Toward in vivo Digital Circuits

Ron Weiss, George Homsy, Tom KnightMIT Artificial Intelligence Laboratory

Goal: program biological cells Characteristics

small (E.coli: 1x2m , 109/ml) self replicating energy efficient

Potential applications “smart” drugs / medicine agriculture embedded systems

Motivation

Approach

logiccircuit

microbialcircuit

compiler

genomehigh-levelprogram

in vivo chemical activity of genomeimplements

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

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

Outline

Compute using Inversion Model and Simulations Measuring signals and circuits Microbial Circuit Design Related 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

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

Stage II: Transcription

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

invert signal

repression mRNAsynthesis

transcription

T

T

Stage III: Translation

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

scale output

outputprotein

mRNAsynthesis

mRNA

translation

L

L

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

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

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

Steady-State Behavior Simulated transfer curves:

CB

B B C

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

activegene

Inverter’s Dynamic Behavior

Dynamic behavior shows switching times

[A]

[Z]

[ ]

time (x100 sec)

Connect: Ring Oscillator

Connected gates show oscillation, phase shift

time (x100 sec)

[A]

[C]

[B]

B_S

_R

Memory: RS Latch

time (x100 sec)

_[R]

[B]

_[S]

[A]

=A

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

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:

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[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

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

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

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

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

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

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

Matching Gates

Need to match gates according to thresholds

input

output

Iil Iih

Imax(Iih)

Imin(Iil)

Imax

Imin

LOW

LOW

HIGH

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

Modifying Repression Reduce repressor/operator binding affinity

use base-pair substitutions

C

Schematic effect on cooperative-binding stage:

Simulated effect onentire transfer curve:

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Modifying Promoter

Reduce RNAp affinity to promoterSchematic effect on transcription stage:

Simulated effect onentire transfer curve:

T

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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

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 proteinprotein interactions for faster circuits

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.

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