Download Synthesizing Stochastic Biochemistry

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
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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
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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
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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
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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'''
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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'''
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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
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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.
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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.
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