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Li Y, Yang L, Yang LQ. Effects of intrinsically disordered regions in gp120 underlying HIV neutralization phenotypes. Biochem Biophys Res Commun 2024; 709:149830. [PMID: 38547606 DOI: 10.1016/j.bbrc.2024.149830] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/30/2024] [Revised: 03/18/2024] [Accepted: 03/24/2024] [Indexed: 04/13/2024]
Abstract
HIV envelope protein gp120 is considered a primary molecular determinant of viral neutralization phenotype due to its critical role in viral entry and immune evasion. The intrinsically disordered regions (IDRs) in gp120 are responsible for their extensive sequence variations and significant structural rearrangements. Despite HIV neutralization phenotype and sequence/structural information of gp120 have been experimentally characterized, there remains a gap in our understanding of the correlation between the viral phenotype and IDRs in gp120. Here, we combined machine learning (ML) techniques and molecular dynamics (MD) simulations to gain data-driven and molecule-mechanism insights into relationships between viral sequence, structure, and phenotypes from the perspective of IDRs in gp120. ML models, trained only on the length and disorder score of IDRs, achieved equivalent performance to the best baseline model using amino acid sequences to discriminate HIV neutralization phenotype, indicating that the lengths or disorder of specific IDRs are strongly related to HIV neutralization phenotypes. Comparative MD analysis reveals that gp120 with extreme neutralization phenotypes in multiple conformational states, especially some IDRs, exhibit significantly distinct structural dynamics, conformational flexibility, and thermodynamic distributions. Taken together, our study provided insights into the role of IDRs in gp120 responding to HIV neutralization phenotypes, which will advance the understanding of molecular mechanisms underlying viral function associated with HIV neutralization phenotype and help develop antiviral vaccines or drugs.
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Affiliation(s)
- Yi Li
- College of Mathematics and Computer Science, Dali University, Dali, China
| | - Li Yang
- College of Mathematics and Computer Science, Dali University, Dali, China
| | - Li-Quan Yang
- College of Agriculture and Biological Science, Dali University, Dali, China; Key Laboratory of Bioinformatics and Computational Biology, Department of Education of Yunnan Province, Dali University, Dali, China.
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2
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Li Y, Peng HQ, Yang LQ. Structural determinants underlying high-temperature adaptation of thermophilic xylanase from hot-spring microorganisms. Front Microbiol 2023; 14:1210420. [PMID: 37485531 PMCID: PMC10360402 DOI: 10.3389/fmicb.2023.1210420] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/22/2023] [Accepted: 06/21/2023] [Indexed: 07/25/2023] Open
Abstract
Thermophilic xylanases from hot-spring microorganisms play potential biological and industrial applications for renewable and sustainable social development. However, high-temperature adaptation mechanisms of these thermophilic xylanases remain elusive at the molecular and evolutionary levels. Here, two recently reported xylanases, named XynDRTY1 and XynM1, from hot springs were subjected to molecular dynamics (MD) simulations at a series of temperature gradients and comparatively analyzed in comparison with the evolutionary background of the xylanase family. Comparative analysis of MD trajectories revealed that the XynM1 exhibits smaller structural dynamics and greater thermal stability than the XynDRTY1, although both share a similar fold architecture with structural differences in the βα_loops. Local regions whose conformational flexibility and regular secondary structure exhibited differences as temperature increases were closely related to the high-temperature adaptation of xylanase, implying that stabilization of these regions is a feasible strategy to improve the thermal stability of xylanases. Furthermore, coevolutionary information from the xylanase family further specified the structural basis of xylanases. Thanks to these results about the sequence, structure, and dynamics of thermophilic xylanases from hot springs, a series of high-temperature-related structural determinants were resolved to promote understanding of the molecular mechanism of xylanase high-temperature adaptation and to provide direct assistance in the improvement of xylanase thermal stability.
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Affiliation(s)
- Yi Li
- College of Mathematics and Computer Science, Dali University, Dali, China
- College of Agriculture and Biological Science, Dali University, Dali, China
- Key Laboratory of Bioinformatics and Computational Biology, Department of Education of Yunnan Province, Dali University, Dali, China
- State Key Laboratory for Conservation and Utilization of Bio-Resource in Yunnan, Yunnan University, Kunming, China
| | - Hong-Qian Peng
- College of Mathematics and Computer Science, Dali University, Dali, China
| | - Li-Quan Yang
- College of Agriculture and Biological Science, Dali University, Dali, China
- Key Laboratory of Bioinformatics and Computational Biology, Department of Education of Yunnan Province, Dali University, Dali, China
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3
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Liu MT, Shen JX, Li XW, Yang L, Li Y, Sang P, Yang LQ. Study on molecular mechanisms of CD4 dependency and independency of HIV-1 gp120. RSC Adv 2023; 13:6274-6286. [PMID: 36825290 PMCID: PMC9942563 DOI: 10.1039/d3ra00433c] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/20/2023] [Accepted: 02/16/2023] [Indexed: 02/25/2023] Open
Abstract
Different HIV-1 strains have different antibody neutralization phenotypes (or CD4-dependencies). However, the molecular mechanisms underlying these differences remain to be elucidated. In this study, we constructed gp120 structural models from the CD4-dependent, neutralization-resistant JR-FL strain and the CD4-independent, neutralization-sensitive R2 strain and carried out several conventional molecular dynamics (MD) simulations and free energy landscape (FEL) constructions. Comparative analyses of the MD simulations and FELs indicated that R2 gp120 had higher global structural flexibility and greater conformational diversity than JR-FL gp120. This provides the preconditions for R2 gp120 to adopt a more open conformation than JR-FL gp120. Essential dynamics (ED) analysis showed that the collective motions of R2 gp120 tend towards an open state while those of JR-FL gp120 tend to retain a closed state. Based on conformational selection theory, R2 gp120's more readily sampled open state makes it more sensitive to neutralizing antibodies (or more CD4-independent) than JR-FL gp120, which may explain why the HIV-1 R2 and JR-FL strains show CD4-independent and -dependent phenotypes, respectively. Our study provides thermodynamic and kinetic insights into the CD4-dependent and -independent molecular mechanisms of HIV-1 gp120 and helps shed light on HIV-1 immune evasion.
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Affiliation(s)
- Meng-Ting Liu
- College of Agriculture and Biological Science, Dali University Dali 671000 China .,Key Laboratory of Bioinformatics and Computational Biology of the Department of Education of Yunnan Province, Dali University Dali 671000 China
| | - Jian-Xin Shen
- State Key Laboratory for Conservation and Utilization of Bio-Resources in Yunnan, School of Life Sciences, Yunnan UniversityKunmingChina
| | - Xin-Wei Li
- College of Agriculture and Biological Science, Dali University Dali 671000 China .,Key Laboratory of Bioinformatics and Computational Biology of the Department of Education of Yunnan Province, Dali University Dali 671000 China
| | - Li Yang
- College of Mathematics and Computer Science, Dali UniversityDali 671000China
| | - Yi Li
- College of Mathematics and Computer Science, Dali UniversityDali 671000China
| | - Peng Sang
- College of Agriculture and Biological Science, Dali University Dali 671000 China .,Key Laboratory of Bioinformatics and Computational Biology of the Department of Education of Yunnan Province, Dali University Dali 671000 China.,Yunnan Key Laboratory of Screening and Research on Anti-pathogenic Plant Resources from West Yunnan, Dali University Dali 671000 China
| | - Li-Quan Yang
- College of Agriculture and Biological Science, Dali University Dali 671000 China .,Key Laboratory of Bioinformatics and Computational Biology of the Department of Education of Yunnan Province, Dali University Dali 671000 China.,Yunnan Key Laboratory of Screening and Research on Anti-pathogenic Plant Resources from West Yunnan, Dali University Dali 671000 China
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4
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Li Y, Guo Y, Cheng H, Zeng X, Zhang X, Sang P, Chen B, Yang L. Deciphering gp120 sequence variation and structural dynamics in
HIV
neutralization phenotype by molecular dynamics simulations and graph machine learning. Proteins 2022; 90:1413-1424. [DOI: 10.1002/prot.26322] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/03/2021] [Revised: 01/21/2022] [Accepted: 02/10/2022] [Indexed: 02/04/2023]
Affiliation(s)
- Yi Li
- College of Mathematics and Computer Science Dali University Dali Yunnan China
| | - Yu‐Chen Guo
- College of Mathematics and Computer Science Dali University Dali Yunnan China
| | - Hong‐Han Cheng
- College of Mathematics and Computer Science Dali University Dali Yunnan China
| | - Xin Zeng
- College of Mathematics and Computer Science Dali University Dali Yunnan China
| | - Xiao‐Ling Zhang
- College of Mathematics and Computer Science Dali University Dali Yunnan China
| | - Peng Sang
- College of Agriculture and Biological Science Dali University Dali Yunnan China
| | - Ben‐Hui Chen
- College of Mathematics and Computer Science Dali University Dali Yunnan China
| | - Li‐Quan Yang
- College of Agriculture and Biological Science Dali University Dali Yunnan China
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Mechanistic Origin of Different Binding Affinities of SARS-CoV and SARS-CoV-2 Spike RBDs to Human ACE2. Cells 2022; 11:cells11081274. [PMID: 35455955 PMCID: PMC9032924 DOI: 10.3390/cells11081274] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/05/2022] [Revised: 04/03/2022] [Accepted: 04/06/2022] [Indexed: 12/04/2022] Open
Abstract
The receptor-binding domain (RBD) of the SARS-CoV-2 spike protein (RBDCoV2) has a higher binding affinity to the human receptor angiotensin-converting enzyme 2 (ACE2) than the SARS-CoV RBD (RBDCoV). Here, we performed molecular dynamics (MD) simulations, binding free energy (BFE) calculations, and interface residue contact network (IRCN) analysis to explore the mechanistic origin of different ACE2-binding affinities of the two RBDs. The results demonstrate that, when compared to the RBDCoV2-ACE2 complex, RBDCoV-ACE2 features enhanced dynamicsand inter-protein positional movements and increased conformational entropy and conformational diversity. Although the inter-protein electrostatic attractive interactions are the primary determinant for the high ACE2-binding affinities of both RBDs, the significantly enhanced electrostatic attractive interactions between ACE2 and RBDCoV2 determine the higher ACE2-binding affinity of RBDCoV2 than of RBDCoV. Comprehensive comparative analyses of the residue BFE components and IRCNs between the two complexes reveal that it is the residue changes at the RBD interface that lead to the overall stronger inter-protein electrostatic attractive force in RBDCoV2-ACE2, which not only tightens the interface packing and suppresses the dynamics of RBDCoV2-ACE2, but also enhances the ACE2-binding affinity of RBDCoV2. Since the RBD residue changes involving gain/loss of the positively/negatively charged residues can greatly enhance the binding affinity, special attention should be paid to the SARS-CoV-2 variants carrying such mutations, particularly those near or at the binding interfaces with the potential to form hydrogen bonds and/or salt bridges with ACE2.
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Bennett AL, Henderson R. HIV-1 Envelope Conformation, Allostery, and Dynamics. Viruses 2021; 13:852. [PMID: 34067073 PMCID: PMC8150877 DOI: 10.3390/v13050852] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/07/2021] [Revised: 04/28/2021] [Accepted: 05/04/2021] [Indexed: 11/16/2022] Open
Abstract
The HIV-1 envelope glycoprotein (Env) mediates host cell fusion and is the primary target for HIV-1 vaccine design. The Env undergoes a series of functionally important conformational rearrangements upon engagement of its host cell receptor, CD4. As the sole target for broadly neutralizing antibodies, our understanding of these transitions plays a critical role in vaccine immunogen design. Here, we review available experimental data interrogating the HIV-1 Env conformation and detail computational efforts aimed at delineating the series of conformational changes connecting these rearrangements. These studies have provided a structural mapping of prefusion closed, open, and transition intermediate structures, the allosteric elements controlling rearrangements, and state-to-state transition dynamics. The combination of these investigations and innovations in molecular modeling set the stage for advanced studies examining rearrangements at greater spatial and temporal resolution.
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Affiliation(s)
| | - Rory Henderson
- Duke Human Vaccine Institute, Durham, NC 27710, USA;
- Department of Medicine, Duke University, Durham, NC 27710, USA
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Yandrapally S, Mohareer K, Arekuti G, Vadankula GR, Banerjee S. HIV co-receptor-tropism: cellular and molecular events behind the enigmatic co-receptor switching. Crit Rev Microbiol 2021; 47:499-516. [PMID: 33900141 DOI: 10.1080/1040841x.2021.1902941] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022]
Abstract
Recognition of cell-surface receptors and co-receptors is a crucial molecular event towards the establishment of HIV infection. HIV exists as several variants that differentially recognize the principal co-receptors, CCR5 and CXCR4, in different cell types, known as HIV co-receptor-tropism. The relative levels of these variants dynamically adjust to the changing host selection pressures to infect a vast repertoire of cells in a stage-specific manner. HIV infection sets in through immune cells such as dendritic cells, macrophages, and T-lymphocytes in the acute stage, while a wide range of other cells, including astrocytes, glial cells, B-lymphocytes, and epithelial cells, are infected during chronic stages. A change in tropism occurs during the transition from acute to a chronic phase, termed as co-receptor switching marked by a change in disease severity. The cellular and molecular events leading to co-receptor switching are poorly understood. This review aims to collate our present understanding of the dynamics of HIV co-receptor-tropism vis-à-vis host and viral factors, highlighting the cellular and molecular events involved therein. We present the possible correlations between virus entry, cell tropism, and co-receptor switching, speculating its consequences on disease progression, and proposing new scientific pursuits to help in an in-depth understanding of HIV biology.
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Affiliation(s)
| | | | - Geethika Arekuti
- Department of Biochemistry, University of Hyderabad, Hyderabad, India
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Zhang ZB, Xia YL, Dong GH, Fu YX, Liu SQ. Exploring the Cold-Adaptation Mechanism of Serine Hydroxymethyltransferase by Comparative Molecular Dynamics Simulations. Int J Mol Sci 2021; 22:1781. [PMID: 33670090 PMCID: PMC7916883 DOI: 10.3390/ijms22041781] [Citation(s) in RCA: 2] [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: 01/24/2021] [Revised: 02/08/2021] [Accepted: 02/08/2021] [Indexed: 12/20/2022] Open
Abstract
Cold-adapted enzymes feature a lower thermostability and higher catalytic activity compared to their warm-active homologues, which are considered as a consequence of increased flexibility of their molecular structures. The complexity of the (thermo)stability-flexibility-activity relationship makes it difficult to define the strategies and formulate a general theory for enzyme cold adaptation. Here, the psychrophilic serine hydroxymethyltransferase (pSHMT) from Psychromonas ingrahamii and its mesophilic counterpart, mSHMT from Escherichia coli, were subjected to μs-scale multiple-replica molecular dynamics (MD) simulations to explore the cold-adaptation mechanism of the dimeric SHMT. The comparative analyses of MD trajectories reveal that pSHMT exhibits larger structural fluctuations and inter-monomer positional movements, a higher global flexibility, and considerably enhanced local flexibility involving the surface loops and active sites. The largest-amplitude motion mode of pSHMT describes the trends of inter-monomer dissociation and enlargement of the active-site cavity, whereas that of mSHMT characterizes the opposite trends. Based on the comparison of the calculated structural parameters and constructed free energy landscapes (FELs) between the two enzymes, we discuss in-depth the physicochemical principles underlying the stability-flexibility-activity relationships and conclude that (i) pSHMT adopts the global-flexibility mechanism to adapt to the cold environment and, (ii) optimizing the protein-solvent interactions and loosening the inter-monomer association are the main strategies for pSHMT to enhance its flexibility.
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Affiliation(s)
- Zhi-Bi Zhang
- State Key Laboratory for Conservation and Utilization of Bio-Resources in Yunnan & School of Life Sciences, Yunnan University, Kunming 650091, China; (Z.-B.Z.); (Y.-L.X.); (G.-H.D.)
- Yunnan Key Laboratory of Stem Cell and Regenerative Medicine & Biomedical Engineering Research Center, Kunming Medical University, Kunming 650500, China
| | - Yuan-Ling Xia
- State Key Laboratory for Conservation and Utilization of Bio-Resources in Yunnan & School of Life Sciences, Yunnan University, Kunming 650091, China; (Z.-B.Z.); (Y.-L.X.); (G.-H.D.)
| | - Guang-Heng Dong
- State Key Laboratory for Conservation and Utilization of Bio-Resources in Yunnan & School of Life Sciences, Yunnan University, Kunming 650091, China; (Z.-B.Z.); (Y.-L.X.); (G.-H.D.)
| | - Yun-Xin Fu
- State Key Laboratory for Conservation and Utilization of Bio-Resources in Yunnan & School of Life Sciences, Yunnan University, Kunming 650091, China; (Z.-B.Z.); (Y.-L.X.); (G.-H.D.)
- Human Genetics Center and Division of Biostatistics, School of Public Health, The University of Texas Health Science Center, Houston, TX 77030, USA
| | - Shu-Qun Liu
- State Key Laboratory for Conservation and Utilization of Bio-Resources in Yunnan & School of Life Sciences, Yunnan University, Kunming 650091, China; (Z.-B.Z.); (Y.-L.X.); (G.-H.D.)
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Bruxelle JF, Trattnig N, Mureithi MW, Landais E, Pantophlet R. HIV-1 Entry and Prospects for Protecting against Infection. Microorganisms 2021; 9:microorganisms9020228. [PMID: 33499233 PMCID: PMC7911371 DOI: 10.3390/microorganisms9020228] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/23/2020] [Revised: 01/19/2021] [Accepted: 01/20/2021] [Indexed: 12/19/2022] Open
Abstract
Human Immunodeficiency Virus type-1 (HIV-1) establishes a latent viral reservoir soon after infection, which poses a major challenge for drug treatment and curative strategies. Many efforts are therefore focused on blocking infection. To this end, both viral and host factors relevant to the onset of infection need to be considered. Given that HIV-1 is most often transmitted mucosally, strategies designed to protect against infection need to be effective at mucosal portals of entry. These strategies need to contend also with cell-free and cell-associated transmitted/founder (T/F) virus forms; both can initiate and establish infection. This review will discuss how insight from the current model of HIV-1 mucosal transmission and cell entry has highlighted challenges in developing effective strategies to prevent infection. First, we examine key viral and host factors that play a role in transmission and infection. We then discuss preventive strategies based on antibody-mediated protection, with emphasis on targeting T/F viruses and mucosal immunity. Lastly, we review treatment strategies targeting viral entry, with focus on the most clinically advanced entry inhibitors.
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Affiliation(s)
- Jean-François Bruxelle
- Faculty of Health Sciences, Simon Fraser University, Burnaby, BC V5A 1S6, Canada
- Correspondence: (J.-F.B.); (R.P.)
| | - Nino Trattnig
- Chemical Biology and Drug Discovery, Utrecht University, 3584 CG Utrecht, The Netherlands;
| | - Marianne W. Mureithi
- KAVI—Institute of Clinical Research, College of Health Sciences, University of Nairobi, P.O. Box, Nairobi 19676–00202, Kenya;
| | - Elise Landais
- IAVI Neutralizing Antibody Center, La Jolla, CA 92037, USA;
- Department of Immunology and Microbiology, Scripps Research, La Jolla, CA 92037, USA
| | - Ralph Pantophlet
- Faculty of Health Sciences, Simon Fraser University, Burnaby, BC V5A 1S6, Canada
- Department of Molecular Biology and Biochemistry, Simon Fraser University, Burnaby, BC V5A 1S6, Canada
- Correspondence: (J.-F.B.); (R.P.)
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Abstract
Molecular dynamics (MD) simulations have become increasingly useful in the modern drug development process. In this review, we give a broad overview of the current application possibilities of MD in drug discovery and pharmaceutical development. Starting from the target validation step of the drug development process, we give several examples of how MD studies can give important insights into the dynamics and function of identified drug targets such as sirtuins, RAS proteins, or intrinsically disordered proteins. The role of MD in antibody design is also reviewed. In the lead discovery and lead optimization phases, MD facilitates the evaluation of the binding energetics and kinetics of the ligand-receptor interactions, therefore guiding the choice of the best candidate molecules for further development. The importance of considering the biological lipid bilayer environment in the MD simulations of membrane proteins is also discussed, using G-protein coupled receptors and ion channels as well as the drug-metabolizing cytochrome P450 enzymes as relevant examples. Lastly, we discuss the emerging role of MD simulations in facilitating the pharmaceutical formulation development of drugs and candidate drugs. Specifically, we look at how MD can be used in studying the crystalline and amorphous solids, the stability of amorphous drug or drug-polymer formulations, and drug solubility. Moreover, since nanoparticle drug formulations are of great interest in the field of drug delivery research, different applications of nano-particle simulations are also briefly summarized using multiple recent studies as examples. In the future, the role of MD simulations in facilitating the drug development process is likely to grow substantially with the increasing computer power and advancements in the development of force fields and enhanced MD methodologies.
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Li Y, Zhang XL, Yuan X, Hou JC, Sang P, Yang LQ. Probing intrinsic dynamics and conformational transition of HIV gp120 by molecular dynamics simulation. RSC Adv 2020; 10:30499-30507. [PMID: 35516019 PMCID: PMC9056330 DOI: 10.1039/d0ra06416e] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/23/2020] [Revised: 10/07/2020] [Accepted: 08/04/2020] [Indexed: 11/21/2022] Open
Abstract
The HIV envelope glycoprotein gp120 has evolved two distinct conformational states to balance viral infection and immune escape. One is a closed state resistant to most neutralization antibodies, and the other is an open state responsible for the binding of the receptor and coreceptors. Although the structures of gp120 in these two conformational states have been determined, a detailed molecular mechanism involving intrinsic dynamics and conformational transition is still elusive. In this study, μs-scale molecular dynamics simulation is performed to probe molecular dynamics and conformational transition away from the open state and approach the closed state. Our results reveal that open gp120 shows a larger structural deviation, higher conformational flexibility, and more conformational diversity than the form in the closed state, providing a structural explanation for receptor or coreceptor affinity at the open state and the neutralization resistance of closed conformation. Seven regions with greatly decreased coupled motions in the open states have been observed by dynamic cross-correlation analysis, indicating that conformational transition can be mainly attributed to the relaxation of intrinsic dynamics. Three conformations characterized by the structural orientations of the V1/V2 region and the V3 loop, suggesting gp120 is intrinsically dynamic from the open state to the closed state. Taken together, these findings shed light on the understanding of the conformational control mechanism of HIV. The HIV envelope glycoprotein gp120 has evolved two distinct conformational states to balance viral infection and immune escape.![]()
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Affiliation(s)
- Yi Li
- College of Mathematics and Computer Science
- Dali University
- Dali
- China
- Science and Education Department
| | - Xiao-Ling Zhang
- College of Mathematics and Computer Science
- Dali University
- Dali
- China
| | - Xue Yuan
- College of Mathematics and Computer Science
- Dali University
- Dali
- China
| | - Jiang-Chun Hou
- Science and Education Department
- Second People's Hospital of Yunnan Province
- Kunming
- China
| | - Peng Sang
- College of Agriculture and Biological Science
- Dali University
- Dali
- China
| | - Li-Quan Yang
- College of Agriculture and Biological Science
- Dali University
- Dali
- China
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