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-ma chines 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 “p ogrammable”. These walkers either require adding an extra DNA strand for each step of walker mov ement [3, 4] or just repeat the same action such as moving towards a fixed direction [6, 5] or moving rando mly on a two-dimensional surface [1]. Sahuet al. [2] proposed a walker that simulates a restricted class of fin ite automata. However, not all finite state automata can be implemented in their design. In this paper, we propose autonomous DNA walkers that can sim ulate arbitrary Turing machines. This shows that our walker can do many interesting operation s such as copying, counting and pattern recognition. Our proposal extends the walker proposed by Yi n et al. [6] and provides a method for controlling the movement of the walker and for the walker to r ead and change the DNA sequences on the substrate. In our design, the substrate is a long 1-dimensio nal structure with many DNA strands anchored to it. We call these DNA strands anchorages. The input string of the Turing machinea1a2 . . . an is encoded on the anchorages. The i-th symbolai 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 t he head position of the Turing machine, as shown in figure 1(a). The walker encodes the current state of t he 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 (thi s 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 anchora ge below the walker and cleaves the walker at a corresponding location, as shown in figure 1(b). The reve al d sequence encodes the next state of the Turing machineSj . Several reactions happen and allow the walker to bind to an a djacent anchorage B, as shown in figure 1(c). This operation corresponds to the hea d movement. Two restriction enzymes will cleave at the middle of the walker and separate the two anchor ages, as shown in figure 1(d). Next, a series of reactions happen on anchorage A and change the location of the restriction site, correspond ing to the “write” operation. Finally, a DNA strand that encodes the tr ansition 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 Informati on, California Institute of Technology. Email: holin@stanford.edu. Anindya De is at the Department of Computer Science and Engin eeri g, Indian Institute of Technology, Kanpur, India. Ema il: anindya@cse.iitk.ac.in Ashish Goel is at the Department of Management Science and En gineering and (by courtesy) Computer Science, Stanford University, Terman 311, Stanford CA 94305. Email: ashishg@ stanford.edu. Research supported by **************.