computational methods for systems and synthetic...
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Computational Methods for
Systems and Synthetic Biology
François Fages
The French National Institute for Research in
Computer Science and Control
INRIA Paris-Rocquencourt
Constraint Programming Group
http://contraintes.inria.fr/
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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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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
Nobel Prizes Watson and Crick (1956)
Size of DNA = number of pairs
A gene is a sequence of DNA pairs coding for a protein or an RNA having a function in the organism
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DNA: Genome Size
Species Genome size Chromosomes Coding DNA
E. Coli (bacteria) 5 Mb 1 circular 100 %
12 Mb
… 3 Gb
… 15 Gb
… 140 Gb
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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DNA: Genome Size
Species Genome size Chromosomes Coding DNA
E. Coli (bacteria) 5 Mb 1 circular 100 %
S. Cerevisae (yeast) 12 Mb 16 70 %
… 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 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)
3. Segregation
4. Mitosis (cell division)
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Gene Transcription and Translation
1. 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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Formal Genes: Syntax
• Part of DNA #E2
• Activation
binding of promotion factor #E2-(E2f13-DP12)
• Repression (inhibition) Genes and signals [Ptashne Gann 01]
binding of another molecule #E2-Rep
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Transcription and Translation Rules
Activation
#E2 + E2f13-DP12 => #E2-E2f13-DP12
Repression
#E2 + Rep => #E2-Rep
Genes and signals [Ptashne Gann 01]
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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
(mRNAcycA2::cyt =[ribosome::cyt]=> cycA2::cyt)
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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: Syntax
• Cyclin dependent kinase 1 Cdk1
(free, inactive)
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Formal Proteins: Syntax
• Cyclin dependent kinase 1 Cdk1
(free, inactive)
• Complex Cdk1-Cyclin B Cdk1–CycB
(low activity)
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Formal Proteins: Syntax
• Cyclin dependent kinase 1 Cdk1
(free, inactive)
• Complex Cdk1-Cyclin B Cdk1–CycB
(low activity)
• Phosphorylated form 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 Cdk1–CycB
(low activity)
• Phosphorylated form Cdk1~{thr161}-CycB
at site threonine 161
(high activity)
“Mitosis-Promoting Factor”
phosphorylates actin in microtubules nuclear division
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Elementary Rule Schemas
• Complexation: A + B => A-B. Decomplexation A-B => A + B.
cdk1+cycB => cdk1–cycB
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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.
Cdk1-CycB =[Myt1]=> Cdk1~{thr161}-CycB
Cdk1~{thr14,tyr15}-CycB =[Cdc25~{Nterm}]=> Cdk1-CycB
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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.
Cdk1-CycB =[Myt1]=> Cdk1~{thr161}-CycB
Cdk1~{thr14,tyr15}-CycB =[Cdc25~{Nterm}]=> Cdk1-CycB
• Synthesis: _ =[C]=> A. Degradation: A =[C]=> _.
_=[#E2-E2f13-Dp12]=>cycA cycE =[@UbiPro]=> _
(not for cycE-cdk2 which is stable)
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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.
Cdk1-CycB =[Myt1]=> Cdk1~{thr161}-CycB
Cdk1~{thr14,tyr15}-CycB =[Cdc25~{Nterm}]=> Cdk1-CycB
• Synthesis: _ =[C]=> A. Degradation: A =[C]=> _.
_=[#E2-E2f13-Dp12]=>cycA 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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Graphical Representation
Hypergraph of reactions represented by a bipartite graph (S,R,A) with
vertices for species S and for reactions R (Petri net representation)
A+B => A-B
Systems Biology Graphical Notation (SBGN)
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Biocham Syntax of Objects
Entities E == name | #name | E-E | E~{p1,…,pn}
name of molecular compound or 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).
Induce a congruence on objects
Objects O == E | E::location
location: symbolic compartment (nucleus, cytoplasm, membrane, …)
dynamic volume
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Biocham Syntax of Rules
Solutions S ::= _ | O + S | i*O + S
+ : solution operator (Associative, Commutative, Neutral element _)
Rules R ::= S => S | kinetic-expression for R
Abbreviations for catalytic reactions: A =[C]=> B stands for A+C => B+C
reversible reactions: A <=> B stands for A=>B and B=>A,
Syntax compatible with the Systems Biology Markup Language SBML
Import/export exchange format for reaction models in XML
Biomodels.net: repository of 241 curated SBML models of cell processes
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Biocham Models
A Biocham model is a finite set of Biocham reaction rules over a finite set of
molecular species.
(a Kappa model is a finite set of Kappa rules over an infinite universe of
molecular species)
Questions:
• Compared to kappa, which type of chemical reactions cannot be
represented ?
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Biocham Models
A Biocham model is a finite set of Biocham reaction rules over a finite set of
molecular species.
(a Kappa model is a finite set of Kappa rules over an infinite universe of
molecular species)
Questions:
• Compared to kappa, which type of chemical reactions cannot be
represented ?
• Which type of locations cannot be represented ?
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Biocham Models
A Biocham model is a finite set of Biocham reaction rules over a finite set of
molecular species.
(a Kappa model is a finite set of Kappa rules over an infinite universe of
molecular species)
Questions:
• Compared to kappa, which type of chemical reactions cannot be
represented ?
• Which type of locations cannot be represented ?
• Decidability properties when rules are interpreted as an asynchronuous
Boolean transition system ? As multiset rewriting?
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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
(cells are 10-100μm long)
• 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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Kinetic Expressions
Mass action law kinetics:
k*[A] for A => B
k*[A]*[B] for A+B => C
k*[A]^m*[B]^n for m*A + n*B => R
…
Michaelis Menten kinetics:
Vm*[A]/(Km+[A]) for A => B
Hill kinetics:
Vm*[A]^n/(Km+[A]^n) for A => B
Guldberg and Waage, 1864
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Semantics of Rule-based Models
Reaction rule k*[A]*[B] for A+B => C
1. Differential Semantics: concentrations
– Ordinary Differential Equations dA/dt = -k*[A]*[B]
dB/dt = -k*[A]*[B]
dC/dt = k*[A]*[B]
– Hybrid automata (for kinetics with conditional expressions)
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14/10/2013 François Fages - MPRI C2-19 37
Semantics of Rule-based Models
Reaction rule k*[A]*[B] for A+B => C
1. Differential Semantics: concentrations
– Ordinary Differential Equations dA/dt = -k*[A]*[B]
dB/dt = -k*[A]*[B]
dC/dt = k*[A]*[B]
– Hybrid automata (for kinetics with conditional expressions)
2. Stochastic Semantics: numbers of molecules
– Continuous time Markov chain A, B p A--, B--, C++
![Page 38: Computational Methods for Systems and Synthetic Biologycontraintes.inria.fr/~fages/BioTeaching/M1.pdf · 14/10/2013 François Fages - MPRI C2-19 32 Biocham Models A Biocham model](https://reader033.vdocuments.site/reader033/viewer/2022060412/5f1128660227001d6f38c513/html5/thumbnails/38.jpg)
14/10/2013 François Fages - MPRI C2-19 38
Semantics of Rule-based Models
Reaction rule k*[A]*[B] for A+B => C
1. Differential Semantics: concentrations
– Ordinary Differential Equations dA/dt = -k*[A]*[B]
dB/dt = -k*[A]*[B]
dC/dt = k*[A]*[B]
– Hybrid automata (for kinetics with conditional expressions)
2. Stochastic Semantics: numbers of molecules
– Continuous time Markov chain A, B p A--, B--, C++
3. Boolean Semantics: presence-absence of molecules
– Asynchronous Transition System A, B C, A/A, B/B
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14/10/2013 François Fages - MPRI C2-19 39
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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14/10/2013 François Fages - MPRI C2-19 40
Regulation Graphs as Abstractions
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)
Stochastic model Differential model
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14/10/2013 François Fages - MPRI C2-19 41
Regulation Graph Circuit Analyses
Discrete model
abstraction
concretization
Boolean model
Syntactical
model
Jacobian circuit analysis
Discrete circuit analysis
Boolean circuit analysis
abstraction
abstraction
abstraction
Thm. Positive (resp. negative) circuits are a necessary condition for multistationarity (resp. oscillations)
[Thomas 81] [Snoussi 89] [Soulé 03] [Remy Ruet Thieffry 05] [Richard 07]
Stochastic model Differential model