RNAFolding

RNAFolding - RNA Folding Algorithms BioE131, Ian Holmes...

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RNA Folding Algorithms BioE131, Ian Holmes
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Free energy of RNA folding
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Watson-Crick base pairing
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Nussinov Algorithm γ (i,j) is the max number of basepairs in subsequence i. .j ∂(i,j) is 1 iff (i,j) form a basepair
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Example implementation For j = 1 to L (in ascending order) Set γ (j,j) = 0 If j>1: Set γ (j-1,j) = δ (j-1,j) If j>2: For i = j-2 to 1 (in descending order) Set γ (i,j) = For k = i+1 to j-1 (in ascending order) Set γ (i,j) = max g i +1, j - 1 ( ) + d i , j ( ) g i +1, j ( ) g i , j - 1 ( ) ae è ç ç ç ö ø ÷ ÷ ÷ max g ( i , j ) g ( i , k ) + g ( k +1, j ) ae è ç ö ø ÷ Rate-limiting step
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Nussinov: memory complexity Number of stored values γ (i,j) is using the result. .. n n =1 N å = 1 2 N ( N +1) 1= 1 2 L 2 j = i +2 L å i =1 L å - 3 2 L
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Asymptotic memory complexity Number of stored values γ (i,j) is For sufficiently large L, the L 2 term will come to dominate the coefficient (1/2) will be irrelevant if we compare to other powers of L (e.g. L, L 3 , L 4 ) 1= 1 2 L 2 j = i +2 L å i =1 L å - 3 2 L
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RNAFolding - RNA Folding Algorithms BioE131, Ian Holmes...

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