Figure 1.
The double-stranded DNA dodecamer system.
(A) The initial DNA structure (PDB 1bna) with the explicit TIP3P water molecules (cyan), Na+ ions (orange) and Cl− ions (green). The atom colors of DNA are the CPK colors. (B) A snapshot at 50 ps by the RESA method with rc = 18 Å. (C) A snapshot at 10 ns by the ZD method, with rc = 12 Å and α = 0.0. (D) A snapshot at 10 ns by the PME method, with rc = 12 Å and α = 0.35 Å−1. Hydrogen atoms are not shown in (B) to (D).
Figure 2.
Relative electrostatic energy deviations by the ZD and RESA methods with the cutoff distance rc, averaged for 1,000 sampled structures produced by MD with the PME method, compared with those calculated by the Ewald method (Eq. 5).
The thin solid line, dotted line, dashed line, and dash-dotted line with filled circles are the results from the ZD method with damping factor α values = 0.0, 0.06, 0.10, and 0.14 (Å−1), respectively. The thick solid line with open circles represents the results from the RESA method. The error bars are the standard deviations for 1,000 samples.
Figure 3.
Relative individual contributions to electrostatic energy deviations by the ZD and RESA methods from the Ewald electrostatic energy, averaged for 1,000 sample structures produced by MD with the PME method (Eq. 9).
Solid blue, red, and black bars are the contributions by the ZD method with the cutoff distance rc values = 12, 14, and 16 (Å), respectively, and the damping factor α = 0.0. Hatched blue, red, and black bars are those with rc = 12, 14, and 16 (Å), respectively, with α = 0.1 (Å−1). Open blue, red, and black bars are those obtained by the RESA method with rc = 12, 14, and 16 (Å), respectively. The numbers in parentheses are the numbers of nucleotides in DNA, the numbers of water molecules, and the numbers of Na+ and Cl− ions. The error bars are the standard deviations for 1,000 samples.
Figure 4.
Relative contributions of each nucleotide to the electrostatic energy deviations, determined by the ZD and RESA methods from the Ewald electrostatic energy averaged for 1,000 sample structures produced by MD with the PME method (Eq. 10).
The parameters for the individual bars are the same as those in Figure 3. The numbers in parentheses are the numbers of nucleotide types. The error bars are the standard deviations for 1,000 samples.
Figure 5.
The trajectories of the rmsd values of the backbone heavy atoms of the double-stranded dodecamer DNA from those atoms of the initial crystal structure, along 10 ns MD simulations with the PME method (black line, rc = 12 Å and α = 0.35 Å−1) and with the ZD method (red line, rc = 12Å and α = 0.0).
Both methods started from the same initial structure.
Figure 6.
The rmsf (root-mean-square fluctuation) values of the backbone heavy atoms (thick solid lines with filled circles for A-chain, and thick dotted lines with open circles for B-chain), and that of the base heavy atoms (thin solid lines for A-chain, and thin dotted lines for B-chain), averaged along the last 7 ns of the total 10 ns MD trajectories shown in Figure 5 by the PME method (black lines, rc = 12 Å and α = 0.35 Å−1) and the ZD method (red lines, rc = 12 Å and α = 0.0).
The abbreviations are used for deoxyribonucleotides: C, cytosine; G, guanine; A, adenine; T, thymine.
Figure 7.
The cross-correlation matrix elements in the fluctuations of (A) the DNA backbone heavy atoms, and (B) the base heavy atoms, averaged along the trajectories of the last 7 ns of the total 10 ns MD simulations.
The cross correlation values from 1.0 to –1.0 are colored red (positive) to blue (negative). The lower triangles show the values obtained by the PME method (rc = 12 Å and α = 0.35 Å−1), and the upper triangles show the correlations provided by the ZD method (rc = 12 Å and α = 0.0), respectively. The A- and B-chains are indicated with the nucleotide abbreviated names.
Table 1.
Execution time (sec) for 1 step MD simulation of the DNA system by the ZD method and by the real space part of the PME (RPME) method.