Double crossover

FIG. 13 Synthetic DN A motifs for the construction of DNA framework Three- [75] (13) and four-arm (14) DNA junction [8] DNA double-crossover (DX) molecules 15,16 were used for initial studies of enzymatic oligomerization [79]. The DX motif 17, containing four cohesive ends of individual nucleotide sequence, was used for the construction of two-dimensional DNA crystals [80]. 

The mechanism proposed for this transformation is outlined in Scheme 24 (235). The slow step of this reaction is silyl transfer from the copper alkoxide 353. This step may occur through the intermediacy of an external silicon source (intermolecular) or by internal transfer of the silyl group (intramolecular). To probe this issue, these workers conducted a double-crossover experiment involving two distinct nucleophiles with different silyl groups, 342a and 359, and examined the products prior to desilylation. The results show conclusively that silicon transfer has a significant intermolecular component, and is somewhat sensitive to the solvent, Eq. 199. 

The Holliday junction is a well-known intermediate in recombination, but it is not the only one. Another species is the DNA double-crossover molecule, termed DX. The DX molecule consists of two four-arm branched junctions that have been joined at two adjacent arms, to create a molecule containing two helical domains joined by two crossover points (Fu and Seeman 1993). There are five different motifs of the DX molecule these are illustrated in Figure 14, with a modification of one of them. The names of the DX molecules all begin with D, for double crossover . Those in the top row have P for their second letter, indicating that their helix axes are parallel hence, there is a dyad axis, vertical in the plane of the page and parallel to the helix axes, relating each helical domain of the DP molecules to the other domain. 

Figure 14. Motifs of double crossover molecules. The top row contains the three parallel isomers of double crossover (DX) molecules, DPE, DPOW and DPON P in their name indicates their parallel structure. Arrowheads indicate 3 ends of strands. Strands drawn with the same thickness are related by the vertical dyad axis indicated in the plane of the paper. DPE contains crossovers separated by an even number (two) of half-turns of DNA, DPOx by an odd number in DPOW, the extra half turn is a major groove spacing, in DPON, it is a minor groove spacing. The middle row illustrates two other DX isomers, DAE, and DAO. The symmetry axis of DAE is normal to the page (and broken by the nick in the central strand) the symmetry axis of DAO is horizontal within the page in DAO, strands of opposite thickness are related by symmetry. DAE+J, in the second row, is a DAE molecule, in which an extra junction replaces the nick shown in DAE.

Double-crossover molecules have been used extensively to characterize the properties of Holliday junctions. The strong torsional coupling between their crossover points has been exploited to construct symmetric immobile junctions (S. Zhang et al. 1993), junctions in which one of the crossovers is flanked by homology, but is nevertheless unable to branch migrate. Symmetric immobile junctions have been used to characterize crossover isomerization thermodynamics (S. Zhang and Seeman 1994) and, more recently, the sequence dependence of the branch point stability (W. Sun et al., 1998). Double crossover molecules have also been employed to establish the cleavage patterns of endonuclease VII, an enzyme that resolves branched junctions (Fu et al. 1994 a). 

Figure 17. The ligation products of antiparallel double crossover molecules. Ligations of the DAE, DAO, and DAE+J molecules, respectively, from the top to the bottom of the drawing. One domain has been capped by hairpins. Ligation of the DAE molecule leads to a reporter strand, which is drawn more darkly. Ligation of the DAE+J molecule also leads to a reporter strand, similar to the one in DAE. However, ligation of the DAO molecule produces to a polycatenated structure.

It is very hard to analyze such an experiment if it does not produce a reporter strand, either directly, as described for the three-arm and four-arm junction, or after restriction frees it from catenated partners (Li et al. 1996). To characterize the flexibility of double-crossover molecules, it is useful to examine the crossover topology of the products of an oligomerization reaction. These are shown in Figure 17 for DAE, DAO and DAE+J motifs. It is clear that both DAE and DAE+J motifs produce a reporter strand, but DAO does not. Therefore, in our initial experiments, we have analyzed only DAE and DAE+J. In both, these motifs can be shown to behave as rigid species, because they do not cyclize to any appreciable extent. 

Double-Crossover Molecules as a Route to Linear Catenanes and Rotaxanes... 

Figure 20. Two-dimensional arrays constructed from DAE and DAE+J motifs. Two arrays are shown, one containing two components, A and B, and a second containing four components, A, B, C, and D. Each of die starred components contains one or two hairpins perpendicular to the plane of the array. The double-crossover molecules are represented as two closed figures connected by two short lines. The helix axis of each domain is represented by a dotted line. The sticky ends are drawn schematically as complementary geometrical shapes, representing Watson-Crick complementarity. The horizontal repeat is two units in the top array and four in the bottom array the vertical repeat is a single unit in both arrays. The perpendicular hairpins are visible as stripes when this array is examined in the atomic force microscope.

Fu, T.-J., Kemper, B., Seeman, N.C. (1994a) Endonuclease VII cleavage of DNA double crossover molecules. Biochemistry 33, 3896-3905. 

Using Eq (14 8) together with the full form (14.7) of the mapping we can easily map1 out the double crossover from the dilute to the semidilute excluded volume regimes and further to the semidilute <9-regime. Figure 14.1a shows an example, where we plotted R2/Rq as function of the concentration... 

The very broad crossover has important implications for an experimental test of the theory. Indeed, to illustrate clearly the effects, in the figures of this chapter we have driven the parameters into extreme regions. No experiment, for instance, will cover six decades of overlap, nor will wre reach a range of z sufficient to cover both the 0- and the excluded volume limits. Any physical experiment or any simulation will see only some small section of the crossover function, the full function being tested only by combining results for several chemical systems. In particular we have no chance to see a double crossover as typically exhibited here, in a single experiment. 

Fig. 17 (a) Six-helix bundle consisting of six helices connected by double crossovers the strands shared by different helices are identified by colors, (b) AFM image of two-dimensional hexagonal arrangement of bundles (edge size is 324 nm). Adapted with permission from [74]... 

Fig. 18 (a) Tiles with colored edges are formed by DNA helices connected through double crossover motifs and interacting through sticky ends. The pairing rules determine a two-dimensional striped lattice, as observed in AFM imaging (b). Scale bar is 300 nm. Adapted with permission from [75]. 

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