Fig 1.
The representations of all-atom and CG model for each deoxynucleotide and ss/dsDNA molecules, as well as the schematics of base-pairing and base-stacking in the present model.
(A) Our coarse-grained representation of a DNA fragments including deoxynucleotides of A, T, G, and C superimposed on the all-atom representation. The three beads are located at phosphate (P), sugar (C4’) and pyrimidine (N1) or purine (N9). θ and φ are the schematics of CG bonded angle (CPC) and dihedral (CPCP), respectively. (B) The schematic representation of base-pairing (blue) and base-stacking (red) interaction. (C,D) The 3D structures of (C) a dsDNA with bulge loop (PDB:1qsk) and (D) an ssDNA hairpin (PDB: 1jve) in all-atomistic (left) and our CG representation (right). The 3D structures are shown with PyMol (http://www.pymol.org).
Table 1.
The melting temperatures (Tm) for dsDNAs at 1M [Na+].
Table 2.
The melting temperatures (Tm) for single-stranded DNAs at given ion conditions.
Fig 2.
3D structure prediction for the paradigm dsDNA/ssDNA in the present model.
(A,B) The time-evolution of system energy, number of base-pairs, RMSD from native structure, and typical 3D conformations (from top to bottom, respectively) during the Monte Carlo simulated annealing simulation for (A) a dsDNA (PDB: 1qsk) and (B) an ssDNA (PDB: 1jve). The insets show the RMSDs of refined conformations calculated over all CG beads from the corresponding atoms in native structures. The 3D structures are shown with PyMol (http://www.pymol.org).
Fig 3.
The display of typical predicted 3D structures, and comparisons of RMSDs between the present model and other models.
(A,C) The predicted 3D structures (ball-stick) with the mean (top) and minimum (bottom) RMSDs for (A) three sample dsDNAs (PDBs: 1agh, 1qsk, and 1mnm) and (C) three ssDNAs (PDBs: 4kbl, 2l5k, and 1jve) from their native structures (cartoon). (B,D) The comparison of the predicted structures between the present model and the existing models including the 3dRNA/DNA and the models from Scheraga’s or Saiz’s group for (B) 20 dsDNAs and (D) 20 ssDNAs. The results of 3dRNA/DNA are predicted through their online server based on the native secondary structures [53]. The other data is taken from refs. 56 and 59. The 3D structures are shown with PyMol (http://www.pymol.org).
Fig 4.
The stability predictions for dsDNAs in the present model.
(A) The time-evolution of the number of base-pairs for a dsDNA (sequence: (GGACGTCC)2; strand concentration: 1mM) at different temperatures (90°C, 65°C, 40°C from top to bottom, respectively) in 1M NaCl solution. (B) The fractions of unfolded state f as functions of temperature for the dsDNA in (A). Green triangle: predictions at high strand concentration (1mM). Purple square: predictions at experimental strand concentration (0.1mM). Two dotted lines are the fitted melting curves to the corresponding predicted data. The solid line is calculated through Eq 7. Ball-stick: the typical 3D structures predicted at low and high temperatures shown with PyMol (http://www.pymol.org). (C) The melting temperatures (Tm’s) as functions of strand concentration for three dsDNAs: purple, (GGACGTCC)2, blue, (GTTGCAAC)2, and red, (CGATATCG)2 at 1M [Na+]. Symbols: experimental results [71]. Lines: predictions from the present model. (D) The predicted (solid lines) and experimental (dotted lines) melting curves [89] for the dsDNA harboring symmetric internal loops with sequences of CTCGTC(T)NCAGTGC/GCACTG(T)NGACGAG in 1M NaCl solution. Green: N = 0, i.e., the double helix without internal loop. Blue: N = 2. Purple: N = 6.
Fig 5.
The stability predictions for ssDNA hairpins in the present model.
(A) The time-evolution of the number of base-pairs for a simple hairpin (GCGC(T)5GCGC) at different temperatures (90°C, 70°C, 50°C from top to bottom, respectively) in 0.1M NaCl solution. (B) The fraction of unfolded state f as a function of temperature for the hairpin in (A). Symbols: predictions from the present model. Line: fitted melting curve to the predicted data through Eqs 4–6. Ball-stick: the typical 3D structures predicted at low and high temperatures shown with PyMol (http://www.pymol.org). (C) The comparisons between predictions (solid lines) and experiments (dotted lines) for four DNA hairpins (GCGC(T)NGCGC) with different loop lengths at 0.1M [Na+]. Red: N = 3. Green: N = 5. Blue: N = 7. Black: N = 9. df/dT: the first derivative of predicted f with the temperature. Cp: the heat capacity from experiment [90].
Fig 6.
The stability prediction for an ssDNA with two hairpins and a DNA pseudoknot in the present model.
(A) The schematics of secondary structure for the ssDNA with two hairpins (top) and the DNA pseudoknot (bottom). (B,C) The comparisons between predictions (solid lines) and experiments (dotted lines) for the two ssDNAs in (a). df/dT: the first derivative of predicted f with the temperature. Cp: the heat capacity from experiments [90,92]. Ball-stick: the typical 3D structures predicted at different temperatures shown with PyMol (http://www.pymol.org).
Fig 7.
The comparisons of stability between predictions (lines) and experiments (symbols) for dsDNAs in monovalent/divalent ion solutions.
(A) The melting temperatures (Tm’s) as functions of [Na+] for three dsDNAs with sequences of (GCATGC)2, (GATGCGCTCG)2, (ACCCCGCAATACATG)2 from bottom to top, respectively. Symbols: experimental data [87,97]. Lines: predictions from the present model. (B) The melting temperatures (Tm’s) as functions of [Mg2+] for the dsDNA with sequence of (GCATGC)2 at different [Na+]’s: 0.012M, 0.15M, and 1M from bottom to top, respectively. Symbols: experimental data [87]. Lines: predictions from the present model.
Fig 8.
The comparisons of stability between predictions (lines) and experiments (symbols) for ssDNAs in monovalent/divalent ion solutions.
(A) The melting temperatures (Tm’s) as functions of [Na+] for the DNA hairpins (GCGC(T)NGCGC) with different loop lengths: 5, 7, and 9 from top to bottom, respectively. Symbols: experimental data [90]. Lines: predictions from the present model. (B) The melting temperatures (Tm’s) as functions of [Mg2+] for the DNA hairpins (CGGATAA(T)NTTATCCG) with different loop lengths: 8, 12, and 16 from top to bottom, respectively. Symbols: experimental data at 2.5mM or 33mM [Mg2+] with 10mM Tris-HCl buffer [96]. Lines: predictions from the present model at extensive [Mg2+]’s without Na+.