design principles in synthetic biology...design principles in biological systems april 24, 2008 c....
TRANSCRIPT
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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
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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.).
C. Myers et al. (U. of Utah) Design Principles in Synthetic Biology IMA Workshop / April 24, 2008
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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.
C. Myers et al. (U. of Utah) Design Principles in Synthetic Biology IMA Workshop / April 24, 2008
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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.
C. Myers et al. (U. of Utah) Design Principles in Synthetic Biology IMA Workshop / April 24, 2008
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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.).
C. Myers et al. (U. of Utah) Design Principles in Synthetic Biology IMA Workshop / April 24, 2008
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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.
C. Myers et al. (U. of Utah) Design Principles in Synthetic Biology IMA Workshop / April 24, 2008
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BioSim
Genetic Circuit
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Insert intoHost
oo Plasmidoo
PerformExperiments
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ConstructPlasmid
OO
ExperimentalData
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BiologicalKnowledge
vvnnnnnnnnn
DNASequence
OO
Learn Model // GCM // Synthesis
OO
��SimulationData
Abstraction/Simulation
oo SBML Modeloo
C. Myers et al. (U. of Utah) Design Principles in Synthetic Biology IMA Workshop / April 24, 2008
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BioSim: Analysis
Genetic Circuit
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Insert intoHost
oo Plasmidoo
PerformExperiments
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ConstructPlasmid
OO
ExperimentalData
��
BiologicalKnowledge
vvnnnnnnnnn
DNASequence
OO
Learn Model // GCM // Synthesis
OO
��SimulationData
Abstraction/Simulation
oo SBML Modeloo
C. Myers et al. (U. of Utah) Design Principles in Synthetic Biology IMA Workshop / April 24, 2008
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BioSim: Design
Genetic Circuit
��
Insert intoHost
oo Plasmidoo
PerformExperiments
��
ConstructPlasmid
OO
ExperimentalData
��
BiologicalKnowledge
vvnnnnnnnnn
DNASequence
OO
Learn Model // GCM // Synthesis
OO
��SimulationData
Abstraction/Simulation
oo SBML Modeloo
C. Myers et al. (U. of Utah) Design Principles in Synthetic Biology IMA Workshop / April 24, 2008
![Page 10: Design Principles in Synthetic Biology...Design Principles in Biological Systems April 24, 2008 C. Myers et al. (U. of Utah) Design Principles in Synthetic Biology IMA Workshop / April](https://reader034.vdocuments.us/reader034/viewer/2022050307/5f6f9f8a4ebe0f1bed3e645f/html5/thumbnails/10.jpg)
BioSim: Design
Genetic Circuit
��
Insert intoHost
oo Plasmidoo
PerformExperiments
��
ConstructPlasmid
OO
ExperimentalData
��
BiologicalKnowledge
vvnnnnnnnnn
DNASequence
OO
Learn Model // GCM // Synthesis
OO
��SimulationData
Abstraction/Simulation
oo SBML Modeloo
C. Myers et al. (U. of Utah) Design Principles in Synthetic Biology IMA Workshop / April 24, 2008
![Page 11: Design Principles in Synthetic Biology...Design Principles in Biological Systems April 24, 2008 C. Myers et al. (U. of Utah) Design Principles in Synthetic Biology IMA Workshop / April](https://reader034.vdocuments.us/reader034/viewer/2022050307/5f6f9f8a4ebe0f1bed3e645f/html5/thumbnails/11.jpg)
BioSim: Genetic Circuit Model
Genetic Circuit
��
Insert intoHost
oo Plasmidoo
PerformExperiments
��
ConstructPlasmid
OO
ExperimentalData
��
BiologicalKnowledge
vvnnnnnnnnn
DNASequence
OO
Learn Model // GCM // Synthesis
OO
��SimulationData
Abstraction/Simulation
oo SBML Modeloo
C. Myers et al. (U. of Utah) Design Principles in Synthetic Biology IMA Workshop / April 24, 2008
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Phage λ Virus
C. Myers et al. (U. of Utah) Design Principles in Synthetic Biology IMA Workshop / April 24, 2008
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Phage λ Decision Circuit
C. Myers et al. (U. of Utah) Design Principles in Synthetic Biology IMA Workshop / April 24, 2008
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Phage λ Decision Circuit
C. Myers et al. (U. of Utah) Design Principles in Synthetic Biology IMA Workshop / April 24, 2008
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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
C. Myers et al. (U. of Utah) Design Principles in Synthetic Biology IMA Workshop / April 24, 2008
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Genetic Circuits
RNAPRNAPRNAP RNAPRNAP
Repression
DegradationDimerization
Pr
CI Dimer
Activation
CI Protein
mRNA
Translation
CII Protein
Operator Sites
Promoters
Transcription
CI Dimer
DNAPre
Genes
OR
cI cII
OE
C. Myers et al. (U. of Utah) Design Principles in Synthetic Biology IMA Workshop / April 24, 2008
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Genetic Circuits
RNAPRNAPRNAP RNAPRNAP
Repression
DegradationDimerization
Pr
CI Dimer
Activation
CI Protein
mRNA
Translation
CII Protein
Operator Sites
Transcription
CI Dimer
DNAPre
PromotersGenes
OR
cI cII
OE
C. Myers et al. (U. of Utah) Design Principles in Synthetic Biology IMA Workshop / April 24, 2008
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Genetic Circuits
RNAPRNAP RNAPRNAP
Repression
DegradationDimerization
RNAP
CI Dimer
Activation
CI Protein
mRNA
Translation
CII Protein
Operator Sites
CI Dimer
DNAPre
PromotersGenes
Transcription
OR
cI cII
OE
C. Myers et al. (U. of Utah) Design Principles in Synthetic Biology IMA Workshop / April 24, 2008
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Genetic Circuits
RNAPRNAP RNAPRNAP
Repression
DegradationDimerization
RNAP
CI Dimer
Activation
CI Protein
mRNA
Translation
CII Protein
Operator Sites
CI Dimer
DNAPre
PromotersGenes
Transcription
OR
cI cII
OE
C. Myers et al. (U. of Utah) Design Principles in Synthetic Biology IMA Workshop / April 24, 2008
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Genetic Circuits
RNAPRNAP RNAPRNAP
Repression
DegradationDimerization
RNAP
CI Dimer
Activation
CI Protein
mRNA
Translation
CII Protein
Operator Sites
CI Dimer
DNAPre
PromotersGenes
Transcription
OR
cI cII
OE
C. Myers et al. (U. of Utah) Design Principles in Synthetic Biology IMA Workshop / April 24, 2008
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Genetic Circuits
RNAPRNAPRNAP RNAP
Repression
DegradationDimerization
RNAPPr
CI Dimer
Activation
CI Protein
mRNA
Translation
CII Protein
Operator Sites
CI Dimer
DNAPre
PromotersGenes
Transcription
OR
cI cII
OE
C. Myers et al. (U. of Utah) Design Principles in Synthetic Biology IMA Workshop / April 24, 2008
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Genetic Circuits
RNAPRNAPRNAPRNAP
Repression
DegradationDimerization
RNAPPr
CI Dimer
Activation
CI Protein
mRNA
Translation
CII Protein
Operator Sites
CI Dimer
DNAPre
PromotersGenes
Transcription
OR
cI cII
OE
C. Myers et al. (U. of Utah) Design Principles in Synthetic Biology IMA Workshop / April 24, 2008
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Genetic Circuits
RNAPRNAPRNAP RNAPRNAP
Repression
DegradationDimerization
Pr
CI Dimer
Activation
CI ProteinTranslation
CII Protein
Operator Sites
Transcription
CI Dimer
DNAPre
mRNA
PromotersGenes
OR
cI cII
OE
C. Myers et al. (U. of Utah) Design Principles in Synthetic Biology IMA Workshop / April 24, 2008
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Genetic Circuits
RNAPRNAPRNAP RNAPRNAP
Repression
DegradationDimerization
Pr
CI Dimer
Activation
CI Protein
Operator Sites
CI Dimer
DNAPre
mRNA
Translation
CII Protein
PromotersGenes
Transcription
OR
cI cII
OE
C. Myers et al. (U. of Utah) Design Principles in Synthetic Biology IMA Workshop / April 24, 2008
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Genetic Circuits
RNAPRNAPRNAP RNAPRNAP
Repression
DegradationDimerization
Pr
CI Dimer
Activation
CI Protein
CI Dimer
DNAPre
mRNA
Translation
CII Protein
Operator Sites
PromotersGenes
Transcription
OR
cI cII
OE
C. Myers et al. (U. of Utah) Design Principles in Synthetic Biology IMA Workshop / April 24, 2008
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Genetic Circuits
RNAPRNAPRNAP RNAPRNAP
Repression
DegradationDimerization
Pr
CI Dimer
CI Protein
CI Dimer
DNAPre
ActivationmRNA
Translation
CII Protein
Operator Sites
PromotersGenes
Transcription
OR
cI cII
OE
C. Myers et al. (U. of Utah) Design Principles in Synthetic Biology IMA Workshop / April 24, 2008
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Genetic Circuits
RNAPRNAPRNAP RNAPRNAP
Repression
DegradationDimerization
Pr
CI DimerCI Dimer
DNAPre
Activation
CI Protein
mRNA
Translation
CII Protein
Operator Sites
PromotersGenes
Transcription
OR
cI cII
OE
C. Myers et al. (U. of Utah) Design Principles in Synthetic Biology IMA Workshop / April 24, 2008
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Genetic Circuits
RNAPRNAPRNAP RNAPRNAP
Repression
DegradationDimerization
Pr
CI Dimer
DNAPre
CI Dimer
Activation
CI Protein
mRNA
Translation
CII Protein
Operator Sites
PromotersGenes
Transcription
OR
cI cII
OE
C. Myers et al. (U. of Utah) Design Principles in Synthetic Biology IMA Workshop / April 24, 2008
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Genetic Circuits
RNAPRNAPRNAP RNAPRNAP
Degradation
Repression
Dimerization
Pr
CI Dimer
DNAPre
CI Dimer
Activation
CI Protein
mRNA
Translation
CII Protein
Operator Sites
PromotersGenes
Transcription
OR
cI cII
OE
C. Myers et al. (U. of Utah) Design Principles in Synthetic Biology IMA Workshop / April 24, 2008
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Genetic Circuits
RNAPRNAPRNAP RNAPRNAP
Repression
DegradationDimerization
Pr
mRNA
Translation
Transcription
CI Dimer
DNAPre
CI Dimer
Activation
CI ProteinCII Protein
Operator Sites
PromotersGenes
OR
cI cII
OE
C. Myers et al. (U. of Utah) Design Principles in Synthetic Biology IMA Workshop / April 24, 2008
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Genetic Circuits
RNAPRNAPRNAP RNAPRNAP
DegradationDimerization
Repression
PrActivation
CI Protein
mRNA
Translation
CII Protein
Transcription
CI Dimer
DNAPre
CI Dimer
Operator Sites
PromotersGenes
OR
cI cII
OE
C. Myers et al. (U. of Utah) Design Principles in Synthetic Biology IMA Workshop / April 24, 2008
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Genetic Circuits
RNAPRNAPRNAP RNAPRNAP
Repression
DegradationDimerization
Pr
CI Dimer
Activation
CI Protein
Transcription
CI Dimer
DNAPre
mRNA
Translation
CII Protein
Operator Sites
PromotersGenes
OR
cI cII
OE
C. Myers et al. (U. of Utah) Design Principles in Synthetic Biology IMA Workshop / April 24, 2008
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Logical Representation
CI CII
C. Myers et al. (U. of Utah) Design Principles in Synthetic Biology IMA Workshop / April 24, 2008
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Graphical Representation
CI
CII
Pre Pr
C. Myers et al. (U. of Utah) Design Principles in Synthetic Biology IMA Workshop / April 24, 2008
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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.
C. Myers et al. (U. of Utah) Design Principles in Synthetic Biology IMA Workshop / April 24, 2008
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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.
C. Myers et al. (U. of Utah) Design Principles in Synthetic Biology IMA Workshop / April 24, 2008
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Influences on the Same Promoter
B
C
P1 P1
A CA B
P1 c
C. Myers et al. (U. of Utah) Design Principles in Synthetic Biology IMA Workshop / April 24, 2008
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Influences on the Same Promoter
B
C
P1 P1
A CA B
P1 c
B
AC
C. Myers et al. (U. of Utah) Design Principles in Synthetic Biology IMA Workshop / April 24, 2008
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Influences on Different Promoters
A B
C
P1 P2
CB
CA
P1
P2
c
c
C. Myers et al. (U. of Utah) Design Principles in Synthetic Biology IMA Workshop / April 24, 2008
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Influences on Different Promoters
A B
C
P1 P2
CB
CA
P1
P2
c
c
CA
B
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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)
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GCM versus SBML Representation
CI
CII
Pre Pr
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SBML Example
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SBML Example
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SBML Example
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SBML Example
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SBML Example
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SBML Example
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SBML Example
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SBML Example
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Synthesizing SBML from a GCM Representation
Create degradation reactions
Create open complex formation reactions
Create dimerization reactions
Create repression reactions
Create activation reactions
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Degradation Reactions
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Open Complex Formation Reactions
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Dimerization Reactions
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Repression Reactions
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Activation Reactions
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Complete SBML Model
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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.
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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.
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Automatic Abstraction
ReactionModel
//
@A
//
Reaction-basedAbstraction
//AbstractedReaction
Model//
��
State-basedAbstraction
// SACModel
//
MarkovChain
Analysis
BC
ooStochasticSimulation
// Results
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.
C. Myers et al. (U. of Utah) Design Principles in Synthetic Biology IMA Workshop / April 24, 2008
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Automatic Abstraction
ReactionModel
//
@A
//
Reaction-basedAbstraction
//AbstractedReaction
Model//
��
State-basedAbstraction
// SACModel
//
MarkovChain
Analysis
BC
ooStochasticSimulation
// Results
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.
C. Myers et al. (U. of Utah) Design Principles in Synthetic Biology IMA Workshop / April 24, 2008
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Automatic Abstraction
ReactionModel
//
@A
//
Reaction-basedAbstraction
//AbstractedReaction
Model//
��
State-basedAbstraction
// SACModel
//
MarkovChain
Analysis
BC
ooStochasticSimulation
// Results
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.
C. Myers et al. (U. of Utah) Design Principles in Synthetic Biology IMA Workshop / April 24, 2008
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Automatic Abstraction
ReactionModel
//
@A
//
Reaction-basedAbstraction
//AbstractedReaction
Model//
��
State-basedAbstraction
// SACModel
//
MarkovChain
Analysis
BC
ooStochasticSimulation
// Results
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.
C. Myers et al. (U. of Utah) Design Principles in Synthetic Biology IMA Workshop / April 24, 2008
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Automatic Abstraction
ReactionModel
//
@A
//
Reaction-basedAbstraction
//AbstractedReaction
Model//
��
State-basedAbstraction
// SACModel
//
MarkovChain
Analysis
BC
ooStochasticSimulation
// Results
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.
C. Myers et al. (U. of Utah) Design Principles in Synthetic Biology IMA Workshop / April 24, 2008
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Automatic Abstraction
ReactionModel
//
@A
//
Reaction-basedAbstraction
//AbstractedReaction
Model//
��
State-basedAbstraction
// SACModel
//
MarkovChain
Analysis
BC
ooStochasticSimulation
// Results
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.
C. Myers et al. (U. of Utah) Design Principles in Synthetic Biology IMA Workshop / April 24, 2008
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Automatic Abstraction
ReactionModel
//
@A
//
Reaction-basedAbstraction
//AbstractedReaction
Model//
��
State-basedAbstraction
// SACModel
//
MarkovChain
Analysis
BC
ooStochasticSimulation
// Results
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.
C. Myers et al. (U. of Utah) Design Principles in Synthetic Biology IMA Workshop / April 24, 2008
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Dimerization Reduction
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Dimerization Reduction
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Operator Site Reduction (PR)
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Operator Site Reduction (PR)
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Operator Site Reduction (PRE)
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Operator Site Reduction (PRE)
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Similar Reaction Combination
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Modifier Constant Propagation
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Final SBML Model
10 species and 10 reactions reduced to 2 species and 4 reactions
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BioSim: Genetic Circuit Editor
http://www.async.ece.utah.edu/BioSim/
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BioSim: SBML Editor
http://www.async.ece.utah.edu/BioSim/
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BioSim: Simulator
http://www.async.ece.utah.edu/BioSim/
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BioSim: Parameter Editor
http://www.async.ece.utah.edu/BioSim/
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BioSim: Graph Editor
http://www.async.ece.utah.edu/BioSim/
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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.
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Genetic Muller C-Element
C
B
A
C’
A B C’0 0 00 1 C1 0 C1 1 1
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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
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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
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Toggle Switch C-Element (SBML)
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Toggle Switch C-Element (Abstracted)
Reduced from 34 species and 31 reactions to 9 species and 15 reactions.
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Toggle Switch C-Element (Simulation)
Simulation time improved from 312 seconds to 20 seconds.
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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
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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
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Majority Gate C-Element (Simulation)
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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
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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
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Speed-Independent C-Element (Simulation)
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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.
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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
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ODE Analysis: Nullclines for Toggle C-Element
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
Toggle, Inputs Mixed
Z
Y
dY=0dZ=0
Stable
UnstableStable
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ODE Analysis: Nullclines for Toggle C-Element
0 20 40 60 80 100 1200
20
40
60
80
100
120
Toggle, Inputs High
Z
Y
dY=0dZ=0
Stable
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ODE Analysis: Nullclines for Toggle C-Element
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
Toggle, Inputs Mixed
Z
Y
dY=0dZ=0
Stable
UnstableStable
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Stochastic Simulation: State Change from Low to High
0 20 40 60 80 100 1200
20
40
60
80
100
120
Toggle, Inputs Mixed
Z
Y
dY=0dZ=0
?
Stable
UnstableStable
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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
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Stochastic Simulation: State Change from High to Low
0 20 40 60 80 100 1200
20
40
60
80
100
120
Toggle, Inputs Mixed
Z
Y
dY=0dZ=0
Stable
UnstableStable
?
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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
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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
maj−heat−highmaj−light−hightog−heat−hightog−light−highsi−heat−highsi−light−high
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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
maj−heat−highmaj−light−hightog−heat−hightog−light−highsi−heat−highsi−light−high
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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
maj−heat−highmaj−light−hightog−heat−hightog−light−highsi−heat−highsi−light−high
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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
maj−heat−highmaj−light−hightog−heat−hightog−light−highsi−heat−highsi−light−high
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Effect of Dual Rail
0 20 40 60 80 100 1200
20
40
60
80
100
120
Toggle, Inputs Mixed
Z
Y
dY=0dZ=0
?
Stable
UnstableStable
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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
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Effect of Dual Rail
0 20 40 60 80 100 1200
20
40
60
80
100
120
Toggle, Inputs Mixed
Z
Y
dY=0dZ=0
Stable
UnstableStable
?
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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
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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.
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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.
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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.
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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.
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