Sequence effects in the melting and renaturation of short DNA oligonucleotides: structure and mechanistic pathways

Abstract

The renaturation/denaturation of DNA oligonucleotides is characterized in the context of expanded ensemble (EXE) and transition path sampling (TPS) simulations. Free energy profiles have been determined from EXE for DNA sequences of varying composition, chain length, and ionic strength. TPS simulations within a Langevin dynamics formalism have been carried out to obtain further information of the transition state for renaturation. Simulation results reveal that free energy profiles are strikingly similar for the various DNA sequences considered in this work. Taking intact double-stranded DNA to have an extent of reaction ξ = 1.0, the maximum of the free energy profile appears at ξ≈0.15, corresponding to ∼2 base pairs. In terms of chain length, the free energy barrier of longer oligonucleotides (30 versus 15 base pairs) is higher and slightly narrower, due to increased sharpness associated with the transition. Low ionic strength tends to decrease free energy barriers, whereby increasing strand rigidity facilitates reassociation. Two mechanisms for DNA reassociation emerge from our analysis of the transition state ensemble. Repetitive sequences tend to reassociate through a non-specific pathway involving molecular slithering. In contrast, random sequences associate through a more restrictive pathway involving the formation of specific contacts, which then leads to overall molecular zippering. In both random and repetitive sequences, the distribution of contacts suggests that nucleation is favored for sites located within the middle region of the chain. The prevalent extent of reaction for the transition state is ξ≈0.25, and the critical size of the nucleus as obtained from our analysis involves ∼4 base pairs.

Figure 1

Comparison of denaturation temperatures from a melting curve (solid line) where the fraction of melting base pairs (1 − ξ) is plotted as a function of temperature T. Shown are data for n = 15 (f_CG = 0.2), which has an empirical melting temperature of T_m = 308.4 K. The corresponding results from EXE (dashed line) yields T_m = 296 K while REMD (dot-dashed line) yields at the half-point T_m = 309 K. The alternate definition for T_m is given by the slopes depicted (dotted lines), whose intersection defines the melting temperature at the onset of denaturation.

Figure 2

Determination of the thermodynamic melting temperature. Shown is the free energy profile as a function of ξ, for the system in figure 1, using the half-point melting temperature from REMD (dashed curve) and that determined by setting ΔA = 0 (solid curve), consistent with the alternate definition for T_m depicted in figure 1.

Figure 3

Implementation of WHAM to combine results for the weighting factors ϒ(ξ) from multiple simulation windows in the determination of free energy profiles. Shown are the raw data [panel (a)] and the data after applying the additive constants [panel (b)].

Figure 3

Implementation of WHAM to combine results for the weighting factors ϒ(ξ) from multiple simulation windows in the determination of free energy profiles. Shown are the raw data [panel (a)] and the data after applying the additive constants [panel (b)].

Figure 4

Verification of uniform sampling. Data are shown for the histogram of visits [panel (a)] and potential energy distributions [panel (b)] for each state. For panel (b), ξ decreases from left to right, some values of ξ for P(U, ξ) are highlighted in color.

Figure 4

Verification of uniform sampling. Data are shown for the histogram of visits [panel (a)] and potential energy distributions [panel (b)] for each state. For panel (b), ξ decreases from left to right, some values of ξ for P(U, ξ) are highlighted in color.

Figure 5

Free energy profiles for different systems. Data are shown for n = 15 with f_CG = 0.0 (dot-dashed line), f_CG = 0.2 (dashed line), and f_CG = 0.4 (solid line).

Figure 6

Same as in figure 5, but for n = 30 with f_CG = 0.0 (dashed line) and f_CG = 0.2 (solid line).

Figure 7

Free energy (βA) landscapes [panels (a) and (c)] and entropy [βT(S − S₀)] landscapes [panels (b) and (d)] as a function of ξ and T. Data are shown for n = 15 with f_CG = 0.0 [panels (a) and (b)] and f_CG = 0.4 [panels (c) and (d)]. The profile at the melting temperature for each system is denoted with a magenta line. S₀ corresponds to the entropy of the system for intact dsDNA (ξ = 1.0) for the lowest temperature shown.

Figure 7

Free energy (βA) landscapes [panels (a) and (c)] and entropy [βT(S − S₀)] landscapes [panels (b) and (d)] as a function of ξ and T. Data are shown for n = 15 with f_CG = 0.0 [panels (a) and (b)] and f_CG = 0.4 [panels (c) and (d)]. The profile at the melting temperature for each system is denoted with a magenta line. S₀ corresponds to the entropy of the system for intact dsDNA (ξ = 1.0) for the lowest temperature shown.

Figure 7

Free energy (βA) landscapes [panels (a) and (c)] and entropy [βT(S − S₀)] landscapes [panels (b) and (d)] as a function of ξ and T. Data are shown for n = 15 with f_CG = 0.0 [panels (a) and (b)] and f_CG = 0.4 [panels (c) and (d)]. The profile at the melting temperature for each system is denoted with a magenta line. S₀ corresponds to the entropy of the system for intact dsDNA (ξ = 1.0) for the lowest temperature shown.

Figure 7

Free energy (βA) landscapes [panels (a) and (c)] and entropy [βT(S − S₀)] landscapes [panels (b) and (d)] as a function of ξ and T. Data are shown for n = 15 with f_CG = 0.0 [panels (a) and (b)] and f_CG = 0.4 [panels (c) and (d)]. The profile at the melting temperature for each system is denoted with a magenta line. S₀ corresponds to the entropy of the system for intact dsDNA (ξ = 1.0) for the lowest temperature shown.

Figure 8

Salt effects on the free energy profile. Results are shown for n = 15 (f_CG = 0.2) with [Na⁺] = 0.005 M (dashed line) and 0.069 M (solid line).

Figure 9

Probability of extents of reaction in the TSE. Results are shown for f_CG = 0.0 (solid line) and f_CG = 0.2 (dashed line).

Figure 10

Joint probability of base pair contacts P(χ) for all extents of reaction ξ shown in figure 9. Data are shown for f_CG = 0.0 [panel (a)] and f_CG = 0.2 [panel (b)]. The sequence for each strand is denoted along the axes, with “chain 1” being the sense strand. Arrows along the axes denote the 5′-to-3′ direction for each chain. Native base pair contacts are denoted along the diagonal (magenta line).

Figure 10

Joint probability of base pair contacts P(χ) for all extents of reaction ξ shown in figure 9. Data are shown for f_CG = 0.0 [panel (a)] and f_CG = 0.2 [panel (b)]. The sequence for each strand is denoted along the axes, with “chain 1” being the sense strand. Arrows along the axes denote the 5′-to-3′ direction for each chain. Native base pair contacts are denoted along the diagonal (magenta line).

Figure 11

Same as in figure 10, but for nξ = 1.

Figure 11

Same as in figure 10, but for nξ = 1.

Figure 12

Schematic of DNA systems identifying base pairs (dotted, magenta lines) with highest probability in the TSE. Shown are characteristic reassociation sites for f_CG = 0.2 [panel (a)] and f_CG = 0.0 [panel (b)]. The sense strand for each case is placed on the left. Moieties are denoted by color as sugar (gray), phosphate (yellow), adenine (red), cytosine (green), guanine (orange), and thymine (blue) sites.

Figure 12

Schematic of DNA systems identifying base pairs (dotted, magenta lines) with highest probability in the TSE. Shown are characteristic reassociation sites for f_CG = 0.2 [panel (a)] and f_CG = 0.0 [panel (b)]. The sense strand for each case is placed on the left. Moieties are denoted by color as sugar (gray), phosphate (yellow), adenine (red), cytosine (green), guanine (orange), and thymine (blue) sites.