- Algorithm Alignment score Dynamic Programming Initialization Recursion Base pair probability
- See also
- References
- External links
Probalign is a sequence alignment tool that calculates a maximum expected accuracy alignment using partition function posterior probabilities.[1] Base pair probabilities are estimated using an estimate similar to Boltzmann distribution. The partition function is calculated using a dynamic programming approach.
Algorithm
The following describes the algorithm used by probalign to determine the base pair probabilities.[2]
Alignment score
To score an alignment of two sequences two things are needed:
- a similarity function
(e.g. PAM, BLOSUM,...) - affine gap penalty:
The score 
of an alignment a is defined as:
Now the boltzmann weighted score of an alignment a is:
Where 
is a scaling factor.
The probability of an alignment assuming boltzmann distribution is given by
Where 
is the partition function, i.e. the sum of the boltzmann weights of all alignments.
Dynamic Programming
Let 
denote the partition function of the prefixes 
and 
. Three different cases are considered:
-
the partition function of all alignments of the two prefixes that end in a match. -
the partition function of all alignments of the two prefixes that end in an insertion 
. -
the partition function of all alignments of the two prefixes that end in a deletion 
.
Then we have: 
Initialization
The matrixes are initialized as follows:
Recursion
The partition function for the alignments of two sequences 
and 
is given by 
, which can be recursively computed:
-
-
-
analogously
Base pair probability
Finally the probability that positions 
and 
form a base pair is given by:
are the respective values for the recalculated with inversed base pair strings.
See also
- ProbCons
- Multiple Sequence Alignment
References
2. ^Lecture "Bioinformatics II" at University of Freiburg
External links
- Probalign Webservice
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