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Rapid Communication

Molecular dynamics simulations of the spike trimeric ectodomain of the SARS-CoV-2 Omicron variant: structural relationships with infectivity, evasion to immune system and transmissibility

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Pages 9326-9343 | Received 01 Apr 2022, Accepted 24 Oct 2022, Published online: 08 Nov 2022

References

  • Abraham, M. J., Murtola, T., Schulz, R., Páll, S., Smith, J. C., Hess, B., & Lindahl, E. (2015). GROMACS: High performance molecular simulations through multi-level parallelism from laptops to supercomputers. In SoftwareX, 1–2, 19–25. https://doi.org/10.1016/j.softx.2015.06.001
  • Amadei, A., Linssen, A. B. M., & Berendsen, H. J. C. (1993). Essential dynamics of proteins. Proteins: Structure, Function, and Genetics, 17(4), 412–425. https://doi.org/10.1002/prot.340170408
  • Banoun, H. (2021). Evolution of SARS-CoV-2: Review of mutations, role of the host immune system. Nephron, 145(4), 392–403.
  • Bertoni, M., Kiefer, F., Biasini, M., Bordoli, L., & Schwede, T. (2017). Modeling protein quaternary structure of homo- and hetero-oligomers beyond binary interactions by homology. Scientific Reports, 7(1), 1–15. https://doi.org/10.1038/s41598-017-09654-8
  • Bienert, S., Waterhouse, A., de Beer, T. A. P., Tauriello, G., Studer, G., Bordoli, L., & Schwede, T. (2017). The SWISS-MODEL Repository—new features and functionality. Nucleic Acids Research, 45(D1), D313–D319.
  • Cai, Y., Zhang, J., Xiao, T., Lavine, C. L., Rawson, S., Peng, H., Zhu, H., Anand, K., Tong, P., Gautam, A., Lu, S., Sterling, S. M., Walsh, R. M., Jr., Rits-Volloch, S., Lu, J., Wesemann, D. R., Yang, W., Seaman, M. S., & Chen, B. (2021). Structural basis for enhanced infectivity and immune evasion of SARS-CoV-2 variants. Science, 373(6555), 642–648. https://doi.org/10.1126/science.abi9745[Mismatch
  • Casadevall, A., Henderson, J. P., Joyner, M. J., & Pirofski, L.-A. (2021). SARS-CoV-2 variants and convalescent plasma: Reality, fallacies, and opportunities. Journal of Clinical Investigation, 131(7), 1-3. https://doi.org/10.1172/JCI148832
  • Chan, W.-E., Chuang, C.-K., Yeh, S.-H., Chang, M.-S., & Chen, S. S.-L. (2006). Functional characterization of heptad repeat 1 and 2 mutants of the spike protein of severe acute respiratory syndrome coronavirus. Journal of Virology, 80(7), 3225–3237.
  • Chen, C., Boorla, V. S., Banerjee, D., Chowdhury, R., Cavener, V. S., Nissly, R. H., Gontu, A., Boyle, N. R., Vandegrift, K., Nair, M. S., Kuchipudi, S. V., & Maranas, C. D. (2021). Computational prediction of the effect of amino acid changes on the binding affinity between SARS-CoV-2 spike RBD and human ACE2. Proceedings of the National Academy of Sciences, 118(42), 1-10. https://doi.org/10.1073/pnas.2106480118[Mismatch
  • Chen, J., Wang, R., Wang, M., & Wei, G.-W. (2020). Mutations strengthened SARS-CoV-2 infectivity. Journal of Molecular Biology, 432(19), 5212–5226.
  • GISAID. (2022). Genomic epidemiology of SARS-CoV-2 with subsampling focused globally over the past 6 months. GISAID NextStrain. https://www.gisaid.org/phylodynamics/global/nextstrain/
  • Gobeil, S. M.-C., Henderson, R., Stalls, V., Janowska, K., Huang, X., May, A., Speakman, M., Beaudoin, E., Manne, K., Li, D., Parks, R., Barr, M., Deyton, M., Martin, M., Mansouri, K., Edwards, R. J., Eaton, A., Montefiori, D. C., Sempowski, G. D., … Acharya, P. (2022). Structural diversity of the SARS-CoV-2 Omicron spike. Molecular Cell, 82(11), 2050–2068.e6.
  • Gobeil, S. M.-C., Janowska, K., McDowell, S., Mansouri, K., Parks, R., Manne, K., Stalls, V., Kopp, M. F., Henderson, R., Edwards, R. J., Haynes, B. F., & Acharya, P. (2021). D614G mutation alters SARS-CoV-2 spike conformation and enhances protease cleavage at the S1/S2 junction. Cell Reports, 34(2), 108630. https://doi.org/10.1016/j.celrep.2020.108630
  • Grant, B. J., Rodrigues, A. P. C., ElSawy, K. M., McCammon, J. A., & Caves, L. S. D. (2006). Bio3d: An R package for the comparative analysis of protein structures. Bioinformatics (Oxford, England), 22(21), 2695–2696. https://doi.org/10.1093/bioinformatics/btl461[Mismatch
  • Humphrey, W., Dalke, A., & Schulten, K. (1996). VMD: Visual molecular dynamics. Journal of Molecular Graphics, 14(1), 33–38. https://doi.org/10.1016/0263-7855(96)00018-5[Mismatch
  • Jackson, C. B., Farzan, M., Chen, B., & Choe, H. (2022). Mechanisms of SARS-CoV-2 entry into cells. Nature Reviews. Molecular Cell Biology, 23(1), 3–20. https://doi.org/10.1038/s41580-021-00418-x[Mismatch
  • Khan, A., Gui, J., Ahmad, W., Haq, I., Shahid, M., Khan, A. A., Shah, A., Khan, A., Ali, L., Anwar, Z., Safdar, M., Abubaker, J., Uddin, N. N., Cao, L., Wei, D.-Q., & Mohammad, A. (2021). The SARS-CoV-2 B.1.618 variant slightly alters the spike RBD-ACE2 binding affinity and is an antibody escaping variant: A computational structural perspective. RSC Advances, 11(48), 30132–30147.
  • Khan, A., Waris, H., Rafique, M., Suleman, M., Mohammad, A., Ali, S. S., Khan, T., Waheed, Y., Liao, C., & Wei, D.-Q. (2022). The Omicron (B.1.1.529) variant of SARS-CoV-2 binds to the hACE2 receptor more strongly and escapes the antibody response: Insights from structural and simulation data. International Journal of Biological Macromolecules, 200, 438–448. https://doi.org/10.1016/j.ijbiomac.2022.01.059
  • Ku, Z., Xie, X., Davidson, E., Ye, X., Su, H., Menachery, V. D., Li, Y., Yuan, Z., Zhang, X., Muruato, A. E., I Escuer, A. G., Tyrell, B., Doolan, K., Doranz, B. J., Wrapp, D., Bates, P. F., McLellan, J. S., Weiss, S. R., Zhang, N., Shi, P.-Y., & An, Z. (2021). Author correction: Molecular determinants and mechanism for antibody cocktail preventing SARS-CoV-2 escape. Nature Communications, 12(1), 4177.
  • Lan, J., Ge, J., Yu, J., Shan, S., Zhou, H., Fan, S., Zhang, Q., Shi, X., Wang, Q., Zhang, L., & Wang, X. (2020). Structure of the SARS-CoV-2 spike receptor-binding domain bound to the ACE2 receptor. Nature, 581(7807), 215–220. https://doi.org/10.1038/s41586-020-2180-5
  • Lindahl, E., Hess, B., & van der Spoel, D. (2001). GROMACS 3.0: A package for molecular simulation and trajectory analysis. Journal of Molecular Modeling, 7(8), 306–317. https://doi.org/10.1007/s008940100045[Mismatch
  • Li, Q., Wu, J., Nie, J., Zhang, L., Hao, H., Liu, S., Zhao, C., Zhang, Q., Liu, H., Nie, L., Qin, H., Wang, M., Lu, Q., Li, X., Sun, Q., Liu, J., Zhang, L., Li, X., Huang, W., & Wang, Y. (2020). The impact of mutations in SARS-CoV-2 spike on viral infectivity and antigenicity. Cell, 182(5), 1284–1294.e9.
  • Li, Y., Wang, T., Zhang, J., Shao, B., Gong, H., Wang, Y., He, X., Liu, S., & Liu, T.-Y. (2021). Exploring the regulatory function of the N-terminal domain of SARS-CoV-2 spike protein through molecular dynamics simulation. Advanced Theory and Simulations, 4(10), 2100152.
  • Lubinski, B., Fernandes, M. H. V., Frazier, L., Tang, T., Daniel, S., Diel, D. G., Jaimes, J. A., & Whittaker, G. R. (2022). Functional evaluation of the P681H mutation on the proteolytic activation of the SARS-CoV-2 variant B.1.1.7 (Alpha) spike. iScience, 25(1), 103589.
  • Lupala, C. S., Ye, Y., Chen, H., Su, X.-D., & Liu, H. (2022). Mutations on RBD of SARS-CoV-2 Omicron variant result in stronger binding to human ACE2 receptor. Biochemical and Biophysical Research Communications, 590, 34–41.
  • Lv, Z., Deng, Y.-Q., Ye, Q., Cao, L., Sun, C.-Y., Fan, C., Huang, W., Sun, S., Sun, Y., Zhu, L., Chen, Q., Wang, N., Nie, J., Cui, Z., Zhu, D., Shaw, N., Li, X.-F., Li, Q., Xie, L., … Wang, X. (2020). Structural basis for neutralization of SARS-CoV-2 and SARS-CoV by a potent therapeutic antibody. Science (New York, N.Y.), 369(6510), 1505–1509.
  • Mannar, D., Saville, J. W., Zhu, X., Srivastava, S. S., Berezuk, A. M., Tuttle, K. S., Marquez, A. C., Sekirov, I., & Subramaniam, S. (2022). SARS-CoV-2 Omicron variant: Antibody evasion and cryo-EM structure of spike protein-ACE2 complex. Science, 375(6582), eabn7760. https://doi.org/10.1126/science.abn7760[Mismatch
  • Mansbach, R. A., Chakraborty, S., Nguyen, K., Montefiori, D. C., Korber, B., & Gnanakaran, S. (2021). The SARS-CoV-2 Spike variant D614G favors an open conformational state. Science Advances, 7(16), 1-10. https://doi.org/10.1126/sciadv.abf3671[Mismatch
  • Meng, B., Abdullahi, A., Ferreira, I. A. T. M., Goonawardane, N., Saito, A., Kimura, I., Yamasoba, D., Gerber, P. P., Fatihi, S., Rathore, S., Zepeda, S. K., Papa, G., Kemp, S. A., Ikeda, T., Toyoda, M., Tan, T. S., Kuramochi, J., Mitsunaga, S., Ueno, T., … Gupta, R. K., Ecuador-COVID19 Consortium. (2022). Altered TMPRSS2 usage by SARS-CoV-2 Omicron impacts infectivity and fusogenicity. Nature, 603(7902), 706–714.
  • Meng, B., Datir, R., Choi, J., Bradley, J. R., Smith, K., G., C., Lee, J. H., & Gupta, R. K., CITIID-NIHR Bioresource COVID-19 Collaboration. (2022). SARS-CoV-2 spike N-terminal domain modulates TMPRSS2-dependent viral entry and fusogenicity. Cell Reports, 40(7), 111220.
  • Outbreak. (2022). Omicron variant report. Outbreak. https://outbreak.info/
  • Ou, T., Mou, H., Zhang, L., Ojha, A., Choe, H., & Farzan, M. (2021). Hydroxychloroquine-mediated inhibition of SARS-CoV-2 entry is attenuated by TMPRSS2. PLoS Pathogens, 17(1), e1009212.
  • Petit, C. M., Melancon, J. M., Chouljenko, V. N., Colgrove, R., Farzan, M., Knipe, D. M., & Kousoulas, K. G. (2005). Genetic analysis of the SARS-coronavirus spike glycoprotein functional domains involved in cell-surface expression and cell-to-cell fusion. Virology, 341(2), 215–230.
  • Pronk, S., Páll, S., Schulz, R., Larsson, P., Bjelkmar, P., Apostolov, R., Shirts, M. R., Smith, J. C., Kasson, P. M., van der Spoel, D., Hess, B., & Lindahl, E. (2013). GROMACS 4.5: A high-throughput and highly parallel open source molecular simulation toolkit. Bioinformatics (Oxford, England), 29(7), 845–854.
  • Puhach, O., Adea, K., Hulo, N., Sattonnet, P., Genecand, C., Iten, A., Jacquérioz, F., Kaiser, L., Vetter, P., Eckerle, I., & Meyer, B. (2022). Infectious viral load in unvaccinated and vaccinated individuals infected with ancestral, Delta or Omicron SARS-CoV-2. Nature Medicine, 28(7), 1491–1500.
  • Qing, E., Kicmal, T., Kumar, B., Hawkins, G. M., Timm, E., Perlman, S., & Gallagher, T. (2021). Dynamics of SARS-CoV-2 spike proteins in cell entry: Control elements in the amino-terminal domains. mBio, 12(4), e0159021.
  • Riediker, M., Briceno-Ayala, L., Ichihara, G., Albani, D., Poffet, D., Tsai, D.-H., Iff, S., & Monn, C. (2022). Higher viral load and infectivity increase risk of aerosol transmission for Delta and Omicron variants of SARS-CoV-2. Swiss Medical Weekly, 152, w30133.
  • Robertson, M. J., Tirado-Rives, J., & Jorgensen, W. L. (2015). Improved peptide and protein torsional energetics with the OPLSAA force field. Journal of Chemical Theory and Computation, 11(7), 3499–3509.
  • Saito, A., Irie, T., Suzuki, R., Maemura, T., Nasser, H., Uriu, K., Kosugi, Y., Shirakawa, K., Sadamasu, K., Kimura, I., Ito, J., Wu, J., Iwatsuki-Horimoto, K., Ito, M., Yamayoshi, S., Loeber, S., Tsuda, M., Wang, L., Ozono, S., … Sato, K., Genotype to Phenotype Japan (G2P-Japan) Consortium. (2022). Enhanced fusogenicity and pathogenicity of SARS-CoV-2 Delta P681R mutation. Nature, 602(7896), 300–306.
  • Sakkiah, S., Guo, W., Pan, B., Ji, Z., Yavas, G., Azevedo, M., Hawes, J., Patterson, T. A., & Hong, H. (2020). Elucidating interactions between SARS-CoV-2 trimeric spike protein and ACE2 using homology modeling and molecular dynamics simulations. Frontiers in Chemistry, 8, 622632.
  • Schlitter, J. (1993). Estimation of absolute and relative entropies of macromolecules using the covariance matrix. Chemical Physics Letters, 215(6), 617–621. https://doi.org/10.1016/0009-2614(93)89366-P
  • Schrodinger. (2021). Maestro. Schrodinger. https://www.schrodinger.com/maestro
  • Schroth-Diez, B., Ludwig, K., Baljinnyam, B., Kozerski, C., Huang, Q., & Herrmann, A. (2000). The role of the transmembrane and of the intraviral domain of glycoproteins in membrane fusion of enveloped viruses. Bioscience Reports, 20(6), 571–595.
  • Sentis, C., Billaud, G., Bal, A., Frobert, E., Bouscambert, M., Destras, G., Josset, L., Lina, B., Morfin, F., & Gaymard, A., The Covid-Diagnosis Hcl Study Group. (2022). SARS-CoV-2 omicron variant, lineage BA.1, is associated with lower viral load in nasopharyngeal samples compared to delta variant. Viruses, 14(5), 919. https://doi.org/10.3390/v14050919
  • Sironi, M., Hasnain, S. E., Rosenthal, B., Phan, T., Luciani, F., Shaw, M.-A., Sallum, M. A., Mirhashemi, M. E., Morand, S., & González-Candelas, F., Editors of Infection, Genetics and Evolution. (2020). SARS-CoV-2 and COVID-19: A genetic, epidemiological, and evolutionary perspective. Infection, Genetics and Evolution, 84, 104384.
  • Socher, E., Conrad, M., Heger, L., Paulsen, F., Sticht, H., Zunke, F., & Arnold, P. (2021). Mutations in the B.1.1.7 SARS-CoV-2 spike protein reduce receptor-binding affinity and induce a flexible link to the fusion peptide. Biomedicines, 9(5), 525–513. https://doi.org/10.3390/biomedicines9050525[Mismatch
  • Souza, A. S., Rivera, J. D., Almeida, V. M., Ge, P., Souza, R. F., Farah, C. S., Ulrich, H., Marana, S. R., Salinas, R. K., & Guzzo, C. R. (2020). Molecular dynamics reveals complex compensatory effects of ionic strength on the severe acute respiratory syndrome coronavirus 2 spike/human angiotensin-converting enzyme 2 interaction. The Journal of Physical Chemistry Letters, 11(24), 10446–10453.
  • Souza, A. S., Amorim, V. M. F., Guardia, G. D. A., Santos, F. F. d., Ulrich, H., Galante, P. A. F., Souza, R. F. d., & Guzzo, C. R. (2022a). Severe acute respiratory syndrome Coronavirus 2 variants of concern: A perspective for emerging more transmissible and vaccine-resistant strains. Viruses, 14(4), 827–821. https://doi.org/10.3390/v14040827
  • Souza, A. S., Amorim, V. M. F., Guardia, G. D. A., dos Santos, F. R. C., dos Santos, F. F., de Souza, R. F., de Araujo Juvenal, G., Huang, Y., Ge, P., Jiang, Y., Li, C., Paudel, P., Ulrich, H., Galante, P. A. F., & Guzzo, C. R. (2022b). Molecular dynamics analysis of fast-spreading severe acute respiratory syndrome Coronavirus 2 variants and their effects on the interaction with human angiotensin-converting enzyme 2. ACS Omega, 7(35), 30700–30709. https://doi.org/10.1021/acsomega.1c07240
  • Tian, F., Tong, B., Sun, L., Shi, S., Zheng, B., Wang, Z., Dong, X., & Zheng, P. (2021). N501Y mutation of spike protein in SARS-CoV-2 strengthens its binding to receptor ACE2. eLife, 10, 1–17. https://doi.org/10.7554/eLife.69091
  • Van Der Spoel, D., Lindahl, E., Hess, B., Groenhof, G., Mark, A. E., Berendsen, H., & J., C. (2005). GROMACS: Fast, flexible, and free. Journal of Computational Chemistry, 26(16), 1701–1718.
  • Walls, A. C., Park, Y.-J., Tortorici, M. A., Wall, A., McGuire, A. T., & Veesler, D. (2020). Structure, function, and antigenicity of the SARS-CoV-2 spike glycoprotein. Cell, 183(6), 1735.
  • Wang, Y., Xu, C., Wang, Y., Hong, Q., Zhang, C., Li, Z., Xu, S., Zuo, Q., Liu, C., Huang, Z., & Cong, Y. (2021). Conformational dynamics of the Beta and Kappa SARS-CoV-2 spike proteins and their complexes with ACE2 receptor revealed by cryo-EM. Nature Communications, 12(1), 7345.
  • Waterhouse, A., Bertoni, M., Bienert, S., Studer, G., Tauriello, G., Gumienny, R., Heer, F. T., de Beer, T. A. P., Rempfer, C., Bordoli, L., Lepore, R., & Schwede, T. (2018). SWISS-MODEL: Homology modelling of protein structures and complexes. Nucleic Acids Research, 46(W1), W296–W303.
  • WHO. (2022). WHO Coronavirus (COVID-19) dashboard. World Health Organization. https://covid19.who.int
  • Wrapp, D., Wang, N., Corbett, K. S., Goldsmith, J. A., Hsieh, C.-L., Abiona, O., Graham, B. S., & McLellan, J. S. (2020). Cryo-EM structure of the 2019-nCoV spike in the prefusion conformation. Science, 367(6483), 1260–1263.
  • Xia, S., Wen, Z., Wang, L., Lan, Q., Jiao, F., Tai, L., Wang, Q., Sun, F., Jiang, S., Lu, L., & Zhu, Y. (2021). Structure-based evidence for the enhanced transmissibility of the dominant SARS-CoV-2 B.1.1.7 variant (Alpha). Cell Discovery, 7(1), 109.
  • Xia, S., Zhu, Y., Liu, M., Lan, Q., Xu, W., Wu, Y., Ying, T., Liu, S., Shi, Z., Jiang, S., & Lu, L. (2020). Fusion mechanism of 2019-nCoV and fusion inhibitors targeting HR1 domain in spike protein. Cellular & Molecular Immunology, 17(7), 765–767.
  • Xie, X., Liu, Y., Liu, J., Zhang, X., Zou, J., Fontes-Garfias, C. R., Xia, H., Swanson, K. A., Cutler, M., Cooper, D., Menachery, V. D., Weaver, S. C., Dormitzer, P. R., & Shi, P.-Y. (2021). Neutralization of SARS-CoV-2 spike 69/70 deletion, E484K and N501Y variants by BNT162b2 vaccine-elicited sera. Nature Medicine, 27(4), 620–621.
  • Yang, Y., & Du, L. (2021). SARS-CoV-2 spike protein: A key target for eliciting persistent neutralizing antibodies [Review of SARS-CoV-2 spike protein: A key target for eliciting persistent neutralizing antibodies]. Signal Transduction and Targeted Therapy, 6(1), 95.
  • Yurkovetskiy, L., Wang, X., Pascal, K. E., Tomkins-Tinch, C., Nyalile, T. P., Wang, Y., Baum, A., Diehl, W. E., Dauphin, A., Carbone, C., Veinotte, K., Egri, S. B., Schaffner, S. F., Lemieux, J. E., Munro, J. B., Rafique, A., Barve, A., Sabeti, P. C., Kyratsous, C. A., … Luban, J. (2020). Structural and functional analysis of the D614G SARS-CoV-2 spike protein variant. Cell, 183(3), 739–751.e8.
  • Yu, H., Zhao, Y., Guo, C., Gan, Y., & Huang, H. (2015). The role of proline substitutions within flexible regions on thermostability of luciferase. Biochimica et Biophysica Acta, 1854(1), 65–72.
  • Zhang, J., Cai, Y., Xiao, T., Lu, J., Peng, H., Sterling, S. M., Walsh, R. M., Jr., Rits-Volloch, S., Zhu, H., Woosley, A. N., Yang, W., Sliz, P., & Chen, B. (2021). Structural impact on SARS-CoV-2 spike protein by D614G substitution. Science (New York, N.Y.), 372(6541), 525–530.
  • Zhang, J., Xiao, T., Cai, Y., Lavine, C. L., Peng, H., Zhu, H., Anand, K., Tong, P., Gautam, A., Mayer, M. L., Walsh, R. M., Jr., Rits-Volloch, S., Wesemann, D. R., Yang, W., Seaman, M. S., Lu, J., & Chen, B. (2021). Membrane fusion and immune evasion by the spike protein of SARS-CoV-2 Delta variant. Science (New York, N.Y.), 374(6573), 1353–1360.
  • Zhang, L., Jackson, C. B., Mou, H., Ojha, A., Peng, H., Quinlan, B. D., Rangarajan, E. S., Pan, A., Vanderheiden, A., Suthar, M. S., Li, W., Izard, T., Rader, C., Farzan, M., & Choe, H. (2020). SARS-CoV-2 spike-protein D614G mutation increases virion spike density and infectivity. Nature Communications, 11(1), 6013.
  • Zhao, H., Lu, L., Peng, Z., Chen, L.-L., Meng, X., Zhang, C., Ip, J. D., Chan, W.-M., Chu, A. W.-H., Chan, K.-H., Jin, D.-Y., Chen, H., Yuen, K.-Y., & To, K. K.-W. (2022). SARS-CoV-2 Omicron variant shows less efficient replication and fusion activity when compared with Delta variant in TMPRSS2-expressed cells. Emerging Microbes & Infections, 11(1), 277–283.
  • Zhu, C., He, G., Yin, Q., Zeng, L., Ye, X., Shi, Y., & Xu, W. (2021). Molecular biology of the SARs-CoV-2 spike protein: A review of current knowledge. Journal of Medical Virology, 93(10), 5729–5741.
  • Zimmerman, M. I., Porter, J. R., Ward, M. D., Singh, S., Vithani, N., Meller, A., Mallimadugula, U. L., Kuhn, C. E., Borowsky, J. H., Wiewiora, R. P., Hurley, M. F. D., Harbison, A. M., Fogarty, C. A., Coffland, J. E., Fadda, E., Voelz, V. A., Chodera, J. D., & Bowman, G. R. (2021). SARS-CoV-2 simulations go exascale to predict dramatic spike opening and cryptic pockets across the proteome. Nature Chemistry, 13(7), 651–659.

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