Towards programmable molecular machines

One major challenge in nanotechnology is to transport a nano-scale object from one location to another on a nano-structure. Molecular walkers are nano-machines designed for this task they are structures that can attach and move on some substrate. There have been several preliminary experiments for DNA walkers. However, none of these walker designs are “programmable”. These walkers either require adding an extra DNA strand for each step of walker movement [3, 4] or just repeat the same action such as moving towards a fixed direction [6, 5] or moving randomly on a two-dimensional surface [1]. Sahu et al. [2] proposed a walker that simulates a restricted class of finite automata. However, not all finite state automata can be implemented in their design. In this paper, we propose autonomous DNA walkers that can simulate arbitrary Turing machines. This shows that our walker can do many interesting operations such as copying, counting and pattern recognition. Our proposal extends the walker proposed by Yin et al. [6] and provides a method for controlling the movement of the walker and for the walker to read and change the DNA sequences on the substrate. In our design, the substrate is a long 1-dimensional structure with many DNA strands anchored to it. We call these DNA strands anchorages. The input string of the Turing machine a1a2 . . . an is encoded on the anchorages. The i-th symbol ai is encoded on the i-th anchorage by adding a restriction site at a specific location which corresponds to that symbol. The walker is a double-stranded DNA molecule attached on top of an anchorage, corresponding to the head position of the Turing machine, as shown in figure 1(a). The walker encodes the current state of the Turing machine by encoding a transition table corresponding to the current state on its DNA sequence. We now briefly describe one cycle of the walker operation (this corresponds to one operation of the Turing machine). First, the walker is on top of anchorage A and a “read” operation is performed by an enzyme which recognizes the restriction site on the anchorage below the walker and cleaves the walker at a corresponding location, as shown in figure 1(b). The revealed sequence encodes the next state of the Turing machine Sj . Several reactions happen and allow the walker to bind to an adjacent anchorage B, as shown in figure 1(c). This operation corresponds to the head movement. Two restriction enzymes will cleave at the middle of the walker and separate the two anchorages, as shown in figure 1(d). Next, a series of reactions happen on anchorage A and change the location of the restriction site, corresponding to the “write” operation. Finally, a DNA strand that encodes the transition table of the next state attaches to the remaining portion of the walker on anchorage B and completes the cycle. Our construction only requires 2 enzymes to simulate arbitrary finite automata and 5 enzymes to simulate arbitrary Turing machines. Ho-Lin Chen is at the Center for the Mathematics of Information, California Institute of Technology. Email: [email protected]. Anindya De is at the Department of Computer Science and Engineering, Indian Institute of Technology, Kanpur, India. Email: [email protected] Ashish Goel is at the Department of Management Science and Engineering and (by courtesy) Computer Science, Stanford University, Terman 311, Stanford CA 94305. Email: [email protected]. Research supported by **************.