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Sugiyama M, Kosik KS, Panagiotou E. Mathematical topology and geometry-based classification of tauopathies. Sci Rep 2024; 14:7560. [PMID: 38555402 PMCID: PMC10981734 DOI: 10.1038/s41598-024-58221-5] [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: 12/29/2023] [Accepted: 03/26/2024] [Indexed: 04/02/2024] Open
Abstract
Neurodegenerative diseases, like Alzheimer's, are associated with the presence of neurofibrillary lesions formed by tau protein filaments in the cerebral cortex. While it is known that different morphologies of tau filaments characterize different neurodegenerative diseases, there are few metrics of global and local structure complexity that enable to quantify their structural diversity rigorously. In this manuscript, we employ for the first time mathematical topology and geometry to classify neurodegenerative diseases by using cryo-electron microscopy structures of tau filaments that are available in the Protein Data Bank. By employing mathematical topology metrics (Gauss linking integral, writhe and second Vassiliev measure) we achieve a consistent, but more refined classification of tauopathies, than what was previously observed through visual inspection. Our results reveal a hierarchy of classification from global to local topology and geometry characteristics. In particular, we find that tauopathies can be classified with respect to the handedness of their global conformations and the handedness of the relative orientations of their repeats. Progressive supranuclear palsy is identified as an outlier, with a more complex structure than the rest, reflected by a small, but observable knotoid structure (a diagrammatic structure representing non-trivial topology). This topological characteristic can be attributed to a pattern in the beginning of the R3 repeat that is present in all tauopathies but at different extent. Moreover, by comparing single filament to paired filament structures within tauopathies we find a consistent change in the side-chain orientations with respect to the alpha carbon atoms at the area of interaction.
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Affiliation(s)
- Masumi Sugiyama
- Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN, 37403, USA
| | - Kenneth S Kosik
- Neuroscience Research Institute and Department of Molecular, Cellular, and Developmental Biology, University of California Santa Barbara, Santa Barbara, CA, 93106, USA
| | - Eleni Panagiotou
- School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ, 85281, USA.
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2
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Hsu MF, Sriramoju MK, Lai CH, Chen YR, Huang JS, Ko TP, Huang KF, Hsu STD. Structure, dynamics, and stability of the smallest and most complex 7 1 protein knot. J Biol Chem 2024; 300:105553. [PMID: 38072060 PMCID: PMC10840475 DOI: 10.1016/j.jbc.2023.105553] [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: 06/29/2023] [Revised: 11/21/2023] [Accepted: 12/04/2023] [Indexed: 12/29/2023] Open
Abstract
Proteins can spontaneously tie a variety of intricate topological knots through twisting and threading of the polypeptide chains. Recently developed artificial intelligence algorithms have predicted several new classes of topological knotted proteins, but the predictions remain to be authenticated experimentally. Here, we showed by X-ray crystallography and solution-state NMR spectroscopy that Q9PR55, an 89-residue protein from Ureaplasma urealyticum, possesses a novel 71 knotted topology that is accurately predicted by AlphaFold 2, except for the flexible N terminus. Q9PR55 is monomeric in solution, making it the smallest and most complex knotted protein known to date. In addition to its exceptional chemical stability against urea-induced unfolding, Q9PR55 is remarkably robust to resist the mechanical unfolding-coupled proteolysis by a bacterial proteasome, ClpXP. Our results suggest that the mechanical resistance against pulling-induced unfolding is determined by the complexity of the knotted topology rather than the size of the molecule.
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Affiliation(s)
- Min-Feng Hsu
- Institute of Biological Chemistry, Academia Sinica, Taipei, Taiwan
| | | | - Chih-Hsuan Lai
- Institute of Biological Chemistry, Academia Sinica, Taipei, Taiwan
| | - Yun-Ru Chen
- Academia Sinica Protein Clinic, Academia Sinica, Taipei, Taiwan
| | - Jing-Siou Huang
- Academia Sinica Protein Clinic, Academia Sinica, Taipei, Taiwan
| | - Tzu-Ping Ko
- Institute of Biological Chemistry, Academia Sinica, Taipei, Taiwan
| | - Kai-Fa Huang
- Institute of Biological Chemistry, Academia Sinica, Taipei, Taiwan; Academia Sinica Protein Clinic, Academia Sinica, Taipei, Taiwan
| | - Shang-Te Danny Hsu
- Institute of Biological Chemistry, Academia Sinica, Taipei, Taiwan; Academia Sinica Protein Clinic, Academia Sinica, Taipei, Taiwan; Institute of Biochemical Sciences, National Taiwan University, Taipei, Taiwan; International Institute for Sustainability with Knotted Chiral Meta Matter (WPI-SKCM(2)), Hiroshima University, Higashihiroshima, Japan.
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3
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Zayats V, Sikora M, Perlinska AP, Stasiulewicz A, Gren BA, Sulkowska JI. Conservation of knotted and slipknotted topology in transmembrane transporters. Biophys J 2023; 122:4528-4541. [PMID: 37919904 PMCID: PMC10719070 DOI: 10.1016/j.bpj.2023.10.031] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/21/2023] [Revised: 08/25/2023] [Accepted: 10/30/2023] [Indexed: 11/04/2023] Open
Abstract
The existence of nontrivial topology is well accepted in globular proteins but not in membrane proteins. Our comprehensive topological analysis of the Protein Data Bank structures reveals 18 families of transmembrane proteins with nontrivial topology, showing that they constitute a significant number of membrane proteins. Moreover, we found that they comprise one of the largest groups of secondary active transporters. We classified them based on their knotted fingerprint into four groups: three slipknotted and one knotted. Unexpectedly, we found that the same protein can possess two distinct slipknot motifs that correspond to its outward- and inward-open conformational state. Based on the analysis of structures and knotted fingerprints, we show that slipknot topology is directly involved in the conformational transition and substrate transfer. Therefore, entanglement can be used to classify proteins and to find their structure-function relationship. Furthermore, based on the topological analysis of the transmembrane protein structures predicted by AlphaFold, we identified new potentially slipknotted protein families.
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Affiliation(s)
- Vasilina Zayats
- Centre of New Technologies, University of Warsaw, Warsaw, Poland
| | - Maciej Sikora
- Centre of New Technologies, University of Warsaw, Warsaw, Poland; Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Warsaw, Poland
| | | | - Adam Stasiulewicz
- Centre of New Technologies, University of Warsaw, Warsaw, Poland; Department of Drug Chemistry, Faculty of Pharmacy, Medical University of Warsaw, Warsaw, Poland
| | - Bartosz A Gren
- Centre of New Technologies, University of Warsaw, Warsaw, Poland
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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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Dabrowski-Tumanski P, Stasiak A. AlphaFold Blindness to Topological Barriers Affects Its Ability to Correctly Predict Proteins' Topology. Molecules 2023; 28:7462. [PMID: 38005184 PMCID: PMC10672856 DOI: 10.3390/molecules28227462] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/22/2023] [Revised: 11/03/2023] [Accepted: 11/04/2023] [Indexed: 11/26/2023] Open
Abstract
AlphaFold is a groundbreaking deep learning tool for protein structure prediction. It achieved remarkable accuracy in modeling many 3D structures while taking as the user input only the known amino acid sequence of proteins in question. Intriguingly though, in the early steps of each individual structure prediction procedure, AlphaFold does not respect topological barriers that, in real proteins, result from the reciprocal impermeability of polypeptide chains. This study aims to investigate how this failure to respect topological barriers affects AlphaFold predictions with respect to the topology of protein chains. We focus on such classes of proteins that, during their natural folding, reproducibly form the same knot type on their linear polypeptide chain, as revealed by their crystallographic analysis. We use partially artificial test constructs in which the mutual non-permeability of polypeptide chains should not permit the formation of complex composite knots during natural protein folding. We find that despite the formal impossibility that the protein folding process could produce such knots, AlphaFold predicts these proteins to form complex composite knots. Our study underscores the necessity for cautious interpretation and further validation of topological features in protein structures predicted by AlphaFold.
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Affiliation(s)
- Pawel Dabrowski-Tumanski
- Faculty of Mathematics and Natural Sciences, School of Exact Sciences, Cardinal Wyszynski University in Warsaw, Wóycickiego 1/3, 01-938 Warsaw, Poland
| | - Andrzej Stasiak
- Center for Integrative Genomics, University of Lausanne, 1015 Lausanne, Switzerland
- SIB Swiss Institute of Bioinformatics, 1015 Lausanne, Switzerland
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Hou Y, Xie T, He L, Tao L, Huang J. Topological links in predicted protein complex structures reveal limitations of AlphaFold. Commun Biol 2023; 6:1098. [PMID: 37898666 PMCID: PMC10613300 DOI: 10.1038/s42003-023-05489-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/21/2023] [Accepted: 10/19/2023] [Indexed: 10/30/2023] Open
Abstract
AlphaFold is making great progress in protein structure prediction, not only for single-chain proteins but also for multi-chain protein complexes. When using AlphaFold-Multimer to predict protein‒protein complexes, we observed some unusual structures in which chains are looped around each other to form topologically intertwining links at the interface. Based on physical principles, such topological links should generally not exist in native protein complex structures unless covalent modifications of residues are involved. Although it is well known and has been well studied that protein structures may have topologically complex shapes such as knots and links, existing methods are hampered by the chain closure problem and show poor performance in identifying topologically linked structures in protein‒protein complexes. Therefore, we address the chain closure problem by using sliding windows from a local perspective and propose an algorithm to measure the topological-geometric features that can be used to identify topologically linked structures. An application of the method to AlphaFold-Multimer-predicted protein complex structures finds that approximately 1.72% of the predicted structures contain topological links. The method presented in this work will facilitate the computational study of protein‒protein interactions and help further improve the structural prediction of multi-chain protein complexes.
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Affiliation(s)
- Yingnan Hou
- Key Laboratory of Structural Biology of Zhejiang Province, School of Life Sciences, Westlake University, 18 Shilongshan Road, Hangzhou, 310024, Zhejiang, China
- Westlake AI Therapeutics Lab, Westlake Laboratory of Life Sciences and Biomedicine, 18 Shilongshan Road, Hangzhou, 310024, Zhejiang, China
| | - Tengyu Xie
- Key Laboratory of Structural Biology of Zhejiang Province, School of Life Sciences, Westlake University, 18 Shilongshan Road, Hangzhou, 310024, Zhejiang, China
- Westlake AI Therapeutics Lab, Westlake Laboratory of Life Sciences and Biomedicine, 18 Shilongshan Road, Hangzhou, 310024, Zhejiang, China
| | - Liuqing He
- Key Laboratory of Structural Biology of Zhejiang Province, School of Life Sciences, Westlake University, 18 Shilongshan Road, Hangzhou, 310024, Zhejiang, China
- Center for Infectious Disease Research, Westlake Laboratory of Life Sciences and Biomedicine, 18 Shilongshan Road, Hangzhou, 310024, Zhejiang, China
| | - Liang Tao
- Key Laboratory of Structural Biology of Zhejiang Province, School of Life Sciences, Westlake University, 18 Shilongshan Road, Hangzhou, 310024, Zhejiang, China
- Center for Infectious Disease Research, Westlake Laboratory of Life Sciences and Biomedicine, 18 Shilongshan Road, Hangzhou, 310024, Zhejiang, China
| | - Jing Huang
- Key Laboratory of Structural Biology of Zhejiang Province, School of Life Sciences, Westlake University, 18 Shilongshan Road, Hangzhou, 310024, Zhejiang, China.
- Westlake AI Therapeutics Lab, Westlake Laboratory of Life Sciences and Biomedicine, 18 Shilongshan Road, Hangzhou, 310024, Zhejiang, China.
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Doyle LA, Takushi B, Kibler RD, Milles LF, Orozco CT, Jones JD, Jackson SE, Stoddard BL, Bradley P. De novo design of knotted tandem repeat proteins. Nat Commun 2023; 14:6746. [PMID: 37875492 PMCID: PMC10598012 DOI: 10.1038/s41467-023-42388-y] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/17/2023] [Accepted: 10/09/2023] [Indexed: 10/26/2023] Open
Abstract
De novo protein design methods can create proteins with folds not yet seen in nature. These methods largely focus on optimizing the compatibility between the designed sequence and the intended conformation, without explicit consideration of protein folding pathways. Deeply knotted proteins, whose topologies may introduce substantial barriers to folding, thus represent an interesting test case for protein design. Here we report our attempts to design proteins with trefoil (31) and pentafoil (51) knotted topologies. We extended previously described algorithms for tandem repeat protein design in order to construct deeply knotted backbones and matching designed repeat sequences (N = 3 repeats for the trefoil and N = 5 for the pentafoil). We confirmed the intended conformation for the trefoil design by X ray crystallography, and we report here on this protein's structure, stability, and folding behaviour. The pentafoil design misfolded into an asymmetric structure (despite a 5-fold symmetric sequence); two of the four repeat-repeat units matched the designed backbone while the other two diverged to form local contacts, leading to a trefoil rather than pentafoil knotted topology. Our results also provide insights into the folding of knotted proteins.
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Affiliation(s)
- Lindsey A Doyle
- Division of Basic Sciences, Fred Hutchinson Cancer Center, 1100 Fairview Ave. North, Seattle, WA, 98109, USA
| | - Brittany Takushi
- Division of Basic Sciences, Fred Hutchinson Cancer Center, 1100 Fairview Ave. North, Seattle, WA, 98109, USA
| | - Ryan D Kibler
- Department of Biochemistry, University of Washington, Seattle, WA, 98195, USA
| | - Lukas F Milles
- Department of Biochemistry, University of Washington, Seattle, WA, 98195, USA
| | - Carolina T Orozco
- Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge, CB2 1EW, UK
| | - Jonathan D Jones
- Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge, CB2 1EW, UK
| | - Sophie E Jackson
- Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge, CB2 1EW, UK
| | - Barry L Stoddard
- Division of Basic Sciences, Fred Hutchinson Cancer Center, 1100 Fairview Ave. North, Seattle, WA, 98109, USA.
| | - Philip Bradley
- Division of Basic Sciences, Fred Hutchinson Cancer Center, 1100 Fairview Ave. North, Seattle, WA, 98109, USA.
- Division of Public Health Sciences and Program in Computational Biology, Fred Hutchinson Cancer Center, 1100 Fairview Ave. N, Seattle, WA, 98009, USA.
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8
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Especial JNC, Faísca PFN. Effects of sequence-dependent non-native interactions in equilibrium and kinetic folding properties of knotted proteins. J Chem Phys 2023; 159:065101. [PMID: 37551809 DOI: 10.1063/5.0160886] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/06/2023] [Accepted: 07/24/2023] [Indexed: 08/09/2023] Open
Abstract
Determining the role of non-native interactions in folding dynamics, kinetics, and mechanisms is a classic problem in protein folding. More recently, this question has witnessed a renewed interest in light of the hypothesis that knotted proteins require the assistance of non-native interactions to fold efficiently. Here, we conduct extensive equilibrium and kinetic Monte Carlo simulations of a simple off-lattice C-alpha model to explore the role of non-native interactions in the thermodynamics and kinetics of three proteins embedding a trefoil knot in their native structure. We find that equilibrium knotted conformations are stabilized by non-native interactions that are non-local, and proximal to native ones, thus enhancing them. Additionally, non-native interactions increase the knotting frequency at high temperatures, and in partially folded conformations below the transition temperatures. Although non-native interactions clearly enhance the efficiency of transition from an unfolded conformation to a partially folded knotted one, they are not required to efficiently fold a knotted protein. Indeed, a native-centric interaction potential drives the most efficient folding transition, provided that the simulation temperature is well below the transition temperature of the considered model system.
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Affiliation(s)
- João N C Especial
- Departamento de Física, Faculdade de Ciências, Ed. C8, Universidade de Lisboa, Campo Grande, Lisboa, Portugal
- BioISI-Biosystems and Integrative Sciences Institute, Faculdade de Ciências, Universidade de Lisboa, Campo Grande, Lisboa, Portugal
| | - Patrícia F N Faísca
- Departamento de Física, Faculdade de Ciências, Ed. C8, Universidade de Lisboa, Campo Grande, Lisboa, Portugal
- BioISI-Biosystems and Integrative Sciences Institute, Faculdade de Ciências, Universidade de Lisboa, Campo Grande, Lisboa, Portugal
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