PAM matrices evolution

PAM and BLOSUM are the widely used substitution matrices in the sequence alignment. The mathematical modeling of PAM matrices is explained in these slides.

1. PAM MATRICES evolution Mithunjha Anandakumar

2. DNA substitution matrix Simple substitution matrix 4 bases – Adenine, Guanine, Thymine, Cytosine A C T G A 1 -1 -1 -1 C -1 1 -1 -1 T -1 -1 1 -1 G -1 -1 -1 1

3. Protein substitution matrices Protein substitution matrices are complex than DNA substitution matrices – 20 Residues Physio-chemical properties of each individual amino acids vary significantly. A protein substitution matrix can be based on any property – size, polarity, charge and so on. Evolution based substitution matrices are the most important! The needleman-Wunsch algorithm for sequence alignment, 7th melbourne Bioinformatics Course

4. Evolutionary substitution Matrices (Widely used) A model of Evolutionary change in proteins

5. Point accepted mutation (pam) matrices Used to score sequence alignments for proteins. Based on strong evolutionary principles. PAM matrices are symmetrical. PAM matrix gives the probability of single amino acid replaced by another single amino acid, for a given period of evolutionary time- time taken for ‘n’ point accepted mutations to occur per 100 amino acids. A model of Evolutionary change in proteins

6. Construction of PAM matrices Introduced by Margaret Dayhoff in 1978. The data used in study includes 1572 mutations in the phylogenetic trees of 71 families of closely related proteins. Sequence within a tree were 85% similar(only 15% different) to it’s Ancestors. Assumption: aligned mismatch resulted by a single mutation event. Explicit evolution model such as phylogenetic trees are required to identify point accepted mutations and development of matrix of accepted point mutations - Mutations that are accepted by natural selection. Phylogenetic tree

7. Without explicit model such as Phylogenetic tree: A C G H D B G H A D I J C B I J A B G H A B I J CB CD BD BB CB X BD BB A B C D G H I J A 1 1 B 1 1 C 1 1 D 1 1 G 1 H 1 I 1 J 1 Matrix of accepted point mutations A model of Evolutionary change in proteins

8. Assumption – the like hood of amino acid X replacing Y is same as amino acid Y replacing X. Elements in the matrices are (x10). Fractional exchange results when ancestral sequences are unknown What are the information we can acquire from this matrix? Can we directly say Asp-Glu has higher mutability compared to Gly-Trp ? Number of occurrence of each amino acid

9. Relative mutability & frequency = = Sum of normalized frequency = 1   := elements on previous matrix (number of mutation occurred between amino acid i and amino acid j)  

10. A model of Evolutionary change in proteins

11. Mutation probability matrix (basis for 1 PAM)       Non-diagonal elements Diagonal elements   := proportionality constant   Pr (remain same)+ Pr (change into another amino acid)=1 Sum of elements in each column sum up to 1

12. Constant proportionality One pam is the basic time evolutionary unit Mutation matrix for 1 PAM = 99% of the amino acids remain conserved. Above equation gives the total probability of conserved amino acids. value needed to be chosen to produce 99% of conserved probability. (observed percentage difference for 1pam)  

13. 42 36 but, = 1.68 Each elements gives the probability of that the amino acid in column j will be replaced by the amino acid in row i after a given evolutionary interval ( 1 pam) Elements shown are (x10,000)   A model of Evolutionary change in proteins Mutation probability matrix – basis for 1PAM

14. Markov chain model or ? Do we need to make n observation to know the probability of observing j if i was in the initial observation? Then we need examples of proteins at given n evolutionary interval. (relation between mutation matrix of 1PAM and PAMn .  

15. Relatedness odds matrix Ratio of the probability of j- th amino acid replaced by i-th amino acid, to the probability of these amino acids being aligned by chance. Symmetrical PAM( i,j ) = log ( )  

16. Pam250 Elements shown are (x10) Neutral score = 0 Most informative matrix with strong evolutionary priciples A model of Evolutionary change in proteins

17. Thank YOU