Transcript EE 5393: Circuits, Computation and Biology Marc D. Riedel Associate Professor, ECE University of Minnesota x1 x2 AND x3 OR f1 AND f2 f3

EE 5393: Circuits, Computation and Biology
Marc D. Riedel
Associate Professor, ECE University of Minnesota
x1
x2
AND
x3
OR
f1
AND
f2
f3
[computational]
[computational]
Synthetic
Analysis
Biology
“There are known ‘knowns’; and there are unknown
‘unknowns’; but today I’ll speak of the known ‘unknowns’.”
– Donald Rumsfeld, 2004
Molecular
Inputs
Known /
Known
Unknown
Biological
Process
Molecular
Products
Given
Unknown
Unknown
Known
Design Scenario
Bacteria are engineered to produce an anti-cancer drug:
triggering
compound
drug
E. Coli
Biochemistry in a Nutshell
Nucleotides:
{ A, C , T , G}
DNA: string of n nucleotides (n ≈ 109)
... ACCGTTGAATGACG...
Amino acid: coded by a sequence of 3 nucleotides.
{ A, C , T , G }3  {a1 ,
… , a 20 }
Proteins: produced from a sequence of m amino
acids (m ≈ 103) called a “gene”.
m
{a1 ,
,
a
}
 protein
… 20
Design Abstraction
Biochemical Reactions:
rules specifying how types of molecules combine.
2a +
+
b
c
Mass Action Kinetics
The rate at which a given
reaction fires is proportional
to:
+
k1
k2
+
• Its rate constant.
• The concentration of
its reactants.`
+
k3
DNA Strand Displacement
X1
X2 + X3
D. Soloveichik et al: “DNA as a Universal Substrate for
Chemical Kinetics.” PNAS, Mar 2010
DNA Strand Displacement
X1 + X2
X3
D. Soloveichik et al: “DNA as a Universal Substrate for
Chemical Kinetics.” PNAS, Mar 2010
[computational]
Biochemical
Biochemistry
[computation]
x
Molecular
Reactions
y
z
quantity
quantities
Inversion
Produce a quantity of a type only in the
absence of another type.
Duplication
Produce a quantity of a type equal to the
quantity of another type:
Multiplication
pseudo-code
biochemical code
Moving Average Filter (improved)
Signal transfer
Computation
Absence
indicator
Simulation Results: Moving Average
Filter
Concentration (nM)
input: X
output: Y
Time (Hours)
Output obtained by ODE simulations at the DNA level.
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
Requirement:
uniform.
•
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
Linear Threshold Gates
...
x1
x2
w1
w2
xn
wn
w0
Linear Threshold Gates
Useful Model?
Computing With Limited Memory
m states S1 ,, Sm
(log2 m bits memory)
n Boolean inputsx1 ,, xn
Assume n much greater than m
Each instruction:
Examine a specific input bit
xi .
Based on current state, lookup next state.