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cell/test tube

+. Biomolecular Reactions. cell/test tube. types. count. 9. 8. 6. 5. 7. 9. Discrete chemical kinetics; spatial homogeneity. . +. +. +. Biomolecular Reactions. Relative rates or (reaction propensities):. slow. medium. fast. Discrete chemical kinetics; spatial homogeneity. .

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cell/test tube

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  1. + Biomolecular Reactions cell/test tube types count 9 8 6 5 7 9 Discrete chemical kinetics; spatial homogeneity.

  2. + + + Biomolecular Reactions Relative rates or (reaction propensities): slow medium fast Discrete chemical kinetics; spatial homogeneity.

  3. Digital Signal Processing A digital signal processing (DSP) system takes an input sequence and produces an output sequence. A digital signal is a sequence of numbers. 1100 1010 0010 0111 0110 0101 ChemicalReactions Electronics DSP input output 10, 2, 12, 8, 4, 8, 10, 2, … Electronically, numbers are represented by binary strings (zeros and ones are voltages). Chemically, molecular quantities represent the digital signal. 5, 6, 7, 10, 6, 6, 9, 6, …

  4. Building Blocks Most DSP systems can be specified in terms of 4 major components: constant multipliers, fanout, adders and delay operations. These can be implemented by molecular operations. Constant Multiplier Fanout Addition Adder Delay Element Addition occurs when several reactions produce the same type. Molecular quantities are preserved over “computational cycles.”

  5. Moving Average Filter Computes an output value that is one-half the current input value plus one-half the previous input. But how do we implement this with chemical reactions?

  6. Moving Average Filter Generate reactions based on building blocks…

  7. Three-Phase Scheme All reactions are assigned to one of three phases: red, green and blue. Each phase is enabled when no molecular type in its precursor group is present.

  8. Absence Indicators But how do we know that a group of molecules is absent? R r

  9. Moving Average Filter Transfer reactions Redabsence indicator Greenabsence indicator Computation reactions Blueabsence indicator

  10. Simulation Results: Moving Average Filter Simulated quantity of input vs. quantity of output over 40 cycles. • Gillespie’s stochastic simulation algorithm. (Our version: stochastic transient simulation.) • Random input sequence,1000 trajectories, slow = 1, fast = 1000.

  11. Simulation Results: Moving Average Filter Simulated output vs. theoretical (computed) output. • Gillespie’s stochastic simulation algorithm. (Our version: stochastic transient simulation.) • Random input sequence,1000 trajectories, slow = 1, fast = 1000.

  12. Biquad Filter

  13. Biquad Filter Transfer reactions Redabsence indicator Greenabsence indicator Computation reactions Blueabsence indicator

  14. Simulation Results: Biquad Filter Simulated quantity of input vs. quantity of output over 40 cycles. • Gillespie’s stochastic simulation algorithm. (Our version: stochastic transient simulation.) • Random input sequence,1000 trajectories, slow = 1, fast = 1000.

  15. Simulation Results: Biquad Filter Simulated output vs. theoretical (computed) output. • Gillespie’s stochastic simulation algorithm. (Our version: stochastic transient simulation.) • Random input sequence,1000 trajectories, slow = 1, fast = 1000.

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