsif.2022.0727] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/02/2023] Open
Abstract
Quantification and classification of protein structures, such as knotted proteins, often requires noise-free and complete data. Here, we develop a mathematical pipeline that systematically analyses protein structures. We showcase this geometric framework on proteins forming open-ended trefoil knots, and we demonstrate that the mathematical tool, persistent homology, faithfully represents their structural homology. This topological pipeline identifies important geometric features of protein entanglement and clusters the space of trefoil proteins according to their depth. Persistence landscapes quantify the topological difference between a family of knotted and unknotted proteins in the same structural homology class. This difference is localized and interpreted geometrically with recent advancements in systematic computation of homology generators. The topological and geometric quantification we find is robust to noisy input data, which demonstrates the potential of this approach in contexts where standard knot theoretic tools fail.
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Affiliation(s)
| | - Lamisah Mukta
- Mathematical Institute, University of Oxford, Oxford OX2 6GG, UK
| | | | - Christopher Uren
- Mathematical Institute, University of Oxford, Oxford OX2 6GG, UK
| | - Heather A Harrington
- Mathematical Institute, University of Oxford, Oxford OX2 6GG, UK
- Wellcome Centre for Human Genetics, University of Oxford, Oxford OX3 7BN, UK
| | - Ulrike Tillmann
- Mathematical Institute, University of Oxford, Oxford OX2 6GG, UK
- Isaac Newton Institute for Mathematical Sciences, University of Cambridge, Cambridge CB3 0EH, UK
| | - Agnese Barbensi
- Mathematical Institute, University of Oxford, Oxford OX2 6GG, UK
- School of Mathematics and Statistics, University of Melbourne, Melbourne, Victoria 3010, Australia
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11
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Capała K, Szymczak P. Stochastic model of translocation of knotted proteins. Phys Rev E 2022; 106:054406. [PMID: 36559434 DOI: 10.1103/physreve.106.054406] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/30/2022] [Accepted: 10/25/2022] [Indexed: 11/16/2022]
Abstract
Knotted proteins, when forced through the pores, can get stuck if the knots in their backbone tighten under force. Alternatively, the knot can slide off the chain, making translocation possible. We construct a simple energy landscape model of this process with a time-periodic potential that mimics the action of a molecular motor. We calculate the translocation time as a function of the period of the pulling force, discuss the asymptotic limits and biological relevance of the results.
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Affiliation(s)
- Karol Capała
- Personal Health Data Science Group, Sano - Centre for Computational Personalised Medicine, Czarnowiejska 36, 30-054 Kraków, Poland and Institute of Theoretical Physics, Department of Statistical Physics, Jagiellonian University, Łojasiewicza 11, 30-348 Kraków, Poland
| | - Piotr Szymczak
- Institute of Theoretical Physics, Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warsaw, Poland
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12
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Ashbridge Z, Fielden SDP, Leigh DA, Pirvu L, Schaufelberger F, Zhang L. Knotting matters: orderly molecular entanglements. Chem Soc Rev 2022; 51:7779-7809. [PMID: 35979715 PMCID: PMC9486172 DOI: 10.1039/d2cs00323f] [Citation(s) in RCA: 22] [Impact Index Per Article: 11.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/24/2022] [Indexed: 11/29/2022]
Abstract
Entangling strands in a well-ordered manner can produce useful effects, from shoelaces and fishing nets to brown paper packages tied up with strings. At the nanoscale, non-crystalline polymer chains of sufficient length and flexibility randomly form tangled mixtures containing open knots of different sizes, shapes and complexity. However, discrete molecular knots of precise topology can also be obtained by controlling the number, sequence and stereochemistry of strand crossings: orderly molecular entanglements. During the last decade, substantial progress in the nascent field of molecular nanotopology has been made, with general synthetic strategies and new knotting motifs introduced, along with insights into the properties and functions of ordered tangle sequences. Conformational restrictions imparted by knotting can induce allostery, strong and selective anion binding, catalytic activity, lead to effective chiral expression across length scales, binding modes in conformations efficacious for drug delivery, and facilitate mechanical function at the molecular level. As complex molecular topologies become increasingly synthetically accessible they have the potential to play a significant role in molecular and materials design strategies. We highlight particular examples of molecular knots to illustrate why these are a few of our favourite things.
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Affiliation(s)
- Zoe Ashbridge
- Department of Chemistry, The University of Manchester, Manchester, UK
| | | | - David A Leigh
- Department of Chemistry, The University of Manchester, Manchester, UK
- School of Chemistry and Molecular Engineering, East China Normal University, 3663 N Zhongshan Road, Shanghai, China
| | - Lucian Pirvu
- Department of Chemistry, The University of Manchester, Manchester, UK
| | | | - Liang Zhang
- Department of Chemistry, The University of Manchester, Manchester, UK
- School of Chemistry and Molecular Engineering, East China Normal University, 3663 N Zhongshan Road, Shanghai, China
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13
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The protein folding rate and the geometry and topology of the native state. Sci Rep 2022; 12:6384. [PMID: 35430582 PMCID: PMC9013383 DOI: 10.1038/s41598-022-09924-0] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/06/2021] [Accepted: 03/21/2022] [Indexed: 11/08/2022] Open
Abstract
AbstractProteins fold in 3-dimensional conformations which are important for their function. Characterizing the global conformation of proteins rigorously and separating secondary structure effects from topological effects is a challenge. New developments in applied knot theory allow to characterize the topological characteristics of proteins (knotted or not). By analyzing a small set of two-state and multi-state proteins with no knots or slipknots, our results show that 95.4% of the analyzed proteins have non-trivial topological characteristics, as reflected by the second Vassiliev measure, and that the logarithm of the experimental protein folding rate depends on both the local geometry and the topology of the protein’s native state.
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14
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Investigation of the structural dynamics of a knotted protein and its unknotted analog using molecular dynamics. J Mol Model 2022; 28:108. [PMID: 35357594 DOI: 10.1007/s00894-022-05094-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/22/2021] [Accepted: 03/12/2022] [Indexed: 10/18/2022]
Abstract
The role of knots in proteins remains elusive. Some studies suggest an impact on stability; the difficulty in comparing systems to assess this effect, however, has been a significant challenge. In this study, we produced and analyzed molecular dynamic trajectories considering three different temperatures of two variants of ornithine transcarbamylase (OTC), only one of which has a 31 knot, in order to evaluate the relative stability of the two molecules. RMSD showed equilibrated structures for the produced trajectories, and RMSF showed subtle differences in flexibility. In the knot moiety, the knotted protein did not show a great deal of fluctuation at any temperature. For the unknotted protein, the residue GLY243 showed a high fluctuation in the corresponding moiety. The fraction of native contacts (Q) showed a similar profile at all temperatures, with the greatest decrease by 436 K. The investigation of conformational behavior with principal component analysis (PCA) and dynamic cross-correlation map (DCCM) showed that knotted protein is less likely to undergo changes in its conformation under the conditions employed compared to unknotted. PCA data showed that the unknotted protein had greater dispersion in its conformations, which suggests that it has a greater capacity for conformation transitions in response to thermal changes. DCCM graphs comparing the 310 K and 436 K temperatures showed that the knotted protein had less change in its correlation and anti-correlation movements, indicating stability compared to the unknotted.
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15
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Wu WH, Bai X, Shao Y, Yang C, Wei J, Wei W, Zhang WB. Higher Order Protein Catenation Leads to an Artificial Antibody with Enhanced Affinity and In Vivo Stability. J Am Chem Soc 2021; 143:18029-18040. [PMID: 34664942 DOI: 10.1021/jacs.1c06169] [Citation(s) in RCA: 15] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022]
Abstract
The chemical topology is a unique dimension for protein engineering, yet the topological diversity and architectural complexity of proteins remain largely untapped. Herein, we report the biosynthesis of complex topological proteins using a rationally engineered, cross-entwining peptide heterodimer motif derived from p53dim (an entangled homodimeric mutant of the tetramerization domain of the tumor suppressor protein p53). The incorporation of an electrostatic interaction at specific sites converts the p53dim homodimer motif into a pair of heterodimer motifs with high specificity for directing chain entanglement upon folding. Its combination with split-intein-mediated ligation and/or SpyTag/SpyCatcher chemistry facilitates the programmed synthesis of protein heterocatenane or [n]catenanes in cells, leading to a general and modular approach to complex protein catenanes containing various proteins of interest. Concatenation enhances not only the target protein's affinity but also the in vivo stability as shown by its prolonged circulation time in blood. As a proof of concept, artificial antibodies have been developed by embedding a human epidermal growth factor receptor 2-specific affibody onto the [n]catenane scaffolds and shown to exhibit a higher affinity and a better pharmacokinetic profile than the wild-type affibody. These results suggest that topology engineering holds great promise in the development of therapeutic proteins.
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Affiliation(s)
- Wen-Hao Wu
- Beijing National Laboratory for Molecular Sciences, Key Laboratory of Polymer Chemistry & Physics of Ministry of Education, Center for Soft Matter Science and Engineering, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, P. R. China
| | - Xilin Bai
- Beijing National Laboratory for Molecular Sciences, Key Laboratory of Polymer Chemistry & Physics of Ministry of Education, Center for Soft Matter Science and Engineering, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, P. R. China
| | - Yu Shao
- Beijing National Laboratory for Molecular Sciences, Key Laboratory of Polymer Chemistry & Physics of Ministry of Education, Center for Soft Matter Science and Engineering, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, P. R. China
| | - Chao Yang
- College of Chemical and Environmental Engineering, Anyang Institute of Technology, Anyang, Henan 455000, P. R. China
| | - Jingjing Wei
- College of Chemical and Environmental Engineering, Anyang Institute of Technology, Anyang, Henan 455000, P. R. China
| | - Wei Wei
- State Key Laboratory of Biochemical Engineering, Institute of Process Engineering, Chinese Academy of Sciences, Beijing 100190, P. R. China
| | - Wen-Bin Zhang
- Beijing National Laboratory for Molecular Sciences, Key Laboratory of Polymer Chemistry & Physics of Ministry of Education, Center for Soft Matter Science and Engineering, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, P. R. China
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16
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Slipknotted and unknotted monovalent cation-proton antiporters evolved from a common ancestor. PLoS Comput Biol 2021; 17:e1009502. [PMID: 34648493 PMCID: PMC8562792 DOI: 10.1371/journal.pcbi.1009502] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/30/2020] [Revised: 11/02/2021] [Accepted: 09/28/2021] [Indexed: 11/20/2022] Open
Abstract
While the slipknot topology in proteins has been known for over a decade, its evolutionary origin is still a mystery. We have identified a previously overlooked slipknot motif in a family of two-domain membrane transporters. Moreover, we found that these proteins are homologous to several families of unknotted membrane proteins. This allows us to directly investigate the evolution of the slipknot motif. Based on our comprehensive analysis of 17 distantly related protein families, we have found that slipknotted and unknotted proteins share a common structural motif. Furthermore, this motif is conserved on the sequential level as well. Our results suggest that, regardless of topology, the proteins we studied evolved from a common unknotted ancestor single domain protein. Our phylogenetic analysis suggests the presence of at least seven parallel evolutionary scenarios that led to the current diversity of proteins in question. The tools we have developed in the process can now be used to investigate the evolution of other repeated-domain proteins. In proteins with the slipknot topology, the polypeptide chain forms a slipknot—a structure that is not necessarily manifest to a naked eye, but it can be detected using mathematical methods. Slipknots are conserved motifs often found at catalytic sites and are directly involved in molecular transport. Although the first proteins with slipknots were found in 2007, many questions remain unanswered, e.g. how these proteins appeared, or whether the slipknotted proteins evolved from unknotted ones or vice versa. Here we provide the first analysis of homologous slipknotted and unknotted transmembrane proteins in order to elucidate their evolutionary relationship. We show that two-domain slipknotted and unknotted membrane transporters share the same one-domain unknotted protein as an ancestor. The ancestor gene duplicated and underwent various diversification and fusion events during the evolution, which have led to the appearance of a large superfamily of secondary active transporters. The slipknot motif seems to have been created by chance after a fusion of two single domain genes. Therefore, we show here that the slipknotted transporter evolved from an unknotted one-domain protein and that there are at least seven different evolutionary scenarios that gave rise to this large superfamily of transporters.
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17
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Inomata Y, Sawada T, Fujita M. Metal-Peptide Nonafoil Knots and Decafoil Supercoils. J Am Chem Soc 2021; 143:16734-16739. [PMID: 34601872 DOI: 10.1021/jacs.1c08094] [Citation(s) in RCA: 25] [Impact Index Per Article: 8.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022]
Abstract
Despite the frequent occurrence of knotted frameworks in protein structures, the latent potential of peptide strands to form entangled structures is rarely discussed in peptide chemistry. Here we report the construction of highly entangled molecular topologies from Ag(I) ions and tripeptide ligands. The efficient entanglement of metal-peptide strands and the wide scope for design of the amino acid side chains in these ligands enabled the construction of metal-peptide 91 torus knots and 1012 torus links. Moreover, steric control of the peptide side chain induced ring opening and twisting of the torus framework, which resulted in an infinite toroidal supercoil nanostructure.
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Affiliation(s)
- Yuuki Inomata
- Department of Applied Chemistry, School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
| | - Tomohisa Sawada
- Department of Applied Chemistry, School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan.,JST PRESTO, https://www.jst.go.jp/kisoken/presto/en/index.html
| | - Makoto Fujita
- Department of Applied Chemistry, School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan.,Division of Advanced Molecular Science, Institute for Molecular Science (IMS), 5-1 Higashiyama, Myodaiji-cho, Okazaki, Aichi 444-8787, Japan
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18
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A Topological Selection of Folding Pathways from Native States of Knotted Proteins. Symmetry (Basel) 2021. [DOI: 10.3390/sym13091670] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022] Open
Abstract
Understanding how knotted proteins fold is a challenging problem in biology. Researchers have proposed several models for their folding pathways, based on theory, simulations and experiments. The geometry of proteins with the same knot type can vary substantially and recent simulations reveal different folding behaviour for deeply and shallow knotted proteins. We analyse proteins forming open-ended trefoil knots by introducing a topologically inspired statistical metric that measures their entanglement. By looking directly at the geometry and topology of their native states, we are able to probe different folding pathways for such proteins. In particular, the folding pathway of shallow knotted carbonic anhydrases involves the creation of a double-looped structure, contrary to what has been observed for other knotted trefoil proteins. We validate this with Molecular Dynamics simulations. By leveraging the geometry and local symmetries of knotted proteins’ native states, we provide the first numerical evidence of a double-loop folding mechanism in trefoil proteins.
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19
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20
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Especial JNC, Faísca PFN. A Specific Set of Heterogeneous Native Interactions Yields Efficient Knotting in Protein Folding. J Phys Chem B 2021; 125:7359-7367. [PMID: 34197706 DOI: 10.1021/acs.jpcb.1c03127] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023]
Abstract
Native interactions are crucial for folding, and non-native interactions appear to be critical for efficiently knotting proteins. Therefore, it is important to understand both their roles in the folding of knotted proteins. It has been proposed that non-native interactions drive the correct order of contact formation, which is essential to avoid backtracking and efficiently self-tie. In this study, we ask if non-native interactions are strictly necessary to tangle a protein or if the correct order of contact formation can be assured by a specific set of native, but otherwise heterogeneous (i.e., having distinct energies), interactions. In order to address this problem, we conducted extensive Monte Carlo simulations of lattice models of protein-like sequences designed to fold into a preselected knotted conformation embedding a trefoil knot. We were able to identify a specific set of heterogeneous native interactions that drives efficient knotting and is able to fold the protein when combined with the remaining native interactions modeled as homogeneous. This specific set of heterogeneous native interactions is strictly enough to efficiently self-tie. A distinctive feature of these native interactions is that they do not backtrack because their energies ensure the correct order of contact formation. Furthermore, they stabilize a knotted intermediate state, which is en route to the native structure. Our results thus show that-at least in the context of the adopted model-non-native interactions are not necessary to knot a protein. However, when they are taken into account in protein energetics, it is possible to find specific, nonlocal non-native interactions that operate as a scaffold that assists the knotting step.
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Affiliation(s)
- João N C Especial
- Departamento de Física, Universidade de Lisboa, Campo Grande, Ed. C8, 1749-016 Lisboa, Portugal.,BioISI-Biosystems and Integrative Sciences Institute, Faculdade de Ciências, Universidade de Lisboa, Campo Grande, Ed. C8, 1749-016 Lisboa, Portugal
| | - Patrícia F N Faísca
- Departamento de Física, Universidade de Lisboa, Campo Grande, Ed. C8, 1749-016 Lisboa, Portugal.,BioISI-Biosystems and Integrative Sciences Institute, Faculdade de Ciências, Universidade de Lisboa, Campo Grande, Ed. C8, 1749-016 Lisboa, Portugal
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21
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Abstract
Recent studies classify the topology of proteins by analysing the distribution of their projections using knotoids. The approximation of this distribution depends on the number of projection directions that are sampled. Here, we investigate the relation between knotoids differing only by small perturbations of the direction of projection. Since such knotoids are connected by at most a single forbidden move, we characterize forbidden moves in terms of equivariant band attachment between strongly invertible knots and of strand passages between
θ
-curves. This allows for the determination of the optimal sample size needed to produce a well-approximated knotoid distribution. Based on that and on topological properties of the distribution, we probe the depth of knotted proteins with the trefoil as the predominant knot type without using subchain analysis.
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Affiliation(s)
- Agnese barbensi
- Mathematical Institute, University of Oxford, Oxford OX2 6GG, UK
| | - Dimos Goundaroulis
- The Center for Genome Architecture, Baylor College of Medicine, Houston, TX 77030, USA
- Department of Molecular and Human Genetics, Baylor College of Medicine, Houston, TX 77030, USA
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22
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23
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Scalvini B, Sheikhhassani V, Woodard J, Aupič J, Dame RT, Jerala R, Mashaghi A. Topology of Folded Molecular Chains: From Single Biomolecules to Engineered Origami. TRENDS IN CHEMISTRY 2020. [DOI: 10.1016/j.trechm.2020.04.009] [Citation(s) in RCA: 16] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023]
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24
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Piejko M, Niewieczerzal S, Sulkowska JI. The Folding of Knotted Proteins: Distinguishing the Distinct Behavior of Shallow and Deep Knots. Isr J Chem 2020. [DOI: 10.1002/ijch.202000036] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
Affiliation(s)
- Maciej Piejko
- Faculty of ChemistryUniversity of Warsaw Pasteura 1 Warsaw 02-093 Poland
- Centre of New TechnologiesUniversity of Warsaw Banacha 2c Warsaw 02-097 Poland
| | | | - Joanna I. Sulkowska
- Faculty of ChemistryUniversity of Warsaw Pasteura 1 Warsaw 02-093 Poland
- Centre of New TechnologiesUniversity of Warsaw Banacha 2c Warsaw 02-097 Poland
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25
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Sulkowska JI. On folding of entangled proteins: knots, lassos, links and θ-curves. Curr Opin Struct Biol 2020; 60:131-141. [PMID: 32062143 DOI: 10.1016/j.sbi.2020.01.007] [Citation(s) in RCA: 41] [Impact Index Per Article: 10.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/01/2019] [Revised: 01/02/2020] [Accepted: 01/12/2020] [Indexed: 12/15/2022]
Abstract
Around 6% of protein structures deposited in the PDB are entangled, forming knots, slipknots, lassos, links, and θ-curves. In each of these cases, the protein backbone weaves through itself in a complex way, and at some point passes through a closed loop, formed by other regions of the protein structure. Such a passing can be interpreted as crossing a topological barrier. How proteins overcome such barriers, and therefore different degrees of frustration, challenged scientists and has shed new light on the field of protein folding. In this review, we summarize the current knowledge about the free energy landscape of proteins with non-trivial topology. We describe identified mechanisms which lead proteins to self-tying. We discuss the influence of excluded volume, such as crowding and chaperones, on tying, based on available data. We briefly discuss the diversity of topological complexity of proteins and their evolution. We also list available tools to investigate non-trivial topology. Finally, we formulate intriguing and challenging questions at the boundary of biophysics, bioinformatics, biology, and mathematics, which arise from the discovery of entangled proteins.
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Affiliation(s)
- Joanna Ida Sulkowska
- Centre of New Technologies, University of Warsaw, Warsaw, Poland; Faculty of Chemistry, University of Warsaw, Warsaw, Poland.
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26
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Caprice K, Aster A, Cougnon FBL, Kumpulainen T. Untying the Photophysics of Quinolinium-Based Molecular Knots and Links. Chemistry 2020; 26:1576-1587. [PMID: 31670851 DOI: 10.1002/chem.201904456] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/27/2019] [Revised: 10/30/2019] [Indexed: 01/08/2023]
Abstract
Complex molecular knots and links are still difficult to synthesize and the properties arising from their topology are mostly unknown. Here, we report on a comparative photophysical study carried out on a family of closely related quinolinium-based knots and links to determine the impact exerted by topology on the molecular backbone. Our results indicate that topology has a negligible influence on the behavior of loosely braided molecules, which mostly behave like their unbraided equivalents. On the other hand, tightly braided molecules display distinct features. Their higher packing density results in a pronounced ability to resist deformation, a significant reduction in the solvent-accessible surface area and favors close-range π-π interactions between the quinolinium units and neighboring aromatics. Finally, the sharp alteration in behavior between loosely and tightly braided molecules sheds light on the factors contributing to braiding tightness.
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Affiliation(s)
- Kenji Caprice
- Department of Organic Chemistry, University of Geneva, 30 Quai Ernest Ansermet, Geneva, Switzerland
| | - Alexander Aster
- Department of Physical Chemistry, University of Geneva, 30 Quai Ernest Ansermet, Geneva, Switzerland
| | - Fabien B L Cougnon
- Department of Organic Chemistry, University of Geneva, 30 Quai Ernest Ansermet, Geneva, Switzerland
| | - Tatu Kumpulainen
- Department of Physical Chemistry, University of Geneva, 30 Quai Ernest Ansermet, Geneva, Switzerland
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27
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Lewis JE. Knotting to See Here. Chem 2020. [DOI: 10.1016/j.chempr.2019.12.017] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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28
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29
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Dorier J, Goundaroulis D, Benedetti F, Stasiak A. Knoto-ID: a tool to study the entanglement of open protein chains using the concept of knotoids. Bioinformatics 2019; 34:3402-3404. [PMID: 29722808 DOI: 10.1093/bioinformatics/bty365] [Citation(s) in RCA: 17] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/09/2017] [Accepted: 05/01/2018] [Indexed: 11/13/2022] Open
Abstract
Summary The backbone of most proteins forms an open curve. To study their entanglement, a common strategy consists in searching for the presence of knots in their backbones using topological invariants. However, this approach requires to close the curve into a loop, which alters the geometry of curve. Knoto-ID allows evaluating the entanglement of open curves without the need to close them, using the recent concept of knotoids which is a generalization of the classical knot theory to open curves. Knoto-ID can analyse the global topology of the full chain as well as the local topology by exhaustively studying all subchains or only determining the knotted core. Knoto-ID permits to localize topologically non-trivial protein folds that are not detected by informatics tools detecting knotted protein folds. Availability and implementation Knoto-ID is written in C++ and includes R (www.R-project.org) scripts to generate plots of projections maps, fingerprint matrices and disk matrices. Knoto-ID is distributed under the GNU General Public License (GPL), version 2 or any later version and is available at https://github.com/sib-swiss/Knoto-ID. A binary distribution for Mac OS X, Linux and Windows with detailed user guide and examples can be obtained from https://www.vital-it.ch/software/Knoto-ID.
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Affiliation(s)
- Julien Dorier
- Vital-IT, SIB Swiss Institute of Bioinformatics, Lausanne, Switzerland.,Center for Integrative Genomics, University of Lausanne, Lausanne, Switzerland
| | - Dimos Goundaroulis
- Center for Integrative Genomics, University of Lausanne, Lausanne, Switzerland.,SIB Swiss Institute of Bioinformatics, Lausanne, Switzerland
| | - Fabrizio Benedetti
- Vital-IT, SIB Swiss Institute of Bioinformatics, Lausanne, Switzerland.,Center for Integrative Genomics, University of Lausanne, Lausanne, Switzerland
| | - Andrzej Stasiak
- Center for Integrative Genomics, University of Lausanne, Lausanne, Switzerland.,SIB Swiss Institute of Bioinformatics, Lausanne, Switzerland
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30
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Leidreiter F, Roderer D, Meusch D, Gatsogiannis C, Benz R, Raunser S. Common architecture of Tc toxins from human and insect pathogenic bacteria. SCIENCE ADVANCES 2019; 5:eaax6497. [PMID: 31663026 PMCID: PMC6795518 DOI: 10.1126/sciadv.aax6497] [Citation(s) in RCA: 21] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 04/10/2019] [Accepted: 09/18/2019] [Indexed: 06/10/2023]
Abstract
Tc toxins use a syringe-like mechanism to penetrate the membrane and translocate toxic enzymes into the host cytosol. They are composed of three components: TcA, TcB, and TcC. Low-resolution structures of TcAs from different bacteria suggest a considerable difference in their architecture and possibly in their mechanism of action. Here, we present high-resolution structures of five TcAs from insect and human pathogens, which show a similar overall composition and domain organization. Essential structural features, including a trefoil protein knot, are present in all TcAs, suggesting a common mechanism of action. All TcAs form functional pores and can be combined with TcB-TcC subunits from other species to form active chimeric holotoxins. We identified a conserved ionic pair that stabilizes the shell, likely operating as a strong latch that only springs open after destabilization of other regions. Our results provide new insights into the architecture and mechanism of the Tc toxin family.
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Affiliation(s)
- F. Leidreiter
- Department of Structural Biochemistry, Max Planck Institute of Molecular Physiology, Otto-Hahn-Str. 11, 44227 Dortmund, Germany
| | - D. Roderer
- Department of Structural Biochemistry, Max Planck Institute of Molecular Physiology, Otto-Hahn-Str. 11, 44227 Dortmund, Germany
| | - D. Meusch
- Department of Structural Biochemistry, Max Planck Institute of Molecular Physiology, Otto-Hahn-Str. 11, 44227 Dortmund, Germany
| | - C. Gatsogiannis
- Department of Structural Biochemistry, Max Planck Institute of Molecular Physiology, Otto-Hahn-Str. 11, 44227 Dortmund, Germany
| | - R. Benz
- Department of Life Sciences and Chemistry, Jacobs University Bremen, Campusring 1, 28759 Bremen, Germany
| | - S. Raunser
- Department of Structural Biochemistry, Max Planck Institute of Molecular Physiology, Otto-Hahn-Str. 11, 44227 Dortmund, Germany
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31
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Baiesi M, Orlandini E, Seno F, Trovato A. Sequence and structural patterns detected in entangled proteins reveal the importance of co-translational folding. Sci Rep 2019; 9:8426. [PMID: 31182755 PMCID: PMC6557820 DOI: 10.1038/s41598-019-44928-3] [Citation(s) in RCA: 29] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/22/2019] [Accepted: 05/23/2019] [Indexed: 11/09/2022] Open
Abstract
Proteins must fold quickly to acquire their biologically functional three-dimensional native structures. Hence, these are mainly stabilized by local contacts, while intricate topologies such as knots are rare. Here, we reveal the existence of specific patterns adopted by protein sequences and structures to deal with backbone self-entanglement. A large scale analysis of the Protein Data Bank shows that loops significantly intertwined with another chain portion are typically closed by weakly bound amino acids. Why is this energetic frustration maintained? A possible picture is that entangled loops are formed only toward the end of the folding process to avoid kinetic traps. Consistently, these loops are more frequently found to be wrapped around a portion of the chain on their N-terminal side, the one translated earlier at the ribosome. Finally, these motifs are less abundant in natural native states than in simulated protein-like structures, yet they appear in 32% of proteins, which in some cases display an amazingly complex intertwining.
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Affiliation(s)
- Marco Baiesi
- Department of Physics and Astronomy, University of Padova, Via Marzolo 8, I-35131, Padova, Italy
- INFN, Sezione di Padova, Via Marzolo 8, I-35131, Padova, Italy
| | - Enzo Orlandini
- Department of Physics and Astronomy, University of Padova, Via Marzolo 8, I-35131, Padova, Italy
- INFN, Sezione di Padova, Via Marzolo 8, I-35131, Padova, Italy
| | - Flavio Seno
- Department of Physics and Astronomy, University of Padova, Via Marzolo 8, I-35131, Padova, Italy.
- INFN, Sezione di Padova, Via Marzolo 8, I-35131, Padova, Italy.
| | - Antonio Trovato
- Department of Physics and Astronomy, University of Padova, Via Marzolo 8, I-35131, Padova, Italy
- INFN, Sezione di Padova, Via Marzolo 8, I-35131, Padova, Italy
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32
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Perego C, Potestio R. Searching the Optimal Folding Routes of a Complex Lasso Protein. Biophys J 2019; 117:214-228. [PMID: 31235180 PMCID: PMC6700606 DOI: 10.1016/j.bpj.2019.05.025] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/09/2019] [Revised: 04/29/2019] [Accepted: 05/30/2019] [Indexed: 10/27/2022] Open
Abstract
Understanding how polypeptides can efficiently and reproducibly attain a self-entangled conformation is a compelling biophysical challenge that might shed new light on our general knowledge of protein folding. Complex lassos, namely self-entangled protein structures characterized by a covalent loop sealed by a cysteine bridge, represent an ideal test system in the framework of entangled folding. Indeed, because cysteine bridges form in oxidizing conditions, they can be used as on/off switches of the structure topology to investigate the role played by the backbone entanglement in the process. In this work, we have used molecular dynamics to simulate the folding of a complex lasso glycoprotein, granulocyte-macrophage colony-stimulating factor, modeling both reducing and oxidizing conditions. Together with a well-established Gō-like description, we have employed the elastic folder model, a coarse-grained, minimalistic representation of the polypeptide chain driven by a structure-based angular potential. The purpose of this study is to assess the kinetically optimal pathways in relation to the formation of the native topology. To this end, we have implemented an evolutionary strategy that tunes the elastic folder model potentials to maximize the folding probability within the early stages of the dynamics. The resulting protein model is capable of folding with high success rate, avoiding the kinetic traps that hamper the efficient folding in the other tested models. Employing specifically designed topological descriptors, we could observe that the selected folding routes avoid the topological bottleneck by locking the cysteine bridge after the topology is formed. These results provide valuable insights on the selection of mechanisms in self-entangled protein folding while, at the same time, the proposed methodology can complement the usage of established minimalistic models and draw useful guidelines for more detailed simulations.
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Affiliation(s)
- Claudio Perego
- Polymer Theory Department, Max Planck Institute for Polymer Research, Mainz, Germany.
| | - Raffaello Potestio
- Department of Physics, University of Trento, Trento, Italy; INFN-TIFPA, Trento Institute for Fundamental Physics and Applications, Trento, Italy
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33
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Sluysmans D, Stoddart JF. The Burgeoning of Mechanically Interlocked Molecules in Chemistry. TRENDS IN CHEMISTRY 2019. [DOI: 10.1016/j.trechm.2019.02.013] [Citation(s) in RCA: 49] [Impact Index Per Article: 9.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022]
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34
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Dabrowski-Tumanski P, Gren B, Sulkowska JI. Statistical Properties of Lasso-Shape Polymers and Their Implications for Complex Lasso Proteins Function. Polymers (Basel) 2019; 11:E707. [PMID: 30999683 PMCID: PMC6523798 DOI: 10.3390/polym11040707] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/15/2019] [Revised: 04/11/2019] [Accepted: 04/12/2019] [Indexed: 12/19/2022] Open
Abstract
The shape and properties of closed loops depend on various topological factors. One of them is loop-threading, which is present in complex lasso proteins. In this work, we analyze the probability of loop-threading by the tail and its influence on the shape of the loop measured by the radius of gyration, distention, asphericity, and prolateness. In particular, we show that the probability of a trivial lasso for phantom polymer is non-zero even for an infinite structure, as well as that the threading flattens the loop by restricting its motion in one dimension. These results are further used to show that there are fewer non-trivial protein lassos than expected and select potentially functional complex lasso proteins.
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Affiliation(s)
- Pawel Dabrowski-Tumanski
- Centre of New Technologies, University of Warsaw, 02-097 Warsaw, Poland.
- Faculty of Chemistry, University of Warsaw, 02-093 Warsaw, Poland.
| | - Bartosz Gren
- Centre of New Technologies, University of Warsaw, 02-097 Warsaw, Poland.
- Faculty of Physics, University of Warsaw, 02-093 Warsaw, Poland.
| | - Joanna I Sulkowska
- Centre of New Technologies, University of Warsaw, 02-097 Warsaw, Poland.
- Faculty of Chemistry, University of Warsaw, 02-093 Warsaw, Poland.
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35
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Dabrowski-Tumanski P, Rubach P, Goundaroulis D, Dorier J, Sułkowski P, Millett KC, Rawdon EJ, Stasiak A, Sulkowska JI. KnotProt 2.0: a database of proteins with knots and other entangled structures. Nucleic Acids Res 2019; 47:D367-D375. [PMID: 30508159 PMCID: PMC6323932 DOI: 10.1093/nar/gky1140] [Citation(s) in RCA: 57] [Impact Index Per Article: 11.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/15/2018] [Revised: 10/24/2018] [Accepted: 11/30/2018] [Indexed: 01/08/2023] Open
Abstract
The KnotProt 2.0 database (the updated version of the KnotProt database) collects information about proteins which form knots and other entangled structures. New features in KnotProt 2.0 include the characterization of both probabilistic and deterministic entanglements which can be formed by disulfide bonds and interactions via ions, a refined characterization of entanglement in terms of knotoids, the identification of the so-called cysteine knots, the possibility to analyze all or a non-redundant set of proteins, and various technical updates. The KnotProt 2.0 database classifies all entangled proteins, represents their complexity in the form of a knotting fingerprint, and presents many biological and geometrical statistics based on these results. Currently the database contains >2000 entangled structures, and it regularly self-updates based on proteins deposited in the Protein Data Bank (PDB).
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Affiliation(s)
- Pawel Dabrowski-Tumanski
- Faculty of Chemistry, University of Warsaw, Pasteura 1, Warsaw, Poland
- Centre of New Technologies, University of Warsaw, Banacha 2c, Warsaw, Poland
| | - Pawel Rubach
- Centre of New Technologies, University of Warsaw, Banacha 2c, Warsaw, Poland
- Warsaw School of Economics, Al. Niepodlegosci 162, Warsaw, Poland
| | - Dimos Goundaroulis
- Center for Integrative Genomics, University of Lausanne, 1015-Lausanne, Switzerland, SIB Swiss Institute of Bioinformatics, 1015 Lausanne, Switzerland
| | - Julien Dorier
- Vital-IT, SIB Swiss Institute of Bioinformatics, 1015 Lausanne, Switzerland
| | - Piotr Sułkowski
- Faculty of Physics, University of Warsaw, Pasteura 5, Warsaw, Poland
- Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, CA 91125, USA
| | - Kenneth C Millett
- Department of Mathematics, University of California, Santa Barbara, CA 93106, USA
| | - Eric J Rawdon
- Department of Mathematics, University of St. Thomas, Saint Paul, MN 55105, USA
| | - Andrzej Stasiak
- Center for Integrative Genomics, University of Lausanne, 1015-Lausanne, Switzerland, SIB Swiss Institute of Bioinformatics, 1015 Lausanne, Switzerland
| | - Joanna I Sulkowska
- Faculty of Chemistry, University of Warsaw, Pasteura 1, Warsaw, Poland
- Centre of New Technologies, University of Warsaw, Banacha 2c, Warsaw, Poland
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36
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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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37
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Jarmolinska AI, Perlinska AP, Runkel R, Trefz B, Ginn HM, Virnau P, Sulkowska JI. Proteins' Knotty Problems. J Mol Biol 2018; 431:244-257. [PMID: 30391297 DOI: 10.1016/j.jmb.2018.10.012] [Citation(s) in RCA: 28] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/22/2018] [Revised: 10/17/2018] [Accepted: 10/17/2018] [Indexed: 12/20/2022]
Abstract
Knots in proteins are increasingly being recognized as an important structural concept, and the folding of these peculiar structures still poses considerable challenges. From a functional point of view, most protein knots discovered so far are either enzymes or DNA-binding proteins. Our comprehensive topological analysis of the Protein Data Bank reveals several novel structures including knotted mitochondrial proteins and the most deeply embedded protein knot discovered so far. For the latter, we propose a novel folding pathway based on the idea that a loose knot forms at a terminus and slides to its native position. For the mitochondrial proteins, we discuss the folding problem from the perspective of transport and suggest that they fold inside the mitochondria. We also discuss the evolutionary origin of a novel class of knotted membrane proteins and argue that a novel knotted DNA-binding protein constitutes a new fold. Finally, we have also discovered a knot in an artificially designed protein structure.
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Affiliation(s)
- Aleksandra I Jarmolinska
- Centre of New Technologies, University of Warsaw, Banacha 2c, 02-097 Warsaw, Poland; College of Inter-Faculty Individual Studies in Mathematics and Natural Sciences, Banacha 2c, 02-097 Warsaw, Poland
| | - Agata P Perlinska
- Centre of New Technologies, University of Warsaw, Banacha 2c, 02-097 Warsaw, Poland; College of Inter-Faculty Individual Studies in Mathematics and Natural Sciences, Banacha 2c, 02-097 Warsaw, Poland
| | - Robert Runkel
- Department of Physics, Johannes Gutenberg University Mainz, Staudingerweg 7, 55128 Mainz, Germany
| | - Benjamin Trefz
- Department of Physics, Johannes Gutenberg University Mainz, Staudingerweg 7, 55128 Mainz, Germany; Graduate School Material Science in Mainz, Staudinger Weg 9, 55128 Mainz, Germany
| | - Helen M Ginn
- Division of Structural Biology, Wellcome Trust Centre for Human Genetics, University of Oxford, Oxford, UK
| | - Peter Virnau
- Department of Physics, Johannes Gutenberg University Mainz, Staudingerweg 7, 55128 Mainz, Germany
| | - Joanna I Sulkowska
- Centre of New Technologies, University of Warsaw, Banacha 2c, 02-097 Warsaw, Poland.
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38
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Comparative folding analyses of unknotted versus trefoil-knotted ornithine transcarbamylases suggest stabilizing effects of protein knots. Biochem Biophys Res Commun 2018; 503:822-829. [DOI: 10.1016/j.bbrc.2018.06.082] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/11/2018] [Accepted: 06/15/2018] [Indexed: 12/16/2022]
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39
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Jarmolinska AI, Kadlof M, Dabrowski-Tumanski P, Sulkowska JI. GapRepairer: a server to model a structural gap and validate it using topological analysis. Bioinformatics 2018; 34:3300-3307. [DOI: 10.1093/bioinformatics/bty334] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/25/2017] [Accepted: 04/27/2018] [Indexed: 02/07/2023] Open
Affiliation(s)
- Aleksandra I Jarmolinska
- Centre of New Technologies, University of Warsaw, Warsaw, Poland
- College of Inter-Faculty Individual Studies in Mathematics and Natural Sciences, Warsaw, Poland
| | - Michal Kadlof
- Centre of New Technologies, University of Warsaw, Warsaw, Poland
- Faculty of Physics, University of Warsaw, Warsaw, Poland
| | - Pawel Dabrowski-Tumanski
- Centre of New Technologies, University of Warsaw, Warsaw, Poland
- Faculty of Chemistry, University of Warsaw, Warsaw, Poland
| | - Joanna I Sulkowska
- Centre of New Technologies, University of Warsaw, Warsaw, Poland
- Faculty of Chemistry, University of Warsaw, Warsaw, Poland
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40
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Zhao Y, Dabrowski-Tumanski P, Niewieczerzal S, Sulkowska JI. The exclusive effects of chaperonin on the behavior of proteins with 52 knot. PLoS Comput Biol 2018; 14:e1005970. [PMID: 29547629 PMCID: PMC5874080 DOI: 10.1371/journal.pcbi.1005970] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/05/2017] [Revised: 03/28/2018] [Accepted: 01/12/2018] [Indexed: 02/05/2023] Open
Abstract
The folding of proteins with a complex knot is still an unresolved question. Based on representative members of Ubiquitin C-terminal Hydrolases (UCHs) that contain the 52 knot in the native state, we explain how UCHs are able to unfold and refold in vitro reversibly within the structure-based model. In particular, we identify two, topologically different folding/unfolding pathways and corroborate our results with experiment, recreating the chevron plot. We show that confinement effect of chaperonin or weak crowding greatly facilitates folding, simultaneously slowing down the unfolding process of UCHs, compared with bulk conditions. Finally, we analyze the existence of knots in the denaturated state of UCHs. The results of the work show that the crowded environment of the cell should have a positive effect on the kinetics of complex knotted proteins, especially when proteins with deeper knots are found in this family. Self-tying of knotted proteins remains a challenge both for theoreticians and experimentalist. In this work, we study the proteins with complex, the 52 knot, in a bulk and confined within a chaperonin box. We show that in our model we recreate the experimental results, identify two topologically distinct folding pathways and explain the beneficial role of confinement for complex knotted proteins. Encapsulation provides a possibility to fold via alternative pathway—folding via trefoil intermediate knot (N-terminal pathway) from entropic reason while folding via the C-terminal (direct tying) appears with the same probability. The results of this work show, how crowded environment in the real cell may enhance self-tying of proteins. The results are also the first step to the identification of possible oligomerization-prone forms of UCHs, which may cause neurodegenerative diseases.
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Affiliation(s)
- Yani Zhao
- Centre of New Technologies, University of Warsaw, Warsaw, Poland
- Institute of Physics, Polish Academy of Sciences, Warsaw, Poland
| | - Pawel Dabrowski-Tumanski
- Centre of New Technologies, University of Warsaw, Warsaw, Poland
- Faculty of Chemistry, University of Warsaw, Warsaw, Poland
| | | | - Joanna I. Sulkowska
- Centre of New Technologies, University of Warsaw, Warsaw, Poland
- Faculty of Chemistry, University of Warsaw, Warsaw, Poland
- * E-mail:
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41
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Sulkowska JI, Sułkowski P. Entangled Proteins: Knots, Slipknots, Links, and Lassos. SPRINGER SERIES IN SOLID-STATE SCIENCES 2018. [DOI: 10.1007/978-3-319-76596-9_8] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/01/2022]
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42
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43
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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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44
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Goundaroulis D, Gügümcü N, Lambropoulou S, Dorier J, Stasiak A, Kauffman L. Topological Models for Open-Knotted Protein Chains Using the Concepts of Knotoids and Bonded Knotoids. Polymers (Basel) 2017; 9:polym9090444. [PMID: 30965745 PMCID: PMC6418563 DOI: 10.3390/polym9090444] [Citation(s) in RCA: 35] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/26/2017] [Revised: 09/08/2017] [Accepted: 09/11/2017] [Indexed: 11/16/2022] Open
Abstract
In this paper we introduce a method that offers a detailed overview of the entanglement of an open protein chain. Further, we present a purely topological model for classifying open protein chains by also taking into account any bridge involving the backbone. To this end, we implemented the concepts of planar knotoids and bonded knotoids. We show that the planar knotoids technique provides more refined information regarding the knottedness of a protein when compared to established methods in the literature. Moreover, we demonstrate that our topological model for bonded proteins is robust enough to distinguish all types of lassos in proteins.
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Affiliation(s)
- Dimos Goundaroulis
- Center for Integrative Genomics, University of Lausanne, 1015 Lausanne, Switzerland.
- SIB Swiss Institute of Bioinformatics, 1015 Lausanne, Switzerland.
| | - Neslihan Gügümcü
- Department of Mathematics, National Technical University of Athens, Zografou Campus, 15780 Athens, Greece.
| | - Sofia Lambropoulou
- Department of Mathematics, National Technical University of Athens, Zografou Campus, 15780 Athens, Greece.
| | - Julien Dorier
- Center for Integrative Genomics, University of Lausanne, 1015 Lausanne, Switzerland.
- Vital-IT, SIB Swiss Institute of Bioinformatics, 1015 Lausanne, Switzerland.
| | - Andrzej Stasiak
- Center for Integrative Genomics, University of Lausanne, 1015 Lausanne, Switzerland.
- SIB Swiss Institute of Bioinformatics, 1015 Lausanne, Switzerland.
| | - Louis Kauffman
- Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, Chicago, IL 60607-7045, USA.
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45
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Goundaroulis D, Dorier J, Benedetti F, Stasiak A. Studies of global and local entanglements of individual protein chains using the concept of knotoids. Sci Rep 2017; 7:6309. [PMID: 28740166 PMCID: PMC5524787 DOI: 10.1038/s41598-017-06649-3] [Citation(s) in RCA: 33] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/02/2017] [Accepted: 06/20/2017] [Indexed: 11/23/2022] Open
Abstract
We study here global and local entanglements of open protein chains by implementing the concept of knotoids. Knotoids have been introduced in 2012 by Vladimir Turaev as a generalization of knots in 3-dimensional space. More precisely, knotoids are diagrams representing projections of open curves in 3D space, in contrast to knot diagrams which represent projections of closed curves in 3D space. The intrinsic difference with classical knot theory is that the generalization provided by knotoids admits non-trivial topological entanglement of the open curves provided that their geometry is frozen as it is the case for crystallized proteins. Consequently, our approach doesn’t require the closure of chains into loops which implies that the geometry of analysed chains does not need to be changed by closure in order to characterize their topology. Our study revealed that the knotoid approach detects protein regions that were classified earlier as knotted and also new, topologically interesting regions that we classify as pre-knotted.
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Affiliation(s)
- Dimos Goundaroulis
- Center for Integrative Genomics, University of Lausanne, 1015, Lausanne, Switzerland.,Swiss Institute of Bioinformatics, 1015, Lausanne, Switzerland
| | - Julien Dorier
- Center for Integrative Genomics, University of Lausanne, 1015, Lausanne, Switzerland.,Vital-IT, SIB Swiss Institute of Bioinformatics, 1015, Lausanne, Switzerland
| | - Fabrizio Benedetti
- Center for Integrative Genomics, University of Lausanne, 1015, Lausanne, Switzerland.,Vital-IT, SIB Swiss Institute of Bioinformatics, 1015, Lausanne, Switzerland
| | - Andrzej Stasiak
- Center for Integrative Genomics, University of Lausanne, 1015, Lausanne, Switzerland. .,Swiss Institute of Bioinformatics, 1015, Lausanne, Switzerland.
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