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

Echeverria I, Papoian GA - PLoS Comput. Biol. (2015)

Bottom Line: The computed PMFs show that, even for small ligands, the free energy landscapes are complex.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.

View Article: PubMed Central - PubMed

Affiliation: Department of Chemistry and Biochemistry, University of Maryland, College Park, Maryland, United States of America; Institute for Physical Science and Technology, University of Maryland, College Park, Maryland, United States of America.

ABSTRACT
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.

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Schematic representation of the helical coordinates system.A) The helical coordinate system establishes the position of the ligand center of mass with respect to the DNA’s axis. The DNA axis was aligned to the z-axis. The helical coordinate system is defined in terms of coordinates (ρ, ϕ, ξ) (in yellow). Coordinates (r, θ, z) (in red) correspond to a cylindrical coordinate system. p is the pitch of the helix and α the pitch angle. B) The components of a vector V in a surface of constant ρ in both helical (yellow) and cylindrical coordinates (red). C) Snapshot of the initial DNA methyl-guanidinium complex.
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pcbi.1003980.g001: Schematic representation of the helical coordinates system.A) The helical coordinate system establishes the position of the ligand center of mass with respect to the DNA’s axis. The DNA axis was aligned to the z-axis. The helical coordinate system is defined in terms of coordinates (ρ, ϕ, ξ) (in yellow). Coordinates (r, θ, z) (in red) correspond to a cylindrical coordinate system. p is the pitch of the helix and α the pitch angle. B) The components of a vector V in a surface of constant ρ in both helical (yellow) and cylindrical coordinates (red). C) Snapshot of the initial DNA methyl-guanidinium complex.

Mentions: The topological complexity of DNA molecules presents a major challenge in studying the thermodynamics and kinetics of protein-DNA and ligand-DNA interactions at the molecular level. In most cases, enhanced sampling techniques are required [16, 19, 20, 32]. Moreover, the proper choice of a reaction coordinate, which takes into account the helical symmetry of the molecule, is crucial for obtaining meaningful results that describe the energetics of processes such as ligand association or sliding. Here we present a helical coordinate system, with coordinates (ρ, ϕ, ξ), that uniquely defines the position of the ligands with respect to the DNA molecule. In this coordinate system, the DNA’s axis is aligned to the z-axis, such that the ρ and ϕ coordinates are equivalent in magnitude to the r and θ coordinates used in cylindrical coordinate system (r, θ, z) (Fig. 1). Additionally, by fixing the pitch (p) of the helix, this coordinate system allows to naturally track the DNA’s major or minor grooves by simple rotations. The coordinate system, by construction, decomposes the forces acting on a ligand’s center of mass in components that are: perpendicular to the DNA’s axis (Fρ), tangential to the helical path (Fϕ) and parallel to the DNA’s axis (Fξ) (see Methods section for further details). This decomposition provides the means to determine, at every point of the sampled space, the direction in which the motion of the ligand is most favorable. Importantly, all forces are conservative and uniquely defined at every point in the three dimensional space, where the latter is fully and uniquely tiled by the helical coordinate system. These properties are crucial for correctly computing the potential of mean force (PMF) for ligands binding to DNA molecules. In particular, we computed the 3D-PMF using umbrella biasing potentials (see Methods section and S1 Fig.) in the helical coordinate system for two small ligands: Na+ and methyl-guanidinium. We limited our sampling to one helical turn along the DNA’s minor grove, obtaining the binding free-energy landscape at different radial and angular positions.


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

Echeverria I, Papoian GA - PLoS Comput. Biol. (2015)

Schematic representation of the helical coordinates system.A) The helical coordinate system establishes the position of the ligand center of mass with respect to the DNA’s axis. The DNA axis was aligned to the z-axis. The helical coordinate system is defined in terms of coordinates (ρ, ϕ, ξ) (in yellow). Coordinates (r, θ, z) (in red) correspond to a cylindrical coordinate system. p is the pitch of the helix and α the pitch angle. B) The components of a vector V in a surface of constant ρ in both helical (yellow) and cylindrical coordinates (red). C) Snapshot of the initial DNA methyl-guanidinium complex.
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Related In: Results  -  Collection

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pcbi.1003980.g001: Schematic representation of the helical coordinates system.A) The helical coordinate system establishes the position of the ligand center of mass with respect to the DNA’s axis. The DNA axis was aligned to the z-axis. The helical coordinate system is defined in terms of coordinates (ρ, ϕ, ξ) (in yellow). Coordinates (r, θ, z) (in red) correspond to a cylindrical coordinate system. p is the pitch of the helix and α the pitch angle. B) The components of a vector V in a surface of constant ρ in both helical (yellow) and cylindrical coordinates (red). C) Snapshot of the initial DNA methyl-guanidinium complex.
Mentions: The topological complexity of DNA molecules presents a major challenge in studying the thermodynamics and kinetics of protein-DNA and ligand-DNA interactions at the molecular level. In most cases, enhanced sampling techniques are required [16, 19, 20, 32]. Moreover, the proper choice of a reaction coordinate, which takes into account the helical symmetry of the molecule, is crucial for obtaining meaningful results that describe the energetics of processes such as ligand association or sliding. Here we present a helical coordinate system, with coordinates (ρ, ϕ, ξ), that uniquely defines the position of the ligands with respect to the DNA molecule. In this coordinate system, the DNA’s axis is aligned to the z-axis, such that the ρ and ϕ coordinates are equivalent in magnitude to the r and θ coordinates used in cylindrical coordinate system (r, θ, z) (Fig. 1). Additionally, by fixing the pitch (p) of the helix, this coordinate system allows to naturally track the DNA’s major or minor grooves by simple rotations. The coordinate system, by construction, decomposes the forces acting on a ligand’s center of mass in components that are: perpendicular to the DNA’s axis (Fρ), tangential to the helical path (Fϕ) and parallel to the DNA’s axis (Fξ) (see Methods section for further details). This decomposition provides the means to determine, at every point of the sampled space, the direction in which the motion of the ligand is most favorable. Importantly, all forces are conservative and uniquely defined at every point in the three dimensional space, where the latter is fully and uniquely tiled by the helical coordinate system. These properties are crucial for correctly computing the potential of mean force (PMF) for ligands binding to DNA molecules. In particular, we computed the 3D-PMF using umbrella biasing potentials (see Methods section and S1 Fig.) in the helical coordinate system for two small ligands: Na+ and methyl-guanidinium. We limited our sampling to one helical turn along the DNA’s minor grove, obtaining the binding free-energy landscape at different radial and angular positions.

Bottom Line: The computed PMFs show that, even for small ligands, the free energy landscapes are complex.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.

View Article: PubMed Central - PubMed

Affiliation: Department of Chemistry and Biochemistry, University of Maryland, College Park, Maryland, United States of America; Institute for Physical Science and Technology, University of Maryland, College Park, Maryland, United States of America.

ABSTRACT
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.

Show MeSH
Related in: MedlinePlus