The physical determinants of the DNA conformational landscape: an analysis of the potential energy surface of single-strand dinucleotides in the conformational space of duplex DNA

Abstract

A multivariate analysis of the backbone and sugar torsion angles of dinucleotide fragments was used to construct a 3D principal conformational subspace (PCS) of DNA duplex crystal structures. The potential energy surface (PES) within the PCS was mapped for a single-strand dinucleotide model using an empirical energy function. The low energy regions of the surface encompass known DNA forms and also identify previously unclassified conformers. The physical determinants of the conformational landscape are found to be predominantly steric interactions within the dinucleotide backbone, with medium-dependent backbone-base electrostatic interactions serving to tune the relative stability of the different local energy minima. The fidelity of the PES to duplex DNA properties is validated through a correspondence to the conformational distribution of duplex DNA crystal structures and the reproduction of observed sequence specific propensities for the formation of A-form DNA. The utility of the PES is demonstrated through its succinct and accurate description of complex conformational processes in simulations of duplex DNA. The study suggests that stereochemical considerations of the nucleic acid backbone play a role in determining conformational preferences of DNA which is analogous to the role of local steric interactions in determining polypeptide secondary structure.

Figure 1

The torsion angle variables of the dinucleotide backbone fragment included in the PCA (see Table 1). The conformation of the sugar–phosphate backbone is conventionally defined by six torsion angles labelled α to γ, with χ describing the N-C1′ glycosyl linkage to the bases. For each sugar, there are five torsion angles ν₀ to ν₄ in the furanose ring [conventionally described via a pseudorotation phase angle (32)].

Figure 2

Stereo (wall-eyed) diagrams showing the geometric character of the principal components. The individual panels show sequential displacements along each of the first three principal components with respect to the average structure (Table 2) over the range −200° to 200° at 20° increments for (a) PC1 and (b) PC2 and from −100° to 100° at 20° increments for (c) PC3. The colour of the lines changes from light grey to black moving from negative to positive displacements.

Figure 3

Total potential energy slices in the principal conformational plane spanned by PC1 and PC2 for a GC dinucleotide monophosphate fragment using a radius-dependent dielectric model (RDIE) for the electrostatic term of the potential energy function. Low energy regions are labelled from 1 to 6 on the lowest energy slice.

Figure 4

Distributions of the sugar psuedorotation angles P1, P2 and backbone torsion pairs; (ɛ−γ), (α,γ) in each energy valley. P1 and α are shown in green while P2 and γ are in red. Positions of corresponding minima are indicated by dotted lines. Densities are based on a GC subspace PES.

Figure 5

Decomposition of the PES of a GC dinucleotide monophosphate in the principal conformational plane (PC1–PC2) for the slice containing the lowest energy structure: for the vacuum model (CDIE top panel) and for the distance dependent dielectric model (RDIE bottom panel). Row-wise are the component energy terms while column-wise are the interactions between substructures of the system (see Figure 1): 1st column: all atoms, 2nd column: backbone self-interactions, 3rd column: backbone–base interactions, 4th column: base self-interactions.

Figure 6

Selected total potential energy slices in PC1–PC2, PC1–PC3 and PC2–PC3 planes of a GC dinucleotide monophosphate fragment, with the distribution of conformers from duplex crystal structures superposed; A-form in black, Crankshaft A-form in blue, BI-form in green while BII in red.

Figure 7

Trajectories of the steepest descent path of the BI-to-A interconversion computed for a duplex d(AT)₂ step (shown in magenta) projected onto the PES of a single-strand AT dinucleotide. (a) In a plane containing the two minima and the saddle points. (b) Alternative view of the trajectory in the PCS with the PES shown in the slice of the PC1–PC2 plane containing the transition states. The trajectories of the two individual strands of the duplex are very similar and not distinguishable at the resolution presented.

Figure 8

Visualization of a room temperature solvated molecular dynamics simulation of the duplex hexamer d(ATATAT)₂ initiated from the canonical B-form. Projection of the trajectory of the middle base step of ‘strand a’ into the PCS derived from duplex DNA crystal structures. (a) A scatter plot of the trajectory projection within the PCS. BI state is shown in green, A-form in black, BII-form in orange; BII-form is in red. Conformations with mixed sugar puckers (i.e. P_A·P_B or P_B·P_A) in yellow. (b) Density plot of the trajectory projection shown in three perpendicular planes: from top to bottom; PC1–PC2 plane at PC3 = 40, PC1–PC3 plane at PC2 = 0 and PC2–PC3 plane at PC1 = −100. In each plane, the axes extend from −300 to 300 and the tick marks are placed at 20° increments. Relative densities are indicated by gradual change from black (high density) to white (zero density). The trajectory boundary (almost zero density) is indicated by a dashed line. (c) d(AT) PES slices in the planes indicated in (b) with the conformational states indicated in (a) superposed. The colour ramp is similar to that used in Figure 3.