Table 3. The num ber of possib le unroote d and rooted trees asfunction ofthe the n um ber of taxa based on eq. 7. Num ber of taxa Num ber ofunrooted trees Num ber ofrooted trees 3 1 3 4 3 15 5 15 105 6 105 945 7 945 10395 8 10395 135135 9 135135 2027025 10 2027025 34459425 11 34459425 654729075 12 654729075 13749310575 13 13749310575 3.16234E+11 14 3.16234E+11 7.90585E+12 15 7.90585E+12 2.13458E+14 16 2.13458E+14 6.19028E+15 17 6.19028E+15 1.91899E+17 18 1.91899E+17 6.33266E+18 19 6.33266E+18 2.21643E+20 20 2.21643E+20 8.20079E+21 21 8.20079E+21 1.31131E+25
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Emile Zuckerkandl and Linus Pauling, "Evolutionary Divergence and Convergence in Proteins,"
Emile Zuckerkandl and Linus Pauling, "Evolutionary Divergence and Convergence in Proteins," in Evolving Genes and Proteins, eds. V. Bryson and H. Vogel (New York: Academic Press, 1965). pp. 97-166. Comparing Hemoglobin Sequences. “There may thus exist a Molecular Evolutionary Clock” - PowerPoint PPT Presentation
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Table 3. The number of possible unrooted and rooted trees as function of the the number of taxa based on eq. 7.
Number of taxa Number of unrooted trees Number of rooted trees 3 1 3 4 3 15 5 15 105 6 105 945 7 945 10395 8 10395 135135 9 135135 2027025 10 2027025 34459425 11 34459425 654729075 12 654729075 13749310575 13 13749310575 3.16234E+11 14 3.16234E+11 7.90585E+12 15 7.90585E+12 2.13458E+14 16 2.13458E+14 6.19028E+15 17 6.19028E+15 1.91899E+17 18 1.91899E+17 6.33266E+18 19 6.33266E+18 2.21643E+20 20 2.21643E+20 8.20079E+21 21 8.20079E+21 1.31131E+25
Emile Zuckerkandl and Linus Pauling, "Evolutionary Divergence and Convergence in Proteins,"
in Evolving Genes and Proteins, eds. V. Bryson and H. Vogel (New York: Academic Press, 1965). pp. 97-166.
Comparing Hemoglobin Sequences
“There may thus exist a Molecular Evolutionary Clock”Zuckerkandl & Pauling (1965)
A model of sequence divergence can be used to extract the duplication dates of the difference hemoglobin chains
Clock for paralogs
Divergegence between alpha and beta
Divergegence between beta and gamma
“There may thus exist a Molecular Evolutionary Clock”
Table 2. Jukes-Cantor corrected distance values calculated from the dissimilarityvalues in table 1 using eq. 3.
E. coli R. rickettsii B. burgdorferi S. cerevisiaeH. sapiensH. marismortuiE. coli -R. rickettsii 0.36 -B. burgdorferi 0.49 0.48 -S. cerevisiae 0.82 0.82 0.82 -H. sapiens 0.97 0.82 0.76 0.23 -H. marismortui 0.44 0.47 0.57 0.91 0.91 -
E. coli R. rickettsii B. burgdorferi Hs-Sc H. marismortui E. coli - R. rickettsii 0.360 - B. burgdorferi 0.494 0.479 - Hs-Sc 0.896 0.824 0.791 - H. marismortui 0.441 0.471 0.572 0.907 - Ec-Rr B. burgdorferi Hs-Sc H. marismortui Ec-Rr - B. burgdorferi 0.485 - Hs-Sc 0.860 0.791 - H. marismortui 0.455 0.572 0.907 - Ec-Rr-Hm B. burgdorferi Hs-Sc Ec-Rr-Hm - B. burgdorferi 0.530 - Hs-Sc 0.885 0.791 - Ec-Rr-Hm-Bb Hs-Sc Ec-Rr-Hm-Bb - Hs-Sc 0.838 -
E. coli R. rickettsii B. burgdorferi Hs-Sc H. marismortui E. coli - R. rickettsii 0.360 - B. burgdorferi 0.494 0.479 - Hs-Sc 0.896 0.824 0.791 - H. marismortui 0.441 0.471 0.572 0.907 - Ec-Rr B. burgdorferi Hs-Sc H. marismortui Ec-Rr - B. burgdorferi 0.485 - Hs-Sc 0.860 0.791 - H. marismortui 0.455 0.572 0.907 - Ec-Rr-Hm B. burgdorferi Hs-Sc Ec-Rr-Hm - B. burgdorferi 0.530 - Hs-Sc 0.885 0.791 - Ec-Rr-Hm-Bb Hs-Sc Ec-Rr-Hm-Bb - Hs-Sc 0.838 -
E. coli R. rickettsii B. burgdorferi Hs-Sc H. marismortui E. coli - R. rickettsii 0.360 - B. burgdorferi 0.494 0.479 - Hs-Sc 0.896 0.824 0.791 - H. marismortui 0.441 0.471 0.572 0.907 - Ec-Rr B. burgdorferi Hs-Sc H. marismortui Ec-Rr - B. burgdorferi 0.485 - Hs-Sc 0.860 0.791 - H. marismortui 0.455 0.572 0.907 - Ec-Rr-Hm B. burgdorferi Hs-Sc Ec-Rr-Hm - B. burgdorferi 0.530 - Hs-Sc 0.885 0.791 - Ec-Rr-Hm-Bb Hs-Sc Ec-Rr-Hm-Bb - Hs-Sc 0.838 -
E. coli R. rickettsii B. burgdorferi Hs-Sc H. marismortui E. coli - R. rickettsii 0.360 - B. burgdorferi 0.494 0.479 - Hs-Sc 0.896 0.824 0.791 - H. marismortui 0.441 0.471 0.572 0.907 - Ec-Rr B. burgdorferi Hs-Sc H. marismortui Ec-Rr - B. burgdorferi 0.485 - Hs-Sc 0.860 0.791 - H. marismortui 0.455 0.572 0.907 - Ec-Rr-Hm B. burgdorferi Hs-Sc Ec-Rr-Hm - B. burgdorferi 0.530 - Hs-Sc 0.885 0.791 - Ec-Rr-Hm-Bb Hs-Sc Ec-Rr-Hm-Bb - Hs-Sc 0.838 -
E. coli ATGCAAGTCGAACG-GTAACAGGAAGAAG---CTTG-CTTCTTTGCTGACGAGTGGCGGACGGGTG R. rickettsia ATGCAAGTCGAACGGAC--TAA-TTGGGG---CTTG-CTCCAA--TTAGTTAGTGGCAGACGGGTG B. burgdorferi ATGCAAGTCAAACGGGA--TGT------A---GCAA-T-------ACATCTAGTGGCGAACGGGTG S. cerevisiae ATGCATGTCTAAGT-ATAAGCA-------ATTTATAC--------AGTGA-AACTGCGAATGGCTC H. sapiens ATGCATGTCTAAGT-ACGCACG-------GCCGGTAC--------AGTGA-AACTGCGAATGGCTC H. marismortui ATGCTAGTCGCACGGGC---------------TTAG------------ACCCGTGGCATATAGCTC Unweighted mask 111111111111111111111111111111111111111111111111111111111111111111 Weighted mask 11112211111111---------------------------------------1111222222111
Positions 1 10 20 30 40 50 60 R. rickettsii ATGCAAGTCGAACGGAC—-TAA-TTGGGG---CTTG-CTCCAA--TTAGTTAGTGGCAGACGGGTG B. burgdorferi ATGCAAGTCAAACGGGA—-TGT------A---GCAA-T-------ACATCTAGTGGCGAACGGGTG node 1 ATGCAAGTC?AACGG??—-T??-??????---????-??????--??A??TAGTGGC??ACGGGTG E. coli ATGCAAGTCGAACG-GTAACAGGAAGAAG---CTTG-CTTCTTTGCTGACGAGTGGCGGACGGGTG
Positions 1 10 20 30 40 50 60 R. rickettsii ATGCAAGTCGAACGGAC—-TAA-TTGGGG---CTTG-CTCCAA--TTAGTTAGTGGCAGACGGGTG B. burgdorferi ATGCAAGTCAAACGGGA—-TGT------A---GCAA-T-------ACATCTAGTGGCGAACGGGTG node 1 ATGCAAGTCGAACGGG?—-TA?-?????G---CTTG-C?????--?TA?CTAGTGGCGGACGGGTG E. coli ATGCAAGTCGAACG-GTAACAGGAAGAAG---CTTG-CTTCTTTGCTGACGAGTGGCGGACGGGTG
Positions 1 10 20 30 40 50 60 R. rickettsii ATGCAAGTCGAACGGAC—-TAA-TTGGGG---CTTG-CTCCAA--TTAGTTAGTGGCAGACGGGTG B. burgdorferi ATGCAAGTCAAACGGGA—-TGT------A---GCAA-T-------ACATCTAGTGGCGAACGGGTG node 1 ATGCAAGTCGAACGGGA—-TAT-TTGGGG---CTTG-CTCCAA--TTAGCTAGTGGCGGACGGGTG E. coli ATGCAAGTCGAACG-GTAACAGGAAGAAG---CTTG-CTTCTTTGCTGACGAGTGGCGGACGGGTG
Positions 1 10 20 30 40 50 60 R. rickettsii ATGCAAGTCGAACGGAC—-TAA-TTGGGG---CTTG-CTCCAA--TTAGTTAGTGGCAGACGGGTG B. burgdorferi ATGCAAGTCAAACGGGA—-TGT------A---GCAA-T-------ACATCTAGTGGCGAACGGGTG node 1 ATGCAAGTCGAACGGGA—-TAT-TTGGGG---CTTG-CTCCAA--TTAGCTAGTGGCGGACGGGTG E. coli ATGCAAGTCGAACG-GTAACAGGAAGAAG---CTTG-CTTCTTTGCTGACGAGTGGCGGACGGGTG