1
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Radhakrishnan K, Singh SP. Compression of a confined semiflexible polymer under direct and oscillating fields. Phys Rev E 2023; 108:014501. [PMID: 37583203 DOI: 10.1103/physreve.108.014501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/21/2023] [Accepted: 06/19/2023] [Indexed: 08/17/2023]
Abstract
The folding transition of biopolymers from the coil to compact structures has attracted wide research interest in the past and is well studied in polymer physics. Recent seminal works on DNA in confined devices have shown that these long biopolymers tend to collapse under an external field, which is contrary to the previously reported stretching of the chain. In this work, we capture the compression of a confined semiflexible polymer under direct and oscillating fields using a coarse-grained computer simulation model in the presence of long-range hydrodynamics. In the case of a semiflexible polymer chain, the inhomogeneous hydrodynamic drag from the center to the periphery of the coil couples with the chain bending to cause a swirling movement of the chain segments, leading to structural intertwining and compaction. Contrarily, a flexible chain of the same length lacks such structural deformation and forms a well-established tadpole structure. While bending rigidity profoundly influences the chain's folding favorability, we also found that subject to the direct field, chains in stronger confinements exhibit substantial compaction, contrary to the one in moderate confinements or bulk where such compaction is absent. However, an alternating field within an optimum frequency can effectuate this compression even in moderate or no confinement. This field-induced collapse is a quintessential hydrodynamic phenomenon, resulting in intertwined knotted structures even for shorter chains, unlike other spontaneous knotting experiments where it happens exclusively for longer chains.
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Affiliation(s)
- Keerthi Radhakrishnan
- Department of Physics, Indian Institute of Science Education and Research, Bhopal 462 066, Madhya Pradesh, India
| | - Sunil P Singh
- Department of Physics, Indian Institute of Science Education and Research, Bhopal 462 066, Madhya Pradesh, India
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2
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Liang T, Yang C, Song X, Feng Y, Liu Y, Chen H. Quantification of macromolecule crowding at single-molecule level. Phys Rev E 2023; 108:014406. [PMID: 37583195 DOI: 10.1103/physreve.108.014406] [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: 03/24/2023] [Accepted: 06/19/2023] [Indexed: 08/17/2023]
Abstract
Macromolecule crowding has a prominent impact on a series of biochemical processes in the cell. It is also expected to promote macromolecular complexation induced by excluded volume effects, which conflicts with recent advances in the thermodynamic interaction between inert, synthetic polymers, and nucleic acids. Along this line, a method combining high-resolution magnetic tweezers and extended crowder-oxDNA model was applied to resolve these discrepancies by systematically studying the kinetics and thermodynamics of the folding-unfolding transition for an individual DNA hairpin in a crowded environment. More specifically, from the magnetic tweezers-based experiments, the linear dependence of the critical force of the DNA hairpin on the polyethylene glycol (PEG) concentration was demonstrated, which is consistent with the results based on the crowder-oxDNA model in which the Lennard-Jones potential was adopted to express the interaction between the crowders and the DNA hairpin. These consistencies highlight that the excluded volume effects are mainly responsible for the interaction between PEG and the DNA hairpin, which is different from the interaction between dextran and the DNA hairpin. In the meantime, the dependence of the folding rate on the molecule weight of PEG, which was different from fluorescence resonance energy transfer-based results, was identified. The proposed method opens a path to detect the interaction between an inert, synthetic molecule, and the DNA hairpin, which is important to accurately mimic the cytosolic environments using mixtures of different inert molecules.
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Affiliation(s)
- Ting Liang
- College of Physics, Guizhou University, Guiyang 550025, China
| | - Chao Yang
- College of Physics, Guizhou University, Guiyang 550025, China
| | - Xiaoya Song
- College of Physics, Guizhou University, Guiyang 550025, China
| | - Yuyu Feng
- College of Physics, Guizhou University, Guiyang 550025, China
| | - Yanhui Liu
- College of Physics, Guizhou University, Guiyang 550025, China
| | - Hu Chen
- Research Institute for Biomimetics and Soft Matter, Fujian Provincial Key Lab for Soft Functional Materials Research, Department of Physics, Xiamen University, Xiamen 361005, People's Republic of China
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3
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Yang C, Song X, Feng Y, Zhao G, Liu Y. Stability of DNA and RNA hairpins: a comparative study based on ox-DNA. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2023; 35:265101. [PMID: 36972608 DOI: 10.1088/1361-648x/acc7eb] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/22/2022] [Accepted: 03/27/2023] [Indexed: 06/18/2023]
Abstract
Advances in single-molecule experiments on macromolecular crowding urgently need an efficient simulation method to resolve their discrepancies quantitatively. Ox-DNA model has been since reworked to treat the thermodynamics and mechanical properties of DNA/RNA hairpin at a stretching force. In hopping experiments, the critical forces of RNA hairpins at different temperatures are greater than those of DNA hairpins, in addition, the Gibbs free energy at a fixed temperature required to convert an RNA hairpin into a single-stranded molecule at zero force is obviously greater than that of DNA hairpin and gradually decreases by increasing the temperature. As far as force-ramping experiments are concerned, the first-rupture forces of RNA/DNA hairpins corresponding to the maximum probability density linearly pertain to the force-loading rate, with those of RNA hairpins being greater. The extended ox-DNA model could potentially identify the interaction between biologically inert polymer and RNA/DNA hairpins in crowded environments.
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Affiliation(s)
- Chao Yang
- College of Physics, Guizhou University, Guiyang, Guizhou 550025, People's Republic of China
| | - Xiaoya Song
- College of Physics, Guizhou University, Guiyang, Guizhou 550025, People's Republic of China
| | - Yuyu Feng
- College of Physics, Guizhou University, Guiyang, Guizhou 550025, People's Republic of China
| | - Guangju Zhao
- College of Physics, Guizhou University, Guiyang, Guizhou 550025, People's Republic of China
| | - Yanhui Liu
- College of Physics, Guizhou University, Guiyang, Guizhou 550025, People's Republic of China
- Breeding and Reproduction in the Plateau Mountainous Region, Ministry of Education (Guizhou University), Guiyang, Guizhou 550025, People's Republic of China
- State Key Laboratory of Public Big Data, Guizhou University, Guiyang 550025, People's Republic of China
- Kechuang Industrial Development Company Limited,Gui'an New Area, Guiyang 550025, People's Republic of China
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4
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Michieletto D, Fosado YAG, Melas E, Baiesi M, Tubiana L, Orlandini E. Dynamic and facilitated binding of topoisomerase accelerates topological relaxation. Nucleic Acids Res 2022; 50:4659-4668. [PMID: 35474478 PMCID: PMC9071436 DOI: 10.1093/nar/gkac260] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/18/2021] [Revised: 03/28/2022] [Accepted: 04/21/2022] [Indexed: 12/24/2022] Open
Abstract
How type 2 Topoisomerase (TopoII) proteins relax and simplify the topology of DNA molecules is one of the most intriguing open questions in genome and DNA biophysics. Most of the existing models neglect the dynamics of TopoII which is expected of proteins searching their targets via facilitated diffusion. Here, we show that dynamic binding of TopoII speeds up the topological relaxation of knotted substrates by enhancing the search of the knotted arc. Intriguingly, this in turn implies that the timescale of topological relaxation is virtually independent of the substrate length. We then discover that considering binding biases due to facilitated diffusion on looped substrates steers the sampling of the topological space closer to the boundaries between different topoisomers yielding an optimally fast topological relaxation. We discuss our findings in the context of topological simplification in vitro and in vivo.
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Affiliation(s)
| | | | - Elias Melas
- School of Physics and Astronomy, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, UK
| | - Marco Baiesi
- Department of Physics and Astronomy, University of Padova, Via Marzolo 8, I-35131 Padova, Italy,INFN, Sezione di Padova, Via Marzolo 8, I-35131 Padova, Italy
| | - Luca Tubiana
- Physics Department, University of Trento, via Sommarive 14, I-38123 Trento, Italy,INFN-TIFPA, Trento Institute for Fundamental Physics and Applications, I-38123 Trento, Italy,Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
| | - Enzo Orlandini
- Department of Physics and Astronomy, University of Padova, Via Marzolo 8, I-35131 Padova, Italy,INFN, Sezione di Padova, Via Marzolo 8, I-35131 Padova, Italy
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5
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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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6
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Affiliation(s)
- Liang Dai
- Department of Physics, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong, China
| | - Beatrice W. Soh
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Patrick S. Doyle
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
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7
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The Rabl configuration limits topological entanglement of chromosomes in budding yeast. Sci Rep 2019; 9:6795. [PMID: 31043625 PMCID: PMC6494875 DOI: 10.1038/s41598-019-42967-4] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/18/2018] [Accepted: 03/27/2019] [Indexed: 11/25/2022] Open
Abstract
The three dimensional organization of genomes remains mostly unknown due to their high degree of condensation. Biophysical studies predict that condensation promotes the topological entanglement of chromatin fibers and the inhibition of function. How organisms balance between functionally active genomes and a high degree of condensation remains to be determined. Here we hypothesize that the Rabl configuration, characterized by the attachment of centromeres and telomeres to the nuclear envelope, helps to reduce the topological entanglement of chromosomes. To test this hypothesis we developed a novel method to quantify chromosome entanglement complexity in 3D reconstructions obtained from Chromosome Conformation Capture (CCC) data. Applying this method to published data of the yeast genome, we show that computational models implementing the attachment of telomeres or centromeres alone are not sufficient to obtain the reduced entanglement complexity observed in 3D reconstructions. It is only when the centromeres and telomeres are attached to the nuclear envelope (i.e. the Rabl configuration) that the complexity of entanglement of the genome is comparable to that of the 3D reconstructions. We therefore suggest that the Rabl configuration is an essential player in the simplification of the entanglement of chromatin fibers.
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8
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Orlandini E, Marenduzzo D, Michieletto D. Synergy of topoisomerase and structural-maintenance-of-chromosomes proteins creates a universal pathway to simplify genome topology. Proc Natl Acad Sci U S A 2019; 116:8149-8154. [PMID: 30962387 PMCID: PMC6486742 DOI: 10.1073/pnas.1815394116] [Citation(s) in RCA: 45] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Topological entanglements severely interfere with important biological processes. For this reason, genomes must be kept unknotted and unlinked during most of a cell cycle. Type II topoisomerase (TopoII) enzymes play an important role in this process but the precise mechanisms yielding systematic disentanglement of DNA in vivo are not clear. Here we report computational evidence that structural-maintenance-of-chromosomes (SMC) proteins-such as cohesins and condensins-can cooperate with TopoII to establish a synergistic mechanism to resolve topological entanglements. SMC-driven loop extrusion (or diffusion) induces the spatial localization of essential crossings, in turn catalyzing the simplification of knots and links by TopoII enzymes even in crowded and confined conditions. The mechanism we uncover is universal in that it does not qualitatively depend on the specific substrate, whether DNA or chromatin, or on SMC processivity; we thus argue that this synergy may be at work across organisms and throughout the cell cycle.
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Affiliation(s)
- Enzo Orlandini
- Dipartimento di Fisica e Astronomia "Galileo Galilei," Sezione Istituto Nazionale di Fisica Nucleare, Università degli Studi di Padova, I-35131 Padova, Italy
| | - Davide Marenduzzo
- School of Physics and Astronomy, University of Edinburgh, Edinburgh EH9 3FD, United Kingdom
| | - Davide Michieletto
- School of Physics and Astronomy, University of Edinburgh, Edinburgh EH9 3FD, United Kingdom
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9
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Bimodality in the knotting probability of semiflexible rings suggested by mapping with self-avoiding polygons. REACT FUNCT POLYM 2019. [DOI: 10.1016/j.reactfunctpolym.2018.11.008] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/18/2023]
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10
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Chen A, Zhao N. Comparative study of the crowding-induced collapse effect in hard-sphere, flexible polymer and rod-like polymer systems. Phys Chem Chem Phys 2019; 21:12335-12345. [DOI: 10.1039/c9cp01731c] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
A systematic Langevin simulation is performed to study the crowding-induced collapse effect on a probed chain in three typical systems: hard sphere (HS), flexible polymer and rod-like polymer.
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Affiliation(s)
- Anpu Chen
- College of Chemistry
- Sichuan University
- Chengdu 610064
- China
| | - Nanrong Zhao
- College of Chemistry
- Sichuan University
- Chengdu 610064
- China
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11
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Affiliation(s)
- Liang Dai
- BioSystems and Micromechanics IRG, Singapore-MIT Alliance for Research and Technology Centre, Singapore 117543
| | - Patrick S. Doyle
- BioSystems and Micromechanics IRG, Singapore-MIT Alliance for Research and Technology Centre, Singapore 117543
- Department of Chemical Engineering, Massachusetts Institute of Technology (MIT), Cambridge, Massachusetts 02139, United States
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12
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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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Amin S, Khorshid A, Zeng L, Zimny P, Reisner W. A nanofluidic knot factory based on compression of single DNA in nanochannels. Nat Commun 2018; 9:1506. [PMID: 29666466 PMCID: PMC5904144 DOI: 10.1038/s41467-018-03901-w] [Citation(s) in RCA: 49] [Impact Index Per Article: 8.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/15/2017] [Accepted: 03/21/2018] [Indexed: 11/09/2022] Open
Abstract
Knots form when polymers self-entangle, a process enhanced by compaction with important implications in biological and artificial systems involving chain confinement. In particular, new experimental tools are needed to assess the impact of multiple variables influencing knotting probability. Here, we introduce a nanofluidic knot factory for efficient knot formation and detection. Knots are produced during hydrodynamic compression of single DNA molecules against barriers in a nanochannel; subsequent extension of the chain enables direct assessment of the number of independently evolving knots. Knotting probability increases with chain compression as well as with waiting time in the compressed state. Using a free energy derived from scaling arguments, we develop a knot-formation model that can quantify the effect of interactions and the breakdown of Poisson statistics at high compression. Our model suggests that highly compressed knotted states are stabilized by a decreased free energy as knotted contour contributes a lower self-exclusion derived free energy.
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Affiliation(s)
- Susan Amin
- Department of Physics, McGill University, 3600 rue université, Montréal, QC, H3A 2T8, Canada
| | - Ahmed Khorshid
- Department of Physics, McGill University, 3600 rue université, Montréal, QC, H3A 2T8, Canada
| | - Lili Zeng
- Department of Physics, McGill University, 3600 rue université, Montréal, QC, H3A 2T8, Canada
| | - Philip Zimny
- Department of Biomedical Engineering, McGill University, 3775 rue université, Montréal, QC, H3A 2B4, Canada
| | - Walter Reisner
- Department of Physics, McGill University, 3600 rue université, Montréal, QC, H3A 2T8, Canada.
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14
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Liebetreu M, Ripoll M, Likos CN. Trefoil Knot Hydrodynamic Delocalization on Sheared Ring Polymers. ACS Macro Lett 2018; 7:447-452. [PMID: 35619341 DOI: 10.1021/acsmacrolett.8b00059] [Citation(s) in RCA: 34] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/08/2023]
Abstract
The behavior of unknotted and trefoil-knotted ring polymers under shear flow is here examined by means of mesoscopic simulations. In contrast to most polymers, ring polymers in a hydrodynamic solvent at high shear rates do not get shortened in the vorticity direction. This is a consequence of the backflow produced by the interaction of the sheared solvent with the end-free polymer topology. The extended structures of the ring in the vorticity-flow plane, when they are aligned in a constant velocity plane, favor ring contour fluctuations. This variety of conformations largely suppresses the tank-treading type of rotation with extended conformations in favor of the tumbling type of rotations, where stretched and collapsed conformations alternate. The extension of trefoil knots is also enhanced, so that the knots become delocalized. We anticipate that these effects, which disappear in the absence of hydrodynamic interactions, will have a crucial impact on the rheological properties of concentrated ring solutions, and will also influence the behavior of more complicated systems such as mixtures of polymers with different topologies.
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Affiliation(s)
- Maximilian Liebetreu
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
| | - Marisol Ripoll
- Forschungszentrum Jülich, Institute of Complex Systems, Theoretical Soft Matter and Biophysics, 52425 Jülich, Germany
| | - Christos N. Likos
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
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15
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Zhao Y, Dabrowski-Tumanski P, Niewieczerzal S, Sulkowska JI. The exclusive effects of chaperonin on the behavior of proteins with 52 knot. PLoS Comput Biol 2018; 14:e1005970. [PMID: 29547629 PMCID: PMC5874080 DOI: 10.1371/journal.pcbi.1005970] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/05/2017] [Revised: 03/28/2018] [Accepted: 01/12/2018] [Indexed: 02/05/2023] Open
Abstract
The folding of proteins with a complex knot is still an unresolved question. Based on representative members of Ubiquitin C-terminal Hydrolases (UCHs) that contain the 52 knot in the native state, we explain how UCHs are able to unfold and refold in vitro reversibly within the structure-based model. In particular, we identify two, topologically different folding/unfolding pathways and corroborate our results with experiment, recreating the chevron plot. We show that confinement effect of chaperonin or weak crowding greatly facilitates folding, simultaneously slowing down the unfolding process of UCHs, compared with bulk conditions. Finally, we analyze the existence of knots in the denaturated state of UCHs. The results of the work show that the crowded environment of the cell should have a positive effect on the kinetics of complex knotted proteins, especially when proteins with deeper knots are found in this family. Self-tying of knotted proteins remains a challenge both for theoreticians and experimentalist. In this work, we study the proteins with complex, the 52 knot, in a bulk and confined within a chaperonin box. We show that in our model we recreate the experimental results, identify two topologically distinct folding pathways and explain the beneficial role of confinement for complex knotted proteins. Encapsulation provides a possibility to fold via alternative pathway—folding via trefoil intermediate knot (N-terminal pathway) from entropic reason while folding via the C-terminal (direct tying) appears with the same probability. The results of this work show, how crowded environment in the real cell may enhance self-tying of proteins. The results are also the first step to the identification of possible oligomerization-prone forms of UCHs, which may cause neurodegenerative diseases.
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Affiliation(s)
- Yani Zhao
- Centre of New Technologies, University of Warsaw, Warsaw, Poland
- Institute of Physics, Polish Academy of Sciences, Warsaw, Poland
| | - Pawel Dabrowski-Tumanski
- Centre of New Technologies, University of Warsaw, Warsaw, Poland
- Faculty of Chemistry, University of Warsaw, Warsaw, Poland
| | | | - Joanna I. Sulkowska
- Centre of New Technologies, University of Warsaw, Warsaw, Poland
- Faculty of Chemistry, University of Warsaw, Warsaw, Poland
- * E-mail:
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16
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The energy cost of polypeptide knot formation and its folding consequences. Nat Commun 2017; 8:1581. [PMID: 29146980 PMCID: PMC5691195 DOI: 10.1038/s41467-017-01691-1] [Citation(s) in RCA: 21] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/03/2017] [Accepted: 10/09/2017] [Indexed: 11/08/2022] Open
Abstract
Knots are natural topologies of chains. Yet, little is known about spontaneous knot formation in a polypeptide chain—an event that can potentially impair its folding—and about the effect of a knot on the stability and folding kinetics of a protein. Here we used optical tweezers to show that the free energy cost to form a trefoil knot in the denatured state of a polypeptide chain of 120 residues is 5.8 ± 1 kcal mol−1. Monte Carlo dynamics of random chains predict this value, indicating that the free energy cost of knot formation is of entropic origin. This cost is predicted to remain above 3 kcal mol−1 for denatured proteins as large as 900 residues. Therefore, we conclude that naturally knotted proteins cannot attain their knot randomly in the unfolded state but must pay the cost of knotting through contacts along their folding landscape. The effect of knots on protein stability and folding kinetics is not well understood. Here the authors combine optical tweezer experiments and calculations to experimentally determine the energy cost for knot formation, which indicates that knotted proteins evolved specific folding pathways because knot formation in unfolded chains is unfavorable.
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17
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Niewieczerzal S, Sulkowska JI. Knotting and unknotting proteins in the chaperonin cage: Effects of the excluded volume. PLoS One 2017; 12:e0176744. [PMID: 28489858 PMCID: PMC5425179 DOI: 10.1371/journal.pone.0176744] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/03/2017] [Accepted: 04/14/2017] [Indexed: 11/18/2022] Open
Abstract
Molecular dynamics simulations are used to explore the effects of chaperonin-like cages on knotted proteins with very low sequence similarity, different depths of a knot but with a similar fold, and the same type of topology. The investigated proteins are VirC2, DndE and MJ0366 with two depths of a knot. A comprehensive picture how encapsulation influences folding rates is provided based on the analysis of different cage sizes and temperature conditions. Neither of these two effects with regard to knotted proteins has been studied by means of molecular dynamics simulations with coarse-grained structure-based models before. We show that encapsulation in a chaperonin is sufficient to self-tie and untie small knotted proteins (VirC2, DndE), for which the equilibrium process is not accessible in the bulk solvent. Furthermore, we find that encapsulation reduces backtracking that arises from the destabilisation of nucleation sites, smoothing the free energy landscape. However, this effect can also be coupled with temperature rise. Encapsulation facilitates knotting at the early stage of folding and can enhance an alternative folding route. Comparison to unknotted proteins with the same fold shows directly how encapsulation influences the free energy landscape. In addition, we find that as the size of the cage decreases, folding times increase almost exponentially in a certain range of cage sizes, in accordance with confinement theory and experimental data for unknotted proteins.
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Affiliation(s)
- Szymon Niewieczerzal
- Centre of New Technologies, University of Warsaw, Banacha 2c, 02-097 Warsaw, Poland
| | - Joanna I. Sulkowska
- Centre of New Technologies, University of Warsaw, Banacha 2c, 02-097 Warsaw, Poland
- Department of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warsaw, Poland
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18
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Dai L, Doyle PS. Trapping a Knot into Tight Conformations by Intra-Chain Repulsions. Polymers (Basel) 2017; 9:E57. [PMID: 30970736 PMCID: PMC6432319 DOI: 10.3390/polym9020057] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/31/2016] [Revised: 02/07/2017] [Accepted: 02/08/2017] [Indexed: 11/17/2022] Open
Abstract
Knots can occur in biopolymers such as DNA and peptides. In our previous study, we systematically investigated the effects of intra-chain interactions on knots and found that long-range repulsions can surprisingly tighten knots. Here, we use this knowledge to trap a knot into tight conformations in Langevin dynamics simulations. By trapping, we mean that the free energy landscape with respect to the knot size exhibits a potential well around a small knot size in the presence of long-range repulsions, and this potential can well lead to long-lived tight knots when its depth is comparable to or larger than thermal energy. We tune the strength of intra-chain repulsion such that a knot is weakly trapped. Driven by thermal fluctuations, the knot can escape from the trap and is then re-trapped. We find that the knot switches between tight and loose conformations-referred to as "knot breathing". We use a Yukawa potential to model screened electrostatic interactions to explore the relevance of knot trapping and breathing in charged biopolymers. We determine the minimal screened length and the minimal strength of repulsion for knot trapping. We find that Coulomb-induced knot trapping is possible to occur in single-stranded DNA and peptides for normal ionic strengths.
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Affiliation(s)
- Liang Dai
- BioSystems and Micromechanics IRG, Singapore-MIT Alliance for Research and Technology Centre, Singapore 117543, Singapore.
| | - Patrick S Doyle
- BioSystems and Micromechanics IRG, Singapore-MIT Alliance for Research and Technology Centre, Singapore 117543, Singapore.
- Department of Chemical Engineering, Massachusetts Institute of Technology (MIT), Cambridge, MA 02139, USA.
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Affiliation(s)
- Liang Dai
- BioSystems and Micromechanics IRG, Singapore-MIT Alliance for Research and Technology Centre, Singapore 117543
| | - Patrick S. Doyle
- BioSystems and Micromechanics IRG, Singapore-MIT Alliance for Research and Technology Centre, Singapore 117543
- Department
of Chemical Engineering, Massachusetts Institute of Technology (MIT), Cambridge, Massachusetts 02139, United States
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Polles G, Orlandini E, Micheletti C. Optimal Self-Assembly of Linked Constructs and Catenanes via Spatial Confinement. ACS Macro Lett 2016; 5:931-935. [PMID: 35607207 DOI: 10.1021/acsmacrolett.6b00425] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022]
Abstract
How to direct the self-assembly of simple templates toward constructs with complex shape and topology is still an open problem. Recent advancements have made it possible to self-assemble various types of knotted constructs, but targeting general multicomponent topologies, that is, links and catenanes, has proved much harder. Here, we study how the yield and complexity of self-assembled links depends on both intrinsic and extrinsic system properties and, particularly, template shape and spatial confinement. We show that slit confinement does not necessarily suppress linking but can rather enhance it significantly thanks to entropic effects. We also found that only a limited set of binary links are recurrent for different template shapes. These privileged topologies include all those experimentally realized so far plus a few additional ones, such as the 772 and 782 links that, hence, ought to be ideal candidates for broadening the current class of constructs with addressable topology.
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Affiliation(s)
- Guido Polles
- SISSA, International
School for Advanced Studies, via Bonomea
265, I-34136 Trieste, Italy
| | - Enzo Orlandini
- Dipartimento
di Fisica e Astronomia and Sezione INFN, Universita’ 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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D'Adamo G, Dietler G, Micheletti C. Tuning knot abundance in semiflexible chains with crowders of different sizes: a Monte Carlo study of DNA chains. SOFT MATTER 2016; 12:6708-6715. [PMID: 27443238 DOI: 10.1039/c6sm01327a] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
We use stochastic simulation techniques to sample the conformational space of linear semiflexible polymers in a crowded medium and study how the knotting properties depend on the crowder size and concentration. The abundance of physical knots in the chains, which for definiteness we model on 10 kb long DNA filaments, is shown to have a non-monotonic, unimodal dependence on the colloid diameter, dc. The maximum incidence of knots occurs when dc is about equal to half of the gyration radius of the isolated chain. The degree of enhancement of knots grows rapidly with the solution density and can be very conspicuous relative to the case of isolated chains with no crowders. For instance, at 30% volume fraction the relative increase is more than fourfold. This dramatic enhancement is shown to originate from the depletion-induced chain compaction over multiple and concurring length scales. The same effect accounts for the variations of the knot length that accompany the changes in knotting probability. The findings suggest that crowded media could be viably used as a passive physical means for controlling and modulating the incidence and length of knots in DNA and other types of semiflexible polymers.
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Affiliation(s)
- Giuseppe D'Adamo
- SISSA, International School for Advanced Studies, via Bonomea 265, I-34136 Trieste, Italy.
| | - Giovanni Dietler
- Institut de Physique des Systèmes Biologiques, Ecole Polytechnique Fédérale de Lausanne, BSP, CH-1015 Lausanne, Switzerland
| | - Cristian Micheletti
- SISSA, International School for Advanced Studies, via Bonomea 265, I-34136 Trieste, Italy.
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D’Adamo G, Pelissetto A, Pierleoni C. Phase Diagram and Structure of Mixtures of Large Colloids and Linear Polymers under Good-Solvent Conditions. Macromolecules 2016. [DOI: 10.1021/acs.macromol.6b00600] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
| | - Andrea Pelissetto
- Dipartimento di Fisica, Sapienza Università di Roma and INFN, Sezione di Roma I, P.le Aldo Moro
2, I-00185 Rome, Italy
| | - Carlo Pierleoni
- Dipartimento di Scienze Fisiche
e Chimiche, Università dell’Aquila, V. Vetoio 10, Loc. Coppito, I-67100 L’Aquila, Italy
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