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Discriminating membrane proteins using the joint distribution of length sums of success and failure runs

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Abstract

Discriminating integral membrane proteins from water-soluble ones, has been over the past decades an important goal for computational molecular biology. A major drawback of methods appeared in the literature, is that most of the authors tried to solve the problem using machine learning techniques. Specifically, most of the proposed methods require an appropriate dataset for training, and consequently the results depend heavily on the suitability of the dataset, itself. Motivated by these facts, in this paper we develop a formal discrimination procedure that is based on appropriate theoretical observations on the sequence of hydrophobic and polar residues along the protein sequence and on the exact distribution of a two dimensional runs-related statistic defined on the same sequence. Specifically, for setting up our discrimination procedure, we study thoroughly the exact distribution of a bivariate random variable, which accumulates the exact lengths of both success and failure runs of at least a specific length in a sequence of Bernoulli trials. To investigate the properties of this bivariate random variable, we use the Markov chain embedding technique. Finally, we apply the new procedure to a well-defined dataset of proteins.

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References

  • Alberts B, Johnson A, Lewis J, Raff M, Roberts K, Walter P (2002) Molecular biology of the cell, 4th edn. Garland Science, New York

    Google Scholar 

  • Antzoulakos DL, Bersimis S, Koutras MV (2003) On the distribution of the total number of run lengths. Ann Inst Stat Math 55(4):865–884

    Article  MathSciNet  MATH  Google Scholar 

  • Balakrishnan N, Koutras MV (2002) Runs and scans with applications. Wiley, New York

    MATH  Google Scholar 

  • 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 Bioinform 6:7

    Article  Google Scholar 

  • Baldi P, Brunak S (2001) Bioinformatics: the machine learning approach. MIT press, Boston

    MATH  Google Scholar 

  • Berger B, Leighton T (1998) Protein folding in the hydrophobic-hydrophilic (HP) model is NP-complete. J Comput Biol 5(1):27–40

    Article  Google Scholar 

  • Casadio R, Fariselli P, Finocchiaro G, Martelli PL (2003) Fishing new proteins in the twilight zone of genomes: the test case of outer membrane proteins in Escherichia coli K12, Escherichia coli O157:H7, and other Gram-negative bacteria. Protein Sci 12:1158–1168

    Article  Google Scholar 

  • Chakraborti S, Eryilmaz S (2007) A nonparametric Shewhart-type signed-rank control chart based on runs. Commun Stat Theory Methods 36(2):335–356

    MathSciNet  MATH  Google Scholar 

  • Dembo A, Karlin S (1992) Poisson approximations for r-scan processes. Ann Appl Probab 2:329–357

    Article  MathSciNet  MATH  Google Scholar 

  • Dill KA (1985) Theory for the folding and stability of globular proteins. Biochemistry 24(6):1501–1509

    Article  Google Scholar 

  • Eisenberg D, Schwarz E, Komaromy M, Wall R (1984) Analysis of membrane and surface protein sequences with the hydrophobic moment plot. J Mol Biol 179(1):125–142

    Article  Google Scholar 

  • Feller W (1968) An introduction to probability theory and its applications, vol I, 3rd edn. Wiley, New York

    MATH  Google Scholar 

  • Fernández A, Kardos J, Goto Y (2003) Protein folding: could hydrophobic collapse be coupled with hydrogen-bond formation? FEBS Lett 536(1):187–192

    Article  Google Scholar 

  • Freeman TC Jr, Wimley WC (2010) A highly accurate statistical approach for the prediction of transmembrane beta-barrels. Bioinformatics 26:1965–1974

    Article  Google Scholar 

  • Fu JC (1996) Distribution theory of runs and patterns associated with a sequence of multistate trials. Stat Sin 6:957–974

    MATH  Google Scholar 

  • Fu JC, Koutras MV (1994) Distribution theory of runs: a Markov chain approach. J Am Stat Assoc 89:1050–1058

    Article  MathSciNet  MATH  Google Scholar 

  • Gibbons JD, Chakraborti S (2010) Nonparametric statistical inference, 5th edn. Chapman and Hall/CRC, New York

    MATH  Google Scholar 

  • Glaz J, Naus JI (1991) Tight bounds and approximations for scan statistic probabilities for discrete data. Ann Appl Probab 1:306–318

    Article  MathSciNet  MATH  Google Scholar 

  • Glaz J, Naus J, Wallenstein S (2001) Scan statistics. Springer, New-York

    Book  MATH  Google Scholar 

  • Goldstein L (1990) Poisson approximation in DNA sequence matching. Commun Stat Theory Methods 19:4167–4179

    Article  MATH  Google Scholar 

  • Gromiha MM, Suwa M (2005) A simple statistical method for discriminating outer membrane proteins with better accuracy. Bioinformatics 21:961–968

    Article  Google Scholar 

  • Gromiha MM, Ahmad S, Suwa M (2005) Application of residue distribution along the sequence for discriminating outer membrane proteins. Comput Biol Chem 29:135–142

    Article  MATH  Google Scholar 

  • Hertz GZ, Stormo GD (1999) Identifying DNA and protein patterns with statistically significant alignments of multiple sequences. Bioinformatics 15(7):563–577

    Article  Google Scholar 

  • Karlin S, Cardon LR (1994) Computational DNA-sequence analysis. Annu Rev Microbiol 48:619–654

    Article  Google Scholar 

  • Karlin S, Macken C (1991) Some statistical problems in the assessment of inhomogeneities of DNA sequence data. J Am Stat Assoc 86:27–35

    Article  Google Scholar 

  • Koutras MV, Alexandrou VA (1995) Runs, scans and urn model distributions: a unified Markov chain approach. Ann Inst Stat Math‘ 47:743–766

    Article  MathSciNet  MATH  Google Scholar 

  • Koutras MV, Bersimis S, Antzoulakos DL (2008) Bivariate Markov chain embeddable variables of polynomial type. Ann Inst Stat Math 60(1):173–191

    Article  MathSciNet  MATH  Google Scholar 

  • Lapidus LJ et al (2007) Protein hydrophobic collapse and early folding steps observed in a microfluidic mixer. Biophys J 93(1):218–224

    Article  Google Scholar 

  • Leslie RT (1967) Recurrent composite events. J Appl Probab 4:34–61

    Article  MathSciNet  MATH  Google Scholar 

  • Lou WYW (2003) The exact distribution of the k-tuple statistic for sequence homology. Stat Probab Lett 61:51–59

    Article  MathSciNet  MATH  Google Scholar 

  • Martin DEK, Aston JAD (2001) Waiting time distribution of generalized later patterns. Comput Stat Data Anal 52:4879–4890

    Article  MathSciNet  MATH  Google Scholar 

  • Möller S, Croning MD, Apweiler R (2001) Evaluation of methods for the prediction of membrane spanning regions. Bioinformatics 17(7):646–653

    Article  Google Scholar 

  • Mood AM (1940) The distribution theory of runs. Ann Math Stat 11:367–392

    Article  MathSciNet  MATH  Google Scholar 

  • Pagani I, Liolios K, Jansson J, Chen IM, Smirnova T, Nosrat B, Markowitz VM, Kyrpides NC (2012) The genomes online database (GOLD) v. 4: status of genomic and metagenomic projects and their associated metadata. Nucleic Acids Res 40:D571–D579

    Article  Google Scholar 

  • Rajarshi MB (1974) Success runs in a two-state Markov chain. J Appl Probab 11:190–192

    Article  MathSciNet  MATH  Google Scholar 

  • Schulz GE (2002) The structure of bacterial outer membrane proteins. Biochim Biophys Acta 1565(2):308–317

    Article  Google Scholar 

  • Tusnady GE, Zs Dosztanyi, Simon I (2005) PDB_TM: selection and membrane localization of transmembrane proteins in the Protein Data Bank. Nucleic Acids Res 33:D275–D278

    Article  Google Scholar 

  • Wu TL, Glaz J (2015) A new adaptive procedure for multiple window scan statistics. Comput Stat Data Anal 82:164–172

    Article  MathSciNet  Google Scholar 

  • Zhou R, Huang X, Margulis CJ, Berne BJ (2004) Hydrophobic collapse in multidomain protein folding. Science 305(5690):1605–1609

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Statistics and Insurance Science, University of Piraeus, 80 Karaoli and Dimitriou str., 185 34, Piraeus, Greece

    Sotirios Bersimis & Athanasios Sachlas

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

    Pantelis G. Bagos

Authors
  1. Sotirios Bersimis
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  2. Athanasios Sachlas
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  3. Pantelis G. Bagos
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Correspondence to Sotirios Bersimis.

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Bersimis, S., Sachlas, A. & Bagos, P.G. Discriminating membrane proteins using the joint distribution of length sums of success and failure runs. Stat Methods Appl 26, 251–272 (2017). https://doi.org/10.1007/s10260-016-0370-y

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