Design Principles in Synthetic Biology...Design Principles in Biological Systems April 24, 2008 C....

Design Principles in Synthetic Biology

Chris Myers1, Nathan Barker2, Hiroyuki Kuwahara3, Curtis Madsen1,Nam Nguyen1, Michael Samoilov4, and Adam Arkin4

1University of Utah2Southern Utah University

3Microsoft Research, Trento, Italy4University of California, Berkeley

Design Principles in Biological SystemsApril 24, 2008

C. Myers et al. (U. of Utah) Design Principles in Synthetic Biology IMA Workshop / April 24, 2008

Synthetic Biology

Increasing number of labs are designing more ambitious and missioncritical synthetic biology projects.

These projects construct synthetic genetic circuits from DNA.

These synthetic genetic circuits can potentially result in:A better understanding of how microorganisms function by examiningdifferences in vivo compared to in silico (Sprinzak/Elowitz).More efficient pathways for the production of antimalarial drugs (Dae et al.).Bacteria that can metabolize toxic chemicals (Brazil et al.).Bacteria that can hunt and kill tumors (Anderson et al.).


Genetic Design Automation (GDA)

Electronic Design Automation (EDA) tools have facilitated the design ofever more complex integrated circuits each year.

Crucial to the success of synthetic biology is an improvement in methodsand tools for Genetic Design Automation (GDA).

Existing GDA tools require biologists to design at the molecular level.

Roughly equivalent to designing electronic circuits at the layout level.

Analysis of genetic circuits is also performed at this very low level.

A GDA tool that supports higher levels of abstraction is essential.


Overview

This talk describes our research to develop such a GDA tool.

This tool has helped us examine design principles for synthetic biology.

As a case study, will describe the design of a genetic Muller C-element.


Current State of GDA Tools

MIT has created a registry of standard biological parts used to designsynthetic genetic circuits (http://parts.mit.edu).

Methods and tools are needed to assist in the design and analysis ofsynthetic genetic circuits using these parts.

BioJADE provides a schematic capture interface to the MIT parts registry.

Systems Biology Markup Language (SBML) has been proposed as astandard representation for the simulation of biological systems.

Many simulation tools have been developed that accept models in theSBML format (BioPathwise, BioSPICE, CellDesigner, SimBiology, etc.).


Systems Biology Markup Language (SBML)

SBML models biological systems at the molecular level.

A typical SBML model is composed of a number of chemical species (i.e.,proteins, genes, etc.) and reactions that transform these species.

This is a very low level representation which is roughly equivalent to thelayout level for electronic circuits.

Designing and simulating genetic circuits at this level of detail isextremely tedious and time-consuming.

Therefore, there is a need for higher-level abstractions for modeling,analysis, and design of genetic circuits.


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Phage λ Virus


Phage λ Decision Circuit


Genetic Circuits

RNAPRNAPRNAP RNAPRNAP

Repression

DegradationDimerization

Pr

CI Dimer

Activation

CI Protein

mRNA

Translation

CII Protein

Operator Sites

PromotersGenes

Transcription

cI cII

CI Dimer

DNAPre

OROE


Genetic Circuits


Repression


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Activation

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mRNA

Translation

CII Protein

Operator Sites

Promoters

Transcription

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DNAPre

Genes

OR

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OE


Genetic Circuits


Repression


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mRNA

Translation

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Operator Sites

Transcription

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Genetic Circuits

RNAPRNAP RNAPRNAP

Repression


RNAP

CI Dimer

Activation

CI Protein

mRNA

Translation

CII Protein

Operator Sites

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DNAPre

PromotersGenes

Transcription

OR

cI cII

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Genetic Circuits

RNAPRNAPRNAP RNAP

Repression


RNAPPr

CI Dimer

Activation

CI Protein

mRNA

Translation

CII Protein

Operator Sites

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DNAPre

PromotersGenes

Transcription

OR

cI cII

OE


Genetic Circuits

RNAPRNAPRNAPRNAP

Repression


RNAPPr

CI Dimer

Activation

CI Protein

mRNA

Translation

CII Protein

Operator Sites

CI Dimer

DNAPre

PromotersGenes

Transcription

OR

cI cII

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Genetic Circuits


Repression


Pr

CI Dimer

Activation

CI ProteinTranslation

CII Protein

Operator Sites

Transcription

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DNAPre

mRNA

PromotersGenes

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cI cII

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Genetic Circuits


Repression


Pr

CI Dimer

Activation

CI Protein

Operator Sites

CI Dimer

DNAPre

mRNA

Translation

CII Protein

PromotersGenes

Transcription

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Genetic Circuits


Repression


Pr

CI Dimer

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CI Protein

CI Dimer

DNAPre

mRNA

Translation

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Operator Sites

PromotersGenes

Transcription

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cI cII

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Genetic Circuits


Repression


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CI Dimer

CI Protein

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ActivationmRNA

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Operator Sites

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Transcription

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Genetic Circuits


Repression


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mRNA

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Operator Sites

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Repression


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DNAPre

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mRNA

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Operator Sites

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Genetic Circuits


Degradation

Repression

Dimerization

Pr

CI Dimer

DNAPre

CI Dimer

Activation

CI Protein

mRNA

Translation

CII Protein

Operator Sites

PromotersGenes

Transcription

OR

cI cII

OE


Genetic Circuits


Repression


Pr

mRNA

Translation

Transcription

CI Dimer

DNAPre

CI Dimer

Activation

CI ProteinCII Protein

Operator Sites

PromotersGenes

OR

cI cII

OE


Genetic Circuits



Repression

PrActivation

CI Protein

mRNA

Translation

CII Protein

Transcription

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DNAPre

CI Dimer

Operator Sites

PromotersGenes

OR

cI cII

OE


Genetic Circuits


Repression


Pr

CI Dimer

Activation

CI Protein

Transcription

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DNAPre

mRNA

Translation

CII Protein

Operator Sites

PromotersGenes

OR

cI cII

OE


Logical Representation

CI CII


Graphical Representation

CI

CII

Pre Pr


Genetic Circuit Model (GCM)

Provides a higher level of abstraction than SBML.

Includes only important species and their influences upon each other.

A GCM is a tuple 〈S,P,G, I,Sd〉 where:S is a finite set of species;P is a finite set of promoters;G : P 7→ 2S maps promoters to sets of species;I ⊆ S×P ×{a, r} is a finite set of influences;Sd ⊆ S is a set of species that influence as dimers.


GCM Graphical Representation

A bipartite graph with species and promoters as the two types of nodes.

Species are connected to promoters using influences I, and promotersare connected to species using function G.

To simplify presentation, graphs shown using only species as nodes,edges are inferred using I and G, and edges are labeled with thepromoter that links the species.


Influences on the Same Promoter

B

C

P1 P1

A CA B

P1 c


Influences on the Same Promoter

B

C

P1 P1

A CA B

P1 c

B

AC


Influences on Different Promoters

A B

C

P1 P2

CB

CA

P1

P2

c

c


Influences on Different Promoters

A B

C

P1 P2

CB

CA

P1

P2

c

c

CA

B


GCM Parameters

Parameter Sym Structure Value Units

Initial species count ns species 0 molecule

Dimerization equilibrium Kd species .05 1molecule

Degradation rate kd species .0075 1sec

Initial promoter count ng promoter 2 molecule

Stoichiometry of production np promoter 10 molecule

Degree of cooperativity nc promoter 2 molecule

RNAP binding equilibrium Ko promoter .033 1molecule

Open complex production rate ko promoter .05 1sec

Basal production rate kb promoter .0001 1sec

Activated production rate ka promoter .25 1sec

Repression binding equilibrium Kr influence .5 1moleculenc

Activation binding equilibrium Ka influence .0033 1molecule(nc+1)


GCM versus SBML Representation

CI

CII

Pre Pr


SBML Example


Synthesizing SBML from a GCM Representation

Create degradation reactions

Create open complex formation reactions

Create dimerization reactions

Create repression reactions

Create activation reactions


Degradation Reactions


Open Complex Formation Reactions


Dimerization Reactions


Repression Reactions


Activation Reactions


Complete SBML Model


Classical Chemical Kinetics

Uses ordinary differential equations (ODE) to represent the system to beanalyzed, and it assumes:

A system is well-stirred.Number of molecules in a cell is high.Concentrations can be viewed as continuous variables.Reactions occur continuously and deterministically.

Genetic circuits involve small molecule counts.

Gene expression can have substantial fluctuations.

ODEs do not capture non-deterministic behavior.


Stochastic Chemical Kinetics

To more accurately predict the temporal behavior of genetic circuits,stochastic chemical kinetics formalism can be used.

Probabilistically predicts the dynamics of biochemical systems.

Describes the time evolution of a system as a discrete-state jump Markovprocess governed by the chemical master equation (CME).

Can simulate it using Gillespie’s Stochastic Simulation Algorithm (SSA).

It exactly tracks the quantities of each molecular species, and treats eachreaction as a separate random event.

Only practical for small systems with no major time-scale separations.

Abstraction is essential for efficient analysis of any realistic system.


Automatic Abstraction

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Begins with a reaction-based model in SBML.

Next, it automatically abstracts this model leveraging the quasi-steadystate assumption, whenever possible.

Finally, it encodes chemical species concentrations into Boolean (orn-ary) levels to produce a stochastic asynchronous circuit model.

It can now be analyzed using Markov chain analysis.


Dimerization Reduction


Operator Site Reduction (PR)


Operator Site Reduction (PRE)


Similar Reaction Combination


Modifier Constant Propagation


Final SBML Model

10 species and 10 reactions reduced to 2 species and 4 reactions


BioSim: Genetic Circuit Editor

http://www.async.ece.utah.edu/BioSim/


BioSim: SBML Editor



BioSim: Simulator



BioSim: Parameter Editor



BioSim: Graph Editor



GCM Advantages

Greatly increases the speed of model development and reduces thenumber of errors in the resulting models.

Allows efficient exploration of the effects of parameter variation.

Constrains SBML model such that it can be more easily abstractedresulting in substantial improvement in simulation time.


Genetic Muller C-Element

C

B

A

C’

A B C’0 0 00 1 C1 0 C1 1 1


Toggle Switch C-Element (Genetic Circuit)

B

A

E

D

F

B

AX Y

Z

CQS

R

P1

P2 P3

P7

P8 P4

P5 P6

X

XY

A

B E

D

F

ZF

D

CY Z

E

xd

e x y

f

f z

c y z


Toggle Switch C-Element (GCM)

P1

P2 P3

P7

P8 P4

P5 P6

X

XY

A

B E

D

F

ZF

D

CY Z

E

xd

e x y

f

f z

c y z


Toggle Switch C-Element (SBML)


Toggle Switch C-Element (Abstracted)

Reduced from 34 species and 31 reactions to 9 species and 15 reactions.


Toggle Switch C-Element (Simulation)

Simulation time improved from 312 seconds to 20 seconds.


Majority Gate C-Element (Genetic Circuit)

E C

X

Y

Z

D

BA

P8P7

P5

P6

P4

P3

P2

P1

A

B

X

D

D

Y

C

E

D

D

Y Z

Z X

x y d

d e c

dy z

z x


Majority Gate C-Element (GCM)

P8P7

P5

P6

P4

P3

P2

P1

A

B

X

D

D

Y

C

E

D

D

Y Z

Z X

x y d

d e c

dy z

z x


Majority Gate C-Element (Simulation)


Speed-Independent C-Element (Genetic Circuit)

AB

S1S2

S3S4C

Z

P1

P2

P3

P4 P5 P6

P7 P8

P9 P10

S4

S4

X S1

S3S2

S4

A

C

S3S2

S4

B

S2

Z

S3

YS1

xs4

ys4

zs3

s1 s2 s3

s1 s2 z

c s4


Speed-Independent C-Element (GCM)

Z

P1

P2

P3

P4 P5 P6

P7 P8

P9 P10

S4

S4

X S1

S3S2

S4

A

C

S3S2

S4

B

S2

Z

S3

YS1

xs4

ys4

zs3

s1 s2 s3

s1 s2 z

c s4


Speed-Independent C-Element (Simulation)


Ordinary Differential Equation Analysis

Use Law of Mass Action to derive an ODE model.

Study behavior of our model at steady state.

Analyze nullclines to characterize the gate.


ODE Analysis: Nullclines for Toggle C-Element

0 20 40 60 80 100 1200

20

40

60

80

100

120

Toggle, Inputs low

Z

Y

dY=0dZ=0

Stable



0 20 40 60 80 100 1200

20

40

60

80

100

120

Toggle, Inputs Mixed

Z

Y

dY=0dZ=0

0 20 40 60 80 100 1200

20

40

60

80

100

120


Z

Y

dY=0dZ=0

Stable

UnstableStable



0 20 40 60 80 100 1200

20

40

60

80

100

120

Toggle, Inputs High

Z

Y

dY=0dZ=0

Stable



0 20 40 60 80 100 1200

20

40

60

80

100

120


Z

Y

dY=0dZ=0

0 20 40 60 80 100 1200

20

40

60

80

100

120


Z

Y

dY=0dZ=0

Stable

UnstableStable


Stochastic Simulation: State Change from Low to High

0 20 40 60 80 100 1200

20

40

60

80

100

120


Z

Y

dY=0dZ=0

?

Stable

UnstableStable


Stochastic Simulation: State Change from Low to High

0 500 1000 1500 20000

0.005

0.01

0.015

0.02

0.025

0.03Low to High

Time (s)

Fai

lure

Rat

e

maj−heat−highmaj−light−hightog−heat−hightog−light−highsi−heat−highsi−light−high


Stochastic Simulation: State Change from High to Low

0 20 40 60 80 100 1200

20

40

60

80

100

120


Z

Y

dY=0dZ=0

Stable

UnstableStable

?


Stochastic Simulation: State Change from High to Low

0 500 1000 1500 20000

0.005

0.01

0.015

0.02

0.025

0.03High to Low

Time (s)

Fai

lure

Rat

e

maj−heat−lowmaj−light−lowtog−heat−lowtog−light−lowsi−heat−lowsi−light−low


Effect of Gene Count

1 1.5 2 2.5 3 3.5 4 4.5 50

0.05

0.1

0.15

0.2

0.25Low to High

Number of Genes

Fai

lure

Rat

e



Effect of Cooperativity

1 1.5 2 2.5 3 3.5 4 4.5 50

0.1

0.2

0.3

0.4

0.5

0.6

0.7Low to High

Cooperativity

Fai

lure

Rat

e



Effect of Repression Strength

10−1

100

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7Low to High

Repression

Fai

lure

Rat

e



Effect of Decay Rates

0.005 0.01 0.015 0.02 0.025 0.030

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1Low to High

Decay Rate

Fai

lure

Rat

e



Effect of Dual Rail

0 20 40 60 80 100 1200

20

40

60

80

100

120


Z

Y

dY=0dZ=0

?

Stable

UnstableStable


Effect of Dual Rail

0 500 1000 1500 20000

0.005

0.01

0.015

0.02

0.025

0.03Low to High

Time (s)

Fai

lure

Rat

e

single−tog−heat−highsingle−tog−light−highdual−tog−heat−highdual−tog−light−high


Effect of Dual Rail

0 20 40 60 80 100 1200

20

40

60

80

100

120


Z

Y

dY=0dZ=0

Stable

UnstableStable

?


Effect of Dual Rail

0 500 1000 1500 20000

0.05

0.1

0.15

0.2

0.25High to Low

Time (s)

Fai

lure

Rat

e

single−tog−heat−lowsingle−tog−light−lowdual−tog−heat−lowdual−tog−light−low


Design Principles in Synthetic Biology

Speed-independence does not necessarily imply better robustness.

Higher gene counts improve production rates, higher equilibrium values,and more robust operation.

Cooperativity of at least two is required to produce the necessarynon-linearity for state-holding.

Repressors should bind efficiently.

Decay rates cannot be too high.

Dual-rail outputs are essential.


Future Work: Modular Design

More levels of hierarchy are needed in the GCM format.

We plan to create structural constructs that allow us to connect GCM’s forseparate modules through species ports.

Allow design at the logical and higher levels of abstraction.


Biologically Inspired Circuit Design

Human inner ear performs the equivalent of one billion floating pointoperations per second and consumes only 14 µW while a game consolewith similar performance burns about 50 W (Sarpeshkar, 2006).

We believe this difference is due to over designing components in order toachieve an extremely low probability of failure in every device.

Future silicon and nano-devices will be much less reliable.

For Moore’s law to continue, future design methods should support thedesign of reliable systems using unreliable components.

Biological systems constructed from very noisy and unreliable devices.

GDA tools may be useful for future integrated circuit technologies.

Biological systems tend to be more asynchronous and analog in nature,so future engineered circuits will likely need to be also.


Acknowledgments

Nathan Barker Hiroyuki Kuwahara Nam Nguyen

Curtis Madsen Michael Samoilov Adam Arkin

This work is supported by the National Science Foundationunder Grants No. 0331270 and CCF07377655.


Design Principles in Synthetic Biology...Design Principles in Biological Systems April 24, 2008 C....

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