Sequence-Dependent Motions of DNA: A Normal Mode Analysis at the Base-Pair Level  Atsushi Matsumoto, Wilma K. Olson  Biophysical Journal  Volume 83, Issue 1, Pages 22-41 (July 2002) DOI: 10.1016/S0006-3495(02)75147-3 Copyright © 2002 The Biophysical Society Terms and Conditions

Figure 1 Color-coded spectrum of lowest frequency bending (blue), twisting (green), and stretching (red) modes of 200-bp segments of the poly dA · poly dT and poly dG · poly dC homopolymers and the poly d(AT) and poly d(GC) alternating copolymers. As the frequency increases, the amplitude of each normal mode and its consequent importance to the overall motions of the DNA becomes lower. Biophysical Journal 2002 83, 22-41DOI: (10.1016/S0006-3495(02)75147-3) Copyright © 2002 The Biophysical Society Terms and Conditions

Figure 2 Schematic illustration of representative low frequency normal modes of an elastic rod. The arrows point in the directions of bending, twisting, and stretching motions in each mode. Biophysical Journal 2002 83, 22-41DOI: (10.1016/S0006-3495(02)75147-3) Copyright © 2002 The Biophysical Society Terms and Conditions

Figure 3 Superposition of the computed dependence of representative low frequency bending, twisting, stretching modes of poly dA · poly dT (scatter points) on chain length and the predicted variation (thin solid lines for the lowest frequencies, dashed lines for the second lowest frequencies, and thick solid lines for the third lowest frequencies) for an elastic rod with the same contour length. Frequencies are normalized with respect to the lowest frequency of each type of motion in a 200 bp-chain. Biophysical Journal 2002 83, 22-41DOI: (10.1016/S0006-3495(02)75147-3) Copyright © 2002 The Biophysical Society Terms and Conditions

Figure 4 Deformations of local angular “step” parameters, which are collectively responsible for the lowest frequency in-plane bending motions of a 120-bp poly dA · poly dT duplex: (top, middle) degenerate modes of lowest frequency, n b = n b ′=1; (bottom) one of the two second lowest frequency modes, n b =2. Plots illustrate the sequential fluctuations of Tilt (thin solid line), Roll (dashed line), and Twist (thick solid line) at the moment when the potential energy of the molecule is raised by k B T/2; fluctuations are reversed a half cycle later of the mode. Biophysical Journal 2002 83, 22-41DOI: (10.1016/S0006-3495(02)75147-3) Copyright © 2002 The Biophysical Society Terms and Conditions

Figure 5 Fluctuations of local angular “step” parameters, which are collectively responsible for the lowest frequency global twisting modes (n t =1) of 120-bp fragments of poly dA · poly dT, poly d(AT), poly dG · poly dC, and poly d(GC). See legend to Fig. 4. Biophysical Journal 2002 83, 22-41DOI: (10.1016/S0006-3495(02)75147-3) Copyright © 2002 The Biophysical Society Terms and Conditions

Figure 6 Fluctuations of local translational “step” parameters associated with the lowest frequency global stretching (n s =1) of 120-bp fragments of poly dA · poly dT, poly d(AT), poly dG · poly dC, and poly d(GC). Plots illustrate the sequential fluctuations of Shift (thin solid line), Slide (dashed line), and Rise (thick solid line) at the moment when the potential energy of the molecule is raised by k B T/2. See legend to Fig. 4. Biophysical Journal 2002 83, 22-41DOI: (10.1016/S0006-3495(02)75147-3) Copyright © 2002 The Biophysical Society Terms and Conditions

Figure 7 Variation of the mechanical stretching constant as a function of the equilibrium Roll angle for an ideal, naturally straight DNA chain with the force constants of different polymer sequences: poly dA · poly dT (thin solid line), poly dG · poly dC (thick solid line), poly d(AT) (thin dashed line), poly d(GC) (thick dashed line). The remaining equilibrium “step” parameters are held fixed at the following values in all cases: Tilto =0°, Twisto =36°, Shifto =Slideo =0Å, Riseo =3.4Å. Biophysical Journal 2002 83, 22-41DOI: (10.1016/S0006-3495(02)75147-3) Copyright © 2002 The Biophysical Society Terms and Conditions

Figure 8 Comparative plots of the sequential fluctuations of local “step” parameters associated with the lowest frequency global stretching modes (n s =1) of a naturally straight 120-bp “poly dA · poly dT” chain with Rollo =0° or 15°. Other chain parameters are identical to those listed in the legend to Fig. 7. Shift (thin solid line); Slide (dashed line); Rise (thick solid line). Biophysical Journal 2002 83, 22-41DOI: (10.1016/S0006-3495(02)75147-3) Copyright © 2002 The Biophysical Society Terms and Conditions

Figure 9 The first (n b =1) and second (n b ′=1) lowest global bending frequencies (solid and dashed lines, respectively) of a series of intrinsically straight poly d(AmTm) chains of 120-bp plotted as a function of m. Frequencies are normalized with respect to the lowest bending frequency of the poly d(AT) alternating copolymer (m=1). Biophysical Journal 2002 83, 22-41DOI: (10.1016/S0006-3495(02)75147-3) Copyright © 2002 The Biophysical Society Terms and Conditions

Figure 10 Fluctuations of local angular “step” parameters which underlie the global bending anisotropy of the poly d(A5T5) block copolymer. (Top) lowest frequency mode (n b =1); (bottom) second lowest mode (n b ′ =1). See legend to Fig. 4. Biophysical Journal 2002 83, 22-41DOI: (10.1016/S0006-3495(02)75147-3) Copyright © 2002 The Biophysical Society Terms and Conditions

Figure 11 Computed variation of the unperturbed root-mean-square end-to-end distance of poly dA · poly dT, r 2 0 , with chain length N. Values obtained with the Taylor series approximation of Eqs. 11–13 (thin solid line) are compared against exact averages obtained with direct matrix generator approaches (Flory, 1969; Maroun and Olson, 1988; Marky and Olson, 1994) (thick solid line) and the contour length L of the rigid-rod equilibrium state (dashed line). The values obtained by Eq. 14, in which two pairs of the degenerate bending modes are considered, are also plotted by open circles. Biophysical Journal 2002 83, 22-41DOI: (10.1016/S0006-3495(02)75147-3) Copyright © 2002 The Biophysical Society Terms and Conditions