Limits...
Helical coherence of DNA in crystals and solution.

Wynveen A, Lee DJ, Kornyshev AA, Leikin S - Nucleic Acids Res. (2008)

Bottom Line: We find, e.g. that the solution structure of synthetic oligomers is characterized by 100-200 A coherence length, which is similar to approximately 150 A coherence length of natural, salmon-sperm DNA.Packing of oligomers in crystals dramatically alters their helical coherence.The coherence length increases to 800-1200 A, consistent with its theoretically predicted role in interactions between DNA at close separations.

View Article: PubMed Central - PubMed

Affiliation: Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstrasse 1, D-40225 Düsseldorf, Germany. awynveen@googlemail.com

ABSTRACT
The twist, rise, slide, shift, tilt and roll between adjoining base pairs in DNA depend on the identity of the bases. The resulting dependence of the double helix conformation on the nucleotide sequence is important for DNA recognition by proteins, packaging and maintenance of genetic material, and other interactions involving DNA. This dependence, however, is obscured by poorly understood variations in the stacking geometry of the same adjoining base pairs within different sequence contexts. In this article, we approach the problem of sequence-dependent DNA conformation by statistical analysis of X-ray and NMR structures of DNA oligomers. We evaluate the corresponding helical coherence length--a cumulative parameter quantifying sequence-dependent deviations from the ideal double helix geometry. We find, e.g. that the solution structure of synthetic oligomers is characterized by 100-200 A coherence length, which is similar to approximately 150 A coherence length of natural, salmon-sperm DNA. Packing of oligomers in crystals dramatically alters their helical coherence. The coherence length increases to 800-1200 A, consistent with its theoretically predicted role in interactions between DNA at close separations.

Show MeSH

Related in: MedlinePlus

Schematic illustration of non-ideal helical geometry and helical coherence of straight DNA. (A) The base pairs are depicted as rigid blocks oriented at azimuthal angles φi with the twist Ωi and rise hi between them, where the index i numbers the base pairs. (B) The bold line in the top panel shows the dependence of base pair orientations on the distance zi along the helical axis in an ideal helix, in which the twist Ω and rise h per base pair are constant. Sequence dependence of the twist and rise in a DNA molecule (thin line) with the same average twist and rise (<Ωi> = Ω and <hi> = h) results in accumulating mean-square deviation of base pair orientations from the ideal helix. This loss of helical coherence is best illustrated by aligning several molecules with uncorrelated sequences at zi = 0 (bottom panel). Since twist and rise variations at each base pair step are small, these molecules remain close to the ideal helical alignment over many steps. However, accumulating twist and rise displacements eventually disrupt their alignment. (C) To characterize this effect, we introduce the helical phase Φi, which is the difference between the azimuthal angle φi in a DNA molecule and the azimuthal angle expected in the corresponding ideal helix (zi<Ωi>/<hi>). The helical phase of each DNA is determined by its sequence, as illustrated by the plot. The mean-square displacement of Φi averaged over all possible sequences accumulates linearly with zi [Equation (5)]. The helical coherence length is the axial distance at which this mean-square displacement exceeds 1 rad2. At larger distances, azimuthal orientations of base pairs on molecules with different sequences become uncorrelated (B, bottom panel). We describe the contributions of variations in the twist and rise by the twist and rise coherence lengths, correspondingly [Equation (8)]. For instance, the total helical coherence length would be equal to the twist coherence length if the variations in the rise were negligible. The contribution of correlations between the twist and rise is characterized by the twist–rise coherence length. Note that the latter is a mathematical construct rather than a physical length. It may be positive or negative, depending on the sign of twist–rise correlations. All these concepts can be generalized to bent DNA as discussed in the text.
© Copyright Policy - creative-commons
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC2553576&req=5

Figure 1: Schematic illustration of non-ideal helical geometry and helical coherence of straight DNA. (A) The base pairs are depicted as rigid blocks oriented at azimuthal angles φi with the twist Ωi and rise hi between them, where the index i numbers the base pairs. (B) The bold line in the top panel shows the dependence of base pair orientations on the distance zi along the helical axis in an ideal helix, in which the twist Ω and rise h per base pair are constant. Sequence dependence of the twist and rise in a DNA molecule (thin line) with the same average twist and rise (<Ωi> = Ω and <hi> = h) results in accumulating mean-square deviation of base pair orientations from the ideal helix. This loss of helical coherence is best illustrated by aligning several molecules with uncorrelated sequences at zi = 0 (bottom panel). Since twist and rise variations at each base pair step are small, these molecules remain close to the ideal helical alignment over many steps. However, accumulating twist and rise displacements eventually disrupt their alignment. (C) To characterize this effect, we introduce the helical phase Φi, which is the difference between the azimuthal angle φi in a DNA molecule and the azimuthal angle expected in the corresponding ideal helix (zi<Ωi>/<hi>). The helical phase of each DNA is determined by its sequence, as illustrated by the plot. The mean-square displacement of Φi averaged over all possible sequences accumulates linearly with zi [Equation (5)]. The helical coherence length is the axial distance at which this mean-square displacement exceeds 1 rad2. At larger distances, azimuthal orientations of base pairs on molecules with different sequences become uncorrelated (B, bottom panel). We describe the contributions of variations in the twist and rise by the twist and rise coherence lengths, correspondingly [Equation (8)]. For instance, the total helical coherence length would be equal to the twist coherence length if the variations in the rise were negligible. The contribution of correlations between the twist and rise is characterized by the twist–rise coherence length. Note that the latter is a mathematical construct rather than a physical length. It may be positive or negative, depending on the sign of twist–rise correlations. All these concepts can be generalized to bent DNA as discussed in the text.

Mentions: To incorporate cumulative parameters of the sequence-dependent helical structure into the latter approach, we proposed to describe sequence and thermal variations in the twist between adjoining base pairs with the twist coherence length (29–31). This length characterizes the ability of DNA to follow a structure close to a geometrically perfect double helix in the same way as the bending persistence length characterizes the ability of DNA centerline to follow a straight line (Figure 1).Figure 1.


Helical coherence of DNA in crystals and solution.

Wynveen A, Lee DJ, Kornyshev AA, Leikin S - Nucleic Acids Res. (2008)

Schematic illustration of non-ideal helical geometry and helical coherence of straight DNA. (A) The base pairs are depicted as rigid blocks oriented at azimuthal angles φi with the twist Ωi and rise hi between them, where the index i numbers the base pairs. (B) The bold line in the top panel shows the dependence of base pair orientations on the distance zi along the helical axis in an ideal helix, in which the twist Ω and rise h per base pair are constant. Sequence dependence of the twist and rise in a DNA molecule (thin line) with the same average twist and rise (<Ωi> = Ω and <hi> = h) results in accumulating mean-square deviation of base pair orientations from the ideal helix. This loss of helical coherence is best illustrated by aligning several molecules with uncorrelated sequences at zi = 0 (bottom panel). Since twist and rise variations at each base pair step are small, these molecules remain close to the ideal helical alignment over many steps. However, accumulating twist and rise displacements eventually disrupt their alignment. (C) To characterize this effect, we introduce the helical phase Φi, which is the difference between the azimuthal angle φi in a DNA molecule and the azimuthal angle expected in the corresponding ideal helix (zi<Ωi>/<hi>). The helical phase of each DNA is determined by its sequence, as illustrated by the plot. The mean-square displacement of Φi averaged over all possible sequences accumulates linearly with zi [Equation (5)]. The helical coherence length is the axial distance at which this mean-square displacement exceeds 1 rad2. At larger distances, azimuthal orientations of base pairs on molecules with different sequences become uncorrelated (B, bottom panel). We describe the contributions of variations in the twist and rise by the twist and rise coherence lengths, correspondingly [Equation (8)]. For instance, the total helical coherence length would be equal to the twist coherence length if the variations in the rise were negligible. The contribution of correlations between the twist and rise is characterized by the twist–rise coherence length. Note that the latter is a mathematical construct rather than a physical length. It may be positive or negative, depending on the sign of twist–rise correlations. All these concepts can be generalized to bent DNA as discussed in the text.
© Copyright Policy - creative-commons
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC2553576&req=5

Figure 1: Schematic illustration of non-ideal helical geometry and helical coherence of straight DNA. (A) The base pairs are depicted as rigid blocks oriented at azimuthal angles φi with the twist Ωi and rise hi between them, where the index i numbers the base pairs. (B) The bold line in the top panel shows the dependence of base pair orientations on the distance zi along the helical axis in an ideal helix, in which the twist Ω and rise h per base pair are constant. Sequence dependence of the twist and rise in a DNA molecule (thin line) with the same average twist and rise (<Ωi> = Ω and <hi> = h) results in accumulating mean-square deviation of base pair orientations from the ideal helix. This loss of helical coherence is best illustrated by aligning several molecules with uncorrelated sequences at zi = 0 (bottom panel). Since twist and rise variations at each base pair step are small, these molecules remain close to the ideal helical alignment over many steps. However, accumulating twist and rise displacements eventually disrupt their alignment. (C) To characterize this effect, we introduce the helical phase Φi, which is the difference between the azimuthal angle φi in a DNA molecule and the azimuthal angle expected in the corresponding ideal helix (zi<Ωi>/<hi>). The helical phase of each DNA is determined by its sequence, as illustrated by the plot. The mean-square displacement of Φi averaged over all possible sequences accumulates linearly with zi [Equation (5)]. The helical coherence length is the axial distance at which this mean-square displacement exceeds 1 rad2. At larger distances, azimuthal orientations of base pairs on molecules with different sequences become uncorrelated (B, bottom panel). We describe the contributions of variations in the twist and rise by the twist and rise coherence lengths, correspondingly [Equation (8)]. For instance, the total helical coherence length would be equal to the twist coherence length if the variations in the rise were negligible. The contribution of correlations between the twist and rise is characterized by the twist–rise coherence length. Note that the latter is a mathematical construct rather than a physical length. It may be positive or negative, depending on the sign of twist–rise correlations. All these concepts can be generalized to bent DNA as discussed in the text.
Mentions: To incorporate cumulative parameters of the sequence-dependent helical structure into the latter approach, we proposed to describe sequence and thermal variations in the twist between adjoining base pairs with the twist coherence length (29–31). This length characterizes the ability of DNA to follow a structure close to a geometrically perfect double helix in the same way as the bending persistence length characterizes the ability of DNA centerline to follow a straight line (Figure 1).Figure 1.

Bottom Line: We find, e.g. that the solution structure of synthetic oligomers is characterized by 100-200 A coherence length, which is similar to approximately 150 A coherence length of natural, salmon-sperm DNA.Packing of oligomers in crystals dramatically alters their helical coherence.The coherence length increases to 800-1200 A, consistent with its theoretically predicted role in interactions between DNA at close separations.

View Article: PubMed Central - PubMed

Affiliation: Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstrasse 1, D-40225 Düsseldorf, Germany. awynveen@googlemail.com

ABSTRACT
The twist, rise, slide, shift, tilt and roll between adjoining base pairs in DNA depend on the identity of the bases. The resulting dependence of the double helix conformation on the nucleotide sequence is important for DNA recognition by proteins, packaging and maintenance of genetic material, and other interactions involving DNA. This dependence, however, is obscured by poorly understood variations in the stacking geometry of the same adjoining base pairs within different sequence contexts. In this article, we approach the problem of sequence-dependent DNA conformation by statistical analysis of X-ray and NMR structures of DNA oligomers. We evaluate the corresponding helical coherence length--a cumulative parameter quantifying sequence-dependent deviations from the ideal double helix geometry. We find, e.g. that the solution structure of synthetic oligomers is characterized by 100-200 A coherence length, which is similar to approximately 150 A coherence length of natural, salmon-sperm DNA. Packing of oligomers in crystals dramatically alters their helical coherence. The coherence length increases to 800-1200 A, consistent with its theoretically predicted role in interactions between DNA at close separations.

Show MeSH
Related in: MedlinePlus