Toward in vivo Digital Circuits

1
Toward in vivo Digital Circuits

• Ron Weiss, George Homsy, Tom Knight
• MIT Artificial Intelligence Laboratory

2
Motivation

• Goal program biological cells
• Characteristics
• small (E.coli 1x2?m , 109/ml)
• self replicating
• energy efficient
• Potential applications
• smart drugs / medicine
• agriculture
• embedded systems

3
Approach
logic circuit
high-level program
genome
microbial circuit compiler

• in vivo chemical activity of genomeimplementscom
  putation specified by logic circuit

4
Key Biological Inverters

• Propose to build inverters in individual cells
• each cell has a (complex) digital circuit built
  from inverters
• In digital circuit
• signal protein synthesis rate
• computation protein production decay

5
Digital Circuits

• With these inverters, any (finite) digital
  circuit can be built!

C

A
C
D
D
gene
B
C
B
gene
gene

• proteins are the wires, genes are the gates
• NAND gate wire-OR of two genes

6
Outline

• Compute using Inversion
• Model and Simulations
• Measuring signals and circuits
• Microbial Circuit Design
• Related work
• Conclusions Future Work

7
Components of Inversion

• Use existing in vivo biochemical mechanisms
• stage I cooperative binding
• found in many genetic regulatory networks
• stage II transcription
• stage III translation
• decay of proteins (stage I) mRNA (stage III)

• examine the steady-state characteristics of each
  stage to understand how to design gates

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Stage I Cooperative Binding
C
C

• fA input protein synthesis rate
• rA repression activity (concentration
  of bound operator)
• steady-state relation C is sigmoidal

rA
fA
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Stage II Transcription
T
rA
yZ
transcription
repression
mRNA synthesis
T

• rA repression activity
• yZ mRNA synthesis rate
• steady-state relation T is inverse

yZ
rA
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Stage III Translation
L
fZ
yZ
translation
output protein
mRNA synthesis
mRNA
L

• fZ output signal of gate
• steady-state relation L is mostly linear

fZ
yZ
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Putting it together
signal
L
T
C
rA
fA
fZ
yZ
cooperative binding
transcription
translation
repression
input protein
output protein
mRNA synthesis
input protein
mRNA

• inversion relation I
• ideal transfer curve
• gain (flat,steep,flat)
• adequate noise margins

I
fZ I (fA) L T C (fA)
gain
fZ
0
1
fA
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Outline

• Compute using Inversion
• Model and Simulations
• model based on phage ?
• steady-state and dynamic behavior of an inverter
• simulations of gate connectivity, storage
• Measuring signals and circuits
• Microbial Circuit Design
• Related work
• Conclusions Future Work

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Model

• Understand general characteristics of inversion
• Model phage ? elements Hendrix83, Ptashne92
• repressor (CI)
• operator (OR1OR2)
• promoter (PR)
• output protein (dimerize/decay like CI)

OR1
OR2
structural gene
Ptashne92
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Steady-State Behavior

• Simulated transfer curves

• asymmetric (hypersensitive to LOW inputs)
• later in talk ways to fix asymmetry, measure
  noise margins

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Inverters Dynamic Behavior

• Dynamic behavior shows switching times

A

active gene
Z
time (x100 sec)
16
Connect Ring Oscillator

• Connected gates show oscillation, phase shift

A
B
C
time (x100 sec)
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Memory RS Latch
_ R

A
_ S
B
time (x100 sec)
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Outline

• Compute using Inversion
• Model and Simulations
• Measuring signals and circuits
• measure a signal
• approximate a transfer curve (with points)
• the transfer band for measuring fluctuations
• Microbial Circuit Design
• Related work
• Conclusions Future Work

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Measuring a Signal

• Attach a reporter to structural gene
• Translation phase reveals signal
• n copies of output protein Z
• m copies of reporter protein RP (e.g. GFP)
• Signal
• Time derivative
• Measured signal

in equlibrium
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Measuring a Transfer Curve

• To measure a point on the transfer curve of an
  inverter I (input A, output Z)
• Construct a fixed drive (with reporter)
• a constitutive promoter with output protein A
• measure reporter signal ? fA
• Construct fixed drive I (with reporter)
• measure reporter signal ? fZ
• Result point (fA, fZ) on transfer curve of I

A
RP
drive gene
Z
RP
inverter
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Measuring a Transfer Curve II

• Approximate the transfer curve with many points

• Example
• 3 different drives
• each with cistron counts 1 to 10

fZ
fA

• mechanism also useful for more complex circuits

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Models vs. Reality

• Need to measure fluctuations in signals
• Use flow cytometry
• get distribution of fluoresence values for many
  cells

typical histogram of scaled luminosities for
identical cells
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The Transfer Band

• The transfer band
• captures systematic fluctuations in signals
• constructed from dominant peaks in histograms
• For histogram peak
• min/max fA/fA
• Each pair of drive invertersignals yield a
  rectangularregion

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Outline

• Compute using Inversion
• Model and Simulations
• Measuring signals and circuits
• Microbial Circuit Design
• issues in building a circuit
• matching gates
• modifying gates to assemble a library of gates
• BioSpice
• Related work
• Conclusions Future Work

25
Microbial Circuit Design

• Problem gates have varying characteristics
• Need to
• (1) measure gates and construct database
• (2) attempt to match gates
• (3) modify behavior of gates
• (4) measure, add to database, try matching again
• Simulate verify circuits before implementing

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Matching Gates

• Need to match gates according to thresholds

output
HIGH
Imax
Imin
Imin(Iil)
Imax(Iih)
LOW
input
LOW
HIGH
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Modifications to Gates

• modification stage
• Modify repressor/operator affinity C
• Modify the promoter strength T
• Alter degradation rate of a protein C
• Modify RBS strength L
• Increase cistron count T
• Add autorepression C

? Each modification adds an element to the
database
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Modifying Repression

• Reduce repressor/operator binding affinity
• use base-pair substitutions

Schematic effect on cooperative-binding stage
Simulated effect on entire transfer curve
fZ
fA
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Modifying Promoter

• Reduce RNAp affinity to promoter

Schematic effect on transcription stage
Simulated effect on entire transfer curve
fZ
fA
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BioSpice

• Prototype simulation verification tool
• intracellular circuits, intercellular
  communication
• Given a circuit (with proteins specified)
• simulate concentrations/synthesis rates
• Example circuit to simulate
• messaging setting state

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BioSpice Simulation

• Small colony 4x4 grid, 2 cells (outlined)

(1) original I 0
(2) introduce D send msg M
(3) recv msg set I
(4) msg decays I latched
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Limits to Circuit Complexity

• amount of extracellular DNA that can be inserted
  into cells
• reduction in cell viability due to extra
  metabolic requirements
• selective pressures against cells performing
  computation
• probably not different suitable proteins

33
Related Work

• Universal automata with bistable chemical
  reactions Roessler74,Hjelmfelt91
• Mathematical models of genetic regulatory systems
  Arkin94,McAdams97,Neidhart92
• Boolean networks to describe genetic regulatory
  systems Monod61,Sugita63,Kauffman71,Thomas92
• Modifications to genetic systems Draper92,
  vonHippel92,Pakula89

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Conclusions Future Work

• in vivo digital gates are plausible
• Now
• Implement and measure digital gates in E. coli
• Also
• Analyze robustness/sensitivity of gates
• Construct a reaction kinetics database
• Later
• Study protein?protein interactions for faster
  circuits

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Inverter Chemical Reactions