computational methods for systems and synthetic...

20/10/10 François Fages MPRI C219 1

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 Grouphttp://contraintes.inria.fr/


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)


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


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!


DNA: Genome Size

140 Gb&

15 Gb&

3 Gb&

70 %1612 MbS. Cerevisae (yeast)




DNA: Genome Size

140 Gb&

15 Gb&

15 %20, 233 GbMouse, Human




3,200,000,000 pairs of nucleotides

single nucleotide polymorphism 1 / 2kb


Genome Size

140 Gb&

1 %815 GbOnion



100 %14 MbE. Coli (bacteria)



Genome Size

0.7 %140 GbLungfish

1 %815 GbOnion



100 %14 MbE. Coli (bacteria)



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)


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


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


Transcription and Translation Rules

Activation

#E2 + E2f13DP12 => #E2E2f13DP12Repression

#E2 + Rep => #E2Rep

Genes and signals [Ptashne Gann 01]



Activation


#E2 + Rep => #E2RepTranscription

_ =[#E2E2F13DP12]=> pRNAcycA



Activation



_ =[#E2E2F13DP12]=> pRNAcycA(Alternative) Splicing

pRNAcycA => mRNAcycA (pRNAcycA => mRNAcycA2)



Activation



_ =[#E2E2F13DP12]=> pRNAcycA(Alternative) Splicing

pRNAcycA => mRNAcycA (pRNAcycA => mRNAcycA2) Translation

mRNAcycA => mRNAcycA::cyt mRNAcycA::cyt =[ribosome::cyt]=> cycA::cyt(mRNAcycA2::cyt =[ribosome::cyt]=> cycA2::cyt)


Proteins

1) Primary structure: word of n amino acids residues (20n possibilities)

linked with C-N bonds


Proteins



Example: MPRI

Methionine-Proline-Arginine-Isoleucine


Proteins



Example: MPRI


2) Secondary: word of m α−helix, β−strands, random coils,& (3m-10m)

stabilized by hydrogen bonds H---O


Proteins



Example: MPRI


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


Formal Proteins: Syntax" Cyclin dependent kinase 1 Cdk1

(free, inactive)



(free, inactive)

" Complex Cdk1-Cyclin B Cdk1–CycB(low activity)



(free, inactive)


" Phosphorylated form Cdk1~{thr161}CycBat site threonine 161

(high activity)


Formal Proteins" Cyclin dependent kinase 1 Cdk1

(free, inactive)


" Phosphorylated form Cdk1~{thr161}CycBat site threonine 161

(high activity)

�Mitosis-Promoting Factor�

phosphorylates actin in microtubules nuclear division


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)







" 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


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)


Biocham Syntax of Objects Entities E == name | #name | EE | 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


Biocham Syntax of RulesSolutions S ::= _ | O + S | i*O + S

+ : solution operator (Associative, Commutative, Neutral element _)

Rules R ::= S => S | kineticexpression 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


Biocham Models

A Biocham model is a finite set of Biocham rules

Questions:

" Decidability properties ?

" Which type of chemical reactions cannot be represented ?

" Which type of locations cannot be represented ?


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


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


Semantics of Rule-based Models

Reaction rule k*[A]*[B] for A+B => C" 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)





dB/dt = -k*[A]*[B]

dC/dt = k*[A]*[B]


" Stochastic Semantics: numbers of molecules

� Continuous time Markov chain A, B p A--, B--, C++





dB/dt = -k*[A]*[B]

dC/dt = k*[A]*[B]


" Stochastic Semantics: numbers of molecules

� Continuous time Markov chain A, B p A--, B--, C++

" Boolean Semantics: presence-absence of molecules

� Asynchronous Transition System A, B C, A/¬A, B/¬B


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


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)



Regulation Graph Circuit Analyses

Discrete model

abstraction

concretization

Boolean model

Syntactical

model

Jacobian circuit analysis

Discrete circuit analysis

Boolean circuit analysisabstraction

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]


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