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## Nussinov RNA folding algorithm + recursive backtrack. Implemented by Carlos G. Oliver ##
import numpy as np
min_loop_length = 4
def ss_to_bp(ss):
pairs = []
stack = []
for i, b in enumerate(ss):
if b == "(":
if b == ")":
pairs.append((stack.pop(), i))
if len(stack) > 0:
return None
return (ss, pairs)
def pair_check(tup):
if tup in [('A', 'U'), ('U', 'A'), ('C', 'G'), ('G', 'C')]:
return True
return False
def OPT(i,j, sequence):
returns the score of the optimal pairing between indices i and j
#base case: no pairs allowed when i and j are less than 4 bases apart
if i >= j-min_loop_length:
return 0
#i and j can either be paired or not be paired, if not paired then the optimal score is OPT(i,j-1)
unpaired = OPT(i, j-1, sequence)
#check if j can be involved in a pairing with a position t
pairing = [1 + OPT(i, t-1, sequence) + OPT(t+1, j-1, sequence) for t in range(i, j-4)\
if pair_check((sequence[t], sequence[j]))]
if not pairing:
pairing = [0]
paired = max(pairing)
return max(unpaired, paired)
def traceback(i, j, structure, DP, sequence):
#in this case we've gone through the whole sequence. Nothing to do.
if j <= i:
#if j is unpaired, there will be no change in score when we take it out, so we just recurse to the next index
elif DP[i][j] == DP[i][j-1]:
traceback(i, j-1, structure, DP, sequence)
#consider cases where j forms a pair.
#try pairing j with a matching index k to its left.
for k in [b for b in range(i, j-min_loop_length) if pair_check((sequence[b], sequence[j]))]:
#if the score at i,j is the result of adding 1 from pairing (j,k) and whatever score
#comes from the substructure to its left (i, k-1) and to its right (k+1, j-1)
if k-1 < 0:
if DP[i][j] == DP[k+1][j-1] + 1:
traceback(k+1, j-1, structure, DP, sequence)
elif DP[i][j] == DP[i][k-1] + DP[k+1][j-1] + 1:
#add the pair (j,k) to our list of pairs
#move the recursion to the two substructures formed by this pairing
traceback(i, k-1, structure, DP, sequence)
traceback(k+1, j-1, structure, DP, sequence)
def write_structure(sequence, structure):
dot_bracket = ["." for _ in range(len(sequence))]
for s in structure:
dot_bracket[min(s)] = "("
dot_bracket[max(s)] = ")"
return "".join(dot_bracket)
#initialize matrix with zeros where can't have pairings
def initialize(N):
#NxN matrix that stores the scores of the optimal pairings.
DP = np.empty((N,N))
DP[:] = np.NAN
for k in range(0, min_loop_length):
for i in range(N-k):
j = i + k
DP[i][j] = 0
return DP
def nussinov(sequence):
N = len(sequence)
DP = initialize(N)
structure = []
#fill the DP matrix diagonally
for k in range(min_loop_length, N):
for i in range(N-k):
j = i + k
DP[i][j] = OPT(i,j, sequence)
#copy values to lower triangle to avoid null references
for i in range(N):
for j in range(0, i):
DP[i][j] = DP[j][i]
traceback(0,N-1, structure, DP, sequence)
return (write_structure(sequence, structure), structure)
if __name__ == "__main__":
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