Figure 1.
Ball-and-stick representation of an RNA fragment.
The seven relevant dihedral angles in the central nucleotide ( to
) are indicated with red labels. Each label is placed on the central bond of the four consecutive atoms that define the dihedral angle. The
angle describes the rotation of the base relative to the RNA backbone, while the six other angles define the course of the backbone. All atoms in the central nucleotide are labeled and colored according to atom type (oxygen: red, phosphor: yellow, nitrogen: blue and carbon/hydrogen: grey). For clarity, the base is only partly shown.
Figure 2.
BARNACLE: a dynamic Bayesian network (DBN) that models the dihedral angles in an RNA fragment.
In the graph, the nodes represent stochastic variables, and the arrows encode their conditional independencies. That is, the graph structure specifies the form of the joint probability distribution of the variables. The shown DBN represents nine consecutive dihedral angles, where the seven central angles originate from a single nucleotide. Each slice (a column of three variables) corresponds to one dihedral angle in an RNA fragment. The variables in each slice are: an angle identifier, Dj, a hidden variable, Hj, and an angular variable, Aj. The angle identifier keeps track of which dihedral angle (from
to
) is represented by a slice, while the angular node models the actual dihedral angle value. The hidden nodes induce dependencies between all angles along the sequence (and not just between angles in consecutive slices).
Figure 3.
The distributions of the and
angles.
The top figure shows the distributions of the angle and the bottom figure shows the distributions of the
angle. The distributions in the experimental data set are shown as histograms. The density functions for the angles in the mixture model and BARNACLE are shown as light and dark grey lines, respectively. Both models capture the tri-modal nature of the
angle and the skewed distribution of the
angle. See Figure S2 for plots of all 7 angles.
Figure 4.
Histograms of pairwise angle distributions.
The figure shows the distributions in the experimental data set (left column) and in data sampled from BARNACLE (middle column) and the mixture model (right column). Top row: the pairwise distributions of the dihedral angles and
within a nucleotide. Bottom row: the pairwise distributions of the inter-nucleotide angles
and α, where each
angle is paired with the neighboring
angle in the 3′-end direction.
Figure 5.
Histograms of the lengths of helical regions.
The distributions in the experimental data set, and in the data sets sampled from BARNACLE and the mixture model are shown. The length is defined as the number of consecutive A-helix rotamers.
Figure 6.
Histograms of the rotamer distributions in the non-helical regions.
The figure shows the distributions in the experimental data set (top and bottom), in the BARNACLE samples (top) and in the mixture model samples (bottom). The names of the rotamers, as defined by the RNA Ontology Consortium [31], are used as index on the horizontal axis. The rotamers are sorted along the horizontal axis according to their frequency in the experimental data set.
Table 1.
Generation of RNA decoys using secondary structure information.
Figure 7.
Decoys generated using BARNACLE, the mixture model and the uniform model.
The decoys shown are those with the lowest full-atom RMSD from the native structures, among all decoys with good secondary structure (energy less than 1.0 Å). Decoys are shown for PDB structures 1ZIH and 1L2X. Pictures made using PyMOL (http://www.pymol.org).
Table 2.
The average suiteness scores for the lowest RMSD decoys.
Figure 8.
Selection of the best models using the Akaike Information Criterion.
The Akaike Information Criterion (AIC) scores are shown for all trained BARNACLE models (top) and mixture models (bottom). The AIC score reaches a minimum for the best model. The BARNACLE model with 20 hidden states, and the mixture model with 25 states have the best AIC scores (shown in red). The best models for each given number of hidden states are shown in black. The dotted lines are tendency lines constructed by cubic splines [43]. The three outliers in the BARNACLE plot (at 10 and 15 hidden states) illustrate that the stochastic expectation maximization procedure can get stuck in a local optimum. Note that the best BARNACLE model has a lower (better) score than the best mixture model.