Skip to main content
SpringerLink
Log in

Predicting Beta Barrel Transmembrane Proteins Using HMMs

  • Protocol
  • First Online:
Hidden Markov Models

Part of the book series: Methods in Molecular Biology ((MIMB,volume 1552))

Abstract

Transmembrane beta-barrels (TMBBs) constitute an important structural class of membrane proteins located in the outer membrane of gram-negative bacteria, and in the outer membrane of chloroplasts and mitochondria. They are involved in a wide variety of cellular functions and the prediction of their transmembrane topology, as well as their discrimination in newly sequenced genomes is of great importance as they are promising targets for antimicrobial drugs and vaccines. Several methods have been applied for the prediction of the transmembrane segments and the topology of beta barrel transmembrane proteins utilizing different algorithmic techniques. Hidden Markov Models (HMMs) have been efficiently used in the development of several computational methods used for this task. In this chapter we give a brief review of different available prediction methods for beta barrel transmembrane proteins pointing out sequence and structural features that should be incorporated in a prediction method. We then describe the procedure of the design and development of a Hidden Markov Model capable of predicting the transmembrane beta strands of TMBBs and discriminating them from globular proteins.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Protocol
USD 49.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 99.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 129.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 179.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Schulz GE (2003) Transmembrane beta-barrel proteins. Adv Protein Chem 63:47–70

    Article  CAS  PubMed  Google Scholar 

  2. Wimley WC (2003) The versatile beta-barrel membrane protein. Curr Opin Struct Biol 13(4):404–411

    Article  CAS  PubMed  Google Scholar 

  3. Bagos PG, Hamodrakas SJ (2009) Bacterial beta-barrel outer membrane proteins: a common structural theme implicated in a wide variety of functional roles. In: Daskalaki A (ed) Handbook of research on systems biology applications in medicine, pp: 182–207. doi:10.4018/978–1-60566-076-9.ch010

  4. Tsirigos KD, Bagos PG, Hamodrakas SJ (2011) OMPdb: a database of {beta}-barrel outer membrane proteins from Gram-negative bacteria. Nucleic Acids Res 39(Database issue):D324–D331. doi:10.1093/nar/gkq863

    Article  CAS  PubMed  Google Scholar 

  5. Vogel H, Jahnig F (1986) Models for the structure of outer-membrane proteins of Escherichia coli derived from Raman spectroscopy and prediction methods. J Mol Biol 190(2):191–199, doi:0022-2836(86)90292-5 [pii]

    Article  CAS  PubMed  Google Scholar 

  6. Jeanteur D, Lakey JH, Pattus F (1991) The bacterial porin superfamily: sequence alignment and structure prediction. Mol Microbiol 5(9):2153–2164

    Article  CAS  PubMed  Google Scholar 

  7. Rauch G, Moran O (1995) Prediction of polypeptide secondary structures analysing the oscillation of the hydropathy profile. Comput Methods Programs Biomed 48(3):193–200, doi:0169260795016988 [pii]

    Article  CAS  PubMed  Google Scholar 

  8. Schirmer T, Cowan SW (1993) Prediction of membrane-spanning beta-strands and its application to maltoporin. Protein Sci 2(8):1361–1363. doi:10.1002/pro.5560020820

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  9. Neuwald AF, Liu JS, Lawrence CE (1995) Gibbs motif sampling: detection of bacterial outer membrane protein repeats. Protein Sci 4(8):1618–1632. doi:10.1002/pro.5560040820

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  10. Gromiha MM, Majumdar R, Ponnuswamy PK (1997) Identification of membrane spanning beta strands in bacterial porins. Protein Eng 10(5):497–500

    Article  CAS  PubMed  Google Scholar 

  11. Diederichs K, Freigang J, Umhau S et al (1998) Prediction by a neural network of outer membrane beta-strand protein topology. Protein Sci 7(11):2413–2420. doi:10.1002/pro.5560071119

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  12. Gromiha MM, Ahmad S, Suwa M (2004) Neural network-based prediction of transmembrane beta-strand segments in outer membrane proteins. J Comput Chem 25(5):762–767. doi:10.1002/jcc.10386

    Article  CAS  PubMed  Google Scholar 

  13. Jacoboni I, Martelli PL, Fariselli P et al (2001) Prediction of the transmembrane regions of beta-barrel membrane proteins with a neural network-based predictor. Protein Sci 10(4):779–787. doi:10.1110/ps.37201

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  14. Bagos PG, Liakopoulos TD, Spyropoulos IC et al (2004) A Hidden Markov Model method, capable of predicting and discriminating beta-barrel outer membrane proteins. BMC Bioinformatics 5:29. doi:10.1186/1471-2105-5-29

    Article  PubMed  PubMed Central  Google Scholar 

  15. Bigelow HR, Petrey DS, Liu J et al (2004) Predicting transmembrane beta-barrels in proteomes. Nucleic Acids Res 32(8):2566–2577. doi:10.1093/nar/gkh580

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  16. Martelli PL, Fariselli P, Krogh A et al (2002) A sequence-profile-based HMM for predicting and discriminating beta barrel membrane proteins. Bioinformatics 18(Suppl 1):S46–S53

    Article  PubMed  Google Scholar 

  17. Park KJ, Gromiha MM, Horton P et al (2005) Discrimination of outer membrane proteins using support vector machines. Bioinformatics 21(23):4223–4229. doi:10.1093/bioinformatics/bti697

    Article  CAS  PubMed  Google Scholar 

  18. Garrow AG, Agnew A, Westhead DR (2005) TMB-Hunt: an amino acid composition based method to screen proteomes for beta-barrel transmembrane proteins. BMC Bioinformatics 6:56. doi:10.1186/1471-2105-6-56

    Article  PubMed  PubMed Central  Google Scholar 

  19. Yan C, Hu J, Wang Y (2008) Discrimination of outer membrane proteins using a K-nearest neighbor method. Amino Acids 35(1):65–73. doi:10.1007/s00726-007-0628-7

    Article  CAS  PubMed  Google Scholar 

  20. Lin H (2008) The modified Mahalanobis Discriminant for predicting outer membrane proteins by using Chou’s pseudo amino acid composition. J Theor Biol 252(2):350–356. doi:10.1016/j.jtbi.2008.02.004

    Article  CAS  PubMed  Google Scholar 

  21. Ou YY, Gromiha MM, Chen SA et al (2008) TMBETADISC-RBF: discrimination of beta-barrel membrane proteins using RBF networks and PSSM profiles. Comput Biol Chem 32(3):227–231. doi:10.1016/j.compbiolchem.2008.03.002

    Article  CAS  PubMed  Google Scholar 

  22. Fariselli P, Savojardo C, Martelli PL et al (2009) Grammatical-restrained hidden conditional random fields for bioinformatics applications. Algorithms Mol Biol 4:13. doi:10.1186/1748-7188-4-13

    Article  PubMed  PubMed Central  Google Scholar 

  23. Hayat S, Elofsson A (2012) BOCTOPUS: improved topology prediction of transmembrane beta barrel proteins. Bioinformatics 28(4):516–522. doi:10.1093/bioinformatics/btr710

    Article  CAS  PubMed  Google Scholar 

  24. Natt NK, Kaur H, Raghava GP (2004) Prediction of transmembrane regions of beta-barrel proteins using ANN- and SVM-based methods. Proteins 56(1):11–18. doi:10.1002/prot.20092

    Article  CAS  PubMed  Google Scholar 

  25. Bagos PG, Liakopoulos TD, Hamodrakas SJ (2005) Evaluation of methods for predicting the topology of beta-barrel outer membrane proteins and a consensus prediction method. BMC Bioinformatics 6:7. doi:10.1186/1471-2105-6-7

    Article  PubMed  PubMed Central  Google Scholar 

  26. von Heijne G (1992) Membrane protein structure prediction. Hydrophobicity analysis and the positive-inside rule. J Mol Biol 225(2):487–494

    Article  Google Scholar 

  27. Bannwarth M, Schulz GE (2003) The expression of outer membrane proteins for crystallization. Biochim Biophys Acta 1610(1):37–45, doi:S0005273602007113 [pii]

    Article  CAS  PubMed  Google Scholar 

  28. Pautsch A, Schulz GE (1998) Structure of the outer membrane protein A transmembrane domain. Nat Struct Biol 5(11):1013–1017. doi:10.1038/2983

    Article  CAS  PubMed  Google Scholar 

  29. Kozma D, Simon I, Tusnady GE (2013) PDBTM: Protein Data Bank of transmembrane proteins after 8 years. Nucleic Acids Res 41(Database issue):D524–D529. doi:10.1093/nar/gks1169

    Article  CAS  PubMed  Google Scholar 

  30. Delano WL (2002) The PyMOL molecular graphics system. http://www.pymol.org

  31. Schulz GE (2002) The structure of bacterial outer membrane proteins. Biochim Biophys Acta 1565(2):308–317, doi:S0005273602005771 [pii]

    Article  CAS  PubMed  Google Scholar 

  32. Wimley WC (2002) Toward genomic identification of beta-barrel membrane proteins: composition and architecture of known structures. Protein Sci 11(2):301–312. doi:10.1110/ps.29402

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  33. Gromiha MM, Ponnuswamy PK (1993) Prediction of transmembrane beta-strands from hydrophobic characteristics of proteins. Int J Pept Protein Res 42(5):420–431

    Article  CAS  PubMed  Google Scholar 

  34. Zhai Y, Saier MH Jr (2002) The beta-barrel finder (BBF) program, allowing identification of outer membrane beta-barrel proteins encoded within prokaryotic genomes. Protein Sci 11(9):2196–2207. doi:10.1110/ps.0209002

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  35. Bishop CM, Walkenhorst WF, Wimley WC (2001) Folding of beta-sheets in membranes: specificity and promiscuity in peptide model systems. J Mol Biol 309(4):975–988. doi:10.1006/jmbi.2001.4715

    Article  CAS  PubMed  Google Scholar 

  36. Gnanasekaran TV, Peri S, Arockiasamy A et al (2000) Profiles from structure based sequence alignment of porins can identify beta stranded integral membrane proteins. Bioinformatics 16(9):839–842

    Article  CAS  PubMed  Google Scholar 

  37. Freeman TC Jr, Wimley WC (2010) A highly accurate statistical approach for the prediction of transmembrane beta-barrels. Bioinformatics 26(16):1965–1974. doi:10.1093/bioinformatics/btq308

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  38. Liu Q, Zhu Y, Wang B et al (2003) Identification of beta-barrel membrane proteins based on amino acid composition properties and predicted secondary structure. Comput Biol Chem 27(3):355–361, doi:S1476927102000853 [pii]

    Article  CAS  PubMed  Google Scholar 

  39. Berven FS, Flikka K, Jensen HB et al (2004) BOMP: a program to predict integral beta-barrel outer membrane proteins encoded within genomes of Gram-negative bacteria. Nucleic Acids Res 32(Web Server issue):W394–W399. doi:10.1093/nar/gkh351

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  40. Altschul SF, Madden TL, Schaffer AA et al (1997) Gapped BLAST and PSI-BLAST: a new generation of protein database search programs. Nucleic Acids Res 25(17):3389–3402, doi:gka562 [pii]

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  41. Bagos PG, Liakopoulos TD, Spyropoulos IC et al (2004) PRED-TMBB: a web server for predicting the topology of beta-barrel outer membrane proteins. Nucleic Acids Res 32(Web Server issue):W400–W404. doi:10.1093/nar/gkh417

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  42. Randall A, Cheng J, Sweredoski M et al (2008) TMBpro: secondary structure, beta-contact and tertiary structure prediction of transmembrane beta-barrel proteins. Bioinformatics 24(4):513–520. doi:10.1093/bioinformatics/btm548

    Article  CAS  PubMed  Google Scholar 

  43. Waldispuhl J, Berger B, Clote P et al (2006) transFold: a web server for predicting the structure and residue contacts of transmembrane beta-barrels. Nucleic Acids Res 34(Web Server issue):W189–193. doi:10.1093/nar/gkl205

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  44. Remmert M, Linke D, Lupas AN et al (2009) HHomp—prediction and classification of outer membrane proteins. Nucleic Acids Res 37(Web Server issue):W446–W451. doi:10.1093/nar/gkp325

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  45. Rabiner L (1989) A tutorial on hidden Markov models and selected applications in speech recognition. Proc IEEE 77(2):257–286

    Article  Google Scholar 

  46. Eddy SR (1998) Profile hidden Markov models. Bioinformatics 14(9):755–763, doi:btb114 [pii]

    Article  CAS  PubMed  Google Scholar 

  47. Krogh A, Larsson B, von Heijne G et al (2001) Predicting transmembrane protein topology with a hidden Markov model: application to complete genomes. J Mol Biol 305(3):567–580. doi:10.1006/jmbi.2000.4315

    Article  CAS  PubMed  Google Scholar 

  48. Nielsen H, Krogh A (1998) Prediction of signal peptides and signal anchors by a hidden Markov model. Proc Int Conf Intell Syst Mol Biol 6:122–130

    CAS  PubMed  Google Scholar 

  49. Krogh A, Mian IS, Haussler D (1994) A hidden Markov model that finds genes in E. coli DNA. Nucleic Acids Res 22(22):4768–4778

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  50. Krogh A (1994) Hidden Markov models for labelled sequences. In: Proceedings of the12th IAPR international conference on pattern recognition, pp 140–144

    Google Scholar 

  51. Chamberlain AK, Bowie JU (2004) Asymmetric amino acid compositions of transmembrane beta-strands. Protein Sci 13(8):2270–2274

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  52. Slusky JS, Dunbrack RL Jr (2013) Charge asymmetry in the proteins of the outer membrane. Bioinformatics 29(17):2122–2128. doi:10.1093/bioinformatics/btt355

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  53. Jackups R Jr, Liang J (2005) Interstrand pairing patterns in beta-barrel membrane proteins: the positive-outside rule, aromatic rescue, and strand registration prediction. J Mol Biol 354(4):979–993. doi:10.1016/j.jmb.2005.09.094

    Article  CAS  PubMed  Google Scholar 

  54. Berman HM, Westbrook J, Feng Z et al (2000) The Protein Data Bank. Nucleic Acids Res 28(1):235–242, doi:gkd090 [pii]

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  55. Andreeva A, Howorth D, Brenner SE et al (2004) SCOP database in 2004: refinements integrate structure and sequence family data. Nucleic Acids Res 32(Database issue):D226–D229. doi:10.1093/nar/gkh039

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  56. Lomize MA, Lomize AL, Pogozheva ID et al (2006) OPM: orientations of proteins in membranes database. Bioinformatics 22(5):623–625. doi:10.1093/bioinformatics/btk023

    Article  CAS  PubMed  Google Scholar 

  57. Dobson L, Lango T, Remenyi I et al (2015) Expediting topology data gathering for the TOPDB database. Nucleic Acids Res 43(Database issue):D283–D289. doi:10.1093/nar/gku1119

    Article  PubMed  CAS  Google Scholar 

  58. Bagos PG, Tsaousis GN, Hamodrakas SJ (2009) How many 3D structures do we need to train a predictor? Genomics Proteomics Bioinformatics 7(3):128–137. doi:10.1016/S1672-0229(08)60041-8

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  59. Bagos PG, Hamodrakas SJ (2009) Bacterial beta-barrel outer membrane proteins: a common structural theme implicated in a wide variety of functional roles. In: Daskalaki A (ed) Handbook of research on systems biology applications in medicine, pp 182–207. doi: 10.4018/978–1-60566-076-9.ch010

  60. Punta M, Coggill PC, Eberhardt RY et al (2012) The Pfam protein families database. Nucleic Acids Res 40(Database issue):D290–D301. doi:10.1093/nar/gkr1065

    Article  CAS  PubMed  Google Scholar 

  61. Fariselli P, Finelli M, Marchignoli D et al (2003) MaxSubSeq: an algorithm for segment-length optimization. The case study of the transmembrane spanning segments. Bioinformatics 19(4):500–505

    Article  CAS  PubMed  Google Scholar 

  62. Zemla A, Venclovas C, Fidelis K et al (1999) A modified definition of Sov, a segment-based measure for protein secondary structure prediction assessment. Proteins 34(2):220–223. doi:10.1002/(SICI)1097-0134(19990201)34:2<220::AID-PROT7>3.0.CO;2-K [pii]

    Article  CAS  PubMed  Google Scholar 

  63. Baldi P, Brunak S, Chauvin Y et al (2000) Assessing the accuracy of prediction algorithms for classification: an overview. Bioinformatics 16(5):412–424

    Article  CAS  PubMed  Google Scholar 

  64. Baum LE (1972) An inequality and associated maximization technique in statistical estimation for probabilistic functions of Markov processes. Inequalities 3:1–8

    Google Scholar 

  65. Dempster AP, Laird NM, Rubin DB (1977) Maximum likelihood from incomplete data via the EM algorithm. J R Stat Soc Ser B Methodol 39(1):1–38. doi:10.2307/2984875

    Google Scholar 

  66. Krogh A (1997) Two methods for improving performance of an HMM and their application for gene finding. Proc Int Conf Intell Syst Mol Biol 5:179–186

    CAS  PubMed  Google Scholar 

  67. Bagos P, Liakopoulos T, Hamodrakas S (2004) Faster gradient descent training of hidden Markov models, using individual learning rate adaptation. In: Paliouras G, Sakakibara Y (eds) Grammatical inference: algorithms and applications, vol 3264, Lecture notes in computer science. Springer, Berlin, Heidelberg, pp 40–52. doi:10.1007/978-3-540-30195-0_5

    Chapter  Google Scholar 

  68. Krogh A, Riis SK (1999) Hidden neural networks. Neural Comput 11(2):541–563

    Article  CAS  PubMed  Google Scholar 

  69. Zou L, Wang Z, Wang Y et al (2010) Combined prediction of transmembrane topology and signal peptide of beta-barrel proteins: using a hidden Markov model and genetic algorithms. Comput Biol Med 40(7):621–628. doi:10.1016/j.compbiomed.2010.04.006

    Article  PubMed  Google Scholar 

  70. Schwartz R, Chow YL (1990) The N-best algorithms: an efficient and exact procedure for finding the N most likely sentence hypotheses. In: 1990 international conference on acoustics, speech, and signal processing, 1990. ICASSP-90, 3–6 Apr 1990, vol 81, pp 81–84. doi:10.1109/icassp.1990.115542

  71. Kall L, Krogh A, Sonnhammer EL (2005) An HMM posterior decoder for sequence feature prediction that includes homology information. Bioinformatics 21(Suppl 1):i251–i257. doi:10.1093/bioinformatics/bti1014

    Article  PubMed  Google Scholar 

  72. Fariselli P, Martelli PL, Casadio R (2005) A new decoding algorithm for hidden Markov models improves the prediction of the topology of all-beta membrane proteins. BMC Bioinformatics 6(Suppl 4):S12

    Article  PubMed  PubMed Central  Google Scholar 

  73. Won KJ, Hamelryck T, Prugel-Bennett A et al (2007) An evolutionary method for learning HMM structure: prediction of protein secondary structure. BMC Bioinformatics 8:357. doi:10.1186/1471-2105-8-357

    Article  PubMed  PubMed Central  Google Scholar 

  74. Won KJ, Prugel-Bennett A, Krogh A (2004) Training HMM structure with genetic algorithm for biological sequence analysis. Bioinformatics 20(18):3613–3619. doi:10.1093/bioinformatics/bth454

    Article  CAS  PubMed  Google Scholar 

  75. Petersen TN, Brunak S, von Heijne G et al (2011) SignalP 4.0: discriminating signal peptides from transmembrane regions. Nat Methods 8(10):785–786. doi:10.1038/nmeth.1701

    Article  CAS  PubMed  Google Scholar 

  76. Lin K, Simossis VA, Taylor WR et al (2005) A simple and fast secondary structure prediction method using hidden neural networks. Bioinformatics 21(2):152–159. doi:10.1093/bioinformatics/bth487

    Article  CAS  PubMed  Google Scholar 

  77. Martelli PL, Fariselli P, Casadio R (2004) Prediction of disulfide-bonded cysteines in proteomes with a hidden neural network. Proteomics 4(6):1665–1671. doi:10.1002/pmic.200300745

    Article  CAS  PubMed  Google Scholar 

  78. Bagos PG, Liakopoulos TD, Hamodrakas SJ (2006) Algorithms for incorporating prior topological information in HMMs: application to transmembrane proteins. BMC Bioinformatics 7:189. doi:10.1186/1471-2105-7-189

    Article  PubMed  PubMed Central  Google Scholar 

  79. Viklund H, Elofsson A (2004) Best alpha-helical transmembrane protein topology predictions are achieved using hidden Markov models and evolutionary information. Protein Sci 13(7):1908–1917. doi:10.1110/ps.04625404

    Article  CAS  PubMed  PubMed Central  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Cell Biology and Biophysics, Faculty of Biology, National and Kapodistrian University of Athens, Panepistimiopolis, Athens, 15701, Greece

    Georgios N. Tsaousis & Stavros J. Hamodrakas

  2. Department of Computer Science and Biomedical Informatics, University of Thessaly, Papasiopoulou 2-4, Lamia, 35100, Greece

    Pantelis G. Bagos

Authors
  1. Georgios N. Tsaousis
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Stavros J. Hamodrakas
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Pantelis G. Bagos
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Pantelis G. Bagos .

Editor information

Editors and Affiliations

  1. University of Leeds School of Molecular and Cellular Biology, Leeds, United Kingdom

    David R. Westhead

  2. University of Leeds School of Cellular and Molecular Biology, Leeds, United Kingdom

    M. S. Vijayabaskar

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer Science+Business Media LLC

About this protocol

Cite this protocol

Tsaousis, G.N., Hamodrakas, S.J., Bagos, P.G. (2017). Predicting Beta Barrel Transmembrane Proteins Using HMMs. In: Westhead, D., Vijayabaskar, M. (eds) Hidden Markov Models. Methods in Molecular Biology, vol 1552. Humana Press, New York, NY. https://doi.org/10.1007/978-1-4939-6753-7_4

Download citation

  • DOI: https://doi.org/10.1007/978-1-4939-6753-7_4

  • Published:

  • Publisher Name: Humana Press, New York, NY

  • Print ISBN: 978-1-4939-6751-3

  • Online ISBN: 978-1-4939-6753-7

  • eBook Packages: Springer Protocols

Publish with us

Policies and ethics

Search

Navigation