Transition bias and substitution models
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Transition Bias and Substitution models Xuhua Xia xxia@uottawa.ca http://dambe.bio.uottawa.ca Transitions and Transversions A G Purine C T Pyrimidine A G C T Transition: the substitution of a purine for a purine or a pyrimidine for a pyrimidine. Symbolized by s. Transversion: the substitution of a purine for a pyrimidine or vice versa. Symbolized by v. What is transition bias? A G C T Xuhua Xia Transition bias refers to the degree by which the s/v ratio deviates from the expected 1/2. The observed s/v ratio is almost always much larger than 1/2. Transition Bias is Ubiquitous. Why? • For both invertebrate and vertebrate genes: sobs 1 vobs 2 • What causes transition bias? – Mutation bias – Selection bias sobs s Ps vobs v Pv Selection bias in fixation probability Protein-coding genes RNA genes Mutation bias Xuhua Xia Mitochondrial Genetic Code Codon Amino acid Codon Amino acid Codon Amino acid Codon Amino acid UUU UUC UUA UUG Phe Phe Leu Leu UCU UCC UCA UCG Ser Ser Ser Ser UAU UAC UAA UAG Tyr Tyr Stop Stop UGU UGC UGA UGG Cys Cys Trp Trp CUU CUC CUA CUG Leu Leu Leu Leu CCU CCC CCA CCG Pro Pro Pro Pro CAU CAC CAA CAG His His Gln Gln CGU CGC CGA CGG Arg Arg Arg Arg AUU AUC AUA AUG lle Ile Met Met ACU ACC ACA ACG Thr Thr Thr Thr AAU AAC AAA AAG Asn Asn Lys Lys AGU AGC AGA AGG Ser Ser Stop Stop GUU GUC GUA GUG Val Val Val Val GCU GCC GCA GCG Ala Ala Ala Ala GAU GAC GAA GAG Asp Asp Glu Glu GGU GGC GGA GGG Gly Gly Gly Gly Xuhua Xia • Synonymous and nonsynonymous • Degeneracy: – Non-degenerate – Two-fold degenerate – Four-fold degenerate • Transitions are synonymous and transversions are nonsynonymous at two-fold degenerate sites. RNA secondary structure Seq1: CACGA ||||| GUGCU Seq1: CACGA ||||| GUGCU Seq2: CAUGA ||||| GUGCU Seq2: CGCGA ||||| GUGCU G/U pair, although not as strong as A/U or C/G pair, generally does not disrupt RNA secondary structure (and occurs frequently in RNA secondary structure). Xuhua Xia Causes of transition bias sobs s Ps vobs v Pv I often say that when you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot measure it, when you cannot express it in numbers, your knowledge is of a meagre and unsatisfactory kind; it may be the beginning of knowledge, but you have scarcely in your thoughts advanced to the state of Science, whatever the matter may be." Lord Kelvin: Phys. Letter A, vol. 1, "Electrical Units of Measurement", 1883-05-03 Xuhua Xia At Four-fold Degenerate Sites At four-fold degenerate sites, all nucleotide substitutions are synonymous and subject to roughly the same selection pressure (similar fixation probabilities) Glycine codon: GGA GGC GGG Gly Asn Lys Gly Asp Lys Ala Ala Pro Ala Cys ... Fold 4 2 2 2 2 4 4 4 2 S1 GGA AAU AAA GGA GAC AAA GCC GCC CCU GCG UGU ... S2 GGG AAC AAA GAA GAU AAG GCC GCU CCA GGG UGG ... s s v Glu Gly Trp sobs s Ps s 2 vobs v Pv v Xuhua Xia GGT Four-fold degenerate site At Nondegenerate Sites At nondegenerate sites, all nucleotide substitutions are nonsynonymous and subject to roughly the same selection pressure (similar fixation probabilities) S1 S2 Glycine codon: GGA GGC Gly Asn Lys Gly Asp Lys Ala Ala Pro Ala Cys ... GGA AAU AAA GGA GAC AAA GCC GCC CCU GCG UGU ... GGG AAC AAA GAA GAU AAG GCC GCU CCA GGG UGG ... s v Glu Gly Trp sobs s Ps s 2 vobs v Pv v Xuhua Xia GGG GGT nondegenerate site At Two-fold Degenerate Sites At two-fold degenerate sites, all transitional substitutions are synonymous, and all transversional substitutions are nonsynonymous Gly Asn Lys Gly Asp Lys Ala Ala Pro Ala Cys ... Fold 4 2 2 2 2 4 4 4 2 S1 GGA AAU AAA GGA GAC AAA GCC GCC CCU GCG UGU ... S2 GGG AAC AAA GAA GAU AAG GCC GCU CCA GGG UGG ... s s s v Glu Gly Trp sobs s Ps Ps 2 80 vobs v Pv Pv A transition is about 40 time as like to become fixed as a transversion. Xuhua Xia GAA His GAG His GAC Gln GAT Gln 2-fold degenerate site Methylation and deamination H3CDonor Xuhua Xia Methyltransferase + Acceptor H3C- Methylation and DNA Repair in E. coli • DNA alphabets: ACGT • RNA alphabets: ACGU • DNA duplication and Watson-Crick paring rule: A-T, C-G H3C H3C H 3C 3’--CTAG----CTAGGTAT----C-----C--CTAG-----------5’ |||| |||||||| ? ? |||| 5’--GATC----GATCCATA----U-----T--GATC-----... 3’ H3C Xuhua Xia mutH mutS mutL Methylation-Modification System Bacterial Genome Methylase TGGC*CA AC*CGGT Transcription and Translation Restriction enzyme ----TGG|CCA------ACC|GGT--- dsDNA phage Xuhua Xia Bacterial Membrane Brevibacterium albidum CpG-Specific DNA Methylation • Mammalian DNA methyltransferase 1 (DNMT1) – NLS-containing domain – replication foci-directing domain – ZnD, Zn-binding domain – polybromo domain – CatD, the catalytic domain CpG mCpG 343 1 NlsD 350 609 RFDD 613 mCpG 748 1110 PBD ZnD 746 CatD 1124 1620 Fatemi, M., A. Hermann, S. Pradhan and A. Jeltsch, 2001 J Mol Biol 309: 1189-99. Xuhua Xia CpG-Specific DNA Methylation H3C H3C 5’ATGCGA-------CCGA--------ACGGC--TAA 3’ |||||| |||| ||||| 3’TACGCT-------GGCT--------TGCCG--ATT 5’ H3C Fully methylated Hemi-methylated Unmethylated Note: 5’CG3’ = CpG Xuhua Xia Methylation and Gene Regulation • Proteins with a methyl-CpG binding domain (MBD) – MBD1, MBD2, and MBD3 – MeCP2 • • Deacetylases: An enzyme that removes an acetyl group Histone deacetylases: deacetylate lysyl residues in histones (the half life of an acetyl group is ~10min). Acetylation removes a positive charge on the lysine amino group and promote nucleosome melting (and gene expression). Deacetylation tend to decrease or turn off gene expression. Histone deacetylase MBD ---mCpG----------------- Condensed DNA with repressed transcription Wade, P. A., and A. P. Wolffe, 2001 Nat Struct Biol 8: 575-7. Xuhua Xia Lysine demethylation Methylation and Mutation NH O 2 O Spontaneous deamination H3C H3C methylation N N N O Cytocine is converted to Thymine Xuhua Xia N O Vertebrate mitochondrion Parental H OH Parental L Daughter H OL Xuhua Xia Daughter L Spontaneous deamination NH 2 NH 2 NH2 O CH3 N N N N H N H N N Adenine N H NH2 Guanine N H O Cytosine O Methylcytosine NH3 NH3 NH3 O H2O H2O H2O H2O NH3 O N N NH O O CH3 N N NH N H N Hypoxanthine (Pair with C) Xuhua Xia N NH H N H N Xanthine (Pair with C) O N H Uracil (Pair with A) N O N H Thymine (Pair with A) O Transversion can erase transitions Transitions can erase transitions, and transversions can erase transversions. However, a transversion can erase many transitions occurring before it, and subsequent transitions cannot erase the transversion: AACGCTTGACG AACGCTTAACG AACGCTTGACG AACGCTTCACG AACGCTTGACG AACGCTTTACG AACGCTTAACG AACGCTTGACG AACGCTTTACG Although a transition could also erase 2n transversions occurring before it, this is rare because transversions are in generally much rarer than transitions. Transitions tend to be missed in counting much more frequently than transversions. Xuhua Xia Summary • Selection: Transitions are tolerated more than transversion by natural selection because – they are more likely synonymous in protein-coding sequences than transversions – they are less likely to disrupt RNA secondary structure than transversions. • Mutation: Transitional mutation occurs more frequently than transversions because – Misincorporation during DNA replication occur more frequently between two purines or between two pyrimidines than between a purine and a pyrimidine – A purine is more likely to mutate chemically to another purine than to a pyrimidine (e.g., through spontaneous deamination) . The same for pyrimidine. • Bias in counting: Transitions tend to be missed in counting much more frequently than transversions (which necessitates the substitution models) Xuhua Xia Nucleotide Substitutions convergent ATACTCAGGTTAAGCT Observed sequences T C C back ACAATCCGGTTAAGCT multiple ACACTCGGATTAGGCT parallel single coincidental ACACTCGGATTAGGCT AGACTCGGATTAGGCT Actual number of changes during the evolution of the two daughter sequences: 12 Observed number of differences between the two daughter sequences: 3. Correcting for multiple substitutions to to estimate the true number of changes, i.e., 12. Xuhua Xia From WHL Substitution models and phylogenetics • A substitution model is to model the evolutonary process so as to correct for multiple hits. • A phylogenetic reconstruction method implicitly or explicitly assumes a substitution model. • A phylogenetic method assuming a wrong substitution model will typically lead to wrong trees produced. Xuhua Xia A G C T The diagonal of a transition probability matrix is subject to the constraint that each row sums up to 1. K80 i =0.25 a1 = a6 = a7 = a12 = a2 = a3 = a4 = a5 = a8 = a9 = a10 = a11= Unrestricted: no equilibrium i A G C T A a1 a2 a3 G a7 a4 a5 C a8 a9 a6 T a10 a11 a12 A A G C T a1A a2A a3A G C T a1G a2C a3T a4C a5T a4G a6T a5G a6C GTR JC69 i = 0.25 ai = c F81/TN84 A, C, G, T ai = c HKY85 A, C, G, T a1 = a6 = a7 = a12 = a2 = a3 = a4 = a5 = a8 = a9 = a10 = a11= TN93 A, C, G, T a1 = a7 = 1 a6 = a12 = 2 a2 = a3 = a4 = a5 = a8 = a9 = a10 =a11= The TN93 model as an example T A C G T - frequency parameters . 1 T Q T T C A 1 C A A . C C G . G G 2 G 2 A . - rate ratio parameters In addition to illustrated assumptions, it also assumes that the frequency and rate ratio parameters do not change over time, i.e., the substitution process is stationary. Xuhua Xia Substitution Models • There are three types of substitution models in molecular evolution – Nucleotide-based – Amino acid-based – Codon-based • Substitution models are characterized by two categories of parameters: the frequency parameters and the rate ratio parameters, and different models differ by their assumptions concerning these two categories of parameters. Xuhua Xia
