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+. 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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+

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.


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, …


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.”


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?


Moving Average Filter

Generate reactions based on building blocks…


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.


Absence Indicators

But how do we know that a

group of molecules is absent?

R

r


Moving Average Filter

Transfer reactions

Redabsence indicator

Greenabsence indicator

Computation reactions

Blueabsence indicator


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.


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.


Biquad Filter


Biquad Filter

Transfer reactions

Redabsence indicator

Greenabsence indicator

Computation reactions

Blueabsence indicator


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.


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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