# Difference between revisions of "User:Marshall Hampton/ScoringMatrices"

A log-odds scoring matrix is constructed from some empirically found frequencies of single letter alignments $\displaystyle f_{ij}$ from the formula
$\displaystyle s_{ij} = \lambda log(\frac{f_{ij}}{p_i q_j})$
where $\displaystyle p_i$ and $\displaystyle q_i$ are the background frequencies of the amino acids from two sets of proteins. In the vast majority of current treatments, the evolution of amino acid frequencies is considered symmetric in time and it is assumed that $\displaystyle p_i = q_i$ for each amino acid i. In this article we will not make that assumption in order to develop scoring matrices for organisms in which the amino acid frequencies seem biased in time.