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

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

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

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

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

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

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

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

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

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

11. 11 Synthesizing Stochasticity For types d 1, d 2, and d 3, program the response: Example Solution Setup initializing reactions: Initialize e 1, e 2, and e 3, in the ratio: 30 : 40 : 30

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

13. 13 Setup stabilizing reactions: For types d 1, d 2, and d 3, program the response: Example Solution (cont.) Synthesizing Stochasticity

14. 14 Synthesizing Stochasticity Setup purifying reactions: Example Solution (cont.) For types d 1, d 2, and d 3, program the response:

15. 15 Result Synthesizing Stochasticity d1d1 with Prob. d2d2 d3d3 Mutually exclusive production of d 1, d 2, and d 3 : Initialize e 1, e 2, and e 3 in the ratio: x : y : z

16. 16 Initializing Reactions Reinforcing Reactions Stabilizing Purifying Working Reactions where General Method i i k ii odfdi i   '''' : '''''''''' ij iii kkkkk       ''' : i k ji ddij

17. 17 General Method Initializing Reactions Reinforcing Reactions Stabilizing Purifying Working Reactions where General Method i i k ii odfdi i   '''' : '''''''''' ij iii kkkkk       ''' : i k ji ddij

18. 18 Initializing Reactions General Method For all i, to obtain d i with probability p i, select E 1, E 2,…, E n according to: Use as appropriate in working reactions: (where E i is quantity of e i ) i i k ii odfdi i   '''' :

19. 19 Error Analysis Let for three reactions (i.e., i, j = 1,2,3). Require Performed 100,000 trials of Monte Carlo. 2 '''''''''',, 1  ij iii kkkkk '''''''''' iii kkkkk   

20. 20Discussion Synthesize a design for a precise, robust, programmable probability distribution on outcomes – for arbitrary types and reactions. Computational Synthetic Biology vis-a-vis Technology-Independent Synthesis Implement design by selecting specific types and reactions – say from “toolkit”, e.g. MIT BioBricks repository of standard parts. Experimental Design vis-a-vis Technology Mapping