1. Autonomous DNA Nanomechanical Device Capable of Universal Computation and Universal Translational Motion Peng Yin*, Andrew J. Turberfield †, Sudheer Sahu*, John H. Reif* * Department of Computer Science, Duke University † Department of Physics, Clarendon Laboratory, University of Oxford 1

2. Motivation 2 DNA cellular computing devices Finite state automata Turing machineTuring machine Cellular automata Intelligent DNA lattice Intelligent robots, arbitrarily complex motion Parallel, universal computing device DNA nanorobotics DNA lattices ( Benenson et al 03 ) DNA nanocomputation Autonomous unidirectional DNA walker

3. Abstract 3 Intelligent nanomechanical devices that operate in an autonomous fashion are of great theoretical and practical interest. Recent successes in building large scale DNA nano-structures, in constructing DNA mechanical devices, and in DNA computing provide a solid foundation for the next step forward: designing autonomous DNA mechanical devices capable of arbitrarily complex behavior. One prototype system towards this goal can be a DNA mechanical device that is capable of universal computation, by mimicking the operation of a universal Turing machine. Building on our prior theoretical designs and a prototype experimental construction of autonomous unidirectional DNA walking devices that move along linear tracks, we present in this paper the design of a nanomechanical DNA device that autonomously mimics the operation of a 2-state 5-color universal Turing machine. Our autonomous nanomechanical device, which we call an Autonomous DNA Turing Machine, is thus capable of universal computation and hence complex translational motion which we define as universal translational motion.

4. Prior work 4 Self assembly of DNA lattices: DX, rhombus, TX, 4x4, and barcode lattices DNA nano-robotics devices: An autonomous DNA unidirectional walking device (Reif’s group) DNA nano-computation: Design of a non-autonomous universal DNA Turing machine driven by enzymes (Rothemund) Autonomous DNA Finite State Automata (Shapiro’s group)

5. Comp 101: Turing Machine 5 Turing Machine Tape Read/write head Transition rule A Turing machine is a theoretical computational device.

6. DNA Turing Machine: Structure 6 Transitional rules: Rule molecules Turing head:Head molecules Data tape: Symbol molecules Molecular structure

7. Operational overview 7 Autonomous universal DNA Turing machine: 2 states, 5 colors

8. DNA Biochemistry 101: 8 Recognition site cleavage site Complementary sticky ends

9. Restriction enzymes: 9

10. Operation: Step 1 10 In Step1, the active Head Molecule (H) is ligated to the Symbol Molecule (S) directly below it, creating an endonuclease recognition site in the ligation product. The ligation product is subsequently cleaved into two molecules by an endonuclease. The sticky end of each of the two newly generated molecules encodes the current state (q) and the current color (c).

11. Operation: Step 2 11 In Step 2, the Symbol Molecule is ligated to floating Rule Molecule, which possesses complementary sticky end to it and corresponds to one entry in the Turing machine Transitional table. The ligation product is subsequently cleaved, generating a new Symbol Molecule dictated by the current state (q) and color (c) as well as the transitional rule. The new Symbol Molecule encodes the new color (c’) in its sticky end.

12. Operation: Step 3 12 In Step 3, the newly generated Symbol Molecule (S) is further modified by an Assisting Molecule (E) so that it encodes the new color (c’) in its duplex portion (rather than sticky end) and possess a default sticky end ([s]).

13. Operation: Step 4 13 In Step 4, the Head Molecule is ligated to a floating Rule Molecule, which possesses a complementary sticky end to it and corresponds to one entry in the Turing machine Transitional Table. The ligation product is in subsequently cleaved, generating a new Head Molecule whose duplex portion encodes information of Turing machine's next state (q’) and whose sticky end encodes the moving direction of the head (p’).

14. Operation: Step 5 14 In Step 5, the sticky end of the Head Molecule (H) dictates it to hybridize with either the Head Molecule to its left or to its right (H’), depending on which of its neighbors possesses a complementary sticky end. Next, the ligation product between these two Head Molecules is cleaved, generating sticky ends encoding the position information for the head molecules (p, p’) and the new state (q’).

15. Operation: Step 6 15 In Step 6, the Head Molecule, H’, is modified by a floating Assisting Molecule (T) and becomes active: it encodes the state information in its duplex part and possesses an active sticky end ([s]) and thus becomes active, ready to interact with the Symbol Molecule located directly below it.

16. Operation: Step 7 16 In Steps 7 and 8, the Head Molecule H is modified by floating Assisting Molecules and is restored to its inactive configuration (with a default sticky end).

17. Operation: Step 8 17

18. Reaction flow chart 18

19. Technical challenges: encoding space: overlaid molecules 19 Challenge: use limited encoding space dictated by the four (six) letter vocabulary of DNA bases and by the sizes of the recognition, restriction, and spacing regions of endonucleases. Technique: use overlaid molecules and carefully select the sticky ends to avoid undesirable reactions. Overlaid molecules Unique 3-base sticky ends

20. Technical challenges: Futile reactions 20 Many futile reactions happen in the background during the operation of the DNA Turing machine. A key feature of these futile reactions is that they are fully reversible. This is critical in ensuring the autonomous operation: we initially supply the system with sufficiently high concentrations of Rule Molecules and Assisting Molecules as well as all the byproducts generated in the futile reactions. As such, the futile reactions will reach a dynamic balance and the active component will not be depleted by the futile reactions.

21. Conclusion & Future work 21 The design of a DNA Autonomous Universal Turing machine Universal translational motion Computer simulation: http://www.cs.duke.edu/~py/paper/dnaUTM/simulation Autonomous DNA cellular computing devices: DNA Finite state automata  DNA Turing machine  DNA Cellular automata Turing machine Finite state automata Cellular automata Experimental constructionComputer simulationDesign Computer simulation