BLOSUM

Eliminate the sequences that are more than r% identical. There are two ways to eliminate the sequences. It can be done either by removing sequences from the block or just by finding similar sequences and replace them by new sequences which could represent the cluster. Elimination is done to remove protein sequences that are more similar than the specified threshold.

A database storing the sequence alignments of the most conserved regions of protein families. These alignments are used to derive the BLOSUM matrices. Only the sequences with a percentage of identity lower than the threshold are used. By using the block, counting the pairs of amino acids in each column of the multiple alignment.

It gives the ratio of the occurrence each amino acid combination in the observed data to the expected value of occurrence of the pair. It is rounded off and used in the substitution matrix.

${\displaystyle LogOddRatio=2\log _{2}{\left({\frac {P\left(O\right)}{P\left(E\right)}}\right)}}$

where ${\displaystyle P\left(O\right)}$ is the probability of observing the pair and ${\displaystyle P\left(E\right)}$ is the expected probability of such a pair occurring, given the background probabilities of each amino acid.

The odds for relatedness are calculated from log odd ratio, which are then rounded off to get the substitution matrices BLOSUM matrices.

A scoring matrix or a table of values is required for evaluating the significance of a sequence alignment, such as describing the probability of a biologically meaningful amino-acid or nucleotide residue-pair occurring in an alignment. Typically, when two nucleotide sequences are being compared, all that is being scored is whether or not two bases are the same at one position. All matches and mismatches are respectively given the same score (typically +1 or +5 for matches, and -1 or -4 for mismatches).[9] But it is different for proteins. Substitution matrices for amino acids are more complicated and implicitly take into account everything that might affect the frequency with which any amino acid is substituted for another. The objective is to provide a relatively heavy penalty for aligning two residues together if they have a low probability of being homologous (correctly aligned by evolutionary descent). Two major forces drive the amino-acid substitution rates away from uniformity: substitutions occur with the different frequencies, and lessen functionally tolerated than others. Thus, substitutions are selected against.[7]

Commonly used substitution matrices include the blocks substitution (BLOSUM) [1] and point accepted mutation (PAM) [10][11] matrices. Both are based on taking sets of high-confidence alignments of many homologous proteins and assessing the frequencies of all substitutions, but they are computed using different methods.[7]

Scores within a BLOSUM are log-odds scores that measure, in an alignment, the logarithm for the ratio of the likelihood of two amino acids appearing with a biological sense and the likelihood of the same amino acids appearing by chance. The matrices are based on the minimum percentage identity of the aligned protein sequence used in calculating them.[12] Every possible identity or substitution is assigned a score based on its observed frequencies in the alignment of related proteins.[13] A positive score is given to the more likely substitutions while a negative score is given to the less likely substitutions.

To calculate a BLOSUM matrix, the following equation is used:

${\displaystyle S_{ij}={\frac {1}{\lambda }}\log {\frac {p_{ij}}{q_{i}q_{j}}}}$

Here, ${\displaystyle p_{ij}}$ is the probability of two amino acids ${\displaystyle i}$ and ${\displaystyle j}$ replacing each other in a homologous sequence, and ${\displaystyle q_{i}}$ and ${\displaystyle q_{j}}$ are the background probabilities of finding the amino acids ${\displaystyle i}$ and ${\displaystyle j}$ in any protein sequence. The factor ${\displaystyle \lambda }$ is a scaling factor, set such that the matrix contains easily computable integer values.

BLOSUM scores was used to predict and understand the surface gene variants among hepatitis B virus carriers[15] and T-cell epitopes.[16]

DNA sequences of HBsAg were obtained from 180 patients, in which 51 were chronic HBV carrier and 129 newly diagnosed patients, and compared with consensus sequences built with 168 HBV sequences imported from GenBank. Literature review and BLOSUM scores were used to define potentially altered antigenicity.[15]

A novel input representation has been developed consisting of a combination of sparse encoding, Blosum encoding, and input derived from hidden Markov models. this method predicts T-cell epitopes for the genome of hepatitis C virus and discuss possible applications of the prediction method to guide the process of rational vaccine design.[16]

BLOSUM matrices are also used as a scoring matrix when comparing DNA sequences or protein sequences to judge the quality of the alignment. This form of scoring system is utilized by a wide range of alignment software including BLAST.[17]

In addition to BLOSUM matrices, a previously developed scoring matrix can be used. This is known as a PAM. The two result in the same scoring outcome, but use differing methodologies. BLOSUM looks directly at mutations in motifs of related sequences while PAM's extrapolate evolutionary information based on closely related sequences.[1]

Since both PAM and BLOSUM are different methods for showing the same scoring information, the two can be compared but due to the very different method of obtaining this score, a PAM100 does not equal a BLOSUM100.[18]

There are several software packages in different programming languages that allow easy use of Blosum matrices.

Examples are the blosum module for Python, or the BioJava library for Java.