Addition/Correction Cite This: J. Phys. Chem. B 2017, 121, 10292-10292
pubs.acs.org/JPCB
Correction to “Possible Origin of the Increased Torsion Elastic Constant of Small Circular DNAs: Bending-Induced Axial Tension” J. Michael Schurr* J. Phys. Chem. B 2017, 121 (23), 5709−5717. DOI:10.1021/acs.jpcb.7b01869 he results presented in Tables 2 and 3 were not calculated using the direct force according to eq 8, contrary to what was stated in the paper. Instead those results were calculated using the mean projection of the force onto the helix-axis, according to eq 6 of a previous paper, ref 9. They found their way into this paper by inadvertent selection of the wrong files. The results calculated using the direct force according to eq 8 are listed in the revised Tables 2 and 3 below.
T
Table 3. Predicted Torsion Elastic Contants of 200.3 and 210.8 bp Circular DNAs in ∼43−58 mM Univalent Cations plus 10 mM MgCl2 at 310 Ka N (bp) Model 200.3 200.3 200.3 210.8 210.8 210.8
Table 2. Predicted Values of the Torsion Elastic Constants, αlin and αcir, for Linear and Circular 181 bp DNAs in 0.1 M Univalent Ionic Strength at 293 Ka
1
2
3
1
2
3
experiment
experiment
6.22 6.05 5.92 6.4 ± 0.5 αlin × 1019 (J) αcir × 1019 (J) 10.11 10.04 9.72 9.5 ± 0.85 (C) B0 Is Adjusted To Match Observed Value of αlin and Also To Account for −0.238 Turn of Twisting Strain in the Circular DNA model
1
2
3
experiment
αlin × 1019 (J) αcir × 1019 (J)
6.4 10.35
6.4 10.31
6.4 10.05
6.4 ± 0.5 9.5 ± 0.85
αcir × 1019 (J)
19 αexpt cir × 10 (J)
45.6 46.0 46.3 45.6 46.0 46.3
6.63 6.63 6.63 6.63 6.63 6.63
9.89 9.86 9.60 9.63 9.63 9.37
9.12, 9.53 9.12, 9.53 9.12, 9.53
These correspond to 19.0 and 20.0 turns, respectively, under the prevailing conditions, for which the helix repeat was measured to be 10.54 bp/turn. Predictions are made using the cooperative twostate model with each of three sets of model parameters, which are the same as in Table 1, except for P and B0. B0 is chosen so that the unstrained linear DNAs exhibit the value, α = 6.63 × 10−19 J, obtained from the empirical eq 16. For each set of model parameters, P was chosen to yield the j-factor, Jm0 = 1.2415 × 10−8 M, which was reckoned for a 200.3 bp DNA from data reported by Geggier et al. for ∼200 bp DNAs,19 as described in the main text. These same values of P are assumed to apply to the 210.8 bp DNA. The experimental α-values are those reported by Frank-Kamenetskii et al.5 and by Shimada and Yamakawa,4 who analyzed the experimental data of Horowitz and Wang3 by somewhat different methods. Statistical errors in these α-values are unknown, but the relative statistical errors must be at least a few percent.
αlin × 1019 (J) 6.22 6.05 5.92 6.4 ± 0.5 αcir × 1019 (J) 10.14 10.06 9.75 9.5 ± 0.85 (B) B0 Is Adjusted from Its Value in Table 1 To Account for the Effect of −0.238 Turn of Twisting Strain in the Circular DNA model
αlin × 1019 (J)
a
(A) B0 Is Fixed at Its Value in Table 1 in Each Case, and No Account Is Taken of the Effect of the −0.238 Turn of Twisting Strain in the Circular DNA model
1 2 3 1 2 3
P (nm)
a
Predictions are made using the cooperative two-state model with each of the three sets of parameters in Table 1. All parameters remain fixed except for the intrinsic equilibrium constant B0, which is treated differently in each group of calculations, as described.
The αcir values in the corrected Table 2 exceed those in the original Table 2 by factors of 1.037−1.049, and the αcir values in the corrected Table 3 exceed those in the original Table 3 by factors of 1.042−1.053. All αcir values in both versions of Tables 2 and 3 lie within estimated errors in the measured values, and no conclusions are affected by these changes. Because the coherent bend of ∼2°/bp in the circles is smaller than the rms bend, ∼7°/bp, the local helix axis is evidently not always aligned with a mean-axis position that defines the extent of coherent bending of the circle. In such a case, it is not clear that the direct force is more correct than the projected force. However, the results obtained using the direct force should be upper bounds, and those obtained using the projected force should be lower bounds.
Published: October 31, 2017 © 2017 American Chemical Society
10292
DOI: 10.1021/acs.jpcb.7b10123 J. Phys. Chem. B 2017, 121, 10292−10292
