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| '''Probalign''' is a sequence alignment tool that calculates a maximum expected accuracy alignment using partition function posterior probabilities.<ref>U. Roshan and D. R. Livesay, Probalign: multiple sequence alignment using partition function posterior probabilities, Bioinformatics, 22(22):2715-21, 2006 ([http://bioinformatics.oxfordjournals.org/cgi/reprint/btl472?ijkey=GR3m5VV6yTz1jEx&keytype=ref PDF])</ref> Base pair probabilities are estimated using an estimate similar to [[Boltzmann distribution]]. The partition function is calculated using a [[dynamic programming]] approach.
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| == Algorithm ==
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| The following describes the algorithm used by probalign to determine the base pair probabilities.<ref>[http://www.bioinf.uni-freiburg.de//Lehre/Courses/2011_WS/V_BioinfoII/probalign-partition-func.pdf Lecture "Bioinformatics II" at University of Freiburg]</ref>
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| === Alignment score ===
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| To score an alignment of two sequences two things are needed:
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| * a similarity function <math>\sigma(x,y)</math> (e.g. [[PAM matrix|PAM]], [[BLOSUM]],...)
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| * affine gap penalty: <math> g(k) = \alpha + \beta k</math>
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| The score <math>S(a)</math> of an alignment a is defined as:
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| <math> S(a) = \sum_{x_i-y_j \in a} \sigma(x_i,y_j) + \text{gap cost}</math>
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| Now the boltzmann weighted score of an alignment a is:
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| <math> e^{\frac{S(a)}{T}} = e^{\frac{\sum_{x_i-y_j \in a} \sigma(x_i,y_j) + \text{gap cost}}{T}} =
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| \left( \prod_{x_i - y_i \in a} e^{\frac{\sum_{x_i-y_j \in a} \sigma(x_i,y_j)}{T}} \right) \cdot e^{\frac{gapcost}{T}}</math>
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| Where <math>T</math> is a scaling factor.
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| The probability of an alignment assuming boltzmann distribution is given by
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| <math>Pr[a|x,y] = \frac{e^{\frac{S(a)}{T}}}{Z}</math>
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| Where <math>Z</math> is the partition function, i.e. the sum of the boltzmann weights of all alignments.
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| === Dynamic Programming ===
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| Let <math>Z_{i,j}</math> denote the partition function of the prefixes <math>x_0,x_1,...,x_i</math> and <math>y_0,y_1,...,y_j</math>. Three different cases are considered:
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| # <math>Z^{M}_{i,j}:</math> the partition function of all alignments of the two prefixes that end in a match.
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| # <math>Z^{I}_{i,j}:</math> the partition function of all alignments of the two prefixes that end in an insertion <math>(-,y_j)</math>.
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| # <math>Z^{D}_{i,j}:</math> the partition function of all alignments of the two prefixes that end in a deletion <math>(x_i,-)</math>.
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| Then we have: <math>Z_{i,j} = Z^{M}_{i,j} + Z^{D}_{i,j} + Z^{I}_{i,j}</math>
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| ==== Initialization ====
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| The matrixes are initialized as follows:
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| * <math>Z^{M}_{0,j} = Z^{M}_{i,0} = 0</math>
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| * <math>Z^{M}_{0,0} = 1</math>
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| * <math>Z^{D}_{0,j} = 0</math>
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| * <math>Z^{I}_{i,0} = 0</math>
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| ==== Recursion ====
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| The partition function for the alignments of two sequences <math>x</math> and <math>y</math> is given by <math>Z_{|x|,|y|}</math>, which can be recursively computed:
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| * <math>Z^{M}_{i,j} = Z_{i-1,j-1} \cdot e^{\frac{\sigma(x_i,y_j)}{T}}</math>
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| * <math>Z^{D}_{i,j} = Z^{D}_{i-1,j} \cdot e^{\frac{\beta}{T}} + Z^{M}_{i-1,j} \cdot e^{\frac{g(1)}{T}} + Z^{I}_{i-1,j} \cdot e^{\frac{g(1)}{T}}</math>
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| * <math>Z^{I}_{i,j}</math> analogously
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| === Base pair probability ===
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| Finally the probability that positions <math>x_i</math> and <math>y_j</math> form a base pair is given by:
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| <math>P(x_i - y_j|x,y) = \frac{Z_{i-1,j-1} \cdot e^{\frac{\sigma(x_i,y_j)}{T}} \cdot Z'_{i',j'}}{Z_{|x|,|y|}}</math>
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| <math> Z', i', j'</math> are the respective values for the recalculated <math>Z</math> with inversed base pair strings.
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| == See also ==
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| * [[ProbCons]]
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| * [[Multiple Sequence Alignment]]
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| == References ==
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| {{Reflist}}
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| == External links ==
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| * [http://probalign.njit.edu/probalign/login Probalign Webservice]
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| [[Category:Sequence alignment algorithms]]
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5 Hello there friend. Let me present myself. I am Collin Engelke. Among the best things on the work (www.pinterest.com) planet for him is doing ceramics and he would never ever offer it up. My job is an administrative assistant but I've already made an application for another one. Guam is the only place she's been living in. Look into my website right here: http://www.pinterest.com/judyneinstein/