Predicting Alpha Helical Transmembrane Proteins Using HMMs

  • Georgios N. Tsaousis
  • Margarita C. Theodoropoulou
  • Stavros J. Hamodrakas
  • Pantelis G. Bagos
Part of the Methods in Molecular Biology book series (MIMB, volume 1552)


Alpha helical transmembrane (TM) proteins constitute an important structural class of membrane proteins involved in a wide variety of cellular functions. The prediction of their transmembrane topology, as well as their discrimination in newly sequenced genomes, is of great importance for the elucidation of their structure and function. Several methods have been applied for the prediction of the transmembrane segments and the topology of alpha helical 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 alpha helical 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 alpha helices in proteins and discriminating them from globular proteins.

Key words

Hidden Markov model Algorithms Prediction Membrane Transmembrane Alpha helical Protein 


  1. 1.
    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):567–580PubMedCrossRefGoogle Scholar
  2. 2.
    Berman HM, Westbrook J, Feng Z et al (2000) The Protein Data Bank. Nucleic Acids Res 28(1):235–242, doi:gkd090 [pii]PubMedPubMedCentralCrossRefGoogle Scholar
  3. 3.
    Punta M, Forrest LR, Bigelow H et al (2007) Membrane protein prediction methods. Methods 41(4):460–474. doi: 10.1016/j.ymeth.2006.07.026 PubMedPubMedCentralCrossRefGoogle Scholar
  4. 4.
    Kyte J, Doolittle RF (1982) A simple method for displaying the hydropathic character of a protein. J Mol Biol 157(1):105–132, doi:0022-2836(82)90515-0 [pii]PubMedCrossRefGoogle Scholar
  5. 5.
    Claros MG, von Heijne G (1994) TopPred II: an improved software for membrane protein structure predictions. Comput Appl Biosci 10(6):685–686PubMedGoogle Scholar
  6. 6.
    Sipos L, von Heijne G (1993) Predicting the topology of eukaryotic membrane proteins. Eur J Biochem 213(3):1333–1340PubMedCrossRefGoogle Scholar
  7. 7.
    Pasquier C, Promponas VJ, Palaios GA et al (1999) A novel method for predicting transmembrane segments in proteins based on a statistical analysis of the SwissProt database: the PRED-TMR algorithm. Protein Eng Des Sel 12(5):381–385CrossRefGoogle Scholar
  8. 8.
    Jones DT, Taylor WR, Thornton JM (1994) A model recognition approach to the prediction of all-helical membrane protein structure and topology. Biochemistry 33(10):3038–3049PubMedCrossRefGoogle Scholar
  9. 9.
    Rost B, Casadio R, Fariselli P et al (1995) Transmembrane helices predicted at 95% accuracy. Protein Sci 4(3):521–533PubMedPubMedCentralCrossRefGoogle Scholar
  10. 10.
    Pasquier C, Hamodrakas SJ (1999) An hierarchical artificial neural network system for the classification of transmembrane proteins. Protein Eng Des Sel 12(8):631–634CrossRefGoogle Scholar
  11. 11.
    Sonnhammer EL, von Heijne G, Krogh A (1998) A hidden Markov model for predicting transmembrane helices in protein sequences. Proc Int Conf Intell Syst Mol Biol 6:175–182PubMedGoogle Scholar
  12. 12.
    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 PubMedPubMedCentralCrossRefGoogle Scholar
  13. 13.
    Kall L, Krogh A, Sonnhammer EL (2004) A combined transmembrane topology and signal peptide prediction method. J Mol Biol 338(5):1027–1036. doi: 10.1016/j.jmb.2004.03.016 PubMedCrossRefGoogle Scholar
  14. 14.
    Tusnady GE, Simon I (2001) The HMMTOP transmembrane topology prediction server. Bioinformatics 17(9):849–850PubMedCrossRefGoogle Scholar
  15. 15.
    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 PubMedPubMedCentralCrossRefGoogle Scholar
  16. 16.
    Nugent T, Jones DT (2009) Transmembrane protein topology prediction using support vector machines. BMC Bioinformatics 10:159. doi: 10.1186/1471-2105-10-159 PubMedPubMedCentralCrossRefGoogle Scholar
  17. 17.
    Reynolds SM, Kall L, Riffle ME et al (2008) Transmembrane topology and signal peptide prediction using dynamic Bayesian networks. PLoS Comput Biol 4(11):e1000213. doi: 10.1371/journal.pcbi.1000213 PubMedPubMedCentralCrossRefGoogle Scholar
  18. 18.
    Viklund H, Elofsson A (2008) OCTOPUS: improving topology prediction by two-track ANN-based preference scores and an extended topological grammar. Bioinformatics 24(15):1662–1668. doi: 10.1093/bioinformatics/btn221 PubMedCrossRefGoogle Scholar
  19. 19.
    Viklund H, Bernsel A, Skwark M et al (2008) SPOCTOPUS: a combined predictor of signal peptides and membrane protein topology. Bioinformatics 24(24):2928–2929. doi: 10.1093/bioinformatics/btn550 PubMedCrossRefGoogle Scholar
  20. 20.
    Promponas VJ, Palaios GA, Pasquier CM et al (1999) CoPreTHi: a Web tool which combines transmembrane protein segment prediction methods. In Silico Biol 1(3):159–162, doi:1998010014 [pii]PubMedGoogle Scholar
  21. 21.
    Nilsson J, Persson B, Von Heijne G (2002) Prediction of partial membrane protein topologies using a consensus approach. Protein Sci 11(12):2974–2980. doi: 10.1110/ps.0226702 PubMedPubMedCentralCrossRefGoogle Scholar
  22. 22.
    Bernsel A, Viklund H, Hennerdal A et al (2009) TOPCONS: consensus prediction of membrane protein topology. Nucleic Acids Res 37(Web Server issue):W465–W468. doi: 10.1093/nar/gkp363 PubMedPubMedCentralCrossRefGoogle Scholar
  23. 23.
    Klammer M, Messina DN, Schmitt T et al (2009) MetaTM—a consensus method for transmembrane protein topology prediction. BMC Bioinformatics 10:314. doi: 10.1186/1471-2105-10-314 PubMedPubMedCentralCrossRefGoogle Scholar
  24. 24.
    Moller S, Croning MD, Apweiler R (2001) Evaluation of methods for the prediction of membrane spanning regions. Bioinformatics 17(7):646–653PubMedCrossRefGoogle Scholar
  25. 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 PubMedPubMedCentralCrossRefGoogle Scholar
  26. 26.
    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 PubMedCrossRefGoogle Scholar
  27. 27.
    Delano WL (2002) The PyMOL molecular graphics system.
  28. 28.
    Almen MS, Nordstrom KJ, Fredriksson R et al (2009) Mapping the human membrane proteome: a majority of the human membrane proteins can be classified according to function and evolutionary origin. BMC Biol 7:50. doi: 10.1186/1741-7007-7-50 PubMedPubMedCentralCrossRefGoogle Scholar
  29. 29.
    Bowie JU (1997) Helix packing angle preferences. Nat Struct Biol 4(11):915–917PubMedCrossRefGoogle Scholar
  30. 30.
    Chen H, Kendall DA (1995) Artificial transmembrane segments. Requirements for stop transfer and polypeptide orientation. J Biol Chem 270(23):14115–14122PubMedCrossRefGoogle Scholar
  31. 31.
    Nilsson I, von Heijne G (1998) Breaking the camel’s back: proline-induced turns in a model transmembrane helix. J Mol Biol 284(4):1185–1189. doi: 10.1006/jmbi.1998.2219 PubMedCrossRefGoogle Scholar
  32. 32.
    Wallin E, Tsukihara T, Yoshikawa S et al (1997) Architecture of helix bundle membrane proteins: an analysis of cytochrome c oxidase from bovine mitochondria. Protein Sci 6(4):808–815. doi: 10.1002/pro.5560060407 PubMedPubMedCentralCrossRefGoogle Scholar
  33. 33.
    Weiss MS, Kreusch A, Schiltz E et al (1991) The structure of porin from Rhodobacter capsulatus at 1.8 A resolution. FEBS Lett 280(2):379–382, doi:0014-5793(91)80336-2 [pii]PubMedCrossRefGoogle Scholar
  34. 34.
    von Heijne G (1992) Membrane protein structure prediction. Hydrophobicity analysis and the positive-inside rule. J Mol Biol 225(2):487–494CrossRefGoogle Scholar
  35. 35.
    Nilsson J, Persson B, von Heijne G (2005) Comparative analysis of amino acid distributions in integral membrane proteins from 107 genomes. Proteins 60(4):606–616. doi: 10.1002/prot.20583 PubMedCrossRefGoogle Scholar
  36. 36.
    Gafvelin G, Sakaguchi M, Andersson H et al (1997) Topological rules for membrane protein assembly in eukaryotic cells. J Biol Chem 272(10):6119–6127PubMedCrossRefGoogle Scholar
  37. 37.
    Andersson H, von Heijne G (1993) Sec dependent and sec independent assembly of E. coli inner membrane proteins: the topological rules depend on chain length. EMBO J 12(2):683–691PubMedPubMedCentralGoogle Scholar
  38. 38.
    Bogdanov M, Xie J, Dowhan W (2009) Lipid-protein interactions drive membrane protein topogenesis in accordance with the positive inside rule. J Biol Chem 284(15):9637–9641. doi: 10.1074/jbc.R800081200 PubMedPubMedCentralCrossRefGoogle Scholar
  39. 39.
    van Klompenburg W, Nilsson I, von Heijne G et al (1997) Anionic phospholipids are determinants of membrane protein topology. EMBO J 16(14):4261–4266PubMedPubMedCentralCrossRefGoogle Scholar
  40. 40.
    von Heijne G (1991) Proline kinks in transmembrane alpha-helices. J Mol Biol 218(3):499–503, doi:0022-2836(91)90695-3 [pii]CrossRefGoogle Scholar
  41. 41.
    Sansom MS (1992) Proline residues in transmembrane helices of channel and transport proteins: a molecular modelling study. Protein Eng 5(1):53–60PubMedCrossRefGoogle Scholar
  42. 42.
    Park SH, Opella SJ (2005) Tilt angle of a trans-membrane helix is determined by hydrophobic mismatch. J Mol Biol 350(2):310–318. doi: 10.1016/j.jmb.2005.05.004 PubMedCrossRefGoogle Scholar
  43. 43.
    Yeagle PL, Bennett M, Lemaitre V et al (2007) Transmembrane helices of membrane proteins may flex to satisfy hydrophobic mismatch. Biochim Biophys Acta 1768(3):530–537. doi: 10.1016/j.bbamem.2006.11.018 PubMedCrossRefGoogle Scholar
  44. 44.
    Granseth E, von Heijne G, Elofsson A (2005) A study of the membrane-water interface region of membrane proteins. J Mol Biol 346(1):377–385. doi: 10.1016/j.jmb.2004.11.036 PubMedCrossRefGoogle Scholar
  45. 45.
    Liang J, Adamian L, Jackups R Jr (2005) The membrane-water interface region of membrane proteins: structural bias and the anti-snorkeling effect. Trends Biochem Sci 30(7):355–357. doi: 10.1016/j.tibs.2005.05.003 PubMedCrossRefGoogle Scholar
  46. 46.
    Viklund H, Granseth E, Elofsson A (2006) Structural classification and prediction of reentrant regions in alpha-helical transmembrane proteins: application to complete genomes. J Mol Biol 361(3):591–603. doi: 10.1016/j.jmb.2006.06.037 PubMedCrossRefGoogle Scholar
  47. 47.
    Yan C, Luo J (2010) An analysis of reentrant loops. Protein J 29(5):350–354. doi: 10.1007/s10930-010-9259-z PubMedCrossRefGoogle Scholar
  48. 48.
    Van den Berg B, Clemons WM Jr, Collinson I et al (2004) X-ray structure of a protein-conducting channel. Nature 427(6969):36–44. doi: 10.1038/nature02218 PubMedCrossRefGoogle Scholar
  49. 49.
    Dutzler R, Campbell EB, Cadene M et al (2002) X-ray structure of a ClC chloride channel at 3.0 A reveals the molecular basis of anion selectivity. Nature 415(6869):287–294. doi: 10.1038/415287a PubMedCrossRefGoogle Scholar
  50. 50.
    Zhou Y, Morais-Cabral JH, Kaufman A et al (2001) Chemistry of ion coordination and hydration revealed by a K+ channel-Fab complex at 2.0 A resolution. Nature 414(6859):43–48. doi: 10.1038/35102009 PubMedCrossRefGoogle Scholar
  51. 51.
    Mitsuoka K, Murata K, Walz T et al (1999) The structure of aquaporin-1 at 4.5-A resolution reveals short alpha-helices in the center of the monomer. J Struct Biol 128(1):34–43. doi: 10.1006/jsbi.1999.4177 PubMedCrossRefGoogle Scholar
  52. 52.
    Rapp M, Granseth E, Seppala S et al (2006) Identification and evolution of dual-topology membrane proteins. Nat Struct Mol Biol 13(2):112–116. doi: 10.1038/nsmb1057 PubMedCrossRefGoogle Scholar
  53. 53.
    Rost B (1996) PHD: predicting one-dimensional protein structure by profile-based neural networks. Methods Enzymol 266:525–539PubMedCrossRefGoogle Scholar
  54. 54.
    Tusnady GE, Simon I (1998) Principles governing amino acid composition of integral membrane proteins: application to topology prediction. J Mol Biol 283(2):489–506. doi: 10.1006/jmbi.1998.2107 PubMedCrossRefGoogle Scholar
  55. 55.
    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 PubMedCrossRefGoogle Scholar
  56. 56.
    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 PubMedCrossRefGoogle Scholar
  57. 57.
    Tsirigos KD, Peters C, Shu N et al (2015) The TOPCONS web server for consensus prediction of membrane protein topology and signal peptides. Nucleic Acids Res 43(W1):W401–W407. doi: 10.1093/nar/gkv485 PubMedPubMedCentralCrossRefGoogle Scholar
  58. 58.
    Bernsel A, Viklund H, Falk J et al (2008) Prediction of membrane-protein topology from first principles. Proc Natl Acad Sci U S A 105(20):7177–7181. doi: 10.1073/pnas.0711151105 PubMedPubMedCentralCrossRefGoogle Scholar
  59. 59.
    Peters C, Tsirigos KD, Shu N et al (2015) Improved topology prediction using the terminal hydrophobic helices rule. Bioinformatics 32:1158–1162. doi: 10.1093/bioinformatics/btv709 PubMedCrossRefGoogle Scholar
  60. 60.
    Hessa T, Meindl-Beinker NM, Bernsel A et al (2007) Molecular code for transmembrane-helix recognition by the Sec61 translocon. Nature 450(7172):1026–1030. doi: 10.1038/nature06387 PubMedCrossRefGoogle Scholar
  61. 61.
    Granseth E, Viklund H, Elofsson A (2006) ZPRED: predicting the distance to the membrane center for residues in alpha-helical membrane proteins. Bioinformatics 22(14):e191–e196. doi: 10.1093/bioinformatics/btl206 PubMedCrossRefGoogle Scholar
  62. 62.
    van Geest M, Lolkema JS (2000) Membrane topology and insertion of membrane proteins: search for topogenic signals. Microbiol Mol Biol Rev 64(1):13–33PubMedPubMedCentralCrossRefGoogle Scholar
  63. 63.
    Bernsel A, Von Heijne G (2005) Improved membrane protein topology prediction by domain assignments. Protein Sci 14(7):1723–1728. doi: 10.1110/ps.051395305 PubMedPubMedCentralCrossRefGoogle Scholar
  64. 64.
    Letunic I, Copley RR, Pils B et al (2006) SMART 5: domains in the context of genomes and networks. Nucleic Acids Res 34(Database issue):D257–D260. doi: 10.1093/nar/gkj079 PubMedCrossRefGoogle Scholar
  65. 65.
    Mulder NJ, Apweiler R, Attwood TK et al (2007) New developments in the InterPro database. Nucleic Acids Res 35(Database issue):D224–D228. doi: 10.1093/nar/gkl841 PubMedPubMedCentralCrossRefGoogle Scholar
  66. 66.
    Finn RD, Tate J, Mistry J et al (2008) The Pfam protein families database. Nucleic Acids Res 36(Database issue):D281–D288. doi: 10.1093/nar/gkm960 PubMedGoogle Scholar
  67. 67.
    Tusnady GE, Kalmar L, Hegyi H et al (2008) TOPDOM: database of domains and motifs with conservative location in transmembrane proteins. Bioinformatics 24(12):1469–1470. doi: 10.1093/bioinformatics/btn202 PubMedPubMedCentralCrossRefGoogle Scholar
  68. 68.
    Rabiner L (1989) A tutorial on hidden Markov models and selected applications in speech recognition. Proc IEEE 77(2):257–286CrossRefGoogle Scholar
  69. 69.
    Eddy SR (1998) Profile hidden Markov models. Bioinformatics 14(9):755–763, doi:btb114 [pii]PubMedCrossRefGoogle Scholar
  70. 70.
    Nielsen H, Krogh A (1998) Prediction of signal peptides and signal anchors by a hidden Markov model. Proc Int Conf Intell Syst Mol Biol 6:122–130PubMedGoogle Scholar
  71. 71.
    Krogh A (1994) Hidden Markov models for labelled sequences. In: Proceedings of the12th IAPR international conference on pattern recognition, pp 140–144Google Scholar
  72. 72.
    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–S53PubMedCrossRefGoogle Scholar
  73. 73.
    Khoury GA, Baliban RC, Floudas CA (2011) Proteome-wide post-translational modification statistics: frequency analysis and curation of the swiss-prot database. Sci Rep 1:90. doi: 10.1038/srep00090 PubMedCentralCrossRefGoogle Scholar
  74. 74.
    Apweiler R, Hermjakob H, Sharon N (1999) On the frequency of protein glycosylation, as deduced from analysis of the SWISS-PROT database. Biochim Biophys Acta 1473(1):4–8, doi:S0304-4165(99)00165-8 [pii]PubMedCrossRefGoogle Scholar
  75. 75.
    Welply JK, Shenbagamurthi P, Lennarz WJ et al (1983) Substrate recognition by oligosaccharyltransferase. Studies on glycosylation of modified Asn-X-Thr/Ser tripeptides. J Biol Chem 258(19):11856–11863PubMedGoogle Scholar
  76. 76.
    Nilsson IM, von Heijne G (1993) Determination of the distance between the oligosaccharyltransferase active site and the endoplasmic reticulum membrane. J Biol Chem 268(8):5798–5801PubMedGoogle Scholar
  77. 77.
    Popov M, Li J, Reithmeier RA (1999) Transmembrane folding of the human erythrocyte anion exchanger (AE1, Band 3) determined by scanning and insertional N-glycosylation mutagenesis. Biochem J 339(Pt 2):269–279PubMedPubMedCentralCrossRefGoogle Scholar
  78. 78.
    Popov M, Tam LY, Li J et al (1997) Mapping the ends of transmembrane segments in a polytopic membrane protein. Scanning N-glycosylation mutagenesis of extracytosolic loops in the anion exchanger, band 3. J Biol Chem 272(29):18325–18332PubMedCrossRefGoogle Scholar
  79. 79.
    Landolt-Marticorena C, Reithmeier RA (1994) Asparagine-linked oligosaccharides are localized to single extracytosolic segments in multi-span membrane glycoproteins. Biochem J 302(Pt 1):253–260PubMedPubMedCentralCrossRefGoogle Scholar
  80. 80.
    Pawson T, Scott JD (2005) Protein phosphorylation in signaling—50 years and counting. Trends Biochem Sci 30(6):286–290. doi: 10.1016/j.tibs.2005.04.013 PubMedCrossRefGoogle Scholar
  81. 81.
    Hunter T (2009) Tyrosine phosphorylation: thirty years and counting. Curr Opin Cell Biol 21(2):140–146. doi: 10.1016/ PubMedPubMedCentralCrossRefGoogle Scholar
  82. 82.
    Wood CD, Thornton TM, Sabio G et al (2009) Nuclear localization of p38 MAPK in response to DNA damage. Int J Biol Sci 5(5):428–437PubMedPubMedCentralCrossRefGoogle Scholar
  83. 83.
    Zhang J, Johnson GV (2000) Tau protein is hyperphosphorylated in a site-specific manner in apoptotic neuronal PC12 cells. J Neurochem 75(6):2346–2357PubMedCrossRefGoogle Scholar
  84. 84.
    Kalume DE, Molina H, Pandey A (2003) Tackling the phosphoproteome: tools and strategies. Curr Opin Chem Biol 7(1):64–69, doi:S1367593102000091 [pii]PubMedCrossRefGoogle Scholar
  85. 85.
    Tsaousis GN, Bagos PG, Hamodrakas SJ (2014) HMMpTM: Improving transmembrane protein topology prediction using phosphorylation and glycosylation site prediction. Biochim Biophys Acta 1844(2):316–322. doi: 10.1016/j.bbapap.2013.11.001 PubMedCrossRefGoogle Scholar
  86. 86.
    Wistrand M, Käll L, Sonnhammer EL (2006) A general model of G protein-coupled receptor sequences and its application to detect remote homologs. Protein Sci 15(3):509–521. doi: 10.1110/ps.051745906 PubMedPubMedCentralCrossRefGoogle Scholar
  87. 87.
    Theodoropoulou MC, Tsaousis GN, Litou ZI et al (2013) GPCRpipe: a pipeline for the detection of G-protein coupled receptors in proteomes. In: Joint 21st annual international conference on Intelligent Systems for Molecular Biology (ISMB) and 12th European Conference on Computational Biology (ECCB), 2013Google Scholar
  88. 88.
    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 PubMedCrossRefGoogle Scholar
  89. 89.
    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 PubMedCrossRefGoogle Scholar
  90. 90.
    Tsaousis GN, Tsirigos KD, Andrianou XD et al (2010) ExTopoDB: a database of experimentally derived topological models of transmembrane proteins. Bioinformatics 26(19):2490–2492. doi: 10.1093/bioinformatics/btq362 PubMedCrossRefGoogle Scholar
  91. 91.
    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]PubMedPubMedCentralCrossRefGoogle Scholar
  92. 92.
    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 PubMedPubMedCentralCrossRefGoogle Scholar
  93. 93.
    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 PubMedCrossRefGoogle Scholar
  94. 94.
    Baldi P, Brunak S, Chauvin Y et al (2000) Assessing the accuracy of prediction algorithms for classification: an overview. Bioinformatics 16(5):412–424PubMedCrossRefGoogle Scholar
  95. 95.
    Baum LE (1972) An inequality and associated maximization technique in statistical estimation for probabilistic functions of Markov processes. Inequalities 3:1–8Google Scholar
  96. 96.
    Dempster AP, Laird NM, Rubin DB (1977) Maximum likelihood from incomplete data via the EM algorithm. J R Stat Soc B Methodol 39(1):1–38. doi: 10.2307/2984875 Google Scholar
  97. 97.
    Krogh A (1997) Two methods for improving performance of an HMM and their application for gene finding. Proc Int Conf Intell Syst Mol Biol 5:179–186PubMedGoogle Scholar
  98. 98.
    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 CrossRefGoogle Scholar
  99. 99.
    Krogh A, Riis SK (1999) Hidden neural networks. Neural Comput 11(2):541–563PubMedCrossRefGoogle Scholar
  100. 100.
    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
  101. 101.
    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 PubMedPubMedCentralCrossRefGoogle Scholar
  102. 102.
    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):500–505PubMedCrossRefGoogle Scholar
  103. 103.
    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):S12PubMedPubMedCentralCrossRefGoogle Scholar
  104. 104.
    Virkki MT, Peters C, Nilsson D et al (2014) The positive inside rule is stronger when followed by a transmembrane helix. J Mol Biol 426(16):2982–2991. doi: 10.1016/j.jmb.2014.06.002 PubMedCrossRefGoogle Scholar
  105. 105.
    Wang H, Zhang C, Shi X et al (2012) Improving transmembrane protein consensus topology prediction using inter-helical interaction. Biochim Biophys Acta 1818(11):2679–2686. doi: 10.1016/j.bbamem.2012.05.030 PubMedCrossRefGoogle Scholar
  106. 106.
    Nugent T, Ward S, Jones DT (2011) The MEMPACK alpha-helical transmembrane protein structure prediction server. Bioinformatics 27(10):1438–1439. doi: 10.1093/bioinformatics/btr096 PubMedPubMedCentralCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media LLC 2017

Authors and Affiliations

  • Georgios N. Tsaousis
    • 1
  • Margarita C. Theodoropoulou
    • 1
    • 2
  • Stavros J. Hamodrakas
    • 1
  • Pantelis G. Bagos
    • 2
  1. 1.Department of Cell Biology and Biophysics, Faculty of BiologyNational and Kapodistrian University of AthensAthensGreece
  2. 2.Department of Computer Science and Biomedical InformaticsUniversity of ThessalyLamiaGreece

Personalised recommendations