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Volumn 62, Issue 2, 2000, Pages 2576-2596

Electrostatic interaction between long, rigid helical macromolecules at all interaxial angles

Author keywords

[No Author keywords available]

Indexed keywords

ELECTROLYTE SOLUTION; ELECTROSTATIC INTERACTION; HELICAL MACROMOLECULES;

EID: 0034238007     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.62.2576     Document Type: Article
Times cited : (66)

References (70)
  • 32
    • 85036161633 scopus 로고    scopus 로고
    • Such Hamiltonian includes both electrostatic and nonelectrostatic terms. Generally, the latter are not well known
    • Such Hamiltonian includes both electrostatic and nonelectrostatic terms. Generally, the latter are not well known.
  • 39
    • 85036333214 scopus 로고    scopus 로고
    • 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
    • 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.
  • 44
    • 85036333199 scopus 로고    scopus 로고
    • 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)
    • 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)
  • 47
    • 85036227270 scopus 로고    scopus 로고
    • 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
    • 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.
  • 48
    • 85036194320 scopus 로고    scopus 로고
    • 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
    • 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.
  • 49
    • 85036280093 scopus 로고    scopus 로고
    • 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)]
    • 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)].
  • 50
    • 85036135991 scopus 로고    scopus 로고
    • The radius of the cylinder formed by centers of phosphate groups on B-DNA is (Formula presented)
    • The radius of the cylinder formed by centers of phosphate groups on B-DNA is (Formula presented)
  • 51
    • 85036175014 scopus 로고    scopus 로고
    • 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
    • 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.
  • 52
    • 85036300913 scopus 로고    scopus 로고
    • Eq. (43) we used that zero surface-to-surface separation corresponds to (Formula presented)
    • In Eq. (43) we used that zero surface-to-surface separation corresponds to (Formula presented)
  • 56
    • 85036311699 scopus 로고    scopus 로고
    • 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
    • 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.
  • 59
    • 0032607668 scopus 로고    scopus 로고
    • the limit of strong correlations in the rotations, the quantum torque is several orders of magnitude weaker than the electrostatic one
    • 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.
    • (1999) Phys. Rev. E , vol.60 , pp. 578
    • Issaenko, S.A.1    Harris, A.B.2    Lubensky, T.C.3
  • 62
    • 85036177852 scopus 로고    scopus 로고
    • 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
    • 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.
  • 63
    • 85036235001 scopus 로고    scopus 로고
    • 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
    • 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.
  • 65
    • 85036427260 scopus 로고    scopus 로고
    • 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
    • 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.
  • 68
    • 85036152206 scopus 로고    scopus 로고
    • 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
    • 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.
  • 69
    • 0019524530 scopus 로고
    • 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
    • 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.
    • (1981) Polym. Bull. , vol.4 , pp. 291
    • Maret, G.1    Milas, M.2    Rinaudo, M.3
  • 70
    • 85036341440 scopus 로고    scopus 로고
    • 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
    • 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.


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.