Idea: apply Formal Methods of Program Verification to Systems Biology,

François Fages MPRI Bio-info 2006

Formal Biology of the CellModeling, Computing and Reasoning with

Constraints

François Fages, Constraint Programming Group, INRIA Rocquencourt

mailto:[email protected]://contraintes.inria.fr/

Idea: apply • Formal Methods of Program Verification to Systems Biology,• Constraint Logic Programming and Constraint-based Model

Checking

In course, • Learn bits of Biology through computational models,• Study new formalisms, languages and … implementations.


Systems Biology

•Multidisciplinary field aiming at getting over

the complexity walls to reason about

biological processes at the system level.

• Conferences ICSB, CMSB, … journal TCSB

•Virtual cell: emulate high-level biological processes in terms of their biochemical basis at the molecular level (in silico experiments)

•Bioinformatics: end 90’s, genomic sequences post-genomic data (RNA expression, protein synthesis, protein-protein interactions,… )

•Need for a strong effort on:

- the formal representation of biological processes,

- formal tools for modeling and reasoning about their global behavior.


Language Approach to 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]

• Transition systems [Chabrier-Chiaverini-Danos-Fages-Schachter 04]

Biochemical abstract machine BIOCHAM-1 [Chabrier-Fages 03]

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]

• Rules with continuous dynamics BIOCHAM-2 [Chabrier-Fages-Soliman 04]


The Biochemical Abstract Machine BIOCHAM

Software environment based on two formal languages:

1. Biocham Rule Language for Modeling Biochemical Systems 1. Syntax of molecules, compartments and reactions

2. Semantics at 3 abstraction levels: Boolean, Concentrations, Populations

2. Biocham Temporal Logic for Formalizing Biological Properties1. CTL for Boolean semantics

2. Constraint LTL for Concentration semantics

Machine learning Rules and Parameters from Temporal Properties1. Learning reaction rules from CTL specification

2. Learning kinetic parameter values from Constraint-LTL specification

Internship topics: http://contraintes.inria.fr


Overview of the Lectures

1. Introduction. Formal molecules and reactions in BIOCHAM.

2. Formal biological properties in temporal logic. Symbolic model-checking.

3. Continuous dynamics. Kinetics and transport models.

4. Computational models of the cell cycle control.

5. Abstract interpretation and typing of biochemical networks

6. Machine learning reaction rules from temporal properties.

7. Constraint-based model checking. Learning kinetic parameter values.

8. Constraint Logic Programming approach to protein structure prediction.


References

A wonderful textbook:

Molecular Cell Biology. 5th Edition, 1100 pages+CD, Freeman Publ.

Lodish, Berk, Zipursky, Matsudaira, Baltimore, Darnell. Nov. 2003.

Modeling dynamic phenomena in molecular and cellular biology.

Segel. Cambridge Univ. Press. 1987.

Modeling and querying bio-molecular interaction networks.

Chabrier, Chiaverini, Danos, Fages, Schächter. Theoretical Computer Science 04

The Biochemical Abstract Machine BIOCHAM. Chabrier, Fages, Solimanhttp://contraintes.inria.fr/BIOCHAM


Map of Course 1

1. Introduction

2. BIOCHAM syntax• Proteins: complexation and phosphorylation

• DNA: replication and transcription

• Reaction and transport rules

3. Boolean semantics: concurrent transition system, Kripke structure• States and transitions

• Examples: RTK membrane receptors, MAPK signaling pathways


2. Syntax: a Simple Algebra of 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)


Structure Levels of 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 helix, strands, random coils,… (3m-10m)

stabilized by hydrogen bonds H---O

3) Tertiary 3D structure: spatial folding

stabilized by

hydrophobic

interactions


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)

BIOCHAM syntax


Deoxyribonucleic Acid DNA

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

DNA replication: separation of the two helices and

production of one complementary strand for each copy


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


DNA: Genome Size


E. Coli (bacteria) 5 Mb 1 circular 100 %


Mouse, Human 3 Gb 20, 23 15 %

… 15 Gb

… 140 Gb

3,200,000,000 pairs of nucleotides

single nucleotide polymorphism 1 / 2kb


Genome Size


E. Coli (bacteria) 4 Mb 1 100 %



Onion 15 Gb 8 1 %

… 140 Gb


Genome Size


E. Coli (bacteria) 4 Mb 1 100 %



Onion 15 Gb 8 1 %

Lungfish 140 Gb 0.7 %


Transcription: DNA pre-mRNA mRNA Protein

Genes: parts of DNA 1. Activation: transcription factors bind to the

regulatory region of the gene2. 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. Protein synthesis: mRNA moves to cytoplasm and binds to ribosome to assemble a protein

_ =[#E2-E2F13-DP12]=> pRNAcycA


BIOCHAM Syntax of Objects

E == compound | E-E | E~{p1,…,pn}

Compound: molecule, #gene binding site, abstract @process…

- : 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, …)

S == _ | O+S

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


Seven Fundamental 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]=> _.

_=[#Ge2-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


BIOCHAM Syntax of Reaction Rules

R ::= S=>S | S=[O]=>S | S<=>S | S<=[O]=>S

where A=[C]=>B stands for A+C=>B+C

A<=>B stands for A=>B and B=>A, etc.

N ::= kinetic for R (import/export SBML format)

Three abstraction levels:

1. Boolean Semantics: presence-absence of molecules1. Concurrent Transition System (asynchronous, non-deterministic)

2. Concentration Semantics: number / volume of diffusion1. Ordinary Differential Equations or Hybrid system (deterministic)

• Stochastic Semantics: number of molecules • Continuous time Markov chain


The Actin-Myosin two-stroke Engine with ATP fuel Myosin + ATP => Myosin-ATP

Myosin-ATP => Myosin + ADP

http://www.sci.sdsu.edu/movies











Myosin-ATP => Myosin + ADPhttp://www.sci.sdsu.edu/movies

http://www-rocq.inria.fr/sosso/icema2


Cell to Cell Signaling by Hormones and Receptors

Signals: insulin, adrenaline, steroids, EGF, …, Delta, …, nutriments, light, pressure, …

Receptors: tyrosine kinases, G-protein coupled, Notch, …

L + R <=> L-R

RAS-GDP =[L-R]=> RAS-GTP


Five MAP Kinase Pathways in Budding Yeast

(Saccharomyces Cerevisiae)


MAPK Signaling Pathways

Input:

RAF

• Activated by the receptor RAF-p14-3-3 + RAS-GTP

=> RAF + p14-3-3 + RAS-GDP

Output:

MAPK~{T183,Y185}

• moves to the nucleus

• phosphorylates a transcription factor

• which stimulates gene transcription


MAPK Signaling Pathway in BIOCHAMRAF + RAFK <=> RAF-RAFK.RAF-RAFK => RAFK + RAF~{p1}.RAF~{p1} + RAFPH <=> RAF~{p1}-RAFPH.RAF~{p1}-RAFPH => RAF + RAFPH. MEK~$P + RAF~{p1} <=> MEK~$P-RAF~{p1} where p2 not in $P.MEK~{p1}-RAF~{p1} => MEK~{p1,p2} + RAF~{p1}.MEK-RAF~{p1} => MEK~{p1} + RAF~{p1}. MEKPH + MEK~{p1}~$P <=> MEK~{p1}~$P-MEKPH.MEK~{p1}-MEKPH => MEK + MEKPH.MEK~{p1,p2}-MEKPH => MEK~{p1} + MEKPH.MAPK~$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}.

Pattern variables $P for

• Phosphorylation sites

• Molecules

with constraints

BIOCHAM rules are expanded in BIOCHAM-0 rules without patterns


Bipartite Proteins-Reactions Graph of MAPK

GraphVizhttp://www.research.att.co/sw/tools/graphviz


Random Boolean Simulation of MAPK Signaling


Numerical simulation of MAPK in BIOCHAM-2


Boolean Semantics

Associate:

• Boolean state variables to molecules

denoting the presence/absence of molecules in the cell or compartment

• A Finite concurrent transition system [Shankar 93] to rules (asynchronous) over-approximating the set of all possible behaviors

A reaction A+B=>C+D is translated into 4 transition rules for the possibly complete consumption of reactants:

A+BA+B+C+D

A+BA+B +C+D

A+BA+B+C+D

A+BA+B+C+D


Kripke Structure K=(S,R)

Given:

V is a set of state variables, with domain D,

T a set of transition rules between states.

Associate:

a Kripke structure (S,R) where

S=DV is the set of possible states with variables ranging in domain D

RSxS is the total relation induced by T, that is

(A,B) is in R if there exists a transition rule from state A to B

(A,A) is in R if there exist no transition from state A.

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Idea: apply Formal Methods of Program Verification to Systems Biology,