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Baldwin Q, Sumpter B, Panagiotou E. The Local Topological Free Energy of the SARS-CoV-2 Spike Protein. Polymers (Basel) 2022; 14:polym14153014. [PMID: 35893978 PMCID: PMC9332627 DOI: 10.3390/polym14153014] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/04/2022] [Revised: 07/15/2022] [Accepted: 07/19/2022] [Indexed: 02/04/2023] Open
Abstract
The novel coronavirus SARS-CoV-2 infects human cells using a mechanism that involves binding and structural rearrangement of its Spike protein. Understanding protein rearrangement and identifying specific amino acids where mutations affect protein rearrangement has attracted much attention for drug development. In this manuscript, we use a mathematical method to characterize the local topology/geometry of the SARS-CoV-2 Spike protein backbone. Our results show that local conformational changes in the FP, HR1, and CH domains are associated with global conformational changes in the RBD domain. The SARS-CoV-2 variants analyzed in this manuscript (alpha, beta, gamma, delta Mink, G614, N501) show differences in the local conformations of the FP, HR1, and CH domains as well. Finally, most mutations of concern are either in or in the vicinity of high local topological free energy conformations, suggesting that high local topological free energy conformations could be targets for mutations with significant impact of protein function. Namely, the residues 484, 570, 614, 796, and 969, which are present in variants of concern and are targeted as important in protein function, are predicted as such from our model.
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Affiliation(s)
- Quenisha Baldwin
- Department of Biology, Tuskegee University, Tuskegee, AL 36088, USA;
| | - Bobby Sumpter
- Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA;
| | - Eleni Panagiotou
- Department of Mathematics and SimCenter, University of Tennessee at Chattanooga, Chattanooga, TN 37403, USA
- Correspondence: or
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2
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Baldwin Q, Panagiotou E. The local topological free energy of proteins. J Theor Biol 2021; 529:110854. [PMID: 34358536 DOI: 10.1016/j.jtbi.2021.110854] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/06/2021] [Revised: 07/27/2021] [Accepted: 07/29/2021] [Indexed: 11/16/2022]
Abstract
Protein folding, the process by which proteins attain a 3-dimensional conformation necessary for their function, remains an important unsolved problem in biology. A major gap in our understanding is how local properties of proteins relate to their global properties. In this manuscript, we use the Writhe and Torsion to introduce a new local topological/geometrical free energy that can be associated to 4 consecutive amino acids along the protein backbone. By analyzing a culled protein dataset from the PDB, our results show that high local topological free energy conformations are independent of sequence and may be involved in the rate limiting step in protein folding. By analyzing a set of 2-state single domain proteins, we find that the total local topological free energy of these proteins correlates with the experimentally observed folding rates reported in Plaxco et al. (2000).
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Affiliation(s)
- Quenisha Baldwin
- Department of Biology, Tuskegee University, 1200 W Montgomery Rd, Tuskegee, AL 36088, USA
| | - Eleni Panagiotou
- Department of Mathematics and SimCenter, University of Tennessee at Chattanooga, 615 McCallie Ave, Chattanooga, TN 37403, USA.
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3
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DNA-Topology Simplification by Topoisomerases. Molecules 2021; 26:molecules26113375. [PMID: 34204901 PMCID: PMC8199745 DOI: 10.3390/molecules26113375] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/25/2021] [Revised: 05/20/2021] [Accepted: 05/26/2021] [Indexed: 11/17/2022] Open
Abstract
The topological properties of DNA molecules, supercoiling, knotting, and catenation, are intimately connected with essential biological processes, such as gene expression, replication, recombination, and chromosome segregation. Non-trivial DNA topologies present challenges to the molecular machines that process and maintain genomic information, for example, by creating unwanted DNA entanglements. At the same time, topological distortion can facilitate DNA-sequence recognition through localized duplex unwinding and longer-range loop-mediated interactions between the DNA sequences. Topoisomerases are a special class of essential enzymes that homeostatically manage DNA topology through the passage of DNA strands. The activities of these enzymes are generally investigated using circular DNA as a model system, in which case it is possible to directly assay the formation and relaxation of DNA supercoils and the formation/resolution of knots and catenanes. Some topoisomerases use ATP as an energy cofactor, whereas others act in an ATP-independent manner. The free energy of ATP hydrolysis can be used to drive negative and positive supercoiling or to specifically relax DNA topologies to levels below those that are expected at thermodynamic equilibrium. The latter activity, which is known as topology simplification, is thus far exclusively associated with type-II topoisomerases and it can be understood through insight into the detailed non-equilibrium behavior of type-II enzymes. We use a non-equilibrium topological-network approach, which stands in contrast to the equilibrium models that are conventionally used in the DNA-topology field, to gain insights into the rates that govern individual transitions between topological states. We anticipate that our quantitative approach will stimulate experimental work and the theoretical/computational modeling of topoisomerases and similar enzyme systems.
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O'Donnol D, Stasiak A, Buck D. Two convergent pathways of DNA knotting in replicating DNA molecules as revealed by θ-curve analysis. Nucleic Acids Res 2019; 46:9181-9188. [PMID: 29982678 PMCID: PMC6158496 DOI: 10.1093/nar/gky559] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/23/2018] [Accepted: 06/13/2018] [Indexed: 11/12/2022] Open
Abstract
During DNA replication in living cells some DNA knots are inadvertently produced by DNA topoisomerases facilitating progression of replication forks. The types of DNA knots formed are conditioned by the 3D organization of replicating DNA molecules. Therefore, by characterizing formed DNA knots it is possible to infer the 3D arrangement of replicating DNA molecules. This topological inference method is highly developed for knotted DNA circles. However, partially replicated DNA molecules have the form of θ-curves. In this article, we use mathematical formalism of θ-curves to characterize the full possibilities of how knotting can occur during replication of DNA molecules in vivo. To do this, we reanalyze earlier experimental studies of knotted, partially replicated DNA molecules and the previously proposed pathway of their formation. We propose a general model of knotting in replication intermediates, and demonstrate that there is an additional, equally important, parallel knotting pathway that also explains how DNA topoisomerases can produce experimentally observed knotted θ-curves. Interestingly, both pathways require intertwining of freshly replicated sister duplexes (precatenanes).
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Affiliation(s)
- Danielle O'Donnol
- Department of Mathematics, Indiana University Bloomington, 831 E. Third Street, Bloomington, IN 47405, USA
| | - Andrzej Stasiak
- Center for Integrative Genomics, University of Lausanne,1015 Lausanne, Switzerland.,Swiss Institute of Bioinformatics, 1015 Lausanne, Switzerland
| | - Dorothy Buck
- Centre for Mathematical Biology, and Department of Mathematical Sciences, University of Bath, North Rd, Bath BA2 7AY, England
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5
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Valdés A, Segura J, Dyson S, Martínez-García B, Roca J. DNA knots occur in intracellular chromatin. Nucleic Acids Res 2019; 46:650-660. [PMID: 29149297 PMCID: PMC5778459 DOI: 10.1093/nar/gkx1137] [Citation(s) in RCA: 30] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/25/2017] [Accepted: 10/28/2017] [Indexed: 01/12/2023] Open
Abstract
In vivo DNA molecules are narrowly folded within chromatin fibers and self-interacting chromatin domains. Therefore, intra-molecular DNA entanglements (knots) might occur via DNA strand passage activity of topoisomerase II. Here, we assessed the presence of such DNA knots in a variety of yeast circular minichromosomes. We found that small steady state fractions of DNA knots are common in intracellular chromatin. These knots occur irrespective of DNA replication and cell proliferation, though their abundance is reduced during DNA transcription. We found also that in vivo DNA knotting probability does not scale proportionately with chromatin length: it reaches a value of ∼0.025 in domains of ∼20 nucleosomes but tends to level off in longer chromatin fibers. These figures suggest that, while high flexibility of nucleosomal fibers and clustering of nearby nucleosomes facilitate DNA knotting locally, some mechanism minimizes the scaling of DNA knot formation throughout intracellular chromatin. We postulate that regulation of topoisomerase II activity and the fractal architecture of chromatin might be crucial to prevent a potentially massive and harmful self-entanglement of DNA molecules in vivo.
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Affiliation(s)
- Antonio Valdés
- Molecular Biology Institute of Barcelona (IBMB); Spanish National Research Council (CSIC); Barcelona 08028; Spain
| | - Joana Segura
- Molecular Biology Institute of Barcelona (IBMB); Spanish National Research Council (CSIC); Barcelona 08028; Spain
| | - Sílvia Dyson
- Molecular Biology Institute of Barcelona (IBMB); Spanish National Research Council (CSIC); Barcelona 08028; Spain
| | - Belén Martínez-García
- Molecular Biology Institute of Barcelona (IBMB); Spanish National Research Council (CSIC); Barcelona 08028; Spain
| | - Joaquim Roca
- Molecular Biology Institute of Barcelona (IBMB); Spanish National Research Council (CSIC); Barcelona 08028; Spain
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6
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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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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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FtsK-dependent XerCD-dif recombination unlinks replication catenanes in a stepwise manner. Proc Natl Acad Sci U S A 2013; 110:20906-11. [PMID: 24218579 DOI: 10.1073/pnas.1308450110] [Citation(s) in RCA: 56] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
In Escherichia coli, complete unlinking of newly replicated sister chromosomes is required to ensure their proper segregation at cell division. Whereas replication links are removed primarily by topoisomerase IV, XerC/XerD-dif site-specific recombination can mediate sister chromosome unlinking in Topoisomerase IV-deficient cells. This reaction is activated at the division septum by the DNA translocase FtsK, which coordinates the last stages of chromosome segregation with cell division. It has been proposed that, after being activated by FtsK, XerC/XerD-dif recombination removes DNA links in a stepwise manner. Here, we provide a mathematically rigorous characterization of this topological mechanism of DNA unlinking. We show that stepwise unlinking is the only possible pathway that strictly reduces the complexity of the substrates at each step. Finally, we propose a topological mechanism for this unlinking reaction.
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Abstract
Difference topology is an experimental technique that can be used to unveil the topological structure adopted by two or more DNA segments in a stable protein–DNA complex. Difference topology has also been used to detect intermediates in a reaction pathway and to investigate the role of DNA supercoiling. In the present article, we review difference topology as applied to the Mu transpososome. The tools discussed can be applied to any stable nucleoprotein complex.
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Predicting Knot and Catenane Type of Products of Site-Specific Recombination on Twist Knot Substrates. J Mol Biol 2011; 411:350-67. [DOI: 10.1016/j.jmb.2011.05.048] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/22/2011] [Revised: 05/30/2011] [Accepted: 05/31/2011] [Indexed: 11/19/2022]
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11
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Topological Analysis of Enzymatic Actions on DNA Polyhedral Links. Bull Math Biol 2011; 73:3030-46. [DOI: 10.1007/s11538-011-9659-z] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/21/2010] [Accepted: 04/05/2011] [Indexed: 10/18/2022]
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Yang Z, Li D, Li T. Design and synthesis of catenated rings based on toroidal DNA structures. Chem Commun (Camb) 2011; 47:11930-2. [DOI: 10.1039/c1cc14957a] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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13
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Abstract
Knots appear in a wide variety of biophysical systems, ranging from biopolymers, such as DNA and proteins, to macroscopic objects, such as umbilical cords and catheters. Although significant advancements have been made in the mathematical theory of knots and some progress has been made in the statistical mechanics of knots in idealized chains, the mechanisms and dynamics of knotting in biophysical systems remain far from fully understood. We report on recent progress in the biophysics of knotting-the formation, characterization, and dynamics of knots in various biophysical contexts.
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Affiliation(s)
- Dario Meluzzi
- Department of Nanoengineering, University of California at San Diego, La Jolla, California 92093, USA
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Arsuaga J, Diao Y, Vazquez M. Mathematical Methods in Dna Topology: Applications to Chromosome Organization and Site-Specific Recombination. ACTA ACUST UNITED AC 2009. [DOI: 10.1007/978-1-4419-0670-0_2] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/18/2023]
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