Fig 1.
Implied timescales of Markov state models of unbound RNA.
(A) Implied timescale plot for the 5000-state microstate MSM. (B) Implied timescale plot for the 8-state macrostate MSM. (C) Bayes factor as a function of number of coarse-grained macrostates. The smallest number of macrostates immediately preceding a large increase in the Bayes factor (8) was selected as the number of macrostates to include in the macrostate MSM.
Fig 2.
Solution NMR structure of theophylline aptamer in the bound state.
(A) Secondary structure. (B) Tertiary structure. The bound theophylline molecule is colored magenta. (C) Theophylline structure. Depicted RNA structures are based on the first conformer of PDB entry 1EHT. Secondary structure diagram was generated by the RNApdbee webserver[88].
Fig 3.
Conformational diversity of unbound RNA in the presence of 10 mM Mg2+.
Shown are centroid structures of the eight macrostates (M1-M8) taken from the macrostate MSM constructed from 21 μs of MD simulation data. Within parentheses, binding-competent and binding-incompetent macrostates are labeled active and inactive, respectively, and relative populations of macrostates are indicated. Free energies FEi (units of kT) of macrostates relative to FEref, the free energy of the most populated macrostate (macrostate 6, labeled M6), are listed. FEi values are computed as FEi = –ln(pi/pref), where pi and pref are respectively the relative populations of the ith macrostate and the most populated macrostate. Average AutoDock Vina scores for theophylline docking to 500 randomly sampled conformations from each macrostate are listed below the RNA images. Nucleotides defining the theophylline binding site are colored magenta, and C27 is colored green. To enable comparison with the experimental bound-state structure, the first conformer of the solution NMR structure (PDB entry 1EHT) is also shown; the molecular surface of bound theophylline is colored orange.
Fig 4.
Computed mean first passage times (MFPTs) between different macrostates.
Average MFPTs into each ending macrostate are listed above the columns, and average MFPTs out of each starting macrostate are listed to the right of the rows. All times are in terms of nanoseconds.
Fig 5.
Free energy barriers separating MSM macrostates relative to the two lowest free energy barriers.
Average relative free energy barriers for transitions into each ending macrostate are listed above the columns, and average relative free energy barriers for transitions out of each starting macrostate are listed to the right of the rows. All energies are in units of kT. (The two lowest free energy barriers correspond to transitions from state 1 to state 6 and from state 3 to state 6.)
Fig 6.
Variability of RNA tertiary structure in the unbound state.
(A) All-versus-all root-mean-squared deviation (RMSD) chart for pairs of macrostates. Average main chain RMSD values (in nm) for all conformations within each macrostate pair are listed. (B) Main chain overlay of 50 conformations selected randomly from each macrostate. (C) Main chain RMSD ranges of individual nucleotides relative to the reference NMR structure after main chain fitting. The NMR structure is depicted, and per-nucleotide RMSD ranges are colored by nucleotide. (D) Bar plot of ranges of RMSD values of individual nucleotides relative to the NMR structure after main chain fitting. Bars corresponding to nucleotides in the theophylline binding site and nucleotides of the GAAA tetraloop are colored black and gray, respectively.
Fig 7.
Six most frequently observed RNA secondary structures in the absence of bound theophylline.
Numbers denote proportions of all analyzed simulation snapshots in which the RNA adopts the depicted secondary structures. Bases that participate in canonical and non-canonical base pairing interactions are depicted in blue circles and yellow circles connected by dotted lines, respectively. Unpaired bases are depicted in unconnected yellow circles. The secondary structure of the bound-state NMR structure is shown on the far right. Secondary structure diagrams were generated by the RNApdbee webserver[88].
Fig 8.
Spatial arrangements of the bases that form the theophylline binding site in macrostates 1–8.
The base of nucleotide C27 is colored green. Hydrogen bonds are depicted as dotted lines.
Fig 9.
Loss of S-turn between C22 and G26 in unbound RNA.
The main chain of residues 22–26 is colored red; phosphorous atoms of residues 22–26 are depicted as orange spheres. Distances between main chain phosphate atoms of C22 and G25 are indicated. The sharp S-turn in the theophylline-bound state is shown for comparison.
Fig 10.
Previously proposed theophylline binding mechanism based on NMR data.
(Figure adapted from ref. [4]).
Fig 11.
Complete modeled theophylline binding pathway.
(A) Schematic showing the main intermediate states between initial diffusion of theophylline into the RNA binding site (RNAactive,C27-fully-buried + Theo) and the final, fully associated RNA–theophylline complex observed in the NMR structure (RNAactive,C27-fully-out•Theo). (B) Molecular view of the binding pathway. Mean first-passage times (MFPT) required to transition between consecutive intermediate states are shown. The conformational transition from the RNAactive,C27-partially-buried•Theo state, in which theophylline is bound within a non-optimal binding pocket, to the state RNAactive,C27-fully-out•Theo, in which the binding pocket has reached its final, optimal conformation, is characteristic of an induced fit process. This induced fit follows the previously known conformational selection binding mechanism. Theophylline and the C27 base are colored magenta and green, respectively.
Fig 12.
Conformational diversity of unbound RNA in the absence of Mg2+.
Shown are molecular surfaces for binding site regions (residues 5–9 and 22–29) of centroid structures of the six macrostates (M1-M6) taken from the MSM that was constructed from 5.4 μs of MD simulation data. Binding-competent and binding-incompetent macrostates are labeled as active and inactive, respectively, and relative populations of macrostates are indicated. The average theophylline docking score for each macrostate as calculated by AutoDock Vina is listed below each structure. The best-scoring theophylline pose for each structure is shown as an orange surface.
Fig 13.
Absence of Mg2+ distorts the S-turn formed by residues 22–26 and prevents binding site formation.
(A) Ribbon diagrams of the NMR structure (left) and global centroid structure of the five binding-incompetent macrostates from the MD simulations of unbound RNA in the absence of Mg2+. The S-turn region is shown as a wider ribbon colored red. (B) Binding site residues of the global centroid structure. A28 stacks with the C8:G26 base pair, forming a cluster of three residues that prevents binding pocket formation. Ribbon coloring and S-turn region depiction are the same as in panel A.