The prediction of RNA secondary structure including pseudoknots remains a challenge due to the intractable computation of the sequence conformation from nucleotide interactions. Optimal algorithms often assume a restricted class for the predicted RNA structures and yet still require a high-degree polynomial time complexity, which is too expensive to use. Heuristic methods may yield time-efficient algorithms but they do not guarantee optimality of the predicted structure. This paper introduces a new and efficient algorithm for the prediction of RNA structure with pseudoknots for which the structure is not restricted. Novel prediction techniques are developed based on graph tree decomposition. In particular, stem overlapping relationships are defined with a graph, in which a specialized maximum independent set corresponds to the desired optimal structure. Such a graph is tree decomposable; dynamic programming over a tree decomposition of the graph leads to an efficient optimal algorithm. The new algorithm is evaluated on a large number of RNA sequence sets taken from diverse resources. It demonstrates overall sensitivity and specificity that outperforms or is comparable with those of previous optimal and heuristic algorithms yet it requires significantly less time than other optimal algorithms.

The prediction of RNA secondary structure including pseudoknots remains a challenge due to the intractable computation of the sequence conformation from nucleotide interactions under free energy models. Optimal algorithms often assume a restricted class for the predicted RNA structures and yet still require a high-degree polynomial time complexity, which is too expensive to use. Heuristic methods may yield time-efficient algorithms but they do not guarantee optimality of the predicted structure. This paper introduces a new and efficient algorithm for the prediction of RNA structure with pseudoknots for which the structure is not restricted. Novel prediction techniques are developed based on graph tree decomposition. In particular, based on a simplified energy model, stem overlapping relationships are defined with a graph, in which a specialized maximum independent set corresponds to the desired optimal structure. Such a graph is tree decomposable; dynamic programming over a tree decomposition of the graph leads to an efficient optimal algorithm. The final structure predictions are then based on re-ranking a list of suboptimal structures under a more comprehensive free energy model. The new algorithm is evaluated on a large number of RNA sequence sets taken from diverse resources. It demonstrates overall sensitivity and specificity that outperforms or is comparable with those of previous optimal and heuristic algorithms yet it requires significantly less time than the compared optimal algorithms.

Template-based comparative analysis is a viable approach to the prediction and annotation of pathways in genomes. Methods based solely on sequence similarity may not be effective enough; functional and structural information such as protein-DNA interactions and operons can prove useful in improving the prediction accuracy. In this paper, we present a novel approach to predicting pathways by seeking high overall sequence similarity, functional and structural consistency between the predicted pathways and their templates. In particular, the prediction problem is formulated into finding the maximum independent set (MIS) in the graph constructed based on operon or interaction structures as well as homologous relationships of the involved genes. On such graphs, the MIS problem is solved efficiently via non-trivial tree decomposition of the graphs. The developed algorithm is evaluated based on the annotation of 40 pathways in Escherichia coli (E. coli) K12 using those in Bacillus subtilis (B. subtilis) 168 as templates. It demonstrates overall accuracy that outperforms those of the methods based solely on sequence similarity or using structural information of the genome with integer programming.

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