RNA-RNA interaction is used in many biological processes such as gene expression regulation. In this process, an RNA molecule prohibits the translation of another RNA molecule by establishing stable interactions with it. In this regard, some algorithms have been formed to predict the structure of the interaction between two RNA molecules. One common pitfall in the most algorithms is their high computational time. In this paper, we introduce a novel algorithm called TIRNA to accurately predict the secondary structure between two RNA molecules based on minimum free energy (MFE). The algorithm is stand on a heuristic approach which employs some dot matrices for finding the secondary structure of each RNA and between two RNAs. The proposed algorithm has been performed on some standard datasets such as CopA-CopT, R1inv-R2inv, Tar-Tar*, DIS-DIS and IncRNA₅₄-RepZ in the Escherichia coli bacteria. The time and space complexity of the algorithm are 0(k² log k²) and 0(k²), respectively, where k indicates the sum of the length of two RNAs. The experimental results show the high validity and efficiency of the TIRNA.
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