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I gave this talk at the BEACON center for the study of evolution in action, Michigan State University, July 2010.
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BEACON, Michigan State University, July 2010 /82
Natalio KrasnogorASAP - Interdisciplinary Optimisation LaboratorySchool of Computer Science
Centre for Integrative Systems BiologySchool of Biology
Centre for Healthcare Associated InfectionsInstitute of Infection, Immunity & Inflammation
University of Nottingham
Towards a Rapid Model Prototyping Strategy for Systems & Synthetic Biology
1
BEACON, Michigan State University, July 2010 /82
Outline•Conceptual Viewpoint & CAD tools
•Model Specification Framework
•Examples of Modeling for Top Down SB
• In Silico Model Evolution
•Conclusions
2
BEACON, Michigan State University, July 2010 /82
A (Proto)Cell as an Information Processing Device
LeDuc et al. Towards an in vivo biologically inspired nanofactory. Nature (2007)
3
BEACON, Michigan State University, July 2010 /82
Functional EntitiesContainer
• A boundary defining self/non-self (symmetry breaking).• Maintain concentration gradients and avoid environmental damage.
Metabolism
• Energy utilisation • Confining raw materials to be processed.• Maintenance of internal structures (autopoiesis).
Information
• Sensing environmental signals / release of signals.• Genetic information
4
BEACON, Michigan State University, July 2010 /82
•The Cell senses the environment and its own internal states•Makes Plans, Takes Decisions and Acts•Evolution is the master programmer
5
The Cell as an Intelligent (Evolved) Machine
Cell
Internal States
Environmental Inputs
Actions
Amir Mitchell, et al., Adaptive prediction of environmental changes by microorganisms. Nature June 2009.
BEACON, Michigan State University, July 2010 /82
•The Cell senses the environment and its own internal states•Makes Plans, Takes Decisions and Acts•Evolution is the master programmer
5
The Cell as an Intelligent (Evolved) Machine
Cell
Internal States
Environmental Inputs
Actions
Amir Mitchell, et al., Adaptive prediction of environmental changes by microorganisms. Nature June 2009.
Wikimedia Commons
BEACON, Michigan State University, July 2010 /82
Network Motifs: Evolution’s Preferred Circuits•Biological networks are complex and vast•To understand their functionality in a scalable way one must choose the correct abstraction
•Moreover, these patterns are organised in non-trivial/non-random hierarchies
•Each network motif carries out a specific information-processing function
6
“Patterns that occur in the real network significantly more often than in randomized networks are called network motifs” Shai S. Shen-Orr et al., Network motifs in the transcriptional regulation
network of Escherichia coli. Nature Genetics 31, 64 - 68 (2002)
Radu Dobrin et al., Aggregation of topological motifs in the Escherichia coli transcriptional regulatory network. BMC Bioinformatics. 2004; 5: 10.
BEACON, Michigan State University, July 2010 /827
Y positively regulates X
Negative autoregulation
Positive autoregulation
The C1-FFL is a ‘sign-sensitive delay’ element and a persistence detector.The I1-FFL is a pulse generator and response accelerator
U. Alon. Network motifs: theory and experimental approaches. Nature Reviews Genetics (2007) vol. 8 (6) pp. 450-461
Shai S. Shen-Orr et al., Network motifs in the transcriptional regulation network of Escherichia coli. Nature Genetics 31, 64 - 68 (2002)
BEACON, Michigan State University, July 2010 /828
BEACON, Michigan State University, July 2010 /828
BEACON, Michigan State University, July 2010 /82
•Cells (and most biologists) don’t do differential calculus! •P systems are a executable specifications that closely mimic biological reality.•These are programs that explicitly mimic the internal behavior of cell systems.•These programs are executed in a virtual machine that captures the intrinsic stochasticity inherent in biology
8
BEACON, Michigan State University, July 2010 /82
Modelling Frameworks•Denotational Semantics Models:
Set of equations showing relationships between molecular quantities and how they change over time.They are approximated numerically. (I.e. Ordinary Differential Equations, PDEs, etc)
•Operational Semantics Models:
Algorithm (list of instructions) executable by an abstract machine whose computation resembles the behaviour of the system under study. (i.e. Finite State Machine)
Jasmin Fisher and Thomas Henzinger. Executable cell biology. Nature Biotechnology, 25, 11, 1239-1249 (2008)9
A. Regev, E. Shapiro. The π-calculus as an abstraction for biomolecular systems. Modelling in Molecular Biology., pages 1–50. Springer Berlin., 2004.
D. Harel, "A Grand Challenge for Computing: Full Reactive Modeling of a Multi-Cellular Animal", Bulletin of the EATCS , European Association for Theoretical Computer Science, no. 81, 2003, pp. 226-235
BEACON, Michigan State University, July 2010 /82
•A readable language but still a formal language with unambiguous semantics•Close to graphical depictions of metabolic networks normally used by biologists
Erythrocyte cell’s glycolytic and pentose phospate pathway from [Reddy et al., Comput. Biol. Med., 1996]
Properties of Petri Net Models
10
BEACON, Michigan State University, July 2010 /82
•A readable language but still a formal language with unambiguous semantics•Close to graphical depictions of metabolic networks normally used by biologists
Erythrocyte cell’s glycolytic and pentose phospate pathway from [Reddy et al., Comput. Biol. Med., 1996]
Properties of Petri Net Models
10
BEACON, Michigan State University, July 2010 /82
Some Limitations
•Not designed to handle spatial events or spatial processes such as diffusion, mechanical transduction, Brownian motion, collisions, transport, etc.•Stochasticity is loaded onto W, i.e. it is not a property of rules or interactions•Although very elegant computing invariants and other properties can really only be done for small systems.•Although due to composability, to certain extent, you can “divide & conquer”
11
BEACON, Michigan State University, July 2010 /82
Elementary Concepts in π-calculus
•A program specifies a network of interacting processes•Processes are defined by their potential communication activities •Communication occurs on complementary channels, identified by names•Message content: Channel name
12
Biological reactions are thusabstracted as communications.
BEACON, Michigan State University, July 2010 /82
π-calculusProcess expressionsP ::= 0 a null process π.P P + P mutually exclusive processes P | P concurrent processes (νx)P new channel x in P ! P create a copy of P
Action prefixes π ::= x? (y) receive y along x x! <y> send y along x τ unobservable (internal) action
syntax
13
BEACON, Michigan State University, July 2010 /82
π-calculusProcess expressionsP ::= 0 a null process π.P P + P mutually exclusive processes P | P concurrent processes (νx)P new channel x in P ! P create a copy of P
Action prefixes π ::= x? (y) receive y along x x! <y> send y along x τ unobservable (internal) action
syntax a molecule / domain
13
BEACON, Michigan State University, July 2010 /82
π-calculusProcess expressionsP ::= 0 a null process π.P P + P mutually exclusive processes P | P concurrent processes (νx)P new channel x in P ! P create a copy of P
Action prefixes π ::= x? (y) receive y along x x! <y> send y along x τ unobservable (internal) action
syntax a molecule / domain
A set of molecules / domains
13
BEACON, Michigan State University, July 2010 /82
π-calculusProcess expressionsP ::= 0 a null process π.P P + P mutually exclusive processes P | P concurrent processes (νx)P new channel x in P ! P create a copy of P
Action prefixes π ::= x? (y) receive y along x x! <y> send y along x τ unobservable (internal) action
syntax a molecule / domain
A set of molecules / domains
a capability to do something(e.g. phosporilate, cleave, etc)
13
BEACON, Michigan State University, July 2010 /82
π-calculusProcess expressionsP ::= 0 a null process π.P P + P mutually exclusive processes P | P concurrent processes (νx)P new channel x in P ! P create a copy of P
Action prefixes π ::= x? (y) receive y along x x! <y> send y along x τ unobservable (internal) action
syntax a molecule / domain
A set of molecules / domains
a capability to do something(e.g. phosporilate, cleave, etc)
This process (enzyme)knows how to do action π (e.g. ligate)
13
BEACON, Michigan State University, July 2010 /82
Some Limitations•Non-mobile/mobile approaches offer a tradeoff between relevance and utility.•Computational problem: each molecule is an instance of a process.•Some abstraction are obscure:
•private channels for compartments is cumbersome, requires multi-step encoding of the formation of complexes, not really a nature encoding of proximity and biochemical complementarity.
•Communication always involves exactly two processes.
14
BEACON, Michigan State University, July 2010 /82
Biochemical Process Calculi
π-calculus (Stochastic, Causal) BioAmbients (mobile compartments) Brane calculi (membranes, Projective) Beta Binders (dynamic compartments)
increasing emphasison intracellular organisation
based on π-calculus
15
BEACON, Michigan State University, July 2010 /82
•From [D.E Goldberg, 2002] (adapted): “Since science and math are in the description
business, the model is the thing…The engineer or inventor has much different motives. The engineered object is the thing”
ε, e
rror
C, cost of modelling
BU/TD Synthetic & Systems Biologist
Mathematician
Tools Suitability and Cost
Computer Scientist/Engineer
16
BEACON, Michigan State University, July 2010 /8217
InfoBiotics Workbench and Dashboard
Spec
ifica
tion
Sim
ulat
ion
Analysis
VerificationO
ptimisation
Managementwww.infobiotics.net
BEACON, Michigan State University, July 2010 /82
Outline•Conceptual Viewpoint & CAD tools
•Model Specification Framework
•Examples of Modeling for Top Down SB
• In Silico Model Evolution
•Conclusions
18
BEACON, Michigan State University, July 2010 /8219
InfoBiotics Workbench and Dashboard
BEACON, Michigan State University, July 2010 /8219
InfoBiotics Workbench and Dashboard
Spec
ifica
tion
BEACON, Michigan State University, July 2010 /82
Model Specification with P systems•Field of membrane computing initiated by Gheorghe Păun in 2000
•Inspired by the hierarchical membrane structure of eukaryotic cells
•A formal language: precisely defined and machine processable
•An executable biology methodology
20
F. J. Romero-Campero, J. Twycross, M. Camara, M. Bennett, M. Gheorghe, and N. Krasnogor. Modular assembly of cell systems biology models using p systems. International Journal of Foundations of Computer
Science, 20(3):427-442, 2009
G. Paun. Computing with membranes. Journal of Computer and System Sciences, 61(1):108–143, 2000
BEACON, Michigan State University, July 2010 /82
Distributed and parallel rewritting systems in compartmentalised hierarchical structures.
Compartments
Objects
Rewriting Rules
• Computational universality and efficiency.
• Modelling Framework
21
What is a P Systems?
BEACON, Michigan State University, July 2010 /82
P-Systems’ Principal Entities
Molecules (ATP, ADP, OHL, etc)
Letters (objects) from an alphabet
Structured Molecules (DNA, RNA,Proteins, etc)
Strings in the alphabet
Molecules in “bulk” Multisets of objects/strings
Membranes/organelles
Membrane
Biochemical activity RulesBiochemical transport Communication rules
22
BEACON, Michigan State University, July 2010 /82
Rewriting Rules
used by Multi-volume Gillespie’s algorithm
23
BEACON, Michigan State University, July 2010 /82
Molecular Interactions Comprehensive and relevant rule-based schema
for the most common molecular interactions taking place in living cells.
Transformation/Degradation Complex Formation and Dissociation Diffusion in / out Binding and Debinding Recruitment and Releasing Transcription Factor Binding/Debinding Transcription/Translation
24
BEACON, Michigan State University, July 2010 /82
Compartments / Cells Compartments and regions are explicitly
specified using membrane structures.
25
BEACON, Michigan State University, July 2010 /82
Colonies / Tissues Colonies and tissues are representing as a
collection of P systems distributed over a lattice.
Objects can travel around the lattice through translocation rules.
v
26
BEACON, Michigan State University, July 2010 /82
Molecular Interactions Inside Compartments
27
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Passive Diffusion of Molecules
28
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Specification of Transcriptional Regulatory Networks
29
BEACON, Michigan State University, July 2010 /82
Post-Transcriptional Processes For each protein in the system, post-transcriptional processes like
translational initiation, messenger and protein degradation, protein dimerisation, signal sensing, signal diffusion etc are represented using modules of rules.
Modules may also have (as parameters) the stochastic kinetic constants associated with the corresponding rules in order to allow us to explore possible mutations in the promoters and ribosome binding sites in order to optimise the behaviour of the system.
30
BEACON, Michigan State University, July 2010 /82
Scalability through Modularity
• Cellular functions arise from orchestrated interactions between motifs consisting of many molecular interacting species.
A P System model is a set of modules of rules representing molecular interactions (network) motifs that appear in many cellular systems.
31
BEACON, Michigan State University, July 2010 /82
Basic P System Modules Used
32
BEACON, Michigan State University, July 2010 /82 21
Characterisation/Encapsulation of Cellular Parts: Gene Promoters
A modeling language for the design of synthetic bacterial colonies.
A module, set of rules describing the molecular interactions involving a cellular part, provides encapsulation and abstraction. Collection or libraries of reusable cellular parts and reusable models.
E. Davidson (2006) The Regulatory Genome, Gene Regulation Networks in Development and Evolution, Elsevier
33
BEACON, Michigan State University, July 2010 /82 21
Characterisation/Encapsulation of Cellular Parts: Gene Promoters
A modeling language for the design of synthetic bacterial colonies.
A module, set of rules describing the molecular interactions involving a cellular part, provides encapsulation and abstraction. Collection or libraries of reusable cellular parts and reusable models.
01101110100001010100011110001011101010100011010100
E. Davidson (2006) The Regulatory Genome, Gene Regulation Networks in Development and Evolution, Elsevier
33
BEACON, Michigan State University, July 2010 /82 21
Characterisation/Encapsulation of Cellular Parts: Gene Promoters
A modeling language for the design of synthetic bacterial colonies.
A module, set of rules describing the molecular interactions involving a cellular part, provides encapsulation and abstraction. Collection or libraries of reusable cellular parts and reusable models.
E. Davidson (2006) The Regulatory Genome, Gene Regulation Networks in Development and Evolution, Elsevier
33
BEACON, Michigan State University, July 2010 /82 21
Characterisation/Encapsulation of Cellular Parts: Gene Promoters
A modeling language for the design of synthetic bacterial colonies.
A module, set of rules describing the molecular interactions involving a cellular part, provides encapsulation and abstraction. Collection or libraries of reusable cellular parts and reusable models.
LuxRAHL
CI
E. Davidson (2006) The Regulatory Genome, Gene Regulation Networks in Development and Evolution, Elsevier
33
BEACON, Michigan State University, July 2010 /82 21
Characterisation/Encapsulation of Cellular Parts: Gene Promoters
A modeling language for the design of synthetic bacterial colonies.
A module, set of rules describing the molecular interactions involving a cellular part, provides encapsulation and abstraction. Collection or libraries of reusable cellular parts and reusable models.
LuxRAHL
CI
PluxOR1({X},{c1, c2, c3, c4, c5, c6, c7, c8, c9},{l}) = {
type: promoter
sequence: ACCTGTAGGATCGTACAGGTTTACGCAAGAA ATGGTTTGTATAGTCGAATACCTCTGGCGGTGATA
rules: r1: [ LuxR2 + PluxPR.X ]_l -c1-> [ PluxPR.LuxR2.X ]_l r2: [ PluxPR.LuxR2.X ]_l -c2-> [ LuxR2 + PluxPR.X ]_l ... r5: [ CI2 + PluxPR.X ]_l -c5-> [ PluxPR.CI2.X ]_l r6: [ PluxPR.CI2.X ]_l -c6-> [ CI2 + PluxPR.X ]_l ... r9: [ PluxPR.LuxR2.X ]_l -c9-> [ PluxPR.LuxR2.X + RNAP.X ]_l}
E. Davidson (2006) The Regulatory Genome, Gene Regulation Networks in Development and Evolution, Elsevier
33
BEACON, Michigan State University, July 2010 /82 22
Module Variables: Recombinant DNA, Directed Evolution, Chassis selection
34
BEACON, Michigan State University, July 2010 /82 22
Module Variables: Recombinant DNA, Directed Evolution, Chassis selection
Recombinant DNA: Objects variables can be instantiated with the name of specific genes.
34
BEACON, Michigan State University, July 2010 /82 22
Module Variables: Recombinant DNA, Directed Evolution, Chassis selection
Recombinant DNA: Objects variables can be instantiated with the name of specific genes.
34
BEACON, Michigan State University, July 2010 /82 22
Module Variables: Recombinant DNA, Directed Evolution, Chassis selection
Recombinant DNA: Objects variables can be instantiated with the name of specific genes.
PluxOR1({X=tetR})
34
BEACON, Michigan State University, July 2010 /82 22
Module Variables: Recombinant DNA, Directed Evolution, Chassis selection
Recombinant DNA: Objects variables can be instantiated with the name of specific genes.
34
BEACON, Michigan State University, July 2010 /82 22
Module Variables: Recombinant DNA, Directed Evolution, Chassis selection
Recombinant DNA: Objects variables can be instantiated with the name of specific genes.
PluxOR1({X=GFP})
34
BEACON, Michigan State University, July 2010 /82 22
Module Variables: Recombinant DNA, Directed Evolution, Chassis selection
Recombinant DNA: Objects variables can be instantiated with the name of specific genes.
PluxOR1({X=GFP})
34
BEACON, Michigan State University, July 2010 /82 22
Module Variables: Recombinant DNA, Directed Evolution, Chassis selection
Directed evolution: Variables for stochastic constants can be instantiated with specific values.
Recombinant DNA: Objects variables can be instantiated with the name of specific genes.
PluxOR1({X=GFP})
34
BEACON, Michigan State University, July 2010 /82 22
Module Variables: Recombinant DNA, Directed Evolution, Chassis selection
A
Directed evolution: Variables for stochastic constants can be instantiated with specific values.
Recombinant DNA: Objects variables can be instantiated with the name of specific genes.
PluxOR1({X=GFP})
34
BEACON, Michigan State University, July 2010 /82 22
Module Variables: Recombinant DNA, Directed Evolution, Chassis selection
A
Directed evolution: Variables for stochastic constants can be instantiated with specific values.
Recombinant DNA: Objects variables can be instantiated with the name of specific genes.
PluxOR1({X=GFP})
PluxOR1({X=GFP},{...,c4=10,...})
34
BEACON, Michigan State University, July 2010 /82 22
Module Variables: Recombinant DNA, Directed Evolution, Chassis selection
A
Directed evolution: Variables for stochastic constants can be instantiated with specific values.
Recombinant DNA: Objects variables can be instantiated with the name of specific genes.
PluxOR1({X=GFP})
PluxOR1({X=GFP},{...,c4=10,...}) Chassis Selection: The variable for the label can be instantiated with the name of a
chassis.
PluxOR1({X=GFP},{...,c4=10,...},{l=DH5α })
34
BEACON, Michigan State University, July 2010 /82 23
Characterisation/Encapsulation of Cellular Parts: Riboswitches
A riboswitch is a piece of RNA that folds in different ways depending on the presence of absence of specific molecules regulating translation.
ToppRibo({X},{c1, c2, c3, c4, c5, c6},{l}) = {
type: riboswitch
sequence:GGTGATACCAGCATCGTCTTGATGCCCTTGG CAGCACCCCGCTGCAAGACAACAAGATG rules: r1: [ RNAP.ToppRibo.X ]_l -c1-> [ ToppRibo.X ]_l r2: [ ToppRibo.X ]_l -c2-> [ ]_l r3: [ ToppRibo.X + theop ]_l –c3-> [ ToppRibo*.X ]_l r4: [ ToppRibo*.X ]_l –c4-> [ ToppRibo.X + theop ]_l r5: [ ToppRibo*.X ]_l –c5-> [ ]_l r6: [ ToppRibo*.X ]_l –c6-> [ToppRibo*.X + Rib.X ]_l}
35
BEACON, Michigan State University, July 2010 /82 24
Characterisation/Encapsulation of Cellular Parts: Degradation Tags
Degradation tags are amino acid sequences recognised by proteases. Once the corresponding DNA sequence is fused to a gene the half life of the protein is reduced considerably.
degLVA({X},{c1, c2},{l}) = {
type: degradation tag
sequence: CAGCAAACGACGAAAACTACGCTTTAGTAGCT
rules: r1: [ Rib.X.degLVA ]_l -c1-> [ X.degLVA ]_l r2: [ X.degLVA ]_l -c2-> [ ]_l}
36
BEACON, Michigan State University, July 2010 /82 25
Higher Order Modules: Building Synthetic Gene Circuits
PluxOR1 geneXToppRibo degLVA
37
BEACON, Michigan State University, July 2010 /82 25
Higher Order Modules: Building Synthetic Gene Circuits
PluxOR1 geneXToppRibo degLVA
3OC6_repressible_sensor({X}) = {
37
BEACON, Michigan State University, July 2010 /82 25
Higher Order Modules: Building Synthetic Gene Circuits
PluxOR1 geneXToppRibo degLVA
3OC6_repressible_sensor({X}) = { PluxOR1({X=ToppRibo.geneX.degLVA},{...},{l=DH5α})
37
BEACON, Michigan State University, July 2010 /82 25
Higher Order Modules: Building Synthetic Gene Circuits
PluxOR1 geneXToppRibo degLVA
3OC6_repressible_sensor({X}) = { PluxOR1({X=ToppRibo.geneX.degLVA},{...},{l=DH5α}) ToppRibo({X=geneX.degLVA},{...},{l=DH5α})
37
BEACON, Michigan State University, July 2010 /82 25
Higher Order Modules: Building Synthetic Gene Circuits
PluxOR1 geneXToppRibo degLVA
3OC6_repressible_sensor({X}) = { PluxOR1({X=ToppRibo.geneX.degLVA},{...},{l=DH5α}) ToppRibo({X=geneX.degLVA},{...},{l=DH5α}) degLVA({X},{...},{l=DH5α})
37
BEACON, Michigan State University, July 2010 /82 25
Higher Order Modules: Building Synthetic Gene Circuits
PluxOR1 geneXToppRibo degLVA
3OC6_repressible_sensor({X}) = { PluxOR1({X=ToppRibo.geneX.degLVA},{...},{l=DH5α}) ToppRibo({X=geneX.degLVA},{...},{l=DH5α}) degLVA({X},{...},{l=DH5α})}
37
BEACON, Michigan State University, July 2010 /82 25
Higher Order Modules: Building Synthetic Gene Circuits
PluxOR1 geneXToppRibo degLVA
3OC6_repressible_sensor({X}) = { PluxOR1({X=ToppRibo.geneX.degLVA},{...},{l=DH5α}) ToppRibo({X=geneX.degLVA},{...},{l=DH5α}) degLVA({X},{...},{l=DH5α})}
X=GFP
37
BEACON, Michigan State University, July 2010 /82 25
Higher Order Modules: Building Synthetic Gene Circuits
PluxOR1 geneXToppRibo degLVA
3OC6_repressible_sensor({X}) = { PluxOR1({X=ToppRibo.geneX.degLVA},{...},{l=DH5α}) ToppRibo({X=geneX.degLVA},{...},{l=DH5α}) degLVA({X},{...},{l=DH5α})}
X=GFP
37
BEACON, Michigan State University, July 2010 /82 25
Higher Order Modules: Building Synthetic Gene Circuits
PluxOR1 geneXToppRibo degLVA
3OC6_repressible_sensor({X}) = { PluxOR1({X=ToppRibo.geneX.degLVA},{...},{l=DH5α}) ToppRibo({X=geneX.degLVA},{...},{l=DH5α}) degLVA({X},{...},{l=DH5α})}
X=GFP
Plux({X=ToppRibo.geneCI.degLVA},{...},{l=DH5α}) ToppRibo({X=geneCI.degLVA},{...},{l=DH5α}) degLVA({CI},{...},{l=DH5α})
PtetR({X=ToppRibo.geneLuxR.degLVA},{...},{l=DH5α}) Weiss_RBS({X=LuxR},{...},{l=DH5α}) Deg({X=LuxR},{...},{l=DH5α})
37
BEACON, Michigan State University, July 2010 /82
luxIPconst
LuxI AHL
AHL
luxRPconst
cIPlux
gfpPluxOR1
LuxR
CI
GFPAHL
AHLSpecification of Multi-cellular
Systems: LPP systems
38
BEACON, Michigan State University, July 2010 /82 29
Infobiotics: An Integrated Frameworkhttp://www.infobiotics.org/infobiotics-workbench/
Synthetic Multi-cellular Systems
Libraries of Modules
P systems LPP systems
Multi Compartmental Stochastic Simulations
based on Gillespie’s algorithm
Spatio-temporal Dynamics Analysis
using Model Checking with PRISM and MC2
Automatic Design of Synthetic Gene
Regulatory Circuits using Evolutionary Algorithms
A compiler based on a BNF grammar
Single Cells
Cellular Parts
Synthetic Circuits
Module Combinations
39
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Stochastic P Systems Are Executable Programs
The virtual machine running these programs is a “Gillespie Algorithm (SSA)”. It generates trajectories of a stochastic system:
A stochastic constant is associated with each rule.A propensity is computed for each rule by multiplying the stochastic constant by the number of distinct possible combinations of the elements on the left hand side of the rule.
F. J. Romero-Campero, J. Twycross, M. Camara, M. Bennett, M. Gheorghe, and N. Krasnogor. Modular assembly of cell systems biology models using p systems. International Journal of Foundations of Computer Science, 2009
40
BEACON, Michigan State University, July 2010 /82
•Using P systems modules one can model a large variety of commonly occurring BRN:
•Gene Regulatory Networks•Signaling Networks•(Metabolic Networks)
•This can be done in an incremental way.
F.J. Romero-Campero, J. Twycross, M. Camara, M. Bennett, M. Gheorghe, N. Krasnogor. Modular Assembly of Cell Systems Biology Models Using P Systems. Internatnional Journal of Foundations of Computer Science, 20(3):427-442, 2009.
41
Degano P., Prandi D., Priami C., and Quaglia P. Beta-binders for biological quantitative experiments.ENTCS, 164:101-117, 2006. Proc. 4th Workshop on Quantitative Aspects of Programming Languages, QAPL 2006.
BEACON, Michigan State University, July 2010 /82
Outline•Conceptual Viewpoint & CAD tools
•Model Specification Framework
•Examples of Modeling for Top Down SB
• In Silico Model Evolution
•Conclusions
42
BEACON, Michigan State University, July 2010 /8243
InfoBiotics Workbench and Dashboard
Spec
ifica
tion
BEACON, Michigan State University, July 2010 /8243
InfoBiotics Workbench and Dashboard
Spec
ifica
tion
Sim
ulat
ion
Analysis
BEACON, Michigan State University, July 2010 /82
Two different bacterial strains carrying specific synthetic gene regulatory networks are used.
The first strain produces a diffusible signal AHL.
The second strain possesses a synthetic gene regulatory network which produces a pulse of GFP after AHL sensing.
These two bacterial strains and their respective synthetic networks are modelled as a combination of modules.
An example: Ron Weiss' Pulse Generator
S. Basu, R. Mehreja, et al. (2004) Spatiotemporal control of gene expression with pulse generating networks, PNAS, 101, 6355-6360
44
BEACON, Michigan State University, July 2010 /82
Pconst
LuxI AHL
AHL
Pconst({X = luxI },…)
PostTransc({X=LuxI},{c1=3.2,…})
Diff({X=AHL},{c=0.1})
luxI
luxRPconst
cIPlux
gfpPluxOR
LuxRGFPAHL
AHL
Pconst({X=luxR},…)
PluxOR1({X=gfp},…)
Plux({X=cI},…) …
An example: Ron Weiss' Pulse Generator
Signal Sender Pulse Generator
45
CI
BEACON, Michigan State University, July 2010 /82
Spatial Distribution of Senders and Pulse Generators
luxIPconst
LuxI AHL
AHL
luxRPconst
cIPlux
gfpPluxOR1
LuxR GFPAHL
AHL
46
CI
BEACON, Michigan State University, July 2010 /82
Pulse propagation - simulation I
47
Simulation I
BEACON, Michigan State University, July 2010 /82
Pulse Generating Cells With Relay
luxRPconst
cIPlux
gfpPluxOR1
LuxR GFPAHL
AHL
48
CI
BEACON, Michigan State University, July 2010 /82
Pulse Generating Cells With Relay
luxRPconst
cIPlux
gfpPluxOR1
LuxR GFPAHL
AHL
luxIPlux
LuxI
AHL
48
CI
BEACON, Michigan State University, July 2010 /82
Pulse Generating Cells With Relay
luxRPconst
cIPlux
gfpPluxOR1
LuxR GFPAHL
AHL
luxIPlux
LuxI
AHL
Pconst({X=luxR},…)
48
CI
BEACON, Michigan State University, July 2010 /82
Pulse Generating Cells With Relay
luxRPconst
cIPlux
gfpPluxOR1
LuxR GFPAHL
AHL
luxIPlux
LuxI
AHL
Pconst({X=luxR},…)
PluxOR1({X=gfp},…)
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CI
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Pulse Generating Cells With Relay
luxRPconst
cIPlux
gfpPluxOR1
LuxR GFPAHL
AHL
luxIPlux
LuxI
AHL
Pconst({X=luxR},…)
PluxOR1({X=gfp},…)
Plux({X=cI},…)
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CI
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Pulse Generating Cells With Relay
luxRPconst
cIPlux
gfpPluxOR1
LuxR GFPAHL
AHL
luxIPlux
LuxI
AHL
Pconst({X=luxR},…)
PluxOR1({X=gfp},…)
Plux({X=cI},…)
…
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CI
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Pulse Generating Cells With Relay
luxRPconst
cIPlux
gfpPluxOR1
LuxR GFPAHL
AHL
luxIPlux
LuxI
AHL
Pconst({X=luxR},…)
PluxOR1({X=gfp},…)
Plux({X=cI},…)
…
…
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CI
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Pulse Generating Cells With Relay
luxRPconst
cIPlux
gfpPluxOR1
LuxR GFPAHL
AHL
luxIPlux
LuxI
AHL
Pconst({X=luxR},…)
PluxOR1({X=gfp},…)
Plux({X=cI},…)
…
…
Diff({X=AHL},…)
48
CI
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Pulse Generating Cells With Relay
luxRPconst
cIPlux
gfpPluxOR1
LuxR GFPAHL
AHL
luxIPlux
LuxI
AHL
Pconst({X=luxR},…)
PluxOR1({X=gfp},…)
Plux({X=cI},…)
…
…
Diff({X=AHL},…)
Plux({X=luxI},…)
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CI
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Simulation II
Pulse propagation & Rely- simulation II
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A Signal Translatorfor Pattern Formation
act1Prep2
act2Prep1
rep1Pact1
rep2Pact2
rep3Prep1
rep4Prep2
I2Prep3
I1Prep4
FP2Pact2
FP1Pact1
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Uniform Spatial Distribution of Signal Translators for Pattern Formation
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Pattern Formation in synthetic bacterial colonies
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Simulation III
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Spatial Distribution of Signal Translators and propagators
luxRPconst
cIPlux
gfpPluxOR1
LuxR GFPSi
Si
luxI
LuxI
Si
Plux
53
CI
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Alternating signal pulses in synthetic bacterial colonies
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Simulation IV
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Outline•Conceptual Viewpoint & CAD tools
•Model Specification Framework
•Examples of Modeling for Top Down SB
• In Silico Model Evolution
•Conclusions
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Automated Model Synthesis and Optimisation
• Modeling is an intrinsically difficult process
• It involves “feature selection” and disambiguation
• Model Synthesis requires• design the topology or structure of the
system in terms of molecular interactions• estimate the kinetic parameters associated
with each molecular interaction
• All the above iterated56
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Large Literature on Model Synthesis• Mason et al. use a random Local Search (LS) as the mutation to
evolve electronic networks with desired dynamics
• Chickarmane et al. use a standard GA to optimize the kinetic parameters of a population of ODE-based reaction networks having the desired topology.
• Spieth et al. propose a Memetic Algorithm to find gene regulatory networks from experimental DNA microarray data where the network structure is optimized with a GA and the parameters are optimized with an Evolution Strategy (ES).
• Jaramillo et al. use Simulated Annealing as the main search strategy for model inference based on (O)DEs
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Rui Dilão, Daniele Muraro, Miguel Nicolau, Marc Schoenauer. Validation of a morphogenesis model of Drosophila early development by a multi-objective evolutionary optimization algorithm. Proc. 7th European Conference on Evolutionary Computation, ML and Data Mining in BioInformatics (EvoBIO'09), April 2009
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Multi-Objective Optimisation in Morphogenesis
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Parameter Optimisation in Metabolic Models
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A. Drager et al. (2009). Modeling metabolic networks in C. glutamicum: a comparison of rate laws in combination with various parameter optimization strategies. BMC Systems Biol ogy 2009, 3:5
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Evolutionary Algorithms for Automated Model Synthesis and Optimisation
EA are potentially very useful for AMSO• There’s a substantial amount of work on:
• using GP-like systems to evolve executable structures
• using EAs for continuous/discrete optimisation
• An EA population represents alternative models (could lead to different experimental setups)
• EAs have the potential to capture evolvability of models/network motifs
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Nested EA for Model SynthesisF. Romero-Campero, H.Cao, M. Camara, and N. Krasnogor. Structure and parameter estimation for cell systems biology models. Proceedings of the Genetic and Evolutionary Computation Conference (GECCO-2008), pages 331-338. ACM Publisher, 2008. (Best Paper award at the Bioinformatics track.)
H. Cao, F.J. Romero-Campero, S. Heeb, M. Camara, and N. Krasnogor. Evolving cell models for systems and synthetic biology. Systems and Synthetic Biology, 4(1), 2010.
C. Garcia-Martinez, C. Lima, J. Twycross, M. Lozano, N. Krasnogor. P System Model Optimisation by Means of Evolutionary Based Search Algorithms. Proceedings of the 2010 Genetic and Evolutionary Computation Conference (GECCO-2010). (Nominated for best paper award at the Bioinformatics track.)
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Fitness Evaluation
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The Fitness Function• Multiple time-series per target
• Different time series have very different profiles, e.g., maxima occur at different times/places
• Transient states (sometimes) as important as steady states
•RMSE not the only possibility
H. Cao, F.J. Romero-Campero, S. Heeb, M. Camara, and N. Krasnogor. Evolving cell models for systems and synthetic biology. Systems and Synthetic Biology, 4(1), 2010.
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Some Case Studies
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Problem Specification
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Results Study Case 4
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Target
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Target
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The fact that this algorithm produces alternative models for a specific biological signature is very encouraging as it could help biologists to design new experiments to discriminate among competing hypothesis (models).
Alternative models can be formally analysed and compared based on other than “fitness” criteria:
★Sensitivity analysis / Robustness ★Average properties (model checking)★Parsimony
Comparing results by only using elementary modules or by adding newly found modules to the library shows the obvious advantage of the incremental methodology with modules.
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Outline•Conceptual Viewpoint & CAD tools
•Model Specification Framework
•Examples of Modeling for Top Down SB
• In Silico Model Evolution
•Conclusions
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BEACON, Michigan State University, July 2010 /8275InfoBiotics Workbench and Dashboard
Spec
ifica
tion
Sim
ulat
ion
Analysis
VerificationManagement
Optim
isation
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• P systems are a handy way of specifying discrete and stochastic rule-based compartmental models.
• Modularity in P systems as a design principle for synthetic networks that enables reusability, hierarchical abstraction and standardisation.
• Can be linked to DPD-type simulations. • Model Checking for the formal analysis of our models.
• Automated explorations (evolutionary search) on models’ structure and parameters.
• Computer Aided analysis of modular and alternative designs (e.g. synthetic network functionality).
TAKE HOME MESSAGE
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An Important Difference with “Normal” Programs: a GP challenge?
•Executable Stochastic P systems are not programs with stochastic behavior
•A cell is a living example of distributed stochastic computing.
•How does this impact GP techniques? can they cope? scale? are they parsimonious?
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function f1(p1,p2,p3,p4){if (p1<p2) RND print p3 RNDelse RND print p4 RND}
function f1(p1,p2,p3,p4){if (p1<p2) and (rand<0.5) print p3else print p4}
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•Three Key Ingredients•Inheritable traits•Variation•Selection Pressure
Crazy Idea: Evolution by Natural Selection as a Search Algorithm
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•Three Key Ingredients•Inheritable traits•Variation•Selection Pressure
Crazy Idea: Evolution by Natural Selection as a Search Algorithm
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A More Fundamental Question•Fundamental CS results: Averaged over all problems, all search methods perform equally well (or rather bad).
•So why does Nature use Evolution as its search mechanism? why not other methods?
•In Synt Bio people worry a lot about evolvability (cellularity scale video)
•Can we engineer in vivo new search mechanism? e.g. a biological Variable Neighborhood Search?
Wolpert, D.H., Macready, W.G. (1997), "No Free Lunch Theorems for Optimization," IEEE Transactions on Evolutionary Computation 1, 67
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Could, e.g., an in vivo VNS “defeat” Evolution? in which environments?
• Perhaps SB rather than trying to stop evolution should try to outsmart/outpace it! 80
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Could, e.g., an in vivo VNS “defeat” Evolution? in which environments?
• Perhaps SB rather than trying to stop evolution should try to outsmart/outpace it! 80
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Could, e.g., an in vivo VNS “defeat” Evolution? in which environments?
• Perhaps SB rather than trying to stop evolution should try to outsmart/outpace it! 80
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Could, e.g., an in vivo VNS “defeat” Evolution? in which environments?
• Perhaps SB rather than trying to stop evolution should try to outsmart/outpace it! 80
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Acknowledgements
•Jonathan Blake
•Claudio Lima
•Francisco Romero-Campero
•James Smaldon
•Jamie Twycross
•Karima Righetti
Infobiotics Dashboard, Integrated Environment
Infobiotics Workbench Machine Learning & Optimisation
Infobiotics Modeling & Model Checking
Infobiotics Dissipative Particle Dynamics
Infobiotics Stochastic Simulations
Members of my team working on SB2
EP/E017215/1
EP/D021847/1
BB/F01855X/1
BB/D019613/1
• Prof. M. Camara (CBS, UoN)
• Prof. C. Alexander (Pharmacy , UoN)
• Dr. S. Heeb (CBS, UoN)
• Dr. G. Rampioni (CBS, UoN)
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Molecular Micro-Biology
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