partition function for circular rna and applicationronny/chribska2006.pdf · partition function for...

Partition function for linear RNAsExtension for circular RNAs

Application

Partition function for circular RNA and Application

Ronny [email protected]

Department of BioinformaticsUniversity of Leipzig

October 30, 2006

Ronny Lorenz Partition function for circular RNA and Application


Application

1 Partition function for linear RNAsStructure decomposition



Application


2 Extension for circular RNAsStructure decomposition



Application


2 Extension for circular RNAsStructure decomposition

3 ApplicationOccurence of circular RNAsMetastable Structures



ApplicationStructure decomposition

let S be the set of all possible secondary structures for a givenRNA sequence

each s ∈ S is associated with a free energy Gs

The partition function Q for a given sequence

Q = ∑s∈S

e−GsRT (1)




i and j do not pair

i and j form a hairpin loop, with closing pair [i,j],

there exist two positions k,l with i < k < l < j so that thesubsequence i,j forms an interior loop with closing pairs i,j andk,l

i and j are the closing pair of a multiloop

dynamic programming approach, that calculates the partitionfunction for all subsequences x [i, j] and ends with the partitionfunction for the whole sequence...




Decomposition of paired/unpaired i,j

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i j=

i i+1 j|

i jk+1k

Q




Decomposition of paired/unpaired i,j

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i j=

i i+1 j|

i jk+1k

Q

Qi,j = 1+ ∑1<k<j

Qbi,k ·Qk+1,j (2)




Decomposition with constraint that i pair with j

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| |=i j i j i ij jd e u u+1

Qb




Decomposition with constraint that i pair with j

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| |=i j i j i ij jd e u u+1

Qb

Qbi,j = e

−GHi ,j

RT +

∑i<d<e<j

e−G

Ii ,d ,e,jRT ·Qb

d ,e +

∑i<u<j

Qmi+1,u ·Q

m1u+1,j−1 ·e

−aRT (3)




Decomposition of multiloop

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= | |i j ji i ij jj−1 uu+1 u+1u

mQ




Decomposition of multiloop

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= | |i j ji i ij jj−1 uu+1 u+1u

mQ

Qmi,j = Qm

i,j−1 ·e−cRT +

∑i<u<j

e−(u−i−1)·c−b

RT ·Qbu+1,j +

∑i<u<j

Qmi,u ·Q

bu+1,j ·e

−bRT (4)




Decomposition of multiloop part with exactly one component

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i j|=

j jii j−1

Qm1




Decomposition of multiloop part with exactly one component

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i j|=

j jii j−1

Qm1

Qm1i,j = Qm1

i,j−1 ·e−cRT +

Qbi,j ·e

−bRT (5)




Similarities to linear case:





Q is also computed by previously computing Qi,j for allsubsequences






structure decomposition for Qi,j∀1 ≤ i < j ≤ n







Difference:







Difference:

computing sum of weighted energies for all loops that containbases xn and x1







Difference:

computing sum of weighted energies for all loops that containbases xn and x1

leads to the computation of so called ”exterior loops”




Computation of M2 Array

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k n=

k nu u+1




Computation of M2 Array

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k n=

k nu u+1

QM2k ,n = ∑

k<u<n

Qm1k ,u ·Q

m1u+1,n (6)




Computation of exterior hairpin loop

1n

1n

=

p

q




Computation of exterior hairpin loop

1n

1n

=

p

q

QoH = ∑

p<qQb

p,q ·e−GHq,p

RT (7)




Computation of exterior interior loop

1n

1n

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k

l

p

q

=




Computation of exterior interior loop

1n

1n

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k

l

p

q

=

QoI = ∑

k<l<p<q

Qbk ,l ·Q

bp,q ·e

−GIk ,l ,p,qRT (8)




Computation of exterior multiloop

1n

1n��

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=

kk+1




Computation of exterior multiloop

1n

1n��

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=

kk+1

QoM = ∑

1<k<n

Qm1,k ·Q

M2k+1,n ·e

−aRT (9)




Partition function for circular case:

Qo = QoH +Qo

I +QoM (10)




This is the step where i am actually in my diploma thesis




This is the step where i am actually in my diploma thesisI will skip





equations for base pairing probability matrix





equations for base pairing probability matrix

way of backtracking to obtain secondary structures



Application

Occurence of circular RNAsMetastable Structures

Most known RNAs are linear and circular RNAs are not found veryoftenBut they are found in:



Application



Viroids and satellite RNAs (sizes arround 300-400 nt)



Application




Genome of Hepatitis δ virus



Application





spliced Group I Introns



Application






Box C/D RNAs in Pyrococcus furiosus



Application







other



Application







other

In almost all cases, circular RNAs code not for any mRNA but fortheir own structure



Application


What can be the aim for application of CPF?



Application



finding metastable structure states



Application




better prediction of circular RNA structures



Application




better prediction of circular RNA structures

other things I did not have thought about yet



Application


Thank you for your attention


partition function for circular rna and applicationronny/chribska2006.pdf · partition function for...

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