Skip to main content
SpringerLink
Log in

Distribution on Contingency of Alignment of Two Literal Sequences Under Constrains

  • Regular Article
  • Published:
Acta Biotheoretica Aims and scope Submit manuscript

Abstract

The case of ungapped alignment of two literal sequences under constrains is considered. The analysis lead to general formulas for probability mass function and cumulative distribution function for the general case of using an alphabet with a chosen number of letters (e.g. 4 for deoxyribonucleic acid sequences) in the expression of the literal sequences. Formulas for three statistics including mean, mode, and standard deviation were obtained. Distributions are depicted for three important particular cases: alignment on binary sequences, alignment of trinomial series (such as coming from generalized Kronecker delta), and alignment of genetic sequences (with four literals in the alphabet). A particular case when sequences contain each letter of the alphabet at least once in both sequences has also been analyzed and some statistics for this restricted case are given.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  • Allali J, Saule C, Chauve C et al (2012) BRASERO: a resource for benchmarking RNA secondary structure comparison algorithms. Adv Bioinform. art no. 893048

  • Altschul SF, Madden TL, Schäffer AA et al (1997) Gapped BLAST and PSI-BLAST: a new generation of protein database search programs. Nucleic Acids Res 25:3389–3402

    Article  Google Scholar 

  • Altschul SF, Bundschuh R, Olsen R et al (2001) The estimation of statistical parameters for local alignment score distribution. Nucleic Acids Res 29:351–361

    Article  Google Scholar 

  • Bolboacă SD, Jäntschi L, Sestraş RE (2011) Distribution fitting 12. Sampling distribution of compounds abundance from plant species measured by instrumentation. Application to plants metabolism classification. Bull UASVM Hortic 68:54–61

    Google Scholar 

  • Brualdi RA (2010) Introductory combinatorics, 5th edn. Prentice-Hall, Englewood Cliffs

  • Do CB, Mahabhashyam MS, Brudno M et al (2005) ProbCons: probabilistic consistency-based multiple sequence alignment. Genome Res 15:330–340

    Article  Google Scholar 

  • Fisher RA, Tippett LHC (1928) Limiting forms of the frequency distribution of the largest and smallest member of a sample. Proc Camb Philos Soc 24:180–190

    Article  Google Scholar 

  • Frith MC, Hamada M, Horton P (2010) Parameters for accurate genome alignment. BMC Bioinform 11:80

    Article  Google Scholar 

  • Jäntschi L, Bolboacă SD (2010) Exact probabilities and confidence limits for binomial samples: applied to the difference between two proportions. Sci World J 10:865–878

    Article  Google Scholar 

  • Jäntschi L, Bolboacă SD (2011) Distributing correlation coefficients of linear structure-activity/property model. Leonardo J Sci 19:27–48

    Google Scholar 

  • Jäntschi L, Bolboacă SD, Bălan M et al (2011) Distribution fitting 13. Analysis of independent, multiplicative effect of factors. Application to the effect of essential oils extracts from plant species on bacterial species. Application to the factors of antibacterial activity of plant species. Bull UASVM Anim Sci Biotechnol 68:323–331

    Google Scholar 

  • Jäntschi L, Sobolu RS, Bolboacă SD (2012a) An analysis of the distribution of seed size: a case study of the gymnosperms. Not Bot Horti Agrobot 40:46–52

    Google Scholar 

  • Jäntschi L, Bolboacă SD, Sestraş RE (2012b) A simulation study for the distribution law of relative moments of evolution. Complexity 17:52–63

    Article  Google Scholar 

  • Karlin S, Altschul SF (1990) Methods for assessing the statistical significance of molecular sequence features by using general scoring schemas. Proc Natl Acad Sci USA 87:2264–2268

    Article  Google Scholar 

  • Kim J, Ma J (2011) PSAR: measuring multiple sequence alignment reliability by probabilistic sampling. Nucleic Acids Res 39:6359–6368

    Article  Google Scholar 

  • Kim J, Ma J (2014) PSAR-Align: improving multiple sequence alignment using probabilistic sampling. Bioinformatics 30(7):1010–1012

    Article  Google Scholar 

  • Li H, Durbin R (2009) Fast and accurate short read alignment with Burrows–Wheeler transform. Bioinformatics 25:1754–1760

    Article  Google Scholar 

  • Mantaci S, Restivo A, Rosone G et al (2008) A new combinatorial approach to sequence comparison. Theory Comput Syst 42:411–429

    Article  Google Scholar 

  • Mitrophanov AY, Borodovsky M (2006) Statistical significance in biological sequence analysis. Brief Bioinform 7:2–24

    Article  Google Scholar 

  • Mokaddeml, A., Elloumi, M. (2013) Motalign: a multiple sequence alignment algorithm based on a new distance and a new score function. In: International workshop on database and expert systems applications, DEXA, Article number 6621350, pp 81–84

  • Mongiovì M, Sharan R (2013) Global alignment of protein–protein interaction networks. Methods Mol Biol 939:21–34

    Article  Google Scholar 

  • Mott R (2005) Alignment: statistical significance. Encyclopedia of life sciences. http://mrw.interscience.wiley.com/emrw/9780470015902/els/article/a0005264/current/abstract. Accessed 24 Feb 2014

  • Mount DM (2004) Bioinformatics: sequence and genome analysis, 2nd edn. Cold Spring Harbor Laboratory Press, Cold Spring Harbor

    Google Scholar 

  • Olsen R, Bundschuh R, Hwa T.(1999) Rapid assessment of extremal statistics for gapped local alignment. In: Lengauer T, Schneider R, Bork P et al. (eds.) Proceedings of the seventh international conference on intelligent systems for molecular biology, AAAI Press, Menlo Park, pp 211–222

  • Pearson WR (2000) Flexible sequence similarity searching with the FASTA3 program package. Methods Mol Biol 132:185–219

    Google Scholar 

  • Phuong TM, Do CB, Edgar RC et al (2006) Multiple alignment of protein sequences with repeats and rearrangements. Nucleic Acids Res 34:5932–5942

    Article  Google Scholar 

  • Pruitt KD, Tatusova T, Brown GR et al (2012) NCBI reference sequences (RefSeq): current status, new features and genome annotation policy. Nucleic Acids Res 40:D130–D135

    Article  Google Scholar 

  • Rahrig RR, Petrov AI, Leontis NB et al (2013) R3D Align web server for global nucleotide to nucleotide alignments of RNA 3D structures. Nucleic Acids Res 41:W15–W21

    Article  Google Scholar 

  • Sharp H (1968) Cardinality of finite topologies. J Comb Theory 5:82–86. doi:10.1016/S0021-9800(68)80031-6

    Article  Google Scholar 

  • Smith TF, Waterman MS, Burks C (1985) The statistical distribution of nucleic acid similarities. Nucleic Acids Res 13:645–656

    Article  Google Scholar 

  • Szalkowski AM, Anisimova M (2013) Graph-based modeling of tandem repeats improves global multiple sequence alignment. Nucleic Acids Res 41:e162

    Article  Google Scholar 

  • Tabei Y, Asai K (2009) A local multiple alignment method for detection of non-coding RNA sequences. Bioinformatics 25:1498–1505

    Article  Google Scholar 

  • Waterman M (1994) Estimating statistical significance of sequence alignments. Philos Trans R Soc Lond B 344:383–390

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics and Chemistry, Technical University of Cluj-Napoca, 103-105 Muncii Bvd., 400641, Cluj-Napoca, Romania

    Lorentz Jäntschi

  2. Institute for Doctoral Studies, Babeş-Bolyai University, 1st Mihail Kogalniceanu Street, 400084, Cluj-Napoca, Romania

    Lorentz Jäntschi

  3. University of Agricultural Science and Veterinary Medicine Cluj-Napoca, 3-5 Calea Mănăştur, 400372, Cluj-Napoca, Romania

    Lorentz Jäntschi & Sorana D. Bolboacă

  4. Department of Chemistry, The University of Oradea, 1st Universităţii Street, 410087, Oradea, Romania

    Lorentz Jäntschi

  5. Department of Medical Informatics and Biostatistics, Iuliu Haţieganu University of Medicine and Pharmacy, 6 Louis Pasteur, 400349, Cluj-Napoca, Romania

    Sorana D. Bolboacă

Authors
  1. Lorentz Jäntschi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sorana D. Bolboacă
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sorana D. Bolboacă.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Jäntschi, L., Bolboacă, S.D. Distribution on Contingency of Alignment of Two Literal Sequences Under Constrains. Acta Biotheor 63, 55–69 (2015). https://doi.org/10.1007/s10441-014-9243-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10441-014-9243-7

Keywords

Search

Navigation