New Motifs
In DNA Nanotechnology
by
Nadrian C. Seeman, Hui Wang, Xiaoping Yang,
Furong Liu, Chengde Mao, Weiqiong Sun,
Lisa Wenzler, Zhiyong Shen, Ruojie Sha,
Hao Yan, Man Hoi Wong, Phiset Sa-Ardyen,
Bing Liu, Hangxia Qiu, Xiaojun Li, Jing Qi,
Shou Ming Du, Yuwen Zhang, John E. Mueller,
Tsu-Ju Fu, Yinli Wang, and Junghuei Chen
Department
of Chemistry
New York University
New York, NY 10003, USA
[email protected]
This is a draft paper
for a talk at the
Fifth
Foresight Conference on Molecular Nanotechnology.
The final version has been submitted
for publication in the special Conference issue of Nanotechnology.
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Abstract
In recent years, we have invested a great deal of effort to
construct molecular building blocks from unusual DNA motifs. DNA
is an extremely favorable construction medium: The sticky-ended
association of DNA molecules occurs with high specificity, and it
results in the formation of B-DNA, whose structure is well known.
The use of stable branched DNA molecules permits one to make
stick-figures. We have used this strategy to construct a
covalently closed DNA molecule whose helix axes have the
connectivity of a cube, and a second molecule, whose helix axes
have the connectivity of a truncated octahedron.
In addition to branching topology, DNA also affords control of
linking topology, because double helical half-turns of B-DNA or
Z-DNA can be equated, respectively, with negative or positive
crossings in topological objects. Consequently, we have been able
to use DNA to make trefoil knots of both signs and figure-8
knots. By making RNA knots, we have discovered the existence of
an RNA topoisomerase. DNA-based topological control has also led
to the construction of Borromean rings, which could be used in
DNA-based computing applications.
The key feature previously lacking in DNA construction has
been a rigid molecule. We have discovered that DNA double
crossover molecules can provide this capability. We have
incorporated these components in DNA assemblies that make use of
this rigidity to achieve control on the geometrical level, as
well as on the topological level. Some of these involve double
crossover molecules, and others involve double crossovers
associated with geometrical figures, such as triangles and
deltahedra.
Introduction
DNA is well-known as the polymeric molecule that
contains the genetic information for life. Its key chemical
feature is its ability to associate with and recognize other DNA
molecules by means of specific base pairing relationships: Thus,
an adenine (A) on one strand will pair preferentially with a
thymine (T) on the other strand; likewise, guanine (G) will pair
with cytosine (C). This complementary relationship has been known
for about 45 years as the chemical basis for heredity [1]. Since the early 1970's, genetic
engineers have been using a variation on this theme to associate
specific DNA double helices with each other [2]. As shown in Figure 1, a double
helix with a single-stranded overhang (often called a 'sticky
end') will hydrogen bond with a complementary overhang to bring
two DNA molecules into proximity; Figure 1 also shows
that if desired the two pieces of DNA can be joined covalently to
form a single double helix.
Fig. 1.
Sticky Ended Association
Figure 1. Sticky-Ended Cohesion and
Ligation. Two linear double helical molecules of DNA are
shown at the top of the drawing. The antiparallel backbones
are indicated by the black lines terminating in half-arrows.
The half-arrows indicate the 5'-->3' directions of the
backbones. The right end of the left molecule and the left
end of the right molecule have single-stranded extensions
('sticky ends') that are complementary to each other. The
middle portion shows that, under the proper conditions, these
bind to each other specifically by hydrogen bonding. The
bottom of the drawing shows that they can be ligated to
covalency by the proper enzymes and cofactors.
Assemblies involving traditional linear double
helical pieces of DNA correspond to the concatenation of line
segments. However, it is possible to design and assemble
sequences of synthetic DNA molecules that form stable branches
(called 'junctions') flanked by 3-6 arms [3].
The same logic applies to the association of branched molecules
that applies to linear molecules. However, by using branched
molecules, it is possible to form stick figures whose
connectivity is no longer trivial. An example of this type of
construction is illustrated in Figure 2. In this regard,
we have previously reported the construction of a cube [4], shown in Figure 3, and a truncated
octahedron [5], shown in Figure 4. The edges of each of
these stick polyhedra are composed of double helical DNA.
Fig. 2. Branched
Junction Assembly
Figure 2. Formation of a Two-Dimensional Lattice
from an Immobile Junction with Sticky Ends. A is a sticky
end and A' is its complement. The same relationship exists
between B and B'. Four of the monomeric junctions on the left
are complexed in parallel orientation to yield the structure
on the right. A and B are different from each other, as
indicated by the pairing in the complex. Ligation by DNA
ligase can close the gaps left in the complex. The complex
has maintained open valences, so that it could be extended by
the addition of more monomers.
Fig. 3. A DNA Cube
Figure 3. A DNA Molecule with the Connectivity
of a Cube. This representation of a DNA cube shows that
it contains six different cyclic strands. Each nucleotide is
represented by a single colored dot for the backbone and a
single white dot representing the base. Note that the helix
axes of the molecule have the connectivity of a cube.
However, the strands are linked to each other twice on every
edge. Therefore, this molecule is a hexacatenane. To get a
feeling for the molecule, follow the front strand around its
cycle: It is linked twice to to each of the four strands that
flank it, and only indirectly to the strand at the rear. Note
that each edge of the cube is a piece of double helical DNA,
containing two turns of the double helix.
Fig. 4. A DNA
Truncated Octahedron
Figure 4. A DNA Molecule with the Connectivity
of a Truncated Octahedron. A truncated octahedron
contains six squares and eight hexagons. This is a view down
the fourfold axis of one of the squares. Each edge of the
truncated octahedron contains two double helical turns of
DNA. The molecule contains 14 cyclic strands of DNA. Each
face of the octahedron corresponds to a different cyclic
strand. In this drawing, each nucleotide is shown with a
colored dot corresponding to the backbone, and a white dot
corresponding to the base. This picture shows the strand
corresponding to the square at the center of the figure and
parts of the four strands at the cardinal points of the
figure. In addition to the 36 edges of the truncated
octahedron, each vertex contains a hairpin of DNA extending
from it. These hairpins are all parts of the strands that
correspond to the squares. The molecular weight of this
molecule as about 790,000 Daltons.
In this article, we will first summarize the properties of DNA
as a construction material. We will review briefly the techniques
for the construction and demonstration of DNA polyhedra. Next, we
will describe the relationships that act as the basis for the
construction of DNA knots and catenanes. Finally, we will discuss
the search for rigid DNA motifs, and the means to incorporate
them into DNA nanotechnology.
DNA as a Construction Material
There are several advantages to using DNA for
nanotechnological constructions. First, the ability to get sticky
ends to associate makes DNA the molecule whose intermolecular
interactions are the most readily programmed and reliably
predicted: Sophisticated docking experiments needed for other
systems reduce in DNA to the simple rules that A pairs with T and
G pairs with C. In addition to the specificity of interaction,
the local structure of the complex at the interface is also
known: Sticky ends associate to form B-DNA [6]. A second advantage of DNA is the
availability of arbitrary sequences, due to convenient solid
support synthesis [7]. The needs of
the biotechnology industry have also led to straightforward
chemistry to produce modifications, such as biotin groups,
fluorescent labels, and linking functions. The recent advent of
parallel synthesis [8] is likely to
increase the availability of DNA molecules for nanotechnological
purposes. DNA-based computing [9] is
another area driving the demand for DNA synthetic capabilities.
Third, DNA can be manipulated and modified by a large battery of
enzymes, including DNA ligase, restriction endonucleases, kinases
and exonucleases. In addition, double helical DNA is a stiff
polymer [10] in 1-3 turn lengths, it
is a stable molecule, and it has an external code that can be
read by proteins and nucleic acids [11].
There are two properties of branched DNA that one cannot
ignore: First, the angles between the arms of branched junctions
are variable. In contrast, to the trigonal or tetrahedral carbon
atom, ligation-closure experiments [12],
[13] have demonstrated branched
junctions are not well-defined geometrically. Thus, the cube and
the truncated octahedron discussed above are molecules whose
graphs correspond to the graphs of those ideal objects (e.g., [14]), but only their branching
connectivity has been (or probably can be) demonstrated. Simple
branched junctions apparently do not lead to geometrical control.
This places a greater burden on specificity: The construction
illustrated in Figure 2
would not lead exclusively to the quadrilateral depicted there
unless the inter-arm angles were fixed to be right angles.
Nevertheless, it is possible to generate a quadrilateral by using
four different sticky end pairs to make each of the four edges [15].
Second, it is imperative to recognize that DNA is
a helical molecule. For many purposes, the double helical
half-turn is the quantum of single-stranded DNA topology. Figure 5
illustrates two variants of Figure 1, one with an even number of
half-turns between vertices, and the other with an odd number.
With an even number of half-turns, the underlying substructure is
a series of catenated single-stranded cycles, much like
chain-mail, but an odd number leads to an interweaving of long
strands. If the edges flanking a face of a polyhedron contain an
exact number of helical turns, then that face contains a cyclic
strand as one of its components; this strand will be linked (in
the topological sense) to the strands of the adjacent faces, once
for every turn in their shared edges. We used this design motif
with both the cube and the truncated octahedron, so they
are really a hexacatenane and a 14-catenane. In general, the
level control over linking topology available from DNA is almost
equal to the level of control over branching topology.
Consequently, a number of topological species have been
constructed relatively easily from DNA, even though they
represented extremely difficult syntheses using the standard
tools of organic and inorganic chemistry.
Fig.
5. Topological Assembly
Figure 5. Topological Consequences of Ligating
DNA Molecules Containing Even and Odd Numbers of DNA
Half-Turns in Each Edge. These diagrams represent the
same ligation shown in Figure 2. However, they indicate the
plectonemic winding of the DNA, and its consequences. The DNA
is drawn as a series of right-angled turns. In the left
panel, each edge of each square contains two turns of double
helix. Therefore, each square contains a cyclic molecule
linked to four others. In the right panel, each edge of each
square contains 1.5 turns of DNA. Therefore, the strands do
not form cycles, but extend infinitely in a warp and weft
meshwork.
The Construction and Analysis of DNA Polyhedra
The combination of branched DNA and sticky-ended ligation
results in the ability to form stick figures whose edges consist
of double helical DNA, and whose vertices are the branch points
of the junctions. The flexibility of the angles that flank the
branch points of junctions results in the need to specify
connectivity explicitly. This may be done either by a set of
unique sticky end pairs, one for each edge [4], [15],
or by utilizing a protection-deprotection strategy [16] so that only a given pair is
available for ligation at a particular moment. The first strategy
was used in the construction of the DNA cube, which was done in
solution [4].
We found that we had too little control over the synthesis
when it was done in solution, so we developed a
solid-support-based methodology [16].
This approach allows convenient removal of reagents and catalysts
from the growing product. Each ligation cycle creates a robust
intermediate object that is covalently closed and topologically
bonded together. The method permits one to build a single edge of
an object at a time, and to perform intermolecular ligations
under conditions different from intramolecular ligations. Control
derives from the restriction of hairpin loops forming each side
of the new edge, thus incorporating the technique of successive
deprotection. Intermolecular reactions are done best with
asymmetric sticky ends, to generate specificity. Sequences are
chosen in such a way that restriction sites are destroyed when
the edge forms. One of the major advantages of using the solid
support is that the growing objects are isolated from each other.
This permits the use of symmetric sticky ends, without
intermolecular ligation occurring. More generally, the solid
support methodology permits one to plan a construction as though
there were only a single object to consider. Many of the
differences between a single molecule and a solution containing
1012 molecules disappear if the molecules are isolated
on a solid support. We utilized the solid-support methodology to
construct the DNA truncated
octahedron.
The polyhedra we made were objects that were
topologically specified, rather than geometrically specified;
consequently, our proofs of synthesis were also proofs of
topology. In each case, we incorporated restriction sites in
appropriate edges of the objects, and then broke them down to
target catenanes, whose electrophoretic properties could be
characterized against standards [17].
For example, the first step of synthesizing the cube resulted in
the linear triple catenane corresponding to the ultimate
left-front-right sides of the target. When the target was
achieved, one of the most robust proofs of synthesis came from
the restriction of the two edges in the starting linear triple
catenane, to yield the linear triple catenane corresponding to
the top-back-bottom of the cube, as shown in Figure 6. A similar approach
was taken with the proof of the truncated octahedron synthesis:
The presence of the six square strands was demonstrated first.
Then the octacatenane corresponding to the eight hexagonal faces
was shown by restricting it down to the tetracatenane flanking
each square, for which we were able to make a marker.
Fig. 6. The Cube
as a Sum of Linear Catenanes
Figure 6. The Linear Triple Catenanes that Link
to Form the Cube. The target cube is shown at the left of
the figure. The starting material for its synthesis was the
linear triple catenane shown at the center of the drawing.
This catenane corresponds to the left, front and right faces
of the cube. When the cube is restricted on its two front
edges, the starting linear triple catenane is destroyed.
However, when the cube is successfully synthesized, a linear
triple catenane results. This catenane corresponds to the
top, back and bottom faces of the cube.
The solid-support based methodology appears to be quite
powerful. We feel that we could probably construct most Platonic,
Archimedean, Catalan, or irregular polyhedra by using it. The
cube is a 3-connected object, as is the truncated octahedron. The
cube was constructed from 3-arm branched junctions, but the
truncated octahedron was constructed from 4-arm branched
junctions, because we had originally planned to link the
truncated octahedra together. The connectivity [18], [19]
of an object or a network determines the minimum number of arms
that can flank the junctions that act as its vertices. Thus, one
must have at least 5-arm branched junctions to construct an
icosahedron, and one must have 12-arm branched junctions to build
a cubic-close-packed (face-centered cubic) lattice. We have built
junctions with up to 6 arms [3], but
there seem to be no impediments to making junctions containing
arbitrary numbers of arms. The one caveat to observe is
that the lengths of the arms necessary for stabilization tend to
increase with the number of arms.
Topological Construction
In the last section, we have emphasized that the construction
of DNA polyhedra ultimately becomes an exercise in synthetic
topology: The resulting structures are characterized best by
their branching and linking rather than by their geometry. In
addition to the construction of polyhedral catenanes, DNA
nanotechnology is also an extremely powerful methodology for the
construction of knots, unusual links, and other species defined
by their linking. Indeed, it is arguably the most powerful system
for creating these targets.
The key requisite for constructing topological
targets is the ability to produce at will a chemical version of a
node or a crossing (sometimes called a unit tangle) in the
target. The strength of DNA in this regard derives from the fact
that a half-turn of DNA corresponds exactly to this necessary
component [20]. It is easy to
understand this relationship by looking at Figure 7. Here, a trefoil
knot has been drawn, with an arbitrary polarity. Squares have
been placed about each of the crossings, so that the portions of
the knot contained within each square act as its diagonals. These
diagonals divide the square into four regions, two between
parallel strands, and two between antiparallel strands. Whereas
the strands of double helical DNA are antiparallel, one should
design the sequence of the DNA strand so that pairing occurs over
a half-turn segment (ca. 6 nucleotide pairs) in the regions
between antiparallel strands. Thus, it is possible to make the
transition from topology to nucleic acid chemistry by specifying
complementary sequences to form desired nodes. Linker regions
between the nodes usually consist of oligo-dT.
Fig. 7. Nodes
as Half-Turns of Double Helical DNA
Figure 7. The Relationship Between Nodes and
Antiparallel B-DNA Illustrated on a Trefoil Knot. A
trefoil knot is drawn with negative nodes. Nodes are also
known as crossings or unit tangles. The path is indicated by
the arrows and the very thick curved lines connecting them.
The nodes formed by the individual arrows are drawn at right
angles to each other. Each pair of arrows forming a node
defines a quadrilateral (a square in this figure), which is
drawn in dotted lines. Each square is divided by the arrows
into four domains, two between parallel arrows and two
between antiparallel arrows. The domains between antiparallel
arrows contain lines that correspond to base pairing between
antiparallel DNA (or RNA) strands. Dotted double-arrowheaded
helix axes are shown perpendicular to these lines. The
twofold axis that relates the two strands is perpendicular to
the helix axis; its ends are indicated by lens-shaped
figures. The twofold axis intersects the helix axis and lies
halfway between the upper and lower strands. The amount of
DNA shown corresponds to about half a helical turn. It can be
seen that three helical segments of this length could
assemble to form a trefoil knot. The DNA shown could be in
the form of a 3-arm DNA branched junction. A trefoil of the
opposite sense would need to be made from Z-DNA, in order to
generate positive nodes.
There are two kinds of nodes found in topological
species, positive nodes and negative nodes. As illustrated at the
top of Figure 8,
these nodes are mirror images of each other. B-DNA is a
right-handed helical molecule. Its crossings generate nodes that
are designated to have negative signs, as illustrated at the
bottom-left side of the drawing. Fortunately, there is another
form of DNA, Z-DNA, shown at the bottom-right, whose helix is
left-handed [21]. Z-DNA is not the
geometrical mirror image of B-DNA, because it still contains
D-deoxyribose sugar residues, and, in addition, its structure is
qualitatively different. However, from a topological standpoint,
it is the mirror image of B-DNA, and it can be used to supply
positive nodes when they are needed.
Fig. 8.
Node Chirality
Figure 8. Nodes and DNA Handedness. The
upper part of this drawing shows positive and negative nodes,
with their signs indicated. It is useful to think of the
arrows as indicating the 5'-->3' directions of the DNA
backbone. Below the negative node is a representation of
about one and a half turns of a right-handed B-DNA molecule.
Note that the nodes are all negative. Below the positive node
is a left-handed DNA molecule, termed Z-DNA. The Z-DNA
molecule has a zig-zag backbone, which we have tried to
indicate here. However, the zig-zag nature of the backbone
does not affect the fact that all the nodes are positive.
The Z-forming propensity of a segment of DNA is a function of
two variables, the sequence, and the conditions. Not all
sequences undergo the B-->Z transition under the mild
conditions compatible with enzymatic ligation. The sequence of
conventional nucleotides that undergoes the transition most
readily contains the repeating dinucleotide sequence dCdG.
Furthermore, the ease with which a segment undergoes the B-->Z
transition can be made a function of base modification; DNA in
which a methyl group has been added to the 5-position of cytosine
undergoes the transition under milder conditions [21]. However, in the absence of
Z-promoting conditions, the sequence will remain in the B-form.
We have utilized this basic framework to
construct a number of knotted species from DNA molecules. Figure 9 illustrates
a molecule with two pairing domains, each containing one turn of
DNA double helix. Each of the two domains is capable of
undergoing the B-->Z transition, but one of the domains
undergoes the transition more readily than the other one. At very
low ionic strength, neither domain forms double helical DNA, and
a molecule with circular topology results. At higher ionic
strength, both domains form B-DNA, and a trefoil knot results,
with all of its nodes negative. Under mild Z-promoting
conditions, the more sensitive domain converts to Z-DNA, and a
figure-8 knot is the product. When the solution presents more
vigorous Z-promoting conditions, the other domain also converts
to Z-DNA, and ligation yields the trefoil knot with positive
nodes [22].
Fig. 9. A
DNA Strand in Four Topological States
Figure 9. A DNA Strand is Ligated into Four
Topological States by Variation of Ligation Conditions. The
left side of this synthetic scheme indicates the molecule
from which the target products are produced. The four pairing
regions, X and its complement X', Y and its complement Y' are
indicated by the bulges from the square. The 3' end of the
molecule is denoted by the arrowhead. The four independent
solution conditions used to generate the target products are
shown to the right of the basic structure. The pairing and
helical handedness expected in each case is shown to the
right of these conditions, and the molecular topology of the
products is shown on the far right of the figure. The species
are, from the top, the circle, the trefoil knot with negative
nodes, the figure-8 knot, and the trefoil knot with positive
nodes.
The favored topology of each of the species in Figure 9 is a
function of solution conditions. If one of these molecules is
placed in solution conditions that favor one of the other knots,
it cannot convert to the new favored structure without breaking
and rejoining its backbone. However, type I DNA topoisomerases
can catalyze this interconversion [23].
Figure 10 illustrates
the stepwise interconversion of the different species, under
solution conditions that promote the B-->Z or Z-->B
transitions.
Fig. 10.
Interconversion of DNA Knots
Figure 10. DNA Knots Interconverted by Type I
DNA topoisomerases. On the top of this figure are the
three knots that are interconverted, the trefoil knot with
positive nodes, The figure-8 knot, and the trefoil knot with
negative nodes. The nucleotide pairs that give rise to the
nodes are indicated between strands. The same knots are shown
in the bottom portion of the figure, interspersed by circles
drawn with the node structures of dumbbells. The lines
indicating the base pairs have been removed for clarity. The
'+' and '-' signs near the nodes indicate their topological
signs. The equilibria indicated between structures are
catalyzed by the E. coli DNA Topoisomerases I and III.
The trefoil knot on the left has all positive signs, and the
signs of a single node at a time are switched from positive
to negative in each of the structures as one proceeds towards
the right of the figure. Changing the sign of a single node
in the positive trefoil knot produces a circle (dumbbell),
and changing a second node in the same domain produces a
figure-8 knot. Changing the sign of another positive node in
the figure-8 knot produces the circle (dumbbell) on the
right, and changing the sign of the last node generates the
negative trefoil knot. It is important to realize that the
two circles shown may interconvert without the catalytic
activity of a topoisomerase.
This ability of topoisomerases to interconvert
synthetic DNA knots suggested to us that it would be possible to
use an RNA knot to assay the presence of an RNA topoisomerase, a
species unknown previously. By preparing both an RNA knot and an
RNA circle, we found that it was possible to catalyze the
interconversion of these cyclic molecules by the presence of E.
coli DNA topoisomerase III [24].
This experiment is illustrated in Figure 11.
Fig. 11.
Discovery of an RNA Topoisomerase
Figure 11. The Discovery of an RNA Topoisomerase
An RNA single strand is shown at the top of this diagram.
Its Watson-Crick pairing regions, X, Y, X' and Y' are
illustrated at bumps on the square, and the spacers, denoted
by S are shown as the corners of the square. The arrowhead
denotes the 3' end of the strand. The pathway to the left
illustrates formation of the RNA circle: A 40 nucleotide DNA
linker (incompatible with knot formation) is annealed to the
molecule, and it is ligated together to form an RNA circle,
which survives treatment with DNase. In the other pathway, a
16 nucleotide DNA linker is used in the same protocol to
produce the RNA trefoil knot, whose three negative nodes are
indicated. The interconversion of the two species by E.
coli DNA Topoisomerase III (Topo III) is shown at the
bottom of the figure. The 40-mer RNA strand promotes somewhat
the formation of the circle from the knot. E. coli DNA
Topoisomerase I does not catalyze this reaction.
In order to illustrate the power of DNA as a
medium for the assembly of topological targets, we have recently
used this system to construct Borromean rings from DNA [25]. Borromean rings are a rich family
of topological structures [26] whose
simplest member (section [a] of Figure 12) appears
on the coat of arms of the Borromeo family, prominent in the
Italian Renaissance. Their key property is that removal of any
individual circle unlinks the remaining rings. The innermost
three nodes are negative, and the outermost three are positive.
Although it is possible to fashion topological targets from DNA
molecules held together by a single half-turn of DNA [27], it is often more convenient to
use 1.5 turns of DNA, if this does not change any key features of
the target. Therefore, we converted the traditional Borromean
ring structure to one that replaced each crossing with three
crossings (part [b] of Figure 12). It is
evident that the innermost three segments correspond to a 3-arm
DNA branched junction made from B-DNA.
Fig. 12.
Borromean Rings
Figure 12. The Design and Construction of
Borromean Rings from DNA
[a] Traditional Borromean Rings. Borromean rings
are special links, because linkage between any pair of rings
disappears in the absence of the third. The signs of the
three nodes near the center of the drawing are negative, and
the signs of the outer three nodes are positive.
[b] Borromean Rings with Each Node Replaced by Three
Nodes. Each node of [a] has been replaced by three nodes,
derived from 1.5 turns of DNA double helix. The inner double
helices are right handed, corresponding to B-DNA, and the
outer double helices are left handed, corresponding to Z-DNA.
Think of this drawing like a polar projection of the Earth,
where the center is at the North Pole, and every point on the
circumference corresponds to the South Pole.
[c] Stereoscopic Representation of [b]. View this
picture with stereo glasses, or you can learn to see stereo
by diverging your eyes. The 'projection' of [b] is
represented in 3-D, now. The three outer double helices have
been folded under the inner double helices, so that a B-DNA
3-arm branched junction flanks the 'North Pole' of the object
and a Z-DNA 3-arm branched junction flanks the 'South Pole'
of the object.
[d] Stereoscopic Views of the DNA Molecules
Synthesized. Two hairpins have been added to the
'equatorial' sections of each strand. Each hairpin contains a
site for a restriction endonuclease, so that the Borromean
property can be demonstrated in the test tube.
With a topological picture, it is always permissible to deform
it. One can imagine that this picture corresponds to a polar map
of the earth, where the center is at the North Pole, and every
point on the circumference represents the South Pole. Thus, the
three points at the outermost radii of the three helices could
all abut each other at the South Pole. Section [c] of Figure 12 is a
stereoscopic view that illustrates what this molecule would look
like if it were wrapped around a sphere. From this view, it is
clear that the three outermost helices represent a 3-arm branched
junction made from Z-DNA. From both synthetic and analytical
standpoints, it is convenient to have a series of hairpins at
'the equator', as illustrated in section [d] of Figure 12. We have
been able to use them as sites both to ligate the two junctions
together, and to restrict them. By designing them to be slightly
different lengths, it is easy to separate the restriction
products on a gel.
Our ability to construct Borromean rings demonstrates that the
3-D geometrical approach we used has facilitated the exploitation
of the relationship between nodes and DNA half-turns. This scheme
consists of {1} identifying components to serve as positive and
negative nodes (or their odd multiples), {2} linking components
in a minimal number of spatially condensed stable units (3-arm
branched junctions here), followed by {3} recognition-directed
ligation; this approach should provide topological control in
other chemical systems. Conversely, it may be possible to use
this or other successful systems to act as scaffolding that
guides the formation of target topological products from other
polymers.
Besides being a holy grail for synthetic chemistry, Borromean
rings might be able to serve a role in DNA-based computing. It is
possible to design Borromean rings that contain an arbitrary
number of circles, so they are not limited to just three strands.
A complete Borromean complex can be separated readily from its
dissociated components. It is not hard to imagine that the
integrity of a Borromean link can represent the truth of each of
a group of logical statements. If any one of them is false, then
one of the rings would not be closed. From a chemical point of
view, these two cases would be separated easily by denaturing gel
electrophoresis. For example, one could use the integrity of a
Borromean link as a check that the right molecules had
associated, in a set of interactions orthogonal to the main
calculation. In this capacity, the presence of the Borromean link
would function as parity-checking did on early computers: If the
calculation has been done right, the link is established, and
otherwise it is broken, and those molecules lacking an intact
link could be discarded.
The Quest for Rigidity
We have emphasized above the power of the solid-support based
synthetic approach to DNA nanotechnology. It allows us to
construct discrete objects containing a finite number of edges.
However, one of the key goals of DNA nanotechnology is the
ability to construct precisely configured materials on a much
larger scale. A particularly important goal in this regard is the
assembly of periodic matter, namely crystals [28]; this ability offers both a window
on the crystallization problem for macromolecules, [28] and on the assembly of molecular
electronic components [29]. Periodic
matter entails a whole new series of problems. The strength of
DNA nanotechnology is that the specificity of intermolecular
interactions can be used to make defined objects. In particular,
the ability to program different sticky ends to form the
edges of a polyhedron or other target gives us a tremendous
amount of control over the product. Another way to say this is
that we have used an asymmetric set of sticky ends, because none
of them are the same. The key to control over the products of a
reaction is the minimization of symmetry. Symmetry is
antithetical to control.
However, when we wish to make crystalline materials, we are
forced to consider the case where symmetry dominates. The
distinguishing characteristic of crystals is their translational
symmetry: The contacts on the left side of a crystalline unit
cell must complement those on the right side in an infinite
array; the top and bottom, and the front and the rear bear the
same relationship. It is very hard to achieve an infinite
arrangement with flexible components. The reason is that flexible
components do not maintain the same spatial relationships between
each member of a set. Consequently, instead of periodic matter,
one often obtains a random network. In addition, a flexible
system can cyclize on itself, thereby poisoning growth. Hence, it
is key for the success of building periodic matter to discover
rigid DNA components.
Recognition of this situation has led us to two different
complementary approaches in the quest for rigidity. The first of
these is to abandon potentially flexible polygonal and polyhedral
motifs. A theory of bracing such systems exists (e.g., [14]), but it is simplest to restrict
ourselves to triangles and deltahedra (polygons whose faces are
all triangles). A convex polyhedron can be shown to be rigid if
and only if its faces are exclusively triangular [14]. The second approach has been to
seek rigid DNA motifs. We have investigated the flexibility of
bulged DNA branched junctions. Initially, they seemed promising
because they were stiffer than conventional junctions [30]. Ultimately, however, they did not
bear up to rigorous testing [31].
Fortunately, we have discovered another motif, the antiparallel
DNA double crossover molecule [32],
that appears to be far stiffer than bulged junctions [33].
DNA double crossover molecules (abbreviated DX)
are analogs of intermediates in the process of genetic
recombination [34]. They correspond
to pairs of 4-arm branched junctions that have been ligated at
two adjacent arms. We have used them extensively to explore the
properties of conventional branched junctions, including their
susceptibility to enzymes [35],
their crossover topology [36], and
their crossover isomerization [37], [38]; we have also used them to make
symmetric immobile branched junctions [39].
Figure 13 shows that there are
five possible isomers of DX molecules. Three of them contain
parallel helical domains (DPE, DPOW and DPON), and two contain
antiparallel helical domains (DAE and DAO). Those with the
parallel domains are relevant to biological processes, but those
with antiparallel domains are far more stable in systems with a
small separation between the crossovers. The difference between
DAE and DAO is the number of double helical half-turns between
crossovers, an even number (DAE) or an odd number (DAO). The two
odd parallel DX molecules differ by whether the extra half-turn
is a wide groove (DPOW) or narrow groove (DPON) segment; this
issue does not arise in antiparallel DX molecules.
Fig. 13. DNA Double
Crossover Molecules
Figure 13. The Isomers of DNA Double Crossover
Molecules. The structures shown are named by the acronym
describing their basic characteristics. All names begin with
'D' for double crossover. The second character refers to the
relative orientations of their two double helical domains,
'A' for antiparallel and 'P' for parallel. The third
character refers to the number (modulus 2) of helical
half-turns between crossovers, 'E' for an even number and 'O'
for an odd number. A fourth character is needed to describe
parallel double crossover molecules with an odd number of
helical half-turns between crossovers. The extra half-turn
can correspond to a major (wide) groove separation,
designated by 'W', or an extra minor (narrow) groove
separation, designated by 'N'. The strands are drawn as
zig-zag helical structures, where two consecutive,
perpendicular lines correspond to a full helical turn for a
strand. The arrowheads at the ends of the strands designate
their 3' ends. The structures contain implicit symmetry,
which is indicated by the conventional markings, a
lens-shaped figure (DAE) indicating a potential dyad
perpendicular to the plane of the page, and arrows indicating
a twofold axis lying in the plane of the page. Note that the
dyad in DAE is only approximate, because the central strand
contains a nick, which destroys the symmetry. The strands
have been drawn with pens of two different colors (three for
DAE), as an aid to visualizing the symmetry. In the case of
the parallel strands, the red strands are related to the
other red strands by the twofold axes vertical on the page;
similarly, the blue strands are symmetrically related to the
blue strands. The twofold axis perpendicular to the page
(DAE) relates the two red helical strands to each other, and
the two blue outer crossover strands to each other. The 5'
end of the central green double crossover strand is related
to the 3' end by the same dyad element. A different
convention is used with DAO. Here, the blue strands are
related to the red strands by the dyad axis lying horizontal
on the page. An attempt has been made to portray the
differences between the major and minor grooves. Note the
differences between the central portions of DPOW and DPON.
Also note that the symmetry brings symmetrically related
portions of backbones into apposition along the center lines
in parallel molecules, in these projections. The same
contacts are seen to be skewed in projection for the
antiparallel molecules.
Our usual means for assaying rigidity is a
ligation-closure experiment. Figure 14
illustrates such an experiment for a 3-arm branched junction. The
products are assayed to see whether oligomerization has led to
cyclization, and, if so, whether there is a single product or a
collection of them. A collection of cyclic products suggests that
the angles between the arms of the molecule being tested are not
well-fixed. A key feature of this experiment is that the
oligomerized species must contain an accessible 'reporter
strand', whose fate is the same as that of the complex. Figure 15 illustrates
the topological consequences of ligating DAE and DAO molecules;
only the DAE molecule generates a reporter strand. The DAE
molecule contains 5 strands (in contrast to 4 strands in a DAO
molecule), and the central strand is often difficult to seal
shut. However, another option is to extend it as a bulged 3-arm
junction. Figure 15
shows that ligation of this molecule (DAE+J) also generates a
reporter strand. Ligation of both DAE and DAE+J result in
negligible amounts of cyclization: A small amount is detected for
DAE+J, but none is seen for DAE.
Fig. 14.
Reporter Strands in Ligation-Closure Experiments
Figure 14. Reporter Strands in Ligation-Closure
Experiments. The 3-arm junction employed is indicated at
the upper left of the diagram. The 3' ends of the strands are
indicated by half-arrowheads. The 5' end of the top strand
contains a radioactive phosphate, indicated by the starburst
pattern, and the 5' end of the strand on the right contains a
non-radioactive phosphate, indicated by the filled circle.
The third strand corresponds to the blunt end, and is not
phosphorylated. Beneath this molecule are shown the earliest
products of ligation, the linear dimer, the linear trimer and
the linear tetramer. The earliest cyclic products are shown
on the right, the cyclic trimer and the cyclic tetramer. The
blunt ends form the exocyclic arms of these cyclic molecules.
Note that in each case the labeled strand has the same
characteristics as the entire complex: It is an oligomer of
the same multiplicity as the complex, and its state of
cyclization is that of the complex. Hence, it can function as
a reporter strand When the reaction is complete, the
reaction mixture is loaded onto a denaturing gel, and its
autoradiogram is obtained. Both cyclic and linear products
are found, as indicated on the left of the gel. If an aliquot
of the reaction mixture is treated with exo III and/or exo I,
the linear molecules are digested, and only the cyclic
molecules remain. Not shown in this cartoon are the linear
and cyclic markers also run on the gel, so that the strands
can be sized absolutely.
Fig. 15.
Antiparallel Double Crossover Ligation
Figure 15. The Products of Antiparallel Double
Crossover Ligation. Shown at the top of the diagram are
three types of antiparallel double crossover molecules, DAE,
with an even number of double helical half-turns between the
crossover, DAO, with an odd number of half-turns between the
crossovers, and DAE+J, similar to DAE, but with a bulged
junction emanating from the nick in the central strand. The
DAE and DAE+J molecules contain 5 strands, two of which are
continuous, or helical strands, and three of which are
crossover strands including the cyclic strands in the middle.
The 3' ends of each strand are indicated by an arrowhead. The
DAO molecule contains only 4 strands. The twofold symmetry
element is indicated perpendicular to the page for the DAE
molecule, and it is horizontal within the page for the DAO
molecule. The drawing below these diagrams represents DAE,
DAO and DAE+J molecules in which one helical domain has been
sealed by hairpin loops, and then the molecules have been
ligated together. The ligated DAE and DAE+J molecules contain
a reporter strand. By contrast, the ligated DAO molecule is a
series of catenated molecules.
This motif is significantly different from the
single branched junction motif, and we have to figure out how to
use it, particularly in combination with triangles and
deltahedra. Figure 16
shows a series of double crossover molecules oriented to form a
trigonal set of vectors by means of their attachment to a
triangle. The triangles are connected, so as to tile a plane.
Thus, it appears possible to use DAE molecules to form a two
dimensional DNA lattice. In our hands, DAO molecules are usually
better behaved than DAE molecules, so it is likely that they can
be used even more effectively than DAE molecules for this
purpose, so long as a reporter strand is not needed to ascertain
the results of the construction.
Fig. 16.
DNA Double Crossover Triangle Lattice
Figure 16. A Two-Dimensional Lattice Formed from
Triangles Flanked by Double Crossover Molecules This
diagram shows a series of equilateral triangles whose sides
consist of double crossover molecules. These triangles have
been assembled into an hexagonally-symmetric two-dimensional
lattice. The basic assumption here is that triangles will
retain their angular distributions here, so that they
represent eccentric trigonal valence clusters of DNA.
We have tested whether it is possible for a
double crossover molecule to be attached to a triangular motif
and still maintain its structural integrity. Figure 17 illustrates
an experiment in which two DNA double crossover molecules have
been used to form the sides of a DNA triangle. The domains that
form the sides of the triangle correspond to the domains in Figure 15 that were
capped with hairpins. The other domains have been ligated to
oligomerize the structure, either the domain at the bottom, or
the domain on the left side, in two separate experiments. In both
cases, linear reporter strands are recovered, and no cyclic
reporter strands are detected. Thus, it is possible to
incorporate DX molecules into the sides of a triangle, and to
maintain their structural integrity.
Fig. 17.
Ligation of a Triangle With Two DX Edges
Figure 17. A Ligation Experiment Using a
Triangle With Two DX Edges. The triangle shown at the top
contains two DAE double crossover molecules in its edges. In
the experiment shown, one of them has biotin groups on each
of its hairpins. When the triangle is restricted, to unmask
sticky ends, restriction may not be complete. Molecules that
have been properly restricted will contain no biotins, but
those with incomplete restriction will have a biotin
attached. These incompletely restricted molecules can be
removed by treatment with streptavidin beads. The purified
triangles with sticky ends can be ligated together. There is
no evidence of cyclization in the reporter strands produced
by this experiment. The representation of the DNA as a ladder
makes it appear that there are no reporter strands, but this
is not the case, when the DNA is drawn as a double helix.
Figure
18 illustrates a means of utilizing DAE+J molecules to form a
lattice. This figure shows the same lattice employed in Figure 16. However,
the extra junction is used to form the triangles, and the other
domain of the double crossover molecule is used to buttress the
edge and to keep its helix axis linear.
Fig. 18.
DNA+J Triangle Lattice
Figure 18. A Triangle Lattice Formed from the
DAE+J Motif. The DAE+J molecules used here serve to
buttress branched junctions, to keep them from bending. The
triangles are formed using the extra junction, so that it is
part of the lattice, in contrast to the triangular lattice
formed from simple DAE molecules, shown in Figure 16.
Exactly the same arrangement of triangles has been employed
here.
Figure
19 shows the extension to three dimensions of the scheme
illustrated in Figure
16. A single octahedron is drawn, containing three double
crossover molecules. The free helical domains of these DX edges
span a three-dimensional space, and they will not intersect each
other, no matter how far they are extended. An enantiomorphous
set of three arms could also be chosen. If each of the three arms
were connected to its corresponding arm in another octahedron,
the resulting structure would nucleate an array resembling the
arrangement of octahedral subunits in cubic close packed
structures (face-centered cubic structures). However, the
structure would be of lower symmetry, because of the connections
through the outer helical domains. Figure 20 shows a
schematic representation of the components of this rhombohedral
system. Figure 21
shows a view down the 3-fold axis of the array.
Fig. 19. A
DNA Octahedron Flanked by Double Crossover Molecules
Figure 19. An Octahedron Containing Three Edges
Made from Double Crossovers. This drawing of an
octahedron down one of its three-fold axes shows only four of
its eight equilateral triangular faces. The three edges shown
constructed from DAE molecules are not coplanar, but span a
three-dimensional space. An enantiomorphous set also exists.
Connecting their outside domains to similar domains in other
octahedra would yield a lattice resembling the octahedral
portion of a face-centered cubic lattice, but of lower
symmetry.
Fig.
20. Components of a DX Octahedron Lattice
Figure 20. Components of a DX Octahedron
Lattice. The drawing on the upper left contains an
octahedron, three of whose edges contain a second domain. The
second domain is indicated by a ball at either end and a ball
in the middle, all connected by a linear stick. The three DX
domains span a three dimensional space. The center of the
octahedron is indicated by a small ball. The upper right
contains a drawing of only the extra domains, but
extended over two unit cells in each direction. The three
drawings on the bottom show the complete octahedron twice,
each time joined by a different one of the three domains.
Fig. 21.
Trigonal View of a Lattice Made of DX Octahedra
Figure 21. Trigonal View of a Lattice Made of DX
Octahedra. This is a view down the 3-fold axis of the
lattice shown in Figure 20.
Eight unit cells are shown. The 'impossible structure'
interlacing of the extra domains is a consequence of the fact
that the contents of only seven of the unit cells are visible
in this projection.
Concluding Comments
DNA nanotechnology is a promising avenue to achieve the goals
of nanotechnology in general. The specificity of DNA interactions
combined with branched molecules represent a system whereby it is
possible to gain large amounts of control over both linking and
branching topology. Two features of the system remain to be
developed. One of these, discussed above, entails the
construction of periodic matter, including the attachment of
guests and pendent molecules. As noted above, this will give us a
rational means for determining macromolecular structure by
generating crystals for x-ray diffraction experiments [28], as well as allowing us to direct
the assembly of arrays of other molecules besides DNA [29]. Among the targets for x-ray
diffraction experiments, one must include complex knots and
catenanes: We can demonstrate the synthesis of the simplest
members of these classes by gel electrophoresis, but more complex
topological figures require direct physical observation. Winfree
has proposed using DX arrays in DNA-based computing [40]. That approach, too, requires the
ability to build periodic backbones, although the bases would
differ from unit cell to unit cell.
The other goal for DNA nanotechnology does not
require periodic matter. This is the use of DNA structural
transitions to drive nanomechanical devices. Two transitions have
been mentioned prominently, branch migration and the B-Z
transition. It is known that applying torque to a cruciform can
lead to the extrusion or intrusion of a cruciform [41]. A synthetic branched junction
with two opposite arms linked can relocate its branch point in
response to positive supercoiling induced by ethidium [42]. The experimental system used to
demonstrate this level of control is illustrated in Figure 22. This
molecule represents the very first step in using DNA structural
transitions to achieve a nanomechanical result. We are also
exploring the use of the B-Z transition in nanomechanical
devices.
Fig. 22.
Control of Branch Migration
Figure 22. An Experiment Demonstrating Control
of Branch Migration. The features of the molecule used in
this experiment are illustrated at the top left of the
drawing. It is a circular duplex molecule containing a
tetramobile branched junction. The four mobile nucleotides on
each strand are drawn to be extruded from the main circle.
There are 262 nucleotides in the circle to the base of the
extruded junction, 4 mobile pairs, 12 immobile pairs above
the mobile section, and a tetrathymidine loop in each strand,
for a total of 298 nucleotides in each strand. The molecule
is constructed from three segments, a duplex consisting of
strands L1 and L2, a duplex consisting of strands R1 and R2,
and the tetramobile junction, consisting of strands JT and
JB. The divisions between the segments are indicated by
vertical lines, except that the 5' ends of JT and JB are
indicated by starbursts, indicating the 5' radioactive
phosphate labels that are attached individually for analysis
(never in pairs). These starburst sites are the scission
points of EcoR V and Sca I restriction nucleases. The
immobile junction contains Pst I and Stu I restriction sites,
which are indicated. The experiment is done by positively
supercoiling the circle in order to relocate the branch point
by means of branch migration; this is shown in the transition
to the upper right of the drawing. The positive supercoiling
is achieved by adding ethidium. The molecule is then cleaved
by the junction resolvase, endo VII (lower right). Following
endo VII cleavage, the molecule is restricted (center
bottom), and the points of scission are analyzed on a
sequencing gel (lower left).
The ideas behind DNA nanotechnology have been around since
1980 [43]. However, the realities of
experimental practice have slowed their realization. No
experiment works in the laboratory as readily as it works on
paper: One must obtain proper conditions, refine designs and
determine experimental windows through the tedious and often
expensive process of trial and error. Many of these are in place
now for the goals outlined above. The past few years have
witnessed increasing interest in the field. Mirkin, Letsinger and
their colleagues [44] have attached
DNA molecules to colloidal gold, with the goal of assembling
nanoparticles into macroscopic materials, and more recently for
diagnostic purposes [45].
Alivisatos, Schultz, and their colleagues [46] have used DNA to organize
nanocrystals of gold. Niemeyer et al. have used DNA
specificity to generate protein arrays [47].
Shi and Bergstrom have attached DNA single strands to rigid
organic linkers; they have shown that they can form cycles of
various sizes with these molecules [48].
It is to be hoped that this marked increase in experimental
activity will lead to the achievement of its key goals within the
near future.
Acknowledgments
This research has been supported by grant GM-29554 from the
National Institute of General Medical Sciences, grant
N00014-89-J-3078 from the Office of Naval Research, and grant
NSF-CCR-97-25021 from the National Science Foundation.
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