SpringerLink
Log in

Protein Evolutionary Rates Correlate with Expression Independently of Synonymous Substitutions in Helicobacter pylori

  • Published:
Journal of Molecular Evolution Aims and scope Submit manuscript

Abstract

In free-living microorganisms, such as Escherichia coli and Saccharomyces cerevisiae, both synonymous and nonsynonymous substitution frequencies correlate with expression levels. Here, we have tested the hypothesis that the correlation between amino acid substitution rates and expression is a by-product of selection for codon bias and translational efficiency in highly expressed genes. To this end, we have examined the correlation between protein evolutionary rates and expression in the human gastric pathogen Helicobacter pylori, where the absence of selection on synonymous sites enables the two types of substitutions to be uncoupled. The results revealed a statistically significant negative correlation between expression levels and nonsynonymous substitutions in both H. pylori and E. coli. We also found that neighboring genes located on the same, but not on opposite strands, evolve at significantly more similar rates than random gene pairs, as expected by co-expression of genes located in the same operon. However, the two species differ in that synonymous substitutions show a strand-specific pattern in E. coli, whereas the weak similarity in synonymous substitutions for neighbors in H. pylori is independent of gene orientation. These results suggest a direct influence of expression levels on nonsynonymous substitution frequencies independent of codon bias and selective constraints on synonymous sites.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Instant access to the full article PDF.

Institutional subscriptions

Figure 1
Figure 2
Figure 3
Figure 4
Figure 5

Similar content being viewed by others

References

  • Akashi H (1994) Synonymous codon usage in Drosophila melanogaster: natural selection and translational accuracy. Genetics 136:927–936

    CAS  PubMed  Google Scholar 

  • Akashi H (2003) Translational selection and yeast proteome evolution. Genetics 164:1291–1303

    CAS  PubMed  Google Scholar 

  • Akashi H, Gojobori T (2002) Metabolic efficiency and amino acid composition in the proteomes of Escherichia coli and Bacillus subtilis. Proc Natl Acad Sci USA 99:3695–3700

    Article  CAS  PubMed  Google Scholar 

  • Alm RA, Ling LS, Moir DT, King BL, Brown ED, Doig PC, Smith DR, Noonan B, Guild BC, deJonge BL, Carmel G, Tummino PJ, Caruso A, Uria-Nickelsen M, Mills DM, Ives C, Gibson R, Merberg D, Mills SD, Jiang Q, Taylor DE, Vovis GF, Trust TJ (1999) Genomic-sequence comparison of two unrelated isolates of the human gastric pathogen Helicobacter pylori. Nature 397:176–180

    Article  PubMed  CAS  Google Scholar 

  • Altschul SF, Madden TL, Schaffer AA, Zhang J, Zhang Z, Miller W, Lipman DJ (1997) Gapped BLAST and PSI-BLAST: a new generation of protein database search programs. Nucleic Acids Res 25:3389–3402

    Article  CAS  PubMed  Google Scholar 

  • Andersson SG, Kurland CG (1990) Codon preferences in free-living microorganisms. Microbiol Rev 54:198–210

    CAS  PubMed  Google Scholar 

  • Andersson SGE, Sharp PM (1996) Codon usage and base composition in Rickettsia prowazekii. J Mol Evol 42:525–536

    Article  CAS  PubMed  Google Scholar 

  • Ball CA, Awad IA, Demeter J, Gollub J, Hebert JM, Hernandez-Boussard T, ** H, Matese JC, Nitzberg M, Wymore F, Zachariah ZK, Brown PO, Sherlock G (2005) The Stanford Microarray Database accommodates additional microarray platforms and data formats. Nucleic Acids Res 33:D580–582

    Article  CAS  PubMed  Google Scholar 

  • Banerjee T, Basak S, Gupta SK, Ghosh TC (2004) Evolutionary forces in sha** the codon and amino acid usages in Blochmannia floridanus. J Biomol Struct Dyn 22:13–23

    CAS  PubMed  Google Scholar 

  • Bernstein JA, Khodursky AB, Lin PH, Lin-Chao S, Cohen SN (2002) Global analysis of mRNA decay and abundance in Escherichia coli at single-gene resolution using two-color fluorescent DNA microarrays. Proc Natl Acad Sci USA 99:9697–9702

    Article  CAS  PubMed  Google Scholar 

  • Bhardwaj N, Lu H (2005) Correlation between gene expression profiles and protein-protein interactions within and across genomes. Bioinformatics 21:2730–2738

    Article  CAS  PubMed  Google Scholar 

  • Bjellqvist B, Hughes GJ, Pasquali C, Paquet N, Ravier F, Sanchez J-C, Frutiger S, Hochstrasser DF (1993) The focusing positions of polypeptides in immobilized pH gradients can be predicted from their amino acid sequences. Electrophoresis 14:1023–1031

    Article  CAS  PubMed  Google Scholar 

  • Blattner FR, Plunkett III G, Bloch CA, Perna NT, Burland V, Riley M, Collado-Viodes J, Glasner JD, Rode CK, Mayhew GF et al. (1997) The complete genome sequence of Escherichia coli K-12. Science 277:1453–1462

    Article  CAS  PubMed  Google Scholar 

  • Bloom JD, Adami C (2003) Apparent dependence of protein evolutionary rate on number of interactions is linked to biases in protein-protein interactions data sets. BMC Evol Biol 3:21

    Article  PubMed  Google Scholar 

  • Bloom JD, Adami C (2004) Evolutionary rate depends on number of protein-protein interactions independently of gene expression level: response. BMC Evol Biol 4:14

    Article  PubMed  Google Scholar 

  • Butland G, Peregrin-Alvarez JM, Li J, Yang W, Yang X, Canadien V, Starostine A, Richards D, Beattie B, Krogan N, Davey M, Parkinson J, Greenblatt J, Emili A (2005) Interaction network containing conserved and essential protein complexes in Escherichia coli. Nature 433:531–537

    Article  CAS  PubMed  Google Scholar 

  • Coghlan A, Wolfe KH (2000) Relationship of codon bias to mRNA concentration and protein length in Saccharomyces cerevisiae. Yeast 16:1131–1145

    Article  CAS  PubMed  Google Scholar 

  • Dong H, Nilsson L, Kurland CG (1996) Co-variation of tRNA abundance and codon usage in Escherichia coli at different growth rates. J Mol Biol 260:649–663

    Article  CAS  PubMed  Google Scholar 

  • Dos Reis, Wernisch L, Saava R (2003) Unexpected correlations between gene expression and codon usage bias from microarray data for the whole Escherichia coli K-12 genome. Nucleic Acids Res 31:6976–6985

    Article  CAS  Google Scholar 

  • Duret L, Mouchiroud D (1999) Expression pattern and, surprisingly, gene length shape codon usage in Caenorhabditis, Drosophila, and Arabidopsis. Proc Natl Acad Sci USA 96:4482–4487

    Article  CAS  PubMed  Google Scholar 

  • Duret L, Mouchiroud D (2000) Determinants of substitution rates in mammalian genes: expression patterns affect selection intensity but not mutation rate. Mol Biol Evol 17:68–74

    CAS  PubMed  Google Scholar 

  • Drummond DA, Bloom JD, Adami C, Wilke CO, Arnold FH (2005) Why highly expressed proteins evolve slowly. Proc Natl Acad Sci USA 102:14338–14343

    Article  CAS  PubMed  Google Scholar 

  • Finlay BB, Falkow S (1997) Common themes in microbial pathogenicity revisited. Microbiol Mol Biol Rev 61:136–169

    CAS  PubMed  Google Scholar 

  • Fraser HB, Hirsh AE, Steinmetz LM, Scharfe C, Feldman MW (2002) Evolutionary rate in the protein interaction network. Science 296:750–752

    Article  CAS  PubMed  Google Scholar 

  • Fraser HB, Wall DP, Hirsh AE (2003) A simple dependence between protein evolution rate and the number of protein-protein interactions. BMC Evol Biol 3:11

    Article  PubMed  Google Scholar 

  • Fraser HB, Hirsh AE (2004) Evolutionary rate depends on number of protein-protein interactions independently of gene expression level. BMC Evol Biol 4:13

    Article  PubMed  Google Scholar 

  • Goetz RM, Fuglsang A (2005) Correlation of codon bias measures with mRNA levels: analysis of transcriptome data from Escherichia coli. Biochem Biophys Acta 327:4–7

    CAS  Google Scholar 

  • Goto S, Nishioka T, Kanehisa M (1998) LIGAND: chemical database for enzyme reactions. Bioinformatics 14:591–599

    Article  CAS  PubMed  Google Scholar 

  • Herbeck JT, Wall DP, Wernegreen JJ (2003) Gene expression level influences amino acid usage, but not codon usage, in the tsetse fly endosymbiont Wigglesworthia. Microbiology 149:2585–2598

    Article  CAS  PubMed  Google Scholar 

  • Herbeck JT, Wall DP (2005) Converging on a general model of protein evolution. Trends Biotechnol 23:485–487

    Article  CAS  PubMed  Google Scholar 

  • Hirsh AE, Fraser HB (2001) Protein dispensability and rate of evolution. Nature 411:1046–1049

    Article  CAS  PubMed  Google Scholar 

  • Hirsh AE (2003) Rate of evolution and gene dispensability—reply. Nature 421:497–498

    Article  CAS  Google Scholar 

  • Ikemura T (1981) Correlation between the abundance of Escherichia coli transfer RNAs and the occurrence of the respective codons in its protein genes. J Mol Biol 146:1–21

    Article  CAS  PubMed  Google Scholar 

  • Ikemura T (1982) Correlation between the abundance of yeast transfer RNAs and the occurrence of the respective codons in protein genes. J Mol Biol 158:573–597

    Article  CAS  PubMed  Google Scholar 

  • Ikemura T (1985) Codon usage and tRNA content in unicellular and multicellular organisms. Mol Biol Evol 2:13–34

    CAS  PubMed  Google Scholar 

  • Jeong H, Tombor B, Albert R, Oltvai ZN, Barabasi AL (2000) The large-scale organization of metabolic networks. Nature 407:651–654

    Article  CAS  PubMed  Google Scholar 

  • Jordan IK, Rogozin IB, Wolf YI, Koonin EV (2002) Essential genes are more evolutionarily conserved than are nonessential genes in bacteria. Genome Res 12:962–968

    Article  CAS  PubMed  Google Scholar 

  • Jordan IK, Wolf YI, Koonin EV (2003) No simple dependence between protein evolution rate and the number of protein-protein interactions: only the most prolific interactors tend to evolve slowly. BMC Evol Biol 3:1

    Article  PubMed  Google Scholar 

  • Jordan IK, Marino-Ramirez L, Wolf YI, Koonin EV (2004) Conservation and coevolution in the scale-free human gene coexpression network. Mol Biol Evol 21:2058–2070

    Article  CAS  PubMed  Google Scholar 

  • Kanaya S, Yamada Y, Kudo Y, Ikemura T (1999) Studies of codon usage and tRNA genes of 18 unicellular organisms and quantification of Bacillus subtilis tRNAs: gene expression level and species-specific diversity of codon usage based on multivariate analysis. Gene 238:143–155

    Article  CAS  PubMed  Google Scholar 

  • Kavermann H, Burns BP, Angermuller K, Odenbreit S, Fischer W, Haas R (2003) Identification and characterization of Helicobacter pylori genes essential for gastric colonization. J Exp Med 197:813–822

    Article  CAS  PubMed  Google Scholar 

  • Klasson L, Andersson SGE (2004) Evolution of minimal-gene-sets in host-dependent bacteria. Trends Microbiol 12:37–43

    Article  CAS  PubMed  Google Scholar 

  • Koonin EV (2000) How many genes can make a cell: the minimal-gene-set concept. Annu Rev Genomics Hum Genet 1:99–116

    Article  CAS  PubMed  Google Scholar 

  • Krogh A, Larsson B, von Heijne G, Sonnhammer ELL (2001) Predicting transmembrane protein topology with a hidden Markov model: Application to complete genomes. J Mol Biol 305:567–580

    Article  CAS  PubMed  Google Scholar 

  • Krylov DM, Wolf YI, Rogozin IB, Koonin EV (2003) Gene loss, protein sequence divergence, gene dispensability, expression level, and interactivity are correlated in eukaryotic evolution. Genome Res 13:2229–22235

    Article  CAS  PubMed  Google Scholar 

  • Kurland CG (1987) Strategies for efficiency and accuracy in gene expression. 1. The major codon preference: a growth optimization strategy. Trends Biochem Sci 12:126–128

    Article  CAS  Google Scholar 

  • Lafay B, Atherton JC, Sharp PM (2000) Absence of translationally selected synonymous codon usage bias in Helicobacter pylori. Microbiology 146:851–860

    CAS  PubMed  Google Scholar 

  • Li W-H, Wu CI, Luo CC (1985) A new method for estimating synonymous and nonsynonymous rates of nucleotide substitutions considering the relative likelihood of nucleotide codon change. Mol Biol Evol 2:150–174

    PubMed  Google Scholar 

  • Lobry JR, Gautier C (1994) Hydrophobicity, expressivity and aromaticity are the major trends of amino-acid usage in 999 Escherichia coli chromosome-encoded genes. Nucleic Acids Res 22:3174–3180

    CAS  PubMed  Google Scholar 

  • Lu H, Zhao WM, Zheng Y, Wang H, Qi M, Yu XP (2005) Analysis of synonymous codon usage bias in Chlamydia. Acta Biochem Biophys Sin 37:1–10

    Article  CAS  Google Scholar 

  • Maniloff J (1996) The minimal cell genome: on being the right size. Proc Natl Acad Sci USA 93:10004–10006

    Article  CAS  PubMed  Google Scholar 

  • Marais G, Domazet-Loso T, Tautz D, Charlesworth B (2004) Correlated evolution of synonymous and nonsynonymous sites in Drosophila. J Mol Evol 59:771–779

    Article  CAS  PubMed  Google Scholar 

  • Marshall B, Warren R (1984) Unidentified curved bacilli in the stomach of patients with gastritis and peptic ulceration. Lancet 8390:1311–1315

    Article  Google Scholar 

  • Moran NA, Dunbar HE, Wilcox JL (2005) Regulation of transcription in a reduced bacterial genome: Nutrient-provisioning genes of obligate symbiont Buchnera aphidicola. J Bacteriol 187:4229–4237

    Article  CAS  PubMed  Google Scholar 

  • Mouchiroud D, Gautier C, Bernardi G (1995) Frequencies of synonymous substitutions in mammals are gene-specific and correlated with frequencies of nonsynonymous substitutions. J Mol Evol 40:107–113

    Article  CAS  PubMed  Google Scholar 

  • Mushegian AR, Kooonin EV (1996) A minimal gene set for cellular life derived by comparison of complete bacterial genomes. Proc Natl Acad Sci USA 93:10268–10273

    Article  CAS  PubMed  Google Scholar 

  • Mushegian AR (1999) The minimal genome concept. Curr Opin Genet Dev 9:709–714

    Article  CAS  PubMed  Google Scholar 

  • Newman MEJ (2001) Scientific collaboration networks. II. Shortest paths, weighted networks, and centrality. Phys Rev E 64:016132

    Article  CAS  Google Scholar 

  • Nuzhdin SV, Wayne ML, Harmon KL, McIntyre LM (2004) Common pattern of evolution of gene expression level and protein sequence in Drosophila. Mol Biol Evol 21:1308–1317

    Article  CAS  PubMed  Google Scholar 

  • Pal C, Papp B, Hurst LD (2001) Highly expressed genes in yeast evolve slowly. Genetics 158:927–931

    CAS  PubMed  Google Scholar 

  • Pal C, Papp B, Hurst LD (2003) Genomic function: Rate of evolution and gene dispensability. Nature 421:496–497

    Article  CAS  PubMed  Google Scholar 

  • Papp B, Pal C, Hurst LD (2004) Metabolic network analysis of the causes and evolution of enzyme dispensability in yeast. Nature 429:661–664

    Article  CAS  PubMed  Google Scholar 

  • Peek RM, Blaser MJ (2002) Helicobacter pylori and gastrointestinal tract adenocarcinomas. Nat Rev Camcer 2:28–37

    Article  CAS  Google Scholar 

  • Pleissner K-P, Eifert T, Buettner S, Schmidt F, Boehme M, Meyer TF, Kaufmann SHE, Jungblut PR (2004) Web-accessible proteome databases for microbial research. Proteomics 4:1305–1313

    Article  CAS  PubMed  Google Scholar 

  • Rain JC, Selig L, De Reuse H, Battaglia V, Reverdy C, Simon S, Lenzen G, Petel F, Wojcik J, Schachter V, Chemama Y, Labigne A, Legrain P (2001) The protein–protein interaction map of Helicobacter pylori. Nature 409:211–215

    Article  CAS  PubMed  Google Scholar 

  • Rison SCG, Teichmann SA, Thorton JM (2002) Homology, pathway distance and chromosomal localization of the small molecule metabolism enzymes in Escherichia coli. J Mol Biol 318:911–932

    Article  CAS  PubMed  Google Scholar 

  • Rispe C, Delmotte F, van Ham RCHJ, Moya A (2004) Mutational and selective pressures on codon and amino acid usage in Buchnera, endosymbiotic bacteria of aphids. Genome Res 14:44–53

    Article  CAS  PubMed  Google Scholar 

  • Rocha EP, Danchin A (2004) An analysis of determinants of amino acids substitution rates in bacterial proteins. Mol Biol Evol 21:108–116

    Article  CAS  PubMed  Google Scholar 

  • Salama NR, Shepherd B, Falkow S (2004) Global transposon mutagenesis and essential gene analysis of Helicobacter pylori. J Bacteriol 186:7926–7935

    Article  CAS  PubMed  Google Scholar 

  • Schaber J, Rispe C, Wernegree J, Burness A, Delmotte F, Silva FJ, Moya A (2005) Gene expression levels influence amino acid usage and evolutionary rates in endosymbiotic bacteria. Gene 352:109–117

    Article  CAS  PubMed  Google Scholar 

  • Sharp PM (1991) Determinants of DNA sequence divergence between Escherichia coli and Salmonella typhimurium: codon usage, map position and concerted evolution. J Mol Evol 33:23–33

    Article  CAS  PubMed  Google Scholar 

  • Sharp PM, Bailes E, Grocook RJ, Peden JF, Sockett RE (2005) Variation in the strength of selected codon usage bias among genes. Nucl Acids Res 33:1141–1153

    Article  CAS  PubMed  Google Scholar 

  • Sharp PM, Li W-H (1987) The codon adaptation index—a measure of directional synonymous codon usage bias, and its potential applications. Nucleic Acids Res 15:1281–1295

    CAS  PubMed  Google Scholar 

  • Smith MJ, Smith NH, O’Rourke M, Spratt BG (1993) How clonal are bacteria? Proc Natl Acad Sci USA 90:4384–4388

    CAS  PubMed  Google Scholar 

  • Suerbaum S, Michetti P (2002) Helicobacter pylori infection. N Engl J Med 347:1175–1186

    Article  CAS  PubMed  Google Scholar 

  • Suerbaum S, Smith JM, Bapumia K, Morelli G, Smith NH, Kunstmann E, Dyrek I, Achtman M (1998) Free recombination within Helicobacter pylori. Proc Natl Acad Sci USA 95:12619–12624

    Article  CAS  PubMed  Google Scholar 

  • Teichmann S (2002) The constraints protein-protein interactions place on sequence divergence. J Mol Biol 324:399–407

    Article  CAS  PubMed  Google Scholar 

  • Thompson JD, Higgins DG, Gibson TJ (1994) CLUSTAL W: improving the sensitivity of progressive multiple sequence alignment through sequence weighting, position-specific gap penalties and weight matrix choice. Nucleic Acids Res 22:4673–4680

    CAS  PubMed  Google Scholar 

  • Tomb JF, White O, Kerlavage AR, Clayton RA, Sutton GG, Fleischmann RD, Ketchum KA, Klenk HP, Gill S, Dougherty BA, Nelson K, Quackenbush J, Zhou L, Kirkness EF, Peterson S, Loftus B, Richardson D, Dodson R, Khalak HG, Glodek A, McKenney K, Fitzegerald LM, Lee N, Adams MD, Hickey EK, Berg DE, Gocayne JD, Utterback TR, Peterson JD, Kelley JM, Cotton MD, Weidman JM, Fujii C, Bowman C, Watthey L, Wallin E, Hayes WS, Borodovsky M, Karp PD, Smith HO, Fraser CM, Venter JC (1997) The complete genome sequence of the gastric pathogen Helicobacter pylori. Nature 388:539–547

    Article  CAS  PubMed  Google Scholar 

  • Wall DP, Hirsh AE, Fraser HB, Kumm J, Giaever G, Eisen MB, Feldman MW. (2005) Functional genomic analysis of the rates of protein evolution. Proc Natl Acad Sci USA 102:5483–5488

    Article  CAS  PubMed  Google Scholar 

  • Wei Y, Lee JM, Richmond C, Blattner FR, Rafalski JA, LaRossa RA (2001) High-density microarray-mediated gene expression profiling of Escherichia coli. J Bacteriol 183:545–556

    Article  CAS  PubMed  Google Scholar 

  • Wilcox JL, Dunbar HE, Wolfinger RD, Moran NA (2003) Consequences of reductive evolution for gene expression in an obligate endosymbiont. Mol Microbiol 48:1491–1500

    Article  CAS  PubMed  Google Scholar 

  • Williams EJB, Hurst LC (2000) The proteins of linked genes evolve at similar rates. Nature 407:900–903

    Article  CAS  PubMed  Google Scholar 

  • Yang J, Gu Z, Li WH (2003) Rate of protein evolution versus fitness effect of gene deletion. Mol Biol Evol 20:772–774

    Article  PubMed  CAS  Google Scholar 

  • Yang Z (1997) PAML: a program package for phylogenetic analysis by maximum likelihood. Comput Appl Biosci 13:555–556

    CAS  PubMed  Google Scholar 

  • Yang Z, Nielsen R (2000) Estimating synonymous and nonsynonymous substitution rates under realistic evolutionary models. Mol Biol Evol 17:32–43

    CAS  PubMed  Google Scholar 

  • Zhang J, He X (2005) Significant impact of protein dispensability on the instantaneous rate of protein evolution. Mol Biol Evol 22:1147–1155

    Article  CAS  PubMed  Google Scholar 

  • Zhang L, Li WH (2004) Mammalian house-kee** genes evolve more slowly than tissue-specific genes. Mol Biol Evol 21:236–239

    Article  PubMed  CAS  Google Scholar 

Download references

Acknowledgments

We thank Eduardo P. Rocha for kindly providing data on E. coli/S. typhimarium/Y. pestis orthologs. This work was supported by the Swedish Research Council (VR), the Swedish Foundation for Strategic Research (SSF), the Knut and Alice Wallenberg Foundation (KAW), and the European Union (EU).

Author information

Authors and Affiliations

  1. Program of Molecular Evolution, Department of Evolution, Genomics and Systematics, Evolutionary Biology Center, Uppsala University, 752 36, Uppsala, Sweden

    Björn Sällström, Wagied Davids, Pär Bjelkmar & Siv G. E. Andersson

  2. Department of Pathology, Brigham and Women’s Hospital, Boston, MA, 02115, USA

    Ramy A. Arnaout

  3. Program in Evolutionary Dynamics, Harvard University, Cambridge, MA, 02141, USA

    Ramy A. Arnaout

  4. The Broad Institute of Harvard and MIT, Cambridge, MA, 02141, USA

    Ramy A. Arnaout

Authors
  1. Björn Sällström
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ramy A. Arnaout
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Wagied Davids
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Pär Bjelkmar
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Siv G. E. Andersson
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Siv G. E. Andersson.

Additional information

[Reviewing Editor: Dr. Nicolas Galtier]

Electronic Supplementary Material

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sällström, B., Arnaout, R.A., Davids, W. et al. Protein Evolutionary Rates Correlate with Expression Independently of Synonymous Substitutions in Helicobacter pylori . J Mol Evol 62, 600–614 (2006). https://doi.org/10.1007/s00239-005-0104-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00239-005-0104-5

Keywords

Search

Navigation