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Design Scenario

Design Scenario. Bacteria are engineered to produce an anti-cancer drug:. triggering compound. drug. E. Coli. Design Scenario. Bacteria invade the cancerous tissue:. cancerous tissue. Design Scenario. The trigger elicits the bacteria to produce the drug: .

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Design Scenario

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  1. Design Scenario Bacteria are engineered to produce an anti-cancer drug: triggering compound drug E. Coli

  2. Design Scenario Bacteria invade the cancerous tissue: cancerous tissue

  3. Design Scenario The trigger elicits the bacteria to produce the drug: Bacteria invade the cancerous tissue: cancerous tissue

  4. Design Scenario The trigger elicits the bacteria produce the drug: Problem: patient receives too high of a dose of the drug. cancerous tissue

  5. Design Scenario Conceptual design problem. • Bacteria are all identical. • Population density is fixed. • Exposure to triggering compound is uniform. Constraints: Requirement: • Control quantity of drug that is produced.

  6. Design Scenario cancerous tissue Approach: elicit a fractional response.

  7. Synthesizing Stochasticity E. Coli Approach: engineer a probabilistic response in each bacterium. produce drug with Prob.0.3 triggering compound don’t produce drug with Prob.0.7

  8. Synthesizing Stochasticity Generalization: engineer a probability distribution on logical combinations of different outcomes. A with Prob.0.3 B with Prob.0.2 cell C with Prob.0.5

  9. Synthesizing Stochasticity A and B with Prob.0.3 B and C with Prob.0.7 Generalization: engineer a probability distribution on logical combinations of different outcomes. A with Prob.0.3 B with Prob.0.2 cell C with Prob.0.5

  10. Synthesizing Stochasticity A and B with Prob.0.3 B and C with Prob.0.7 Generalization: engineer a probability distribution on logical combinations of different outcomes. X Y cell Further: program probability distribution with (relative) quantity of input compounds.

  11. Synthesizing Stochasticity Example For types d1, d2, and d3, program the response: Solution Setup initializing reactions: Initialize e1, e2, and e3, in the ratio: 30 : 40 : 30

  12. Synthesizing Stochasticity 3 10 d e + 2 d 1 1 1 3 10 d e + 2 d 2 2 2 3 10 d e + 2 d 3 3 3 Example For types d1, d2, and d3, program the response: Solution (cont.) Setup reinforcing reactions:

  13. Synthesizing Stochasticity Example For types d1, d2, and d3, program the response: Solution (cont.) Setup stabilizing reactions:

  14. Synthesizing Stochasticity Example For types d1, d2, and d3, program the response: Solution (cont.) Setup purifying reactions:

  15. Synthesizing Stochasticity d1 with Prob. d2 with Prob. d3 with Prob. Initialize e1, e2, and e3 in the ratio: x : y : z Result Mutually exclusive production of d1, d2, and d3:

  16. General Method ' ' ' k + ¹ j i : d d " i i j ' ' ' ' k + + " i : d f d o i i i i i » » < < < < ' ' ' ' ' ' ' ' ' ' k k k k k i i i ij ij Initializing Reactions Reinforcing Reactions Stabilizing Purifying Working Reactions where

  17. General Method General Method ' ' ' k + ¹ j i : d d " i i j ' ' ' ' k + + " i : d f d o i i i i i » » < < < < ' ' ' ' ' ' ' ' ' ' k k k k k i i i ij ij Initializing Reactions Reinforcing Reactions Stabilizing Purifying Working Reactions where

  18. General Method ' ' ' ' k + + " i : d f d o i i i i i Initializing Reactions For alli,to obtaindiwith probabilitypi, selectE1,E2,…, Enaccording to: (where Ei is quantity of ei) Use as appropriate in working reactions:

  19. Error Analysis 2 = = = = = ' ' ' ' ' ' ' ' ' ' , , l l k k 1 k k k i i i ij ij » » < < < < ' ' ' ' ' ' ' ' ' ' k k k k k i i i ij ij Require Let for three reactions (i.e.,i, j= 1,2,3). Performed 100,000 trials of Monte Carlo.

  20. 1 1 3 1 16 16 0 1 4 8 choose R2 0.07123 Randomness Pseudo-random numbers needed: R1 R2 R3 R4 probabilities generate a random number:

  21. 0 1 choose R4 choose R2 0.07123 0.8973 Randomness Pseudo-random numbers needed: R1 R2 R3 R4 probabilities generate a random number:

  22. probabilities 0 1 generate a random number: choose R4 0.8973 Randomness Pseudo-random numbers needed: • Generating random numbers is time consuming. • If variance in probabilities is large, accuracy is wasted. R1 R2 R3 R4

  23. 1 1 3 3 3 3 3 1 16 16 16 16 16 16 4 8 Event Leaping Explore high probability events further. Along each path, probabilities are multiplicative.

  24. 7 1 7 1 3 3 7 3 1 3 1 32 16 32 16 16 32 16 32 16 16 8 Event Leaping Explore high probability events further. Along each path, probabilities are multiplicative. When paths merge, probabilities are additive.

  25. 7 1 7 7 3 1 1 16 32 32 32 16 32 16 Event Leaping Based on a single random number, leap directly to the boundary of explored region. Explore high probability events further. When paths merge, probabilities are additive.

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