1
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Berx J, Mashaghi A. Aggregation and structural phase transitions of semiflexible polymer bundles: A braided circuit topology approach. iScience 2024; 27:108995. [PMID: 38361617 PMCID: PMC10867648 DOI: 10.1016/j.isci.2024.108995] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/29/2023] [Revised: 11/23/2023] [Accepted: 01/19/2024] [Indexed: 02/17/2024] Open
Abstract
We present a braided circuit topology framework for investigating topology and structural phase transitions in aggregates of semiflexible polymers. In the conventional approach to circuit topology, which specifically applies to single isolated folded linear chains, the number and arrangement of contacts within the circuitry of a folded chain give rise to increasingly complex fold topologies. Another avenue for achieving complexity is through the interaction and entanglement of two or more folded linear chains. The braided circuit topology approach describes the topology of such multiple-chain systems and offers topological measures such as writhe, complexity, braid length, and isotopy class. This extension of circuit topology to multichains reveals the interplay between collapse, aggregation, and entanglement. In this work, we show that circuit topological motif fractions are ideally suited order parameters to characterize structural phase transitions in entangled systems that can detect structural re-ordering other measures cannot.
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Affiliation(s)
- Jonas Berx
- Medical Systems Biophysics and Bioengineering, Leiden Academic Centre for Drug Research, Leiden University, Leiden 2333CC, the Netherlands
- Laboratory for Interdisciplinary Medical Innovations, Centre for Interdisciplinary Genome Research, Leiden University, Leiden 2333CC, the Netherlands
| | - Alireza Mashaghi
- Medical Systems Biophysics and Bioengineering, Leiden Academic Centre for Drug Research, Leiden University, Leiden 2333CC, the Netherlands
- Laboratory for Interdisciplinary Medical Innovations, Centre for Interdisciplinary Genome Research, Leiden University, Leiden 2333CC, the Netherlands
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2
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Ye W, Feng HN, Zhang ZH, Zhang L. A protocol for the stereoselective synthesis of a Star of David [2]catenane. STAR Protoc 2024; 5:102821. [PMID: 38184851 PMCID: PMC10806347 DOI: 10.1016/j.xpro.2023.102821] [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: 11/28/2023] [Revised: 12/06/2023] [Accepted: 12/19/2023] [Indexed: 01/09/2024] Open
Abstract
Most complex prime links exhibit inherent topological chirality, yet their high stereoinduction remains a rare occurrence. Here, we present a protocol for the stereoselective synthesis of a molecular link comprising two triple entwined rings. We describe steps for constructing the precursor circular helicate, performing ring closure metathesis, and demetallation. We also outline procedures for bio-beads separation and data analysis. This protocol holds promise for applications in molecular nanotopology. For complete details on the use and execution of this protocol, please refer to Zhang et al. (2022).1.
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Affiliation(s)
- Weitao Ye
- School of Chemistry and Molecular Engineering, East China Normal University, Shanghai 200062, P.R. China; School Frontiers Science Center of Molecular Intelligent Synthesis, School of Chemistry and Molecular Engineering, East China Normal University, Shanghai 200062, P.R. China
| | - Hai-Na Feng
- School of Chemistry and Molecular Engineering, East China Normal University, Shanghai 200062, P.R. China; School Frontiers Science Center of Molecular Intelligent Synthesis, School of Chemistry and Molecular Engineering, East China Normal University, Shanghai 200062, P.R. China
| | - Zhi-Hui Zhang
- School of Chemistry and Molecular Engineering, East China Normal University, Shanghai 200062, P.R. China; School Frontiers Science Center of Molecular Intelligent Synthesis, School of Chemistry and Molecular Engineering, East China Normal University, Shanghai 200062, P.R. China.
| | - Liang Zhang
- School of Chemistry and Molecular Engineering, East China Normal University, Shanghai 200062, P.R. China; School Frontiers Science Center of Molecular Intelligent Synthesis, School of Chemistry and Molecular Engineering, East China Normal University, Shanghai 200062, P.R. China.
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3
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Scalvini B, Heling LWHJ, Sheikhhassani V, Sunderlikova V, Tans SJ, Mashaghi A. Cytosolic Interactome Protects Against Protein Unfolding in a Single Molecule Experiment. Adv Biol (Weinh) 2023; 7:e2300105. [PMID: 37409427 DOI: 10.1002/adbi.202300105] [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: 03/08/2023] [Revised: 06/13/2023] [Indexed: 07/07/2023]
Abstract
Single molecule techniques are particularly well suited for investigating the processes of protein folding and chaperone assistance. However, current assays provide only a limited perspective on the various ways in which the cellular environment can influence the folding pathway of a protein. In this study, a single molecule mechanical interrogation assay is developed and used to monitor protein unfolding and refolding within a cytosolic solution. This allows to test the cumulative topological effect of the cytoplasmic interactome on the folding process. The results reveal a stabilization against forced unfolding for partial folds, which are attributed to the protective effect of the cytoplasmic environment against unfolding and aggregation. This research opens the possibility of conducting single molecule molecular folding experiments in quasi-biological environments.
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Affiliation(s)
- Barbara Scalvini
- Medical Systems Biophysics and Bioengineering, Leiden Academic Centre for Drug Research, Faculty of Science, Leiden University, Einsteinweg 55, Leiden, 2333CC, The Netherlands
- Centre for Interdisciplinary Genome Research, Faculty of Science, Leiden University, Einsteinweg 55, Leiden, 2333CC, The Netherlands
| | - Laurens W H J Heling
- Medical Systems Biophysics and Bioengineering, Leiden Academic Centre for Drug Research, Faculty of Science, Leiden University, Einsteinweg 55, Leiden, 2333CC, The Netherlands
- Centre for Interdisciplinary Genome Research, Faculty of Science, Leiden University, Einsteinweg 55, Leiden, 2333CC, The Netherlands
| | - Vahid Sheikhhassani
- Medical Systems Biophysics and Bioengineering, Leiden Academic Centre for Drug Research, Faculty of Science, Leiden University, Einsteinweg 55, Leiden, 2333CC, The Netherlands
- Centre for Interdisciplinary Genome Research, Faculty of Science, Leiden University, Einsteinweg 55, Leiden, 2333CC, The Netherlands
| | | | - Sander J Tans
- AMOLF, Science Park 104, Amsterdam, 1098 XG, The Netherlands
- Department of Bionanoscience, Kavli Institute of Nanoscience, Delft University of Technology, Van der Maasweg 9, Delft, 2629HZ, The Netherlands
| | - Alireza Mashaghi
- Medical Systems Biophysics and Bioengineering, Leiden Academic Centre for Drug Research, Faculty of Science, Leiden University, Einsteinweg 55, Leiden, 2333CC, The Netherlands
- Centre for Interdisciplinary Genome Research, Faculty of Science, Leiden University, Einsteinweg 55, Leiden, 2333CC, The Netherlands
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4
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Feng HN, Sun Z, Chen S, Zhang ZH, Li Z, Zhong Z, Sun T, Ma Y, Zhang L. A Star of David [2]catenane of single handedness. Chem 2022. [DOI: 10.1016/j.chempr.2022.11.010] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/07/2022]
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5
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ProteinCT: An implementation of the protein circuit topology framework. MethodsX 2022; 9:101861. [PMID: 36187158 PMCID: PMC9520010 DOI: 10.1016/j.mex.2022.101861] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/29/2022] [Accepted: 09/11/2022] [Indexed: 11/22/2022] Open
Abstract
The ability to describe the topology of a folded protein conformation is critically important for functional analysis, protein engineering, and drug design. Circuit topology is a unique topological framework which is widely applicable to protein analysis, yet a state-of-the art implementation of this concept is lacking. Here, we present an open-source Python-implemented circuit topology tool called ProteinCT. The platform provides a method for acquiring, visualizing, analyzing, and quantifying circuit topology data from proteins of interest. We mapped the universe of human proteins to a circuit topology space using conventional hardware within a few hours, demonstrating the performance of ProteinCT. In brief,•A Python-implemented circuit topology tool is developed to extract global and local topological information from a protein structure file.•Modules are developed to combine topological information with geometric and energetic information.•It is demonstrated that the method can be efficiently applied to a large set of proteins, opening a wide range of possibilities for structural proteomics research.
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6
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Woodard J, Iqbal S, Mashaghi A. Circuit topology predicts pathogenicity of missense mutations. Proteins 2022; 90:1634-1644. [PMID: 35394672 PMCID: PMC9543832 DOI: 10.1002/prot.26342] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/15/2021] [Revised: 03/07/2022] [Accepted: 03/30/2022] [Indexed: 12/05/2022]
Abstract
The contact topology of a protein determines important aspects of the folding process. The topological measure of contact order has been shown to be predictive of the rate of folding. Circuit topology is emerging as another fundamental descriptor of biomolecular structure, with predicted effects on the folding rate. We analyze the residue‐based circuit topological environments of 21 K mutations labeled as pathogenic or benign. Multiple statistical lines of reasoning support the conclusion that the number of contacts in two specific circuit topological arrangements, namely inverse parallel and cross relations, with contacts involving the mutated residue have discriminatory value in determining the pathogenicity of human variants. We investigate how results vary with residue type and according to whether the gene is essential. We further explore the relationship to a number of structural features and find that circuit topology provides nonredundant information on protein structures and pathogenicity of mutations. Results may have implications for the polymer physics of protein folding and suggest that “local” topological information, including residue‐based circuit topology and residue contact order, could be useful in improving state‐of‐the‐art machine learning algorithms for pathogenicity prediction.
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Affiliation(s)
- Jaie Woodard
- Medical Systems Biophysics and Bioengineering, Leiden Academic Centre for Drug Research, Faculty of Science, Leiden University, Leiden, The Netherlands.,Department of Computational Medicine and Bioinformatics, University of Michigan, Ann Arbor, Michigan, USA
| | - Sumaiya Iqbal
- Center for the Development of Therapeutics, Broad Institute of MIT and Harvard, Cambridge, Massachusetts, USA.,Stanley Center for Psychiatric Research, Broad Institute of MIT and Harvard, Cambridge, Massachusetts, USA.,Program in Medical and Population Genetics, Broad Institute of MIT and Harvard, Cambridge, Massachusetts, USA.,Analytic and Translational Genetics Unit, Massachusetts General Hospital, Boston, Massachusetts, USA
| | - Alireza Mashaghi
- Medical Systems Biophysics and Bioengineering, Leiden Academic Centre for Drug Research, Faculty of Science, Leiden University, Leiden, The Netherlands.,Centre for Interdisciplinary Genome Research, Faculty of Science, Leiden University, Leiden, The Netherlands
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7
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Sheikhhassani V, Scalvini B, Ng J, Heling LWHJ, Ayache Y, Evers TMJ, Estébanez‐Perpiñá E, McEwan IJ, Mashaghi A. Topological dynamics of an intrinsically disordered N‐terminal domain of the human androgen receptor. Protein Sci 2022; 31:e4334. [PMID: 35634773 PMCID: PMC9134807 DOI: 10.1002/pro.4334] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/25/2022] [Revised: 05/02/2022] [Accepted: 05/03/2022] [Indexed: 12/28/2022]
Abstract
Human androgen receptor contains a large N‐terminal domain (AR‐NTD) that is highly dynamic and this poses a major challenge for experimental and computational analysis to decipher its conformation. Misfolding of the AR‐NTD is implicated in prostate cancer and Kennedy's disease, yet our knowledge of its structure is limited to primary sequence information of the chain and a few functionally important secondary structure motifs. Here, we employed an innovative combination of molecular dynamics simulations and circuit topology (CT) analysis to identify the tertiary structure of AR‐NTD. We found that the AR‐NTD adopts highly dynamic loopy conformations with two identifiable regions with distinct topological make‐up and dynamics. This consists of a N‐terminal region (NR, residues 1–224) and a C‐terminal region (CR, residues 225–538), which carries a dense core. Topological mapping of the dynamics reveals a traceable time‐scale dependent topological evolution. NR adopts different positioning with respect to the CR and forms a cleft that can partly enclose the hormone‐bound ligand‐binding domain (LBD) of the androgen receptor. Furthermore, our data suggest a model in which dynamic NR and CR compete for binding to the DNA‐binding domain of the receptor, thereby regulating the accessibility of its DNA‐binding site. Our approach allowed for the identification of a previously unknown regulatory binding site within the CR core, revealing the structural mechanisms of action of AR inhibitor EPI‐001, and paving the way for other drug discovery applications.
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Affiliation(s)
- Vahid Sheikhhassani
- Medical Systems Biophysics and Bioengineering, Leiden Academic Centre for Drug Research, Faculty of Science Leiden University Leiden The Netherlands
- Centre for Interdisciplinary Genome Research, Faculty of Science Leiden University Leiden The Netherlands
| | - Barbara Scalvini
- Medical Systems Biophysics and Bioengineering, Leiden Academic Centre for Drug Research, Faculty of Science Leiden University Leiden The Netherlands
- Centre for Interdisciplinary Genome Research, Faculty of Science Leiden University Leiden The Netherlands
| | - Julian Ng
- Medical Systems Biophysics and Bioengineering, Leiden Academic Centre for Drug Research, Faculty of Science Leiden University Leiden The Netherlands
- Centre for Interdisciplinary Genome Research, Faculty of Science Leiden University Leiden The Netherlands
| | - Laurens W. H. J. Heling
- Medical Systems Biophysics and Bioengineering, Leiden Academic Centre for Drug Research, Faculty of Science Leiden University Leiden The Netherlands
- Centre for Interdisciplinary Genome Research, Faculty of Science Leiden University Leiden The Netherlands
| | - Yosri Ayache
- Medical Systems Biophysics and Bioengineering, Leiden Academic Centre for Drug Research, Faculty of Science Leiden University Leiden The Netherlands
- Centre for Interdisciplinary Genome Research, Faculty of Science Leiden University Leiden The Netherlands
| | - Tom M. J. Evers
- Medical Systems Biophysics and Bioengineering, Leiden Academic Centre for Drug Research, Faculty of Science Leiden University Leiden The Netherlands
- Centre for Interdisciplinary Genome Research, Faculty of Science Leiden University Leiden The Netherlands
| | - Eva Estébanez‐Perpiñá
- Department of Biochemistry and Molecular Biomedicine Institute of Biomedicine (IBUB) of the University of Barcelona (UB) Barcelona Spain
| | - Iain J. McEwan
- Institute of Medical Sciences, School of Medicine, Medical Sciences and Nutrition, University of Aberdeen Scotland UK
| | - Alireza Mashaghi
- Medical Systems Biophysics and Bioengineering, Leiden Academic Centre for Drug Research, Faculty of Science Leiden University Leiden The Netherlands
- Centre for Interdisciplinary Genome Research, Faculty of Science Leiden University Leiden The Netherlands
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8
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Scalvini B, Schiessel H, Golovnev A, Mashaghi A. Circuit topology analysis of cellular genome reveals signature motifs, conformational heterogeneity, and scaling. iScience 2022; 25:103866. [PMID: 35243229 PMCID: PMC8861635 DOI: 10.1016/j.isci.2022.103866] [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: 06/25/2021] [Revised: 12/14/2021] [Accepted: 01/31/2022] [Indexed: 11/30/2022] Open
Abstract
Reciprocal regulation of genome topology and function is a fundamental and enduring puzzle in biology. The wealth of data provided by Hi-C libraries offers the opportunity to unravel this relationship. However, there is a need for a comprehensive theoretical framework in order to extract topological information for genome characterization and comparison. Here, we develop a toolbox for topological analysis based on Circuit Topology, allowing for the quantification of inter- and intracellular genomic heterogeneity, at various levels of fold complexity: pairwise contact arrangement, higher-order contact arrangement, and topological fractal dimension. Single-cell Hi-C data were analyzed and characterized based on topological content, revealing not only a strong multiscale heterogeneity but also highly conserved features such as a characteristic topological length scale and topological signature motifs in the genome. We propose that these motifs inform on the topological state of the nucleus and indicate the presence of active loop extrusion. Circuit topology quantifies heterogeneity in genomic arrangement Scale analysis reveals a characteristic length scale of 10 Mb in genome topology We identify highly conserved topological structures related to loop extrusion We suggest a topological model of chromatin arrangement for loop extrusion, the L-loop
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Affiliation(s)
- Barbara Scalvini
- Medical Systems Biophysics and Bioengineering, Leiden Academic Centre for Drug Research, Faculty of Science, Leiden University, Einsteinweg 55, 2333CC Leiden, the Netherlands
- Centre for Interdisciplinary Genome Research, Faculty of Science, Leiden University, Einsteinweg 55, 2333CC Leiden, the Netherlands
| | - Helmut Schiessel
- Cluster of Excellence Physics of Life, Technical University of Dresden, 01062 Dresden, Germany
| | - Anatoly Golovnev
- Medical Systems Biophysics and Bioengineering, Leiden Academic Centre for Drug Research, Faculty of Science, Leiden University, Einsteinweg 55, 2333CC Leiden, the Netherlands
- Centre for Interdisciplinary Genome Research, Faculty of Science, Leiden University, Einsteinweg 55, 2333CC Leiden, the Netherlands
| | - Alireza Mashaghi
- Medical Systems Biophysics and Bioengineering, Leiden Academic Centre for Drug Research, Faculty of Science, Leiden University, Einsteinweg 55, 2333CC Leiden, the Netherlands
- Centre for Interdisciplinary Genome Research, Faculty of Science, Leiden University, Einsteinweg 55, 2333CC Leiden, the Netherlands
- Corresponding author
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9
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Abstract
The art of tying knots is exploited in nature and occurs in multiple applications ranging from being an essential part of scouting programs to engineering molecular knots. Biomolecular knots, such as knotted proteins, bear various cellular functions, and their entanglement is believed to provide them with thermal and kinetic stability. Yet, little is known about the design principles of naturally evolved molecular knots. Intra-chain contacts and chain entanglement contribute to the folding of knotted proteins. Circuit topology, a theory that describes intra-chain contacts, was recently generalized to account for chain entanglement. This generalization is unique to circuit topology and not motivated by other theories. In this conceptual paper, we systematically analyze the circuit topology approach to a description of linear chain entanglement. We utilize a bottom-up approach, i.e., we express entanglement by a set of four fundamental structural units subjected to three (or five) binary topological operations. All knots found in proteins form a well-defined, distinct group which naturally appears if expressed in terms of these basic structural units. We believe that such a detailed, bottom-up understanding of the structure of molecular knots should be beneficial for molecular engineering.
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10
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Scalvini B, Sheikhhassani V, Mashaghi A. Topological principles of protein folding. Phys Chem Chem Phys 2021; 23:21316-21328. [PMID: 34545868 DOI: 10.1039/d1cp03390e] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
What is the topology of a protein and what governs protein folding to a specific topology? This is a fundamental question in biology. The protein folding reaction is a critically important cellular process, which is failing in many prevalent diseases. Understanding protein folding is also key to the design of new proteins for applications. However, our ability to predict the folding of a protein chain is quite limited and much is still unknown about the topological principles of folding. Current predictors of folding kinetics, including the contact order and size, present a limited predictive power, suggesting that these models are fundamentally incomplete. Here, we use a newly developed mathematical framework to define and extract the topology of a native protein conformation beyond knot theory, and investigate the relationship between native topology and folding kinetics in experimentally characterized proteins. We show that not only the folding rate, but also the mechanistic insight into folding mechanisms can be inferred from topological parameters. We identify basic topological features that speed up or slow down the folding process. The approach enabled the decomposition of protein 3D conformation into topologically independent elementary folding units, called circuits. The number of circuits correlates significantly with the folding rate, offering not only an efficient kinetic predictor, but also a tool for a deeper understanding of theoretical folding models. This study contributes to recent work that reveals the critical relevance of topology to protein folding with a new, contact-based, mathematically rigorous perspective. We show that topology can predict folding kinetics when geometry-based predictors like contact order and size fail.
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Affiliation(s)
- Barbara Scalvini
- Medical Systems Biophysics and Bioengineering, Leiden Academic Centre for Drug Research, Faculty of Science, Leiden University, Einsteinweg 55, 2333CC Leiden, The Netherlands.
| | - Vahid Sheikhhassani
- Medical Systems Biophysics and Bioengineering, Leiden Academic Centre for Drug Research, Faculty of Science, Leiden University, Einsteinweg 55, 2333CC Leiden, The Netherlands.
| | - Alireza Mashaghi
- Medical Systems Biophysics and Bioengineering, Leiden Academic Centre for Drug Research, Faculty of Science, Leiden University, Einsteinweg 55, 2333CC Leiden, The Netherlands.
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11
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Abstract
The topological framework of circuit topology has recently been introduced to complement knot theory and to help in understanding the physics of molecular folding. Naturally evolved linear molecular chains, such as proteins and nucleic acids, often fold into 3D conformations with critical chain entanglements and local or global structural symmetries stabilised by formation contacts between different parts of the chain. Circuit topology captures the arrangements of intra-chain contacts within a given folded linear chain and allows for the classification and comparison of chains. Contacts keep chain segments in physical proximity and can be either mechanically hard attachments or soft entanglements that constrain a physical chain. Contrary to knot theory, which offers many established knot invariants, circuit invariants are just being developed. Here, we present polynomial invariants that are both efficient and sufficiently powerful to deal with any combination of soft and hard contacts. A computer implementation and table of chains with up to three contacts is also provided.
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12
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Woodard J, Zheng W, Zhang Y. Protein structural features predict responsiveness to pharmacological chaperone treatment for three lysosomal storage disorders. PLoS Comput Biol 2021; 17:e1009370. [PMID: 34529671 PMCID: PMC8478239 DOI: 10.1371/journal.pcbi.1009370] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/07/2021] [Revised: 09/28/2021] [Accepted: 08/21/2021] [Indexed: 12/15/2022] Open
Abstract
Three-dimensional structures of proteins can provide important clues into the efficacy of personalized treatment. We perform a structural analysis of variants within three inherited lysosomal storage disorders, comparing variants responsive to pharmacological chaperone treatment to those unresponsive to such treatment. We find that predicted ΔΔG of mutation is higher on average for variants unresponsive to treatment, in the case of datasets for both Fabry disease and Pompe disease, in line with previous findings. Using both a single decision tree and an advanced machine learning approach based on the larger Fabry dataset, we correctly predict responsiveness of three Gaucher disease variants, and we provide predictions for untested variants. Many variants are predicted to be responsive to treatment, suggesting that drug-based treatments may be effective for a number of variants in Gaucher disease. In our analysis, we observe dependence on a topological feature reporting on contact arrangements which is likely connected to the order of folding of protein residues, and we provide a potential justification for this observation based on steady-state cellular kinetics. Pharmacological chaperones are small molecule drugs that bind to proteins to help stabilize the folded state. One set of diseases for which this treatment has been effective is the lysosomal storage disorders, which are caused by defective lysosomal enzymes. However, not all genotypes are equally responsive to treatment. For instance, missense mutants that are particularly destabilized relative to WT are less likely to respond. The availability of datasets containing responsiveness data for large numbers of mutants, along with crystal structures of the protein involved in each disease, make machine learning methods incorporating sequence-based and structural data feasible. We hypothesize that data from two diseases, Fabry and Pompe disease, may be useful for predicting responsiveness of variants in the related Gaucher disease. Results suggest that many rare variants in Gaucher disease could be amenable to existing drugs. Results also suggest that drug responsiveness depends on protein topology in such a way that mutations in early-to-fold residues are more likely to be non-responsive to pharmacological chaperone treatment, which is consistent with a simple kinetic model of stability rescue. This study provides an example of how machine learning can be used to inform further studies towards personalized treatment in medicine.
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Affiliation(s)
- Jaie Woodard
- Department of Computational Medicine and Bioinformatics, University of Michigan, Ann Arbor, Michigan, United States of America
| | - Wei Zheng
- Department of Computational Medicine and Bioinformatics, University of Michigan, Ann Arbor, Michigan, United States of America
| | - Yang Zhang
- Department of Computational Medicine and Bioinformatics, University of Michigan, Ann Arbor, Michigan, United States of America
- Department of Biological Chemistry, University of Michigan, Ann Arbor, Michigan, United States of America
- * E-mail:
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14
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Golovnev A, Mashaghi A. Generalized Circuit Topology of Folded Linear Chains. iScience 2020; 23:101492. [PMID: 32896769 PMCID: PMC7481252 DOI: 10.1016/j.isci.2020.101492] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/24/2020] [Revised: 06/20/2020] [Accepted: 08/18/2020] [Indexed: 11/14/2022] Open
Abstract
A wide range of physical systems can be formally mapped to a linear chain of sorted objects. Upon introduction of intrachain interactions, such a chain can "fold" to elaborate topological structures, analogous to folded linear polymer systems. Two distinct chain-topology theories, knot theory and circuit topology, have separately provided insight into the structure, dynamics, and evolution of folded linear polymers such as proteins and genomic DNA. Knot theory, however, ignores intrachain interactions (contacts), whereas chain crossings are ignored in circuit topology. Thus, there is a need for a universal approach that can provide topological description of any folded linear chain. Here, we generalize circuit topology in order to grasp particularities typically addressed by knot theory. We develop a generic approach that is simple, mathematically rigorous, and practically useful for structural classification, analysis of structural dynamics, and engineering applications.
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Affiliation(s)
- Anatoly Golovnev
- Medical Systems Biophysics and Bioengineering, Leiden Academic Centre for Drug Research, Faculty of Science, Leiden University, 2333CC Leiden, the Netherlands
| | - Alireza Mashaghi
- Medical Systems Biophysics and Bioengineering, Leiden Academic Centre for Drug Research, Faculty of Science, Leiden University, 2333CC Leiden, the Netherlands
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15
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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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16
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Heidari M, Schiessel H, Mashaghi A. Circuit Topology Analysis of Polymer Folding Reactions. ACS CENTRAL SCIENCE 2020; 6:839-847. [PMID: 32607431 PMCID: PMC7318069 DOI: 10.1021/acscentsci.0c00308] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/17/2020] [Indexed: 06/03/2023]
Abstract
Circuit topology is emerging as a versatile measure to classify the internal structures of folded linear polymers such as proteins and nucleic acids. The topology framework can be applied to a wide range of problems, most notably molecular folding reactions that are central to biology and molecular engineering. In this Outlook, we discuss the state-of-the art of the technology and elaborate on the opportunities and challenges that lie ahead.
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Affiliation(s)
- Maziar Heidari
- Leiden
Academic Centre for Drug Research, Faculty of Science, Leiden University, Leiden2300 RA, The Netherlands
- Laboratoire
Gulliver, UMR 7083, ESPCI Paris and PSL
University, 75005 Paris, France
| | - Helmut Schiessel
- Institute
Lorentz for Theoretical Physics, Faculty of Science, Leiden University, Leiden 2333 CA, The Netherlands
| | - Alireza Mashaghi
- Leiden
Academic Centre for Drug Research, Faculty of Science, Leiden University, Leiden2300 RA, The Netherlands
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17
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Heidari M, Satarifard V, Mashaghi A. Mapping a single-molecule folding process onto a topological space. Phys Chem Chem Phys 2019; 21:20338-20345. [PMID: 31497825 DOI: 10.1039/c9cp03175h] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023]
Abstract
Physics of protein folding has been dominated by conceptual frameworks including the nucleation-propagation mechanism and the diffusion-collision model, and none address the topological properties of a chain during a folding process. Single-molecule interrogation of folded biomolecules has enabled real-time monitoring of folding processes at an unprecedented resolution. Despite these advances, the topology landscape has not been fully mapped for any chain. Using a novel circuit topology approach, we map the topology landscape of a model polymeric chain. Inspired by single-molecule mechanical interrogation studies, we restrained the ends of a chain and followed fold nucleation dynamics. We find that, before the nucleation, transient local entropic loops dominate. Although the nucleation length of globules is dependent on the cohesive interaction, the ultimate topological states of the collapsed polymer are largely independent of the interaction but depend on the speed of the folding process. After the nucleation, transient topological rearrangements are observed that converge to a steady-state, where the fold grows in a self-similar manner.
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Affiliation(s)
- Maziar Heidari
- Leiden Academic Centre for Drug Research, Faculty of Mathematics and Natural Sciences, Leiden University, Leiden, The Netherlands.
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Kumar A, Chaudhuri D. Cross-linker mediated compaction and local morphologies in a model chromosome. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2019; 31:354001. [PMID: 31112939 DOI: 10.1088/1361-648x/ab2350] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
Chromatin and associated proteins constitute the highly folded structure of chromosomes. We consider a self-avoiding polymer model of the chromatin, segments of which may get cross-linked via protein binders that repel each other. The binders cluster together via the polymer mediated attraction, in turn, folding the polymer. Using molecular dynamics simulations, and a mean field description, we explicitly demonstrate the continuous nature of the folding transition, characterized by unimodal distributions of the polymer size across the transition. At the transition point the chromatin size and cross-linker clusters display large fluctuations, and a maximum in their negative cross-correlation, apart from a critical slowing down. Along the transition, we distinguish the local chain morphologies in terms of topological loops, inter-loop gaps, and zippering. The topologies are dominated by simply connected loops at the criticality, and by zippering in the folded phase.
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Affiliation(s)
- Amit Kumar
- Institute of Physics, Sachivalaya Marg, Bhubaneswar 751005, India. Homi Bhaba National Institute, Anushaktigar, Mumbai 400094, India
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19
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Nikoofard N, Mashaghi A. Implications of Molecular Topology for Nanoscale Mechanical Unfolding. J Phys Chem B 2018; 122:9703-9712. [PMID: 30351148 DOI: 10.1021/acs.jpcb.8b09454] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Abstract
Biopolymer unfolding events are ubiquitous in biology and mechanical unfolding is an established approach to study the structure and function of biomolecules, yet whether and how mechanical unfolding processes depend on native state topology remain unexplored. Here, we investigate how the number of unfolding pathways via mechanical methods depends on the circuit topology of a folded chain, which categorizes the arrangement of intrachain contacts into parallel, crossing, and series. Three unfolding strategies, namely, threading through a pore, pulling from the ends, and pulling by threading, are compared. Considering that some contacts may be unbreakable within the relevant forces, we also study the dependence of the unfolding efficiency on the chain topology. Our analysis reveals that the number of pathways and the efficiency of unfolding are critically determined by topology in a manner that depends on the employed mechanical approach, a significant result for interpretation of the unfolding experiments.
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Affiliation(s)
- Narges Nikoofard
- Institute of Nanoscience and Nanotechnology , University of Kashan , Kashan 51167-87317 , Iran
| | - Alireza Mashaghi
- Leiden Academic Centre for Drug Research, Faculty of Science , Leiden University , Leiden 2333 CC , The Netherlands
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20
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Wruck F, Avellaneda MJ, Koers EJ, Minde DP, Mayer MP, Kramer G, Mashaghi A, Tans SJ. Protein Folding Mediated by Trigger Factor and Hsp70: New Insights from Single-Molecule Approaches. J Mol Biol 2017; 430:438-449. [PMID: 28911846 DOI: 10.1016/j.jmb.2017.09.004] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/27/2017] [Revised: 08/26/2017] [Accepted: 09/04/2017] [Indexed: 01/01/2023]
Abstract
Chaperones assist in protein folding, but what this common phrase means in concrete terms has remained surprisingly poorly understood. We can readily measure chaperone binding to unfolded proteins, but how they bind and affect proteins along folding trajectories has remained obscure. Here we review recent efforts by our labs and others that are beginning to pry into this issue, with a focus on the chaperones trigger factor and Hsp70. Single-molecule methods are central, as they allow the stepwise process of folding to be followed directly. First results have already revealed contrasts with long-standing paradigms: rather than acting only "early" by stabilizing unfolded chain segments, these chaperones can bind and stabilize partially folded structures as they grow to their native state. The findings suggest a fundamental redefinition of the protein folding problem and a more extensive functional repertoire of chaperones than previously assumed.
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Affiliation(s)
- Florian Wruck
- AMOLF, Science Park 104, 1098 XG Amsterdam, the Netherlands
| | | | - Eline J Koers
- AMOLF, Science Park 104, 1098 XG Amsterdam, the Netherlands
| | - David P Minde
- AMOLF, Science Park 104, 1098 XG Amsterdam, the Netherlands
| | - Matthias P Mayer
- Center for Molecular Biology of Heidelberg University (ZMBH), DKFZ-ZMBH Alliance, Im Neuenheimer Feld 282, D-69120 Heidelberg, Germany; German Cancer Research Center (DKFZ), Im Neuenheimer Feld 282, D-69120 Heidelberg, Germany
| | - Günter Kramer
- Center for Molecular Biology of Heidelberg University (ZMBH), DKFZ-ZMBH Alliance, Im Neuenheimer Feld 282, D-69120 Heidelberg, Germany; German Cancer Research Center (DKFZ), Im Neuenheimer Feld 282, D-69120 Heidelberg, Germany
| | - Alireza Mashaghi
- Leiden Academic Centre for Drug Research, Faculty of Mathematics and Natural Sciences, Leiden University, Einsteinweg 55, 2333 CC Leiden, the Netherlands
| | - Sander J Tans
- AMOLF, Science Park 104, 1098 XG Amsterdam, the Netherlands.
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21
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Satarifard V, Heidari M, Mashaghi S, Tans SJ, Ejtehadi MR, Mashaghi A. Topology of polymer chains under nanoscale confinement. NANOSCALE 2017; 9:12170-12177. [PMID: 28805849 DOI: 10.1039/c7nr04220e] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Spatial confinement limits the conformational space accessible to biomolecules but the implications for bimolecular topology are not yet known. Folded linear biopolymers can be seen as molecular circuits formed by intramolecular contacts. The pairwise arrangement of intra-chain contacts can be categorized as parallel, series or cross, and has been identified as a topological property. Using molecular dynamics simulations, we determine the contact order distributions and topological circuits of short semi-flexible linear and ring polymer chains with a persistence length of lp under a spherical confinement of radius Rc. At low values of lp/Rc, the entropy of the linear chain leads to the formation of independent contacts along the chain and accordingly, increases the fraction of series topology with respect to other topologies. However, at high lp/Rc, the fraction of cross and parallel topologies are enhanced in the chain topological circuits with cross becoming predominant. At an intermediate confining regime, we identify a critical value of lp/Rc, at which all topological states have equal probability. Confinement thus equalizes the probability of more complex cross and parallel topologies to the level of the more simple, non-cooperative series topology. Moreover, our topology analysis reveals distinct behaviours for ring- and linear polymers under weak confinement; however, we find no difference between ring- and linear polymers under strong confinement. Under weak confinement, ring polymers adopt parallel and series topologies with equal likelihood, while linear polymers show a higher tendency for series arrangement. The radial distribution analysis of the topology reveals a non-uniform effect of confinement on the topology of polymer chains, thereby imposing more pronounced effects on the core region than on the confinement surface. Additionally, our results reveal that over a wide range of confining radii, loops arranged in parallel and cross topologies have nearly the same contact orders. Such degeneracy implies that the kinetics and transition rates between the topological states cannot be solely explained by contact order. We expect these findings to be of general importance in understanding chaperone assisted protein folding, chromosome architecture, and the evolution of molecular folds.
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Affiliation(s)
- Vahid Satarifard
- Leiden Academic Centre for Drug Research, Faculty of Mathematics and Natural Sciences, Leiden University, Leiden, The Netherlands.
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22
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Heidari M, Satarifard V, Tans SJ, Ejtehadi MR, Mashaghi S, Mashaghi A. Topology of internally constrained polymer chains. Phys Chem Chem Phys 2017; 19:18389-18393. [DOI: 10.1039/c7cp02145c] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023]
Abstract
An interacting partner can provide external control over folding rates and realized topologies.
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Affiliation(s)
- Maziar Heidari
- Leiden Academic Centre for Drug Research
- Faculty of Mathematics and Natural Sciences
- Leiden University
- Leiden
- The Netherlands
| | - Vahid Satarifard
- Leiden Academic Centre for Drug Research
- Faculty of Mathematics and Natural Sciences
- Leiden University
- Leiden
- The Netherlands
| | | | | | - Samaneh Mashaghi
- School of Engineering and Applied Sciences and Department of Physics
- Harvard University
- Cambridge
- USA
| | - Alireza Mashaghi
- Leiden Academic Centre for Drug Research
- Faculty of Mathematics and Natural Sciences
- Leiden University
- Leiden
- The Netherlands
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23
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Ghafari M, Mashaghi A. On the role of topology in regulating transcriptional cascades. Phys Chem Chem Phys 2017; 19:25168-25179. [DOI: 10.1039/c7cp02671d] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Topology of interactions in a transcriptional cascade determines the behavior of its signal-response profile and the activation states of genes.
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Affiliation(s)
- Mahan Ghafari
- Leiden Academic Centre for Drug Research
- Faculty of Mathematics and Natural Sciences
- Leiden University
- Leiden
- The Netherlands
| | - Alireza Mashaghi
- Leiden Academic Centre for Drug Research
- Faculty of Mathematics and Natural Sciences
- Leiden University
- Leiden
- The Netherlands
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24
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Kumar V, Krishna KV, Khanna S, Joshi KB. Aggregation propensity of amyloidogenic and elastomeric dipeptides constituents. Tetrahedron 2016. [DOI: 10.1016/j.tet.2016.07.022] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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Abstract
![]()
We review how major cell behaviors,
such as bacterial growth laws,
are derived from the physical chemistry of the cell’s proteins.
On one hand, cell actions depend on the individual biological functionalities
of their many genes and proteins. On the other hand, the common physics
among proteins can be as important as the unique biology that distinguishes
them. For example, bacterial growth rates depend strongly on temperature.
This dependence can be explained by the folding stabilities across
a cell’s proteome. Such modeling explains how thermophilic
and mesophilic organisms differ, and how oxidative damage of highly
charged proteins can lead to unfolding and aggregation in aging cells.
Cells have characteristic time scales. For example, E. coli can duplicate as fast as 2–3 times per hour. These time scales
can be explained by protein dynamics (the rates of synthesis and degradation,
folding, and diffusional transport). It rationalizes how bacterial
growth is slowed down by added salt. In the same way that the behaviors
of inanimate materials can be expressed in terms of the statistical
distributions of atoms and molecules, some cell behaviors can be expressed
in terms of distributions of protein properties, giving insights into
the microscopic basis of growth laws in simple cells.
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Affiliation(s)
- Kingshuk Ghosh
- Department of Physics and Astronomy, University of Denver , Denver, Colorado 80209, United States
| | - Adam M R de Graff
- Laufer Center for Physical and Quantitative Biology and Departments of Chemistry and Physics and Astronomy, Stony Brook University , Stony Brook, New York 11794, United States
| | - Lucas Sawle
- Department of Physics and Astronomy, University of Denver , Denver, Colorado 80209, United States
| | - Ken A Dill
- Laufer Center for Physical and Quantitative Biology and Departments of Chemistry and Physics and Astronomy, Stony Brook University , Stony Brook, New York 11794, United States
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Nikoofard N, Mashaghi A. Topology sorting and characterization of folded polymers using nano-pores. NANOSCALE 2016; 8:4643-4649. [PMID: 26853059 DOI: 10.1039/c5nr08828c] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
Here we report on the translocation of folded polymers through nano-pores using molecular dynamic simulations. Two cases are studied: one in which a folded molecule unfolds upon passage and one in which the folding remains intact as the molecule passes through the nano-pore. The topology of a folded polymer chain is defined as the arrangement of the intramolecular contacts, known as circuit topology. In the case where intramolecular contacts remain intact, we show that the dynamics of passage through a nano-pore varies for molecules with differing topologies: a phenomenon that can be exploited to enrich certain topologies in mixtures. We find that the nano-pore allows reading of the topology for short chains. Moreover, when the passage is coupled with unfolding, the nano-pore enables discrimination between pure states, i.e., states in which the majority of contacts are arranged identically. In this case, as we show here, it is also possible to read the positions of the contact sites along a chain. Our results demonstrate the applicability of nano-pore technology to characterize and sort molecules based on their topology.
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Affiliation(s)
- Narges Nikoofard
- Institute of Nanoscience and Nanotechnology, University of Kashan, Kashan 51167-87317, Iran
| | - Alireza Mashaghi
- Harvard Medical School, Harvard University, Boston, MA 02115, USA.
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27
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Design principles for rapid folding of knotted DNA nanostructures. Nat Commun 2016; 7:10803. [PMID: 26887681 PMCID: PMC4759626 DOI: 10.1038/ncomms10803] [Citation(s) in RCA: 38] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/02/2015] [Accepted: 01/20/2016] [Indexed: 12/27/2022] Open
Abstract
Knots are some of the most remarkable topological features in nature. Self-assembly of knotted polymers without breaking or forming covalent bonds is challenging, as the chain needs to be threaded through previously formed loops in an exactly defined order. Here we describe principles to guide the folding of highly knotted single-chain DNA nanostructures as demonstrated on a nano-sized square pyramid. Folding of knots is encoded by the arrangement of modules of different stability based on derived topological and kinetic rules. Among DNA designs composed of the same modules and encoding the same topology, only the one with the folding pathway designed according to the ‘free-end' rule folds efficiently into the target structure. Besides high folding yield on slow annealing, this design also folds rapidly on temperature quenching and dilution from chemical denaturant. This strategy could be used to design folding of other knotted programmable polymers such as RNA or proteins. Driven by complementary base pairing, artificial single-chain DNA is capable of forming complex 3D architectures if an appropriate folding pathway can be realised. Here, the authors describe the design principles for rapidly folding structures, exemplified through fabrication of a nanosized square pyramid.
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Mashaghi A, Ramezanpour A. Distance measures and evolution of polymer chains in their topological space. SOFT MATTER 2015; 11:6576-6585. [PMID: 26189822 DOI: 10.1039/c5sm01482d] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
Conformational transitions are ubiquitous in biomolecular systems, have significant functional roles and are subject to evolutionary pressures. Here we provide a first theoretical framework for topological transition, i.e. conformational transitions that are associated with changes in molecular topology. For folded linear biomolecules, arrangement of intramolecular contacts is identified as a key topological property, termed as circuit topology. Distance measures are proposed as reaction coordinates to represent progress along a pathway from initial topology to final topology. Certain topological classes are shown to be more accessible from a random topology. We study dynamic stability and pathway degeneracy associated with a topological reaction and found that off-pathways might seriously hamper evolution to desired topologies. Finally we present an algorithm for estimating the number of intermediate topologies visited during a topological reaction. The results of this study are relevant to, among others, structural studies of RNA and proteins, analysis of topologically associated domains in chromosomes, and molecular evolution.
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Affiliation(s)
- Alireza Mashaghi
- Harvard Medical School, Harvard University, Boston, Massachusetts, USA.
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29
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Mugler A, Tans SJ, Mashaghi A. Circuit topology of self-interacting chains: implications for folding and unfolding dynamics. Phys Chem Chem Phys 2015; 16:22537-44. [PMID: 25228051 DOI: 10.1039/c4cp03402c] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Understanding the relationship between molecular structure and folding is a central problem in disciplines ranging from biology to polymer physics and DNA origami. Topology can be a powerful tool to address this question. For a folded linear chain, the arrangement of intra-chain contacts is a topological property because rearranging the contacts requires discontinuous deformations. Conversely, the topology is preserved when continuously stretching the chain while maintaining the contact arrangement. Here we investigate how the folding and unfolding of linear chains with binary contacts is guided by the topology of contact arrangements. We formalize the topology by describing the relations between any two contacts in the structure, which for a linear chain can either be in parallel, in series, or crossing each other. We show that even when other determinants of folding rate such as contact order and size are kept constant, this 'circuit' topology determines folding kinetics. In particular, we find that the folding rate increases with the fractions of parallel and crossed relations. Moreover, we show how circuit topology constrains the conformational phase space explored during folding and unfolding: the number of forbidden unfolding transitions is found to increase with the fraction of parallel relations and to decrease with the fraction of series relations. Finally, we find that circuit topology influences whether distinct intermediate states are present, with crossed contacts being the key factor. The approach presented here can be more generally applied to questions on molecular dynamics, evolutionary biology, molecular engineering, and single-molecule biophysics.
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Affiliation(s)
- Andrew Mugler
- Department of Physics, Purdue University, 525 Northwestern Avenue, West Lafayette, IN 47907, USA
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30
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Mashaghi A, Ramezanpour A. Circuit topology of linear polymers: a statistical mechanical treatment. RSC Adv 2015. [DOI: 10.1039/c5ra08106h] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022] Open
Abstract
Circuit topology landscapes of linear polymer chains with intra-chain contacts are defined and studied for their properties.
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