DNA exit ramps are revealed in the binding landscapes obtained from simulations in helical coordinates

DNA molecules are highly charged semi-flexible polymers that are involved in a wide variety of dynamical processes such as transcription and replication. Characterizing the binding landscapes around DNA molecules is essential to understanding the energetics and kinetics of various biological processes. We present a curvilinear coordinate system that fully takes into account the helical symmetry of a DNA segment. The latter naturally allows to characterize the spatial organization and motions of ligands tracking the minor or major grooves, in a motion reminiscent of sliding. Using this approach, we performed umbrella sampling (US) molecular dynamics (MD) simulations to calculate the three-dimensional potentials of mean force (3D-PMFs) for a Na+ cation and for methyl guanidinium, an arginine analog. The computed PMFs show that, even for small ligands, the free energy landscapes are complex. In general, energy barriers of up to ~5 kcal/mol were measured for removing the ligands from the minor groove, and of ~1.5 kcal/mol for sliding along the minor groove. We shed light on the way the minor groove geometry, defined mainly by the DNA sequence, shapes the binding landscape around DNA, providing heterogeneous environments for recognition by various ligands. For example, we identified the presence of dissociation points or "exit ramps" that naturally would terminate sliding. We discuss how our findings have important implications for understanding how proteins and ligands associate and slide along DNA.