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Kapoor U, Kim YC, Mittal J. Coarse-Grained Models to Study Protein-DNA Interactions and Liquid-Liquid Phase Separation. J Chem Theory Comput 2024; 20:1717-1731. [PMID: 37988476 PMCID: PMC10911113 DOI: 10.1021/acs.jctc.3c00525] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/19/2023] [Revised: 10/20/2023] [Accepted: 10/27/2023] [Indexed: 11/23/2023]
Abstract
Recent advances in coarse-grained (CG) computational models for DNA have enabled molecular-level insights into the behavior of DNA in complex multiscale systems. However, most existing CG DNA models are not compatible with CG protein models, limiting their applications for emerging topics such as protein-nucleic acid assemblies. Here, we present a new computationally efficient CG DNA model. We first use experimental data to establish the model's ability to predict various aspects of DNA behavior, including melting thermodynamics and relevant local structural properties such as the major and minor grooves. We then employ an all-atom hydropathy scale to define nonbonded interactions between protein and DNA sites, to make our DNA model compatible with an existing CG protein model (HPS-Urry), which is extensively used to study protein phase separation, and show that our new model reasonably reproduces the experimental binding affinity for a prototypical protein-DNA system. To further demonstrate the capabilities of this new model, we simulate a full nucleosome with and without histone tails, on a microsecond time scale, generating conformational ensembles and provide molecular insights into the role of histone tails in influencing the liquid-liquid phase separation (LLPS) of HP1α proteins. We find that histone tails interact favorably with DNA, influencing the conformational ensemble of the DNA and antagonizing the contacts between HP1α and DNA, thus affecting the ability of DNA to promote LLPS of HP1α. These findings shed light on the complex molecular framework that fine-tunes the phase transition properties of heterochromatin proteins and contributes to heterochromatin regulation and function. Overall, the CG DNA model presented here is suitable to facilitate micrometer-scale studies with sub-nm resolution in many biological and engineering applications and can be used to investigate protein-DNA complexes, such as nucleosomes, or LLPS of proteins with DNA, enabling a mechanistic understanding of how molecular information may be propagated at the genome level.
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Affiliation(s)
- Utkarsh Kapoor
- Artie
McFerrin Department of Chemical Engineering, Texas A&M University, College Station, Texas 78743, United States
| | - Young C. Kim
- Center
for Materials Physics and Technology, Naval
Research Laboratory, Washington, District of Columbia 20375, United States
| | - Jeetain Mittal
- Artie
McFerrin Department of Chemical Engineering, Texas A&M University, College Station, Texas 78743, United States
- Department
of Chemistry, Texas A&M University, College Station, Texas 78743, United States
- Interdisciplinary
Graduate Program in Genetics in Genomics, Texas A&M University, College
Station, Texas 78743, United States
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2
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Mu ZC, Tan YL, Liu J, Zhang BG, Shi YZ. Computational Modeling of DNA 3D Structures: From Dynamics and Mechanics to Folding. Molecules 2023; 28:4833. [PMID: 37375388 DOI: 10.3390/molecules28124833] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/09/2023] [Revised: 06/11/2023] [Accepted: 06/14/2023] [Indexed: 06/29/2023] Open
Abstract
DNA carries the genetic information required for the synthesis of RNA and proteins and plays an important role in many processes of biological development. Understanding the three-dimensional (3D) structures and dynamics of DNA is crucial for understanding their biological functions and guiding the development of novel materials. In this review, we discuss the recent advancements in computer methods for studying DNA 3D structures. This includes molecular dynamics simulations to analyze DNA dynamics, flexibility, and ion binding. We also explore various coarse-grained models used for DNA structure prediction or folding, along with fragment assembly methods for constructing DNA 3D structures. Furthermore, we also discuss the advantages and disadvantages of these methods and highlight their differences.
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Affiliation(s)
- Zi-Chun Mu
- Research Center of Nonlinear Science, School of Mathematical & Physical Sciences, Wuhan Textile University, Wuhan 430073, China
- School of Computer Science and Artificial Intelligence, Wuhan Textile University, Wuhan 430073, China
| | - Ya-Lan Tan
- Research Center of Nonlinear Science, School of Mathematical & Physical Sciences, Wuhan Textile University, Wuhan 430073, China
| | - Jie Liu
- Research Center of Nonlinear Science, School of Mathematical & Physical Sciences, Wuhan Textile University, Wuhan 430073, China
| | - Ben-Gong Zhang
- Research Center of Nonlinear Science, School of Mathematical & Physical Sciences, Wuhan Textile University, Wuhan 430073, China
| | - Ya-Zhou Shi
- Research Center of Nonlinear Science, School of Mathematical & Physical Sciences, Wuhan Textile University, Wuhan 430073, China
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Sun LZ, Qian JL, Cai P, Xu X. Mutual effects between single-stranded DNA conformation and Na +-Mg 2+ ion competition in mixed salt solutions. Phys Chem Chem Phys 2022; 24:20867-20881. [PMID: 36043348 DOI: 10.1039/d2cp02737b] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The ion-dependence of single-stranded DNA (ssDNA) conformational changes has attracted growing attention because of its biological and technological importance. Although single-species ion effects have been extensively explored, it is challenging to study the ssDNA conformational properties under mixed monovalent/divalent ion conditions due to the complications of ssDNA flexibility and ion-ion competition. In this study, we apply Langevin dynamics simulations to investigate mixed Na+/Mg2+ ion-dependent ssDNA conformations. The ssDNA structure is described using a coarse-grained model, in which the phosphate, base, and sugar of each nucleotide are represented by three different beads. A novel improvement in our simulation model is that mixed-salt-related electrostatic interactions are computed via combining Manning counterion condensation (MCC) theory with the Monte Carlo tightly bound ion (MCTBI) model. Based on this MCC-MCTBI combination, we report new empirical functions to describe the ion-concentration-dependent and ssDNA conformation/structure-dependent electrostatic effects. The calculation results relating to the ion binding properties and the simulation results relating to the ssDNA conformational properties are validated against experimental results. In addition, our simulation results suggest a quantitative relationship between the ssDNA conformation and Na+-Mg2+ competition; this in turn reveals their mutual impact in the ion atmosphere.
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Affiliation(s)
- Li-Zhen Sun
- Department of Applied Physics, Zhejiang University of Technology, Hangzhou 310023, China.
| | - Jun-Lin Qian
- Department of Applied Physics, Zhejiang University of Technology, Hangzhou 310023, China.
| | - Pinggen Cai
- Department of Applied Physics, Zhejiang University of Technology, Hangzhou 310023, China.
| | - Xiaojun Xu
- Institute of Bioinformatics and Medical Engineering, Jiangsu University of Technology, Changzhou, 213001, China
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Assenza S, Pérez R. Accurate Sequence-Dependent Coarse-Grained Model for Conformational and Elastic Properties of Double-Stranded DNA. J Chem Theory Comput 2022; 18:3239-3256. [PMID: 35394775 PMCID: PMC9097290 DOI: 10.1021/acs.jctc.2c00138] [Citation(s) in RCA: 9] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
Abstract
![]()
We introduce MADna,
a sequence-dependent coarse-grained model of
double-stranded DNA (dsDNA), where each nucleotide is described by
three beads localized at the sugar, at the base moiety, and at the
phosphate group, respectively. The sequence dependence is included
by considering a step-dependent parametrization of the bonded interactions,
which are tuned in order to reproduce the values of key observables
obtained from exhaustive atomistic simulations from the literature.
The predictions of the model are benchmarked against an independent
set of all-atom simulations, showing that it captures with high fidelity
the sequence dependence of conformational and elastic features beyond
the single step considered in its formulation. A remarkably good agreement
with experiments is found for both sequence-averaged and sequence-dependent
conformational and elastic features, including the stretching and
torsion moduli, the twist–stretch and twist–bend couplings,
the persistence length, and the helical pitch. Overall, for the inspected
quantities, the model has a precision comparable to atomistic simulations,
hence providing a reliable coarse-grained description for the rationalization
of single-molecule experiments and the study of cellular processes
involving dsDNA. Owing to the simplicity of its formulation, MADna
can be straightforwardly included in common simulation engines. Particularly,
an implementation of the model in LAMMPS is made available on an online
repository to ease its usage within the DNA research community.
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5
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Nguyen HTL, Huang DM. Systematic bottom-up molecular coarse-graining via force and torque matching using anisotropic particles. J Chem Phys 2022; 156:184118. [DOI: 10.1063/5.0085006] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We derive a systematic and general method for parametrizing coarse-grained molecular models consisting of anisotropic particles from fine-grained (e.g. all-atom) models for condensed-phase molecular dynamics simulations. The method, which we call anisotropic force-matching coarse-graining (AFM-CG), is based on rigorous statistical mechanical principles, enforcing consistency between the coarse-grained and fine-grained phase-space distributions to derive equations for the coarse-grained forces, torques, masses, and moments of inertia in terms of properties of a condensed-phase fine-grained system. We verify the accuracy and efficiency of the method by coarse-graining liquid-state systems of two different anisotropic organic molecules, benzene and perylene, and show that the parametrized coarse-grained models more accurately describe properties of these systems than previous anisotropic coarse-grained models parametrized using other methods that do not account for finite-temperature and many-body effects on the condensed-phase coarse-grained interactions. The AFM-CG method will be useful for developing accurate and efficient dynamical simulation models of condensed-phase systems of molecules consisting of large, rigid, anisotropic fragments, such as liquid crystals, organic semiconductors, and nucleic acids.
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Sun T, Minhas V, Korolev N, Mirzoev A, Lyubartsev AP, Nordenskiöld L. Bottom-Up Coarse-Grained Modeling of DNA. Front Mol Biosci 2021; 8:645527. [PMID: 33816559 PMCID: PMC8010198 DOI: 10.3389/fmolb.2021.645527] [Citation(s) in RCA: 15] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/23/2020] [Accepted: 02/22/2021] [Indexed: 12/22/2022] Open
Abstract
Recent advances in methodology enable effective coarse-grained modeling of deoxyribonucleic acid (DNA) based on underlying atomistic force field simulations. The so-called bottom-up coarse-graining practice separates fast and slow dynamic processes in molecular systems by averaging out fast degrees of freedom represented by the underlying fine-grained model. The resulting effective potential of interaction includes the contribution from fast degrees of freedom effectively in the form of potential of mean force. The pair-wise additive potential is usually adopted to construct the coarse-grained Hamiltonian for its efficiency in a computer simulation. In this review, we present a few well-developed bottom-up coarse-graining methods, discussing their application in modeling DNA properties such as DNA flexibility (persistence length), conformation, "melting," and DNA condensation.
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Affiliation(s)
- Tiedong Sun
- School of Biological Sciences, Nanyang Technological University, Singapore, Singapore
| | - Vishal Minhas
- School of Biological Sciences, Nanyang Technological University, Singapore, Singapore
| | - Nikolay Korolev
- School of Biological Sciences, Nanyang Technological University, Singapore, Singapore
| | - Alexander Mirzoev
- School of Biological Sciences, Nanyang Technological University, Singapore, Singapore
| | - Alexander P. Lyubartsev
- Department of Materials and Environmental Chemistry, Stockholm University, Stockholm, Sweden
| | - Lars Nordenskiöld
- School of Biological Sciences, Nanyang Technological University, Singapore, Singapore
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7
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Jayaraman A. 100th Anniversary of Macromolecular Science Viewpoint: Modeling and Simulation of Macromolecules with Hydrogen Bonds: Challenges, Successes, and Opportunities. ACS Macro Lett 2020; 9:656-665. [PMID: 35648569 DOI: 10.1021/acsmacrolett.0c00134] [Citation(s) in RCA: 33] [Impact Index Per Article: 8.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022]
Abstract
Macromolecular materials with directional interactions such as hydrogen bonds exhibit numerous attractive features in terms of structure, thermodynamics, and dynamics. Besides enabling precise tuning of desirable geometries in the assembled state (e.g., programmable coordination numbers depending on the valency of the directional interaction), mixing in a blend/composite through stabilization via hydrogen bonds between the various components, hydrogen bonds can also impart responsiveness to external stimuli (e.g., temperature, pH). In biomacromolecules (e.g., proteins, DNA, polysaccharides), hydrogen bonds play a key role in stabilizing secondary and tertiary structures, which in turn define the function of these macromolecules. In this Viewpoint, I present the challenges, successes, and opportunities for molecular modeling and simulations to conduct fundamental and application-focused research on macromolecular materials with hydrogen bonding interactions. The past successes and limitations of atomistic simulations are discussed first, followed by highlights from recent developments in coarse-grained modeling and their use in studies of (synthetic and biologically relevant) macromolecular materials. Model development focused on polynucleotides (e.g., DNA, RNA, etc.), polypeptides, polysaccharides, and synthetic polymers at experimentally relevant conditions are highlighted. This viewpoint ends with potential future directions for macromolecular modeling and simulations with other types of directional interactions beyond hydrogen bonding.
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Affiliation(s)
- Arthi Jayaraman
- Department of Chemical and Biomolecular Engineering, University of Delaware, 150 Academy Street, Newark, Delaware 19716, United States
- Department of Materials Science and Engineering, University of Delaware, Newark, Delaware 19716, United States
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8
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Mishra G, Bigman LS, Levy Y. ssDNA diffuses along replication protein A via a reptation mechanism. Nucleic Acids Res 2020; 48:1701-1714. [PMID: 31919510 PMCID: PMC7038930 DOI: 10.1093/nar/gkz1202] [Citation(s) in RCA: 22] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/15/2019] [Revised: 11/23/2019] [Accepted: 01/08/2020] [Indexed: 01/30/2023] Open
Abstract
Replication protein A (RPA) plays a critical role in all eukaryotic DNA processing involving single-stranded DNA (ssDNA). Contrary to the notion that RPA provides solely inert protection to transiently formed ssDNA, the RPA-ssDNA complex acts as a dynamic DNA processing unit. Here, we studied the diffusion of RPA along 60 nt ssDNA using a coarse-grained model in which the ssDNA-RPA interface was modeled by both aromatic and electrostatic interactions. Our study provides direct evidence of bulge formation during the diffusion of ssDNA along RPA. Bulges can form at a few sites along the interface and store 1-7 nt of ssDNA whose release, upon bulge dissolution, leads to propagation of ssDNA diffusion. These findings thus support the reptation mechanism, which involves bulge formation linked to the aromatic interactions, whose short range nature reduces cooperativity in ssDNA diffusion. Greater cooperativity and a larger diffusion coefficient for ssDNA diffusion along RPA are observed for RPA variants with weaker aromatic interactions and for interfaces homogenously stabilized by electrostatic interactions. ssDNA propagation in the latter instance is characterized by lower probabilities of bulge formation; thus, it may fit the sliding-without-bulge model better than the reptation model. Thus, the reptation mechanism allows ssDNA mobility despite the extensive and high affinity interface of RPA with ssDNA. The short-range aromatic interactions support bulge formation while the long-range electrostatic interactions support the release of the stored excess ssDNA in the bulge and thus the overall diffusion.
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Affiliation(s)
- Garima Mishra
- Department of Structural Biology, Weizmann Institute of Science, Rehovot 76100, Israel.,Department of Physics, Indian Institute of Technology Kanpur, Kanpur, 208016, India
| | - Lavi S Bigman
- Department of Structural Biology, Weizmann Institute of Science, Rehovot 76100, Israel
| | - Yaakov Levy
- Department of Structural Biology, Weizmann Institute of Science, Rehovot 76100, Israel
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9
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Kim HS, Brown NA, Zauscher S, Yingling YG. Effect of Octadecylamine Surfactant on DNA Interactions with Graphene Surfaces. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2020; 36:931-938. [PMID: 31917584 DOI: 10.1021/acs.langmuir.9b02926] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Understanding of how to integrate DNA molecules with graphene materials is important for the development of biosensors and biomolecular logic circuits. For some of these applications, controlling DNA structural conformation on the graphene substrate is critically important and can be achieved through the use of self-assembled monolayers. Here, we performed all-atom molecular dynamics simulations to understand how various 1-octadecylamine (ODA) coatings of the graphene surface affect the conformation of double-stranded DNA (dsDNA) on the surface. The simulation results demonstrated that dsDNA structures become more stable as ODA concentration increases due to the formation of DNA-ODA hydrogen bonds and reduction of DNA-surface interactions, which aid in retaining internal DNA interactions. Specifically, the interaction of ODA molecules with DNA prevents nucleobases from forming π-π stacking interactions with the surface. Some dsDNA conformations, such as sharp kinks or unwinding, can occur more frequently in DNA with A-T sequences due to weaker pairing interactions than with G-C sequences. Furthermore, our results conclude that both DNA sequence and ODA concentration play an essential role in experimentally observed conformational changes of DNA on the graphene surface.
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Affiliation(s)
- Ho Shin Kim
- Department of Materials Science and Engineering , North Carolina State University , Raleigh , North Carolina 27695 , United States
| | - Nathanael A Brown
- Department of Materials Science and Engineering , North Carolina State University , Raleigh , North Carolina 27695 , United States
| | - Stefan Zauscher
- Department of Mechanical Engineering and Materials Science , Duke University , Durham , North Carolina 27708 , United States
| | - Yaroslava G Yingling
- Department of Materials Science and Engineering , North Carolina State University , Raleigh , North Carolina 27695 , United States
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10
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Snodin BEK, Schreck JS, Romano F, Louis AA, Doye JPK. Coarse-grained modelling of the structural properties of DNA origami. Nucleic Acids Res 2019; 47:1585-1597. [PMID: 30605514 PMCID: PMC6379721 DOI: 10.1093/nar/gky1304] [Citation(s) in RCA: 55] [Impact Index Per Article: 11.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/27/2018] [Revised: 11/17/2018] [Accepted: 12/20/2018] [Indexed: 01/12/2023] Open
Abstract
We use the oxDNA coarse-grained model to provide a detailed characterization of the fundamental structural properties of DNA origami, focussing on archetypal 2D and 3D origami. The model reproduces well the characteristic pattern of helix bending in a 2D origami, showing that it stems from the intrinsic tendency of anti-parallel four-way junctions to splay apart, a tendency that is enhanced both by less screened electrostatic interactions and by increased thermal motion. We also compare to the structure of a 3D origami whose structure has been determined by cryo-electron microscopy. The oxDNA average structure has a root-mean-square deviation from the experimental structure of 8.4 Å, which is of the order of the experimental resolution. These results illustrate that the oxDNA model is capable of providing detailed and accurate insights into the structure of DNA origami, and has the potential to be used to routinely pre-screen putative origami designs and to investigate the molecular mechanisms that regulate the properties of DNA origami.
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Affiliation(s)
- Benedict E K Snodin
- Physical, and Theoretical Chemistry Laboratory, Department of Chemistry, South Parks Road, Oxford OX1 3QZ, UK
| | - John S Schreck
- Department of Chemical Engineering, Columbia University, 500 W 120th Street, New York, NY 10027, USA
| | - Flavio Romano
- Dipartimento di Scienze Molecolari e Nanosistemi, Universit Ca' Foscari, Via Torino 155, 30172 Venezia Mestre, Italy
| | - Ard A Louis
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, 1 Keble Road, Oxford OX1 3NP, UK
| | - Jonathan P K Doye
- Physical, and Theoretical Chemistry Laboratory, Department of Chemistry, South Parks Road, Oxford OX1 3QZ, UK
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11
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De Bruin L, Maddocks JH. cgDNAweb: a web interface to the cgDNA sequence-dependent coarse-grain model of double-stranded DNA. Nucleic Acids Res 2019; 46:W5-W10. [PMID: 29905876 PMCID: PMC6030996 DOI: 10.1093/nar/gky351] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/09/2018] [Accepted: 05/09/2018] [Indexed: 12/13/2022] Open
Abstract
The sequence-dependent statistical mechanical properties of fragments of double-stranded DNA is believed to be pertinent to its biological function at length scales from a few base pairs (or bp) to a few hundreds of bp, e.g. indirect read-out protein binding sites, nucleosome positioning sequences, phased A-tracts, etc. In turn, the equilibrium statistical mechanics behaviour of DNA depends upon its ground state configuration, or minimum free energy shape, as well as on its fluctuations as governed by its stiffness (in an appropriate sense). We here present cgDNAweb, which provides browser-based interactive visualization of the sequence-dependent ground states of double-stranded DNA molecules, as predicted by the underlying cgDNA coarse-grain rigid-base model of fragments with arbitrary sequence. The cgDNAweb interface is specifically designed to facilitate comparison between ground state shapes of different sequences. The server is freely available at cgDNAweb.epfl.ch with no login requirement.
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Affiliation(s)
- Lennart De Bruin
- Instituut-Lorentz for Theoretical Physics, Leiden University, P.O. Box 9506, 2300 RA Leiden, The Netherlands
| | - John H Maddocks
- Institut de Mathématiques, Station 8, Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne CH-1015, Switzerland
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12
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Zeferino RC, Mota NSRS, Grinevicius VMAS, Filipe KB, Sulis PM, Silva FRMB, Filho DW, Pich CT, Pedrosa RC. Targeting ROS overgeneration by N-benzyl-2-nitro-1-imidazole-acetamide as a potential therapeutic reposition approach for cancer therapy. Invest New Drugs 2019; 38:785-799. [PMID: 31257554 DOI: 10.1007/s10637-019-00820-5] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/19/2019] [Accepted: 06/17/2019] [Indexed: 11/25/2022]
Abstract
BackgroundWe investigated the role of reactive oxygen species (ROS) in the anticancer mechanism of N-benzyl-2-nitro-1-imidazole-acetamide (BZN), a drug used in Chagas' disease treatment. MethodsBALB/c mice, inoculated with Ehrlich ascites carcinoma (EAC), were treated with BZN or BZN + Nacylcysteine (NAC) or NAC for 9 days. Subsequently, the inhibition of tumor growth and angiogenesis as well as animal survival were evaluated. Apoptosis and the cell cycle were evaluated using fluorescence microscopy and flow cytometry, while oxidative stress was evaluated by measuring TBARS content, DNA damage, calcium influx and ROS generation and antioxidant defenses (CAT, SOD, GPx, GST and GR). Immunoblotting was used to evaluate key death and cell cycle proteins. Results BZN treatment inhibited tumor progression (79%), angiogenesis (2.8-fold) and increased animal survival (29%). Moreover, BZN increased ROS levels (42%), calcium influx (55%), TBARS contents (1.9-fold), SOD (4.4-fold), GPx (17.5-fold) and GST (3-fold) activities and GSH depletion (2.5-fold) also caused DNA fragmentation (7.6-fold), increased cleaved PARP and promoted the trapping of cells in the G1 phase, as corroborated by the reduction in cyclin A and increased CDK2 protein levels. In silico DNA and molecular dynamic simulations showed H-bonds and hydrophobic interactions that were confirmed by circular dichroism. Increased apoptosis (232%), induced by treatment with BZN, was demonstrated by apoptotic cell staining and p53 level. Conclusion The current findings indicate that BZN acts as a tumor growth inhibitor and anti-angiogenic agent by ROS overgeneration, which interact with DNA causing damage and triggering apoptosis.
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Affiliation(s)
- Rodrigo C Zeferino
- Biochemistry Department, Federal University of Santa Catarina (UFSC), Florianópolis, SC, Brazil
| | - Nádia S R S Mota
- Biochemistry Department, Federal University of Santa Catarina (UFSC), Florianópolis, SC, Brazil
| | | | - Karina B Filipe
- Department of Clinical Analysis, Federal University of Paraná (UFPR), Curitiba, PR, Brazil
| | - Paola M Sulis
- Biochemistry Department, Federal University of Santa Catarina (UFSC), Florianópolis, SC, Brazil
| | - Fátima R M B Silva
- Biochemistry Department, Federal University of Santa Catarina (UFSC), Florianópolis, SC, Brazil
| | - Danilo W Filho
- Ecology and Zoology Department, Federal University of Santa Catarina (UFSC), Florianópolis, SC, Brazil
| | - Claus T Pich
- Center for Sciences, Technologies and Health, Federal University of Santa Catarina (UFSC), Araranguá, SC, Brazil
| | - Rozangela C Pedrosa
- Biochemistry Department, Federal University of Santa Catarina (UFSC), Florianópolis, SC, Brazil.
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13
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Pal A, Levy Y. Structure, stability and specificity of the binding of ssDNA and ssRNA with proteins. PLoS Comput Biol 2019; 15:e1006768. [PMID: 30933978 PMCID: PMC6467422 DOI: 10.1371/journal.pcbi.1006768] [Citation(s) in RCA: 36] [Impact Index Per Article: 7.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/13/2018] [Revised: 04/16/2019] [Accepted: 01/01/2019] [Indexed: 02/06/2023] Open
Abstract
Recognition of single-stranded DNA (ssDNA) or single-stranded RNA (ssRNA) is important for many fundamental cellular functions. A variety of single-stranded DNA-binding proteins (ssDBPs) and single-stranded RNA-binding proteins (ssRBPs) have evolved that bind ssDNA and ssRNA, respectively, with varying degree of affinities and specificities to form complexes. Structural studies of these complexes provide key insights into their recognition mechanism. However, computational modeling of the specific recognition process and to predict the structure of the complex is challenging, primarily due to the heterogeneity of their binding energy landscape and the greater flexibility of ssDNA or ssRNA compared with double-stranded nucleic acids. Consequently, considerably fewer computational studies have explored interactions between proteins and single-stranded nucleic acids compared with protein interactions with double-stranded nucleic acids. Here, we report a newly developed energy-based coarse-grained model to predict the structure of ssDNA–ssDBP and ssRNA–ssRBP complexes and to assess their sequence-specific interactions and stabilities. We tuned two factors that can modulate specific recognition: base–aromatic stacking strength and the flexibility of the single-stranded nucleic acid. The model was successfully applied to predict the binding conformations of 12 distinct ssDBP and ssRBP structures with their cognate ssDNA and ssRNA partners having various sequences. Estimated binding energies agreed well with the corresponding experimental binding affinities. Bound conformations from the simulation showed a funnel-shaped binding energy distribution where the native-like conformations corresponded to the energy minima. The various ssDNA–protein and ssRNA–protein complexes differed in the balance of electrostatic and aromatic energies. The lower affinity of the ssRNA–ssRBP complexes compared with the ssDNA–ssDBP complexes stems from lower flexibility of ssRNA compared to ssDNA, which results in higher rate constants for the dissociation of the complex (koff) for complexes involving the former. Quantifying bimolecular self-assembly is pivotal to understanding cellular function. In recent years, a large progress has been made in understanding the structure and biophysics of protein-protein interactions. Particularly, various computational tools are available for predicting these structures and to estimate their stability and the driving forces of their formation. The understating of the interactions between proteins and nucleic acids, however, is still limited, presumably due to the involvement of non-specific interactions as well as the high conformational plasticity that may demand an induced-fit mechanism. In particular, the interactions between proteins and single-stranded nucleic acids (i.e., single-stranded DNA and RNA) is very challenging due to their high flexibility. Furthermore, the interface between proteins and single-stranded nucleic acids is often chemically more heterogeneous than the interface between proteins and double-stranded DNA. In this study, we developed a coarse-grained computational model to predict the structure of complexes between proteins and single-stranded nucleic acids. The model was applied to estimate binding affinities and the estimated binding energies agreed well with the corresponding experimental binding affinities. The kinetics of association as well as the specificity of the complexes between proteins and ssDNA are different than those with ssRNA, mostly due to differences in their conformational flexibility.
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Affiliation(s)
- Arumay Pal
- Department of Structural Biology, Weizmann Institute of Science, Rehovot, Israel
| | - Yaakov Levy
- Department of Structural Biology, Weizmann Institute of Science, Rehovot, Israel
- * E-mail:
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15
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Peter EK, Černý J. A Hybrid Hamiltonian for the Accelerated Sampling along Experimental Restraints. Int J Mol Sci 2019; 20:E370. [PMID: 30654563 PMCID: PMC6359555 DOI: 10.3390/ijms20020370] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/17/2018] [Revised: 01/07/2019] [Accepted: 01/10/2019] [Indexed: 12/25/2022] Open
Abstract
In this article, we present an enhanced sampling method based on a hybrid Hamiltonian which combines experimental distance restraints with a bias dependent from multiple path-dependent variables. This simulation method determines the bias-coordinates on the fly and does not require a priori knowledge about reaction coordinates. The hybrid Hamiltonian accelerates the sampling of proteins, and, combined with experimental distance information, the technique considers the restraints adaptively and in dependency of the system's intrinsic dynamics. We validate the methodology on the dipole relaxation of two water models and the conformational landscape of dialanine. Using experimental NMR-restraint data, we explore the folding landscape of the TrpCage mini-protein and in a second example apply distance restraints from chemical crosslinking/mass spectrometry experiments for the sampling of the conformation space of the Killer Cell Lectin-like Receptor Subfamily B Member 1A (NKR-P1A). The new methodology has the potential to adaptively introduce experimental restraints without affecting the conformational space of the system along an ergodic trajectory. Since only a limited number of input- and no-order parameters are required for the setup of the simulation, the method is broadly applicable and has the potential to be combined with coarse-graining methods.
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Affiliation(s)
- Emanuel K Peter
- Institute of Biotechnology of the Czech Academy of Sciences, BIOCEV, Průmyslová 595, 252 50 Vestec, Prague West, Czech Republic.
| | - Jiří Černý
- Institute of Biotechnology of the Czech Academy of Sciences, BIOCEV, Průmyslová 595, 252 50 Vestec, Prague West, Czech Republic.
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16
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Peter EK, Cerny J. Enriched Conformational Sampling of DNA and Proteins with a Hybrid Hamiltonian Derived from the Protein Data Bank. Int J Mol Sci 2018; 19:E3405. [PMID: 30380800 PMCID: PMC6274895 DOI: 10.3390/ijms19113405] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/06/2018] [Revised: 10/22/2018] [Accepted: 10/27/2018] [Indexed: 12/26/2022] Open
Abstract
In this article, we present a method for the enhanced molecular dynamics simulation of protein and DNA systems called potential of mean force (PMF)-enriched sampling. The method uses partitions derived from the potentials of mean force, which we determined from DNA and protein structures in the Protein Data Bank (PDB). We define a partition function from a set of PDB-derived PMFs, which efficiently compensates for the error introduced by the assumption of a homogeneous partition function from the PDB datasets. The bias based on the PDB-derived partitions is added in the form of a hybrid Hamiltonian using a renormalization method, which adds the PMF-enriched gradient to the system depending on a linear weighting factor and the underlying force field. We validated the method using simulations of dialanine, the folding of TrpCage, and the conformational sampling of the Dickerson⁻Drew DNA dodecamer. Our results show the potential for the PMF-enriched simulation technique to enrich the conformational space of biomolecules along their order parameters, while we also observe a considerable speed increase in the sampling by factors ranging from 13.1 to 82. The novel method can effectively be combined with enhanced sampling or coarse-graining methods to enrich conformational sampling with a partition derived from the PDB.
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Affiliation(s)
- Emanuel K Peter
- Institute of Biotechnology of the Czech Academy of Sciences, BIOCEV, Průmyslová 595, 252 50 Vestec, Czech Republic.
| | - Jiri Cerny
- Institute of Biotechnology of the Czech Academy of Sciences, BIOCEV, Průmyslová 595, 252 50 Vestec, Czech Republic.
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17
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Cruz-León S, Vázquez-Mayagoitia A, Melchionna S, Schwierz N, Fyta M. Coarse-Grained Double-Stranded RNA Model from Quantum-Mechanical Calculations. J Phys Chem B 2018; 122:7915-7928. [PMID: 30044622 DOI: 10.1021/acs.jpcb.8b03566] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023]
Abstract
A coarse-grained model for simulating structural properties of double-stranded RNA is developed with parameters obtained from quantum-mechanical calculations. This model follows previous parametrization for double-stranded DNA, which is based on mapping the all-atom picture to a coarse-grained four-bead scheme. Chemical and structural differences between RNA and DNA have been taken into account for the model development. The parametrization is based on simulations using density functional theory (DFT) on separate units of the RNA molecule without implementing experimental data. The total energy is decomposed into four terms of physical significance: hydrogen bonding interaction, stacking interactions, backbone interactions, and electrostatic interactions. The first three interactions are treated within DFT, whereas the last one is included within a mean field approximation. Our double-stranded RNA coarse-grained model predicts stable helical structures for RNA. Other characteristics, such as structural or mechanical properties are reproduced with a very good accuracy. The development of the coarse-grained model for RNA allows extending the spatial and temporal length scales accessed by computer simulations and being able to model RNA-related biophysical processes, as well as novel RNA nanostructures.
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Affiliation(s)
- Sergio Cruz-León
- Institute for Computational Physics , Universität Stuttgart , Allmandring 3 , 70569 Stuttgart , Germany.,Department of Theoretical Biophysics , Max Planck Institute of Biophysics , Max-von-Laue-Str. 3 , 60438 Frankfurt , Germany
| | - Alvaro Vázquez-Mayagoitia
- Argonne National Laboratory , 9700 S. Cass Avenue, Building 240 , Argonne , Illinois , United States
| | - Simone Melchionna
- Dipartimento di Fisica, ISC-CNR, Istituto Sistemi Complessi , Università Sapienza , P.le A. Moro 2 , 00185 Rome , Italy
| | - Nadine Schwierz
- Department of Theoretical Biophysics , Max Planck Institute of Biophysics , Max-von-Laue-Str. 3 , 60438 Frankfurt , Germany
| | - Maria Fyta
- Institute for Computational Physics , Universität Stuttgart , Allmandring 3 , 70569 Stuttgart , Germany
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18
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Howell SC, Qiu X, Curtis JE. Monte Carlo simulation algorithm for B-DNA. J Comput Chem 2018; 37:2553-63. [PMID: 27671358 DOI: 10.1002/jcc.24474] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/14/2016] [Revised: 07/12/2016] [Accepted: 07/23/2016] [Indexed: 01/12/2023]
Abstract
Understanding the structure-function relationship of biomolecules containing DNA has motivated experiments aimed at determining molecular structure using methods such as small-angle X-ray and neutron scattering (SAXS and SANS). SAXS and SANS are useful for determining macromolecular shape in solution, a process which benefits by using atomistic models that reproduce the scattering data. The variety of algorithms available for creating and modifying model DNA structures lack the ability to rapidly modify all-atom models to generate structure ensembles. This article describes a Monte Carlo algorithm for simulating DNA, not with the goal of predicting an equilibrium structure, but rather to generate an ensemble of plausible structures which can be filtered using experimental results to identify a sub-ensemble of conformations that reproduce the solution scattering of DNA macromolecules. The algorithm generates an ensemble of atomic structures through an iterative cycle in which B-DNA is represented using a wormlike bead-rod model, new configurations are generated by sampling bend and twist moves, then atomic detail is recovered by back mapping from the final coarse-grained configuration. Using this algorithm on commodity computing hardware, one can rapidly generate an ensemble of atomic level models, each model representing a physically realistic configuration that could be further studied using molecular dynamics. © 2016 Wiley Periodicals, Inc.
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Affiliation(s)
- Steven C Howell
- Neutron Condensed Matter Science Group, NIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, Maryland, 20899-8562
| | - Xiangyun Qiu
- Department of Physics, The George Washington University, Washington, District of Columbia, 20052
| | - Joseph E Curtis
- Neutron Condensed Matter Science Group, NIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, Maryland, 20899-8562.
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19
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Chakraborty D, Hori N, Thirumalai D. Sequence-Dependent Three Interaction Site Model for Single- and Double-Stranded DNA. J Chem Theory Comput 2018; 14:3763-3779. [PMID: 29870236 PMCID: PMC6423546 DOI: 10.1021/acs.jctc.8b00091] [Citation(s) in RCA: 41] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023]
Abstract
We develop a robust coarse-grained model for single- and double-stranded DNA by representing each nucleotide by three interaction sites (TIS) located at the centers of mass of sugar, phosphate, and base. The resulting TIS model includes base-stacking, hydrogen bond, and electrostatic interactions as well as bond-stretching and bond angle potentials that account for the polymeric nature of DNA. The choices of force constants for stretching and the bending potentials were guided by a Boltzmann inversion procedure using a large representative set of DNA structures extracted from the Protein Data Bank. Some of the parameters in the stacking interactions were calculated using a learning procedure, which ensured that the experimentally measured melting temperatures of dimers are faithfully reproduced. Without any further adjustments, the calculations based on the TIS model reproduce the experimentally measured salt and sequence-dependence of the size of single-stranded DNA (ssDNA), as well as the persistence lengths of poly(dA) and poly(dT) chains. Interestingly, upon application of mechanical force, the extension of poly(dA) exhibits a plateau, which we trace to the formation of stacked helical domains. In contrast, the force-extension curve (FEC) of poly(dT) is entropic in origin and could be described by a standard polymer model. We also show that the persistence length of double-stranded DNA, formed from two complementary ssDNAs, is consistent with the prediction based on the worm-like chain. The persistence length, which decreases with increasing salt concentration, is in accord with the Odijk-Skolnick-Fixman theory intended for stiff polyelectrolyte chains near the rod limit. Our model predicts the melting temperatures of DNA hairpins with excellent accuracy, and we are able to recover the experimentally known sequence-specific trends. The range of applications, which did not require adjusting any parameter after the initial construction based solely on PDB structures and melting profiles of dimers, attests to the transferability and robustness of the TIS model for ssDNA and dsDNA.
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Affiliation(s)
- Debayan Chakraborty
- Department of Chemistry, The University of Texas at Austin, Austin, Texas 78712, United States
| | - Naoto Hori
- Department of Chemistry, The University of Texas at Austin, Austin, Texas 78712, United States
| | - D. Thirumalai
- Department of Chemistry, The University of Texas at Austin, Austin, Texas 78712, United States
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20
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Jeong KB, Luo K, Lim MC, Jung JY, Yu JS, Kim KB, Kim YR. Reduction of DNA Folding by Ionic Liquids and Its Effects on the Analysis of DNA-Protein Interaction Using Solid-State Nanopore. SMALL (WEINHEIM AN DER BERGSTRASSE, GERMANY) 2018; 14:e1801375. [PMID: 29971919 DOI: 10.1002/smll.201801375] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/10/2018] [Revised: 05/28/2018] [Indexed: 06/08/2023]
Abstract
DNA folding is not desirable for solid-state nanopore techniques when analyzing the interaction of a biomolecule with its specific binding sites on DNA since the signal derived from the binding site could be buried by a large signal from the folding of DNA nearby. To resolve the problems associated with DNA folding, ionic liquids (ILs), which are known to interact with DNA through charge-charge and hydrophobic interactions are employed. 1-n-butyl-3-methylimidazolium chloride (C4 mim) is found to be the most effective in lowering the incident of DNA folding during its translocation through solid-state nanopores (4-5 nm diameter). The rate of folding signals from the translocation of DNA-C4 mim is decreased by half in comparison to that from the control bare DNA. The conformational changes of DNA upon complexation with C4 mim are further examined using atomic force microscopy, showing that the entanglement of DNA which is common in bare DNA is not observed when treated with C4 mim. The stretching effect of C4 mim on DNA strands improves the detection accuracy of nanopore for identifying the location of zinc finger protein bound to its specific binding site in DNA by lowering the incident of DNA folding.
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Affiliation(s)
- Ki-Baek Jeong
- Institute of Life Sciences and Resources, Department of Food Science and Biotechnology, Kyung Hee University, Yongin, 17104, South Korea
| | - Ke Luo
- Institute of Life Sciences and Resources, Department of Food Science and Biotechnology, Kyung Hee University, Yongin, 17104, South Korea
| | - Min-Cheol Lim
- Food Safety Research Group, Korea Food Research Institute, Sungnam, 13539, South Korea
| | - Jong-Yoon Jung
- Institute of Life Sciences and Resources, Department of Food Science and Biotechnology, Kyung Hee University, Yongin, 17104, South Korea
| | - Jae-Seok Yu
- Department of Materials Science and Engineering, Seoul National University, Seoul, 08826, Korea
| | - Ki-Bum Kim
- Department of Materials Science and Engineering, Seoul National University, Seoul, 08826, Korea
| | - Young-Rok Kim
- Institute of Life Sciences and Resources, Department of Food Science and Biotechnology, Kyung Hee University, Yongin, 17104, South Korea
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21
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Wang KW, Barker K, Benner S, Betancourt T, Hall CK. Development of a simple coarse-grained DNA model for analysis of oligonucleotide complex formation. MOLECULAR SIMULATION 2018. [DOI: 10.1080/08927022.2018.1469753] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/30/2022]
Affiliation(s)
- Kye Won Wang
- Department of Chemical and Biomolecular Engineering, North Carolina State University, Raleigh, NC, USA
| | - Karolyn Barker
- Department of Chemistry and Biochemistry, Texas State University, San Marcos, TX, USA
- Materials Science, Engineering, and Commercialization Program, Texas State University, San Marcos, TX, USA
| | - Steven Benner
- Department of Chemical and Biomolecular Engineering, North Carolina State University, Raleigh, NC, USA
| | - Tania Betancourt
- Department of Chemistry and Biochemistry, Texas State University, San Marcos, TX, USA
- Materials Science, Engineering, and Commercialization Program, Texas State University, San Marcos, TX, USA
| | - Carol K. Hall
- Department of Chemical and Biomolecular Engineering, North Carolina State University, Raleigh, NC, USA
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22
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Rovigatti L, Russo J, Romano F. How to simulate patchy particles ⋆. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2018; 41:59. [PMID: 29748868 DOI: 10.1140/epje/i2018-11667-x] [Citation(s) in RCA: 25] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/14/2018] [Accepted: 04/16/2018] [Indexed: 06/08/2023]
Abstract
Patchy particles is the name given to a large class of systems of mesoscopic particles characterized by a repulsive core and a discrete number of short-range and highly directional interaction sites. Numerical simulations have contributed significantly to our understanding of the behaviour of patchy particles, but, although simple in principle, advanced simulation techniques are often required to sample the low temperatures and long time-scales associated with their self-assembly behaviour. In this work we review the most popular simulation techniques that have been used to study patchy particles, with a special focus on Monte Carlo methods. We cover many of the tools required to simulate patchy systems, from interaction potentials to biased moves, cluster moves, and free-energy methods. The review is complemented by an educationally oriented Monte Carlo computer code that implements all the techniques described in the text to simulate a well-known tetrahedral patchy particle model.
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Affiliation(s)
- Lorenzo Rovigatti
- CNR-ISC, Uos Sapienza, Piazzale A. Moro 2, 00185, Roma, Italy.
- Dipartimento di Fisica, Sapienza Università di Roma, Piazzale A. Moro 2, 00185, Roma, Italy.
| | - John Russo
- School of Mathematics, University of Bristol, BS8 1TW, Bristol, UK
| | - Flavio Romano
- Dipartimento di Scienze Molecolari e Nanosistemi, Università Ca' Foscari di Venezia, Via Torino 155, 30172, Venezia Mestre, Italy
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23
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Sharma R, Schreck JS, Romano F, Louis AA, Doye JPK. Characterizing the Motion of Jointed DNA Nanostructures Using a Coarse-Grained Model. ACS NANO 2017; 11:12426-12435. [PMID: 29083876 DOI: 10.1021/acsnano.7b06470] [Citation(s) in RCA: 24] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/21/2023]
Abstract
As detailed structural characterizations of large complex DNA nanostructures are hard to obtain experimentally, particularly if they have substantial flexibility, coarse-grained modeling can potentially provide an important complementary role. Such modeling can provide a detailed view of both the average structure and the structural fluctuations, as well as providing insight into how the nanostructure's design determines its structural properties. Here, we present a case study of jointed DNA nanostructures using the oxDNA model. In particular, we consider archetypal hinge and sliding joints, as well as more complex structures involving a number of such coupled joints. Our results highlight how the nature of the motion in these structures can sensitively depend on the precise details of the joints. Furthermore, the generally good agreement with experiments illustrates the power of this approach and suggests the use of such modeling to prescreen the properties of putative designs.
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Affiliation(s)
- Rahul Sharma
- Department of Chemistry, Indian Institute of Technology Roorkee , Roorkee, 247667, India
| | - John S Schreck
- Department of Chemical Engineering, Columbia University , New York, New York 10027, United States
| | - Flavio Romano
- Dipartimento di Scienze Molecolari e Nanosistemi, Universitá Ca' Foscari Venezia , I-30123 Venezia, Italy
| | - Ard A Louis
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford , 1 Keble Road, Oxford OX1 3NP, United Kingdom
| | - Jonathan P K Doye
- Physical and Theoretical Chemistry Laboratory, Department of Chemistry, University of Oxford , South Parks Road, Oxford OX1 3QZ, United Kingdom
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24
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Pan K, Bricker WP, Ratanalert S, Bathe M. Structure and conformational dynamics of scaffolded DNA origami nanoparticles. Nucleic Acids Res 2017; 45:6284-6298. [PMID: 28482032 PMCID: PMC5499760 DOI: 10.1093/nar/gkx378] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/21/2016] [Accepted: 04/25/2017] [Indexed: 12/22/2022] Open
Abstract
Synthetic DNA is a highly programmable nanoscale material that can be designed to self-assemble into 3D structures that are fully determined by underlying Watson–Crick base pairing. The double crossover (DX) design motif has demonstrated versatility in synthesizing arbitrary DNA nanoparticles on the 5–100 nm scale for diverse applications in biotechnology. Prior computational investigations of these assemblies include all-atom and coarse-grained modeling, but modeling their conformational dynamics remains challenging due to their long relaxation times and associated computational cost. We apply all-atom molecular dynamics and coarse-grained finite element modeling to DX-based nanoparticles to elucidate their fine-scale and global conformational structure and dynamics. We use our coarse-grained model with a set of secondary structural motifs to predict the equilibrium solution structures of 45 DX-based DNA origami nanoparticles including a tetrahedron, octahedron, icosahedron, cuboctahedron and reinforced cube. Coarse-grained models are compared with 3D cryo-electron microscopy density maps for these five DNA nanoparticles and with all-atom molecular dynamics simulations for the tetrahedron and octahedron. Our results elucidate non-intuitive atomic-level structural details of DX-based DNA nanoparticles, and offer a general framework for efficient computational prediction of global and local structural and mechanical properties of DX-based assemblies that are inaccessible to all-atom based models alone.
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Affiliation(s)
- Keyao Pan
- Department of Biological Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - William P Bricker
- Department of Biological Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - Sakul Ratanalert
- Department of Biological Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA.,Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - Mark Bathe
- Department of Biological Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
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25
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Heinemann T, Klapp SHL. Coarse-graining strategy for molecular pair interactions: A reaction coordinate study for two- and three-dimensional systems. J Chem Phys 2017; 146:164107. [PMID: 28456203 DOI: 10.1063/1.4981207] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/13/2023] Open
Abstract
We investigate and provide optimal sets of reaction coordinates for mixed pairs of molecules displaying polar, uniaxial, or spherical symmetry in two and three dimensions. These coordinates are non-redundant, i.e., they implicitly involve the molecules' symmetries. By tabulating pair interactions in these coordinates, resulting tables are thus minimal in length and require a minimal memory space. The intended fields of application are computer simulations of large ensembles of molecules or colloids with rather complex interactions in a fluid or liquid crystalline phase at low densities. Using effective interactions directly in the form of tables can help bridging the time and length scales without introducing errors stemming from any modeling procedure. Finally, we outline an exemplary computational methodology for gaining an effective pair potential in these coordinates, based on the Boltzmann inversion principle, by providing a step-by-step recipe.
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Affiliation(s)
- Thomas Heinemann
- Department of Chemistry, Seoul National University, Seoul 08826, Korea
| | - Sabine H L Klapp
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany
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26
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Mitchell JS, Glowacki J, Grandchamp AE, Manning RS, Maddocks JH. Sequence-Dependent Persistence Lengths of DNA. J Chem Theory Comput 2017; 13:1539-1555. [DOI: 10.1021/acs.jctc.6b00904] [Citation(s) in RCA: 64] [Impact Index Per Article: 9.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
| | - Jaroslaw Glowacki
- Ecole Polytechnique Fédérale de Lausanne, Lausanne CH 1273, Switzerland
| | | | | | - John H. Maddocks
- Ecole Polytechnique Fédérale de Lausanne, Lausanne CH 1273, Switzerland
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27
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Abstract
More than 20 coarse-grained (CG) DNA models have been developed for simulating the behavior of this molecule under various conditions, including those required for nanotechnology. However, none of these models reproduces the DNA polymorphism associated with conformational changes in the ribose rings of the DNA backbone. These changes make an essential contribution to the DNA local deformability and provide the possibility of the transition of the DNA double helix from the B-form to the A-form during interactions with biological molecules. We propose a CG representation of the ribose conformational flexibility. We substantiate the choice of the CG sites (six per nucleotide) needed for the "sugar" GC DNA model, and obtain the potentials of the CG interactions between the sites by the "bottom-up" approach using the all-atom AMBER force field. We show that the representation of the ribose flexibility requires one non-harmonic and one three-particle potential, the forms of both the potentials being different from the ones generally used. The model also includes (i) explicit representation of ions (in an implicit solvent) and (ii) sequence dependence. With these features, the sugar CG DNA model reproduces (with the same parameters) both the B- and A- stable forms under corresponding conditions and demonstrates both the A to B and the B to A phase transitions. Graphical Abstract The proposed coarse-grained DNA model allows to reproduce both the B- and A- DNA forms and the transitions between them under corresponding conditions.
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28
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Netz PA, Potestio R, Kremer K. Adaptive resolution simulation of oligonucleotides. J Chem Phys 2017; 145:234101. [PMID: 27984862 DOI: 10.1063/1.4972014] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Nucleic acids are characterized by a complex hierarchical structure and a variety of interaction mechanisms with other molecules. These features suggest the need of multiscale simulation methods in order to grasp the relevant physical properties of deoxyribonucleic acid (DNA) and RNA using in silico experiments. Here we report an implementation of a dual-resolution modeling of a DNA oligonucleotide in physiological conditions; in the presented setup only the nucleotide molecule and the solvent and ions in its proximity are described at the atomistic level; in contrast, the water molecules and ions far from the DNA are represented as computationally less expensive coarse-grained particles. Through the analysis of several structural and dynamical parameters, we show that this setup reliably reproduces the physical properties of the DNA molecule as observed in reference atomistic simulations. These results represent a first step towards a realistic multiscale modeling of nucleic acids and provide a quantitatively solid ground for their simulation using dual-resolution methods.
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Affiliation(s)
- Paulo A Netz
- Departamento de Físico-Química, Instituto de Química, Universidade Federal do Rio Grande do Sul, Porto Alegre, RS 91501-970, Brazil
| | - Raffaello Potestio
- Max Planck Institut für Polymerforschung, Ackermannweg 10, 55128 Mainz, Germany
| | - Kurt Kremer
- Max Planck Institut für Polymerforschung, Ackermannweg 10, 55128 Mainz, Germany
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29
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Stadlbauer P, Mazzanti L, Cragnolini T, Wales DJ, Derreumaux P, Pasquali S, Šponer J. Coarse-Grained Simulations Complemented by Atomistic Molecular Dynamics Provide New Insights into Folding and Unfolding of Human Telomeric G-Quadruplexes. J Chem Theory Comput 2016; 12:6077-6097. [DOI: 10.1021/acs.jctc.6b00667] [Citation(s) in RCA: 40] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
Affiliation(s)
- Petr Stadlbauer
- Institute
of Biophysics, Academy of Sciences of the Czech Republic, Královopolská
135, 612 65 Brno, Czech Republic
- Regional
Centre of Advanced Technologies and Materials, Departments of Physical
Chemistry, Faculty of Science, Palacký University, 17. listopadu
1192/12, 771 46 Olomouc, Czech Republic
| | - Liuba Mazzanti
- Laboratoire
de Biochimie Théorique, IBPC, CNRS UPR9080, Université Sorbonne Paris Cite, Paris Diderot, 13 rue Pierre et Marie Curie, 75005 Paris, France
| | - Tristan Cragnolini
- Department
of Chemistry, Cambridge University, Lensfield Road, Cambridge CB2 1EW, U.K
| | - David J. Wales
- Department
of Chemistry, Cambridge University, Lensfield Road, Cambridge CB2 1EW, U.K
| | - Philippe Derreumaux
- Laboratoire
de Biochimie Théorique, IBPC, CNRS UPR9080, Université Sorbonne Paris Cite, Paris Diderot, 13 rue Pierre et Marie Curie, 75005 Paris, France
| | - Samuela Pasquali
- Laboratoire
de Biochimie Théorique, IBPC, CNRS UPR9080, Université Sorbonne Paris Cite, Paris Diderot, 13 rue Pierre et Marie Curie, 75005 Paris, France
| | - Jiří Šponer
- Institute
of Biophysics, Academy of Sciences of the Czech Republic, Královopolská
135, 612 65 Brno, Czech Republic
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30
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He Y, Liwo A, Scheraga HA. Optimization of a Nucleic Acids united-RESidue 2-Point model (NARES-2P) with a maximum-likelihood approach. J Chem Phys 2016; 143:243111. [PMID: 26723596 DOI: 10.1063/1.4932082] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022] Open
Abstract
Coarse-grained models are useful tools to investigate the structural and thermodynamic properties of biomolecules. They are obtained by merging several atoms into one interaction site. Such simplified models try to capture as much as possible information of the original biomolecular system in all-atom representation but the resulting parameters of these coarse-grained force fields still need further optimization. In this paper, a force field optimization method, which is based on maximum-likelihood fitting of the simulated to the experimental conformational ensembles and least-squares fitting of the simulated to the experimental heat-capacity curves, is applied to optimize the Nucleic Acid united-RESidue 2-point (NARES-2P) model for coarse-grained simulations of nucleic acids recently developed in our laboratory. The optimized NARES-2P force field reproduces the structural and thermodynamic data of small DNA molecules much better than the original force field.
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Affiliation(s)
- Yi He
- Department of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853, USA
| | - Adam Liwo
- Faculty of Chemistry, University of Gdańsk, Wita Stwosza 63, 80-308 Gdańsk, Poland
| | - Harold A Scheraga
- Department of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853, USA
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31
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Markegard CB, Gallivan CP, Cheng DD, Nguyen HD. Effects of Concentration and Temperature on DNA Hybridization by Two Closely Related Sequences via Large-Scale Coarse-Grained Simulations. J Phys Chem B 2016; 120:7795-806. [PMID: 27447850 DOI: 10.1021/acs.jpcb.6b03937] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/04/2023]
Abstract
A newly developed coarse-grained model called BioModi is utilized to elucidate the effects of temperature and concentration on DNA hybridization in self-assembly. Large-scale simulations demonstrate that complementary strands of either the tetrablock sequence or randomized sequence with equivalent number of cytosine or guanine nucleotides can form completely hybridized double helices. Even though the end states are the same for the two sequences, there exist multiple kinetic pathways that are populated with a wider range of transient aggregates of different sizes in the system of random sequences compared to that of the tetrablock sequence. The ability of these aggregates to undergo the strand displacement mechanism to form only double helices depends upon the temperature and DNA concentration. On one hand, low temperatures and high concentrations drive the formation and enhance stability of large aggregating species. On the other hand, high temperatures destabilize base-pair interactions and large aggregates. There exists an optimal range of moderate temperatures and low concentrations that allow minimization of large aggregate formation and maximization of fully hybridized dimers. Such investigation on structural dynamics of aggregating species by two closely related sequences during the self-assembly process demonstrates the importance of sequence design in avoiding the formation of metastable species. Finally, from kinetic modeling of self-assembly dynamics, the activation energy for the formation of double helices was found to be in agreement with experimental results. The framework developed in this work can be applied to the future design of DNA nanostructures in both fields of structural DNA nanotechnology and dynamic DNA nanotechnology wherein equilibrium end states and nonequilibrium dynamics are equally important requiring investigation in cooperation.
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Affiliation(s)
- Cade B Markegard
- Department of Chemical Engineering and Materials Science, University of California, Irvine , Irvine, California 92697, United States
| | - Cameron P Gallivan
- Department of Chemical Engineering and Materials Science, University of California, Irvine , Irvine, California 92697, United States
| | - Darrell D Cheng
- Department of Chemical Engineering and Materials Science, University of California, Irvine , Irvine, California 92697, United States
| | - Hung D Nguyen
- Department of Chemical Engineering and Materials Science, University of California, Irvine , Irvine, California 92697, United States
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32
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Snodin BEK, Randisi F, Mosayebi M, Šulc P, Schreck JS, Romano F, Ouldridge TE, Tsukanov R, Nir E, Louis AA, Doye JPK. Introducing improved structural properties and salt dependence into a coarse-grained model of DNA. J Chem Phys 2016; 142:234901. [PMID: 26093573 DOI: 10.1063/1.4921957] [Citation(s) in RCA: 210] [Impact Index Per Article: 26.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023] Open
Abstract
We introduce an extended version of oxDNA, a coarse-grained model of deoxyribonucleic acid (DNA) designed to capture the thermodynamic, structural, and mechanical properties of single- and double-stranded DNA. By including explicit major and minor grooves and by slightly modifying the coaxial stacking and backbone-backbone interactions, we improve the ability of the model to treat large (kilobase-pair) structures, such as DNA origami, which are sensitive to these geometric features. Further, we extend the model, which was previously parameterised to just one salt concentration ([Na(+)] = 0.5M), so that it can be used for a range of salt concentrations including those corresponding to physiological conditions. Finally, we use new experimental data to parameterise the oxDNA potential so that consecutive adenine bases stack with a different strength to consecutive thymine bases, a feature which allows a more accurate treatment of systems where the flexibility of single-stranded regions is important. We illustrate the new possibilities opened up by the updated model, oxDNA2, by presenting results from simulations of the structure of large DNA objects and by using the model to investigate some salt-dependent properties of DNA.
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Affiliation(s)
- Benedict E K Snodin
- Physical and Theoretical Chemistry Laboratory, Department of Chemistry, University of Oxford, South Parks Road, Oxford OX1 3QZ, United Kingdom
| | - Ferdinando Randisi
- Life Sciences Interface Doctoral Training Center, South Parks Road, Oxford OX1 3QU, United Kingdom
| | - Majid Mosayebi
- Physical and Theoretical Chemistry Laboratory, Department of Chemistry, University of Oxford, South Parks Road, Oxford OX1 3QZ, United Kingdom
| | - Petr Šulc
- Center for Studies in Physics and Biology, The Rockefeller University, 1230 York Avenue, New York, New York 10065, USA
| | - John S Schreck
- Physical and Theoretical Chemistry Laboratory, Department of Chemistry, University of Oxford, South Parks Road, Oxford OX1 3QZ, United Kingdom
| | - Flavio Romano
- Physical and Theoretical Chemistry Laboratory, Department of Chemistry, University of Oxford, South Parks Road, Oxford OX1 3QZ, United Kingdom
| | - Thomas E Ouldridge
- Department of Mathematics, Imperial College, 180 Queen's Gate, London SW7 2AZ, United Kingdom
| | - Roman Tsukanov
- Department of Chemistry and the Ilse Katz Institute for Nanoscale Science and Technology, Ben-Gurion University of the Negev, Beer Sheva, Israel
| | - Eyal Nir
- Department of Chemistry and the Ilse Katz Institute for Nanoscale Science and Technology, Ben-Gurion University of the Negev, Beer Sheva, Israel
| | - Ard A Louis
- Rudolf Peierls Centre for Theoretical Physics, 1 Keble Road, Oxford OX1 3NP, United Kingdom
| | - Jonathan P K Doye
- Physical and Theoretical Chemistry Laboratory, Department of Chemistry, University of Oxford, South Parks Road, Oxford OX1 3QZ, United Kingdom
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33
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Wolf-Brandstetter C, Hänchen V, Schwenzer B, Aeckerle N, Schliephake H, Scharnweber D. Application of Lateral and Distance Spacers in an Oligonucleotide Based Immobilization System for Bioactive Molecules onto Titanium Implants. ACS APPLIED MATERIALS & INTERFACES 2016; 8:3755-3764. [PMID: 26779926 DOI: 10.1021/acsami.5b09073] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
Immobilization of bioactive molecules (BAMs) on a nanometer scale is of great interest for functionalization of implant and scaffold surfaces in current biomaterials research. A system for immobilization of one or more compounds is described, which is based on nanomechanical fixation of single-stranded nucleic acids into an anodic titanium oxide layer and their subsequent hybridization with BAMs conjugated to the respective complementary strands. This paper focuses on further development and in depth understanding of the immobilization system, as some of the major findings established for common sensor applications for immobilization of single-stranded DNA onto gold surfaces cannot be transferred to the TiO2 surface. The first approach concerning the influence of the internal spacer sequence revealed the best performance for a polyadenine based sequence out of four homologous spacer sequences (A30, T30, C30, and G30). This overall best performance of the A30 spacer is attributed to an increased contour length by nucleotide staggering, which resulted in the best protection of the hybridization sequence from unfavorable interactions with the surface or damaging attacks by reactive oxygen species. The second approach comprises the implementation of a lateral spacer, also based on a homologous sequence of A30. Simultaneous as well as sequential adsorption of anchor strands and spacer strands were performed, and it could be shown that a preadsorption with high density of the spacer was most effective to increase hybridization efficiency.
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Affiliation(s)
| | | | | | - Nelia Aeckerle
- Department of Oral and Maxillofacial Surgery, George-Augusta-University , D-37075 Göttingen, Germany
| | - Henning Schliephake
- Department of Oral and Maxillofacial Surgery, George-Augusta-University , D-37075 Göttingen, Germany
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34
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Li G, Shen H, Zhang D, Li Y, Wang H. Coarse-Grained Modeling of Nucleic Acids Using Anisotropic Gay-Berne and Electric Multipole Potentials. J Chem Theory Comput 2016; 12:676-93. [PMID: 26717419 DOI: 10.1021/acs.jctc.5b00903] [Citation(s) in RCA: 44] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/20/2023]
Abstract
In this work, we attempt to apply a coarse-grained (CG) model, which is based on anisotropic Gay-Berne and electric multipole (EMP) potentials, to the modeling of nucleic acids. First, a comparison has been made between the CG and atomistic models (AMBER point-charge model) in the modeling of DNA and RNA hairpin structures. The CG results have demonstrated a good quality in maintaining the nucleic acid hairpin structures, in reproducing the dynamics of backbone atoms of nucleic acids, and in describing the hydrogen-bonding interactions between nucleic acid base pairs. Second, the CG and atomistic AMBER models yield comparable results in modeling double-stranded DNA and RNA molecules. It is encouraging that our CG model is capable of reproducing many elastic features of nucleic acid base pairs in terms of the distributions of the interbase pair step parameters (such as shift, slide, tilt, and twist) and the intrabase pair parameters (such as buckle, propeller, shear, and stretch). Finally, The GBEMP model has shown a promising ability to predict the melting temperatures of DNA duplexes with different lengths.
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Affiliation(s)
- Guohui Li
- Laboratory of Molecular Modeling and Design, State Key Laboratory of Molecular Reaction Dynamics, Dalian Institute of Chemical Physics, Chinese Academy of Sciences , Dalian 116023, Liaoning Province, People's Republic of China
| | - Hujun Shen
- Laboratory of Molecular Modeling and Design, State Key Laboratory of Molecular Reaction Dynamics, Dalian Institute of Chemical Physics, Chinese Academy of Sciences , Dalian 116023, Liaoning Province, People's Republic of China
| | - Dinglin Zhang
- Laboratory of Molecular Modeling and Design, State Key Laboratory of Molecular Reaction Dynamics, Dalian Institute of Chemical Physics, Chinese Academy of Sciences , Dalian 116023, Liaoning Province, People's Republic of China
| | - Yan Li
- Laboratory of Molecular Modeling and Design, State Key Laboratory of Molecular Reaction Dynamics, Dalian Institute of Chemical Physics, Chinese Academy of Sciences , Dalian 116023, Liaoning Province, People's Republic of China
| | - Honglei Wang
- Laboratory of Molecular Modeling and Design, State Key Laboratory of Molecular Reaction Dynamics, Dalian Institute of Chemical Physics, Chinese Academy of Sciences , Dalian 116023, Liaoning Province, People's Republic of China
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35
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Naômé A, Laaksonen A, Vercauteren DP. A Solvent-Mediated Coarse-Grained Model of DNA Derived with the Systematic Newton Inversion Method. J Chem Theory Comput 2015; 10:3541-9. [PMID: 26588318 DOI: 10.1021/ct500222s] [Citation(s) in RCA: 30] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/20/2023]
Abstract
We present a new class of coarse-grained (CG) force fields (FFs) for B-DNA with explicit ions suited for large-scale mesoscale simulations at microsecond-micrometer scale using a wide spectrum of particle simulation methods from molecular dynamics to dissipative particle dynamics. The effective solvent-mediated pairwise interactions making up the FFs are obtained by inverting radial distribution functions and other particle-particle distributions obtained from all-atom simulations of numbers of octadecamer DNA fragments from the Ascona B-DNA library. The inverse Monte Carlo (IMC) method, later known as Newton inversion (NI) (Lyubartsev, A. P.; Laaksonen, A. Phys. Rev. E, 1995, 52, 3730-3737), was used together with the iterative Boltzmann inversion (IBI) scheme to compute the effective CG potentials. We show that this systematic structure-based approach is capable of providing converged potentials that accurately reproduce the structural features of the underlying atomistic system within a few percents of relative difference. We also show that a simple one-site-per-nucleotide model with 10 intramolecular pair interaction potentials is able to reproduce key features of DNA, for example, the persistence length and its dependence on the ionic concentration, experimentally determined around 50 nm at physiological salt concentration.
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Affiliation(s)
- Aymeric Naômé
- Laboratoire de Physico-Chimie Informatique, Unité de Chimie Physique Théorique et Structurale, University of Namur , 5000 Namur, Belgium.,Division of Physical Chemistry, Department of Materials and Environmental Chemistry, Arrhenius Laboratory, Stockholm University , 10691 Stockholm, Sweden.,Science for Life Laboratory, 17121 Solna, Sweden
| | - Aatto Laaksonen
- Division of Physical Chemistry, Department of Materials and Environmental Chemistry, Arrhenius Laboratory, Stockholm University , 10691 Stockholm, Sweden.,Science for Life Laboratory, 17121 Solna, Sweden.,Stellenbosch Institute of Advanced Studies (STIAS), Wallenberg Research Centre, Stellenbosch University , 7600 Stellenbosch, South Africa
| | - Daniel P Vercauteren
- Laboratoire de Physico-Chimie Informatique, Unité de Chimie Physique Théorique et Structurale, University of Namur , 5000 Namur, Belgium
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36
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Sedeh RS, Pan K, Adendorff MR, Hallatschek O, Bathe KJ, Bathe M. Computing Nonequilibrium Conformational Dynamics of Structured Nucleic Acid Assemblies. J Chem Theory Comput 2015; 12:261-73. [PMID: 26636351 DOI: 10.1021/acs.jctc.5b00965] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Synthetic nucleic acids can be programmed to form precise three-dimensional structures on the nanometer-scale. These thermodynamically stable complexes can serve as structural scaffolds to spatially organize functional molecules including multiple enzymes, chromophores, and force-sensing elements with internal dynamics that include substrate reaction-diffusion, excitonic energy transfer, and force-displacement response that often depend critically on both the local and global conformational dynamics of the nucleic acid assembly. However, high molecular weight assemblies exhibit long time-scale and large length-scale motions that cannot easily be sampled using all-atom computational procedures such as molecular dynamics. As an alternative, here we present a computational framework to compute the overdamped conformational dynamics of structured nucleic acid assemblies and apply it to a DNA-based tweezer, a nine-layer DNA origami ring, and a pointer-shaped DNA origami object, which consist of 204, 3,600, and over 7,000 basepairs, respectively. The framework employs a mechanical finite element model for the DNA nanostructure combined with an implicit solvent model to either simulate the Brownian dynamics of the assembly or alternatively compute its Brownian modes. Computational results are compared with an all-atom molecular dynamics simulation of the DNA-based tweezer. Several hundred microseconds of Brownian dynamics are simulated for the nine-layer ring origami object to reveal its long time-scale conformational dynamics, and the first ten Brownian modes of the pointer-shaped structure are predicted.
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Affiliation(s)
| | | | | | - Oskar Hallatschek
- Department of Physics, University of California, Berkeley , Berkeley, California 94720, United States
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37
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Isami S, Sakamoto N, Nishimori H, Awazu A. Simple Elastic Network Models for Exhaustive Analysis of Long Double-Stranded DNA Dynamics with Sequence Geometry Dependence. PLoS One 2015; 10:e0143760. [PMID: 26624614 PMCID: PMC4666469 DOI: 10.1371/journal.pone.0143760] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/23/2015] [Accepted: 11/09/2015] [Indexed: 11/19/2022] Open
Abstract
Simple elastic network models of DNA were developed to reveal the structure-dynamics relationships for several nucleotide sequences. First, we propose a simple all-atom elastic network model of DNA that can explain the profiles of temperature factors for several crystal structures of DNA. Second, we propose a coarse-grained elastic network model of DNA, where each nucleotide is described only by one node. This model could effectively reproduce the detailed dynamics obtained with the all-atom elastic network model according to the sequence-dependent geometry. Through normal-mode analysis for the coarse-grained elastic network model, we exhaustively analyzed the dynamic features of a large number of long DNA sequences, approximately ∼150 bp in length. These analyses revealed positive correlations between the nucleosome-forming abilities and the inter-strand fluctuation strength of double-stranded DNA for several DNA sequences.
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Affiliation(s)
- Shuhei Isami
- Department of Mathematical and Life Sciences, Hiroshima University, Kagami-yama 1-3-1, Higashi-Hiroshima 739-8526, Japan
| | - Naoaki Sakamoto
- Department of Mathematical and Life Sciences, Hiroshima University, Kagami-yama 1-3-1, Higashi-Hiroshima 739-8526, Japan
- Research Center for Mathematics on Chromatin Live Dynamics, Hiroshima University, Kagami-yama 1-3-1, Higashi-Hiroshima 739-8526, Japan
| | - Hiraku Nishimori
- Department of Mathematical and Life Sciences, Hiroshima University, Kagami-yama 1-3-1, Higashi-Hiroshima 739-8526, Japan
- Research Center for Mathematics on Chromatin Live Dynamics, Hiroshima University, Kagami-yama 1-3-1, Higashi-Hiroshima 739-8526, Japan
| | - Akinori Awazu
- Department of Mathematical and Life Sciences, Hiroshima University, Kagami-yama 1-3-1, Higashi-Hiroshima 739-8526, Japan
- Research Center for Mathematics on Chromatin Live Dynamics, Hiroshima University, Kagami-yama 1-3-1, Higashi-Hiroshima 739-8526, Japan
- * E-mail:
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38
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Heinemann T, Palczynski K, Dzubiella J, Klapp SHL. Coarse-grained electrostatic interactions of coronene: Towards the crystalline phase. J Chem Phys 2015; 143:174110. [DOI: 10.1063/1.4935063] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023] Open
Affiliation(s)
- Thomas Heinemann
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstr. 36, 10623 Berlin, Germany
| | - Karol Palczynski
- Institut für Physik, Humboldt Universität zu Berlin, Newtonstraße 15, 12489 Berlin, Germany
- Institut für Weiche Materie und Funktionale Materialen, Helmholtz-Zentrum Berlin für Materialien und Energie, Hahn-Meitner Platz 1, 14109 Berlin, Germany
| | - Joachim Dzubiella
- Institut für Physik, Humboldt Universität zu Berlin, Newtonstraße 15, 12489 Berlin, Germany
- Institut für Weiche Materie und Funktionale Materialen, Helmholtz-Zentrum Berlin für Materialien und Energie, Hahn-Meitner Platz 1, 14109 Berlin, Germany
| | - Sabine H. L. Klapp
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstr. 36, 10623 Berlin, Germany
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39
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Abstract
We present a general coarse-grained model of sodium, magnesium, spermidine, and chlorine in implicit solvent. The effective potentials between ions are systematically parametrized using a relative entropy coarse-graining approach [Carmichael, S. P. and M. S. Shell, J. Phys. Chem. B, 116, 8383-93 (2012)] that maximizes the information retained in a coarse-grained model. We describe the local distribution of ions in the vicinity of a recently published coarse-grained DNA model and demonstrate a dependence of persistence length on ionic strength that differs from that predicted by Odijk-Skolnick-Fixman theory. Consistent with experimental observations, we show that spermidine induces DNA condensation whereas magnesium and sodium do not. This model can be used alongside any coarse-grained DNA model that has explicit charges and an accurate reproduction of the excluded volume of dsDNA.
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Affiliation(s)
- Daniel M Hinckley
- Department of Chemical and Biological Engineering, University of Wisconsin-Madison , Madison, Wisconsin 53706, United States
| | - Juan J de Pablo
- Institute for Molecular Engineering, University of Chicago , Chicago, Illinois 60637, United States.,Materials Science Division Argonne National Laboratory , Argonne, Illinois 60439, United States
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40
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Szklarczyk OM, Bieler NS, Hünenberger PH, van Gunsteren WF. Flexible Boundaries for Multiresolution Solvation: An Algorithm for Spatial Multiscaling in Molecular Dynamics Simulations. J Chem Theory Comput 2015; 11:5447-63. [PMID: 26574333 DOI: 10.1021/acs.jctc.5b00406] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
An algorithm is proposed for performing molecular dynamics (MD) simulations of a biomolecular solute represented at atomistic resolution surrounded by a surface layer of atomistic fine-grained (FG) solvent molecules within a bulk represented by coarse-grained (CG) solvent beads. The method, called flexible boundaries for multiresolution solvation (FBMS), is based on: (i) a three-region layering of the solvent around the solute, involving an FG layer surrounded by a mixed FG-CG buffer layer, itself surrounded by a bulk CG region; (ii) a definition of the layer boundary that relies on an effective distance to the solute surface and is thus adapted to the shape of the solute as well as adjusts to its conformational changes. The effective surface distance is defined by inverse-nth power averaging over the distances to all non-hydrogen solute atoms, and the layering is enforced by means of half-harmonic distance restraints, attractive for the FG molecules and repulsive for the CG beads. A restraint-free region at intermediate distances enables the formation of the buffer layer, where the FG and CG solvents can mix freely. The algorithm is tested and validated using the GROMOS force field and the associated FG (SPC) and CG (polarizable CGW) water models. The test systems include pure-water systems, where one FG molecule plays the role of a solute, and a deca-alanine peptide with two widely different solute shapes considered, α-helical and fully extended. In particular, as the peptide unfolds, the number of FG molecules required to fill its close-range solvation layer increases, with the additional molecules being provided by the buffer layer. Further validation involves simulations of four proteins in multiresolution FG/CG mixtures. The resulting structural, energetic, and solvation properties are found to be similar to those observed in corresponding pure FG simulations.
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Affiliation(s)
- Oliwia M Szklarczyk
- Laboratory of Physical Chemistry, Department of Chemistry and Applied Biosciences, Swiss Federal Institute of Technology ETH , 8093 Zürich, Switzerland
| | - Noah S Bieler
- Laboratory of Physical Chemistry, Department of Chemistry and Applied Biosciences, Swiss Federal Institute of Technology ETH , 8093 Zürich, Switzerland
| | - Philippe H Hünenberger
- Laboratory of Physical Chemistry, Department of Chemistry and Applied Biosciences, Swiss Federal Institute of Technology ETH , 8093 Zürich, Switzerland
| | - Wilfred F van Gunsteren
- Laboratory of Physical Chemistry, Department of Chemistry and Applied Biosciences, Swiss Federal Institute of Technology ETH , 8093 Zürich, Switzerland
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41
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Jabbari H, Aminpour M, Montemagno C. Computational Approaches to Nucleic Acid Origami. ACS COMBINATORIAL SCIENCE 2015; 17:535-47. [PMID: 26348196 DOI: 10.1021/acscombsci.5b00079] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/28/2022]
Abstract
Recent advances in experimental DNA origami have dramatically expanded the horizon of DNA nanotechnology. Complex 3D suprastructures have been designed and developed using DNA origami with applications in biomaterial science, nanomedicine, nanorobotics, and molecular computation. Ribonucleic acid (RNA) origami has recently been realized as a new approach. Similar to DNA, RNA molecules can be designed to form complex 3D structures through complementary base pairings. RNA origami structures are, however, more compact and more thermodynamically stable due to RNA's non-canonical base pairing and tertiary interactions. With all these advantages, the development of RNA origami lags behind DNA origami by a large gap. Furthermore, although computational methods have proven to be effective in designing DNA and RNA origami structures and in their evaluation, advances in computational nucleic acid origami is even more limited. In this paper, we review major milestones in experimental and computational DNA and RNA origami and present current challenges in these fields. We believe collaboration between experimental nanotechnologists and computer scientists are critical for advancing these new research paradigms.
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Affiliation(s)
- Hosna Jabbari
- Ingenuity Lab, 11421 Saskatchewan
Drive, Edmonton, Alberta T6G 2M9, Canada
- Department
of Chemical and Materials Engineering, University of Alberta, Edmonton T6G 2V4, Canada
| | - Maral Aminpour
- Ingenuity Lab, 11421 Saskatchewan
Drive, Edmonton, Alberta T6G 2M9, Canada
- Department
of Chemical and Materials Engineering, University of Alberta, Edmonton T6G 2V4, Canada
| | - Carlo Montemagno
- Ingenuity Lab, 11421 Saskatchewan
Drive, Edmonton, Alberta T6G 2M9, Canada
- Department
of Chemical and Materials Engineering, University of Alberta, Edmonton T6G 2V4, Canada
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42
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Hinckley DM, Lequieu JP, de Pablo JJ. Coarse-grained modeling of DNA oligomer hybridization: length, sequence, and salt effects. J Chem Phys 2015; 141:035102. [PMID: 25053341 DOI: 10.1063/1.4886336] [Citation(s) in RCA: 44] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023] Open
Abstract
A recently published coarse-grained DNA model [D. M. Hinckley, G. S. Freeman, J. K. Whitmer, and J. J. de Pablo, J. Chem. Phys. 139, 144903 (2013)] is used to study the hybridization mechanism of DNA oligomers. Forward flux sampling is used to construct ensembles of reactive trajectories from which the effects of sequence, length, and ionic strength are revealed. Heterogeneous sequences are observed to hybridize via the canonical zippering mechanism. In contrast, homogeneous sequences hybridize through a slithering mechanism, while more complex base pair displacement processes are observed for repetitive sequences. In all cases, the formation of non-native base pairs leads to an increase in the observed hybridization rate constants beyond those observed in sequences where only native base pairs are permitted. The scaling of rate constants with length is captured by extending existing hybridization theories to account for the formation of non-native base pairs. Furthermore, that scaling is found to be similar for oligomeric and polymeric systems, suggesting that similar physics is involved.
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Affiliation(s)
- Daniel M Hinckley
- Department of Chemical and Biological Engineering, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA
| | - Joshua P Lequieu
- Institute for Molecular Engineering, University of Chicago, Chicago, Illinois 60637, USA
| | - Juan J de Pablo
- Institute for Molecular Engineering, University of Chicago, Chicago, Illinois 60637, USA
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43
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Cragnolini T, Derreumaux P, Pasquali S. Ab initio RNA folding. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2015; 27:233102. [PMID: 25993396 DOI: 10.1088/0953-8984/27/23/233102] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
RNA molecules are essential cellular machines performing a wide variety of functions for which a specific three-dimensional structure is required. Over the last several years, the experimental determination of RNA structures through x-ray crystallography and NMR seems to have reached a plateau in the number of structures resolved each year, but as more and more RNA sequences are being discovered, the need for structure prediction tools to complement experimental data is strong. Theoretical approaches to RNA folding have been developed since the late nineties, when the first algorithms for secondary structure prediction appeared. Over the last 10 years a number of prediction methods for 3D structures have been developed, first based on bioinformatics and data-mining, and more recently based on a coarse-grained physical representation of the systems. In this review we are going to present the challenges of RNA structure prediction and the main ideas behind bioinformatic approaches and physics-based approaches. We will focus on the description of the more recent physics-based phenomenological models and on how they are built to include the specificity of the interactions of RNA bases, whose role is critical in folding. Through examples from different models, we will point out the strengths of physics-based approaches, which are able not only to predict equilibrium structures, but also to investigate dynamical and thermodynamical behavior, and the open challenges to include more key interactions ruling RNA folding.
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Affiliation(s)
- Tristan Cragnolini
- Laboratoire de Biochimie Théorique UPR 9080 CNRS, Université Paris Diderot, Sorbonne, Paris Cité, IBPC 13 rue Pierre et Marie Curie, 75005 Paris, France
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44
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Cragnolini T, Laurin Y, Derreumaux P, Pasquali S. Coarse-Grained HiRE-RNA Model for ab Initio RNA Folding beyond Simple Molecules, Including Noncanonical and Multiple Base Pairings. J Chem Theory Comput 2015; 11:3510-22. [PMID: 26575783 DOI: 10.1021/acs.jctc.5b00200] [Citation(s) in RCA: 51] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
HiRE-RNA is a coarse-grained model for RNA structure prediction and the dynamical study of RNA folding. Using a reduced set of particles and detailed interactions accounting for base-pairing and stacking, we show that noncanonical and multiple base interactions are necessary to capture the full physical behavior of complex RNAs. In this paper, we give a full account of the model and present results on the folding, stability, and free energy surfaces of 16 systems with 12 to 76 nucleotides of increasingly complex architectures, ranging from monomers to dimers, using a total of 850 μs of simulation time.
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Affiliation(s)
- Tristan Cragnolini
- Laboratoire de Biochimie Théorique UPR 9080 CNRS, Université Paris Diderot , Sorbonne, Paris Cité, IBPC 13 rue Pierre et Marie Curie, 75005 Paris, France
| | - Yoann Laurin
- Laboratoire de Biochimie Théorique UPR 9080 CNRS, Université Paris Diderot , Sorbonne, Paris Cité, IBPC 13 rue Pierre et Marie Curie, 75005 Paris, France
| | - Philippe Derreumaux
- Laboratoire de Biochimie Théorique UPR 9080 CNRS, Université Paris Diderot , Sorbonne, Paris Cité, IBPC 13 rue Pierre et Marie Curie, 75005 Paris, France.,Institut Universitaire de France , Boulevard Saint-Michel, 75005 Paris, France
| | - Samuela Pasquali
- Laboratoire de Biochimie Théorique UPR 9080 CNRS, Université Paris Diderot , Sorbonne, Paris Cité, IBPC 13 rue Pierre et Marie Curie, 75005 Paris, France
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45
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Szklarczyk OM, Arvaniti E, van Gunsteren WF. Polarizable coarse-grained models for molecular dynamics simulation of liquid cyclohexane. J Comput Chem 2015; 36:1311-21. [DOI: 10.1002/jcc.23929] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/17/2014] [Revised: 03/09/2015] [Accepted: 03/12/2015] [Indexed: 11/08/2022]
Affiliation(s)
- Oliwia M. Szklarczyk
- Laboratory of Physical Chemistry, Department of Chemistry and Applied Biosciences; Swiss Federal Institute of Technology ETH; 8093 Zürich Switzerland
| | - Eirini Arvaniti
- Laboratory of Physical Chemistry, Department of Chemistry and Applied Biosciences; Swiss Federal Institute of Technology ETH; 8093 Zürich Switzerland
| | - Wilfred F. van Gunsteren
- Laboratory of Physical Chemistry, Department of Chemistry and Applied Biosciences; Swiss Federal Institute of Technology ETH; 8093 Zürich Switzerland
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46
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Naômé A, Laaksonen A, Vercauteren DP. A Coarse-Grained Simulation Study of the Structures, Energetics, and Dynamics of Linear and Circular DNA with Its Ions. J Chem Theory Comput 2015; 11:2813-26. [DOI: 10.1021/acs.jctc.5b00113] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Aymeric Naômé
- Laboratoire
de Physico-Chimie Informatique, Unité de Chimie Physique Théorique
et Structurale, University of Namur, 5000 Namur, Belgium
- Namur Medicine & Drug Innovation Center (NAMEDIC), University of Namur, 5000 Namur, Belgium
- Division
of Physical Chemistry, Department of Materials and Environmental Chemistry,
Arrhenius Laboratory, Stockholm University, 10691 Stockholm, Sweden
- Science for Life
Laboratory, 17121 Solna, Sweden
| | - Aatto Laaksonen
- Division
of Physical Chemistry, Department of Materials and Environmental Chemistry,
Arrhenius Laboratory, Stockholm University, 10691 Stockholm, Sweden
- Science for Life
Laboratory, 17121 Solna, Sweden
- Stellenbosch
Institute of Advanced Study (STIAS), Wallenberg Research Centre at Stellenbosch University, 7600 Stellenbosch, South Africa
| | - Daniel P. Vercauteren
- Laboratoire
de Physico-Chimie Informatique, Unité de Chimie Physique Théorique
et Structurale, University of Namur, 5000 Namur, Belgium
- Namur Medicine & Drug Innovation Center (NAMEDIC), University of Namur, 5000 Namur, Belgium
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47
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Abstract
ssDNA binding proteins (SSBs) protect ssDNA from chemical and enzymatic assault that can derail DNA processing machinery. Complexes between SSBs and ssDNA are often highly stable, but predicting their structures is challenging, mostly because of the inherent flexibility of ssDNA and the geometric and energetic complexity of the interfaces that it forms. Here, we report a newly developed coarse-grained model to predict the structure of SSB-ssDNA complexes. The model is successfully applied to predict the binding modes of six SSBs with ssDNA strands of lengths of 6-65 nt. In addition to charge-charge interactions (which are often central to governing protein interactions with nucleic acids by means of electrostatic complementarity), an essential energetic term to predict SSB-ssDNA complexes is the interactions between aromatic residues and DNA bases. For some systems, flexibility is required from not only the ssDNA but also, the SSB to allow it to undergo conformational changes and the penetration of the ssDNA into its binding pocket. The association mechanisms can be quite varied, and in several cases, they involve the ssDNA sliding along the protein surface. The binding mechanism suggests that coarse-grained models are appropriate to study the motion of SSBs along ssDNA, which is expected to be central to the function carried out by the SSBs.
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48
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Haxton TK. High-Resolution Coarse-Grained Modeling Using Oriented Coarse-Grained Sites. J Chem Theory Comput 2015; 11:1244-54. [DOI: 10.1021/ct500881x] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022]
Affiliation(s)
- Thomas K. Haxton
- Molecular
Foundry, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
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49
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Stachiewicz A, Molski A. A coarse-grained MARTINI-like force field for DNA unzipping in nanopores. J Comput Chem 2015; 36:947-56. [DOI: 10.1002/jcc.23874] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/25/2014] [Revised: 01/14/2015] [Accepted: 01/17/2015] [Indexed: 11/08/2022]
Affiliation(s)
- Anna Stachiewicz
- Department of Chemistry; Adam Mickiewicz University; Poznan Poland
| | - Andrzej Molski
- Department of Chemistry; Adam Mickiewicz University; Poznan Poland
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50
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Markegard CB, Fu IW, Reddy KA, Nguyen HD. Coarse-grained simulation study of sequence effects on DNA hybridization in a concentrated environment. J Phys Chem B 2015; 119:1823-34. [PMID: 25581253 DOI: 10.1021/jp509857k] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022]
Abstract
A novel coarse-grained model is developed to elucidate thermodynamics and kinetic mechanisms of DNA self-assembly. It accounts for sequence and solvent conditions to capture key experimental results such as sequence-dependent thermal property and salt-dependent persistence length of ssDNA and dsDNA. Moreover, constant-temperature simulations on two single strands of a homogeneous sequence show two main mechanisms of hybridization: a slow slithering mechanism and a one-order faster zippering mechanism. Furthermore, large-scale simulations at a high DNA strand concentration demonstrate that DNA self-assembly is a robust and enthalpically driven process in which the formation of double helices is deciphered to occur via multiple self-assembly pathways including the strand displacement mechanism. However, sequence plays an important role in shifting the majority of one pathway over the others and controlling size distribution of self-assembled aggregates. This study yields a complex picture on the role of sequence on programmable self-assembly and demonstrates a promising simulation tool that is suitable for studies in DNA nanotechnology.
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Affiliation(s)
- Cade B Markegard
- Department of Chemical Engineering and Materials Science, University of California-Irvine , Irvine, California 92697-2575, United States
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