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10
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0025699245
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D. H. Van Winkle, M. W. Davidson, W.-H. Chen, and R. L. Rill, Macromolecules 23, 4140 (1990).
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(1990)
Macromolecules
, vol.23
, pp. 4140
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Van Winkle, D.H.1
Davidson, M.W.2
Chen, W.-H.3
Rill, R.L.4
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12
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0000857395
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H. H. Strey, J. Wang, R. Podgornik, A. Rupprecht, L. Yu, V. A. Parsegian, and E. B. Sirota, Phys. Rev. Lett. 84, 3105 (2000).
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(2000)
Phys. Rev. Lett.
, vol.84
, pp. 3105
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Strey, H.H.1
Wang, J.2
Podgornik, R.3
Rupprecht, A.4
Yu, L.5
Parsegian, V.A.6
Sirota, E.B.7
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16
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0031643028
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T. C. Lubensky, A. B. Harris, R. D. Kamien, and G. Yan, Ferroelectrics 212, 1 (1998).
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(1998)
Ferroelectrics
, vol.212
, pp. 1
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Lubensky, T.C.1
Harris, A.B.2
Kamien, R.D.3
Yan, G.4
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25
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0030957189
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K. Wagner, E. Keyes, T. W. Kephart, and G. Edwards, Biophys. J. 73, 21 (1997).
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(1997)
Biophys. J.
, vol.73
, pp. 21
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Wagner, K.1
Keyes, E.2
Kephart, T.W.3
Edwards, G.4
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32
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85036161633
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Such Hamiltonian includes both electrostatic and nonelectrostatic terms. Generally, the latter are not well known
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Such Hamiltonian includes both electrostatic and nonelectrostatic terms. Generally, the latter are not well known.
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39
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85036333214
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We neglect dielectric saturation of the solvent in immediate vicinity of ions since we do not apply our results at such short distances. Furthermore, we do not account for nonlocal dielectric response of water and neglect hydration forces that may be caused by specific water ordering near molecular groups
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We neglect dielectric saturation of the solvent in immediate vicinity of ions since we do not apply our results at such short distances. Furthermore, we do not account for nonlocal dielectric response of water and neglect hydration forces that may be caused by specific water ordering near molecular groups.
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44
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85036333199
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DNA contains fixed phosphate charges and bound counterions so that (Formula presented) is the surface charge density of phosphates. Protein helices typically contain both negative and positive charges. If fixed charges of one sign dominate, we define (Formula presented) as their mean surface charge density. If a helix contains equal number of positive and negative charges, either one can be used to define (Formula presented)
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DNA contains fixed phosphate charges and bound counterions so that (Formula presented) is the surface charge density of phosphates. Protein helices typically contain both negative and positive charges. If fixed charges of one sign dominate, we define (Formula presented) as their mean surface charge density. If a helix contains equal number of positive and negative charges, either one can be used to define (Formula presented)
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46
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0030947539
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C. G. Baumann, S. B. Smith, V. A. Bloomfield, and C. Bustamante, Proc. Natl. Acad. Sci. USA 94, 6185 (1997).
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(1997)
Proc. Natl. Acad. Sci. USA
, vol.94
, pp. 6185
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Baumann, C.G.1
Smith, S.B.2
Bloomfield, V.A.3
Bustamante, C.4
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47
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85036227270
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Based on the crystallographic data 44 the deviation of the axial rise per base pair (bp) from its average value 3.34 Å is about 0.1 Å. For 150-bp -long DNA with random base pair sequence, this leads to axial deviation from the ideal helix (Formula presented) that is negligibly small compared to the helical pitch (Formula presented) Similarly, the deviation of the angle between adjacent base pairs from its average value 36° is ∼4°. The deviation over the whole length of the molecule is, therefore, ∼50°, which is still small enough compared to the full 360° turn that would disrupt orientational correlations between strands on opposing molecules
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Based on the crystallographic data 44 the deviation of the axial rise per base pair (bp) from its average value 3.34 Å is about 0.1 Å. For 150-bp -long DNA with random base pair sequence, this leads to axial deviation from the ideal helix (Formula presented) that is negligibly small compared to the helical pitch (Formula presented) Similarly, the deviation of the angle between adjacent base pairs from its average value 36° is ∼4°. The deviation over the whole length of the molecule is, therefore, ∼50°, which is still small enough compared to the full 360° turn that would disrupt orientational correlations between strands on opposing molecules.
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48
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85036194320
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The average distance between neighboring charges on DNA surface is ∼7 Å, much smaller than the helical pitch and than the separation between molecules in the cholesteric phase. Even when the molecules are in direct contact with each other, the effects from charge discreteness contribute only ∼10% to the interaction energy 29. In the cholesteric phase, their contribution should be much smaller
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The average distance between neighboring charges on DNA surface is ∼7 Å, much smaller than the helical pitch and than the separation between molecules in the cholesteric phase. Even when the molecules are in direct contact with each other, the effects from charge discreteness contribute only ∼10% to the interaction energy 29. In the cholesteric phase, their contribution should be much smaller.
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49
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85036280093
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Equation (17) differs from the result reported in Ref. 18 by a factor of 2 due to a misprint there [V. A. Parsegian, (private communication)]
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Equation (17) differs from the result reported in Ref. 18 by a factor of 2 due to a misprint there [V. A. Parsegian, (private communication)].
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50
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85036135991
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The radius of the cylinder formed by centers of phosphate groups on B-DNA is (Formula presented)
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The radius of the cylinder formed by centers of phosphate groups on B-DNA is (Formula presented)
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51
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85036175014
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The distance range where this approximation is valid depends on the symmetry of molecular charge pattern that determines the “weight factors” (Formula presented) For example, when (Formula presented) at all (Formula presented) this approximation is valid at all separations. In contrast, when (Formula presented) this approximation cannot be used at all
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The distance range where this approximation is valid depends on the symmetry of molecular charge pattern that determines the “weight factors” (Formula presented) For example, when (Formula presented) at all (Formula presented) this approximation is valid at all separations. In contrast, when (Formula presented) this approximation cannot be used at all.
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52
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85036300913
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Eq. (43) we used that zero surface-to-surface separation corresponds to (Formula presented)
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In Eq. (43) we used that zero surface-to-surface separation corresponds to (Formula presented)
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56
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85036311699
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The exact nature of this phase is not entirely clear. Originally, it was reported as a hexagonal columnar phase (see, e.g., 56 and references therein). Later studies of phase behavior of long DNA raised the possibility that this may be a line hexatic pase 1256. It is clear, however, that this phase is not chiral, the averaged local packing of molecules is hexagonal, and the averaged orientation of all molecules is the same
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The exact nature of this phase is not entirely clear. Originally, it was reported as a hexagonal columnar phase (see, e.g., 56 and references therein). Later studies of phase behavior of long DNA raised the possibility that this may be a line hexatic pase 1256. It is clear, however, that this phase is not chiral, the averaged local packing of molecules is hexagonal, and the averaged orientation of all molecules is the same.
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57
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0029978845
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R. Podgornik, H. H. Strey, K. Gawrisch, D. C. Rau, A. Rupprecht, and V. A. Parsegian, Proc. Natl. Acad. Sci. USA 93, 4261 (1996).
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(1996)
Proc. Natl. Acad. Sci. USA
, vol.93
, pp. 4261
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Podgornik, R.1
Strey, H.H.2
Gawrisch, K.3
Rau, D.C.4
Rupprecht, A.5
Parsegian, V.A.6
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59
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0032607668
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the limit of strong correlations in the rotations, the quantum torque is several orders of magnitude weaker than the electrostatic one
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This is true only in the presence of at least some mutual alignment between nearest neighbors. At completely uncorrelated rotations of molecules about their principal axes, only quantum interactions between fluctuating charge moments contribute to the net torque [S. A. Issaenko, A. B. Harris, and T. C. Lubensky, Phys. Rev. E 60, 578 (1999)]. In the limit of strong correlations in the rotations, the quantum torque is several orders of magnitude weaker than the electrostatic one.
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(1999)
Phys. Rev. E
, vol.60
, pp. 578
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Issaenko, S.A.1
Harris, A.B.2
Lubensky, T.C.3
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61
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36749118773
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B. W. van der Meer, G. Vetrogen, A. J. Dekker, and J. G. J. Yptma, J. Chem. Phys. 65, 3935 (1976).
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(1976)
J. Chem. Phys.
, vol.65
, pp. 3935
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van der Meer, B.W.1
Vetrogen, G.2
Dekker, A.J.3
Yptma, J.G.J.4
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62
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85036177852
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Based on Eqs. (23242526), such screw motion has zero energetic cost. However, to derive Eqs. (23242526) we neglected edge effects for finite length helices. The edge effects will create some energetic cost, but to the extent that they are weak, the cost should be small
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Based on Eqs. (23242526), such screw motion has zero energetic cost. However, to derive Eqs. (23242526) we neglected edge effects for finite length helices. The edge effects will create some energetic cost, but to the extent that they are weak, the cost should be small.
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63
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85036235001
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The persistence length of DNA (500–1000 Å 45) is larger than the helical pitch by more than an order of magnitude and it is even larger than the total length of 150-bp fragments. In the first order approximation, undulations are essentially equivalent to long-wavelength fluctuations of the interaxial distance that do not change the (Formula presented) alignment of neighboring molecules
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The persistence length of DNA (500–1000 Å 45) is larger than the helical pitch by more than an order of magnitude and it is even larger than the total length of 150-bp fragments. In the first order approximation, undulations are essentially equivalent to long-wavelength fluctuations of the interaxial distance that do not change the (Formula presented) alignment of neighboring molecules.
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65
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85036427260
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Since molecular packing in the cholesteric phase is nearly hexagonal, the distance between neighboring layers is (Formula presented) The rotation per layer is ψ. The pitch corresponds to the rotation by 2π
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Since molecular packing in the cholesteric phase is nearly hexagonal, the distance between neighboring layers is (Formula presented) The rotation per layer is ψ. The pitch corresponds to the rotation by 2π.
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66
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33845282562
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L. Salem, X. Chapuisat, G. Segal, P. C. Hiberty, C. Minot, C. Leforestier, and P. Sautet, J. Am. Chem. Soc. 109, 2887 (1987).
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(1987)
J. Am. Chem. Soc.
, vol.109
, pp. 2887
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Salem, L.1
Chapuisat, X.2
Segal, G.3
Hiberty, P.C.4
Minot, C.5
Leforestier, C.6
Sautet, P.7
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68
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85036152206
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Circular dichroism of DNA in the base pair absorption band (∼260 nm) is due to electronic transitions caused by interaction of the electric vector of light with the conjugated π electron system of DNA bases. The corresponding transition dipoles lie in the plane of the bases which is normal 44 to the principal axis of B-DNA. This plane is parallel to the cholesteric twist axis and, correspondingly, to the direction in which the anomalous CD signal is supposed to be observed. Then, only one component of the electric vector of light is parallel to transition dipoles while the second component is normal to them and it cannot cause electronic transitions. Only the first component can be absorbed so that B-DNA should not be able to distinguish left from right circularly polarized light in the direction of the cholesteric twist axis. Of course, real B-DNA molecules may have base pairs that are not perfectly parallel to the cholesteric twist axis so that some circular dichroism may be observed in this direction. However, the corresponding CD signal should be small rather than anomalously large
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Circular dichroism of DNA in the base pair absorption band (∼260 nm) is due to electronic transitions caused by interaction of the electric vector of light with the conjugated π electron system of DNA bases. The corresponding transition dipoles lie in the plane of the bases which is normal 44 to the principal axis of B-DNA. This plane is parallel to the cholesteric twist axis and, correspondingly, to the direction in which the anomalous CD signal is supposed to be observed. Then, only one component of the electric vector of light is parallel to transition dipoles while the second component is normal to them and it cannot cause electronic transitions. Only the first component can be absorbed so that B-DNA should not be able to distinguish left from right circularly polarized light in the direction of the cholesteric twist axis. Of course, real B-DNA molecules may have base pairs that are not perfectly parallel to the cholesteric twist axis so that some circular dichroism may be observed in this direction. However, the corresponding CD signal should be small rather than anomalously large.
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69
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0019524530
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The anomalous optical rotary dispersion in the absorption band of xanthan was attributed to the left-handed cholesteric twist. However, later direct measurements revealed a right-handed cholesteric twist 1
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It may be useful to recall a similar measurement of the twist sense in the cholesteric phase of xanthan (a charged, double-stranded, right-handed helical polysaccharide) [G. Maret, M. Milas, and M. Rinaudo, Polym. Bull. 4, 291 (1981)]. The anomalous optical rotary dispersion in the absorption band of xanthan was attributed to the left-handed cholesteric twist. However, later direct measurements revealed a right-handed cholesteric twist 1.
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(1981)
Polym. Bull.
, vol.4
, pp. 291
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Maret, G.1
Milas, M.2
Rinaudo, M.3
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70
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85036341440
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Note that for biological helices immersed into an aqueous electrolyte solution (Formula presented) because (Formula presented) In this case, Eq. (A15) can be simplified to yield the expression (Formula presented) used in our previous work 27. However, here we will also discuss interactions between macromolecules in nonpolar media when (Formula presented) and (Formula presented) Then, such approximation cannot be used and, thus, we avoid it
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Note that for biological helices immersed into an aqueous electrolyte solution (Formula presented) because (Formula presented) In this case, Eq. (A15) can be simplified to yield the expression (Formula presented) used in our previous work 27. However, here we will also discuss interactions between macromolecules in nonpolar media when (Formula presented) and (Formula presented) Then, such approximation cannot be used and, thus, we avoid it.
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