NAME¶

pbsScoreMatrix - Generate log-odds score matrices for use in alignment of

DESCRIPTION¶

Generate log-odds score matrices for use in alignment of probabilistic biological sequences (PBSs). By default, generates a matrix for every branch of the tree (as defined in tree.mod), but can also generate a matrix for a given branch length (see --branch-length). For a code size of N, an N x N matrix is generated by default; --half-pbs will produce an N x 4 matrix, and --no-pbs will produce a 4 x 4 matrix (assuming a four-character nucleotide alphabet).

Two sequences are assumed to have evolved from a common ancestor by a reversible continuous-time Markov substitution process, and to be separated by a branch of length t. The conditional probability of a base j in one sequence given a base i in the other, P(j | i, t) is given by element (i, j) of the matrix

P(t) = exp(Qt)

where Q is the rate matrix defining the substitution process, and element (i, j) of Q is the instantaneous rate at which base i changes to base j.

Let S_t(i, j) be a log odds score for the alignment of two bases, i and j, based on P(t):

S_t(i, j) = log P(i, j | t) / (pi(i) * pi(j))

= log P(j | i, t) pi(i) / (pi(i) * pi(j))

= log P(j | i, t) / pi(j) (1)

where pi(x) is the "equilibrium" or "background" probability of base x. Because of reversibility, S(i, j) = S(j, i), and the S(i, j) form a symmetric 4 x 4 matrix. This is the matrix that is generated by pbsScoreMatrix with the --no-pbs option. If each "letter" in each sequence represents a probability distribution over bases, as in a PBS, then the score for two letters k and l can be shown to be

S'_t(k, l) = log sum_i sum_j p_k(i) p_l(j) exp S_t(i, j) (2)

where the two sums are over the four bases, p_k(i) is the probability of base i under the distribution for k, and p_l(j) is the probability of base j under the distribution for l.

Notice that (2) reduces to (1) when p_k(i) = p_l(j) = 1 for some i and j and for all other i' and j' p_k(i') = p_l(j') = 0 (i.e., when all of the probability mass is on a single base in both distributions and the PBS reduces to an ordinary nucleotide sequence). The special case of p_l(j) = 1 only is also of interest when aligning a PBS and a nucleotide sequence:

S''_t(k, j) = log sum_i p_k(i) exp S_t(i, j) (3)

This is the matrix generated by pbsScoreMatrix with the --half-pbs option. Note: all logs are base 2.

EXAMPLE¶

Generate an N x N matrix for every branch of the tree, using a code file "code" (generated by pbsTrain) and a tree model file "mytree.mod" (generated by phyloFit):

pbsScoreMatrix mytree.mod code > matrices.dat

Generate an N x N matrix for a branch length of 0.2 expected substitutions per site.

pbsScoreMatrix --branch-length 0.2 mytree.mod code > matrix.dat

Generate an N x 4 matrix:

pbsScoreMatrix --branch-length 0.2 --half-pbs mytree.mod code > matrix.dat

Generate a 4 x 4 matrix:

pbsScoreMatrix --branch-length 0.2 --no-pbs code mytree.mod > matrix.dat

(In this case, a code file is not needed.)

OPTIONS¶

--branch-length, -t <length>

Output a matrix for a branch of the specified length, rather than a matrix for every branch of the tree. The given length must be non-negative and in units of expected substitutions per site.

--half-pbs, -H

Output an N x 4 matrix, as described above.

--no-pbs, -N Output a 4 x 4 matrix, as described above. With this option, a code file is not needed.

--help, -h

Show this help message.