Electrostatic Free Energy Landscapes in Nucleic Acid Helix Assembly

The DNA helices are taken as the canonical B-form and are produced from the previously developed grooved primitive model [1]. The grooved primitive model retains a high degree of realistic helical structure and phosphate charge distribution of DNA [2], and is tractable for analytical statistical mechanical theories [3]-[5]. We use the B-form DNA helix since it is the most common and stable form over a wide range of ionic conditions and sequences [6, 7]. In the grooved primitive model, for each nucleotide backbone, the phosphate is represented by a charged sphere with the charge placed at the center of the sphere, and the neutral groups are represented by a neutral sphere. Both spheres have radii of 2.1Å. The radius is determined from all-atom simulations such that the grooved primitive model gives the same detailed ion distribution as the all-atom computation [1]. In the grooved primitive model, a base pair is represented by five spheres: one large central sphere with radius 4Å, two phosphate spheres and two neutral spheres [1]. The centers of the large central spheres are on the axis of DNA helices with equal spacing, and the phosphate spheres are placed at the centers of the phosphate groups, while the neutral spheres lie between the phosphate spheres and the central large sphere. The coordinates of the phosphate spheres (ρs i , θ s i , z s i ) are determined from the atomic coordinates of B-DNA from X-ray measurements [2]: ρs i = 8.9 (Å); θ s i = θ s 0+i 36 ◦; zs i = z s 0+i 3.4 (Å), where s = 1, 2 denotes the two strands and i = 1, 2, ...N denotes the nucleotides on each strand. The parameters (θs 0, z s 0) for the initial position are (0 ◦, 0Å) for the first strand and (154.4◦, 0.78 Å) for the second strand, respectively. The neutral spheres have the same angular coordinates except they have the smaller radial coordinates 5.9Å [1, 3, 4, 5]. Every phosphate sphere carry a negative elementary charge −q at its center. In the way, a B-DNA helix is constructed; see Fig. 1.