Download Programming Biological Cells - MIT Computer Science and Artificial

Toward in vivo Digital Circuits
Ron Weiss, George Homsy, Tom Knight
MIT Artificial Intelligence Laboratory
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
Approach
high-level
program
logic
circuit
genome
microbial
circuit
compiler
in vivo chemical activity of genome
implements
computation specified by logic circuit
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
Digital Circuits

With these inverters, any (finite) digital circuit can be built!
A
A
B
C
D
=
C
D
gene
C
B
gene


proteins are the wires, genes are the gates
NAND gate = “wire-OR” of two genes
gene
Outline
 Compute
 Model
using Inversion
and Simulations
 Measuring
 Microbial
 Related
signals and circuits
Circuit Design
work
 Conclusions
& Future Work
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
Stage I: Cooperative Binding
fA
input
protein
C
cooperative
binding
rA
repression
input
protein
C
 fA = input protein synthesis rate
 rA = repression activity
rA
(concentration of bound operator)

steady-state relation C is sigmoidal
“clean” digital signal
0
fA
1
Stage II: Transcription
T
rA
yZ
transcription
repression
mRNA
synthesis
 rA = repression activity
 yZ = mRNA synthesis rate

steady-state relation T is inverse
invert signal
T
yZ
rA
Stage III: Translation
L
yZ
fZ
translation
mRNA
synthesis
output
protein
mRNA
 fZ = output signal of gate

steady-state relation L is mostly linear
L
fZ
yZ
scale output
Putting it together
fA
input
protein
C
cooperative
binding
rA
T
transcription
repression
yZ
L
mRNA
synthesis
output
protein
mRNA
inversion relation I :
fZ = I (fA) = L ∘ T

fZ
translation
input
protein

signal
I
∘ C (fA)
“ideal” transfer curve:
 gain (flat,steep,flat)
 adequate noise
margins
“gain”
fZ
0
fA
1
Outline
 Compute
 Model
using Inversion
and Simulations
 model based on phage 
 steady-state and dynamic behavior of an inverter
 simulations of gate connectivity, storage
 Measuring
 Microbial
 Related
signals and circuits
Circuit Design
work
 Conclusions
& Future Work
Model
 Understand
 Model
general characteristics of inversion
phage  elements [Hendrix83, Ptashne92]
 repressor (CI)
 operator (OR1:OR2)
 promoter (PR)
 output protein (dimerize/decay like CI)
OR2
OR 1
structural gene
[Ptashne92]
Steady-State Behavior

Simulated transfer curves:
fA
fB
fA
fB
Title:
inv erter-eqlb-for-dimacs 99-talk.eps
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gnuplot 3.5 (pre 3.6) patc hlev el beta 340
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fC
Title:
tw o-inv erters -eqlb-for-dimacs 99-talk.eps
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fA

fB
fA
asymmetric (hypersensitive to LOW inputs)
 later in talk: ways to fix asymmetry, measure noise margins
fC
Inverter’s Dynamic Behavior
 Dynamic
behavior shows switching times
[A]
[ active
gene ]
[Z]
time (x100 sec)
Connect: Ring Oscillator
 Connected
gates show oscillation, phase shift
[A]
[B]
[C]
time (x100 sec)
Memory: RS Latch
_
R
=
A
_
S
B
_
[R]
_
[S]
[B]
[A]
time (x100 sec)
Outline
 Compute
 Model
using Inversion
and Simulations
 Measuring
signals and circuits
 measure a signal
 approximate a transfer curve (with points)
 the transfer band for measuring fluctuations
 Microbial
 Related
Circuit Design
work
 Conclusions
& Future Work
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:
Title:
meas ure-signal-eqn-3.dv i
Creator:
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[in equlibrium]

Measured signal:
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
A
RP
Z
RP
“drive” gene
 Construct “fixed drive” + I (with reporter)

measure reporter signal  fZ
“drive” gene
 Result:
A
inverter
point (fA, fZ) on transfer curve of I
Measuring a Transfer Curve II
Approximate the transfer curve with many points
Example:
• 3 different drives
• each with cistron
counts 1 to 10
Title:
meas ure-tf-w ith-points-talk.eps
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fZ
fA

mechanism also useful for more complex circuits
Models vs. Reality
Need to measure fluctuations in signals
 Use flow cytometry

 get distribution of fluoresence values for many cells
Title:
cell suspension
single-cell
luminosity
readout
Creator:
gnuplot
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typical histogram of scaled luminosities
for “identical” cells
The Transfer Band
 The
transfer band:
 captures systematic fluctuations in signals
 constructed from dominant peaks in histograms
 For
histogram peak:
output
 min/max = fA/fA
 Each
pair of drive + inverter
signals yield a rectangular
region
fZ
fZ
fA
fA
input
Outline
 Compute
 Model
using Inversion
and Simulations
 Measuring
 Microbial
signals and circuits
Circuit Design
 issues in building a circuit
 matching gates
 modifying gates to assemble a library of gates
 BioSpice
 Related
work
 Conclusions
& Future Work
Microbial Circuit Design
 Problem:
 Need
gates have varying characteristics
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
Matching Gates
 Need
to match gates according to thresholds
output
HIGH
Imax
Imin
Imin(Iil)
Imax(Iih)
LOW
Iil
LOW
Iih
Title:
match-gates-eqn-1.dvi
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-eqn-3.dvi
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HIGH
Comment:
Modifications to Gates
modification
stage
 Modify
repressor/operator affinity
C
 Modify
the promoter strength
T
 Alter
degradation rate of a protein
 Modify
RBS strength
 Increase
 Add
cistron count
autorepression
C
L
T
C
 Each modification adds an element to the
Modifying Repression
 Reduce
repressor/operator binding affinity
 use base-pair substitutions
Schematic effect on
cooperative-binding stage:
Simulated effect on
entire transfer curve:
C
fZ
rA
Title:
inv erter-eqlb-k_rprs-for-dimac s99-talk.eps
Creator:
gnuplot 3.5 (pre 3.6) patc hlev el beta 340
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fA
fA
Modifying Promoter
 Reduce
RNAp affinity to promoter
Schematic effect on
transcription stage:
Simulated effect on
entire transfer curve:
T
yZ
fZ
Title:
inv erter-eqlb-k_prom-dimacs 99-talk.eps
Creator:
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rA
fA
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
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
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
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]
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
Inverter: Chemical Reactions
Title:
reac tions -table.dvi
Creator:
dvips k 5.58f Copyright 1986, 1994 Radic al Ey e Softw are
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kinetic -rates.dv i
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