1
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Bowers SR, Lockhart C, Klimov DK. Replica Exchange with Hybrid Tempering Efficiently Samples PGLa Peptide Binding to Anionic Bilayer. J Chem Theory Comput 2023; 19:6532-6550. [PMID: 37676235 DOI: 10.1021/acs.jctc.3c00787] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/08/2023]
Abstract
We evaluated the utility of a variant of the replica exchange method, a replica exchange with hybrid tempering (REHT), for all-atom explicit water biomolecular simulations and compared it with a more traditional replica exchange with the solute tempering (REST) algorithm. As a test system, we selected a 21-mer antimicrobial peptide PGLa binding to an anionic DMPC/DMPG lipid bilayer. Application of REHT revealed the following binding mechanism. Due to the strong hydrophobic moment, the bound PGLa adopts an extensive helical structure. The binding free energy landscape identifies two major bound states, a metastable surface bound state and a dominant inserted state. In both states, positively charged PGLa amino acids maintain electrostatic interactions with anionic phosphate groups by rotating the PGLa helix around its axis. PGLa binding causes an influx of anionic DMPG and an efflux of zwitterionic DMPC lipids from the peptide proximity. PGLa thins the bilayer and disorders the adjacent fatty acid tails. Deep invasion of water wires into the bilayer hydrophobic core is detected in the inserted peptide state. The analysis of charge density distributions indicated that peptide positive charges are nearly compensated for by lipid negative charges and water dipole ordering, whereas ions play no role in peptide binding. Thus, electrostatic interactions are the key energetic factor in binding cationic PGLa to an anionic DMPC/DMPG bilayer. Comparison of REHT and REST shows that due to exclusion of lipids from tempered partition, REST lags behind REHT in peptide equilibration, particularly, with respect to peptide insertion and helix acquisition. As a result, REST struggles to provide accurate details of PGLa binding, although it still qualitatively maps the bimodal binding mechanism. Importantly, REHT not only equilibrates PGLa in the bilayer faster than REST, but also with less computational effort. We conclude that REHT is a preferable choice for studying interfacial biomolecular systems.
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Affiliation(s)
- Steven R Bowers
- School of Systems Biology, George Mason University, Manassas, Virginia 20110, United States
| | - Christopher Lockhart
- School of Systems Biology, George Mason University, Manassas, Virginia 20110, United States
| | - Dmitri K Klimov
- School of Systems Biology, George Mason University, Manassas, Virginia 20110, United States
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2
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Ahyayauch H, García-Arribas AB, Masserini ME, Pantano S, Goñi FM, Alonso A. β-Amyloid (1-42) peptide adsorbs but does not insert into ganglioside-containing phospholipid membranes in the liquid-disordered state: modelling and experimental studies. Int J Biol Macromol 2020; 164:2651-2658. [PMID: 32846182 DOI: 10.1016/j.ijbiomac.2020.08.165] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/16/2020] [Revised: 08/09/2020] [Accepted: 08/21/2020] [Indexed: 12/14/2022]
Abstract
β-Amyloid (Aβ) is a 39-43 residue peptide involved in the pathogenesis of Alzheimer's disease. Aβ deposits onto the cells and gives rise to the plaques that are characteristic of the disease. In an effort to understand the molecular mechanism of plaque formation, we have examined the interaction of Aβ42, considered to be the most pathogenic of the peptides, with lipid bilayers consisting of 1-palmitoyl-2-oleoyl phosphatidylcholine (POPC) to which small amounts of GM1 ganglioside (1-5 mol%) were incorporated. POPC bilayers exist in the fluid, or liquid-disordered state at room temperature, mimicking the fluidity of cell membranes. An Aβ42 preparation consisting essentially of peptide monomers was used. A combination of molecular dynamics (MD), isothermal calorimetry and Langmuir balance measurements was applied. Our results show that Aβ binds POPC bilayers, and that binding increases (ΔG of binding decreases) with GM1, but only up to 3 mol% of the ganglioside, larger concentrations appearing to have a lower effect. MD and Langmuir balance measurements concur in showing that the peptide adsorbs onto the bilayer surface, but does not become inserted into it at surface pressures compatible with the cell membrane conditions. Thioflavin T measurements agree with MD in revealing a very low degree of peptide oligomerization/aggregation under our conditions. This is in contrast with previous studies showing peptide aggregation and insertion when interacting with membranes in the liquid-ordered state. The present contribution underlines the importance of bilayer lipid composition and properties for Aβ plaque formation.
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Affiliation(s)
- Hasna Ahyayauch
- Instituto Biofisika (CSIC, UPV/EHU) and Departamento de Bioquímica, Universidad del País Vasco, Bilbao, Spain; Institut Supérieur des Professions Infirmières et Techniques de Santé, Rabat, Morocco; Neuroendocrinology Unit, Laboratory of Genetics, Neuroendocrinology and Biotechnology, Faculty of Sciences, Ibn Tofail University, Kénitra, Morocco
| | - Aritz B García-Arribas
- Instituto Biofisika (CSIC, UPV/EHU) and Departamento de Bioquímica, Universidad del País Vasco, Bilbao, Spain
| | | | - Sergio Pantano
- Biomolecular Simulations Group, Institut Pasteur de Montevideo, Montevideo, Uruguay
| | - Félix M Goñi
- Instituto Biofisika (CSIC, UPV/EHU) and Departamento de Bioquímica, Universidad del País Vasco, Bilbao, Spain
| | - Alicia Alonso
- Instituto Biofisika (CSIC, UPV/EHU) and Departamento de Bioquímica, Universidad del País Vasco, Bilbao, Spain.
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3
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Kargar F, Emadi S, Fazli H. Dimerization of Aβ40 inside dipalmitoylphosphatidylcholine bilayer and its effect on bilayer integrity: Atomistic simulation at three temperatures. Proteins 2020; 88:1540-1552. [PMID: 32557766 DOI: 10.1002/prot.25972] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/13/2019] [Revised: 04/28/2020] [Accepted: 06/07/2020] [Indexed: 11/10/2022]
Abstract
Amyloid-beta (Aβ) protein is related to Alzheimer disease (AD), and various experiments have shown that oligomers as small as dimers are cytotoxic. Recent studies have concluded that interactions of Aβ with neuronal cell membranes lead to disruption of membrane integrity and toxicity and they play a key role in the development of AD. Molecular dynamics (MD) simulations have been used to investigate Aβ in aqueous solution and membranes. We have previously studied monomeric Aβ40 embedded in dipalmitoylphosphatidylcholine (DPPC) membrane using MD simulations. Here, we explore interactions of two Aβ40 peptides in DPPC bilayer and its consequences on dimer distribution in a lipid bilayer and on the secondary structure of the peptides. We explored that N-terminals played an important role in dimeric Aβ peptide aggregations and Aβ-bilayer interactions, while C-terminals bound peptides to bilayer like anchors. We did not observe exiting of peptides in our simulations although we observed insertion of peptides into the core of bilayer in some of our simulations. So it seems that the presence of Aβ on membrane surface increases its aggregation rate, and as diffusion occurs in two dimensions, it can increase the probability of interpeptide interactions. We found that dimeric Aβ, like monomeric one, had the ability to cause structural destabilization of DPPC membrane, which in turn might ultimately lead to cell death in an in vivo system. This information could have important implications for understanding the affinity of Aβ oligomers (here dimer) for membranes and the mechanism of Aβ oligomer toxicity in AD.
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Affiliation(s)
- Faezeh Kargar
- Department of Physics, Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan, Iran
| | - Saeed Emadi
- Department of Biological Sciences, Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan, Iran
| | - Hossein Fazli
- Department of Physics, Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan, Iran.,Department of Biological Sciences, Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan, Iran
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4
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Familial Alzheimer's disease patient-derived neurons reveal distinct mutation-specific effects on amyloid beta. Mol Psychiatry 2020; 25:2919-2931. [PMID: 30980041 PMCID: PMC7577860 DOI: 10.1038/s41380-019-0410-8] [Citation(s) in RCA: 87] [Impact Index Per Article: 17.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 09/13/2018] [Revised: 01/04/2019] [Accepted: 03/18/2019] [Indexed: 02/07/2023]
Abstract
Familial Alzheimer's disease (fAD) mutations alter amyloid precursor protein (APP) cleavage by γ-secretase, increasing the proportion of longer amyloidogenic amyloid-β (Aβ) peptides. Using five control induced pluripotent stem cell (iPSC) lines and seven iPSC lines generated from fAD patients, we investigated the effects of mutations on the Aβ secretome in human neurons generated in 2D and 3D. We also analysed matched CSF, post-mortem brain tissue, and iPSCs from the same participant with the APP V717I mutation. All fAD mutation lines demonstrated an increased Aβ42:40 ratio relative to controls, yet displayed varied signatures for Aβ43, Aβ38, and short Aβ fragments. We propose four qualitatively distinct mechanisms behind raised Aβ42:40. (1) APP V717I mutations alter γ-secretase cleavage site preference. Whereas, distinct presenilin 1 (PSEN1) mutations lead to either (2) reduced γ-secretase activity, (3) altered protein stability or (4) reduced PSEN1 maturation, all culminating in reduced γ-secretase carboxypeptidase-like activity. These data support Aβ mechanistic tenets in a human physiological model and substantiate iPSC-neurons for modelling fAD.
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5
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Carballo-Pacheco M, Ismail AE, Strodel B. On the Applicability of Force Fields To Study the Aggregation of Amyloidogenic Peptides Using Molecular Dynamics Simulations. J Chem Theory Comput 2018; 14:6063-6075. [PMID: 30336669 DOI: 10.1021/acs.jctc.8b00579] [Citation(s) in RCA: 60] [Impact Index Per Article: 8.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Molecular dynamics simulations play an essential role in understanding biomolecular processes such as protein aggregation at temporal and spatial resolutions which are not attainable by experimental methods. For a correct modeling of protein aggregation, force fields must accurately represent molecular interactions. Here, we study the effect of five different force fields on the oligomer formation of Alzheimer's Aβ16-22 peptide and two of its mutants: Aβ16-22(F19V,F20V), which does not form fibrils, and Aβ16-22(F19L) which forms fibrils faster than the wild type. We observe that while oligomer formation kinetics depends strongly on the force field, structural properties, such as the most relevant protein-protein contacts, are similar between them. The oligomer formation kinetics obtained with different force fields differ more from each other than the kinetics between aggregating and nonaggregating peptides simulated with a single force field. We discuss the difficulties in comparing atomistic simulations of amyloid oligomer formation with experimental observables.
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Affiliation(s)
- Martín Carballo-Pacheco
- Institute of Complex Systems: Structural Biochemistry (ICS-6) , Forschungszentrum Jülich GmbH , 52425 Jülich , Germany.,AICES Graduate School , RWTH Aachen University , Schinkelstraße 2 , 52062 Aachen , Germany
| | - Ahmed E Ismail
- AICES Graduate School , RWTH Aachen University , Schinkelstraße 2 , 52062 Aachen , Germany.,Aachener Verfahrenstechnik, Faculty of Mechanical Engineering , RWTH Aachen University , Schinkelstraße 2 , 52062 Aachen , Germany
| | - Birgit Strodel
- Institute of Complex Systems: Structural Biochemistry (ICS-6) , Forschungszentrum Jülich GmbH , 52425 Jülich , Germany.,Institute of Theoretical and Computational Chemistry , Heinrich Heine University Düsseldorf , Universitätstrasse 1 , 40225 Düsseldorf , Germany
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6
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Menon S, Sengupta N. Influence of Hyperglycemic Conditions on Self-Association of the Alzheimer's Amyloid β (Aβ 1-42) Peptide. ACS OMEGA 2017; 2:2134-2147. [PMID: 30023655 PMCID: PMC6044820 DOI: 10.1021/acsomega.7b00018] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 01/09/2017] [Accepted: 05/08/2017] [Indexed: 06/08/2023]
Abstract
Clinical studies have identified a correlation between type-2 diabetes mellitus and cognitive decrements en route to the onset of Alzheimer's disease (AD). Recent studies have established that post-translational modifications of the amyloid β (Aβ) peptide occur under hyperglycemic conditions; particularly, the process of glycation exacerbates its neurotoxicity and accelerates AD progression. In view of the assertion that macromolecular crowding has an altering effect on protein self-assembly, it is crucial to characterize the effects of hyperglycemic conditions via crowding on Aβ self-assembly. Toward this purpose, fully atomistic molecular dynamics simulations were performed to study the effects of glucose crowding on Aβ dimerization, which is the smallest known neurotoxic species. The dimers formed in the glucose-crowded environment were found to have weaker associations as compared to that of those formed in water. Binding free energy calculations show that the reduced binding strength of the dimers can be mainly attributed to the overall weakening of the dispersion interactions correlated with substantial loss of interpeptide contacts in the hydrophobic patches of the Aβ units. Analysis to discern the differential solvation pattern in the glucose-crowded and pure water systems revealed that glucose molecules cluster around the protein, at a distance of 5-7 Å, which traps the water molecules in close association with the protein surface. This preferential exclusion of glucose molecules and resulting hydration of the Aβ peptides has a screening effect on the hydrophobic interactions, which in turn diminishes the binding strength of the resulting dimers. Our results imply that physical effects attributed to crowded hyperglycemic environments are incapable of solely promoting Aβ self-assembly, indicating that further mechanistic studies are required to provide insights into the self-assembly of post-translationally modified Aβ peptides, known to possess aggravated toxicity, under these conditions.
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Affiliation(s)
- Sneha Menon
- Physical
Chemistry Division, CSIR-National Chemical
Laboratory, Dr. Homi
Bhabha Road, Pune 411008, India
- Academy
of Scientific and Innovative Research (AcSIR), Training and Development Complex, CSIR Campus,
CSIR Road, Chennai 600113, India
| | - Neelanjana Sengupta
- Department
of Biological Sciences, Indian Institute
of Science Education and Research (IISER) Kolkata, Mohanpur 741246, West Bengal, India
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7
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Smith AK, Lockhart C, Klimov DK. Does Replica Exchange with Solute Tempering Efficiently Sample Aβ Peptide Conformational Ensembles? J Chem Theory Comput 2016; 12:5201-5214. [DOI: 10.1021/acs.jctc.6b00660] [Citation(s) in RCA: 36] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022]
Affiliation(s)
- Amy K. Smith
- School
of Systems Biology
and Computational Materials Science Center, George Mason University, Manassas, Virginia 20110, United States
| | - Christopher Lockhart
- School
of Systems Biology
and Computational Materials Science Center, George Mason University, Manassas, Virginia 20110, United States
| | - Dmitri K. Klimov
- School
of Systems Biology
and Computational Materials Science Center, George Mason University, Manassas, Virginia 20110, United States
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8
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The binding of small carbazole derivative (P7C3) to protofibrils of the Alzheimer’s disease and β-secretase: Molecular dynamics simulation studies. Chem Phys 2015. [DOI: 10.1016/j.chemphys.2015.07.026] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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9
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Parikh ND, Klimov DK. Molecular Mechanisms of Alzheimer’s Biomarker FDDNP Binding to Aβ Amyloid Fibril. J Phys Chem B 2015; 119:11568-80. [DOI: 10.1021/acs.jpcb.5b06112] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/18/2023]
Affiliation(s)
- Niyati D. Parikh
- School
of Systems Biology, George Mason University, Manassas, Virginia 20110, United States
| | - Dmitri K. Klimov
- School
of Systems Biology, George Mason University, Manassas, Virginia 20110, United States
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10
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Effect of pH on the Aggregation of α-syn12 Dimer in Explicit Water by Replica-Exchange Molecular Dynamics Simulation. Int J Mol Sci 2015; 16:14291-304. [PMID: 26114384 PMCID: PMC4519842 DOI: 10.3390/ijms160714291] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/31/2015] [Revised: 06/09/2015] [Accepted: 06/10/2015] [Indexed: 01/22/2023] Open
Abstract
The dimeric structure of the N-terminal 12 residues drives the interaction of α-synuclein protein with membranes. Moreover, experimental studies indicated that the aggregation of α-synuclein is faster at low pH than neutral pH. Nevertheless, the effects of different pH on the structural characteristics of the α-syn12 dimer remain poorly understood. We performed 500 ns temperature replica exchange molecular dynamics (T-REMD) simulations of two α-syn12 peptides in explicit solvent. The free energy surfaces contain ten highly populated regions at physiological pH, while there are only three highly populated regions contained at acidic pH. The anti-parallel β-sheet conformations were found as the lowest free energy state. Additionally, these states are nearly flat with a very small barrier which indicates that these states can easily transit between themselves. The dimer undergoes a disorder to order transition from physiological pH to acidic pH and the α-syn12 dimer at acidic pH involves a faster dimerization process. Further, the Lys6–Asp2 contact may prevent the dimerization.
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11
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Xu L, Shan S, Chen Y, Wang X, Nussinov R, Ma B. Coupling of Zinc-Binding and Secondary Structure in Nonfibrillar Aβ40 Peptide Oligomerization. J Chem Inf Model 2015; 55:1218-30. [PMID: 26017140 PMCID: PMC6407634 DOI: 10.1021/acs.jcim.5b00063] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022]
Abstract
Nonfibrillar neurotoxic amyloid β (Aβ) oligomer structures are typically rich in β-sheets, which could be promoted by metal ions like Zn(2+). Here, using molecular dynamics (MD) simulations, we systematically examined combinations of Aβ40 peptide conformations and Zn(2+) binding modes to probe the effects of secondary structure on Aβ dimerization energies and kinetics. We found that random conformations do not contribute to dimerization either thermodynamically or kinetically. Zn(2+) couples with preformed secondary structures (α-helix and β-hairpin) to speed dimerization and stabilize the resulting dimer. Partial α-helices increase the dimerization speed, and dimers with α-helix rich conformations have the lowest energy. When Zn(2+) coordinates with residues D1, H6, H13, and H14, Aβ40 β-hairpin monomers have the fastest dimerization speed. Dimers with experimentally observed zinc coordination (E11, H6, H13, and H14) form with slower rate but have lower energy. Zn(2+) cannot stabilize fibril-like β-arch dimers. However, Zn(2+)-bound β-arch tetramers have the lowest energy. Collectively, zinc-stabilized β-hairpin oligomers could be important in the nucleation-polymerization of cross-β structures. Our results are consistent with experimental findings that α-helix to β-structural transition should accompany Aβ aggregation in the presence of zinc ions and that Zn(2+) stabilizes nonfibrillar Aβ oligomers and, thus, inhibits formation of less toxic Aβ fibrils.
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Affiliation(s)
- Liang Xu
- School of Chemistry, Dalian University of Technology, Dalian, China
| | - Shengsheng Shan
- School of Chemistry, Dalian University of Technology, Dalian, China
| | - Yonggang Chen
- Network and Information Center, Dalian University of Technology, Dalian, China
| | - Xiaojuan Wang
- School of Chemical Machinery, Dalian University of Technology, Dalian, China
| | - Ruth Nussinov
- Sackler Inst. of Molecular Medicine Department of Human Genetics and Molecular Medicine Sackler School of Medicine, Tel Aviv University, Tel Aviv 69978, Israel
- Basic Science Program, Leidos Biomedical Research, Inc. Cancer and Inflammation Program, National Cancer Institute, Frederick, Maryland 21702
| | - Buyong Ma
- Basic Science Program, Leidos Biomedical Research, Inc. Cancer and Inflammation Program, National Cancer Institute, Frederick, Maryland 21702
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12
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Nasica-Labouze J, Nguyen PH, Sterpone F, Berthoumieu O, Buchete NV, Coté S, De Simone A, Doig AJ, Faller P, Garcia A, Laio A, Li MS, Melchionna S, Mousseau N, Mu Y, Paravastu A, Pasquali S, Rosenman DJ, Strodel B, Tarus B, Viles JH, Zhang T, Wang C, Derreumaux P. Amyloid β Protein and Alzheimer's Disease: When Computer Simulations Complement Experimental Studies. Chem Rev 2015; 115:3518-63. [PMID: 25789869 DOI: 10.1021/cr500638n] [Citation(s) in RCA: 499] [Impact Index Per Article: 49.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Affiliation(s)
- Jessica Nasica-Labouze
- †Laboratoire de Biochimie Théorique, Institut de Biologie Physico-Chimique (IBPC), UPR9080 CNRS, Université Paris Diderot, Sorbonne Paris Cité, 13 rue Pierre et Marie Curie, 75005 Paris, France
| | - Phuong H Nguyen
- †Laboratoire de Biochimie Théorique, Institut de Biologie Physico-Chimique (IBPC), UPR9080 CNRS, Université Paris Diderot, Sorbonne Paris Cité, 13 rue Pierre et Marie Curie, 75005 Paris, France
| | - Fabio Sterpone
- †Laboratoire de Biochimie Théorique, Institut de Biologie Physico-Chimique (IBPC), UPR9080 CNRS, Université Paris Diderot, Sorbonne Paris Cité, 13 rue Pierre et Marie Curie, 75005 Paris, France
| | - Olivia Berthoumieu
- ‡LCC (Laboratoire de Chimie de Coordination), CNRS, Université de Toulouse, Université Paul Sabatier (UPS), Institut National Polytechnique de Toulouse (INPT), 205 route de Narbonne, BP 44099, Toulouse F-31077 Cedex 4, France
| | | | - Sébastien Coté
- ∥Département de Physique and Groupe de recherche sur les protéines membranaires (GEPROM), Université de Montréal, C.P. 6128, succursale Centre-ville, Montréal, Québec H3C 3T5, Canada
| | - Alfonso De Simone
- ⊥Department of Life Sciences, Imperial College London, London SW7 2AZ, United Kingdom
| | - Andrew J Doig
- #Manchester Institute of Biotechnology, University of Manchester, 131 Princess Street, Manchester M1 7DN, United Kingdom
| | - Peter Faller
- ‡LCC (Laboratoire de Chimie de Coordination), CNRS, Université de Toulouse, Université Paul Sabatier (UPS), Institut National Polytechnique de Toulouse (INPT), 205 route de Narbonne, BP 44099, Toulouse F-31077 Cedex 4, France
| | | | - Alessandro Laio
- ○The International School for Advanced Studies (SISSA), Via Bonomea 265, 34136 Trieste, Italy
| | - Mai Suan Li
- ◆Institute of Physics, Polish Academy of Sciences, Al. Lotnikow 32/46, 02-668 Warsaw, Poland.,¶Institute for Computational Science and Technology, SBI Building, Quang Trung Software City, Tan Chanh Hiep Ward, District 12, Ho Chi Minh City, Vietnam
| | - Simone Melchionna
- ⬠Instituto Processi Chimico-Fisici, CNR-IPCF, Consiglio Nazionale delle Ricerche, 00185 Roma, Italy
| | | | - Yuguang Mu
- ▲School of Biological Sciences, Nanyang Technological University, 60 Nanyang Drive, 637551 Singapore
| | - Anant Paravastu
- ⊕National High Magnetic Field Laboratory, 1800 East Paul Dirac Drive, Tallahassee, Florida 32310, United States
| | - Samuela Pasquali
- †Laboratoire de Biochimie Théorique, Institut de Biologie Physico-Chimique (IBPC), UPR9080 CNRS, Université Paris Diderot, Sorbonne Paris Cité, 13 rue Pierre et Marie Curie, 75005 Paris, France
| | | | - Birgit Strodel
- △Institute of Complex Systems: Structural Biochemistry (ICS-6), Forschungszentrum Jülich GmbH, 52425 Jülich, Germany
| | - Bogdan Tarus
- †Laboratoire de Biochimie Théorique, Institut de Biologie Physico-Chimique (IBPC), UPR9080 CNRS, Université Paris Diderot, Sorbonne Paris Cité, 13 rue Pierre et Marie Curie, 75005 Paris, France
| | - John H Viles
- ▼School of Biological and Chemical Sciences, Queen Mary University of London, London E1 4NS, United Kingdom
| | - Tong Zhang
- †Laboratoire de Biochimie Théorique, Institut de Biologie Physico-Chimique (IBPC), UPR9080 CNRS, Université Paris Diderot, Sorbonne Paris Cité, 13 rue Pierre et Marie Curie, 75005 Paris, France.,▲School of Biological Sciences, Nanyang Technological University, 60 Nanyang Drive, 637551 Singapore
| | | | - Philippe Derreumaux
- †Laboratoire de Biochimie Théorique, Institut de Biologie Physico-Chimique (IBPC), UPR9080 CNRS, Université Paris Diderot, Sorbonne Paris Cité, 13 rue Pierre et Marie Curie, 75005 Paris, France.,□Institut Universitaire de France, 75005 Paris, France
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13
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Jose JC, Chatterjee P, Sengupta N. Cross dimerization of amyloid-β and αsynuclein proteins in aqueous environment: a molecular dynamics simulations study. PLoS One 2014; 9:e106883. [PMID: 25210774 PMCID: PMC4161357 DOI: 10.1371/journal.pone.0106883] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/08/2014] [Accepted: 08/07/2014] [Indexed: 11/18/2022] Open
Abstract
Self-assembly of the intrinsically unstructured proteins, amyloid beta (Aβ) and alpha synclein (αSyn), are associated with Alzheimer's Disease, and Parkinson's and Lewy Body Diseases, respectively. Importantly, pathological overlaps between these neurodegenerative diseases, and the possibilities of interactions between Aβ and αSyn in biological milieu emerge from several recent clinical reports and in vitro studies. Nevertheless, there are very few molecular level studies that have probed the nature of spontaneous interactions between these two sequentially dissimilar proteins and key characteristics of the resulting cross complexes. In this study, we have used atomistic molecular dynamics simulations to probe the possibility of cross dimerization between αSyn1-95 and Aβ1-42, and thereby gain insights into their plausible early assembly pathways in aqueous environment. Our analyses indicate a strong probability of association between the two sequences, with inter-protein attractive electrostatic interactions playing dominant roles. Principal component analysis revealed significant heterogeneity in the strength and nature of the associations in the key interaction modes. In most, the interactions of repeating Lys residues, mainly in the imperfect repeats 'KTKEGV' present in αSyn1-95 were found to be essential for cross interactions and formation of inter-protein salt bridges. Additionally, a hydrophobicity driven interaction mode devoid of salt bridges, where the non-amyloid component (NAC) region of αSyn1-95 came in contact with the hydrophobic core of Aβ1-42 was observed. The existence of such hetero complexes, and therefore hetero assembly pathways may lead to polymorphic aggregates with variations in pathological attributes. Our results provide a perspective on development of therapeutic strategies for preventing pathogenic interactions between these proteins.
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Affiliation(s)
- Jaya C. Jose
- Physical Chemistry Division, CSIR-National Chemical Laboratory, Pune, Maharashtra, India
| | - Prathit Chatterjee
- Physical Chemistry Division, CSIR-National Chemical Laboratory, Pune, Maharashtra, India
| | - Neelanjana Sengupta
- Physical Chemistry Division, CSIR-National Chemical Laboratory, Pune, Maharashtra, India
- * E-mail:
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14
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Berhanu WM, Hansmann UHE. Stability of amyloid oligomers. ADVANCES IN PROTEIN CHEMISTRY AND STRUCTURAL BIOLOGY 2014; 96:113-41. [PMID: 25443956 DOI: 10.1016/bs.apcsb.2014.06.006] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 03/12/2023]
Abstract
Molecular simulations are now commonly used to complement experimental techniques in investigating amyloids and their role in human diseases. In this chapter, we will summarize techniques and approaches often used in amyloid simulations and will present recent success stories. Our examples will be focused on lessons learned from molecular dynamics simulations in aqueous environments that start from preformed aggregates. These studies explore the limitations that arise from the choice of force field, the role of mutations in the growth of amyloid aggregates, segmental polymorphism, and the importance of cross-seeding. Furthermore, they give evidence for potential toxicity mechanisms. We finally discuss the role of molecular simulations in the search for aggregation inhibitors.
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Affiliation(s)
- Workalemahu M Berhanu
- Department of Chemistry & Biochemistry, University of Oklahoma, Norman, Oklahoma, USA
| | - Ulrich H E Hansmann
- Department of Chemistry & Biochemistry, University of Oklahoma, Norman, Oklahoma, USA.
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15
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Viet MH, Nguyen PH, Derreumaux P, Li MS. Effect of the English familial disease mutation (H6R) on the monomers and dimers of Aβ40 and Aβ42. ACS Chem Neurosci 2014; 5:646-57. [PMID: 24949887 DOI: 10.1021/cn500007j] [Citation(s) in RCA: 47] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022] Open
Abstract
The self-assembly of the amyloid beta (Aβ) peptides into senile plaques is the hallmark of Alzheimer's disease. Recent experiments have shown that the English familial disease mutation (H6R) speeds up the fibril formation process of alloforms Aβ40 and Aβ42 peptides altering their toxicity to cells. We used all-atom molecular dynamics simulations at microsecond time scales with the OPLS-AA force field and TIP4P explicit water model to study the structural dynamics of the monomer and dimer of H6R sequences of both peptides. The reason behind the self-assembly acceleration is common that upon mutation the net charge is reduced leading to the weaker repulsive interaction between chains that facilitates the peptide association. In addition, our estimation of the solvation free energy shows that the mutation enhances the hydrophobicity of both peptides speeding up their aggregation. However, we can show that the acceleration mechanisms are different for different peptides: the rate of fibril formation of Aβ42 increases due to increased β-structure at the C-terminal in both monomer and dimer and enhanced stability of salt bridge Asp23-Lys28 in monomer, while the enhancement of turn at residues 25-29 and reduction of coil in regions 10-13, 26-19, and 30-34 would play the key role for Aβ40. Overall, our study provides a detailed atomistic picture of the H6R-mediated conformational changes that are consistent with the experimental findings and highlights the important role of the N-terminal in Aβ peptide aggregation.
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Affiliation(s)
- Man Hoang Viet
- Institute
of Physics, Polish Academy of Sciences, Al. Lotnikow 32/46, 02-668 Warsaw, Poland
| | - Phuong H. Nguyen
- Laboratoire
de Biochimie Theorique, UPR 9080 CNRS, IBPC, Universite Paris 7, 13 rue Pierre et Marie Curie, 75005 Paris, France
| | - Philippe Derreumaux
- Laboratoire
de Biochimie Theorique, UPR 9080 CNRS, IBPC, Universite Denis Diderot, Paris Sorbonne Cité 13 rue Pierre et Marie Curie, 75005 Paris, France
- Institut Universitaire de France, Bvd Saint Michel, 75005 Paris, France
| | - Mai Suan Li
- Institute
of Physics, Polish Academy of Sciences, Al. Lotnikow 32/46, 02-668 Warsaw, Poland
- Institute for Computational Science and Technology, Quang Trung Software City, Tan Chanh Hiep Ward,
District 12, Ho Chi Minh City, Vietnam
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16
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Xu L, Chen Y, Wang X. Assembly of Amyloid β Peptides in the Presence of Fibril Seeds: One-Pot Coarse-Grained Molecular Dynamics Simulations. J Phys Chem B 2014; 118:9238-46. [DOI: 10.1021/jp505551m] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023]
Affiliation(s)
- Liang Xu
- School of Chemistry, ‡Network and Information Center, and §School of Chemical Machinery, Dalian University of Technology, Dalian, China
| | - Yonggang Chen
- School of Chemistry, ‡Network and Information Center, and §School of Chemical Machinery, Dalian University of Technology, Dalian, China
| | - Xiaojuan Wang
- School of Chemistry, ‡Network and Information Center, and §School of Chemical Machinery, Dalian University of Technology, Dalian, China
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17
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Okamoto A, Yano A, Nomura K, Higai S, Kurita N. Effect of D23N mutation on the dimer conformation of amyloid β-proteins: Ab initio molecular simulations in water. J Mol Graph Model 2014; 50:113-24. [DOI: 10.1016/j.jmgm.2014.03.004] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/25/2013] [Revised: 03/12/2014] [Accepted: 03/15/2014] [Indexed: 10/25/2022]
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18
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Socher E, Sticht H, Horn AHC. The conformational stability of nonfibrillar amyloid-β peptide oligomers critically depends on the C-terminal peptide length. ACS Chem Neurosci 2014; 5:161-7. [PMID: 24494584 DOI: 10.1021/cn400208r] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/16/2023] Open
Abstract
The amyloid-β (Aβ) peptide is one key molecule in the pathogenesis of Alzheimer's disease. We investigated the conformational stability of a nonfibrillar tetrameric Aβ structure by molecular dynamics (MD) simulations revealing that the stability of the Aβ tetramer depends critically on the C-terminal length. In contrast to the Aβ17-40 tetramer, which proved to be instable, the simulations demonstrate structural integrity of the Aβ17-42 and Aβ17-43 tetramers. These differences in stability can be attributed to an extension of the middle strand of a three-stranded antiparallel β sheet through residues 41-43, only present in the longer Aβ species that aggregate faster and are more neurotoxic. Additional MD simulations demonstrate that this higher stability is also present in the monomers forming the tetramer. In conclusion, our findings suggest the existence of a nonfibrillar oligomer topology that is significantly more stable for the longer Aβ species, thus offering a structural explanation for their higher neurotoxicity.
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Affiliation(s)
- Eileen Socher
- Bioinformatik,
Institut für Biochemie, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Fahrstraße 17, 91054 Erlangen, Germany
| | - Heinrich Sticht
- Bioinformatik,
Institut für Biochemie, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Fahrstraße 17, 91054 Erlangen, Germany
| | - Anselm H. C. Horn
- Bioinformatik,
Institut für Biochemie, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Fahrstraße 17, 91054 Erlangen, Germany
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19
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Zhang T, Xu W, Mu Y, Derreumaux P. Atomic and dynamic insights into the beneficial effect of the 1,4-naphthoquinon-2-yl-L-tryptophan inhibitor on Alzheimer's Aβ1-42 dimer in terms of aggregation and toxicity. ACS Chem Neurosci 2014; 5:148-59. [PMID: 24246047 DOI: 10.1021/cn400197x] [Citation(s) in RCA: 63] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022] Open
Abstract
Aggregation of the amyloid β protein (Aβ) peptide with 40 or 42 residues is one key feature in Alzheimer's disease (AD). The 1,4-naphthoquinon-2-yl-L-tryptophan (NQTrp) molecule was reported to alter Aβ self-assembly and reduce toxicity. Though nuclear magnetic resonance experiments and various simulations provided atomic information about the interaction of NQTrp with Aβ peptides spanning the regions of residues 12-28 and 17-42, none of these studies were conducted on the full-length Aβ1-42 peptide. To this end, we performed extensive atomistic replica exchange molecular dynamics simulations of Aβ1-42 dimer with two NQTrp molecules in explicit solvent, by using a force field known to fold diverse proteins correctly. The interactions between NQTrp and Aβ1-42, which change the Aβ interface by reducing most of the intermolecular contacts, are found to be very dynamic and multiple, leading to many transient binding sites. The most favorable binding residues are Arg5, Asp7, Tyr10, His13, Lys16, Lys18, Phe19/Phe20, and Leu34/Met35, providing therefore a completely different picture from in vitro and in silico experiments with NQTrp with shorter Aβ fragments. Importantly, the 10 hot residues that we identified explain the beneficial effect of NQTrp in reducing both the level of Aβ1-42 aggregation and toxicity. Our results also indicate that there is room to design more efficient drugs targeting Aβ1-42 dimer against AD.
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Affiliation(s)
- Tong Zhang
- Laboratoire de Biochimie Théorique, UPR9080 CNRS, Université
Paris Diderot, Sorbonne Paris Cité, Institut de Biologie Physico-Chimique, 13 rue Pierre et Marie Curie, 75005 Paris, France
- School of Biological Sciences, Nanyang Technological University, 60 Nanyang Drive, Singapore 637551
| | - Weixin Xu
- School of Biological Sciences, Nanyang Technological University, 60 Nanyang Drive, Singapore 637551
- State Key Laboratory of Precision Spectroscopy, Department
of Physics, Institute of Theoretical and Computational Science, East China Normal University, Shanghai 200062, China
| | - Yuguang Mu
- School of Biological Sciences, Nanyang Technological University, 60 Nanyang Drive, Singapore 637551
| | - Philippe Derreumaux
- Laboratoire de Biochimie Théorique, UPR9080 CNRS, Université
Paris Diderot, Sorbonne Paris Cité, Institut de Biologie Physico-Chimique, 13 rue Pierre et Marie Curie, 75005 Paris, France
- Institut Universitaire de France, 103 Boulevard Saint-Michel, 75005 Paris, France
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20
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Smith MD, Srinivasa Rao J, Cruz L. Spontaneous dimer states of the Aβ21–30decapeptide. Phys Chem Chem Phys 2014; 16:13069-73. [DOI: 10.1039/c4cp01090f] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/25/2022]
Abstract
Computational examination of the spontaneous dimerization of Aβ21–30and stability measures of the resulting parallel and anti-parallel aligned dimers.
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Affiliation(s)
| | - J. Srinivasa Rao
- Department of Physics
- New Jersey Institute of Technology
- University Heights
- Newark, USA
| | - Luis Cruz
- Department of Physics
- Drexel University
- Philadelphia, USA
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21
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Irbäck A, Mohanty S. All-Atom Monte Carlo Simulations of Protein Folding and Aggregation. COMPUTATIONAL METHODS TO STUDY THE STRUCTURE AND DYNAMICS OF BIOMOLECULES AND BIOMOLECULAR PROCESSES 2014. [DOI: 10.1007/978-3-642-28554-7_13] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/28/2022]
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22
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Molecular interactions of Alzheimer's biomarker FDDNP with Aβ peptide. Biophys J 2013; 103:2341-51. [PMID: 23283233 DOI: 10.1016/j.bpj.2012.10.003] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/16/2012] [Revised: 09/29/2012] [Accepted: 10/03/2012] [Indexed: 12/28/2022] Open
Abstract
All-atom explicit solvent model and replica exchange molecular dynamics were used to investigate binding of Alzheimer's biomarker FDDNP to the Aβ(10-40) monomer. At low and high concentrations, FDDNP binds with high affinity to two sites in the Aβ(10-40) monomer located near the central hydrophobic cluster and in the C-terminal. Analysis of ligand- Aβ(10-40) interactions at both concentrations identifies hydrophobic effect as a main binding factor. However, with the increase in ligand concentration the interactions between FDDNP molecules also become important due to strong FDDNP self-aggregation propensity and few specific binding locations. As a result, FDDNP ligands partially penetrate the core of the Aβ(10-40) monomer, forming large self-aggregated clusters. Ligand self-aggregation does not affect hydrophobic interactions as a main binding factor or the location of binding sites in Aβ(10-40). Using the Aβ(10-40) conformational ensemble in ligand-free water as reference, we show that FDDNP induces minor changes in the Aβ(10-40) secondary structure at two ligand concentrations studied. At the same time, FDDNP significantly alters the peptide tertiary fold in a concentration-dependent manner by redistributing long-range, side-chain interactions. We argue that because FDDNP does not change Aβ(10-40) secondary structure, its antiaggregation effect is likely to be weak. Our study raises the possibility that FDDNP may serve as a biomarker of not only Aβ fibril species, but of monomers as well.
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23
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Ahyayauch H, Raab M, Busto JV, Andraka N, Arrondo JLR, Masserini M, Tvaroska I, Goñi FM. Binding of β-amyloid (1-42) peptide to negatively charged phospholipid membranes in the liquid-ordered state: modeling and experimental studies. Biophys J 2013; 103:453-463. [PMID: 22947861 DOI: 10.1016/j.bpj.2012.06.043] [Citation(s) in RCA: 60] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/14/2012] [Revised: 06/22/2012] [Accepted: 06/27/2012] [Indexed: 12/12/2022] Open
Abstract
To explore the initial stages of amyloid β peptide (Aβ42) deposition on membranes, we have studied the interaction of Aβ42 in the monomeric form with lipid monolayers and with bilayers in either the liquid-disordered or the liquid-ordered (L(o)) state, containing negatively charged phospholipids. Molecular dynamics (MD) simulations of the system have been performed, as well as experimental measurements. For bilayers in the L(o) state, in the absence of the negatively charged lipids, interaction is weak and it cannot be detected by isothermal calorimetry. However, in the presence of phosphatidic acid, or of cardiolipin, interaction is detected by different methods and in all cases interaction is strongest with lower (2.5-5 mol%) than higher (10-20 mol%) proportions of negatively charged phospholipids. Liquid-disordered bilayers consistently allowed a higher Aβ42 binding than L(o) ones. Thioflavin T assays and infrared spectroscopy confirmed a higher proportion of β-sheet formation under conditions when higher peptide binding was measured. The experimental results were supported by MD simulations. We used 100 ns MD to examine interactions between Aβ42 and three different 512 lipid bilayers consisting of palmitoylsphingomyelin, dimyristoyl phosphatidic acid, and cholesterol in three different proportions. MD pictures are different for the low- and high-charge bilayers, in the former case the peptide is bound through many contact points to the bilayer, whereas for the bilayer containing 20 mol% anionic phospholipid only a small fragment of the peptide appears to be bound. The MD results indicate that the binding and fibril formation on the membrane surface depends on the composition of the bilayer, and is the result of a subtle balance of many inter- and intramolecular interactions between the Aβ42 and membrane.
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Affiliation(s)
- Hasna Ahyayauch
- Unidad de Biofísica (CSIC, UPV/EHU) and Departamento de Bioquímica, Universidad del País Vasco, Bilbao, Spain
| | - Michal Raab
- Institute of Chemistry, Slovak Academy of Sciences, Bratislava, Slovakia
| | - Jon V Busto
- Unidad de Biofísica (CSIC, UPV/EHU) and Departamento de Bioquímica, Universidad del País Vasco, Bilbao, Spain
| | - Nagore Andraka
- Unidad de Biofísica (CSIC, UPV/EHU) and Departamento de Bioquímica, Universidad del País Vasco, Bilbao, Spain
| | - José-Luis R Arrondo
- Unidad de Biofísica (CSIC, UPV/EHU) and Departamento de Bioquímica, Universidad del País Vasco, Bilbao, Spain
| | - Massimo Masserini
- Department of Experimental Medicine, University of Milano Bicocca, Monza, Italy
| | - Igor Tvaroska
- Institute of Chemistry, Slovak Academy of Sciences, Bratislava, Slovakia
| | - Félix M Goñi
- Unidad de Biofísica (CSIC, UPV/EHU) and Departamento de Bioquímica, Universidad del País Vasco, Bilbao, Spain.
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24
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Ozbil M, Barman A, Bora RP, Prabhakar R. Computational Insights into Dynamics of Protein Aggregation and Enzyme-Substrate Interactions. J Phys Chem Lett 2012; 3:3460-3469. [PMID: 26290973 DOI: 10.1021/jz301597k] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
In this Perspective, the roles of protein dynamics have been discussed in the aggregation of amyloid beta (Aβ) peptides and formation of enzyme-substrate complexes of beta-secretase (BACE1) and insulin-degrading enzyme (IDE). The studies regarding the influence of individual amino acid residues and specific regions on the structures and oligomerization of early Aβ aggregates and computations of their translational and rotational diffusion coefficients and order parameters exhibited that even the short-time-scale molecular dynamics simulations can reproduce certain experimental parameters with reasonable accuracy. The simulations elucidating the enzyme-substrate interactions of BACE1 and IDE successfully showed that the chemical nature and length of the substrates influence the dynamics and plasticity of both the enzyme and substrate. An atomic-level understanding of these processes will advance our efforts to develop therapeutic strategies for several deadly diseases through the design of small molecules with antiaggregation properties and substrate-specific "designer" forms of enzymes.
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Affiliation(s)
- Mehmet Ozbil
- Department of Chemistry, University of Miami, Coral Gables, Florida 33146, United States
| | - Arghya Barman
- Department of Chemistry, University of Miami, Coral Gables, Florida 33146, United States
| | - Ram Prasad Bora
- Department of Chemistry, University of Miami, Coral Gables, Florida 33146, United States
| | - Rajeev Prabhakar
- Department of Chemistry, University of Miami, Coral Gables, Florida 33146, United States
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25
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Lu Y, Wei G, Derreumaux P. Structural, thermodynamical, and dynamical properties of oligomers formed by the amyloid NNQQ peptide: insights from coarse-grained simulations. J Chem Phys 2012; 137:025101. [PMID: 22803563 DOI: 10.1063/1.4732761] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2022] Open
Abstract
Characterizing the early formed oligomeric intermediates of amyloid peptides is of particular interest due to their links with neurodegenerative diseases. Here we study the NNQQ peptide, known to display parallel β-strands in amyloid fibrils by x-ray microcrystallography, and investigate the structural, thermodynamical, and dynamical properties of 20 NNQQ peptides using molecular dynamics and replica exchange molecular dynamics simulations coupled to a coarse-grained force field. All simulations are initiated from randomized and fully dispersed monomeric conformations. Our simulations reveal that the phase transition is characterized by a change in the oligomer and β-sheet size distributions and the percentage of mixed parallel/antiparallel β-strands when the sheets are formed. At all temperatures, however, the fraction of parallel β-strands remains low, though there are many association/fragmentation events. This work and a growing body of computational studies provide strong evidence that the critical nucleus goes beyond 20 chains and reordering of the β-strands occurs in larger oligomers.
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Affiliation(s)
- Yan Lu
- State Key Laboratory of Surface Physics, and Department of Physics, Fudan University, 220 Handan Road, Shanghai 200433, China
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26
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Lockhart C, Kim S, Klimov DK. Explicit Solvent Molecular Dynamics Simulations of Aβ Peptide Interacting with Ibuprofen Ligands. J Phys Chem B 2012; 116:12922-32. [DOI: 10.1021/jp306208n] [Citation(s) in RCA: 29] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022]
Affiliation(s)
- Christopher Lockhart
- School of Systems Biology, George Mason University, Manassas, Virginia 20110, United States
| | - Seongwon Kim
- School of Systems Biology, George Mason University, Manassas, Virginia 20110, United States
| | - Dmitri K. Klimov
- School of Systems Biology, George Mason University, Manassas, Virginia 20110, United States
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27
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Zhu X, Bora RP, Barman A, Singh R, Prabhakar R. Dimerization of the Full-Length Alzheimer Amyloid β-Peptide (Aβ42) in Explicit Aqueous Solution: A Molecular Dynamics Study. J Phys Chem B 2012; 116:4405-16. [DOI: 10.1021/jp210019h] [Citation(s) in RCA: 47] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2022]
Affiliation(s)
- Xiaoxia Zhu
- Department of Chemistry, University of Miami, 1301 Memorial Drive, Coral Gables, Florida 33146,
United States
| | - Ram Prasad Bora
- Department of Chemistry, University of Miami, 1301 Memorial Drive, Coral Gables, Florida 33146,
United States
| | - Arghya Barman
- Department of Chemistry, University of Miami, 1301 Memorial Drive, Coral Gables, Florida 33146,
United States
| | - Rajiv Singh
- Department of Chemistry, University of Miami, 1301 Memorial Drive, Coral Gables, Florida 33146,
United States
| | - Rajeev Prabhakar
- Department of Chemistry, University of Miami, 1301 Memorial Drive, Coral Gables, Florida 33146,
United States
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28
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Han M, Hansmann UHE. Replica exchange molecular dynamics of the thermodynamics of fibril growth of Alzheimer's Aβ42 peptide. J Chem Phys 2012; 135:065101. [PMID: 21842950 DOI: 10.1063/1.3617250] [Citation(s) in RCA: 41] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023] Open
Abstract
The growth of amyloid fibrils is studied by replica exchange molecular dynamics in an implicit solvent. Our data indicate that extremely long simulation times (at least a few hundred ns) are necessary to study the thermodynamics of fibril elongation in detail. However some aspects of the aggregation process are already accessible on the time scales available in the present study. A peak in the specific heat indicates a docking temperature of T(dock) ≈ 320 K. Irreversible locking requires lower temperatures with the locking temperature estimated as T(lock) ≈ 280 K. In our simulation the fibril grows from both sides with the C-terminal of the incoming monomer attaching to the C-terminal of the peptides in the fibril forming a β-sheet on the fibril edge. Our simulation indicates that the C-terminal is crucial for aggregation.
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Affiliation(s)
- Ming Han
- Department of Physics, Michigan Technological University, Houghton, Michigan 49931, USA.
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29
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Chong SH, Ham S. Atomic-level investigations on the amyloid-β dimerization process and its driving forces in water. Phys Chem Chem Phys 2012; 14:1573-5. [DOI: 10.1039/c2cp23326f] [Citation(s) in RCA: 36] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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30
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Lockhart C, Kim S, Kumar R, Klimov DK. Does amino acid sequence determine the properties of Aβ dimer? J Chem Phys 2011; 135:035103. [PMID: 21787025 DOI: 10.1063/1.3610427] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The effect of random reshuffling of amino acids on the properties of dimers formed by Aβ peptides is studied using replica exchange molecular dynamics and united atom implicit solvent model. We show that thermodynamics of dimer assembly and the dimer globule-like state are not affected by sequence permutation. Furthermore, sequence reshuffling does not change the distributions of non-local interactions and, to a large extent, amino acids in the dimer volume. To rationalize these results, we demonstrate that Gaussian statistics applies surprisingly well to the end-to-end distances of the peptides in the dimer implying that non-bonded interactions between distant along the chain amino acids are effectively screened. This observation suggests that peptides in the dimer behave as ideal chains in polymer melt, in which amino acids lose their "identity" and therefore the memory of sequence position. As a result large-scale properties of the dimer become universal or sequence independent. Comparison of our simulations with the prior theoretical studies and their implications for experiments are discussed.
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Affiliation(s)
- Christopher Lockhart
- School of Systems Biology, George Mason University, Manassas, Virginia 20110, USA
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31
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Kim S, Chang WE, Kumar R, Klimov DK. Naproxen interferes with the assembly of Aβ oligomers implicated in Alzheimer's disease. Biophys J 2011; 100:2024-32. [PMID: 21504739 DOI: 10.1016/j.bpj.2011.02.044] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/22/2010] [Revised: 02/15/2011] [Accepted: 02/24/2011] [Indexed: 12/23/2022] Open
Abstract
Experimental and epidemiological studies have shown that the nonsteroidal antiinflammatory drug naproxen may be useful in the treatment of Alzheimer's disease. To investigate the interactions of naproxen with Aβ dimers, which are the smallest cytotoxic aggregated Aβ peptide species, we use united atom implicit solvent model and exhaustive replica exchange molecular dynamics. We show that naproxen ligands bind to Aβ dimer and penetrate its volume interfering with the interpeptide interactions. As a result naproxen induces a destabilizing effect on Aβ dimer. By comparing the free-energy landscapes of naproxen interactions with Aβ dimers and fibrils, we conclude that this ligand has stronger antiaggregation potential against Aβ fibrils rather than against dimers. The analysis of naproxen binding energetics shows that the location of ligand binding sites in Aβ dimer is dictated by the Aβ amino acid sequence. Comparison of the in silico findings with experimental observations reveals potential limitations of naproxen as an effective therapeutic agent in the treatment of Alzheimer's disease.
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Affiliation(s)
- Seongwon Kim
- School of Systems Biology, George Mason University, Manassas, Virginia, USA
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32
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Computational insights into the development of novel therapeutic strategies for Alzheimer's disease. Future Med Chem 2011; 1:119-35. [PMID: 21426072 DOI: 10.4155/fmc.09.10] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022] Open
Abstract
BACKGROUND β-amyloidosis and oxidative stress have been implicated as root causes of Alzheimer's disease (AD). Current potential therapeutic strategies for the treatment of AD include inhibition of amyloid β (Aβ) production, stimulation of Aβ degradation and prevention of Aβ oligomerization. However, efforts in this direction are hindered by the lack of understanding of the biochemical processes occurring at the atomic level in AD. DISCUSSION A radically different approach to achieve this goal would be the application of comprehensive theoretical and computational techniques such as molecular dynamics, quantum mechanics, hybrid quantum mechanics/molecular mechanics, bioinformatics and rotational spectroscopy to investigate complex chemical and physical processes in β-amyloidosis and the oxidative stress mechanism. CONCLUSION Results obtained from these studies will provide an atomic level understanding of biochemical processes occurring in AD and advance efforts to develop effective therapeutic strategies for this disease.
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33
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Côté S, Derreumaux P, Mousseau N. Distinct Morphologies for Amyloid Beta Protein Monomer: Aβ1–40, Aβ1–42, and Aβ1–40(D23N). J Chem Theory Comput 2011; 7:2584-92. [DOI: 10.1021/ct1006967] [Citation(s) in RCA: 73] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/04/2023]
Affiliation(s)
- Sébastien Côté
- Département de Physique and Groupe de Recherche Sur Les Protéines Membranaires (GEPROM), Université de Montréal, C.P. 6128, succursale Centre-ville, Montréal (Québec), Canada
| | - Philippe Derreumaux
- Laboratoire de Biochimie Théorique, UPR 9080 CNRS, Institut de Biologie Physico Chimique, Institut Universitaire de France, Université Paris Diderot - Paris 7, 13 rue Pierre et Marie Curie, 75005 Paris, France
| | - Normand Mousseau
- Département de Physique and Groupe de Recherche Sur Les Protéines Membranaires (GEPROM), Université de Montréal, C.P. 6128, succursale Centre-ville, Montréal (Québec), Canada
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34
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Mitternacht S, Staneva I, Härd T, Irbäck A. Monte Carlo study of the formation and conformational properties of dimers of Aβ42 variants. J Mol Biol 2011; 410:357-67. [PMID: 21616081 DOI: 10.1016/j.jmb.2011.05.014] [Citation(s) in RCA: 46] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/19/2011] [Revised: 04/25/2011] [Accepted: 05/08/2011] [Indexed: 11/17/2022]
Abstract
Small soluble oligomers, and dimers in particular, of the amyloid β-peptide (Aβ) are believed to play an important pathological role in Alzheimer's disease. Here, we investigate the spontaneous dimerization of Aβ42, with 42 residues, by implicit solvent all-atom Monte Carlo simulations, for the wild-type peptide and the mutants F20E, E22G and E22G/I31E. The observed dimers of these variants share many overall conformational characteristics but differ in several aspects at a detailed level. In all four cases, the most common type of secondary structure is intramolecular antiparallel β-sheets. Parallel, in-register β-sheet structure, as in models for Aβ fibrils, is rare. The primary force driving the formation of dimers is hydrophobic attraction. The conformational differences that we do see involve turns centered in the 20-30 region. The probability of finding turns centered in the 25-30 region, where there is a loop in Aβ fibrils, is found to increase upon dimerization and to correlate with experimentally measured rates of fibril formation for the different Aβ42 variants. Our findings hint at reorganization of this part of the molecule as a potentially critical step in Aβ aggregation.
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Affiliation(s)
- Simon Mitternacht
- Computational Biology and Biological Physics, Lund University, Sölvegatan 14A, SE-223 62 Lund, Sweden
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35
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Anand P, Hansmann UHE. Internal and environmental effects on folding and dimerization of the Alzheimer's β amyloid peptide. MOLECULAR SIMULATION 2011; 37:10.1080/08927022.2011.551879. [PMID: 24353373 PMCID: PMC3864693 DOI: 10.1080/08927022.2011.551879] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/11/2023]
Abstract
Amyloid deposits are a hallmark of many diseases. In the case of Alzheimer's disease a turn between 21Ala and 30Ala, stabilized by a salt bridge between 22Glu/23Asp and 28Lys, may nucleate folding and aggregation of the Aβ peptide. In the present paper we test this hypothesis by studying how salt bridge and turn formation vary with intrinsic and environmental changes, and how these changes effect folding and aggregation of the Aβ peptide.
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Affiliation(s)
- Priya Anand
- Department of Physics, Michigan Technological University, Houghton, MI 49931, USA
| | - Ulrich H E Hansmann
- Department of Physics, Michigan Technological University, Houghton, MI 49931, USA
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36
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Velez-Vega C, Escobedo FA. Characterizing the structural behavior of selected Aβ-42 monomers with different solubilities. J Phys Chem B 2011; 115:4900-10. [PMID: 21486050 DOI: 10.1021/jp1086575] [Citation(s) in RCA: 43] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
Abstract
The conformational behavior of the wild-type amyloid β-42 (Aβ-42) monomer and two of its mutants was explored via all-atom replica exchange molecular dynamics simulations in explicit solvent, to identify structural features that may promote or deter early-stage oligomerization. The markers used for this purpose indicate that while the three peptides are relatively flexible they have distinct preferential structures and degree of rigidity. In particular, we found that one mutant that remains in the monomeric state in experiments displays a characteristic N-terminal structure that significantly enhances its rigidity. This finding is consistent with various studies that have detected a reduction in oligomerization frequency and Aβ-related toxicity upon sequence-specific antibody or ligand binding to the N-terminal tail of wild-type monomers, likely leading to the stabilization of this region. In general, our results highlight a potential role of the N-terminal segment on Aβ oligomerization and give insights into specific interactions that may be responsible for promoting the pronounced structural changes observed upon introducing point mutations on the wild-type Aβ-42 peptide.
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Affiliation(s)
- Camilo Velez-Vega
- School of Chemical and Biomolecular Engineering, Cornell University, Ithaca, New York 14853, USA
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37
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Takeda T, Chang WE, Raman EP, Klimov DK. Binding of nonsteroidal anti-inflammatory drugs to Abeta fibril. Proteins 2011; 78:2849-60. [PMID: 20635343 DOI: 10.1002/prot.22804] [Citation(s) in RCA: 29] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
Abstract
Nonsteroidal anti-inflammatory drugs are considered as potential therapeutic agents against Alzheimer's disease. Using replica exchange molecular dynamics and atomistic implicit solvent model, we studied the mechanisms of binding of naproxen and ibuprofen to the Abeta fibril derived from solid-state NMR measurements. The binding temperature of naproxen is found to be almost 40 K higher than of ibuprofen implicating higher binding affinity of naproxen. The key factor, which enhances naproxen binding, is strong interactions between ligands bound to the surface of the fibril. The naphthalene ring in naproxen appears to provide a dominant contribution to ligand-ligand interactions. In contrast, ligand-fibril interactions cannot explain differences in the binding affinities of naproxen and ibuprofen. The concave fibril edge with the groove is identified as the primary binding location for both ligands. We show that confinement of the ligands to the groove facilitates ligand-ligand interactions that lowers the energy of the ligands bound to the concave edge compared with those bound to the convex edge. Our simulations appear to provide microscopic rationale for the differing binding affinities of naproxen and ibuprofen observed experimentally.
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Affiliation(s)
- Takako Takeda
- Department of Bioinformatics and Computational Biology, George Mason University, Manassas, Virginia 20110, USA
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38
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Gee J, Shell MS. Two-dimensional replica exchange approach for peptide–peptide interactions. J Chem Phys 2011; 134:064112. [DOI: 10.1063/1.3551576] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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39
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Kim S, Takeda T, Klimov DK. Mapping conformational ensembles of aβ oligomers in molecular dynamics simulations. Biophys J 2011; 99:1949-58. [PMID: 20858441 DOI: 10.1016/j.bpj.2010.07.008] [Citation(s) in RCA: 39] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/17/2010] [Revised: 06/27/2010] [Accepted: 07/07/2010] [Indexed: 11/30/2022] Open
Abstract
Although the oligomers formed by Aβ peptides appear to be the primary cytotoxic species in Alzheimer's disease, detailed information about their structures appears to be lacking. In this article, we use exhaustive replica exchange molecular dynamics and an implicit solvent united-atom model to study the structural properties of Aβ monomers, dimers, and tetramers. Our analysis suggests that the conformational ensembles of Aβ dimers and tetramers are very similar, but sharply distinct from those sampled by the monomers. The key conformational difference between monomers and oligomers is the formation of β-structure in the oligomers occurring together with the loss of intrapeptide interactions and helix structure. Our simulations indicate that, independent of oligomer order, the Aβ aggregation interface is largely confined to the sequence region 10-23, which forms the bulk of interpeptide interactions. We show that the fractions of β structure computed in our simulations and measured experimentally are in good agreement.
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Affiliation(s)
- Seongwon Kim
- Department of Bioinformatics and Computational Biology, George Mason University, Manassas, Virginia, USA
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40
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Takeda T, Kumar R, Raman EP, Klimov DK. Nonsteroidal anti-inflammatory drug naproxen destabilizes Aβ amyloid fibrils: a molecular dynamics investigation. J Phys Chem B 2010; 114:15394-402. [PMID: 20979356 PMCID: PMC3034367 DOI: 10.1021/jp107955v] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022]
Abstract
Using implicit solvent model and replica exchange molecular dynamics, we examine the propensity of a nonsteroidal anti-inflammatory drug, naproxen, to interfere with Aβ fibril growth. We also compare the antiaggregation propensity of naproxen with that of ibuprofen. Naproxen's antiaggregation effect is influenced by two factors. Similar to ibuprofen, naproxen destabilizes binding of incoming Aβ peptides to the fibril due to direct competition between the ligands and the peptides for the same binding location on the fibril surface (the edge). However, in contrast to ibuprofen, naproxen binding also alters the conformational ensemble of Aβ monomers by promoting β-structure. The second factor weakens naproxen's antiaggregation effect. These findings appear to explain the experimental observations, in which naproxen binds to the Aβ fibril with higher affinity than ibuprofen, yet produces weaker antiaggregation action.
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Affiliation(s)
- Takako Takeda
- Department of Bioinformatics and Computational Biology, George Mason University, Manassas, VA 20110
| | - Rashmi Kumar
- Department of Bioinformatics and Computational Biology, George Mason University, Manassas, VA 20110
| | - E. Prabhu Raman
- Department of Pharmaceutical Sciences, School of Pharmacy, University of Maryland, Baltimore, Maryland 21201
| | - Dmitri K. Klimov
- Department of Bioinformatics and Computational Biology, George Mason University, Manassas, VA 20110
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41
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Davis CH, Berkowitz ML. A molecular dynamics study of the early stages of amyloid-beta(1-42) oligomerization: the role of lipid membranes. Proteins 2010; 78:2533-45. [PMID: 20602359 DOI: 10.1002/prot.22763] [Citation(s) in RCA: 51] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/10/2023]
Abstract
As research progresses toward understanding the role of the amyloid-beta (Abeta) peptide in Alzheimer's disease, certain aspects of the aggregation process for Abeta are still not clear. In particular, the accepted constitution of toxic aggregates in neurons has shifted toward small oligomers. However, the process of forming these oligomers in cells is also not full clear. Even more interestingly, it has been implied that cell membranes, and, in particular, anionic lipids within those membranes, play a key role in the progression of Abeta aggregation, but the exact nature of the Abeta-membrane interaction in this process is unknown. In this work, we use a thermodynamic cycle and umbrella sampling molecular dynamics to investigate dimerization of the 42-residue Abeta peptide on model zwitterionic dipalmitoylphosphatidylcholine (DPPC) or model anionic dioleoylphosphatidylserine (DOPS) bilayer surfaces. We determined that Abeta dimerization was strongly favored through interactions with the DOPS bilayer. Further, our calculations showed that the DOPS bilayer promoted strong protein-protein interactions within the Abeta dimer, whereas DPPC favored strong protein-lipid interactions. By promoting dimer formation and subsequent dimer release into the solvent, the DOPS bilayer acts as a catalyst in Abeta aggregation.
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Affiliation(s)
- Charles H Davis
- Department of Biochemistry and Biophysics, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599, USA
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42
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Lin EI, Shell MS. Can Peptide Folding Simulations Provide Predictive Information for Aggregation Propensity? J Phys Chem B 2010; 114:11899-908. [DOI: 10.1021/jp104114n] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Edmund I. Lin
- Department of Chemical Engineering, University of California Santa Barbara, Santa Barbara, California 93106-5080
| | - M. Scott Shell
- Department of Chemical Engineering, University of California Santa Barbara, Santa Barbara, California 93106-5080
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Kim S, Takeda T, Klimov DK. Globular state in the oligomers formed by Abeta peptides. J Chem Phys 2010; 132:225101. [PMID: 20550420 PMCID: PMC2896418 DOI: 10.1063/1.3447894] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/19/2010] [Accepted: 05/14/2010] [Indexed: 01/04/2023] Open
Abstract
Replica exchange molecular dynamics and implicit solvent model are used to study two oligomeric species of Abeta peptides, dimer and tetramer, which are typically observed in in vitro experiments. Based on the analysis of free energy landscapes, density distributions, and chain flexibility, we propose that the oligomer formation is a continuous transition occurring without metastable states. The density distribution computations suggest that Abeta oligomer consists of two volume regions-the core with fairly flat density profile and the surface layer with rapidly decreasing density. The core is mostly formed by the N-terminal residues, whereas the C-terminal tends to occur in the surface layer. Lowering the temperature results in the redistribution of peptide atoms from the surface layer into the core. Using these findings, we argue that Abeta oligomer resembles polymer globule in poor solvent. Abeta dimers and tetramers are found to be structurally similar suggesting that the conformations of Abeta peptides do not depend on the order of small oligomers.
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Affiliation(s)
- Seongwon Kim
- Department of Bioinformatics and Computational Biology, George Mason University, Manassas, Virginia 20110, USA
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Berhanu WM, Masunov AE. Natural polyphenols as inhibitors of amyloid aggregation. Molecular dynamics study of GNNQQNY heptapeptide decamer. Biophys Chem 2010; 149:12-21. [DOI: 10.1016/j.bpc.2010.03.003] [Citation(s) in RCA: 33] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/23/2009] [Revised: 02/25/2010] [Accepted: 03/04/2010] [Indexed: 10/19/2022]
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