1. Binary Counting with Chemical Reactions Aleksandra Kharam, Hua Jiang, Marc Riedel, and Keshab Parhi Electrical and Computer Engineering University of Minnesota

2. Signal 10, 2, 12, 8, 4, 8, 10, 2, … 5, 6, 7, 10, 6, 6, 9, 6, … 1010 0101 00101100 01100111 inputoutput Electronics Chemical Reactions Molecular computations In ElectronicsIn Chemistry Input Output

3. Modeled by Ordinary Differential Equations: inputoutput ac Playing by The Rules + k b cba

4. Principles of Binary Counting ZYX 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1 0 0 0

5. ZYX 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1 0 0 0 Intuitive Model

6. Algorithm ` X inj ZYX 0 0 0

7. Prereactants and Absence Indicators Molecular Type X Absence indicator a x

8. Prereactants and Absence Indicators Molecular Type X Absence indicator a x Prereactant X p Prereactant for the next type Y p

9. Modified Algorithm

10. Three-Phase Synchronization But how do we know that a group of molecules is absent ? R r

11. Basic AlgorithmThree-Phase Synchronization

13. Final Design

14. Simulation Results

15. zx Mapping to Experimental Chassis Auxiliary Complexes Reactants Products * D. Soloveichik et al: “DNA as a Universal Substrate for Chemical Kinetics.” PNAS, Mar 2010

16. Conclusion Robustness: - the design is rate independent. Future and related work: - generalizing to n-bit counter; - borrowing idea from digital logic (edge triggered clock ); - computing variety of functions

17. Questions? Thanks to PSB organizers, NSF, BICB, and UROP NSF CAREER Award #0845650 NSF EAGER Grant #0946601 Biomedical Informatics & Computational Biology UMN / Mayo Clinic / IBM

18. Some additional slides

19. Synchronization

20. Three-Phase Synchronization