Transition Bias and Substitution models

1. Transition Bias and Substitution models Xuhua Xia xxia@uottawa.ca http://dambe.bio.uottawa.ca

2. Transitions and Transversions Purine Pyrimidine Transition: the substitution of a purine for a purine or a pyrimidine for a pyrimidine. Symbolized by s. A G C T A G C T Transversion: the substitution of a purine for a pyrimidine or vice versa. Symbolized by v. What is transition bias? 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. A G C T

3. Transition Bias is Ubiquitous. Why? • For both invertebrate and vertebrate genes: • What causes transition bias? • Mutation bias • Selection bias • Selection bias in fixation probability • Protein-coding genesRNA genes • Mutation bias

4. Mitochondrial Genetic Code • Synonymous and nonsynonymous • Degeneracy: • Non-degenerate • Two-fold degenerate • Four-fold degenerate • Transitions are synonymous and transversions are nonsynonymous at two-fold degenerate sites.

5. RNA secondary structure Seq1: CACGA ||||| GUGCU Seq2: CAUGA ||||| GUGCU Seq1: CACGA ||||| GUGCU Seq2: CGCGA ||||| GUGCU CCAAU CCAAU CCAAU CCAAU 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).

6. Causes of transition bias 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

7. At Four-fold Degenerate Sites Glycine codon: GGA GGC GGG GGT Four-fold degenerate site At four-fold degenerate sites, all nucleotide substitutions are synonymous and subject to roughly the same selection pressure (similar fixation probabilities) 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

8. At Nondegenerate Sites Glycine codon: GGA GGC GGG GGT nondegenerate site At nondegenerate sites, all nucleotide substitutions are nonsynonymous and subject to roughly the same selection pressure (similar fixation probabilities) Gly Asn Lys Gly Asp Lys Ala Ala Pro Ala Cys ...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 v Glu Gly Trp

9. At Two-fold Degenerate Sites GAA His GAG His GAC Gln GAT Gln 2-fold degenerate site 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 A transition is about 40 time as like to become fixed as a transversion.

10. Methylation and deamination H3C- Methyltransferase H3C- + Donor Acceptor

11. Methylation and DNA Repair in E. coli mutL mutH mutS • DNA alphabets: ACGT • RNA alphabets: ACGU • DNA duplication and Watson-Crick paring rule: A-T, C-G H3C H3C H3C 3’--CTAG----CTAGGTAT----C-----C--CTAG-----------5’ |||| |||||||| ? ? |||| 5’--GATC----GATCCATA----U-----T--GATC-----... 3’ H3C

12. Methylation-Modification System Bacterial Genome Restriction enzyme Methylase TGGC*CA AC*CGGT Transcription and Translation ----TGG|CCA-------ACC|GGT--- Bacterial Membrane dsDNA phage Brevibacterium albidum

13. 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 mCpG 748 343 609 1110 1 RFDD PBD NlsD ZnD CatD 350 746 1620 613 1124 Fatemi, M., A. Hermann, S. Pradhan and A. Jeltsch, 2001 J Mol Biol 309: 1189-99.

14. 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

15. Methylation and Gene Regulation MBD • 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 Condensed DNA with repressed transcription ---mCpG----------------- Wade, P. A., and A. P. Wolffe, 2001 Nat Struct Biol 8: 575-7. Lysine demethylation

16. Methylation and Mutation O H3C NH2 N N O N N O H3C Spontaneous deamination methylation O Cytocine is converted to Thymine

17. Vertebrate mitochondrion

18. Spontaneous deamination

19. 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 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. AACGCTTGACG AACGCTTTACG AACGCTTAACG AACGCTTGACG

20. 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)

21. Nucleotide Substitutions ACACTCGGATTAGGCT ATACTCAGGTTAAGCT ACAATCCGGTTAAGCT T C C AGACTCGGATTAGGCT parallel convergent coincidental single Observed sequences ACACTCGGATTAGGCT multiple back From WHL 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.

22. 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. A G C T

23. The diagonal of a transition probability matrix is subject to the constraint that each row sums up to 1. JC69 i = 0.25ai = c K80i =0.25a1 = a6 = a7 = a12 = a2 = a3 = a4 = a5 = a8 = a9 = a10 = a11=  F81/TN84A, C, G, Tai = c Unrestricted: no equilibrium i A G C TA a1 a2 a3G a7 a4 a5C a8 a9 a6T a10 a11 a12 HKY85A, C, G, Ta1 = a6 = a7 = a12 = a2 = a3 = a4 = a5 = a8 = a9 = a10 = a11=  A G C TA a1Ga2Ca3TG a1Aa4Ca5TC a2A a4G a6TT a3A a5G a6C TN93A, C, G, Ta1 = a7 = 1a6 = a12 = 2a2 = a3 = a4 = a5 = a8 = a9 = a10 =a11=  GTR

24. The TN93 model as an example T C A G A G C T • - frequency parameters • - 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.

25. 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.