1. … … Sequential Computation (e.g., filtering) Chemical Reactions Time-varying changes in concentrations of an input molecular type. Time-varying changes in concentrations of output molecular type. 10, 2, 12, 8, 4, 8, 10, 2, … 5, 6, 7, 10, 6, 6, 9, 6, … InputOutput

2. Circuit Representation

3. Constant Multiplier Adder Delay Element

4. Jiang, Riedel, and Parhi, “Synchronous Sequential Computation with Chemical Reactions,” DAC 2011. Clock Signal

5. Delay Element An Asynchronous Methodology No clock: self-timed. Rate-independent (only coarse rates, e.g., “fast” and “slow”).

6. Inversion Produce a quantity of a type only in the absence of another type.

7. Duplication Produce a quantity of a type equal to the quantity of another type:

8. 3-Phase Scheme We use a three compartment configuration for delay elements: we categorize the types into three groups: red, green and blue. Every delay element D i is assigned R i, G i, and B i

9. Chemical Reactions time Moving Average Filter y(n) = 0.5 x(n) + 0.5 x(n-1)

10. Moving Average Filter New cycle!

11. Moving Average Filter Blue absence indicator Green absence indicator Red absence indicator Computation reactions Transfer reactions

12. Moving Average Filter (improved) Signal transfer Computation Absence indicator

13. Technology Mapping: DNA Strand Displacement X1X1 X2X2 X3X3 + D. Soloveichik et al: “DNA as a Universal Substrate for Chemical Kinetics.” PNAS, Mar 2010

14. Technology Mapping: DNA Strand Displacement X1X1 X3X3 X2X2 + D. Soloveichik et al: “DNA as a Universal Substrate for Chemical Kinetics.” PNAS, Mar 2010

15. DNA Reactions for Moving Average Filters Absence Indicator Reactions

16. DNA Reactions for Moving Average Filters Transfer Reactions

17. DNA Reactions for Moving Average Filters Computation Reactions

18. Output obtained by ODE simulations at the DNA level. Simulation Results: Moving Average Filter input: X output: Y Time (Hours) Concentration (nM)

19. Biquad Filter

20. Absence indicator Signal transfer Computation

21. Simulation Results: Biquad Filter Output obtained by ODE simulations of chemical kinetics at the DNA level.