RNA. 2007 Jul;13(7):939-51. Epub 2007 May 16.

Predicting helical coaxial stacking in RNA multibranch loops.

Source

Department of Biochemistry and Biophysics, University of Rochester Medical Center, Rochester, NY 14642, USA.

Abstract

The hypothesis that RNA coaxial stacking can be predicted by free energy minimization using nearest-neighbor parameters is tested. The results show 58.2% positive predictive value (PPV) and 65.7% sensitivity for accuracy of the lowest free energy configuration compared with crystal structures. The probability of each stacking configuration can be predicted using a partition function calculation. Based on the dependence of accuracy on the calculated probability of the stacks, a probability threshold of 0.7 was chosen for predicting coaxial stacks. When scoring these likely stacks, the PPV was 66.7% at a sensitivity of 51.9%. It is observed that the coaxial stacks of helices that are not separated by unpaired nucleotides can be predicted with a significantly higher accuracy (74.0% PPV, 66.1% sensitivity) than the coaxial stacks mediated by noncanonical base pairs (55.9% PPV, 36.5% sensitivity). It is also shown that the prediction accuracy does not show any obvious trend with multibranch loop complexity as measured by three different parameters.

PMID:: 17507661; [PubMed - indexed for MEDLINE]
PMCID: PMC1894924

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FIGURE 4.

Distribution of (A) number of branches and (B) MBL size (as measured by total bases, including those in the terminal base pairs of helices).

Predicting helical coaxial stacking in RNA multibranch loops

RNA. RNA;13(7):939-951.

FIGURE 3.

Contribution of different RNA types to the data. The rRNAs, by virtue of being the largest and most complex RNAs whose structures are available, contribute a majority of MBLs to the data. Consequently, most of the predicted and total existing stacks also belong to rRNAs.

Predicting helical coaxial stacking in RNA multibranch loops

RNA. RNA;13(7):939-951.

FIGURE 6.

Same stack, different mismatch. Two helices can stack on each other with different bases forming the intervening mismatch leading to a MM stack. These two configurations have different predicted energy and stability. For the purpose of testing the hypothesis, either of these alternative configurations is considered to be correct if helices 1 and 2 have been predicted to stack.

Predicting helical coaxial stacking in RNA multibranch loops

RNA. RNA;13(7):939-951.

FIGURE 5.

Positive predictive value (PPV) and sensitivity for the lowest free energy configuration hypothesis. The number of stacks in each category is plotted on the secondary Y-axis (on the right), and the PPV and sensitivity are plotted on the primary Y-axis (on the left). Flush stacks are predicted with much higher accuracy than MM stacks. The predicted stacks are distributed almost equally among flush and MM types.

Predicting helical coaxial stacking in RNA multibranch loops

RNA. RNA;13(7):939-951.

FIGURE 8.

Dependence of accuracy on elements/branches ratio (e/b ratio). Number of MBLs is plotted on the secondary Y-axis (on the right), and PPV/sensitivity percentage values are plotted on the primary Y-axis (on the left). No monotonous trend is observed, with the highest accuracy tending to coincide with intermediate e/b values. There are many sparse MBLs (e/b = 3) that do not allow any stack predictions. For the MBLs with e/b = 1, all of the predicted stacks existed in the crystal structures.

Predicting helical coaxial stacking in RNA multibranch loops

RNA. RNA;13(7):939-951.

FIGURE 7.

Dependence of accuracy on (A) number of branches and (B) MBL size. Number of MBLs is plotted on the secondary Y-axis (on the right), and PPV/sensitivity percentages are plotted on the primary Y-axis (on the left). There is no apparent trend in either case. Note that the PPV/sensitivity values for eight-way MBLs and 40–56 base-sized MBLs are not defined as is the PPV value for 24–27 base-sized MBL because these are the cases with zero predicted and/or existing stacks.

Predicting helical coaxial stacking in RNA multibranch loops

RNA. RNA;13(7):939-951.

FIGURE 2.

Calculation of free energy contribution of a MM stack. A MM stack with one intervening noncanonical base pair consists of two stacks. Stack A in the figure is a stack where the backbone is continuous on both sides. Stack B, on the other hand, spans a break in the backbone. The overall stacking free energy is calculated in the nearest-neighbor model by adding the terminal mismatch free energy corresponding to stack A to a sequence-independent contribution (−2.1 kcal/mol) for stack B.

Predicting helical coaxial stacking in RNA multibranch loops

RNA. RNA;13(7):939-951.

FIGURE 11.

Accuracy with probability threshold set at 0.7. The number of predicted stacks is plotted on the secondary Y-axis (on the right), and the PPV/sensitivity percentages are plotted on the primary Y-axis (on the left). Note that we predicted considerably more flush stacks than MM stacks, unlike in Figure 5. This is because most of the flush stacks are predicted with higher probability than MM stacks that tend to have more alternative configurations available (and consequently, lower probabilities for any given MM stacking configuration). Again, compared to Figure 5, the partition function approach helps in attaining higher predictive values at the cost of sensitivity.

Predicting helical coaxial stacking in RNA multibranch loops

RNA. RNA;13(7):939-951.

FIGURE 10.

Accuracy dependence on probability threshold: (A) PPV versus probability threshold; (B) sensitivity versus probability threshold. Probabilities are calculated using a partition function based algorithm. Any stacks that are found to have a probability less than the probability threshold are not predicted to stack. This leads to a filtering of low-confidence stacks at the cost of a loss of sensitivity as some of the correctly predicted stacks fall below the probability threshold. This shows up as a monotonous decrease in sensitivity values as we set higher probability thresholds. Note that there is a sharp fall in the sensitivity at probability threshold = 0.7. This is why 0.7 was chosen as the optimal probability threshold.

Predicting helical coaxial stacking in RNA multibranch loops

RNA. RNA;13(7):939-951.

FIGURE 12.

Isolated base pairs as MBL branches. On the left is the schematic representation of the secondary structure of a region of LSU RNA (Ban et al. 2000) of H. marismortui (NDB ID RR0011) with isolated base pairs shown as broken lines. Note that in this case, this region represents one single MBL (as shown by the offset curve with the arrowhead). On the right we have the same region with the isolated base pairs considered as legitimate closing branches of an MBL. This results in the division of the region into two separate MBLs (MBL A and MBL B as shown by the offset curves with arrowheads).

Predicting helical coaxial stacking in RNA multibranch loops

RNA. RNA;13(7):939-951.

FIGURE 13.

Definition of base-pair planes. The planes of the canonical base pairs are determined by finding the average of normal vectors to the planes containing three atoms from the base pair, two of them involved in one of the canonical base-pair hydrogen bonds. In the figure above, it amounts to taking average of the vector products of all the solid lines (hydrogen bonds) and broken lines that intersect at one of the atoms. For example, in a canonical UA base pair (top), the normal vector to the base-pair plane is calculated by

. Note that even though these vectors seem to be coplanar in the figure, this is only for the purpose of clarity. The actual vectors are almost always noncoplanar because the concerned atoms often lie just outside the average plane.

Predicting helical coaxial stacking in RNA multibranch loops

RNA. RNA;13(7):939-951.

FIGURE 14.

Shear criterion for stacking determination. Even if two base pairs lie in parallel planes, they can be sheared so that there is no overlap in the bases and consequently no stacking interaction. The shear criterion is introduced to guard against this situation. In the figure above, C_1,2 is the line joining the centers of the two base pairs and

and

are normal vectors to the planes of the two base pairs. The first subcriterion is that θ₁ and θ₂, the angles that C_1,2 forms with

and

respectively, should be <60° (top). If this condition is satisfied, then the distance between the center of one base pair (bottom, gray) and the normal vector to the other base pair positioned on its center (

, bottom) is determined. The base pairs are deemed not to be stacked if this distance is >10 Å.

Predicting helical coaxial stacking in RNA multibranch loops

RNA. RNA;13(7):939-951.

FIGURE 9.

A four-way MBL without any unpaired bases. This is an MBL with e/b = 1 that contains two coaxial stacks. Each of the base pairs here is the terminal base pair of one of the four helices than come together to form this MBL (i.e., red, blue, faded red, and faded blue are all separate helices). The stacking configurations are predicted correctly in all the three MBLs. This MBL is part of the S domain of Bacillus subtilis RNase P RNA. The four helices that form the branches of this MBL are P7, P8, P9, and P10 helices of the structure (NDB ID: UR0027) (Krasilnikov et al. 2003).

Predicting helical coaxial stacking in RNA multibranch loops

RNA. RNA;13(7):939-951.

FIGURE 1.

Types of coaxial stacking. (A) The secondary structure representation of a typical four-way MBL. The helices are shown in shades of gray and are labeled 1 through 4. The black line segments are unpaired bases. (B) One of the possible configurations that have helix 1 stacking on helix 2 with one intervening mismatch (black segments with a gap). Such a stack is called a mismatch-mediated stack and is abbreviated as an MM stack throughout the text. (C) One of the possible configurations that have helix 2 stacking on helix 3 without any intervening mismatch. Such a stack is called a flush stack and is abbreviated as “F” in the Figures. (D) One of the possible stacking configurations that have helix 1 stacking on helix 4 with two intervening mismatches. Such stacks cannot be predicted by free-energy minimization because the nearest-neighbor model does not assign any stability to mismatches stacking on each other. However, stacks of this kind do exist in the database (see Fig. 15 for one MM stack with as many as four intervening mismatches).

Predicting helical coaxial stacking in RNA multibranch loops

RNA. RNA;13(7):939-951.

FIGURE 15.

Coaxial stacking by base-stack cascade. Shown is an example of coaxial stacking among helical branches of an MBL, intervened by more than a single mismatch and verified by finding a cascade of bases stacking on each other from the terminal base pair of one helix to the terminal base pair of the other helix. The structure is a part of a seven-way MBL in the LSU RNA (Ban et al. 2000) of H. marismortui (NDB ID RR0011). The two terminal base pairs of Helix 36 (blue) and Helix 39 (red) are shown along with a single base cascade composed of four bases (colors cyan, green, purple, and orange) that was found by the base-stack verification algorithm (see Materials and Methods). The hydrogen bonding partners forming the mismatches with the cascade bases are shown (gray) in the first perspective but are removed from the following perspectives for clarity.

Predicting helical coaxial stacking in RNA multibranch loops

RNA. RNA;13(7):939-951.

Publication Types, MeSH Terms, Substances, Grant Support

Publication Types

Evaluation Studies
Research Support, N.I.H., Extramural
Research Support, Non-U.S. Gov't

MeSH Terms

Computational Biology/methods*
Crystallography, X-Ray
Models, Biological
Models, Molecular
Nucleic Acid Conformation*
RNA/chemistry*
RNA, Ribosomal/chemistry
Sensitivity and Specificity
Sequence Analysis, RNA/methods*

Substances

RNA, Ribosomal
RNA

Grant Support

R01 GM076485/GM/NIGMS NIH HHS/United States

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Predicting helical coaxial stacking in RNA multibranch loops.

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