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Ferreira SGF, Sriramoju MK, Hsu STD, Faísca PFN, Machuqueiro M. Is There a Functional Role for the Knotted Topology in Protein UCH-L1? J Chem Inf Model 2024. [PMID: 39045738 DOI: 10.1021/acs.jcim.4c00880] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/25/2024]
Abstract
Knotted proteins are present in nature, but there is still an open issue regarding the existence of a universal role for these remarkable structures. To address this question, we used classical molecular dynamics (MD) simulations combined with in vitro experiments to investigate the role of the Gordian knot in the catalytic activity of UCH-L1. To create an unknotted form of UCH-L1, we modified its amino acid sequence by truncating several residues from its N-terminus. Remarkably, we find that deleting the first two N-terminal residues leads to a partial loss of enzyme activity with conservation of secondary structural content and knotted topological state. This happens because the integrity of the N-terminus is critical to ensure the correct alignment of the catalytic triad. However, the removal of five residues from the N-terminus, which significantly disrupts the native structure and the topological state, leads to a complete loss of enzymatic activity. Overall, our findings indicate that UCH-L1's catalytic activity depends critically on the integrity of the N-terminus and the secondary structure content, with the latter being strongly coupled with the knotted topological state.
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Affiliation(s)
- Sara G F Ferreira
- BioISI - Instituto de Biossistemas e Ciências Integrativas, Departamento de Química e Bioquímica, Faculdade de Ciências, Universidade de Lisboa, 1749-016 Lisboa, Portugal
| | - Manoj K Sriramoju
- Institute of Biological Chemistry, Academia Sinica, Taipei 11529, Taiwan
| | - Shang-Te Danny Hsu
- Institute of Biological Chemistry, Academia Sinica, Taipei 11529, Taiwan
- International Institute for Sustainability with Knotted Chiral Meta Matter (WPI-SKCM2), Hiroshima University, 1-3-1 Kagamiyama, Higashi-Hiroshima, Hiroshima 739-8526, Japan
- Institute of Biochemical Sciences, National Taiwan University, Taipei 11529, Taiwan
| | - Patrícia F N Faísca
- BioISI - Instituto de Biossistemas e Ciências Integrativas, Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, 1749-016 Lisboa, Portugal
| | - Miguel Machuqueiro
- BioISI - Instituto de Biossistemas e Ciências Integrativas, Departamento de Química e Bioquímica, Faculdade de Ciências, Universidade de Lisboa, 1749-016 Lisboa, Portugal
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2
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Recurrent Generalization of F-Polynomials for Virtual Knots and Links. Symmetry (Basel) 2021. [DOI: 10.3390/sym14010015] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
F-polynomials for virtual knots were defined by Kaur, Prabhakar and Vesnin in 2018 using flat virtual knot invariants. These polynomials naturally generalize Kauffman’s affine index polynomial and use smoothing in the classical crossing of a virtual knot diagram. In this paper, we introduce weight functions for ordered orientable virtual and flat virtual links. A flat virtual link is an equivalence class of virtual links with respect to a local symmetry changing a type of classical crossing in a diagram. By considering three types of smoothing in classical crossings of a virtual link diagram and suitable weight functions, there is provided a recurrent construction for new invariants. It is demonstrated by explicit examples that newly defined polynomial invariants are stronger than F-polynomials.
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3
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Mohamed MS, Hazawa M, Kobayashi A, Guillaud L, Watanabe-Nakayama T, Nakayama M, Wang H, Kodera N, Oshima M, Ando T, Wong RW. Spatiotemporally tracking of nano-biofilaments inside the nuclear pore complex core. Biomaterials 2020; 256:120198. [DOI: 10.1016/j.biomaterials.2020.120198] [Citation(s) in RCA: 25] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/13/2019] [Revised: 04/07/2020] [Accepted: 06/09/2020] [Indexed: 02/07/2023]
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4
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Scalvini B, Sheikhhassani V, Woodard J, Aupič J, Dame RT, Jerala R, Mashaghi A. Topology of Folded Molecular Chains: From Single Biomolecules to Engineered Origami. TRENDS IN CHEMISTRY 2020. [DOI: 10.1016/j.trechm.2020.04.009] [Citation(s) in RCA: 16] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023]
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5
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Škrbić T, Banavar JR, Giacometti A. Chain stiffness bridges conventional polymer and bio-molecular phases. J Chem Phys 2019; 151:174901. [PMID: 31703491 DOI: 10.1063/1.5123720] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/19/2023] Open
Abstract
Chain molecules play important roles in industry and in living cells. Our focus here is on distinct ways of modeling the stiffness inherent in a chain molecule. We consider three types of stiffnesses-one yielding an energy penalty for local bends (energetic stiffness) and the other two forbidding certain classes of chain conformations (entropic stiffness). Using detailed Wang-Landau microcanonical Monte Carlo simulations, we study the interplay between the nature of the stiffness and the ground state conformation of a self-attracting chain. We find a wide range of ground state conformations, including a coil, a globule, a toroid, rods, helices, and zig-zag strands resembling β-sheets, as well as knotted conformations allowing us to bridge conventional polymer phases and biomolecular phases. An analytical mapping is derived between the persistence lengths stemming from energetic and entropic stiffness. Our study shows unambiguously that different stiffnesses play different physical roles and have very distinct effects on the nature of the ground state of the conformation of a chain, even if they lead to identical persistence lengths.
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Affiliation(s)
- Tatjana Škrbić
- Department of Physics and Institute for Theoretical Science, 1274 University of Oregon, Eugene, Oregon 97403-1274, USA
| | - Jayanth R Banavar
- Department of Physics and Institute for Theoretical Science, 1274 University of Oregon, Eugene, Oregon 97403-1274, USA
| | - Achille Giacometti
- Dipartimento di Scienze Molecolari e Nanosistemi, Università Ca' Foscari di Venezia Campus Scientifico, Edificio Alfa, via Torino 155, 30170 Venezia Mestre, Italy
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6
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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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7
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Dorier J, Goundaroulis D, Benedetti F, Stasiak A. Knoto-ID: a tool to study the entanglement of open protein chains using the concept of knotoids. Bioinformatics 2019; 34:3402-3404. [PMID: 29722808 DOI: 10.1093/bioinformatics/bty365] [Citation(s) in RCA: 17] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/09/2017] [Accepted: 05/01/2018] [Indexed: 11/13/2022] Open
Abstract
Summary The backbone of most proteins forms an open curve. To study their entanglement, a common strategy consists in searching for the presence of knots in their backbones using topological invariants. However, this approach requires to close the curve into a loop, which alters the geometry of curve. Knoto-ID allows evaluating the entanglement of open curves without the need to close them, using the recent concept of knotoids which is a generalization of the classical knot theory to open curves. Knoto-ID can analyse the global topology of the full chain as well as the local topology by exhaustively studying all subchains or only determining the knotted core. Knoto-ID permits to localize topologically non-trivial protein folds that are not detected by informatics tools detecting knotted protein folds. Availability and implementation Knoto-ID is written in C++ and includes R (www.R-project.org) scripts to generate plots of projections maps, fingerprint matrices and disk matrices. Knoto-ID is distributed under the GNU General Public License (GPL), version 2 or any later version and is available at https://github.com/sib-swiss/Knoto-ID. A binary distribution for Mac OS X, Linux and Windows with detailed user guide and examples can be obtained from https://www.vital-it.ch/software/Knoto-ID.
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Affiliation(s)
- Julien Dorier
- Vital-IT, SIB Swiss Institute of Bioinformatics, Lausanne, Switzerland.,Center for Integrative Genomics, University of Lausanne, Lausanne, Switzerland
| | - Dimos Goundaroulis
- Center for Integrative Genomics, University of Lausanne, Lausanne, Switzerland.,SIB Swiss Institute of Bioinformatics, Lausanne, Switzerland
| | - Fabrizio Benedetti
- Vital-IT, SIB Swiss Institute of Bioinformatics, Lausanne, Switzerland.,Center for Integrative Genomics, University of Lausanne, Lausanne, Switzerland
| | - Andrzej Stasiak
- Center for Integrative Genomics, University of Lausanne, Lausanne, Switzerland.,SIB Swiss Institute of Bioinformatics, Lausanne, Switzerland
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Especial J, Nunes A, Rey A, Faísca PF. Hydrophobic confinement modulates thermal stability and assists knotting in the folding of tangled proteins. Phys Chem Chem Phys 2019; 21:11764-11775. [PMID: 31114834 DOI: 10.1039/c9cp01701a] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/27/2023]
Abstract
There is growing support for the idea that the in vivo folding process of knotted proteins is assisted by chaperonins, but the mechanism of chaperonin assisted folding remains elusive. Here, we conduct extensive Monte Carlo simulations of lattice and off-lattice models to explore the effects of confinement and hydrophobic intermolecular interactions with the chaperonin cage in the folding and knotting processes. We find that moderate to high protein-cavity interactions (which are likely to be established in the beginning of the chaperonin working cycle) cause an energetic destabilization of the protein that overcomes the entropic stabilization driven by excluded volume, and leads to a decrease of the melting temperature relative to bulk conditions. Moreover, mild-to-moderate hydrophobic interactions with the cavity (which would be established later in the cycle) lead to a significant enhancement of knotting probability in relation to bulk conditions while simultaneously moderating the effect of steric confinement in the enhancement of thermal stability. Our results thus indicate that the chaperonin may be able to assist knotting without simultaneously thermally stabilizing potential misfolded states to a point that would hamper productive folding thus compromising its functional role.
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Affiliation(s)
- João Especial
- Departamento de Física, Universidade de Lisboa, Campo Grande, Ed. C8, 1749-016 Lisboa, Portugal.
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9
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Abstract
How knotted proteins fold has remained controversial since the identification of deeply knotted proteins nearly two decades ago. Both computational and experimental approaches have been used to investigate protein knot formation. Motivated by the computer simulations of Bölinger et al. [Bölinger D, et al. (2010) PLoS Comput Biol 6:e1000731] for the folding of the [Formula: see text]-knotted α-haloacid dehalogenase (DehI) protein, we introduce a topological description of knot folding that could describe pathways for the formation of all currently known protein knot types and predicts knot types that might be identified in the future. We analyze fingerprint data from crystal structures of protein knots as evidence that particular protein knots may fold according to specific pathways from our theory. Our results confirm Taylor's twisted hairpin theory of knot folding for the [Formula: see text]-knotted proteins and the [Formula: see text]-knotted ketol-acid reductoisomerases and present alternative folding mechanisms for the [Formula: see text]-knotted phytochromes and the [Formula: see text]- and [Formula: see text]-knotted proteins.
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10
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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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11
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Goundaroulis D, Gügümcü N, Lambropoulou S, Dorier J, Stasiak A, Kauffman L. Topological Models for Open-Knotted Protein Chains Using the Concepts of Knotoids and Bonded Knotoids. Polymers (Basel) 2017; 9:polym9090444. [PMID: 30965745 PMCID: PMC6418563 DOI: 10.3390/polym9090444] [Citation(s) in RCA: 35] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/26/2017] [Revised: 09/08/2017] [Accepted: 09/11/2017] [Indexed: 11/16/2022] Open
Abstract
In this paper we introduce a method that offers a detailed overview of the entanglement of an open protein chain. Further, we present a purely topological model for classifying open protein chains by also taking into account any bridge involving the backbone. To this end, we implemented the concepts of planar knotoids and bonded knotoids. We show that the planar knotoids technique provides more refined information regarding the knottedness of a protein when compared to established methods in the literature. Moreover, we demonstrate that our topological model for bonded proteins is robust enough to distinguish all types of lassos in proteins.
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Affiliation(s)
- Dimos Goundaroulis
- Center for Integrative Genomics, University of Lausanne, 1015 Lausanne, Switzerland.
- SIB Swiss Institute of Bioinformatics, 1015 Lausanne, Switzerland.
| | - Neslihan Gügümcü
- Department of Mathematics, National Technical University of Athens, Zografou Campus, 15780 Athens, Greece.
| | - Sofia Lambropoulou
- Department of Mathematics, National Technical University of Athens, Zografou Campus, 15780 Athens, Greece.
| | - Julien Dorier
- Center for Integrative Genomics, University of Lausanne, 1015 Lausanne, Switzerland.
- Vital-IT, SIB Swiss Institute of Bioinformatics, 1015 Lausanne, Switzerland.
| | - Andrzej Stasiak
- Center for Integrative Genomics, University of Lausanne, 1015 Lausanne, Switzerland.
- SIB Swiss Institute of Bioinformatics, 1015 Lausanne, Switzerland.
| | - Louis Kauffman
- Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, Chicago, IL 60607-7045, USA.
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12
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Goundaroulis D, Dorier J, Benedetti F, Stasiak A. Studies of global and local entanglements of individual protein chains using the concept of knotoids. Sci Rep 2017; 7:6309. [PMID: 28740166 PMCID: PMC5524787 DOI: 10.1038/s41598-017-06649-3] [Citation(s) in RCA: 33] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/02/2017] [Accepted: 06/20/2017] [Indexed: 11/23/2022] Open
Abstract
We study here global and local entanglements of open protein chains by implementing the concept of knotoids. Knotoids have been introduced in 2012 by Vladimir Turaev as a generalization of knots in 3-dimensional space. More precisely, knotoids are diagrams representing projections of open curves in 3D space, in contrast to knot diagrams which represent projections of closed curves in 3D space. The intrinsic difference with classical knot theory is that the generalization provided by knotoids admits non-trivial topological entanglement of the open curves provided that their geometry is frozen as it is the case for crystallized proteins. Consequently, our approach doesn’t require the closure of chains into loops which implies that the geometry of analysed chains does not need to be changed by closure in order to characterize their topology. Our study revealed that the knotoid approach detects protein regions that were classified earlier as knotted and also new, topologically interesting regions that we classify as pre-knotted.
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Affiliation(s)
- Dimos Goundaroulis
- Center for Integrative Genomics, University of Lausanne, 1015, Lausanne, Switzerland.,Swiss Institute of Bioinformatics, 1015, Lausanne, Switzerland
| | - Julien Dorier
- Center for Integrative Genomics, University of Lausanne, 1015, Lausanne, Switzerland.,Vital-IT, SIB Swiss Institute of Bioinformatics, 1015, Lausanne, Switzerland
| | - Fabrizio Benedetti
- Center for Integrative Genomics, University of Lausanne, 1015, Lausanne, Switzerland.,Vital-IT, SIB Swiss Institute of Bioinformatics, 1015, Lausanne, Switzerland
| | - Andrzej Stasiak
- Center for Integrative Genomics, University of Lausanne, 1015, Lausanne, Switzerland. .,Swiss Institute of Bioinformatics, 1015, Lausanne, Switzerland.
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