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Alves Silva JC, Barden Grillo I, A Urquiza-Carvalho G, Bruno Rocha G. Exploring the electronic structure of knotted proteins: the case of two ornithine transcarbamylase family. J Mol Model 2024; 30:265. [PMID: 39008190 DOI: 10.1007/s00894-024-06009-9] [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: 01/31/2024] [Accepted: 06/06/2024] [Indexed: 07/16/2024]
Abstract
CONTEXT Geometrical knots are rare structural arrangements in proteins in which the polypeptide chain ties itself into a knot, which is very intriguing due to the uncertainty of their impact on the protein properties. Presently, classical molecular dynamics is the most employed technique in the few studies found on this topic, so any information on how the presence of knots affects the reactivity and electronic properties of proteins is even scarcer. Using the electronic structure methods and quantum chemical descriptors analysis, we found that the same amino-acid residues in the knot core have statistically larger values for the unknotted protein, for both hard-hard and soft-soft interaction descriptors. In addition, we present a computationally feasible protocol, where we show it is possible to separate the contribution of the geometrical knot to the reactivity and other electronic structure properties. METHODS In order to investigate these systems, we used PRIMoRDiA, a new software developed by our research group, to explore the electronic structure of biological macromolecules. We evaluated several local quantum chemical descriptors to unveil relevant patterns potentially originating from the presence of the geometrical knot in two proteins, belonging to the ornithine transcarbamylase family. We compared several sampled structures from these two enzymes that are highly similar in both tertiary structure and function, but one of them has a knot whereas the other does not. The sampling was carried out through molecular dynamics simulations using ff14SB force field along 50 ns, and the semiempirical convergence was performed with PM7 Hamiltonian.
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Affiliation(s)
- José Cícero Alves Silva
- Department of Chemistry, Federal University of Paraíba, Cid. Universitária, João Pessoa, 58051-900, Paraíba, Brazil
| | - Igor Barden Grillo
- Department of Chemistry, Federal University of Paraíba, Cid. Universitária, João Pessoa, 58051-900, Paraíba, Brazil
| | - Gabriel A Urquiza-Carvalho
- Department of Chemistry, Federal University of Pernambuco, Cid. Universitária, Recife, 50670-901, Pernambuco, Brazil
| | - Gerd Bruno Rocha
- Department of Chemistry, Federal University of Paraíba, Cid. Universitária, João Pessoa, 58051-900, Paraíba, Brazil.
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2
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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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3
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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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4
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Hsu STD. Folding and functions of knotted proteins. Curr Opin Struct Biol 2023; 83:102709. [PMID: 37778185 DOI: 10.1016/j.sbi.2023.102709] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/30/2023] [Revised: 09/02/2023] [Accepted: 09/05/2023] [Indexed: 10/03/2023]
Abstract
Topologically knotted proteins have entangled structural elements within their native structures that cannot be disentangled simply by pulling from the N- and C-termini. Systematic surveys have identified different types of knotted protein structures, constituting as much as 1% of the total entries within the Protein Data Bank. Many knotted proteins rely on their knotted structural elements to carry out evolutionarily conserved biological functions. Being knotted may also provide mechanical stability to withstand unfolding-coupled proteolysis. Reconfiguring a knotted protein topology by circular permutation or cyclization provides insights into the importance of being knotted in the context of folding and functions. With the explosion of predicted protein structures by artificial intelligence, we are now entering a new era of exploring the entangled protein universe.
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Affiliation(s)
- Shang-Te Danny Hsu
- Institute of Biological Chemistry, Academia Sinica, Taipei 11529, Taiwan; Institute of Biochemical Sciences, National Taiwan University, Taipei 10617, Taiwan; International Institute for Sustainability with Knotted Chiral Meta Matter (WPI-SKCM(2)), Hiroshima University, Higashi-Hiroshima, Hiroshima 739-8526, Japan.
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5
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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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6
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Tagliabue A, Micheletti C, Mella M. Tuning Knotted Copolyelectrolyte Conformations via Solution Properties. Macromolecules 2022. [DOI: 10.1021/acs.macromol.2c01933] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/05/2022]
Affiliation(s)
- Andrea Tagliabue
- Dipartimento di Scienza ed Alta Tecnologia, Università degli Studi dell’Insubria, via Valleggio 11, 22100Como, Italy
- SISSA (Scuola Internazionale Superiore di Studi Avanzati), via Bonomea 265, 34136Trieste, Italy
| | - Cristian Micheletti
- SISSA (Scuola Internazionale Superiore di Studi Avanzati), via Bonomea 265, 34136Trieste, Italy
| | - Massimo Mella
- Dipartimento di Scienza ed Alta Tecnologia, Università degli Studi dell’Insubria, via Valleggio 11, 22100Como, Italy
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7
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Brems MA, Runkel R, Yeates TO, Virnau P. AlphaFold predicts the most complex protein knot and composite protein knots. Protein Sci 2022; 31:e4380. [PMID: 35900026 PMCID: PMC9278004 DOI: 10.1002/pro.4380] [Citation(s) in RCA: 15] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/06/2022] [Revised: 06/09/2022] [Accepted: 06/11/2022] [Indexed: 11/06/2022]
Abstract
The computer artificial intelligence system AlphaFold has recently predicted previously unknown three-dimensional structures of thousands of proteins. Focusing on the subset with high-confidence scores, we algorithmically analyze these predictions for cases where the protein backbone exhibits rare topological complexity, that is, knotting. Amongst others, we discovered a 71 -knot, the most topologically complex knot ever found in a protein, as well several six-crossing composite knots comprised of two methyltransferase or carbonic anhydrase domains, each containing a simple trefoil knot. These deeply embedded composite knots occur evidently by gene duplication and interconnection of knotted dimers. Finally, we report two new five-crossing knots including the first 51 -knot. Our list of analyzed structures forms the basis for future experimental studies to confirm these novel-knotted topologies and to explore their complex folding mechanisms.
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Affiliation(s)
- Maarten A. Brems
- Department of PhysicsJohannes Gutenberg University MainzMainzGermany
| | - Robert Runkel
- Department of PhysicsJohannes Gutenberg University MainzMainzGermany
| | - Todd O. Yeates
- UCLA‐DOE Institute for Genomics and ProteomicsUniversity of California Los AngelesLos AngelesCaliforniaUSA
- UCLA Department of Chemistry and BiochemistryUniversity of California Los AngelesLos AngelesCaliforniaUSA
| | - Peter Virnau
- Department of PhysicsJohannes Gutenberg University MainzMainzGermany
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8
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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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9
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Hagita K, Murashima T, Ogino M, Omiya M, Ono K, Deguchi T, Jinnai H, Kawakatsu T. Efficient compressed database of equilibrated configurations of ring-linear polymer blends for MD simulations. Sci Data 2022; 9:40. [PMID: 35136085 PMCID: PMC8825841 DOI: 10.1038/s41597-022-01138-3] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/19/2021] [Accepted: 12/21/2021] [Indexed: 11/18/2022] Open
Abstract
To effectively archive configuration data during molecular dynamics (MD) simulations of polymer systems, we present an efficient compression method with good numerical accuracy that preserves the topology of ring-linear polymer blends. To compress the fraction of floating-point data, we used the Jointed Hierarchical Precision Compression Number - Data Format (JHPCN-DF) method to apply zero padding for the tailing fraction bits, which did not affect the numerical accuracy, then compressed the data with Huffman coding. We also provided a dataset of well-equilibrated configurations of MD simulations for ring-linear polymer blends with various lengths of linear and ring polymers, including ring complexes composed of multiple rings such as polycatenane. We executed 109 MD steps to obtain 150 equilibrated configurations. The combination of JHPCN-DF and SZ compression achieved the best compression ratio for all cases. Therefore, the proposed method enables efficient archiving of MD trajectories. Moreover, the publicly available dataset of ring-linear polymer blends can be employed for studies of mathematical methods, including topology analysis and data compression, as well as MD simulations.
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Affiliation(s)
- Katsumi Hagita
- Department of Applied Physics, National Defense Academy, 1-10-20, Hashirimizu, Yokosuka, 239-8686, Japan.
| | - Takahiro Murashima
- Department of Physics, Tohoku University, 6-3, Aramaki-aza-Aoba, Aoba-ku, Sendai, 980-8578, Japan
| | - Masao Ogino
- Faculty of Informatics, Daido University, 10-3 Takiharu-cho, Minami-ku, Nagoya, 457-8530, Japan
| | - Manabu Omiya
- Information Initiative Center, Hokkaido University, Kita 11, Nishi 5, Kita-ku, Sapporo, 060-0811, Japan
| | - Kenji Ono
- Research Institute for Information Technology, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka, 819-0395, Japan
| | - Tetsuo Deguchi
- Department of Physics, Ochanomizu University, 2-1-1 Ohtsuka, Bunkyo-ku, Tokyo, 112-8610, Japan
| | - Hiroshi Jinnai
- Institute of Multidisciplinary for Advanced Materials, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai, 980-8577, Japan
| | - Toshihiro Kawakatsu
- Department of Physics, Tohoku University, 6-3, Aramaki-aza-Aoba, Aoba-ku, Sendai, 980-8578, Japan
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10
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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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11
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Fonseka HYY, Javidi A, Oliveira LFL, Micheletti C, Stan G. Unfolding and Translocation of Knotted Proteins by Clp Biological Nanomachines: Synergistic Contribution of Primary Sequence and Topology Revealed by Molecular Dynamics Simulations. J Phys Chem B 2021; 125:7335-7350. [PMID: 34110163 DOI: 10.1021/acs.jpcb.1c00898] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We use Langevin dynamics simulations to model, at an atomistic resolution, how various natively knotted proteins are unfolded in repeated allosteric translocating cycles of the ClpY ATPase. We consider proteins representative of different topologies, from the simplest knot (trefoil 31), to the three-twist 52 knot, to the most complex stevedore, 61, knot. We harness the atomistic detail of the simulations to address aspects that have so far remained largely unexplored, such as sequence-dependent effects on the ruggedness of the landscape traversed during knot sliding. Our simulations reveal the combined effect on translocation of the knotted protein structure, i.e., backbone topology and geometry, and primary sequence, i.e., side chain size and interactions, and show that the latter can dominate translocation hindrance. In addition, we observe that due to the interplay between the knotted topology and intramolecular contacts the transmission of tension along the polypeptide chain occurs very differently from that of homopolymers. Finally, by considering native and non-native interactions, we examine how the disruption or formation of such contacts can affect the translocation processivity and concomitantly create multiple unfolding pathways with very different activation barriers.
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Affiliation(s)
| | - Alex Javidi
- Data Sciences, Janssen Research and Development, Spring House, Pennsylvania 19477, United States
| | - Luiz F L Oliveira
- Department of Chemistry, University of Cincinnati, Cincinnati, Ohio 45221, United States
| | - Cristian Micheletti
- Molecular and Statistical Biophysics, Scuola Internazionale Superiore di Studi Avanzati (SISSA), 34136 Trieste, Italy
| | - George Stan
- Department of Chemistry, University of Cincinnati, Cincinnati, Ohio 45221, United States
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12
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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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13
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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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14
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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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15
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Ko KT, Hu IC, Huang KF, Lyu PC, Hsu STD. Untying a Knotted SPOUT RNA Methyltransferase by Circular Permutation Results in a Domain-Swapped Dimer. Structure 2019; 27:1224-1233.e4. [DOI: 10.1016/j.str.2019.04.004] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/07/2019] [Revised: 03/01/2019] [Accepted: 04/05/2019] [Indexed: 11/28/2022]
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16
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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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17
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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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18
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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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19
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Tubiana L, Polles G, Orlandini E, Micheletti C. KymoKnot: A web server and software package to identify and locate knots in trajectories of linear or circular polymers. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2018; 41:72. [PMID: 29884956 DOI: 10.1140/epje/i2018-11681-0] [Citation(s) in RCA: 35] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/15/2018] [Accepted: 05/18/2018] [Indexed: 06/08/2023]
Abstract
The KymoKnot software package and web server identifies and locates physical knots or proper knots in a series of polymer conformations. It is mainly intended as an analysis tool for trajectories of linear or circular polymers, but it can be used on single instances too, e.g. protein structures in PDB format. A key element of the software package is the so-called minimally interfering chain closure algorithm that is used to detect physical knots in open chains and to locate the knotted region in both open and closed chains. The web server offers a user-friendly graphical interface that identifies the knot type and highlights the knotted region on each frame of the trajectory, which the user can visualize interactively from various viewpoints. The dynamical evolution of the knotted region along the chain contour is presented as a kymograph. All data can be downloaded in text format. The KymoKnot package is licensed under the BSD 3-Clause licence. The server is publicly available at http://kymoknot.sissa.it/kymoknot/interactive.php .
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Affiliation(s)
- Luca Tubiana
- Computational Physics Department, University of Vienna, Sensengasse 8/10, 1090, Vienna, Austria.
| | - Guido Polles
- Molecular and Computational Biology, Department of Biological Sciences, University of Southern California, 90089, Los Angeles, CA, USA
| | - Enzo Orlandini
- Dipartimento di Fisica e Astronomia and Sezione INFN, Università di Padova, Via Marzolo 8, 35131, Padova, Italy
| | - Cristian Micheletti
- SISSA, International School for Advanced Studies, Via Bonomea 265, I-34136, Trieste, Italy
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20
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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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21
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Abstract
The first synthetic molecular trefoil knot was prepared in the late 1980s. However, it is only in the last few years that more complex small-molecule knot topologies have been realized through chemical synthesis. The steric restrictions imposed on molecular strands by knotting can impart significant physical and chemical properties, including chirality, strong and selective ion binding, and catalytic activity. As the number and complexity of accessible molecular knot topologies increases, it will become increasingly useful for chemists to adopt the knot terminology employed by other disciplines. Here we give an overview of synthetic strategies towards molecular knots and outline the principles of knot, braid, and tangle theory appropriate to chemistry and molecular structure.
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Affiliation(s)
| | - David A. Leigh
- School of ChemistryUniversity of ManchesterOxford RoadManchesterM13 9PLUK
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22
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Affiliation(s)
- Stephen D. P. Fielden
- School of Chemistry; University of Manchester; Oxford Road Manchester M13 9PL Großbritannien
| | - David A. Leigh
- School of Chemistry; University of Manchester; Oxford Road Manchester M13 9PL Großbritannien
| | - Steffen L. Woltering
- School of Chemistry; University of Manchester; Oxford Road Manchester M13 9PL Großbritannien
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23
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Siebert JT, Kivel AN, Atkinson LP, Stevens TJ, Laue ED, Virnau P. Are There Knots in Chromosomes? Polymers (Basel) 2017; 9:polym9080317. [PMID: 30971010 PMCID: PMC6418659 DOI: 10.3390/polym9080317] [Citation(s) in RCA: 28] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/30/2017] [Revised: 07/24/2017] [Accepted: 07/25/2017] [Indexed: 02/02/2023] Open
Abstract
Recent developments have for the first time allowed the determination of three-dimensional structures of individual chromosomes and genomes in nuclei of single haploid mouse embryonic stem (ES) cells based on Hi⁻C chromosome conformation contact data. Although these first structures have a relatively low resolution, they provide the first experimental data that can be used to study chromosome and intact genome folding. Here we further analyze these structures and provide the first evidence that G1 phase chromosomes are knotted, consistent with the fact that plots of contact probability vs sequence separation show a power law dependence that is intermediate between that of a fractal globule and an equilibrium structure.
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Affiliation(s)
- Jonathan T Siebert
- Department of Physics, Johannes Gutenberg University Mainz, Staudinger Weg 9, 55128 Mainz, Germany.
| | - Alexey N Kivel
- Department of Physics, Johannes Gutenberg University Mainz, Staudinger Weg 9, 55128 Mainz, Germany.
| | - Liam P Atkinson
- Department of Biochemistry, University of Cambridge, 80 Tennis Court Road, Cambridge CB2 1GA, UK.
| | - Tim J Stevens
- MRC Laboratory of Molecular Biology, Francis Crick Avenue, Cambridge Biomedical Campus, Cambridge CB2 0QH, UK.
| | - Ernest D Laue
- Department of Biochemistry, University of Cambridge, 80 Tennis Court Road, Cambridge CB2 1GA, UK.
| | - Peter Virnau
- Department of Physics, Johannes Gutenberg University Mainz, Staudinger Weg 9, 55128 Mainz, Germany.
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24
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Haglund E, Pilko A, Wollman R, Jennings PA, Onuchic JN. Pierced Lasso Topology Controls Function in Leptin. J Phys Chem B 2017; 121:706-718. [PMID: 28035835 DOI: 10.1021/acs.jpcb.6b11506] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Protein engineering is a powerful tool in drug design and therapeutics, where disulphide bridges are commonly introduced to stabilize proteins. However, these bonds also introduce covalent loops, which are often neglected. These loops may entrap the protein backbone on opposite sides, leading to a "knotted" topology, forming a so-called Pierced Lasso (PL). In this elegant system, the "knot" is held together with a single disulphide bridge where part of the polypeptide chain is threaded through. The size and position of these covalent loops can be manipulated through protein design in vitro, whereas nature uses polymorphism to switch the PL topology. The PL protein leptin shows genetic modification of an N-terminal residue, adding a third cysteine to the same sequence. In an effort to understand the mechanism of threading of these diverse topologies, we designed three loop variants to mimic the polymorphic sequence. This adds elegance to the system under study, as it allows the generation of three possible covalent loops; they are the original wild-type C-terminal loop protein, the fully circularized unthreaded protein, and the N-terminal loop protein, responsible for different lasso topologies. The size of the loop changes the threading mechanism from a slipknotting to a plugging mechanism, with increasing loop size. Interestingly, the ground state of the native protein structure is largely unaffected, but biological assays show that the activity is maximized by properly controlled dynamics in the threaded state. A threaded topology with proper conformational dynamics is important for receptor interaction and activation of the signaling pathways in vivo.
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Affiliation(s)
- Ellinor Haglund
- Center for Theoretical Biological Physics (CTBP) and Departments of Physics and Astronomy, Chemistry and Biosciences, Rice University , Houston, Texas, United States
| | - Anna Pilko
- Department of Chemistry and Biochemistry, The University of California, San Diego (UCSD) , La Jolla, California, United States
| | - Roy Wollman
- Department of Chemistry and Biochemistry, The University of California, San Diego (UCSD) , La Jolla, California, United States
| | - Patricia Ann Jennings
- Department of Chemistry and Biochemistry, The University of California, San Diego (UCSD) , La Jolla, California, United States
| | - José Nelson Onuchic
- Center for Theoretical Biological Physics (CTBP) and Departments of Physics and Astronomy, Chemistry and Biosciences, Rice University , Houston, Texas, United States
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25
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Untangling the Influence of a Protein Knot on Folding. Biophys J 2016; 110:1044-51. [PMID: 26958882 DOI: 10.1016/j.bpj.2016.01.017] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/28/2015] [Revised: 01/01/2016] [Accepted: 01/14/2016] [Indexed: 10/22/2022] Open
Abstract
Entanglement and knots occur across all aspects of the physical world. Despite the common belief that knots are too complicated for incorporation into proteins, knots have been identified in the native fold of a growing number of proteins. The discovery of proteins with this unique backbone characteristic has challenged the preconceptions about the complexity of biological structures, as well as current folding theories. Given the intricacies of the knotted geometry, the interplay between a protein's fold, structure, and function is of particular interest. Interestingly, for most of these proteins, the knotted region appears critical both in folding and function, although full understanding of these contributions is still incomplete. Here, we experimentally reveal the impact of the knot on the landscape, the origin of the bistable nature of the knotted protein, and broaden the view of knot formation as uniquely decoupled from folding.
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26
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Abstract
Physical entanglement, and particularly knots arise spontaneously in equilibrated polymers that are sufficiently long and densely packed. Biopolymers are no exceptions: knots have long been known to occur in proteins as well as in encapsidated viral DNA. The rapidly growing number of RNA structures has recently made it possible to investigate the incidence of physical knots in this type of biomolecule, too. Strikingly, no knots have been found to date in the known RNA structures. In this Point of View Article we discuss the absence of knots in currently available RNAs and consider the reasons why knots in RNA have not yet been found, despite the expectation that they should exist in Nature. We conclude by singling out a number of RNA sequences that, based on the properties of their predicted secondary structures, are good candidates for knotted RNAs.
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Affiliation(s)
| | | | - Niles Lehman
- c Department of Chemistry , Portland State University , Portland OR , 97207 USA
| | - Henri Orland
- d Institut de Physique Théorique, Commissariat à l'énergie atomique CEA, IPhT CNRS, UMR3681 , F-91191 Gif-sur-Yvette France.,e Beijing Computational Science Research Center , Haidian District Beijing , 100084 , China
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27
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Dabrowski-Tumanski P, Stasiak A, Sulkowska JI. In Search of Functional Advantages of Knots in Proteins. PLoS One 2016; 11:e0165986. [PMID: 27806097 PMCID: PMC5091781 DOI: 10.1371/journal.pone.0165986] [Citation(s) in RCA: 40] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/23/2016] [Accepted: 10/20/2016] [Indexed: 11/30/2022] Open
Abstract
We analysed the structure of deeply knotted proteins representing three unrelated families of knotted proteins. We looked at the correlation between positions of knotted cores in these proteins and such local structural characteristics as the number of intra-chain contacts, structural stability and solvent accessibility. We observed that the knotted cores and especially their borders showed strong enrichment in the number of contacts. These regions showed also increased thermal stability, whereas their solvent accessibility was decreased. Interestingly, the active sites within these knotted proteins preferentially located in the regions with increased number of contacts that also have increased thermal stability and decreased solvent accessibility. Our results suggest that knotting of polypeptide chains provides a favourable environment for the active sites observed in knotted proteins. Some knotted proteins have homologues without a knot. Interestingly, these unknotted homologues form local entanglements that retain structural characteristics of the knotted cores.
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Affiliation(s)
- Pawel Dabrowski-Tumanski
- Centre of New Technologies, Banacha 2c, 02–097, Warsaw, Poland
- Faculty of Chemistry, University of Warsaw, Pasteura 1, 02–093, Warsaw, Poland
- Center for Integrative Genomics, University of Lausanne, 1015-Lausanne, Switzerland
| | - Andrzej Stasiak
- Center for Integrative Genomics, University of Lausanne, 1015-Lausanne, Switzerland
- SIB Swiss Institute of Bioinformatics, 1015-Lausanne, Switzerland
- * E-mail: (AS); (JIS)
| | - Joanna I. Sulkowska
- Centre of New Technologies, Banacha 2c, 02–097, Warsaw, Poland
- Faculty of Chemistry, University of Warsaw, Pasteura 1, 02–093, Warsaw, Poland
- * E-mail: (AS); (JIS)
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28
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Jackson SE, Suma A, Micheletti C. How to fold intricately: using theory and experiments to unravel the properties of knotted proteins. Curr Opin Struct Biol 2016; 42:6-14. [PMID: 27794211 DOI: 10.1016/j.sbi.2016.10.002] [Citation(s) in RCA: 56] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/01/2016] [Revised: 09/06/2016] [Accepted: 10/03/2016] [Indexed: 11/15/2022]
Abstract
Over the years, advances in experimental and computational methods have helped us to understand the role of thermodynamic, kinetic and active (chaperone-aided) effects in coordinating the folding steps required to achieving a knotted native state. Here, we review such developments by paying particular attention to the complementarity of experimental and computational studies. Key open issues that could be tackled with either or both approaches are finally pointed out.
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Affiliation(s)
- Sophie E Jackson
- Department of Chemistry, University of Cambridge, Cambridge CB2 1EW, United Kingdom.
| | - Antonio Suma
- SISSA, International School for Advanced Studies, via Bonomea 265, I-34136 Trieste, Italy
| | - Cristian Micheletti
- SISSA, International School for Advanced Studies, via Bonomea 265, I-34136 Trieste, Italy.
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29
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Najafi S, Potestio R. Folding of small knotted proteins: Insights from a mean field coarse-grained model. J Chem Phys 2016; 143:243121. [PMID: 26723606 DOI: 10.1063/1.4934541] [Citation(s) in RCA: 25] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022] Open
Abstract
A small but relevant number of proteins whose native structure is known features nontrivial topology, i.e., they are knotted. Understanding the process of folding from a swollen unknotted state to the biologically relevant native conformation is, for these proteins, particularly difficult, due to their rate-limiting topological entanglement. To shed some light into this conundrum, we introduced a structure-based coarse-grained model of the protein, where the information about the folded conformation is encoded in bonded angular interactions only, which do not favor the formation of native contacts. A stochastic search scheme in parameter space is employed to identify a set of interactions that maximizes the probability to attain the knotted state. The optimal knotting pathways of the two smallest knotted proteins, obtained through this approach, are consistent with the results derived by means of coarse-grained as well as full atomistic simulations.
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Affiliation(s)
- Saeed Najafi
- Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany
| | - Raffaello Potestio
- Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany
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30
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Pandini A, Fornili A. Using Local States To Drive the Sampling of Global Conformations in Proteins. J Chem Theory Comput 2016; 12:1368-79. [PMID: 26808351 PMCID: PMC5356493 DOI: 10.1021/acs.jctc.5b00992] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
![]()
Conformational
changes associated with protein function often occur
beyond the time scale currently accessible to unbiased molecular dynamics
(MD) simulations, so that different approaches have been developed
to accelerate their sampling. Here we investigate how the knowledge
of backbone conformations preferentially adopted by protein fragments,
as contained in precalculated libraries known as structural alphabets
(SA), can be used to explore the landscape of protein conformations
in MD simulations. We find that (a) enhancing the sampling of native
local states in both metadynamics and steered MD simulations allows
the recovery of global folded states in small proteins; (b) folded
states can still be recovered when the amount of information on the
native local states is reduced by using a low-resolution version of
the SA, where states are clustered into macrostates; and (c) sequences
of SA states derived from collections of structural motifs can be
used to sample alternative conformations of preselected protein regions.
The present findings have potential impact on several applications,
ranging from protein model refinement to protein folding and design.
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Affiliation(s)
- Alessandro Pandini
- Department of Computer Science, College of Engineering, Design and Physical Sciences and Synthetic Biology Theme, Institute of Environment, Health and Societies, Brunel University London , Uxbridge UB8 3PH, United Kingdom
| | - Arianna Fornili
- School of Biological and Chemical Sciences, Queen Mary University of London , Mile End Road, London E1 4NS, United Kingdom
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31
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Potestio R, Tubiana L. Discretized knot motion on a tensioned fiber induced by transverse waves. SOFT MATTER 2016; 12:669-673. [PMID: 26510521 DOI: 10.1039/c5sm01766a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
Topological entanglement is a ubiquitous feature of many biological as well as artificial polymers and fibers. While the equilibrium properties of entangled chains have been the subject of several studies, little is known about their out-of-equilibrium behavior. Here, we address the problem of a stretched knotted fiber driven by a periodic force applied to one of its termini. We show that the onset of standing waves kinetically traps the knot in spatially localized states where the amplitude of the oscillations is maximal, while the knot normal diffusive dynamics is replaced by a discrete jump dynamics.
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Affiliation(s)
- Raffaello Potestio
- Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany.
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32
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Trefz B, Virnau P. Scaling behavior of topologically constrained polymer rings in a melt. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2015; 27:354110. [PMID: 26291467 DOI: 10.1088/0953-8984/27/35/354110] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
Large scale molecular dynamics simulations on graphic processing units (GPUs) are employed to study the scaling behavior of ring polymers with various topological constraints in melts. Typical sizes of rings containing 3(1), 5(1) knots and catenanes made up of two unknotted rings scale like N(1/3) in the limit of large ring sizes N. This is consistent with the crumpled globule model and similar findings for unknotted rings. For small ring lengths knots occupy a significant fraction of the ring. The scaling of typical ring sizes for small N thus depends on the particular knot type and the exponent is generally larger than 0.4.
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Affiliation(s)
- Benjamin Trefz
- Graduate School Material Science in Mainz, Staudinger Weg 9, 55128 Mainz, Germany. Johannes Gutenberg University Mainz, Department of Physics, Staudingerweg 7, 55128 Mainz, Germany
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33
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Lim NCH, Jackson SE. Molecular knots in biology and chemistry. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2015; 27:354101. [PMID: 26291690 DOI: 10.1088/0953-8984/27/35/354101] [Citation(s) in RCA: 99] [Impact Index Per Article: 11.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
Knots and entanglements are ubiquitous. Beyond their aesthetic appeal, these fascinating topological entities can be either useful or cumbersome. In recent decades, the importance and prevalence of molecular knots have been increasingly recognised by scientists from different disciplines. In this review, we provide an overview on the various molecular knots found in naturally occurring biological systems (DNA, RNA and proteins), and those created by synthetic chemists. We discuss the current knowledge in these fields, including recent developments in experimental and, in some cases, computational studies which are beginning to shed light into the complex interplay between the structure, formation and properties of these topologically intricate molecules.
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Affiliation(s)
- Nicole C H Lim
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, UK. Faculty of Sciences, Universiti Brunei Darussalam, Gadong BE 1410, Brunei Darussalam
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34
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Faísca PF. Knotted proteins: A tangled tale of Structural Biology. Comput Struct Biotechnol J 2015; 13:459-68. [PMID: 26380658 PMCID: PMC4556803 DOI: 10.1016/j.csbj.2015.08.003] [Citation(s) in RCA: 58] [Impact Index Per Article: 6.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/28/2015] [Revised: 07/31/2015] [Accepted: 08/07/2015] [Indexed: 01/19/2023] Open
Abstract
Knotted proteins have their native structures arranged in the form of an open knot. In the last ten years researchers have been making significant efforts to reveal their folding mechanism and understand which functional advantage(s) knots convey to their carriers. Molecular simulations have been playing a fundamental role in this endeavor, and early computational predictions about the knotting mechanism have just been confirmed in wet lab experiments. Here we review a collection of simulation results that allow outlining the current status of the field of knotted proteins, and discuss directions for future research.
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35
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Najafi S, Potestio R. Two Adhesive Sites Can Enhance the Knotting Probability of DNA. PLoS One 2015; 10:e0132132. [PMID: 26136125 PMCID: PMC4489926 DOI: 10.1371/journal.pone.0132132] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/24/2015] [Accepted: 06/10/2015] [Indexed: 01/05/2023] Open
Abstract
Self-entanglement, or knotting, is entropically favored in long polymers. Relatively short polymers such as proteins can knot as well, but in this case the entanglement is mainly driven by fine-tuned, sequence-specific interactions. The relation between the sequence of a long polymer and its topological state is here investigated by means of a coarse-grained model of DNA. We demonstrate that the introduction of two adhesive regions along the sequence of a self-avoiding chain substantially increases the probability of forming a knot.
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Affiliation(s)
- Saeed Najafi
- Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany
| | - Raffaello Potestio
- Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany
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36
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Wang I, Chen SY, Hsu STD. Unraveling the Folding Mechanism of the Smallest Knotted Protein, MJ0366. J Phys Chem B 2015; 119:4359-70. [DOI: 10.1021/jp511029s] [Citation(s) in RCA: 36] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/25/2022]
Affiliation(s)
- Iren Wang
- Institute
of Biological Chemistry, Academia Sinica, 128, Section 2, Academia Road, Taipei 11529, Taiwan
| | - Szu-Yu Chen
- Institute
of Biological Chemistry, Academia Sinica, 128, Section 2, Academia Road, Taipei 11529, Taiwan
| | - Shang-Te Danny Hsu
- Institute
of Biological Chemistry, Academia Sinica, 128, Section 2, Academia Road, Taipei 11529, Taiwan
- Institute
of Biochemical Sciences, National Taiwan University, 1, Section
4, Roosevelt Road, Taipei 10617, Taiwan
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37
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Self-assembling knots of controlled topology by designing the geometry of patchy templates. Nat Commun 2015; 6:6423. [DOI: 10.1038/ncomms7423] [Citation(s) in RCA: 29] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/04/2014] [Accepted: 01/27/2015] [Indexed: 01/04/2023] Open
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Abstract
The ongoing effort to detect and characterize physical entanglement in biopolymers has so far established that knots are present in many globular proteins and also, abound in viral DNA packaged inside bacteriophages. RNA molecules, however, have not yet been systematically screened for the occurrence of physical knots. We have accordingly undertaken the systematic profiling of the several thousand RNA structures present in the Protein Data Bank (PDB). The search identified no more than three deeply knotted RNA molecules. These entries are rRNAs of about 3,000 nt solved by cryo-EM. Their genuine knotted state is, however, doubtful based on the detailed structural comparison with homologs of higher resolution, which are all unknotted. Compared with the case of proteins and viral DNA, the observed incidence of knots in available RNA structures is, therefore, practically negligible. This fact suggests that either evolutionary selection or thermodynamic and kinetic folding mechanisms act toward minimizing the entanglement of RNA to an extent that is unparalleled by other types of biomolecules. A possible general strategy for designing synthetic RNA sequences capable of self-tying in a twist-knot fold is finally proposed.
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39
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Baiesi M, Orlandini E, Stella AL. Knotted Globular Ring Polymers: How Topology Affects Statistics and Thermodynamics. Macromolecules 2014. [DOI: 10.1021/ma5020287] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022]
Affiliation(s)
- Marco Baiesi
- Department
of Physics and Astronomy, University of Padua, 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 Padua, Via Marzolo 8, I-35131 Padova, Italy
- INFN - Sezione
di Padova, Via Marzolo 8, I-35131 Padova, Italy
| | - Attilio L. Stella
- Department
of Physics and Astronomy, University of Padua, Via Marzolo 8, I-35131 Padova, Italy
- INFN - Sezione
di Padova, Via Marzolo 8, I-35131 Padova, Italy
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40
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Jamroz M, Niemyska W, Rawdon EJ, Stasiak A, Millett KC, Sułkowski P, Sulkowska JI. KnotProt: a database of proteins with knots and slipknots. Nucleic Acids Res 2014; 43:D306-14. [PMID: 25361973 PMCID: PMC4383900 DOI: 10.1093/nar/gku1059] [Citation(s) in RCA: 138] [Impact Index Per Article: 13.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/14/2023] Open
Abstract
The protein topology database KnotProt, http://knotprot.cent.uw.edu.pl/, collects information about protein structures with open polypeptide chains forming knots or slipknots. The knotting complexity of the cataloged proteins is presented in the form of a matrix diagram that shows users the knot type of the entire polypeptide chain and of each of its subchains. The pattern visible in the matrix gives the knotting fingerprint of a given protein and permits users to determine, for example, the minimal length of the knotted regions (knot's core size) or the depth of a knot, i.e. how many amino acids can be removed from either end of the cataloged protein structure before converting it from a knot to a different type of knot. In addition, the database presents extensive information about the biological functions, families and fold types of proteins with non-trivial knotting. As an additional feature, the KnotProt database enables users to submit protein or polymer chains and generate their knotting fingerprints.
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Affiliation(s)
- Michal Jamroz
- Faculty of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warsaw, Poland
| | - Wanda Niemyska
- Institute of Mathematics, University of Silesia, Bankowa 14, 40-007 Katowice, Poland
| | - 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
| | - Kenneth C Millett
- Department of Mathematics, University of California, Santa Barbara, CA 93106, USA
| | - Piotr Sułkowski
- Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warsaw, Poland California Institute of Technology, Pasadena, CA 91125, USA
| | - Joanna I Sulkowska
- Faculty of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warsaw, Poland Centre of New Technologies, University of Warsaw, Banacha 2c, 02-097, Warsaw, Poland
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41
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An intramolecular lock facilitates folding and stabilizes the tertiary structure of Streptococcus mutans adhesin P1. Proc Natl Acad Sci U S A 2014; 111:15746-51. [PMID: 25331888 DOI: 10.1073/pnas.1413018111] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
The cariogenic bacterium Streptococcus mutans uses adhesin P1 to adhere to tooth surfaces, extracellular matrix components, and other bacteria. A composite model of P1 based on partial crystal structures revealed an unusual complex architecture in which the protein forms an elongated hybrid alpha/polyproline type II helical stalk by folding back on itself to display a globular head at the apex and a globular C-terminal region at the base. The structure of P1's N terminus and the nature of its critical interaction with the C-terminal region remained unknown, however. We have cocrystallized a stable complex of recombinant N- and C-terminal fragments and here describe a previously unidentified topological fold in which these widely discontinuous domains are intimately associated. The structure reveals that the N terminus forms a stabilizing scaffold by wrapping behind the base of P1's elongated stalk and physically "locking" it into place. The structure is stabilized through a highly favorable ΔG(solvation) on complex formation, along with extensive hydrogen bonding. We confirm the functional relevance of this intramolecular interaction using differential scanning calorimetry and circular dichroism to show that disruption of the proper spacing of residues 989-1001 impedes folding and diminishes stability of the full-length molecule, including the stalk. Our findings clarify previously unexplained functional and antigenic properties of P1.
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42
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Abstract
We propose a mechanism in which two molecular knots pass through each other and swap positions along a polymer strand. Associated free energy barriers in our simulations only amount to a few kBT, which may enable the interchange of knots on a single DNA strand.
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43
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Tubiana L. Computational study on the progressive factorization of composite polymer knots into separated prime components. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:052602. [PMID: 25353821 DOI: 10.1103/physreve.89.052602] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/28/2013] [Indexed: 06/04/2023]
Abstract
Using Monte Carlo simulations and advanced knot localization methods, we analyze the length and distribution of prime components in composite knots tied on freely jointed rings. For increasing contour length, we observe the progressive factorization of composite knots into separated prime components. However, we observe that a complete factorization, equivalent to the "decorated ring" picture, is not obtained even for rings of contour lengths N ≃ 3 N(0), about tens of times the most probable length of the prime knots tied on the rings. The decorated ring hypothesis has been used in the literature to justify the factorization of composite knot probabilities into the knotting probabilities of their prime components. Following our results, we suggest that such a hypothesis may not be necessary to explain the factorization of the knotting probabilities, at least when polymers excluding volume is not relevant. We rationalize the behavior of the system through a simple one-dimensional model in which prime knots are replaced by slip links randomly placed on a circle, with the only constraint being that the length of the loops has the same distribution as that of the length of the corresponding prime knots.
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Affiliation(s)
- Luca Tubiana
- Department of Theoretical Physics, Jožef Stefan Institute, Jamova cesta 39, SI-1000 Ljubljana (Slovenia) and SISSA-Scuola Internazionale Superiore di Studi Avanzati Via Bonomea 265, 34136 Trieste, Italy
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Covino R, Skrbić T, Beccara SA, Faccioli P, Micheletti C. The role of non-native interactions in the folding of knotted proteins: insights from molecular dynamics simulations. Biomolecules 2013; 4:1-19. [PMID: 24970203 PMCID: PMC4030985 DOI: 10.3390/biom4010001] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/06/2013] [Revised: 12/10/2013] [Accepted: 12/20/2013] [Indexed: 12/14/2022] Open
Abstract
For several decades, the presence of knots in naturally-occurring proteins was largely ruled out a priori for its supposed incompatibility with the efficiency and robustness of folding processes. For this very same reason, the later discovery of several unrelated families of knotted proteins motivated researchers to look into the physico-chemical mechanisms governing the concerted sequence of folding steps leading to the consistent formation of the same knot type in the same protein location. Besides experiments, computational studies are providing considerable insight into these mechanisms. Here, we revisit a number of such recent investigations within a common conceptual and methodological framework. By considering studies employing protein models with different structural resolution (coarse-grained or atomistic) and various force fields (from pure native-centric to realistic atomistic ones), we focus on the role of native and non-native interactions. For various unrelated instances of knotted proteins, non-native interactions are shown to be very important for favoring the emergence of conformations primed for successful self-knotting events.
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Affiliation(s)
- Roberto Covino
- Department of Physics, University of Trento, Via Sommarive 14, Trento 38123, Italy.
| | - Tatjana Skrbić
- SISSA-Scuola Internazionale Superiore di Studi Avanzati, Via Bonomea 265, Trieste 34136, Italy.
| | - Silvio A Beccara
- Interdisciplinary Laboratory for Computational Science, FBK-CMM and University of Trento,Trento 38123, Italy.
| | - Pietro Faccioli
- Department of Physics, University of Trento, Via Sommarive 14, Trento 38123, Italy.
| | - Cristian Micheletti
- SISSA-Scuola Internazionale Superiore di Studi Avanzati, Via Bonomea 265, Trieste 34136, Italy.
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45
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Waudby CA, Launay H, Cabrita LD, Christodoulou J. Protein folding on the ribosome studied using NMR spectroscopy. PROGRESS IN NUCLEAR MAGNETIC RESONANCE SPECTROSCOPY 2013; 74:57-75. [PMID: 24083462 PMCID: PMC3991860 DOI: 10.1016/j.pnmrs.2013.07.003] [Citation(s) in RCA: 27] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/30/2013] [Revised: 07/17/2013] [Accepted: 07/17/2013] [Indexed: 05/11/2023]
Abstract
NMR spectroscopy is a powerful tool for the investigation of protein folding and misfolding, providing a characterization of molecular structure, dynamics and exchange processes, across a very wide range of timescales and with near atomic resolution. In recent years NMR methods have also been developed to study protein folding as it might occur within the cell, in a de novo manner, by observing the folding of nascent polypeptides in the process of emerging from the ribosome during synthesis. Despite the 2.3 MDa molecular weight of the bacterial 70S ribosome, many nascent polypeptides, and some ribosomal proteins, have sufficient local flexibility that sharp resonances may be observed in solution-state NMR spectra. In providing information on dynamic regions of the structure, NMR spectroscopy is therefore highly complementary to alternative methods such as X-ray crystallography and cryo-electron microscopy, which have successfully characterized the rigid core of the ribosome particle. However, the low working concentrations and limited sample stability associated with ribosome-nascent chain complexes means that such studies still present significant technical challenges to the NMR spectroscopist. This review will discuss the progress that has been made in this area, surveying all NMR studies that have been published to date, and with a particular focus on strategies for improving experimental sensitivity.
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46
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Abstract
Most proteins, in order to perform their biological function, have to fold to a compact native state. The increasing number of knotted and slipknotted proteins identified suggests that proteins are able to manoeuvre around topological barriers during folding. In the present article, we review the current progress in elucidating the knotting process in proteins. Although we concentrate on theoretical approaches, where a knotted topology can be unambiguously detected, comparison with experiments is also reviewed. Numerical simulations suggest that the folding process for small knotted proteins is composed of twisted loop formation and then threading by either slipknot geometries or flipping. As the size of the knotted proteins increases, particularly for more deeply threaded termini, the prevalence of traps in the free energy landscape also increases. Thus, in the case of longer knotted and slipknotted proteins, the folding mechanism is probably supported by chaperones. Overall, results imply that knotted proteins can be folded efficiently and survive evolutionary pressure in order to perform their biological functions.
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47
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Abstract
In the present article, we investigate and review the influence of chain stiffness on self-entanglements and knots in a single polymer chain with Monte Carlo simulations spanning good solvent, theta and globular phases. The last-named are of particular importance as a model system for DNA in viral capsids. Intriguingly, the dependence of knot occurrence and complexity with increasing stiffness is non-trivial, but can be understood with a few simple concepts outlined in the present article.
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48
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a Beccara S, Škrbić T, Covino R, Micheletti C, Faccioli P. Folding pathways of a knotted protein with a realistic atomistic force field. PLoS Comput Biol 2013; 9:e1003002. [PMID: 23555232 PMCID: PMC3605060 DOI: 10.1371/journal.pcbi.1003002] [Citation(s) in RCA: 66] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/29/2012] [Accepted: 02/04/2013] [Indexed: 11/20/2022] Open
Abstract
We report on atomistic simulation of the folding of a natively-knotted protein, MJ0366, based on a realistic force field. To the best of our knowledge this is the first reported effort where a realistic force field is used to investigate the folding pathways of a protein with complex native topology. By using the dominant-reaction pathway scheme we collected about 30 successful folding trajectories for the 82-amino acid long trefoil-knotted protein. Despite the dissimilarity of their initial unfolded configuration, these trajectories reach the natively-knotted state through a remarkably similar succession of steps. In particular it is found that knotting occurs essentially through a threading mechanism, involving the passage of the C-terminal through an open region created by the formation of the native -sheet at an earlier stage. The dominance of the knotting by threading mechanism is not observed in MJ0366 folding simulations using simplified, native-centric models. This points to a previously underappreciated role of concerted amino acid interactions, including non-native ones, in aiding the appropriate order of contact formation to achieve knotting. It has been recently observed that the native structure of proteins can contain knots. These are formed during the folding process and are tightened in a specific (i.e. native) location, along the poly-peptide chain. The existence of knots hence implies a high degree coordination of local and global conformational changes, during the folding reaction. In this work we investigate how the knot is formed and what are the dynamical mechanisms which drive the self-entanglement process. To this end, we report on the first atomistically detailed numerical simulation of the folding of a knotted protein, based on a realistic description of the inter-atomic forces. These simulations show that the knot is formed by following a specific sequence of contacts. The comparison of the findings with those based on simplified folding models suggest that the productive succession of contacts is aided by a concerted interplay of amino acid interactions, arguably including non-native ones.
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Affiliation(s)
| | | | - Roberto Covino
- Physics Department, University of Trento, Trento, Italy
- INFN, Gruppo Collegato di Trento, Trento, Italy
| | | | - Pietro Faccioli
- Physics Department, University of Trento, Trento, Italy
- INFN, Gruppo Collegato di Trento, Trento, Italy
- * E-mail:
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49
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Mohazab AR, Plotkin SS. Polymer uncrossing and knotting in protein folding, and their role in minimal folding pathways. PLoS One 2013; 8:e53642. [PMID: 23365638 PMCID: PMC3554774 DOI: 10.1371/journal.pone.0053642] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/22/2012] [Accepted: 11/30/2012] [Indexed: 11/19/2022] Open
Abstract
We introduce a method for calculating the extent to which chain non-crossing is important in the most efficient, optimal trajectories or pathways for a protein to fold. This involves recording all unphysical crossing events of a ghost chain, and calculating the minimal uncrossing cost that would have been required to avoid such events. A depth-first tree search algorithm is applied to find minimal transformations to fold [Formula: see text], [Formula: see text], [Formula: see text], and knotted proteins. In all cases, the extra uncrossing/non-crossing distance is a small fraction of the total distance travelled by a ghost chain. Different structural classes may be distinguished by the amount of extra uncrossing distance, and the effectiveness of such discrimination is compared with other order parameters. It was seen that non-crossing distance over chain length provided the best discrimination between structural and kinetic classes. The scaling of non-crossing distance with chain length implies an inevitable crossover to entanglement-dominated folding mechanisms for sufficiently long chains. We further quantify the minimal folding pathways by collecting the sequence of uncrossing moves, which generally involve leg, loop, and elbow-like uncrossing moves, and rendering the collection of these moves over the unfolded ensemble as a multiple-transformation "alignment". The consensus minimal pathway is constructed and shown schematically for representative cases of an [Formula: see text], [Formula: see text], and knotted protein. An overlap parameter is defined between pathways; we find that [Formula: see text] proteins have minimal overlap indicating diverse folding pathways, knotted proteins are highly constrained to follow a dominant pathway, and [Formula: see text] proteins are somewhere in between. Thus we have shown how topological chain constraints can induce dominant pathway mechanisms in protein folding.
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Affiliation(s)
- Ali R. Mohazab
- Department of Physics and Astronomy, University of British Columbia, Vancouver, B.C, Canada
| | - Steven S. Plotkin
- Department of Physics and Astronomy, University of British Columbia, Vancouver, B.C, Canada
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50
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Škrbić T, Micheletti C, Faccioli P. The role of non-native interactions in the folding of knotted proteins. PLoS Comput Biol 2012; 8:e1002504. [PMID: 22719235 PMCID: PMC3375218 DOI: 10.1371/journal.pcbi.1002504] [Citation(s) in RCA: 49] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/16/2011] [Accepted: 03/16/2012] [Indexed: 12/29/2022] Open
Abstract
Stochastic simulations of coarse-grained protein models are used to investigate the propensity to form knots in early stages of protein folding. The study is carried out comparatively for two homologous carbamoyltransferases, a natively-knotted N-acetylornithine carbamoyltransferase (AOTCase) and an unknotted ornithine carbamoyltransferase (OTCase). In addition, two different sets of pairwise amino acid interactions are considered: one promoting exclusively native interactions, and the other additionally including non-native quasi-chemical and electrostatic interactions. With the former model neither protein shows a propensity to form knots. With the additional non-native interactions, knotting propensity remains negligible for the natively-unknotted OTCase while for AOTCase it is much enhanced. Analysis of the trajectories suggests that the different entanglement of the two transcarbamylases follows from the tendency of the C-terminal to point away from (for OTCase) or approach and eventually thread (for AOTCase) other regions of partly-folded protein. The analysis of the OTCase/AOTCase pair clarifies that natively-knotted proteins can spontaneously knot during early folding stages and that non-native sequence-dependent interactions are important for promoting and disfavouring early knotting events. Knotted proteins provide an ideal ground for examining how amino acid interactions (which are local) can favor their folding into a native state of non-trivial topology (which is a global property). Some of the mechanisms that can aid knot formation are investigated here by comparing coarse-grained folding simulations of two enzymes that are structurally similar, and yet have natively knotted and unknotted states, respectively. In folding simulations that exclusively promote the formation of native contacts, neither protein forms knots. Strikingly, when sequence-dependent non-native interactions between amino acids are introduced, one observes knotting events but only for the natively-knotted protein. The results support the importance of non-native interactions in favoring or disfavoring knotting events in the early stages of folding.
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Affiliation(s)
- Tatjana Škrbić
- ECT* - European Centre for Theoretical Studies in Nuclear Physics and Related Areas, Villazzano (Trento), Italy
- LISC - Interdisciplinary Laboratory for Computational Science, Povo (Trento), Italy
| | - Cristian Micheletti
- SISSA - Scuola Internazionale Superiore di Studi Avanzati and CNR-IOM Democritos, Trieste, Italy
- * E-mail: (CM); (PF)
| | - Pietro Faccioli
- Dipartimento di Fisica, Università degli Studi di Trento, Povo (Trento), Italy
- INFN - Istituto Nazionale di Fisica Nucleare, Gruppo Collegato di Trento, Povo (Trento), Italy
- * E-mail: (CM); (PF)
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