Single-molecule force stability of the SARS-CoV-2-ACE2 interface in variants-of-concern.
Journal
Nature nanotechnology
ISSN: 1748-3395
Titre abrégé: Nat Nanotechnol
Pays: England
ID NLM: 101283273
Informations de publication
Date de publication:
Mar 2024
Mar 2024
Historique:
received:
06
01
2023
accepted:
26
09
2023
pubmed:
28
11
2023
medline:
28
11
2023
entrez:
27
11
2023
Statut:
ppublish
Résumé
Mutations in SARS-CoV-2 have shown effective evasion of population immunity and increased affinity to the cellular receptor angiotensin-converting enzyme 2 (ACE2). However, in the dynamic environment of the respiratory tract, forces act on the binding partners, which raises the question of whether not only affinity but also force stability of the SARS-CoV-2-ACE2 interaction might be a selection factor for mutations. Using magnetic tweezers, we investigate the impact of amino acid substitutions in variants of concern (Alpha, Beta, Gamma and Delta) and on force-stability and bond kinetic of the receptor-binding domain-ACE2 interface at a single-molecule resolution. We find a higher affinity for all of the variants of concern (>fivefold) compared with the wild type. In contrast, Alpha is the only variant of concern that shows higher force stability (by 17%) compared with the wild type. Using molecular dynamics simulations, we rationalize the mechanistic molecular origins of this increase in force stability. Our study emphasizes the diversity of contributions to the transmissibility of variants and establishes force stability as one of the several factors for fitness. Understanding fitness advantages opens the possibility for the prediction of probable mutations, allowing a rapid adjustment of therapeutics, vaccines and intervention measures.
Identifiants
pubmed: 38012274
doi: 10.1038/s41565-023-01536-7
pii: 10.1038/s41565-023-01536-7
doi:
Types de publication
Journal Article
Langues
eng
Sous-ensembles de citation
IM
Pagination
399-405Subventions
Organisme : Deutsche Forschungsgemeinschaft (German Research Foundation)
ID : 386143268
Organisme : Deutsche Forschungsgemeinschaft (German Research Foundation)
ID : 111166240
Organisme : Human Frontier Science Program (HFSP)
ID : LT000395/2020C
Organisme : European Molecular Biology Organization (EMBO)
ID : ALTF 1047-2019
Informations de copyright
© 2023. The Author(s), under exclusive licence to Springer Nature Limited.
Références
Laffeber, C., Koning, K. D., Kanaar, R. & Lebbink, J. H. G. Experimental evidence for enhanced receptor binding by rapidly spreading SARS-CoV-2 variants. J. Mol. Biol. 433, 167058–167058 (2021).
pubmed: 34023401
pmcid: 8139174
doi: 10.1016/j.jmb.2021.167058
Barton, M. I. et al. Effects of common mutations in the SARS-CoV-2 spike RBD and its ligand, the human ACE2 receptor on binding affinity and kinetics. eLife 10, e70658 (2021).
pubmed: 34435953
pmcid: 8480977
doi: 10.7554/eLife.70658
Majumdar, P. & Niyogi, S. SARS-CoV-2 mutations: the biological trackway towards viral fitness. Epidemiol. Infect. 149, E110 (2021).
pubmed: 33928885
doi: 10.1017/S0950268821001060
Bayarri-Olmos, R. et al. The alpha/B.1.1.7 SARS-CoV-2 variant exhibits significantly higher affinity for ACE-2 and requires lower inoculation doses to cause disease in K18-hACE2 mice. eLife 10, e70002 (2021).
pubmed: 34821555
pmcid: 8635972
doi: 10.7554/eLife.70002
Hill, D. B. et al. Force generation and dynamics of individual cilia under external loading. Biophys. J. 98, 57–66 (2010).
pubmed: 20085719
pmcid: 2800978
doi: 10.1016/j.bpj.2009.09.048
Wu, C.-T. et al. SARS-CoV-2 replication in airway epithelia requires motile cilia and microvillar reprogramming. Cell 186, 112–130.e20 (2023).
Milles, L. F., Schulten, K., Gaub, H. E. & Bernardi, R. C. Molecular mechanism of extreme mechanostability in a pathogen adhesin. Science 359, 1527–1533 (2018).
pubmed: 29599244
pmcid: 6451932
doi: 10.1126/science.aar2094
Alsteens, D. et al. Nanomechanical mapping of first binding steps of a virus to animal cells. Nat. Nanotechnol. 12, 177–183 (2017).
pubmed: 27798607
doi: 10.1038/nnano.2016.228
Koehler, M., Delguste, M., Sieben, C., Gillet, L. & Alsteens, D. Initial step of virus entry: virion binding to cell-surface glycans. Annu. Rev. Virol. 7, 143–165 (2020).
pubmed: 32396772
doi: 10.1146/annurev-virology-122019-070025
Sokurenko, E. V., Vogel, V. & Thomas, W. E. Catch-bond mechanism of force-enhanced adhesion: counterintuitive, elusive, but…widespread? Cell Host Microbe 4, 314–323 (2008).
pubmed: 18854236
pmcid: 2610669
doi: 10.1016/j.chom.2008.09.005
Tian, F. et al. N501Y mutation of spike protein in SARS-CoV-2 strengthens its binding to receptor ACE2. eLife 10, e69091 (2021).
pubmed: 34414884
pmcid: 8455130
doi: 10.7554/eLife.69091
Zheng, Bin, et al. S373P mutation stabilizes the receptor-binding domain of the spike protein in omicron and promotes binding. JACS Au https://doi.org/10.1021/jacsau.3c00142 (2023).
Koehler, M. et al. Molecular insights into receptor binding energetics and neutralization of SARS-CoV-2 variants. Nat. Commun. 12, 6977 (2021).
pubmed: 34848718
pmcid: 8633007
doi: 10.1038/s41467-021-27325-1
Yang, J. et al. Molecular interaction and inhibition of SARS-CoV-2 binding to the ACE2 receptor. Nat. Commun. 11, 4541 (2020).
pubmed: 32917884
pmcid: 7486399
doi: 10.1038/s41467-020-18319-6
Cao, W. et al. Biomechanical characterization of SARS-CoV-2 spike RBD and human ACE2 protein-protein interaction. Biophys. J. 120, 1011–1019 (2021).
pubmed: 33607086
pmcid: 7886630
doi: 10.1016/j.bpj.2021.02.007
Zhang, X. et al. Pathogen-host adhesion between SARS-CoV-2 spike proteins from different variants and human ACE2 studied at single-molecule and single-cell levels. Emerging Microbes Infect. 11, 2658–2669 (2022).
doi: 10.1080/22221751.2022.2128887
Zhu, R. et al. Force-tuned avidity of spike variant-ACE2 interactions viewed on the single-molecule level. Nat. Commun. 13, 7926 (2022).
pubmed: 36566234
pmcid: 9789309
doi: 10.1038/s41467-022-35641-3
Bauer, M. S. et al. A tethered ligand assay to probe SARS-CoV-2:ACE2 interactions. Proc. Natl Acad. Sci. USA 119, e2114397119 (2022).
Bauer, M. S. et al. A tethered ligand assay to probe the SARS-CoV-2 ACE2 interaction under constant force. Preprint at biorxiv https://doi.org/10.1101/2020.09.27.315796 (2020).
Löf, A. et al. Multiplexed protein force spectroscopy reveals equilibrium protein folding dynamics and the low-force response of von Willebrand factor. Proc. Natl Acad. Sci. USA 116, 18798–18807 (2019).
Lansdorp, B. M. & Saleh, O. A. Power spectrum and Allan variance methods for calibrating single-molecule video-tracking instruments. Rev. Sci. Instrum. 83, 025115 (2012).
pubmed: 22380133
pmcid: 3306435
doi: 10.1063/1.3687431
Velthuis, A. J. W. T., Kerssemakers, J. W. J., Lipfert, J. & Dekker, N. H. Quantitative guidelines for force calibration through spectral analysis of magnetic tweezers data. Biophys. J. 99, 1292–1302 (2010).
doi: 10.1016/j.bpj.2010.06.008
Neuman, K. C. & Nagy, A. Single-molecule force spectroscopy: optical tweezers, magnetic tweezers and atomic force microscopy. Nat. Methods 5, 491–505 (2008).
pubmed: 18511917
pmcid: 3397402
doi: 10.1038/nmeth.1218
Lipfert, J., Hao, X. & Dekker, N. H. Quantitative modeling and optimization of magnetic tweezers. Biophys. J. 96, 5040–5049 (2009).
pubmed: 19527664
pmcid: 2712044
doi: 10.1016/j.bpj.2009.03.055
Ott, W. et al. Elastin-like polypeptide linkers for single-molecule force spectroscopy. ACS Nano 11, 6346–6354 (2017).
pubmed: 28591514
doi: 10.1021/acsnano.7b02694
Kim, J., Zhang, C. Z., Zhang, X. & Springer, T. A. A mechanically stabilized receptor-ligand flex-bond important in the vasculature. Nature 466, 992–995 (2010).
pubmed: 20725043
pmcid: 4117310
doi: 10.1038/nature09295
Shrestha, P. et al. Single-molecule mechanical fingerprinting with DNA nanoswitch calipers. Nat. Nanotechnol. 16, 1362–1370 (2021).
pubmed: 34675411
pmcid: 8678201
doi: 10.1038/s41565-021-00979-0
Yang, D., Ward, A., Halvorsen, K. & Wong, W. P. Multiplexed single-molecule force spectroscopy using a centrifuge. Nat. Commun. 7, 11026 (2016).
pubmed: 26984516
pmcid: 4800429
doi: 10.1038/ncomms11026
Kilchherr, F. et al. Single-molecule dissection of stacking forces in DNA. Science 353, aaf5508 (2016).
pubmed: 27609897
doi: 10.1126/science.aaf5508
Le, S., Yu, M. & Yan, J. Direct single-molecule quantification reveals unexpectedly high mechanical stability of vinculin—talin/α-catenin linkages. Sci. Adv. 5, eaav2720 (2019).
pubmed: 31897422
pmcid: 6920023
doi: 10.1126/sciadv.aav2720
Halvorsen, K., Schaak, D. & Wong, W. P. Nanoengineering a single-molecule mechanical switch using DNA self-assembly. Nanotechnology 22, 494005 (2011).
pubmed: 22101354
doi: 10.1088/0957-4484/22/49/494005
Kostrz, D. et al. A modular DNA scaffold to study protein-protein interactions at single-molecule resolution. Nat. Nanotechnol. 14, 988–993 (2019).
pubmed: 31548690
doi: 10.1038/s41565-019-0542-7
Gong, S. Y. et al. Contribution of single mutations to selected SARS-CoV-2 emerging variants spike antigenicity. Virology 563, 134–145 (2021).
pubmed: 34536797
doi: 10.1016/j.virol.2021.09.001
Rajah, M. M. et al. SARS‐CoV‐2 Alpha, Beta, and Delta variants display enhanced spike‐mediated syncytia formation. EMBO J. 40, e108944 (2021).
pubmed: 34601723
pmcid: 8646911
doi: 10.15252/embj.2021108944
Gobeil, S. M. C. et al. Effect of natural mutations of SARS-CoV-2 on spike structure, conformation, and antigenicity. Science 373, eabi6226 (2021).
pubmed: 34168071
pmcid: 8611377
doi: 10.1126/science.abi6226
Ren, W. et al. Characterization of SARS-CoV-2 variants B.1.617.1 (Kappa), B.1.617.2 (Delta), and B.1.618 by cell entry and immune evasion. mBio 13, e00099–00022 (2022).
pubmed: 35266815
pmcid: 9040861
doi: 10.1128/mbio.00099-22
McCallum, M. et al. Molecular basis of immune evasion by the Delta and Kappa SARS-CoV-2 variants. Science 374, 1621–1626 (2021).
pubmed: 34751595
doi: 10.1126/science.abl8506
Albrecht, C. et al. DNA: a programmable force sensor. Science 301, 367–370 (2003).
pubmed: 12869761
doi: 10.1126/science.1084713
Gruber, S. et al. Designed anchoring geometries determine lifetimes of biotin–streptavidin bonds under constant load and enable ultra-stable coupling. Nanoscale 12, 21131–21137 (2020).
pubmed: 33079117
doi: 10.1039/D0NR03665J
Webb, B. & Sali, A. Comparative protein structure modeling using MODELLER. Curr. Protoc. Bioinform 54, 5.6.1–5.6.37 (2016).
doi: 10.1002/cpbi.3
Phillips, J. C. et al. Scalable molecular dynamics on CPU and GPU architectures with NAMD. J. Chem. Phys. 153, 044130 (2020).
pubmed: 32752662
pmcid: 7395834
doi: 10.1063/5.0014475
Melo, M. C. R., Bernardi, R. C., Fuente-Nunez, C. D. L. & Luthey-Schulten, Z. Generalized correlation-based dynamical network analysis: a new high-performance approach for identifying allosteric communications in molecular dynamics trajectories. J. Chem. Phys. 153, 134104 (2020).
pubmed: 33032427
doi: 10.1063/5.0018980
Schoeler, C. et al. Mapping mechanical force propagation through biomolecular complexes. Nano Lett. 15, 7370–7376 (2015).
pubmed: 26259544
pmcid: 4721519
doi: 10.1021/acs.nanolett.5b02727
Lan, J. et al. Structure of the SARS-CoV-2 spike receptor-binding domain bound to the ACE2 receptor. Nature 581, 215–220 (2020).
pubmed: 32225176
doi: 10.1038/s41586-020-2180-5
Liu, H. et al. The basis of a more contagious 501Y.V1 variant of SARS-CoV-2. Cell Res. 31, 720–722 (2021).
pubmed: 33893398
pmcid: 8063779
doi: 10.1038/s41422-021-00496-8
Han, P. et al. Receptor binding and complex structures of human ACE2 to spike RBD from Omicron and Delta SARS-CoV-2. Cell 185, 630–640.e610 (2022).
pubmed: 35093192
pmcid: 8733278
doi: 10.1016/j.cell.2022.01.001
Dulin, D., Lipfert, J., Moolman, M. C. & Dekker, N. H. Studying genomic processes at the single-molecule level: introducing the tools and applications. Nat. Rev. Genet. 14, 9–22 (2013).
pubmed: 23150038
doi: 10.1038/nrg3316
Shang, J. et al. Cell entry mechanisms of SARS-CoV-2. Proc. Natl Acad. Sci. USA 117, 11727–11734 (2020).
pubmed: 32376634
pmcid: 7260975
doi: 10.1073/pnas.2003138117
V’kovski, P., Kratzel, A., Steiner, S, Stalder, H. & Thiel, V. Coronavirus biology and replication: implications for SARS-CoV-2. Nat. Rev. Microbiol. 19, 155–170 (2020).
Michaud, W. A., Boland, G. M. & Rabi, S. A. The SARS-CoV-2 spike mutation D614G increases entry fitness across a range of ACE2 levels, directly outcompetes the wild type, and is preferentially incorporated into trimers. Preprint at bioRxiv https://doi.org/10.1101/2020.08.25.267500 (2020).
Jackson, C. B., Farzan, M., Chen, B. & Choe, H. Mechanisms of SARS-CoV-2 entry into cells. Nat. Rev. Mol. Cell Biol. 23, 3–20 (2022).
pubmed: 34611326
doi: 10.1038/s41580-021-00418-x
Harvey, W. T. et al. SARS-CoV-2 variants, spike mutations and immune escape. Nat. Rev. Microbiol. 19, 409–424 (2021).
pubmed: 34075212
pmcid: 8167834
doi: 10.1038/s41579-021-00573-0
Escalera, A. et al. Mutations in SARS-CoV-2 variants of concern link to increased spike cleavage and virus transmission. Cell Host Microbe 30, 373–387.e377 (2022).
pubmed: 35150638
pmcid: 8776496
doi: 10.1016/j.chom.2022.01.006
Ulrich, L. et al. Enhanced fitness of SARS-CoV-2 variant of concern Alpha but not Beta. Nature 602, 307–313 (2022).
pubmed: 34937050
doi: 10.1038/s41586-021-04342-0
Buss, L. F. et al. Three-quarters attack rate of SARS-CoV-2 in the Brazilian Amazon during a largely unmitigated epidemic. Science 371, 288–292 (2021).
pubmed: 33293339
doi: 10.1126/science.abe9728
Sun, K. et al. SARS-CoV-2 transmission, persistence of immunity, and estimates of Omicron’s impact in South African population cohorts. Sci. Transl. Med. 14, eabo7081 (2022).
pubmed: 35638937
doi: 10.1126/scitranslmed.abo7081
Starr, T. N. et al. Deep mutational scanning of SARS-CoV-2 receptor binding domain reveals constraints on folding and ACE2 binding. Cell 182, 1295–1310.e1220 (2020).
pubmed: 32841599
pmcid: 7418704
doi: 10.1016/j.cell.2020.08.012
Liu, C. et al. The antibody response to SARS-CoV-2 Beta underscores the antigenic distance to other variants. Cell Host Microbe 30, 53–68.e12 (2022).
pubmed: 34921776
pmcid: 8626228
doi: 10.1016/j.chom.2021.11.013
Bayarri-Olmos, R. et al. Functional effects of receptor-binding domain mutations of SARS-CoV-2 B.1.351 and P.1 variants. Front. Immunol. 12, 757197 (2021).
pubmed: 34691078
pmcid: 8529273
doi: 10.3389/fimmu.2021.757197
Mlcochova, P. et al. SARS-CoV-2 B.1.617.2 Delta variant replication and immune evasion. Nature 599, 114–119 (2021).
pubmed: 34488225
pmcid: 8566220
doi: 10.1038/s41586-021-03944-y
Hu, J. et al. Increased immune escape of the new SARS-CoV-2 variant of concern Omicron. Cell Mol. Immunol. 19, 293–295 (2022).
pubmed: 35017716
pmcid: 8749347
doi: 10.1038/s41423-021-00836-z
Ju, B. et al. Immune escape by SARS-CoV-2 Omicron variant and structural basis of its effective neutralization by a broad neutralizing human antibody VacW-209. Cell Res. 32, 491–494 (2022).
pubmed: 35260792
pmcid: 8902274
doi: 10.1038/s41422-022-00638-6
Fan, Y. et al. SARS-CoV-2 Omicron variant: recent progress and future perspectives. Sig. Transduct. Target Ther. 7, 141 (2022).
doi: 10.1038/s41392-022-00997-x
Planas, D. et al. Considerable escape of SARS-CoV-2 Omicron to antibody neutralization. Nature 602, 671–675 (2022).
pubmed: 35016199
doi: 10.1038/s41586-021-04389-z
Li, B. et al. Viral infection and transmission in a large, well-traced outbreak caused by the SARS-CoV-2 Delta variant. Nat. Commun. 13, 460 (2022).
pubmed: 35075154
pmcid: 8786931
doi: 10.1038/s41467-022-28089-y
Komatsu, T. et al. Molecular cloning, mRNA expression and chromosomal localization of mouse angiotensin-converting enzyme-related carboxypeptidase (mACE2). DNA Sequence 13, 217–220 (2002).
pubmed: 12487024
doi: 10.1080/1042517021000021608
Marra, M. A. et al. The genome sequence of the SARS-associated coronavirus. Science 300, 1399–1404 (2003).
pubmed: 12730501
doi: 10.1126/science.1085953
Li, F., Li, W., Farzan, M. & Harrison, S. C. Structure of SARS coronavirus spike receptor-binding domain complexed with receptor. Science 309, 1864–1868 (2005).
pubmed: 16166518
doi: 10.1126/science.1116480
Milles, L. F. & Gaub, H. E. Is mechanical receptor ligand dissociation driven by unfolding or unbinding? Preprint at bioRxiv https://doi.org/10.1101/593335 (2019).
Wu, F. et al. A new coronavirus associated with human respiratory disease in China. Nature 579, 265–269 (2020).
pubmed: 32015508
pmcid: 7094943
doi: 10.1038/s41586-020-2008-3
Walker, P. U., Vanderlinden, W. & Lipfert, J. Dynamics and energy landscape of DNA plectoneme nucleation. Phys. Rev. E 98, 042412 (2018).
doi: 10.1103/PhysRevE.98.042412
van Loenhout, M. T., Kerssemakers, J. W., De Vlaminck, I. & Dekker, C. Non-bias-limited tracking of spherical particles, enabling nanometer resolution at low magnification. Biophys. J. 102, 2362–2371 (2012).
pubmed: 22677390
pmcid: 3353059
doi: 10.1016/j.bpj.2012.03.073
Cnossen, J. P., Dulin, D. & Dekker, N. H. An optimized software framework for real-time, high-throughput tracking of spherical beads. Rev. Sci. Instrum. 85, 103712 (2014).
pubmed: 25362408
doi: 10.1063/1.4898178
Lipfert, J. et al. Methods and protocols. Methods Mol. Biol. 582, 71–89 (2009).
pubmed: 19763943
doi: 10.1007/978-1-60761-340-4_7
Yu, Z. et al. A force calibration standard for magnetic tweezers. Rev. Sci. Instrum. 85, 123114 (2014).
pubmed: 25554279
doi: 10.1063/1.4904148
De Vlaminck, I., Henighan, T., van Loenhout, M. T., Burnham, D. R. & Dekker, C. Magnetic forces and DNA mechanics in multiplexed magnetic tweezers. PLoS ONE 7, e41432 (2012).
pubmed: 22870220
pmcid: 3411724
doi: 10.1371/journal.pone.0041432
Zimmermann, J. L., Nicolaus, T., Neuert, G. & Blank, K. Thiol-based, site-specific and covalent immobilization of biomolecules for single-molecule experiments. Nat. Protoc. 5, 975–985 (2010).
pubmed: 20448543
doi: 10.1038/nprot.2010.49
Yin, J., Lin, A. J., Golan, D. E. & Walsh, C. T. Site-specific protein labeling by Sfp phosphopantetheinyl transferase. Nat. Protoc. 1, 280–285 (2006).
pubmed: 17406245
doi: 10.1038/nprot.2006.43
Chen, I., Dorr, B. M. & Liu, D. R. A general strategy for the evolution of bond-forming enzymes using yeast display. Proc. Natl Acad. Sci. USA 108, 11399–11404 (2011).
pubmed: 21697512
pmcid: 3136257
doi: 10.1073/pnas.1101046108
Durner, E., Ott, W., Nash, M. A. & Gaub, H. E. Post-translational sortase-mediated attachment of high-strength force spectroscopy handles. ACS Omega 2, 3064–3069 (2017).
pubmed: 30023682
pmcid: 6044863
doi: 10.1021/acsomega.7b00478
Humphrey, W., Dalke, A. & Schulten, K. VMD: visual molecular dynamics. J. Mol. Graph. 14, 33–38 (1996).
pubmed: 8744570
doi: 10.1016/0263-7855(96)00018-5
Ribeiro, J. V. et al. QwikMD—integrative molecular dynamics toolkit for novices and experts. Sci. Rep. 6, 26536 (2016).
pubmed: 27216779
pmcid: 4877583
doi: 10.1038/srep26536
Bernardi, R. C. et al. Mechanisms of nanonewton mechanostability in a protein complex revealed by molecular dynamics simulations and single-molecule force spectroscopy. J. Am. Chem. Soc. 141, 14752–14763 (2019).
pubmed: 31464132
pmcid: 6939381
doi: 10.1021/jacs.9b06776
Best, R. B. et al. Optimization of the additive CHARMM all-atom protein force field targeting improved sampling of the backbone ϕ, ψ and side-chain χ
pubmed: 23341755
pmcid: 3549273
doi: 10.1021/ct300400x
MacKerell, A. D. et al. All-atom empirical potential for molecular modeling and dynamics studies of proteins. J. Phys. Chem. B 102, 3586–3616 (1998).
pubmed: 24889800
doi: 10.1021/jp973084f
Jorgensen, W. L., Chandrasekhar, J., Madura, J. D., Impey, R. W. & Klein, M. L. Comparison of simple potential functions for simulating liquid water. J. Chem. Phys. 79, 926–935 (1998).
doi: 10.1063/1.445869
Darden, T., York, D. & Pedersen, L. Particle mesh Ewald: an N⋅log(N) method for Ewald sums in large systems. J. Chem. Phys. 98, 10089–10092 (1993).
doi: 10.1063/1.464397
Phillips, J. C. et al. Scalable molecular dynamics with NAMD. J. Comput. Chem. 26, 1781–1802 (2005).
pubmed: 16222654
pmcid: 2486339
doi: 10.1002/jcc.20289
Efron, B. & Tibshirani, R. J. An Introduction to the Bootstrap 372–391 (CRC Press, 1994).
Virtanen, P. et al. SciPy 1.0: fundamental algorithms for scientific computing in Python. Nat. Methods 17, 261–272 (2020).
pubmed: 32015543
pmcid: 7056644
doi: 10.1038/s41592-019-0686-2
Pedregosa, F. et al. Scikit-learn: machine learning in Python. J. Mach. Learn. Res. 12, 2825–2830 (2011).
Hagberg, A. A., Schult, D. A. & Swart, P. J. ExplorkX. In Proc. 7th Python in Science Conference https://www.osti.gov/servlets/purl/960616 (2008).
Hunter, J. D. Matplotlib: a 2D graphics environment. Comput. Sci. Eng. 9, 90–95 (2007).
doi: 10.1109/MCSE.2007.55