Ion motions in molecular dynamics simulations on DNA

Abstract

Counterions play a significant role in DNA structure and function, and molecular dynamics (MD) simulations offer the prospect of detailed description of the dynamical structure of ions at the molecular level. However, the motions of mobile counterions are notably slow to converge in MD on DNA. Obtaining accurate and reliable MD simulations requires knowing just how much sampling is required for convergence of each of the properties of interest. To address this issue, MD on a d(CGCGAATTCGCG) duplex in a dilute aqueous solution of water and 22 Na+ counterions was performed until convergence was achieved. The calculated first shell ion occupancies and DNA-Na+ radial distribution functions were computed as a function of time to assess convergence, and compared with relaxation times of the DNA internal parameters shift, slide, rise, tilt, roll, and twist. The sequence dependence of fractional occupancies of ions in the major and minor grooves of the DNA is examined, and the possibility of correlation between ion proximity and DNA minor groove widths is investigated.

Fig. 1.

Regions of high Na⁺ density around d(CGCGAATTCGCG)₂ obtained as a superposition of 6,007 snapshots corresponding to 60-ns MD.

Fig. 2.

Calculated ion occupancies by atom for the two strands d(CGCGAATTCGCG)₂. Results for one single strand are presented as positive values on the ordinate and results for the other single strand are presented as negative values of the ordinate. Because the sequence is palindromic, convergence in the ion motions can be assessed qualitatively by the extent of mirror image symmetry in this plot and quantitatively by the correlation coefficient between the two single strand distributions.

Fig. 3.

Correlation coefficient between calculated ion occupancies of the two single strands of d(CGCGAATTCGCG)₂ as a function of time, by atom. Triangles indicate MD results from 0 to 60 ns. The solid line indicates exponential fit of the data from 10 to 60 ns and extrapolation to 100 ns.

Fig. 4.

MD calculated ion occupancies as a function of sequence, by nucleotide. Minor (triangles) and major (squares) groove occupancies are shown for 14 (Upper) and 60 (Lower) ns of the simulation.

Fig. 5.

MD calculated correlation functions for the G4pA5 base pair step parameters shift, slide, rise, tilt, roll, and twist of the d(CGCGAATTCGCG)₂.

Fig. 6.

Calculated DNA–Na⁺ cylindrical distribution functions g(R) as a function of radial distance R and time on an accumulated basis. Running coordination number N(R) expressed as the fraction of the total number of ions as a function of distance from the DNA is shown.