All-atom energy vs. RMSD plots for <i>de novo</i> modeling of the four puzzles and for optimizing experimental (“native”) conformations.

<p>Panels correspond exactly to panels in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0020044#pone-0020044-g001" target="_blank">Fig. 1</a>. In protein cases (A)-(C), the default Rosetta all-atom energy function for <i>de novo</i> protein modeling (score12) is plotted against Cα RMSD. In the RNA case (D), the FARFAR energy function (which contains torsional terms for RNA, an orientation-dependent solvation function, and a carbon-hydrogen-bond model <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0020044#pone.0020044-Das4" target="_blank">[19]</a>) is plotted against all-heavy-atom RMSD. The conformational sampling algorithms (ABRELAX, SWA, etc.) used in the runs are denoted in the figure and described in detail in Methods.</p

Accuracy achieved on 40 loop modeling cases.

a<p>SWA runs carried out with simplified O(<i>N</i>) calculation scheme; see methods.</p>b<p>Longer and shorter variants of loops were modeled separately; see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0074830#pone-0074830-t001" target="_blank">Table 1</a>.</p

Loop sequences and sources for all test cases.

<p>For statistics N_contact, N_out, N_SC, and N_HB, residues with sequence positions within two residues of each loop residue were excluded from the calculation; only non-hydrogen atoms were considered.</p>a<p>Average number of residues that make at least one atom-atom contact (distance <4.0 Å) with each loop residue.</p>b<p>Avg. number of residues outside the loop that make an atom-atom contact (dist. <4.0 Å) with each loop residue.</p>c<p>Avg. number of residues that make an atom-atom contact (dist. <4.0 Å) to a loop residue involving an atom requiring side-chain placement (not N, C, Cα, Cβ, O).</p>d<p>Avg. number of hydrogen bonds per residue, defined as donor/acceptor pairs with distance less than 3.2 Å.</p>e<p>Test included two crystallographic neighbors that interact with loop <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0074830#pone.0074830-Sellers1" target="_blank">[21]</a>, <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0074830#pone.0074830-Mandell2" target="_blank">[22]</a>.</p>f<p>Loop with irregular structure that remains rigid upon binding to inhibitors or protein partners; see cited references.</p>g<p>Unpublished 275-residue protein crystal structure from W. Weis and colleagues (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0074830#pone-0074830-g005" target="_blank">Figs. 5A–D</a>).</p

Sub-angstrom accuracy in blind structure prediction of protein loops.

<p>Each panel overlays the best of five lowest energy models from stepwise assembly (SWA; carbon atoms in pink) on the crystallographic loop (blue). The build-up path that gave the SWA model is shown as a dynamic-programming-style matrix (black arrows mark single-residue additions; gray arrow marks chain closure step). (<b>a</b>–<b>d)</b> Recovery of loops of an unreleased structure of 275-residue protein with all loops and all side-chains removed, with Cα RMSDs of 0.91 Å, 0.91 Å, 0.54 Å, 0.52 Å. (<b>e</b>) <i>3v7e</i> RNA-puzzle (RMSD 0.54 Å), with RNA component shown in green.</p

Schematics of stepwise assembly calculation.

<p>(<b>a</b>–<b>c</b>) Degrees of freedom sampled by residue-level enumeration (red torsions in backbone, labeled) and by side-chain combinatorial optimization (green torsions) for addition to N-terminal fragment (<b>a</b>), addition to C-terminal fragment (<b>b</b>), and chain-closure step (<b>c</b>). In (a) and (b), note presence of methylamide and acetyl ‘caps’, respectively, to model peptide connection to next residue. (<b>d</b>) Directed acyclic graph (DAG) outlining overall calculation. Movements leftward or downward in the graph indicate building on loop N-terminal fragment and C-terminal fragment, respectively. Each filled circle represents a stage (<i>i</i>, <i>j</i>) at which models are clustered. The diagram is for a loop with <i>N</i> = 6 residues. Chain closure steps (cyan arrows) for models with one-residue gap between N- and C- terminal fragments are shown; for clarity, steps that close two- or three- residue gaps are not shown. (<b>e</b>) Simplified DAG in which fragments are built from N-terminal end without concomitant growth in C-terminal end, or vice versa, followed by chain closure. This calculation takes O (<i>N</i>) computational expense, compared to O(<i>N</i>²) expense of the full DAG in (a).</p

Small “puzzles” for high resolution Rosetta tests.

<p>(A) Trp cage, (B) α-conotoxin GI, (C) Reactive loop of chymotrypsin inhibitor from barley, (D) the UUCG tetraloop (RNA). Each panel shows experimental structures side-by-side with lowest energy Rosetta <i>de novo</i> model discovered in extensive runs (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0020044#pone-0020044-g002" target="_blank">Fig. 2</a> and <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0020044#pone-0020044-t001" target="_blank">Table 1</a>).</p

Lock-picking analogy for high-resolution protein loop structure prediction.

<p>(<b>a</b>) Starting conformation for loop structure prediction (left panel) includes the crystallographic backbone outside the excised loop (white; gray spheres mark loop boundaries) and side-chains in potentially incorrect configurations (white and green). The situation is analogous to a pin tumbler lock (right panel) with spring-loaded pin doublets (green & pink cylinders) in relaxed configurations that disallow turning of the lock cylinder (gray, in cut-away view). (<b>b</b>) Atomic-accuracy solution for protein loop (left panel) involves precise fit of loop backbone (gold) and side-chains (pink) to surrounding protein. Several surrounding side-chains (green) have switched conformations. The solution is analogous to a key (right panel) that precisely slides up the pin doublets so that the boundaries between top and bottom pins coincide with the boundary of lock cylinder, which can then be turned. (<b>c</b>) ‘Stepwise ansatz’ involves residue-by-residue build-up of the protein loop (gold and pink), with fine, all-atom enumerative search of loop conformations (red arrows mark some of the backbone torsions searched) and surrounding side-chains (green) at each step. The strategy is analogous to picking a tumbler lock with a probing pick (gold, right panel) that finely sets the tumbler pins into the turnable configuration through pin-by-pin fine search. [A wrench (light gray) applying torsion to the cylinder helps trap each pin at the boundary].</p

Effect of build-up path on loop conformations.

<p>(<b>a</b>) Five low energy conformations, and (<b>b</b>) corresponding build-up paths and Rosetta all-atom energies (numerical values given in Rosetta units, approximately 1 <i>k</i>_B<i>T</i>) from the <i>1oyc</i> test case of <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0074830#pone-0074830-g001" target="_blank">Figure 1</a>. Different build up paths can give similar configurations (compare brown and blue loops). Similar but distinct paths can give substantially different configurations (compare green, orange, and pink loops).</p

Landscape dissection of a segment of the <i>V. Vulnificus add</i> adenine riboswitch in 0 and 5 mM adenine.

<p>(a) M² measurements in 0 and 5 mM adenine; (b) REEFFIT bootstrapped fits; (c) base pair probability matrices of the structures in the wild type landscape (upper triangles: base pair probability values using no data, lower triangles: REEFFIT calculated base pair probabilities); (d) structure mediods of the structural ensemble found by REEFFIT. In (a-b), The Shine-Dalgarno (SD) ribosome-binding sequence was observed to be SHAPE-reactive even in the absence of adenine; while consistent with this region's unpaired status without and with ligand in prior NMR studies, our studies indicate a more dramatic switch in this region for more complete <i>add</i> riboswitch constructs and will be reported elsewhere. See Supporting Tables H-I in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004473#pcbi.1004473.s001" target="_blank">S1 Text</a> for RNA sequences and fit summaries.</p

Rich RNA Structure Landscapes Revealed by Mutate-and-Map Analysis - Fig 5

<p>Comparison between reactivities predicted by REEFFIT and mutants designed to stabilize the (a) TBWN-A, (b) TBWN-B, (c) TBWN-C structures are given below each state (arrows in the structures mark mutations); each plot shows the measured reactivates for each pair of mutants (orange and green) and predicted REEFFIT reactivates for the corresponding state (blue with error bars). (d) Determining FMN dissociation constants for stabilizing mutants of the TBWN-A, TBWN-B, and TBWN-C structures of the Tebowned FMN switch using the LIFFT HiTRACE toolkit (showing data for residue 15, see Supporting Fig I in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004473#pcbi.1004473.s001" target="_blank">S1 Text</a>) are shown below the mutants.</p