Rapid ab initio RNA Folding Including Pseudoknots Via Graph Tree Decomposition

Abstract

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.

Inferential Optimization for Simultaneous Fitting of Multiple Components into a CryoEM Map of Their Assembly

“…Combinatorial optimization is a type of optimization in which the set of feasible solutions is discrete, and the goal is to find the best possible solution within this discrete set. Combinatorial optimizers have been suggested for various modeling tasks, such as sidechain packing54–56, threading27, ab initio RNA folding57, and prediction of quaternary structures of multi-protein complexes58. These methods can in principle be re-formulated as a combinatorial optimization of a scoring function represented by a graphical model, benefiting from graph theory techniques23; 24.…”

Text Indexing

“…(See the Locally Testable Codes entry for more details.) This result was later extended by Parnas, Ron, and Samorodnitsky [21]. The class of 1-juntas includes dictator functions, their negations (known as anti-dictator functions), and the constant functions; using the algorithms in [3,21], we can test 1-juntas with O.1= / queries.…”

“…Closely related to the problem of teleportation is the problem of remote state preparation (RSP) introduced by Lo [21]. In teleportation Alice is just given the state to be teleported in some input register and has no other information about it.…”

“…• Polyline grid drawings, where bends in the edges are allowed (at grid-points) [3,8] • Orthogonal 3D drawings, where the edges are routed along the grid-lines [14,21] • Upward 3D drawings of directed acyclic graphs [5,9] • Symmetrical 3D drawings with vertices in R 3 [17] Recommended Reading …”

Tree decomposition-based indexing for efficient shortest path and nearest neighbors query answering on graphs

“…Problems which can be dealt with in this way include many well known NP-complete problems, such as the Independent Set, the Hamiltonian Circuits, etc. Recent applications of tree decomposition based approaches can be found in Constraint Satisfaction [11] and database design [12], and computational biology [13], [14].…”