Efficient in silico exploration of RNA interhelical conformations using Euler angles and WExplore

Abstract

HIV-1 TAR RNA is a two-helix bulge motif that plays a critical role in HIV viral replication and is an important drug target. However, efforts at designing TAR inhibitors have been challenged by its high degree of structural flexibility, which includes slow large-amplitude reorientations of its helices with respect to one another. Here, we use the recently introduced algorithm WExplore in combination with Euler angles to achieve unprecedented sampling of the TAR conformational ensemble. Our ensemble achieves similar agreement with experimental NMR data when compared with previous TAR computational studies, and is generated at a fraction of the computational cost. It clearly emerges from configuration space network analysis that the intermittent formation of the A22-U40 base pair acts as a reversible switch that enables sampling of interhelical conformations that would otherwise be topologically disallowed. We find that most previously determined ligand-bound structures are found in similar location in the network, and we use a sample-and-select approach to guide the construction of a set of novel conformations which can serve as the basis for future drug development efforts. Collectively, our findings demonstrate the utility of WExplore in combination with suitable order parameters as a method for exploring RNA conformational space.

Figure 1.

(A) The secondary structure of the TAR hairpin. Residues are color-coded to match the structures on the right. (B) HIV-1 TAR RNA is shown using cartoon and CPK representations. The structure shown is the first NMR model of PDBID 1ANR (52) after energy minimization. (C) Structures of ligand bound conformations (PDBIDs: 2L8H (23), 1ARJ (70)), 1QD3 (17), 2KX5 (22), 2KDQ (21), 1UUD (19), 1LVJ (18), 1UUI (19) and 1UTS (20)), aligned using Helix I (left) and Helix II (right). Helix I is colored in dark blue, Helix II in light blue and the bulge region is colored red. (D) A diagram showing the interhelical Euler angles α_h, β_h and γ_h. Color figure is available online.

Figure 2.

A comparison of sampling in Euler angle space. (A) A comparison of the volume of Euler angle space sampled by three methods: WExplore, 1D WE, and conventional sampling (see Materials and Methods section for details). The dashed blue line shows the sampling of a separate WExplore simulation with a harmonic restraint between bases A22 and U40. An (α_h, β_h, γ_h) cubit is defined as a cube in Euler angle space with edge lengths of 10°. Projections of sampling distributions are shown on α_h: β_h, α_h: γ_h and β_h: γ_h planes for WExplore (B) and conventional sampling (C). For comparison, (B) and (C) both show sampling distributions after 330 cycles (6.6 ns per replica), although the WExplore simulation is continued to 680 cycles (13.6 ns per replica). The color bar in each panel shows the free energy in kT . Color figure is available online.

Figure 3.

The physical basis of the observed partitioning of the configuration space network of TAR. (A) The configuration space network of TAR colored to show the total twist (α_h + γ_h) of each node. Each node in the network represents a given (α_h, β_h, γ_h) conformation and the links between nodes show the transitions between conformations. (B) The nodes are colored to show the A22-U40 base pair distance within each conformation. All nodes with distances greater than 10 Å are colored blue. (C) Representative conformations of the two network partitions, which we label ‘closed’ and ‘open’ for the left and right partition, respectively. The A22 and U40 bases are shown in van der Waals representation. (D) Scatter plot showing the A22-U40 distance versus the total twist for each node. Color figure is available online.

Figure 4.

Visualization of interhelical conformations. Node coloring shows the sampling along the α_h (top), β_h (middle) and γ_h (bottom) interhelical variables. In contrast to Figure 2, here we enforce that β > 0 through the symmetry transformation (α, β, γ) → (α + 180°, −β, γ + 180°), for better visualization. Color figure is available online.

Figure 5.

(A) Probability of a node to be selected by the RDC-based SAS procedure. (B) Detection of states that are not topologically allowed assuming a 3-0 bulge topology. Color figure is available online.

Figure 6.

Mapping ligand-bound structures on the TAR CSN. For each ligand-bound structure, we show a CSN for TAR with the node colorings indicating the distance in Euler angle space from each node to the ligand-bound structure. For NMR structures with multiple models, we plot the distance to the first model in the structure. Nodes that are greater than 50° are colored blue, and red nodes reveal structures that are close to the ligand-bound structure. Each plot is labeled by the name of the inhibitor molecule, except for PDBID:2L8H (23), which shows the bound structure of arginine 4-methoxy-naphthylamide. The PDB indices for the other bound structures are as follows: ADP-1 (1ARJ (70)), Neomycin B (1QD3 (17)), KP-Z-41 (2KX5 (22)), L-22 (2KDQ (21)), RBT203 (1UUD (19)), Acetylpromazine (1LVJ (18)), RBT158 (1UUI (19)), RBT550 (1UTS (20)). Insets are shown that focus on the nodes that are closest to the bound structure, and the number below each shows the closest distance to the bound structure. The plots are sorted by the overall closest distance, and range from 23° for ADP-1 to 5.6° for Acetylpromazine. The insets are connected to transparent green circles in each network that show the area prior to magnification. Color figure is available online.

Figure 7.

Agreement of our simulated ensemble with experimental RDC values of HIV-1 TAR and three elongated constructs. Each dot compares an experimental RDC value to its value predicted from the simulated ensemble. The dot colors are as follows: green is non-elongated TAR; black is EI-22, where Helix I is elongated by 22 base pairs; yellow is EII-22, where Helix II is elongated by 22 base pairs and blue is EI-3, where Helix I is elongated by three base pairs. The top-left and bottom-left panels show the agreement of the raw ensembles predicted by WExplore and Anton with experiment. The top-right and bottom-right panels show the experimental agreement of ensembles generated by SAS using the WExplore and Anton simulation as starting ensembles. Color figure is available online.