Computational Methods for Systems Biology and Synthetic...
Transcript of Computational Methods for Systems Biology and Synthetic...
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29/07/10 François Fages Ecole Jeunes Chercheurs Porquerolles 1
Computational Methods for Systems Biology and Synthetic
Biology
François Fages, Constraint Programming Group
INRIA Paris-Rocquencourtmailto:[email protected]://contraintes.inria.fr/
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29/07/10 François Fages Ecole Jeunes Chercheurs Porquerolles 2
Overview of the Lectures
1. Introduction
" Transposing concepts from programming to the analysis of living processes
2. Rule-based Modeling in Biocham
" Macromolecules, compartments and elementary processes in the cell
" Boolean, Differential and Stochastic interpretations of reaction rules
" Cell signaling, Gene expression, Retrovirus, Cell cycle
3. Temporal Logic constraints in Biocham
" Qualitative properties in propositional Computation Tree Logic CTL
" Quantitative properties in quantifier-free Linear Time Logic LTL(R)
" Parameter optimization and robustness w.r.t. temporal logic properties
" Conclusion
" Killer lecture: abstract interpretation in Biocham
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29/07/10 François Fages Ecole Jeunes Chercheurs Porquerolles 3
References
A wonderful textbook:
Molecular Cell Biology. 5th Edition, 1100 pages+CD, Freeman Publ.
Lodish, Berk, Zipursky, Matsudaira, Baltimore, Darnell. Nov. 2003.
Formal Cell Biology in BIOCHAM (tutorial). François Fages and Sylvain Soliman.
8th International School on Computational Systems Biology.
ISpringer-Verlag, LNCS 5016. Mar. 2008.(pdf)
The Biochemical Abstract Machine BIOCHAM. http://contraintes.inria.fr/BIOCHAM
Modeling dynamic phenomena in molecular and cellular biology.
Segel. Cambridge Univ. Press. 1987.
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29/07/10 François Fages Ecole Jeunes Chercheurs Porquerolles 4
Systems Biology ?
�Systems Biology aims at systems-level understanding [which]
requires a set of principles and methodologies that links the
behaviors of molecules to systems characteristics and functions.�
H. Kitano, ICSB 2000
" Analyze (post-)genomic data produced with high-throughput technologies (stored in databases like GO, KEGG, BioCyc, etc.);
" Integrate heterogeneous data about a specific problem;
" Understand and predict the behaviors of large networks of genes and proteins.
Systems Biology Markup Language (SBML): model exchange format SBML model repositories: e.g. biomodels.net 261 curated models
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29/07/10 François Fages Ecole Jeunes Chercheurs Porquerolles 5
Issue of Abstraction in Systems Biology
Models are built in Systems Biology with two contradictory perspectives :
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29/07/10 François Fages Ecole Jeunes Chercheurs Porquerolles 6
Issue of Abstraction in Systems Biology
Models are built in Systems Biology with two contradictory perspectives :
1) Models for representing knowledge : the more concrete the better
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29/07/10 François Fages Ecole Jeunes Chercheurs Porquerolles 7
Issue of Abstraction in Systems Biology
Models are built in Systems Biology with two contradictory perspectives :
1) Models for representing knowledge : the more concrete the better
2) Models for making predictions : the more abstract the better !
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29/07/10 François Fages Ecole Jeunes Chercheurs Porquerolles 8
Issue of Abstraction in Systems Biology
Models are built in Systems Biology with two contradictory perspectives :
1) Models for representing knowledge : the more concrete the better
2) Models for making predictions : the more abstract the better !
These perspectives can be reconciled by organizing formalisms and models into a hierarchy of abstractions.
To understand a system is not to know everything about it but to know
abstraction levels that are sufficient for answering questions about it
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29/07/10 François Fages Ecole Jeunes Chercheurs Porquerolles 9
Formal Semantics of Living Processes ?
Formally, � the� behavior of a system depends on our choice of observables.
? ?
Mitosis movie [Lodish et al. 03]
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29/07/10 François Fages Ecole Jeunes Chercheurs Porquerolles 10
Boolean Semantics
" Formally, � the� behavior of a system depends on our choice of observables.
" Presence/absence of molecules
" Boolean transitions
0 1
Mitosis movie [Lodish et al. 03]
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29/07/10 François Fages Ecole Jeunes Chercheurs Porquerolles 11
Continuous Differential Semantics
" Formally, � the� behavior of a system depends on our choice of observables.
" Concentrations of molecules
" Rates of reactions
x ý
Mitosis movie [Lodish et al. 03]
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Stochastic Semantics
" Formally, � the� behavior of a system depends on our choice of observables.
" Numbers of molecules
" Probabilities of reaction
n τ
Mitosis movie [Lodish et al. 03]
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Temporal Logic LTL
" Formally, � the� behavior of a system depends on our choice of observables.
" Presence/absence of molecules
" Temporal logic formulas
F xF x
F (x ^ F (¬ x ^ y))
FG (x v y)
&
Mitosis movie [Lodish et al. 03]
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Temporal Logic LTL(R)
" Formally, � the� behavior of a system depends on our choice of observables.
" Concentrations of molecules
" TL with Constraints over R
F x>1F (x >0.2)
F (x >0.2 ^ F (x<0.1 ^ y>0.2))
FG (x>0.2 v y>0.2)
&
Mitosis movie [Lodish et al. 03]
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29/07/10 François Fages Ecole Jeunes Chercheurs Porquerolles 15
Hierarchy of Semantics
Stochastic model
Differential model
Discrete model
abstraction
concretization
Boolean model
Theory of abstract Interpretation
Abstractions as Galois connections
[Cousot Cousot POPL� 77]
[Fages Soliman CMSB� 06,TCS� 07]
Syntactical
model
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29/07/10 François Fages Ecole Jeunes Chercheurs Porquerolles 16
Regulation Graph as Abstraction
Stochastic model
Differential model
Discrete model
abstraction
concretization
Boolean model
Syntactical
model[Fages Soliman CMSB’06]
Syntactic regulation graph
(pos/neg influences w.r.t.
the stoichiometric coef.
in rules)
Thm. Same graphs for
monotonic kinetics
Jacobian regulation graph
(pos/neg influences w.r.t.
the sign of the coefficients)
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29/07/10 François Fages Ecole Jeunes Chercheurs Porquerolles 17
Regulation Graphs Circuit Analyses
Stochastic model
Differential model
Discrete model
abstraction
concretization
Boolean model
Syntactical
model
Jacobian circuit analysis
Discrete circuit analysis
Boolean circuit analysisabstraction
abstraction
abstraction
Thm. Positive circuits are a necessary condition for multistationarity
[Thomas 81] [Soulé 03]
[Remy Ruet Thieffry 05]
[Richard 07]
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29/07/10 François Fages Ecole Jeunes Chercheurs Porquerolles 18
Reducing and Relating Models
Models of circadian clock in http://www.biomodels.net Reductions as reaction subgraph epimorphisms [Gay Fages Soliman ECCB� 10]
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29/07/10 François Fages Ecole Jeunes Chercheurs Porquerolles 19
Overview of the Lectures
1. Introduction
" Transposing concepts from programming to the analysis of living processes
2. Rule-based Modeling in Biocham
" Macromolecules, compartments and elementary processes in the cell
" Boolean, Differential and Stochastic interpretations of reaction rules
" Cell signaling, cell cycle models
3. Temporal Logic constraints in Biocham
" Qualitative properties in propositional Computation Tree Logic CTL
" Quantitative properties in quantifier-free Linear Time Logic LTL(R)
" Model inference from temporal logic properties
" Conclusion
" Killer lecture: abstract interpretation in Biocham
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29/07/10 François Fages Ecole Jeunes Chercheurs Porquerolles 20
Cell Molecules
" Small molecules: covalent bonds 50-200 kcal/mol
� 70% water
� 1% ions
� 6% amino acids (20), nucleotides (5),
� fats, sugars, ATP, ADP, &
" Macromolecules: hydrogen bonds, ionic, hydrophobic, Waals 1-5 kcal/mol
Stability and bindings determined by the number of weak bonds: 3D shape
� 20% proteins (50-104 amino acids)
� DNA (102-106 nucleotides AGCT)
� RNA (102-104 nucleotides AGCU)
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29/07/10 François Fages Ecole Jeunes Chercheurs Porquerolles 21
DNA Deoxyribonucleic Acid
1) Primary structure: word over 4 nucleotides
Adenine, Guanine, Cytosine, Thymine
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29/07/10 François Fages Ecole Jeunes Chercheurs Porquerolles 22
DNA Deoxyribonucleic Acid
1) Primary structure: word over 4 nucleotides
Adenine, Guanine, Cytosine, Thymine
2) Secondary structure:
double helix of pairs A--T and C---G
stabilized by hydrogen bonds
Size of DNA = number of pairs
Genes are parts of DNA
Nobel Prizes Watson and Crick (1956)
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29/07/10 François Fages Ecole Jeunes Chercheurs Porquerolles 23
DNA: Genome Size
140 Gb&
15 Gb&
3 Gb&
12 Mb
100 %1 circular5 MbE. Coli (bacteria)
Coding DNAChromosomesGenome sizeSpecies
Artificial life by Craig Venter:fully synthetic bacteria genome (0,39 $/b)implemented in a bacteria without DNA still living and proliferating!
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29/07/10 François Fages Ecole Jeunes Chercheurs Porquerolles 24
DNA: Genome Size
140 Gb&
15 Gb&
3 Gb&
70 %1612 MbS. Cerevisae (yeast)
100 %1 circular5 MbE. Coli (bacteria)
Coding DNAChromosomesGenome sizeSpecies
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29/07/10 François Fages Ecole Jeunes Chercheurs Porquerolles 25
DNA: Genome Size
140 Gb&
15 Gb&
15 %20, 233 GbMouse, Human
70 %1612 MbS. Cerevisae (yeast)
100 %1 circular5 MbE. Coli (bacteria)
Coding DNAChromosomesGenome sizeSpecies
3,200,000,000 pairs of nucleotides
single nucleotide polymorphism 1 / 2kb
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29/07/10 François Fages Ecole Jeunes Chercheurs Porquerolles 26
Genome Size
140 Gb&
1 %815 GbOnion
15 %20, 233 GbMouse, Human
70 %1612 MbS. Cerevisae (yeast)
100 %14 MbE. Coli (bacteria)
Coding DNAChromosomesGenome sizeSpecies
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Genome Size
0.7 %140 GbLungfish
1 %815 GbOnion
15 %20, 233 GbMouse, Human
70 %1612 MbS. Cerevisae (yeast)
100 %14 MbE. Coli (bacteria)
Coding DNAChromosomesGenome sizeSpecies
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29/07/10 François Fages Ecole Jeunes Chercheurs Porquerolles 28
DNA Replication
1. Separation of the two helices
2. Production of one complementary strand for each copy
(from one or several starting points of replication)
3. Segregation
4. Mitosis (cell division)
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Gene Transcription and Translation
" Activation (Inhibition): Nobel prize Jakob and Monod (1965)
transcription factors bind to the regulatory region of the gene
2. Transcription:
RNA polymerase copies the DNA from start to stop positions
into a single stranded pre-mature messenger pRNA
3. (Alternative) splicing:
non coding regions of pRNA are removed giving mature messenger mRNA
4. Translation:
mRNA moves to cytoplasm and binds to ribosome to assemble a protein
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29/07/10 François Fages Ecole Jeunes Chercheurs Porquerolles 30
Formal Genes: Syntax
" Part of DNA, unique #E2
" Activation
binding of promotion factor #E2-(E2f13-DP12)
" Repression (inhibition)
binding of another molecule #E2-Rep
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29/07/10 François Fages Ecole Jeunes Chercheurs Porquerolles 31
Transcription and Translation Rules
Activation
#E2 + E2f13DP12 => #E2E2f13DP12Repression
#E2 + Rep => #E2Rep
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29/07/10 François Fages Ecole Jeunes Chercheurs Porquerolles 32
Transcription and Translation Rules
Activation
#E2 + E2f13DP12 => #E2E2f13DP12Repression
#E2 + Rep => #E2RepTranscription
_ =[#E2E2F13DP12]=> pRNAcycA
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29/07/10 François Fages Ecole Jeunes Chercheurs Porquerolles 33
Transcription and Translation Rules
Activation
#E2 + E2f13DP12 => #E2E2f13DP12Repression
#E2 + Rep => #E2RepTranscription
_ =[#E2E2F13DP12]=> pRNAcycA(Alternative) Splicing
pRNAcycA => mRNAcycA (pRNAcycA => mRNAcycA2)
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29/07/10 François Fages Ecole Jeunes Chercheurs Porquerolles 34
Transcription and Translation Rules
Activation
#E2 + E2f13DP12 => #E2E2f13DP12Repression
#E2 + Rep => #E2RepTranscription
_ =[#E2E2F13DP12]=> pRNAcycA(Alternative) Splicing
pRNAcycA => mRNAcycA (pRNAcycA => mRNAcycA2) Translation
mRNAcycA => mRNAcycA::cyt mRNAcycA::cyt + ribosome::cyt => cycA::cyt + ribosome::cyt(mRNAcycA2::cyt + ribosome::cyt => cycA2::cyt + ribosome::cyt)
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29/07/10 François Fages Ecole Jeunes Chercheurs Porquerolles 35
Proteins
1) Primary structure: word of n amino acids residues (20n possibilities)
linked with C-N bonds
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29/07/10 François Fages Ecole Jeunes Chercheurs Porquerolles 36
Proteins
1) Primary structure: word of n amino acids residues (20n possibilities)
linked with C-N bonds
Example: MPRI
Methionine-Proline-Arginine-Isoleucine
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29/07/10 François Fages Ecole Jeunes Chercheurs Porquerolles 37
Proteins
1) Primary structure: word of n amino acids residues (20n possibilities)
linked with C-N bonds
Example: MPRI
Methionine-Proline-Arginine-Isoleucine
2) Secondary: word of m α−helix, β−strands, random coils,& (3m-10m)
stabilized by hydrogen bonds H---O
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29/07/10 François Fages Ecole Jeunes Chercheurs Porquerolles 38
Proteins
1) Primary structure: word of n amino acids residues (20n possibilities)
linked with C-N bonds
Example: MPRI
Methionine-Proline-Arginine-Isoleucine
2) Secondary: word of m α−helix, β−strands, random coils,& (3m-10m)
stabilized by hydrogen bonds H---O
3) Tertiary 3D structure: spatial folding
stabilized by hydrophobic interactions
explains the protein interaction capabilities
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29/07/10 François Fages Ecole Jeunes Chercheurs Porquerolles 39
Formal Proteins: Syntax" Cyclin dependent kinase 1 Cdk1
(free, inactive)
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29/07/10 François Fages Ecole Jeunes Chercheurs Porquerolles 40
Formal Proteins: Syntax" Cyclin dependent kinase 1 Cdk1
(free, inactive)
" Complex Cdk1-Cyclin B Cdk1–CycB(low activity)
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29/07/10 François Fages Ecole Jeunes Chercheurs Porquerolles 41
Formal Proteins: Syntax" Cyclin dependent kinase 1 Cdk1
(free, inactive)
" Complex Cdk1-Cyclin B Cdk1–CycB(low activity)
" Phosphorylated form Cdk1~{thr161}CycBat site threonine 161
(high activity)
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29/07/10 François Fages Ecole Jeunes Chercheurs Porquerolles 42
Formal Proteins" Cyclin dependent kinase 1 Cdk1
(free, inactive)
" Complex Cdk1-Cyclin B Cdk1–CycB(low activity)
" Phosphorylated form Cdk1~{thr161}CycBat site threonine 161
(high activity)
�Mitosis-Promoting Factor�
phosphorylates actin in microtubules nuclear division
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29/07/10 François Fages Ecole Jeunes Chercheurs Porquerolles 43
Elementary Rule Schemas" Complexation: A + B => A-B. Decomplexation A-B => A + B.
cdk1+cycB => cdk1–cycB
" Phosphorylation: A =[C]=> A~{p}. Dephosphorylation A~{p} =[C]=> A.
Cdk1CycB =[Myt1]=> Cdk1~{thr161}CycBCdk1~{thr14,tyr15}CycB =[Cdc25~{Nterm}]=> Cdk1CycB
" Synthesis: _ =[C]=> A. Degradation: A =[C]=> _.
_=[#E2E2f13Dp12]=>cycA cycE =[@UbiPro]=> _ (not for cycEcdk2 which is stable)
" Transport: A::L1 => A::L2.
Cdk1~{p}CycB::cytoplasm=>Cdk1~{p}CycB::nucleus
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29/07/10 François Fages Ecole Jeunes Chercheurs Porquerolles 44
Syntax of Objects E == compound | EE | E~{p1,…,pn}
• compound: name of molecule, #gene binding site• : binding operator for protein complexes, gene binding sites, &
Associative and commutative.• ~{…}: modification operator for phosphorylated sites, &
Set of modified sites (Associative, Commutative, Idempotent).
O == E | E::location
• location: symbolic compartment (nucleus, cytoplasm, membrane, & )
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29/07/10 François Fages Ecole Jeunes Chercheurs Porquerolles 45
Syntax of RulesS ::= _ | O+S
+ : solution operator (Associative, Commutative, Neutral _)
R ::= S => S | kineticexpression for R
Abbreviations
A =[C]=> B stands for A+C => B+CA <=> B stands for A=>B and B=>A,
Compatible with the Systems Biology Markup Language SBML
exchange format for reaction models
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29/07/10 François Fages Ecole Jeunes Chercheurs Porquerolles 46
Kinetic Rate Constants
" Complexation: probability of reaction upon collision (specificity, affinity)
position of matching surfaces
" Decomplexation: total energy of all bonds
(giving dissociation rates)
" Diffusion speeds (small molecules>substrates>enzymes& )
Average travel in one random walk: 1 μm in 1s, 2μm in 4s, 10μm in 100s
" For one enzyme:
500000 random collisions per second with a substrate concentration of 10-5
50000 random collisions per second with a substrate concentration of 10-6
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29/07/10 François Fages Ecole Jeunes Chercheurs Porquerolles 47
From Syntax to Semantics" Boolean Semantics: presence-absence of molecules
� Boolean Transition System
(asynchronous, non-deterministic)
" Discrete semantics: levels of molecules
� Discrete Transition System
" Continuous Semantics: concentrations
� Ordinary Differential Equations
� Deterministic hybrid automata
" Stochastic Semantics: numbers of molecules
� Continuous time Markov chain
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29/07/10 François Fages Ecole Jeunes Chercheurs Porquerolles 48
Cell Signaling" Signals:
� hormones: insulin, adrenaline, steroids, EGF, & ,
� neighboring cell membrane proteins: Delta
� nutriments, light, pressure, &
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29/07/10 François Fages Ecole Jeunes Chercheurs Porquerolles 49
Cell Signaling" Signals:
� hormones: insulin, adrenaline, steroids, EGF, & ,
� neighboring cell membrane proteins: Delta
� nutriments, light, pressure, &
" Receptors transmembrane proteins:
� Tyrosine kinases,
� G protein-coupled,
� TGFβ,
� Notch,
� Ionic channels
� &
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29/07/10 François Fages Ecole Jeunes Chercheurs Porquerolles 50
Receptor Tyrosine Kinase RTK
L + R <=> LRLR + LR => LRLRRASGDP =[LRLR]=> RASGTP
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29/07/10 François Fages Ecole Jeunes Chercheurs Porquerolles 51
MAPK Signaling Pathways " Input:
RAS activated by the receptor activates RAF
RASGTP + RAFP1433 =>RASGDP + RAF + P1433
" Output:
active MAPK moves to the nucleus
phosphorylates a transcription factor which stimulates gene expression
RAF + … => …… => MAPK~{T183,Y185}
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29/07/10 François Fages Ecole Jeunes Chercheurs Porquerolles 52
Five MAP Kinase Pathways in Budding Yeast
(Saccharomyces Cerevisiae)
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29/07/10 François Fages Ecole Jeunes Chercheurs Porquerolles 53
Three Levels MAPK Cascade
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29/07/10 François Fages Ecole Jeunes Chercheurs Porquerolles 54
MAPK Signaling Cascade in BIOCHAMRAF + RAFK <=> RAFRAFK. RAFRAFK => RAFK + RAF~{p1}. RAF~{p1} + RAFPH <=> RAF~{p1}RAFPH. RAF~{p1}RAFPH => RAF + RAFPH. MEK~$P + RAF~{p1} <=> MEK~$PRAF~{p1} where p2 not in $P. MEK~{p1}RAF~{p1} => MEK~{p1,p2} + RAF~{p1}. MEKRAF~{p1} => MEK~{p1} + RAF~{p1}. MEKPH + MEK~{p1}~$P <=> MEK~{p1}~$PMEKPH. MEK~{p1}MEKPH => MEK + MEKPH. MEK~{p1,p2}MEKPH => MEK~{p1} + MEKPH.MAPK~$P + MEK~{p1,p2} <=> MAPK~$PMEK~{p1,p2} where p2 not in $P. MAPKPH + MAPK~{p1}~$P <=> MAPK~{p1}~$PMAPKPH. MAPK~{p1}MAPKPH => MAPK + MAPKPH. MAPK~{p1,p2}MAPKPH => MAPK~{p1} + MAPKPH. MAPKMEK~{p1,p2} => MAPK~{p1} + MEK~{p1,p2}. MAPK~{p1}MEK~{p1,p2} => MAPK~{p1,p2}+MEK~{p1,p2}.
Pattern variables $P for
- Phosphorylation sites
- Molecules
with symbolic constraints
BIOCHAM rules with patterns are expanded in BIOCHAM rules without patterns
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29/07/10 François Fages Ecole Jeunes Chercheurs Porquerolles 55
Reaction Hypergraph
Bipartite ProteinsReactions Graph
GraphVizhttp://www.research.att.co/sw/tools/graphvi
z
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29/07/10 François Fages Ecole Jeunes Chercheurs Porquerolles 56
Influence Graph inferred from the syntactical reaction model of the MAPK � cascade�
Negative feedback loops[Fages Soliman CMSB 06]
Possibility of oscillations[Qiao et al. PLOS 07]
Influence Graph
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29/07/10 François Fages Ecole Jeunes Chercheurs Porquerolles 57
Reaction Model of the MAPK Cascade [Levchenko et al. PNAS 2000]
(MA(1), MA(0.4)) for RAF + RAFK <=> RAFRAFK.(MA(0.5),MA(0.5)) for RAF~{p1} + RAFPH <=> RAF~{p1}RAFPH.(MA(3.3),MA(0.42)) for MEK~$P + RAF~{p1} <=> MEK~$PRAF~{p1}
where p2 not in $P.(MA(10),MA(0.8)) for MEKPH + MEK~{p1}~$P <=> MEK~{p1}~$PMEKPH.(MA(20),MA(0.7)) for MAPK~$P + MEK~{p1,p2} <=> MAPK~$PMEK~{p1,p2}
where p2 not in $P.(MA(5),MA(0.4)) for MAPKPH + MAPK~{p1}~$P <=> MAPK~{p1}~$PMAPKPH.MA(0.1) for RAFRAFK => RAFK + RAF~{p1}.MA(0.1) for RAF~{p1}RAFPH => RAF + RAFPH.MA(0.1) for MEK~{p1}RAF~{p1} => MEK~{p1,p2} + RAF~{p1}.MA(0.1) for MEKRAF~{p1} => MEK~{p1} + RAF~{p1}.MA(0.1) for MEK~{p1}MEKPH => MEK + MEKPH.MA(0.1) for MEK~{p1,p2}MEKPH => MEK~{p1} + MEKPH.MA(0.1) for MAPKMEK~{p1,p2} => MAPK~{p1} + MEK~{p1,p2}.MA(0.1) for MAPK~{p1}MEK~{p1,p2} => MAPK~{p1,p2} + MEK~{p1,p2}.MA(0.1) for MAPK~{p1}MAPKPH => MAPK + MAPKPH.MA(0.1) for MAPK~{p1,p2}MAPKPH => MAPK~{p1} + MAPKPH.
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29/07/10 François Fages Ecole Jeunes Chercheurs Porquerolles 58
Differential Simulation
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29/07/10 François Fages Ecole Jeunes Chercheurs Porquerolles 59
Stochastic Simulation
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29/07/10 François Fages Ecole Jeunes Chercheurs Porquerolles 60
Boolean Simulation
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29/07/10 François Fages Ecole Jeunes Chercheurs Porquerolles 61
Rule-based Models" Reaction rule: k*[A]*[B] for A+B => C
" SBML (Systems Biology Markup Lang.): import/export exchange format
" BIOCHAM three abstraction levels
5. Stochastic Semantics: number of molecules
� Continuous time Markov chain
6. Differential Semantics: concentration
� Ordinary Differential Equations
� Hybrid automata
7. Boolean Semantics: presence-absence of molecules
� Asynchronuous Transition System A & B C & A/¬A & B/¬B
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29/07/10 François Fages Ecole Jeunes Chercheurs Porquerolles 62
Automatic Generation of CTL Propertiesreachable(MAPK~{p1}))
reachable(!(MAPK~{p1})))
oscil(MAPK~{p1}))&
reachable(MAPKPH-MAPK~{p1}))
reachable(!(MAPKPH-MAPK~{p1})))
oscil(MAPKPH-MAPK~{p1}))
AG(!(MAPKPH-MAPK~{p1})->checkpoint(MAPKPH,MAPKPH-MAPK~{p1})))AG(!(MAPKPH-MAPK~{p1})->checkpoint(MAPK~{p1},MAPKPH-MAPK~{p1})))
&
reachable(MAPK~{p1,p2}))
reachable(!(MAPK~{p1,p2})))oscil(MAPK~{p1,p2}))
&
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29/07/10 François Fages Ecole Jeunes Chercheurs Porquerolles 63
Model Reductions Preserving CTL Properties
After reduction, 20 rules remain.
Deletions:
RAF-RAFK=>RAF+RAFK
RAFPH-RAF~{p1}=>RAFPH+RAF~{p1}
MEK-RAF~{p1}=>MEK+RAF~{p1}
MEKPH-MEK~{p1}=>MEKPH+MEK~{p1}
MAPK-MEK~{p1,p2}=>MAPK+MEK~{p1,p2}
MAPKPH-MAPK~{p1}=>MAPKPH+MAPK~{p1}
MEK~{p1}-RAF~{p1}=>MEK~{p1}+RAF~{p1}
MEKPH-MEK~{p1,p2}=>MEKPH+MEK~{p1,p2}
MAPK~{p1}-MEK~{p1,p2}=>MAPK~{p1}+MEK~{p1,p2}
MAPKPH-MAPK~{p1,p2}=>MAPKPH+MAPK~{p1,p2}
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29/07/10 François Fages Ecole Jeunes Chercheurs Porquerolles 64
Model Reduction as Reaction Graph Morphism
011_levc
MAPK models from SBML model repository http://www.biomodels.net
A graphical method for reducing and relating models [Gay Fages Soliman 2010 ECCB, Bioinformatics]4 graph operations: Delete/Merge Molecules/Reactions subgraph morphisms
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29/07/10 François Fages Ecole Jeunes Chercheurs Porquerolles 65
Languages for Cell Systems Biology
Qualitative models: from diagrammatic notation to
" Boolean networks [Thomas 73]
" Petri Nets [Reddy 93]
" Milner� s π� calculus [Regev-Silverman-Shapiro 99-01, Nagasali et al. 00]
" Bio-ambients [Regev-Panina-Silverman-Cardelli-Shapiro 03]
" Pathway logic [Eker-Knapp-Laderoute-Lincoln-Meseguer-Sonmez 02]
" Reaction rules [Chabrier-Chiaverini-Danos-Fages-Schachter 04] BIOCHAM-1, Kappa
Quantitative models: from differential equation systems to
" Hybrid Petri nets [Hofestadt-Thelen 98, Matsuno et al. 00]
" Hybrid automata [Alur et al. 01, Ghosh-Tomlin 01]
" Hybrid concurrent constraint languages [Bockmayr-Courtois 01]
" Stochastic π� calculus [Priami 03, Cardelli 04]
" Rules with continuous/stochastic dynamics BIOCHAM-2, BioNetGen,&
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29/07/10 François Fages Ecole Jeunes Chercheurs Porquerolles 66
A Logical Paradigm for Systems Biology
Biological process model = Concurrent Transition System
Biological property = Temporal Logic Formula
Biological validation = Model-checking
" [Lincoln et al. PSB� 02] [Chabrier Fages CMSB� 03] [Bernot et al. TCS� 04] &
Model: BIOCHAM Biological Properties:
- Boolean - simulation - Temporal logic CTL
- Differential - query evaluation - LTL(R), QFLTL(R) constraints
- Stochastic - rule learning - CSL
(SBML) - parameter search
Abstractions:
- Influence graph, reductions
A Logical Paradigm for Systems Biology
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29/07/10 François Fages Ecole Jeunes Chercheurs Porquerolles 67
A Programmer View at Cell ComputationsSize of genome
" 5 Mb for bacteria: normal size program (Biocham binary: 15Mb as yeast)
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29/07/10 François Fages Ecole Jeunes Chercheurs Porquerolles 68
A Programmer View at Cell ComputationsSize of genome
" 5 Mb for bacteria: normal size program (Biocham binary: 15Mb as yeast)
" 3 Gb for human: normal size of a video not for a program
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29/07/10 François Fages Ecole Jeunes Chercheurs Porquerolles 69
A Programmer View at Cell ComputationsSize of genome
" 5 Mb for bacteria: normal size program (Biocham binary: 15Mb as yeast)
" 3 Gb for human: normal size of a video not for a program
" 140 Gb for lung fish: nature/disk error !
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29/07/10 François Fages Ecole Jeunes Chercheurs Porquerolles 70
A Programmer View at Cell ComputationsSize of genome
" 5 Mb for bacteria: normal size program (Biocham binary: 15Mb as yeast)
" 3 Gb for human: normal size of a video not for a program
" 140 Gb for lung fish: nature/disk error !
Speed of interactions
" Protein interactions: enzyme-substrate collisions at 0,5 Mhz, quite slow
" Gene expression: hours ! as reinstalling an operating system
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29/07/10 François Fages Ecole Jeunes Chercheurs Porquerolles 71
A Programmer View at Cell ComputationsSize of genome
" 5 Mb for bacteria: normal size program (Biocham binary: 15Mb as yeast)
" 3 Gb for human: normal size of a video not for a program
" 140 Gb for lung fish: nature/disk error !
Speed of interactions
" Protein interactions: enzyme-substrate collisions at 0,5 Mhz, quite slow
" Gene expression: hours ! as reinstalling an operating system
Concurrent computation paradigm
" Chemical metaphor for concurrent programming [Banatre, Le Metayer 78]
" CHAM [Berry 85] to express the operational semantics of the Pi-Calculus
" Membranes for modules: just like cell compartments
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A Programmer View at Cell ComputationsSize of genome
" 5 Mb for bacteria: normal size program (Biocham binary: 15Mb as yeast)
" 3 Gb for human: normal size of a video not for a program
" 140 Gb for lung fish: nature/disk error !
Speed of interactions
" Protein interactions: enzyme-substrate collisions at 0,5 Mhz, quite slow
" Gene expression: hours ! as reinstalling an operating system
Concurrent computation paradigm
" Chemical metaphor for concurrent programming [Banatre, Le Metayer 78]
" CHAM [Berry 85] to express the operational semantics of the Pi-Calculus
" Membranes for modules: just like cell compartments
Hybrid continuous+discrete computations (energy + information)
" Trend for future: more physics in informatics, more informatics in physics
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Two-stroke Engine with ATP fuel Myosin + ATP => MyosinATP
MyosinATP => Myosin + ADP
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Two-stroke Engine with ATP fuel Myosin + ATP => MyosinATP
MyosinATP => Myosin + ADP
http://www.sci.sdsu.edu/movies
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Two-stroke Engine with ATP fuel Myosin + ATP => MyosinATP
MyosinATP => Myosin + ADP
http://www.sci.sdsu.edu/movies
http://www-rocq.inria.fr/sosso/icema2
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Two-stroke Engine with ATP fuel Myosin + ATP => MyosinATP
MyosinATP => Myosin + ADP
Actin-Myosin microtubule contraction controlled by MPF that phosphorylates myosin