PAM matrix

The PAM matrices, ° which were developed by Dayhoff et ah, are based on the probability of an amino acid residue mutating to another amino acid residue. The original PAM matrix was derived using a small group of closely related sequences and tracking the amino acid residue substitutions. Each evolutionary PAM matrix is determined by multiplying the original PAM matrix by itself n — 1 times, where n is the number of desired evolutionary... 

These three moves to the point i,j are illustrated in Figure 10,14 and correspond to a match, a gap in sequence B and a gap in sequence A, respectively. The symbol A in Equation (10.1) is used to represent a gap. wa, represents the score associated with aligning residue A,- with residue By. In the simplest identity scoring scheme would equal 1 if the residues were identical and zero otherwise. More typical would be the use of the PAM or BLOSUM scoring matrices. The remaining two scores, WAj.A are gap penalties. The simplest scheme is... 

Specification of the relative rates of substitution among particular residues usually takes the form of a square matrix the nmnber of rows/colmnns is fom in the case of bases, 20 in the case of amino acids (e.g., in PAM and BLOSUM matrices), and 61 in the case of codons (excluding stop codons). The off-diagonal elements of the matrix correspond to the relative costs of going from one base to another. The diagonal elements represent the cost of having the same base in different sequences. 

The most widely used models of amino acid substitution include distance-based methods, which are based on matrixes such as PAM and BLOSUM. Again, such matrices are described fiuther in other chapters in this book. Briefly, Dayhoff s PAM 001 matrix (Dayhoff, 1979) is an empirical model that scales probabilities of change from one amino acid to another in terms of an expected 1% change between two amino acid sequences. This matrix is used to make a transition probability matrix that allows prediction of the probability of changing from one amino acid to another and also predicts equilibriiun amino acid composition. Phylogenetic distances are calculated with the assumption that the probabilities in the matrix are correct. The... 

PAM matrix PAM (percent accepted mutation) and BLOSUM (blocks substitution matrix) are matrices that define scores for each of the 210 possible amino acid substitutions. The scores are based on empirical substitution frequencies observed in alignments of database sequences and in general reflect similar physicochemical properties (e.g., a substitiution of leucine for isoleucine, two amino acids of similar hydrophobicity and size, will score higher than a substitution of leucine for glutamate.)... 

In Eq. (2.38), A, B, and C are the rotational constants in the PAS and H d the usual centrifugal distortion Hamiltonian. The main approximation made in the PAM is that the cross term -2FpP is considered as a perturbation which can be handled by successive Van Vleck transformations. The transformed Hamiltonian matrix can then be factored into smaller effective rotational matrices, one for... 

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