Transcript Computational Methods in Systems Biology and Synthetic Biology François Fages, Constraint Programming Group INRIA Paris-Rocquencourt mailto:[email protected] http://contraintes.inria.fr/ 06/11/2015 François Fages C2-19 MPRI.

Computational Methods in
Systems Biology and Synthetic Biology
François Fages,
Constraint Programming Group
INRIA Paris-Rocquencourt
mailto:[email protected]
http://contraintes.inria.fr/
06/11/2015
François Fages C2-19 MPRI
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Overview of the Lectures
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4.
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Formal molecules and reaction models in BIOCHAM
Kinetics
Qualitative properties formalized in temporal logic CTL
Quantitative properties formalized in LTL(R) and PLTL(R)
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References
A wonderful textbook:
Molecular Cell Biology. 5th Edition, 1100 pages+CD, Freeman Publ.
Lodish, Berk, Zipursky, Matsudaira, Baltimore, Darnell. Nov. 2003.
The Biochemical Abstract Machine BIOCHAM. http://contraintes.inria.fr/BIOCHAM
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)
Modeling dynamic phenomena in molecular and cellular biology.
Segel. Cambridge Univ. Press. 1987.
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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)
– RNA (102-104 nucleotides AGCU)
– DNA (102-106 nucleotides AGCT)
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Proteins
1) Primary structure: word of n amino acids residues (20n possibilities)
linked with C-N bonds
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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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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 a-helix, b-strands, random coils,… (3m-10m)
stabilized by hydrogen bonds H---O
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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 a-helix, b-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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Formal Proteins
• Cyclin dependent kinase 1
Cdk1
(free, inactive)
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Formal Proteins
• Cyclin dependent kinase 1
Cdk1
(free, inactive)
• Complex Cdk1-Cyclin B
(low activity)
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Cdk1–CycB
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Formal Proteins
• Cyclin dependent kinase 1
Cdk1
(free, inactive)
• Complex Cdk1-Cyclin B
(low activity)
• Phosphorylated form
Cdk1–CycB
Cdk1~{thr161}-CycB
at site threonine 161
(high activity)
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Formal Proteins
• Cyclin dependent kinase 1
Cdk1
(free, inactive)
• Complex Cdk1-Cyclin B
(low activity)
Cdk1–CycB
Nuclear division
• Phosphorylated form
Cdk1~{thr161}-CycB
at site threonine 161
(high activity)
“Mitosis-Promoting Factor”
phosphorylates actin in microtubules
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Complexation and Phosphorylation Rules
• Complexation
Cdk1 + CycB => Cdk1-CycB
• Decomplexation
Cdk1-CycB => Cdk1 + CycB
• Phosphorylation
Cdk1-CycB =[Myt1]=> Cdk1~{thr161}-CycB
• Dephosphorylation
Cdk1~{thr14,tyr15}-CycB =[Cdc25~{Nterm}]=> Cdk1-CycB
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DNA Deoxyribonucleic Acid
1) Primary structure: word over 4 nucleotides
Adenine, Guanine, Cytosine, Thymine
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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
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DNA: Genome Size
Species
Genome size
Chromosomes
Coding DNA
E. Coli (bacteria)
5 Mb
1 circular
100 %
S. Cerevisae (yeast)
12 Mb
16
70 %
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…
3 Gb
…
15 Gb
…
140 Gb
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DNA: Genome Size
Species
Genome size
Chromosomes
Coding DNA
E. Coli (bacteria)
5 Mb
1 circular
100 %
S. Cerevisae (yeast)
12 Mb
16
70 %
Mouse, Human
3 Gb
20, 23
15 %
…
15 Gb
…
140 Gb
3,200,000,000 pairs of nucleotides
single nucleotide polymorphism 1 / 2kb
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Genome Size
Species
Genome size
Chromosomes
Coding DNA
E. Coli (bacteria)
4 Mb
1
100 %
S. Cerevisae (yeast)
12 Mb
16
70 %
Mouse, Human
3 Gb
20, 23
15 %
Onion
15 Gb
8
1%
…
140 Gb
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Genome Size
Species
Genome size
Chromosomes
Coding DNA
E. Coli (bacteria)
4 Mb
1
100 %
S. Cerevisae (yeast)
12 Mb
16
70 %
Mouse, Human
3 Gb
20, 23
15 %
Onion
15 Gb
8
1%
Lungfish
140 Gb
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0.7 %
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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)
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Transcription and Translation
1. Activation (Inhibition):
Nobel prize Jakob and Monod
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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Formal Genes
• Part of DNA, unique
• Activation
binding of promotion factor
• Repression (inhibition)
binding of another molecule
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#E2
#E2-E2f13-DP12
#E2-Rep
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Transcription and Translation Rules
Activation
#E2 + E2f13-DP12 => #E2-E2f13-DP12
Repression
#E2 + Rep => #E2-Rep
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Transcription and Translation Rules
Activation
#E2 + E2f13-DP12 => #E2-E2f13-DP12
Repression
#E2 + Rep => #E2-Rep
Transcription
_ =[#E2-E2F13-DP12]=> pRNAcycA
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Transcription and Translation Rules
Activation
#E2 + E2f13-DP12 => #E2-E2f13-DP12
Repression
#E2 + Rep => #E2-Rep
Transcription
_ =[#E2-E2F13-DP12]=> pRNAcycA
(Alternative) Splicing
pRNAcycA => mRNAcycA
pRNAcycA => mRNAcycA2
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Transcription and Translation Rules
Activation
#E2 + E2f13-DP12 => #E2-E2f13-DP12
Repression
#E2 + Rep => #E2-Rep
Transcription
_ =[#E2-E2F13-DP12]=> pRNAcycA
(Alternative) Splicing
pRNAcycA => mRNAcycA
pRNAcycA => mRNAcycA2
Translation
mRNAcycA => mRNAcycA::cyt
mRNAcycA::cyt + ribosome::cyt => cycA::cyt + ribosome::cyt
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BIOCHAM Syntax of Objects
E == compound | E-E | E~{p1,…,pn}
• compound: 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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BIOCHAM Syntax of Rules
S == _ | O+S
+ : solution operator (Associative, Commutative, Neutral _)
R ::= S => S | kinetic-expression for R
Abbreviations
A =[C]=> B stands for A+C => B+C
A <=> 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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Elementary Rule Schemas
• Complexation: A + B => A-B.
cdk1+cycB => cdk1–cycB
Decomplexation A-B => A + B.
• Phosphorylation: A =[C]=> A~{p}.
Dephosphorylation A~{p} =[C]=> A.
Cdk1-CycB =[Myt1]=> Cdk1~{thr161}-CycB
Cdk1~{thr14,tyr15}-CycB =[Cdc25~{Nterm}]=> Cdk1-CycB
• Synthesis: _ =[C]=> A.
_=[#E2-E2f13-Dp12]=>cycA
Degradation: A =[C]=> _.
cycE =[@UbiPro]=> _
(not for cycE-cdk2 which is stable)
• Transport: A::L1 => A::L2.
Cdk1~{p}-CycB::cytoplasm=>Cdk1~{p}-CycB::nucleus
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From Syntax to Semantics
1. Boolean Semantics: presence-absence of molecules
– Concurrent Transition System (asynchronous, non-deterministic)
2. Continuous Semantics: concentrations
– Ordinary Differential Equations
– Hybrid system (deterministic)
3. Stochastic Semantics: numbers of molecules
– Continuous time Markov chain
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Two-stroke Engine with ATP fuel
Myosin + ATP => Myosin-ATP
Myosin-ATP => Myosin + ADP
•
http://www.sci.sdsu.edu/movie
s
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Two-stroke Engine with ATP fuel
Myosin + ATP => Myosin-ATP
Myosin-ATP => Myosin + ADP
http://www.sci.sdsu.edu/movies
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Two-stroke Engine with ATP fuel
Myosin + ATP => Myosin-ATP
Myosin-ATP => 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 => Myosin-ATP
Myosin-ATP => Myosin + ADP
Actin-Myosin microtubule contraction
controlled by MPF that phosphorylates
myosin
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Two-stroke Engine with ATP fuel
Myosin + ATP => Myosin-ATP
Myosin-ATP => Myosin + ADP
Actin-Myosin muscle contraction
controlled by ion Ca2+
http://www-rocq.inria.fr/sosso/icema2
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Cell Signaling
• Signals:
– hormones: insulin, adrenaline, steroids, EGF, …,
– neighboring cell membrane proteins: Delta
– nutriments, light, pressure, …
• Receptors:
– Tyrosine kinases,
– G protein-coupled,
– TGFβ,
– Notch,
– …
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Receptor Tyrosine Kinase RTK
L + R <=> L-R
L-R + L-R => L-R-L-R
RAS-GDP =[L-R-L-R]=> RAS-GTP
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Five MAP Kinase Pathways
in Budding Yeast
(Saccharomyces Cerevisiae)
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MAPK Signaling Pathways
• Input:
RAS activated by the receptor
activates RAF
RAS-GTP + RAF-P14-3-3 =>
RAS-GDP + RAF + P14-3-3
• Output:
active MAPK moves to the nucleus
phosphorylates a transcription
factor which stimulates gene
expression
RAF + … => …
… => MAPK~{T183,Y185}
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Three Levels MAPK Cascade
RAF


RAF~{p1}
MEK
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
MEK~{p1}
 MEK~{p1,p2}

MAPK 

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MAPK~{p1}  MAPK~{p1,p2}
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MAPK Signaling Cascade in BIOCHAM
RAF + RAFK <=> RAF-RAFK.
Pattern variables $P for
RAF-RAFK => RAFK + RAF~{p1}.
- Phosphorylation sites
RAF~{p1} + RAFPH <=> RAF~{p1}-RAFPH.
- Molecules
RAF~{p1}-RAFPH => RAF + RAFPH.
MEK~$P + RAF~{p1} <=> MEK~$P-RAF~{p1}
with symbolic constraints
where p2 not in $P.
MEK~{p1}-RAF~{p1} => MEK~{p1,p2} + RAF~{p1}.
BIOCHAM rules with
MEK-RAF~{p1} => MEK~{p1} + RAF~{p1}.
patterns are expanded
MEKPH + MEK~{p1}~$P <=> MEK~{p1}~$P-MEKPH.
in BIOCHAM rules
MEK~{p1}-MEKPH => MEK + MEKPH.
without patterns
MEK~{p1,p2}-MEKPH => MEK~{p1} + MEKPH.
MAPK~$P + MEK~{p1,p2} <=> MAPK~$P-MEK~{p1,p2}
where p2 not in $P.
MAPKPH + MAPK~{p1}~$P <=> MAPK~{p1}~$P-MAPKPH.
MAPK~{p1}-MAPKPH => MAPK + MAPKPH.
MAPK~{p1,p2}-MAPKPH => MAPK~{p1} + MAPKPH.
MAPK-MEK~{p1,p2} => MAPK~{p1} + MEK~{p1,p2}.
MAPK~{p1}-MEK~{p1,p2} => MAPK~{p1,p2}+MEK~{p1,p2}.
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Bipartite Proteins-Reactions Graph of MAPK
GraphViz
http://www.research.att.co/sw/tools/graphviz
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Influence Graph
Influence Graph inferred from the
syntactical reaction model of the MAPK
“cascade”
Negative feedback loops
[Fages Soliman CMSB 06]
Possibility of oscillations
[Qiao et al. PLOS 07]
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Reaction Model of the MAPK Cascade
[Levchenko et al. PNAS 2000]
(MA(1), MA(0.4)) for RAF + RAFK <=> RAF-RAFK.
(MA(0.5),MA(0.5)) for RAF~{p1} + RAFPH <=> RAF~{p1}-RAFPH.
(MA(3.3),MA(0.42)) for MEK~$P + RAF~{p1} <=> MEK~$P-RAF~{p1}
where p2 not in $P.
(MA(10),MA(0.8)) for MEKPH + MEK~{p1}~$P <=> MEK~{p1}~$P-MEKPH.
(MA(20),MA(0.7)) for MAPK~$P + MEK~{p1,p2} <=> MAPK~$P-MEK~{p1,p2}
where p2 not in $P.
(MA(5),MA(0.4)) for MAPKPH + MAPK~{p1}~$P <=> MAPK~{p1}~$P-MAPKPH.
MA(0.1) for RAF-RAFK => 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 MEK-RAF~{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 MAPK-MEK~{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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Differential Simulation
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Stochastic Simulation
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Boolean Simulation
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Automatic Generation of CTL Properties
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reachable(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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A Logical Paradigm for Systems Biology
Biological process model = Concurrent Transition System
Biological property = Temporal Logic Formula
Biological validation = Model-checking
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[Lincoln et al. PSB’02] [Chabrier Fages CMSB’03] [Bernot et al. TCS’04] …
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Model:
BIOCHAM
- Boolean
- simulation
- Differential
- query evaluation
- Stochastic
- rule learning
(SBML)
- parameter search
Types: static analyses
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Biological Properties:
- Temporal logic CTL
- LTL with constraints
- PCTL with constraints
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The Biochemical Abstract Machine
BIOCHAM
Modeling environment based on two formal languages:
1. Rule Language for Modeling Biochemical Systems
– Syntax of molecules, compartments and reactions
– Semantics at 3 abstraction levels: Boolean, Concentrations, Populations
2. Temporal Logic for Formalizing Biological Properties
– CTL for Boolean semantics
– Constraint LTL for concentration semantics,
– PCTL for stochastic semantics
Learning from Temporal Properties
– Learning reaction rules from CTL specification
– Learning kinetic parameter values from Constraint-LTL specification
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Language Approach to Cell Systems Biology
Qualitative models: from diagrammatic notation to
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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]
Transition systems [Chabrier-Chiaverini-Danos-Fages-Schachter 04] BIOCHAM-1, Kappa
Quantitative models: from differential equation systems to
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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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