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1.
FIGURE 2

FIGURE 2. From: Diffusion and Electrophoretic Mobility of Single-Stranded RNA from Molecular Dynamics Simulations.

Drift velocity of RNA as a function of the electric field E. Solid, dotted, dashed, and dot-dashed lines are the results of linear fits of Eq. 6 for A6, U6, A3, and U3, respectively.

In-Chul Yeh, et al. Biophys J. 2004 February;86(2):681-689.
2.
FIGURE 1

FIGURE 1. From: Diffusion and Electrophoretic Mobility of Single-Stranded RNA from Molecular Dynamics Simulations.

Diffusion coefficients Dapp(L) of A3 RNA as a function of the inverse box length, 1/L (circles). The solid line was obtained by fitting Eq. 3 to the calculated diffusion coefficients. The inset shows the corresponding plot for a single K+ ion in water. Error bars (mean ±1 standard deviation) were estimated from block averages.

In-Chul Yeh, et al. Biophys J. 2004 February;86(2):681-689.
3.
FIGURE 4

FIGURE 4. From: Diffusion and Electrophoretic Mobility of Single-Stranded RNA from Molecular Dynamics Simulations.

Position z(t) of the geometric center of A6 as a function of time along the direction of the electric field (E = 50 mV/Å). The inset is a magnified view of z(t) during a 300-ps time interval. The three straight lines in the inset are the best linear fits for three consecutive 100-ps blocks, with slopes of 18.37, 29.15, and 19.96 m s−1, respectively. The average number of ions bound to the RNA during those 100-ps time intervals are 0.50, 0.03, and 0.14, respectively.

In-Chul Yeh, et al. Biophys J. 2004 February;86(2):681-689.
4.
FIGURE 3

FIGURE 3. From: Diffusion and Electrophoretic Mobility of Single-Stranded RNA from Molecular Dynamics Simulations.

Variance of displacements z(t) along the direction of the electric field (E = 50 mV/Å) for A6 RNA as a function of time t (solid line). Circles represent the results of fitting Eq. 11. Also shown are the variance of the displacement z(t) of A6 without electric field (dotted line), and variances of A6 in directions x and y normal to the electric field with dashed and dot-dashed lines, respectively. Differences between the variances in x(t) and y(t) at finite electric field and z(t) at zero field are within the statistical uncertainties. The inset shows a magnified view of the initial nonlinear diffusive spread.

In-Chul Yeh, et al. Biophys J. 2004 February;86(2):681-689.
5.
FIGURE 5

FIGURE 5. From: Diffusion and Electrophoretic Mobility of Single-Stranded RNA from Molecular Dynamics Simulations.

(a) Average drift velocity of A6 plotted as a function of the average number of bound counterions NK+, calculated for 100-ps time intervals. Circles, squares, and diamonds represent the results at E = 50, 40, and 30 mV/Å, respectively. Solid, dotted, and dashed lines represent the drift velocities predicted by the modified Nernst-Einstein formula, Eq. 13, for E = 50, 40, and 30 mV/Å, respectively, calculated with the diffusion coefficient of A6 RNA in the MD simulation without counterions, D = 2.86 × 10−6 cm2 s−1. (b) Probability distributions of the average number of bound counterions during 100-ps time intervals.

In-Chul Yeh, et al. Biophys J. 2004 February;86(2):681-689.
6.
FIGURE 6

FIGURE 6. From: Diffusion and Electrophoretic Mobility of Single-Stranded RNA from Molecular Dynamics Simulations.

Probability distributions of displacements z(t) of K+ ions during time intervals of t = 100 ps in the A6/K+/water solution at 0, 3, 30, 40, and 50 mV/Å shown as lines with circles, squares, diamonds, solid triangles, and crosses, respectively. Vertical arrows indicate the positions expected from free ionic drift at fields of 30, 40, and 50 mV/Å with a mobility of DK+e/kBT, where DK+ = 3.515 × 10−5 cm2 s−1 is the diffusion coefficient of a free K+ ion estimated from the inset in Fig. 1 for the system size of the A6 simulation. The horizontal arrow indicates the expected average drift position of a K+ ion bound to A6 RNA, −4e DRNA Et/kBT, at E = 40 mV/Å, where DRNA is the diffusion coefficient Dapp(L) of A6 listed in Table 3.

In-Chul Yeh, et al. Biophys J. 2004 February;86(2):681-689.
7.
FIGURE 7

FIGURE 7. From: Diffusion and Electrophoretic Mobility of Single-Stranded RNA from Molecular Dynamics Simulations.

(a) Cosine of the angle between water dipoles and the field direction as a function of the electric field E. Open circles connected with a dotted line represent results obtained from simulations of bulk TIP3P water. Open squares at 0, 3, 30, 40, and 50 mV/Å show the results calculated from water molecules at least 20 Å away from the RNA center in A6/water simulations at corresponding electric field strengths E0. (b) Polarization (P) of bulk TIP3P water as a function of the electric field E (open circles connected with dotted line). The solid line is the linear-response result (Neumann, 1983), P = (ɛ − 1) ɛ0 E, for a dielectric constant of ɛ = 94 that was obtained from a linear fit at small electric fields (inset), where ɛ0 is the vacuum permittivity. The nonlinearity between P and E becomes pronounced at electric fields above E ∼ 7 mV/Å, resulting in an apparent decrease of ɛ (Yeh and Berkowitz, 1999a).

In-Chul Yeh, et al. Biophys J. 2004 February;86(2):681-689.

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