Molecular recognition of DNA by ligands: roughness and complexity of the free energy profile

Abstract

Understanding the molecular mechanism by which probes and chemotherapeutic agents bind to nucleic acids is a fundamental issue in modern drug design. From a computational perspective, valuable insights are gained by the estimation of free energy landscapes as a function of some collective variables (CVs), which are associated with the molecular recognition event. Unfortunately the choice of CVs is highly non-trivial because of DNA's high flexibility and the presence of multiple association-dissociation events at different locations and/or sliding within the grooves. Here we have applied a modified version of Locally-Scaled Diffusion Map (LSDMap), a nonlinear dimensionality reduction technique for decoupling multiple-timescale dynamics in macromolecular systems, to a metadynamics-based free energy landscape calculated using a set of intuitive CVs. We investigated the binding of the organic drug anthramycin to a DNA 14-mer duplex. By performing an extensive set of metadynamics simulations, we observed sliding of anthramycin along the full-length DNA minor groove, as well as several detachments from multiple sites, including the one identified by X-ray crystallography. As in the case of equilibrium processes, the LSDMap analysis is able to extract the most relevant collective motions, which are associated with the slow processes within the system, i.e., ligand diffusion along the minor groove and dissociation from it. Thus, LSDMap in combination with metadynamics (and possibly every equivalent method) emerges as a powerful method to describe the energetics of ligand binding to DNA without resorting to intuitive ad hoc reaction coordinates.

Figure 1

(a) Free energy projection (in units of kcal/mol) onto the first three DCs. States are as marked. (b) Free energy projection onto the 1st DC. (c) Free energy projection onto the 1st DC and 2nd DC, and 2nd DC (inset). (d) Free energy projection onto the 1st DC and 3rd DC, and 3rd DC (inset). (e) Typical configurations picked in the states marked in the free energy profile.

Figure 2

(Upper panel) Free energy projection (in units of kcal/mol) onto the 1st DC and 4th DC, and 4th DC (inset). States are as marked. (Lower panel) Free energy projection onto the 1st DC and 5th DC (c), and the 5th DC (inset).

Figure 3

All the configurations in the data set are projected onto the 1st DC and 2nd DC (a), the 1st DC and 3rd DC (b), the 1st DC and 4th DC (c), the 1st DC and 5th DC (d), the 2nd DC and 5th DC (e), and the 3rd DC and 5th DC (f). The colors indicate the average base pair index $\overline{I}$. The black dots indicate that there are no hydrogen bonds between the ligand and the DNA bases for those configurations. Because the large number of points in the data set introduces a lot of overlaps when $\overline{I}$ is plotted as a function of the DCs, we split the two DCs into 100 × 100 grids and plot the average value of $\overline{I}$ in each bin. The black dots are plotted first so that the colored dots are not covered by the black dots.

Figure 4

(Upper panel) Free energy as a function of the two collective variables used in metadynamics, that is, the distance d_CMs between the center of mass of the ligand and of the DNA tracts d[GTTGG]₂ and the number of hydrophobic contacts n_hph between nonpolar carbons on the ligand and on the bases covered by the ligand in the starting structure. (Lower panel) The typical configurations picked in the region as marked in the free energy plot in the upper panel. The two overlapping configurations marked III show two possible configurations in region III.