Figure 1.
Circles represent nucleotides. Solid lines indicate covalent phosphodiester bonds, and dashed lines indicate hydrogen-bonded base pairs. B. All possible non-pseudoknot pairs for the simple sequence 5′CCCAAAAGGG are listed below. Parentheses indicate pairs, and dots represent nonpaired nucleotides. C. An example of one step of the algorithm. Dashes indicate nucleotides that have not yet been examined. Dots indicate unpaired nucleotides. Parentheses indicate paired nucleotides. Nucleotide pairing follows Watson-Crick and GU pair rules. S is an RNA secondary structure or partial structure represented by a set of pairs (i,j). I is a stack of ranges (i,j]. Each range is a segment of the sequence that has yet to be examined. D. An empty list is defined as I = (). Adding an element X to a list is defined as I = X.I. Removing the most recently added element to the list, i.e. pop an element from the list, is defined as pop(I) = = X, so that I = = ().
Table 1.
Work Distribution in Parallel Computations.
Figure 2.
Ring Graph Parallelization Diagram for Crumple.
Red Arrows indicate the direction of requests for work. Green arrows indicate the flow of distributed work. One node is arbitrarily selected as the first and master node.
Figure 3.
Red squares are ideal speedup. Blue diamonds are the values measured using the gA48 sequence with no constraints on the Sooner supercomputer. Speed up is the ratio of real computation time in serial to real computation time in parallel. Note that one unit of work is assigned to each core, thus one node is equivalent to one core in this case.
Table 2.
Examples of Crumple Computations for Biological RNAs.
Figure 4.
Alfalfa Mosaic Virus RNA 4 Protein Binding Site.
A. Secondary structure with pseudoknots as seen in the crystal structure of the RNA-protein complex [21]. B. Secondary structure without pseudoknot interactions as determined by chemical and enzymatic probing of the RNA in isolation [22], [23]. C. Alternative AMV secondary structure containing a multibranch loop that is also consistent with the set of constraints listed in Table 3 legend. Secondary structures pictures were generated with RNA Pseudoviewer [47].
Table 3.
Experimental Constraints Reduce the Conformation Space for Minimal Protein Binding Site of Alfalfa Mosaic Virus RNA 4.
Figure 5.
Guide RNA Secondary Structures.
A. Secondary structure proposed from chemical and enzymatic probing of RNA in vitro [17]. In the protein-RNA crystal structure [36], only the first short hairpin is observed, and the second hairpin is unwound and only density for four nucleotides is observed. The structure shown in A has a predicted free energy greater than 0 kcal/mol [15]. B. Lowest energy secondary structure consistent with the given set of constraints. The predicted free energy is −1.6 kcal/mol. C. Alternative secondary structures that are consistent with the given set of constraints and that are not sampled by RNAStructure [48] or Sfold [49]. Secondary structures pictures were generated with RNA Pseudoviewer [47]. Experimental constraints include the following: chemically modified nucleotides A12, A13, A19, A24, A25, A27, G18, G21, G35, G40, G44 and single stranded nucleotides A12,A13,G18,U20,G40,G44.