An Approximation Scheme for RNA folding Structure Prediction including
Pseudoknots
Zhendong Liu
1,2
,Daming Zhu
1
1
School of Computer Science and Technology of
Shandong University
Jinan, China
e-mail: liuzd2000@126.com
Wei Cui
2
,Nan Liu
2
2
School of Computer Science and Technology
Shandong Jianzhu University
Jinan, China
e-mail: liuzd2000@tom.com
Abstract—The paper further investigates the computational
problem and complexity of predicting Ribonucleic Acid
structure. In order to find a way to optimize the Ribonucleic
Acid pseudoknotted structure, we investigate the Ribonucleic
Acid pseudoknotted structure based on thermal dynamic
model, computational methods,minimum free energy are
adopted to predict Ribonucleic Acid structure. The
contribution of this paper is to obtain an efficient
Approximation algorithm for finding RNA pseudoknotted
structure,compared with other algorithms, the algorithm takes
O(n
3
) time and O(n
2
) space. The experimental test in
PseudoBase shows that the algorithm is more effective and
exact than other algorithms, and the algorithm can predict
arbitrary pseudoknots. And we also give a proof of existing 1+ε
(ε>0) Polynomial Time Approximation Scheme(PTAS) in
Searching Maximum Number of Stackings.
Keywords-pseudoknotted structure;minimum free energy;
stem ; Polynomial Time Approximation Schem;stacking
I. INTRODUCTION
Ribonucleic Acid (RNA) is an important
biomacromolecule which performs a wide range of function
in biological system. RNA are three-dimensional molecules,
an RNA molecule folds into a three-dimensional structure by
forming pairs of bases, pseudoknots are known to exist in
some RNAs. For predicting secondary structures with
pseudoknots, Nussinov et al. (1978)have studied the case
where the energy function is minimized when the numberof
base pairs is maximized and have obtained an O(n
3
) time
algorithm for predicting RNA secondary structures[1], but
Nussinov algorithm can not predict pseudoknotted structure.
Algebraic dynamic programming algorithm for finding RNA
pseudoknotted structure with simple planar pseudoknots was
proposed by Jens and Robert, the algorithm takes O(n
4
) time
and O(n
2
) space [2]. Efficient algorithms for finding optimal
foldings of an RNA structure have been known first by
Michael Zuker [3]. Pknots algorithm for RNA pseudoknotted
structure of predigesting model based on minimum free
energy have presented by Rivas and Eddy, whose time
complexity and space comlexity are O(n
6
) and O(n
4
)
respectively [4]. The problem for predicting RNA secondary
structure including pseudoknots is NP-complete[5],and
predicting RNA pseudoknotted structure with arbitrary
pseudoknots is a NP-hard problem[6].in mimic RNA
structure, pseudoknots are apparently exist[7]. A heuristic
algorithm including pseudoknots for finding RNA
pseudoknotted structures Jihong Ren [8].
The paper presents a new efficient algorithm including
pseudoknots with thermal dynamic model and stable stems,
and implement the algorithm in VC++ to complete the
computation.
II. H
EURISTIC ALGORITHM
2.1 Terminology
1)RNA: Ribonucleic Acid.
2)RNA Sequence :Let S=s
1
s
2…
s
i…
s
n
be an RNA sequence,
base s
i
∈{A, U, C, G}, 1≤i≤n. The subsequence s
i, j
= s
i
s
i+1…
s
j
is a segment
of S, 1≤i≤j≤ n.
3) MFE: Minimum Free Energy.
4) stem: the RNA structure closed by base pairs (i, j) and
(k, l)∈S, (i, j), (i+1, j-1), ..., (k, l) are base pairs, i≤k<l≤j.
5)PTAS: Polynomial Time Approximation Scheme.
2.2 Dynamic programming algorithm
1)Given S=s
1
s
2
…s
n
, s
ij
=s
i
…s
j
, V(i,j), W(i,j) and W
M
(i,j) can
be computed as follows,1≤i<j≤n.
2013 Ninth International Conference on Computational Intelligence and Security
978-1-4799-2548-3/13 $31.00 © 2013 IEEE
DOI 10.1109/CIS.2013.9
6
2013 Ninth International Conference on Computational Intelligence and Security
978-1-4799-2548-3/13 $31.00 © 2013 IEEE
DOI 10.1109/CIS.2013.9
6
2013 Ninth International Conference on Computational Intelligence and Security
978-1-4799-2548-3/13 $31.00 © 2013 IEEE
DOI 10.1109/CIS.2013.9
6
2013 Ninth International Conference on Computational Intelligence and Security
978-1-4799-2548-3/13 $31.00 © 2013 IEEE
DOI 10.1109/CIS.2013.9
6
2013 Ninth International Conference on Computational Intelligence and Security
978-1-4799-2548-3/13 $31.00 © 2013 IEEE
DOI 10.1109/CIS.2013.9
6
2013 Ninth International Conference on Computational Intelligence and Security
978-1-4799-2548-3/13 $31.00 © 2013 IEEE
DOI 10.1109/CIS.2013.9
6