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Toward in vivo Digital Circuits
Ron Weiss, George Homsy, Tom KnightMIT Artificial Intelligence Laboratory
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Goal: program biological cells Characteristics
small (E.coli: 1x2m , 109/ml) self replicating energy efficient
Potential applications “smart” drugs / medicine agriculture embedded systems
Motivation
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Approach
logiccircuit
microbialcircuit
compiler
genomehigh-levelprogram
in vivo chemical activity of genomeimplements
computation specified by logic circuit
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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
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Digital Circuits
With these inverters, any (finite) digital circuit can be built!
A
B
C D
C
CA
B
D= gene
gene
gene
proteins are the wires, genes are the gates NAND gate = “wire-OR” of two genes
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Outline
Compute using Inversion Model and Simulations Measuring signals and circuits Microbial Circuit Design Related work Conclusions & Future Work
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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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input protein synthesis rate repression activity
(concentration of bound operator)
steady-state relation C is sigmoidal
Stage I: Cooperative Binding
inputprotein
repression
cooperativebinding
inputprotein
“clean” digital signal
C
C
0 1
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Stage II: Transcription
repression activity mRNA synthesis rate steady-state relation T is inverse
invert signal
repression mRNAsynthesis
transcription
T
T
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Stage III: Translation
output signal of gate steady-state relation L is mostly linear
scale output
outputprotein
mRNAsynthesis
mRNA
translation
L
L
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inversion relation I :
“ideal” transfer curve: gain (flat,steep,flat) adequate noise margins
Putting it together
IL ∘ T ∘ C ()
inputprotein
outputprotein
repression
cooperativebinding mRNA
synthesis
transcription
inputprotein mRNA
translation
signal
LTC
I
“gain”
0 1
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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 (OR1:OR2) promoter (PR) output protein (dimerize/decay like CI)
[Ptashne92]OR1OR2 structural gene
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Steady-State Behavior Simulated transfer curves:
CB
B B C
Title:inverter-eqlb-for-dimacs99-talk.epsCreator:gnuplot 3.5 (pre 3.6) patchlevel beta 340Preview:This EPS picture was not savedwith a preview included in it.Comment:This EPS picture will print to aPostScript printer, but not toother types of printers.
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asymmetric (hypersensitive to LOW inputs) later in talk: ways to fix asymmetry, measure noise margins
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activegene
Inverter’s Dynamic Behavior
Dynamic behavior shows switching times
[A]
[Z]
[ ]
time (x100 sec)
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Connect: Ring Oscillator
Connected gates show oscillation, phase shift
time (x100 sec)
[A]
[C]
[B]
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B_S
_R
Memory: RS Latch
time (x100 sec)
_[R]
[B]
_[S]
[A]
=A
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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:
Title:measure-signal-eqn-3.dviCreator:dvips(k) 5.78 Copyright 1998 Radical Eye Software (www.radicaleye.com)Preview:This EPS picture was not savedwith a preview included in it.Comment:This EPS picture will print to aPostScript printer, but not toother types of printers.
Title:measure-signal-eqn-2.dviCreator:dvips(k) 5.78 Copyright 1998 Radical Eye Software (www.radicaleye.com)Preview:This EPS picture was not savedwith a preview included in it.Comment:This EPS picture will print to aPostScript printer, but not toother types of printers.
[in equlibrium]
Title:measure-signal-eqn-7.dviCreator:dvips(k) 5.78 Copyright 1998 Radical Eye Software (www.radicaleye.com)Preview:This EPS picture was not savedwith a preview included in it.Comment:This EPS picture will print to aPostScript printer, but not toother types of printers.
Title:measure-signal-eqn-4.dviCreator:dvips(k) 5.78 Copyright 1998 Radical Eye Software (www.radicaleye.com)Preview:This EPS picture was not savedwith a preview included in it.Comment:This EPS picture will print to aPostScript printer, but not toother types of printers.
Title:measure-signal-eqn-8.dviCreator:dvips(k) 5.78 Copyright 1998 Radical Eye Software (www.radicaleye.com)Preview:This EPS picture was not savedwith a preview included in it.Comment:This EPS picture will print to aPostScript printer, but not toother types of printers.
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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
Construct “fixed drive” + I (with reporter) measure reporter signal
Result: point ()on transfer curve of I
A
“drive” gene
“drive” gene inverter
ZA
RP
RP
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Measuring a Transfer Curve II
Approximate the transfer curve with many points Title:
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Example:• 3 different drives• each with cistron counts 1 to 10
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
Title:
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typical histogram of scaled luminositiesfor “identical” cells
cell suspension
single-cellluminosity readout
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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 = /
Each pair of drive + invertersignals yield a rectangularregion
input
output
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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
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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
input
output
Iil Iih
Imax(Iih)
Imin(Iil)
Imax
Imin
LOW
LOW
HIGH
HIGH
Title:match-gates-eqn-1.dviCreator:dvips(k) 5.78 Copyright 1998 Radical Eye Software (www.radicaleye.com)Preview:This EPS picture was not savedwith a preview included in it.Comment:This EPS picture will print to aPostScript printer, but not toother types of printers.
Title:match-gates-eqn-2.dviCreator:dvips(k) 5.78 Copyright 1998 Radical Eye Software (www.radicaleye.com)Preview:This EPS picture was not savedwith a preview included in it.Comment:This EPS picture will print to aPostScript printer, but not toother types of printers.
Title:match-gates-eqn-3.dviCreator:dvips(k) 5.78 Copyright 1998 Radical Eye Software (www.radicaleye.com)Preview:This EPS picture was not savedwith a preview included in it.Comment:This EPS picture will print to aPostScript printer, but not toother types of printers.
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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
C
Schematic effect on cooperative-binding stage:
Simulated effect onentire transfer curve:
Title:inverter-eqlb-k_rprs-for-dimacs99-talk.epsCreator:gnuplot 3.5 (pre 3.6) patchlevel beta 340Preview:This EPS picture was not savedwith a preview included in it.Comment:This EPS picture will print to aPostScript printer, but not toother types of printers.
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Modifying Promoter
Reduce RNAp affinity to promoterSchematic effect on transcription stage:
Simulated effect onentire transfer curve:
T
Title:inverter-eqlb-k_prom-dimacs99-talk.epsCreator:gnuplot 3.5 (pre 3.6) patchlevel beta 340Preview:This EPS picture was not savedwith a preview included in it.Comment:This EPS picture will print to aPostScript printer, but not toother types of printers.
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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
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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 proteinprotein interactions for faster circuits
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Inverter: Chemical ReactionsTitle:reactions-table.dviCreator:dvipsk 5.58f Copyright 1986, 1994 Radical Eye SoftwarePreview:This EPS picture was not savedwith a preview included in it.Comment:This EPS picture will print to aPostScript printer, but not toother types of printers.
Title:kinetic-rates.dviCreator:dvipsk 5.58f Copyright 1986, 1994 Radical Eye SoftwarePreview:This EPS picture was not savedwith a preview included in it.Comment:This EPS picture will print to aPostScript printer, but not toother types of printers.