DNA- and RNA-Based Computing Systems. Группа авторов
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First, all possible cliques in the graph of N vertices are represented by an N‐digit binary string. In the clique, if the vertex is present, then it is represented by “1,” and if the vertex is absent, then it is represented by “0.” For the case of 5‐vertex graph (shown in Figure 2.6a), a clique involving {5, 4, 2} vertices is represented by a binary string as {11010}. Initially, all possible combinations of this N‐digit binary number are generated. Some of the vertices in the graph are not connected by the edges. A graph of such unconnected vertices is referred to as the complementary graph (see Figure 2.6b). In the next step, the combinations comprising the edges present in the complementary graph are removed. For the given illustrative example (Figure 2.6b), the combinations with {cc11c} and {c11cc} are removed from the data pool (c ɛ {0, 1}). Lastly, find out the binary number having the largest number of “1,” which represents the size of the maximal clique. This procedure is performed using the DNA sequences as follows.
Each bit in the above binary string corresponds to a vertex and is represented as a DNA sequence having three parts. In this, the second part corresponds to the vertex number, whereas the first and the third part correspond to the position number. Further, these vertices have to be connected in sequential order (e.g. V1–VN) as represented in the binary string. In order to have such connection, the value “0” for the first vertex is represented as P1V10P2, whereas the value “1” is represented by P1V11P2. Since the next vertex V2 has to be connected to V1, its “0” value is represented by the complementary sequence
2.2.6 Chao's Model
Chao et al. [13] developed a single‐molecule “DNA navigator” to solve a maze (tree graph) of 10 vertices with three junctions. In this, the desired path is explored out of all possible paths of the maze present on an origami that is used as a substrate. On this origami, some sites are specifically used for the binding of the vertices of the tree graph. This helps in the propagation of the path on the origami.
The DNA used for the process is very specific in size and design. The designing of DNA is described next. Hairpin DNA Y is attached to the origami and has a typical sequence layout of the structure
Figure 2.7 Chao's single‐molecule DNA navigator [13] for solving the maze.
After the binding of the initiator, a hairpin loop of the DNA Y opens to make it free to bind to DNA Z and vice versa as both have complementary sites for free form of each other. This type of hybridization continues until it reaches the exit DNA. This hybridization chain also produces those paths that are not the solution to the maze. The exit DNA corresponding to an end vertex of the maze is biotin labeled. If the path is correct, then this biotin‐labeled DNA is free from the exit vertex; otherwise, biotin remains attached to the DNA corresponding to the exit vertex. All the biotin‐labeled sequences are then removed from the solution by streptavidin magnetic beads. The correct path sequence remained in the solution as it is not attached to the biotin. This solution is then analyzed by AFM for identifying the final path.
2.2.7 DNA Origami
Self‐assembly of DNA is one of the most popular techniques used to create a variety of two‐dimensional and three‐dimensional structures. The DNA origami is an excellent example of self‐assembly of DNA, which was introduced by Rothemund [14]. The procedure of DNA origami is shown in Figure 2.8. DNA origami is generated from a thousand base pair long ssDNA, known as a scaffold. Some shorter and linear ssDNA called staples are mixed with the scaffold to create DNA origami. For this purpose, the solution mixture is first heated to 95 °C. The solution is then cooled down to room temperature from 95 °C; throughout the cooling, the staples bind to the scaffold through Watson–Crick complementary base pairing. The scaffold then becomes a static structure or pattern of DNA. The sequence of DNA staples results in the formation of various shapes, for example, squares, smiley faces, cube, hexagon, star, and many more.