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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 Bacteria elicits invade the bacteria the cancerous to produce tissue: the drug: cancerous tissue Design Scenario The trigger the bacteria Problem: patientelicits receives too high produce of a dosethe of drug: the drug. cancerous tissue Design Scenario Conceptual design problem. Constraints: • Bacteria are all identical. • Population density is fixed. • Exposure to triggering compound is uniform. Requirement: • Control quantity of drug that is produced. Design Scenario Approach: elicit a fractional response. cancerous tissue Synthesizing Stochasticity Approach: engineer a probabilistic response in each bacterium. produce drug with Prob. 0.3 triggering compound E. Coli don’t produce drug with Prob. 0.7 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 Synthesizing Stochasticity Generalization: engineer a probability distribution on logical combinations of different outcomes. A with Prob. 0.3 A and B with Prob. 0.3 B with Prob. 0.2 cell B and C with Prob. 0.7 C with Prob. 0.5 Synthesizing Stochasticity Generalization: engineer a probability distribution on logical combinations of different outcomes. Pr( A) f1 ( X / Y ) X A and B with Prob. 0.3 Pr(B) f2 ( X / Y ) Y cell B and C with Prob. 0.7 Pr(C ) f3 ( X / Y ) Further: program probability distribution with (relative) quantity of input compounds. Synthesizing Stochasticity Example For types d1, d2, and d3, program the response: p1 0.3 p2 0.4 p3 0.3 Solution Setup initializing reactions: e1 e2 1 e3 1 1 d1 d2 d3 Initialize e1, e2, and e3, in the ratio: 30 : 40 : 30 11 Synthesizing Stochasticity Example For types d1, d2, and d3, program the response: p1 0.3 p2 0.4 p3 0.3 Solution (cont.) Setup reinforcing reactions: 3 e1 + d1 10 e2 + d2 10 e3 + d3 2d1 3 2d2 3 10 2d3 12 Synthesizing Stochasticity Example For types d1, d2, and d3, program the response: p1 0.3 p2 0.4 p3 0.3 Solution (cont.) Setup stabilizing reactions: d1 + e2 d1 + e3 3 10 3 10 d1 d1 d2 + e1 d2 + e3 3 10 3 10 d2 d2 d3 + e1 d3 + e2 3 10 3 10 13 d3 d3 Synthesizing Stochasticity Example For types d1, d2, and d3, program the response: p1 0.3 p2 0.4 p3 0.3 Solution (cont.) Setup purifying reactions: 6 d1 + d2 10 d1 + d3 10 d2 + d3 10 6 6 14 Synthesizing Stochasticity Initialize e1, e2, and e3 in the ratio: x:y:z Result Mutually exclusive production of d1, d2, and d3: d1 with Prob. x x+ y+z d2 with Prob. y x+ y+z d3 with Prob. z x+ y+z 15 General Method Initializing Reactions i : ei ki di i : di + ei ki' j i : di + ej k'i' j i : di + dj ki''' Reinforcing Reactions Stabilizing Purifying 2di di Working Reactions ki'''' di + oi ki' kij'' << i : di + fi where ki ki'''' << kij''' 16 General Method Initializing Reactions i : ei ki di i : di + ei ki' j i : di + ej k'i' j i : di + dj ki''' Reinforcing Reactions Stabilizing Purifying 2di di Working Reactions ki'''' di + oi ki' kij'' << i : di + fi where ki ki'''' << kij''' 17 General Method Initializing Reactions i : ei ki di For all i, to obtain di with probability pi, select E1, E2,…, En according to: Ei ki pi j Ej k j (where Ei is quantity of ei) Use as appropriate in working reactions: i : di + fi ki'''' di + oi 18 Error Analysis Require ki ki'''' << Let ki ki'''' 1, ki' kij'' k' i kij'' l , << kij''' k''' ij l 2 for three reactions (i.e., i, j = 1,2,3). Performed 100,000 trials of Monte Carlo. 19 Discussion Computational Synthetic Biology vis-a-vis Technology-Independent Synthesis • Synthesize a design for a precise, robust, programmable probability distribution on outcomes – for arbitrary types and reactions. Experimental Design vis-a-vis Technology Mapping • Implement design by selecting specific types and reactions – say from “toolkit”, e.g. MIT BioBricks repository of standard parts. 20