… … 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
Circuit Representation
Constant Multiplier Adder Delay Element
Jiang, Riedel, and Parhi, “Synchronous Sequential Computation with Chemical Reactions,” DAC Clock Signal
Delay Element An Asynchronous Methodology No clock: self-timed. Rate-independent (only coarse rates, e.g., “fast” and “slow”).
Inversion Produce a quantity of a type only in the absence of another type.
Duplication Produce a quantity of a type equal to the quantity of another type:
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
Chemical Reactions time Moving Average Filter y(n) = 0.5 x(n) x(n-1)
Moving Average Filter New cycle!
Moving Average Filter Blue absence indicator Green absence indicator Red absence indicator Computation reactions Transfer reactions
Moving Average Filter (improved) Signal transfer Computation Absence indicator
Technology Mapping: DNA Strand Displacement X1X1 X2X2 X3X3 + D. Soloveichik et al: “DNA as a Universal Substrate for Chemical Kinetics.” PNAS, Mar 2010
Technology Mapping: DNA Strand Displacement X1X1 X3X3 X2X2 + D. Soloveichik et al: “DNA as a Universal Substrate for Chemical Kinetics.” PNAS, Mar 2010
DNA Reactions for Moving Average Filters Absence Indicator Reactions
DNA Reactions for Moving Average Filters Transfer Reactions
DNA Reactions for Moving Average Filters Computation Reactions
Output obtained by ODE simulations at the DNA level. Simulation Results: Moving Average Filter input: X output: Y Time (Hours) Concentration (nM)
Biquad Filter
Absence indicator Signal transfer Computation
Simulation Results: Biquad Filter Output obtained by ODE simulations of chemical kinetics at the DNA level.