Fig 1.
The representation of all-atom and CG model for an RNA pseudoknot, and 3D structure prediction for a paradigm pseudoknot in the present model.
(a) The 3D structure of MMTV pseudoknot (PDB code: 1rnk) in all-atomistic (left) and our CG representation (right) as well as the schematic representation for one nucleotide in the present CG model (middle). (b) The secondary structure for MMTV pseudoknot consisting of two stems and three loops. The corresponding secondary structure elements in (a) and (b) are in same colors: Stem 1 (red), Stem 2 (green), Loop 1 (blue), Loop 2 (cyan), Loop 3 (magenta) and the 3' dangling nucleotide U (orange). (c, d) The time-evolution of the energy (top panel in (c)), the number of base pairs (middle panel in (c)), the RMSDs between predicted structures and the native structure in PDB (bottom panel in (c)), and the typical 3D structures (d) during the Monte Carlo simulated annealing simulation of the Aquifex aeolicus tmRNA pseudoknot PK1 (PDB code: 2g1w). The inset in bottom panel in (c) shows the zoomed portion of the figure in the interval of [1.6✕107, 2✕107]. The RMSDs are calculated over C beads from the corresponding C4’ atoms in native structure, and the structures in (d) are shown with the PyMol (http://www.pymol.org).
Fig 2.
Comparisons of RMSDs between the present model and other models.
(a) The predicted 3D structures (ball-stick) with the mean RMSDs (top) and the minimum RMSDs (bottom) for four sample RNA pseudoknots (PDB codes: 2g1w, 2tpk, 1e95, and 2lc8) from their native structures (cartoon). The mean (minimum) RMSDs for three pseudoknots are 4.8 Å (3.3 Å), 4.4 Å (2.8 Å), 5.4 Å (3.5 Å) and 7.4 Å (5.1 Å), respectively, and the 3D structures are shown with the PyMol (http://www.pymol.org). (b) The predictions for the 3D structures of 17 RNA pseudoknots from the present model, from the MC-Fold/MC-Sym pipeline and from the RNAComposer. The RMSDs of predicted structures for 17 RNA pseudoknots are calculated over C beads from the corresponding C4’ atoms in native structures.
Fig 3.
The stability prediction for a sample RNA pseudoknot in the present model.
(a) The time-evolution of the number of base pairs for MMTV pseudoknot (shown in Fig 1A) at different temperatures (100°C, 80°C, 60°C, 40°C from top to bottom, respectively) in 50mM KCl solution. (b) The fractions of folded state (F, black), unfolded state (U, blue), and intermediate state (I, red) as a function of temperature for MMTV pseudoknot at 50mM [K+]. The dotted lines are fitted to the predicted data through Eqs. 2 and 3. (c) The fraction of denatured base pairs f as a function of temperature for MMTV pseudoknot at 50mM [K+]; symbols: from the present model; line: from Eq 4. Ball-stick: the typical 3D structures predicted at different temperatures shown with the PyMol (http://www.pymol.org).
Fig 4.
The comparisons between predictions (lines) and experiments (symbols) for six RNA pseudoknots with various sequences at high salt concentrations.
(a) MMTV pseudoknot at 1000mM [K+] [75]; (b) T2 pseudoknot at 1000mM [K+] [77]; (c) PEMV-1 pseudoknot at 500mM [K+] [73]; (d) BWYV pseudoknot at 500mM [K+] [54,72]; (e) PLRV pseudoknot at 500mM [K+] [73]; and (f) ScYLV pseudoknot at 500mM [K+] [74]. Lines: df/dT, the first derivative of f with the temperature. Symbols: the heat capacity Cp or dA/dT, the first derivative of absorbance with respect to temperature.
Fig 5.
The comparisons between predictions (lines) and experiments (symbols) for MMTV and T2 pseudoknots in monovalent ion solutions.
(a) MMTV pseudoknot at 1000mM [K+] (green square) and 50mM [K+] (red triangle), respectively. Lines: df/dT, the first derivative of f with respect to temperature. Symbols: the heat capacity Cp. (c) T2 pseudoknot at 1000mM [K+] (green square) and 100mM [K+] (red triangle), respectively. Symbols: dA/dT, the first derivative of absorbance with respect to temperature. (b, d) The melting temperatures Tm1 and Tm2 of two transitions (F→I and I→U) as functions of [K+] for MMTV (b) and T2 (d) pseudoknots. Symbols: experimental Tm1 (blue square) and Tm2 (red triangle) [75,77]. Lines: corresponding predictions.
Table 1.
The melting temperatures (Tm1 and Tm2)a of six RNA pseudoknots at high salt concentrations.
Fig 6.
The comparisons between predictions (lines) and experiments (symbols) for MMTV and T2 pseudoknots in divalent ion solutions.
(a) MMTV pseudoknot at 50mM [K+] with 0.5mM [Mg2+] and 3.0mM [Mg2+], respectively. Symbols: the heat capacity Cp for MMTV pseudoknot at 50mM [K+] with 0.5mM [Mg2+]. (c) T2 pseudoknot at 100mM [K+] with 0.1mM [Mg2+] and 1.0mM [Mg2+], respectively. Symbols: dA/dT, the first derivative of absorbance with respect to temperature. (b, d) The melting temperatures Tm1 and Tm2 of two transitions (F→I and I→U) as functions of [Mg2+] for MMTV pseudoknot in the presence of 50mM [K+] (b) and T2 pseudoknot in the presence of 100mM [K+] (d). Symbols: experimental Tm1 (blue square) and Tm2 (red triangle) [75,77]. Lines: corresponding predictions.
Fig 7.
The predicted thermal unfolding of MMTV, T2 and T2 variant pseudoknots at 1M [K+].
(a-c) The fractions of F, S1, S2 and U states as functions of temperature in thermal unfolding of MMTV (a), T2 (b), and T2 variant (c) pseudoknots at 1M [K+]. F stands for fully folded RNA; S1, hairpin intermediate with Stem 1; S2, hairpin intermediate with Stem 2; U, fully unfolded RNA. (d) Schematic diagram shows the dominating structural transitions of MMTV pseudoknot along the unfolding pathway inferred from the fraction of states shown in panel (a). (e) Schematic diagram shows the structural transitions of T2 pseudoknot and the variant of T2 pseudoknot along the unfolding pathway inferred from their respective fraction of states shown in panels (b) and (c).
Fig 8.
The fractions of F, S1, S2 and U states as functions of temperature in thermal unfolding of MMTV (a-c) and T2 (d-f) pseudoknots at different [K+]’s. F stands for fully folded RNA; S1, hairpin intermediate with Stem1; S2, hairpin intermediate with Stem2; U, fully unfolded RNA.