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Engineered E. Coli for Targeted Anti-Cancer Drug Production via Stochastic Response

This study explores the engineering of E. Coli bacteria to produce a controlled dosage of an anti-cancer drug in response to a triggering compound. By utilizing a probabilistic approach, the bacteria exhibit a fractional response, limiting undue drug production. The design focuses on creating a uniform population of identical bacteria with fixed density, allowing for an orchestrated drug output. This technique aims to enhance therapeutic efficacy while minimizing the risk of overdosing in patients undergoing cancer treatment.

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Engineered E. Coli for Targeted Anti-Cancer Drug Production via Stochastic Response

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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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