SUPPLEMENTARY INFORMATION

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Marianna Skinner
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1 SUPPLEMENTARY INFORMATION doi: /nature11510 Supplementary Table 1. Indel Index Removal Gene Number of Starting Sequences Number of Final Sequences Percentage of Sequences Removed based on the Indel Contribution Index Number Non- Redundant Sequences Number Unique Species ATP % ATP % COX % COX % COX % CYTB % ND % ND % ND % ND % ND4L % ND % ND % eef1a % H % RuBisCo %

2 RESEARCH SUPPLEMENTARY INFORMATION Supplementary Table 2. Consistency of alignment length and comparison of amino acid usage across three different multiple sequence alignment methods. Number of sites occupied by amino acids in more than half of species in a KM-Coffee alignment Protein sequence length in human and thale cress for RuBisCO Clustal Omega MAFFT KM-Coffee KM-Coffee vs Clustal Omega KM-Coffee vs Mafft Gene ATP ATP COX COX COX CYTB ND ND ND ND ND4L ND ND eef1a H RuBisCO Clustal Omega vs Mafft 2

3 SUPPLEMENTARY INFORMATION RESEARCH Supplementary Table 3. Fraction of species with data on the density of non-fixed states. Gene Number of species Number of species with 2 or more sequences Fraction of species with 2 or more sequences ATP ATP COX COX COX CYTB ND ND ND ND ND4L ND ND eef1a H RuBisCO Supplementary Table 4. Estimating amino acid usage without the contribution of non-fixed states through the elimination of rare amino acid states. Gene Amino acid usage Expected dn/ds from (u-1)/19 ATP ATP COX COX COX CYTB ND ND ND ND ND4L ND ND eef1a H RuBisCO

4 RESEARCH SUPPLEMENTARY INFORMATION Supplementary Table 5. Estimating amino acid usage without the contribution of rare non-fixed states. Gene Number of species with 3 or more sequences Number of species Fraction of species with 3 or more sequences Average amino acid usage excluding rare non-fixed states Average amino acid usage from 1000 replicates of single sequences ATP ATP COX COX COX CYTB ND ND ND ND ND4L ND ND eef1a H RiBisCO Supplementary Table 6. Estimating average dn/ds in different genes Gene Number of nonoverlapping clusters Number of species Average observed dn/ds Standard deviation of the observed dn/ds ATP ATP COX COX COX CYTB ND ND ND ND ND4L ND ND eef1a H RiBisCO

5 SUPPLEMENTARY INFORMATION RESEARCH Frequency Amino acid usage Supplementary Figure 1. Frequency distribution of amino acid usage across sites in all genes in our dataset Frequency The number of times an amino acid state observed at a site Supplementary Figure 2. Frequency distribution of the number of times an amino acid state is observed across sites in all genes in our dataset. 5

6 RESEARCH SUPPLEMENTARY INFORMATION t 0 t 1 t 2 time t 3 t 4 Supplementary Figure 3. A simulated phylogeny with regularly spaced speciation events. The total time on the phylogeny between different depths is indicated by t n ; for example, the total evolutionary time on the phylogeny since the last speciation event is t 0. In this example t 0 is twofold larger than t 1 and t n is twofold larger than t n+1. If the rate of amino acid substitution is constant along the phylogeny than the number of substitutions that happened within the timeframe of t 0 is also twofold higher than the number of substitutions that occurred within the timeframe of t 1. Therefore, given a multiple alignment of orthologues from the species represented on this tree the number of amino acid states found only once is expected to be twofold larger than the number of states that are found twice. Thus, given a realistic phylogeny of many species, without an overwhelming bias of shorter branches close to the terminal areas of the phylogeny, the frequency distribution of amino acid states is expected to be an exponentially declining function closely resembling the relationship reported in Supplementary Figure

7 SUPPLEMENTARY INFORMATION RESEARCH FSupplementary Figure 4A-B 7

8 RESEARCH SUPPLEMENTARY INFORMATION Supplementary Figure4C-D 8

9 SUPPLEMENTARY INFORMATION RESEARCH Supplementary Figure 4E-F 9

10 RESEARCH SUPPLEMENTARY INFORMATION Supplementary Figure 4G-H 10

11 SUPPLEMENTARY INFORMATION RESEARCH Supplementary Figure 4I-J 11

12 RESEARCH SUPPLEMENTARY INFORMATION Supplementary Fgure 4K-L 12

13 SUPPLEMENTARY INFORMATION RESEARCH Supplementary Figure 4M-N 13

14 RESEARCH SUPPLEMENTARY INFORMATION H3.2 Supplementary Figure 4O-P Supplementary Figure 4. The relationship between amino acid usage, u, and the number of sequences included in the multiple alignment. From the multiple alignment we sampled a single sequence without replacement and placed it into a new alignment calculating u in the new alignment at every step until we ran out of sequences. The procedure was repeated 100 times. 14

LETTER. Epistasis as the primary factor in molecular evolution

LETTER. Epistasis as the primary factor in molecular evolution LETTER doi:10.1038/nature11510 Epistasis as the primary factor in molecular evolution Michael S. Breen 1, Carsten Kemena 1, Peter K. Vlasov 1, Cedric Notredame 1 & Fyodor A. Kondrashov 1,2 The main forces