This book is not about biology, but it is hard to separate DNA from biology. Nature uses DNA to store and replicate the information for living organisms, so it is natural to ask whether DNA motifs can be used to replicate information and to select materials that are the most propitious for particular environments. Replication can be used to provide exponential growth in molecular or cellular populations. However, one can ask whether there is any merit to doing that, rather than just making a large batch of whatever you want. Certainly chemicals are not produced by replication; when a large amount of material is wanted, the synthesis methods are just scaled up, from, say, the millimole scale to the mole scale.

Evolution and selection. The key element here is the notion of selection and evolution. If there are many different species produced, then it is useful to be able to select for the best one, given particular selection criteria. If there is a given circumstance existent in the medium, then it is useful to be able to select those individuals, be they molecules, cells, or larger organisms, that are best suited to survive under the selection criteria. If only those particular individuals survive the selection criteria, or if they are better suited to replicate, then self-replication is useful: the best-fitted individuals can then dominate the succeeding populations within that environment. This is hardly new wisdom. The nature of natural selection was pointed out by Darwin and Wallace in the nineteenth century. The idea of applying this notion to molecules (viral genomes) was first suggested by Spiegelman in the last third of the twentieth century, and then was taken up by Ellington and Szostak and by Tuerk and Gold some years later. In the latter cases, the investigators made partially random linear RNA molecules thought likely to fold to give a specific phenotype, either enzymatic or binding activity. Those molecules best suited to have this phenotype were selected and amplified repeatedly until a few molecular species dominated the population and their sequences could be identified.

Can the same thing be done with unusual DNA motifs? It is certainly an open challenge to optimize detailed structural properties in the 1–4 Å range based on selection procedures involving conventional phosphoramidites.

Anybody who has reached this point in the book realizes that DNA and its congeners are special molecules because of their ability to encrypt information. We have seen a variety of examples here of how that information can be used to direct the folding of molecules to produce specifically shaped and organized molecular species. Likewise, everybody alive during the twenty-first century is aware that we live in an age of information. The information that we use is usually encrypted in electronic bits, rather than in DNA; nevertheless, some information has already been stored specifically in DNA molecules, as an alternative to electronic or print media. Of course, the key way in which we are exposed to information in our daily lives is through our computers and their variations: pads and smartphones. These circumstances lead one to ask if it might be useful to try doing computation with DNA. There is a large community of investigators who work in the field of molecular computation, and, more than any other, this community has contributed valuable ideas and workers to the field of structural DNA nanotechnology. The treatment of this topic here is only a simplified introduction to a few topics in an elementary form.

DNA in logical computations: the Adleman experiment. The first use of DNA in computation was done by Leonard Adleman. He solved a Hamiltonian path problem using DNA molecules. The problem he solved, as has been the case for much of the computation performed with DNA, was a toy problem, one that could be solved simply in one's head, but which also represented a class of problems that are potentially challenging to traditional computational techniques. The Hamiltonian path problem is related closely to the “traveling salesman” problem, the optimization of a route through a number of cities in a territory. If there are only a few cities, the problem is easy to work out, but the number of solutions becomes enormous if there are many cities. Thus, if there are 10 cities, the number of possible answers is proportional to 10!, or about 11 million, a large but tractable number. However, if there are 100 cities, the number of possible answers is proportional to 100!, which is not a number readily handled by a computer that examines each possibility in turn.

One of the central concepts in structural science is the notion of resolution. What we're talking about here is the extent of detail or precision with which we wish to work. Resolution is usually thought of as the detail level of analysis, particularly optical analysis, but it can also refer to the detail level of construction. For example, when I was a “small molecule” crystallographer, it was useful to have a mental picture of my structures where the rulings were approximately every 10 picometers. My structures themselves were built up from Fourier components whose crests were separated by about 80 picometers (their nominal resolution) or more, but I was able to find meaningful differences between things such as bond lengths that were about 10 picometers different from each other. It is usually more useful to think of macromolecular crystals (resolution typically 200–400 picometers) more crudely, say in a world where the rulings are around 50 picometers apart. Resolution should fit the subject appropriately: if we were building a house with 5 × 10 × 15 cm bricks, this type of thinking would be far too detailed; we would be wasting out time thinking in a world with rulings closer than about a centimeter. Biology is replete with phenomena that take place on multiple distance scales, everywhere from the sub-nanometer scale (e.g., simple enzymatic reactions) to the nanometer scale (e.g., transcription, translation, recombination, and other aspects of nucleic acid metabolism) to the micron scale (cellular phenomena) to the macroscopic scale (organs like muscles and nerves).

DNA origami. In the aspects of structural DNA nanotechnology we have discussed so far, our basic unit has been the DNA double helix, with a diameter of 2 nm. 2D DX arrays should in principle have a repeat perpendicular to the helix axis of about 4–5 nm, but we usually find that the actual repeat is about 6 nm. Thus, these structures are usually designable to within ±1 nm. If we loosen up our design criteria a bit, say to 6 nm, it is possible to design larger structures readily. This is the technique known as DNA origami, first published by Paul Rothemund in 2006. He took the single-stranded form of the M13 virus, ~7500 nt, which is commercially available, and combined it with around 250 “staple” strands to get it to fold into a series of shapes containing parallel helix axes. These shapes are all based on extended versions of the DAO motif.

We have been talking so far about static DNA structures: we make them with some expectation of their 3D geometry, or perhaps of their topology, and then they sit there, perhaps changing shape as a result of thermal fluctuations. However, it is certainly possible to do more with DNA than just make static species. It is also possible to make molecules that can change their shapes, producing multi-state devices that can produce mechanical action on the nanoscale. The key DNA devices operate on two different principles: either DNA structural transitions, or programmed sequence-dependent devices whose states can be addressed or created individually. DNA structural transitions can be based on the contents of the solution, but they are only individually addressable by nuanced chemistry, such as the formation of the various knots shown in Figure 4-4, or by the action of protein molecules.

Robust devices. As all of you reading this book are aware, things can happen in chemical systems that do not happen on the macroscopic scale. If we are making a DNA-based nanomechanical device, we term it a “robust” device if all of the molecules undergo the same transition, looking the same after the transition as they did before. If the strands of its framework can recombine and perhaps form another species (a dimer or a breakdown product), then we would say that the device is not robust. Exchange of strands while in an intermediate state is another example of non-robust behavior. Sometimes the conditions will define the robustness of the device. If the device is based on a DNA structural transition, a partial transition of the ensemble of molecules will be the result if the transition trigger is not present in an overwhelming quantity; such conditions could be corrected, if necessary. The basic notion of a robust device is that it behaves like a macroscopic device made of simple machines: a lever is either up or down, a torsional element is either rotated or not, a movement occurs or it doesn't, throughout the ensemble of molecules in the system.

Shape-shifters

A key category of devices can be thought of as shape-shifters, molecules that have different structures under different conditions. Clearly a molecule at equilibrium will have a fixed shape or ensemble of shapes, and they won't change.

Let's look again at the molecule shown in Figure 3-5a. It looks like a cube built of DNA. However, as we noted earlier, the molecular geometry has really not been characterized, because the 3-arm junctions on its vertices are floppy units. Thus, it could look as we have drawn it, or it could look like a rhombohedron (a cube-like structure where one of the body diagonals has been stretched or squashed somewhat). The things we can say for sure about the molecule are that each of the edges is two turns long (the sequence was designed that way) and that each face of the object corresponds to a cyclic single strand of DNA. For example, the front face corresponds to the red strand. Because DNA is a double helix, every turn of the double helix results in the strands being interwound. Since each edge is two turns long, that means that the red strand is linked twice to the four strands of the four faces that flank the front: the green strand on the right, the cyan strand on top, the magenta strand on the left, and the dark-blue strand on the bottom. It is only indirectly linked to the yellow strand at the back. When cyclic molecules are linked together like the links of a chain, they form what is known as a catenane. Of course the hexacatenane corresponding to the cube is a much more complex object than just a simple chain. The molecule in Figure 3-5b, with the connectivity of a truncated octahedron, is a 14-catenane. It is even more complex than the cube-like molecule shown in Figure 3-5a.

Catenanes and knots. It turns out that catenanes are closely related to knots. This relationship is indicated in Figure 4-1. The upper left image is of a knot with five nodes and an arbitrary strand polarity. Look at the lower right node in this knot. It is made up of a strand that passes over another strand. You can think of it as four strands: the first half of the strand on top, connected to the second half of the strand on top, the first half of the strand on the bottom, connected to the second half of the strand on the bottom. Now, let's imagine breaking those connections, and reconnecting the strands so that we maintain the same polarity.

However, this bottle was not marked ‘poison’, so Alice ventured to taste it, and finding it very nice (it had, in fact, a sort of mixed flavour of cherry-tart, custard, pine-apple, roast turkey, toffee, and hot buttered toast), she very soon finished it off.