Quel type de modlisation pour des interactions entre composants - - PowerPoint PPT Presentation

Quel type de modélisation pour des interactions entre composants biologiques ?

Andrei Doncescu LAAS-UPR8001/Université Paul Sabatier Pierre Siegel LIF Marseille

Why a biological system is complex ?

• Contains many interacting parts
• Interactions are nonlinear
• Contains feedback loops (+/-)
• Cause and effect intermingled
• Driven out of equilibrium
• Evolves in time (not static)
• Usually chaotic
• Can self-organize and adapt

Emergent behavior is what's left after everything else has been explained.”

Biological Reaction or Regulation by Enzymes

• Living Organisms are open systems O.S. that maintein

their particulary form of organization by utilizing large quantities of energy and metter from the environment

• Prigogine demonstrated that OS driven far from

equilibrium display self-ordering tendancies as they receive an input energy

The Analytic Equation

• f the Tree of Life

Biological Reaction

Catabolisme Substrate Anabolisme Substrate

Microorganism Microorganisme Chemical Pounds Heat

EQUATION BILAN

dt dE E   





V

dV e E .



  

V E E

dV r .

  

         

V E V E V

dV dV r dt dV e d . . . 

Flux d’accumulation = Flux net de conversion + Flux net d’échange Formulation : Flux d'accumulation

avec

Flux net de conversion = Soit :

local change in the reaction volume

=

local inflow-outflow

• local

inflow-outflow

storage element

convective transport diffuse transport

Metabolic Dynamic Modelling

• Mass Balance :
• The flux is :

i j j ij i

C r v dt dC . .   

) , ( .

max j j j j j

P C f r r 

Ci = the concentration of metabolite i,  = is the specific growth rate, ij = is the stoichiometric coefficient for this metabolite in reaction j, which occurs at the rate rj.

Since masses were balanced, the equation for extracellular glucose needs to include a conversion factor for the difference between the intracellular volume and the culture volume.

max j

r

Flux maximum

Dynamic Equilibrum

• A reaction rate determines how fast a reaction proceeds, and is

mathematically defined as the change in concentration of a species

• ver the change in time.
• At dynamic equilibrium, reactants are converted to products and

products are converted to reactants at an equal and constant rate.

• Reactions do not necessarily—and most often do not—end up with

equal concentrations. Equilibrium is the state of equal, opposite rates, not equal concentrations.

                            

ACE v v dt ACE d ACP v v dt ACP d GAP v v dt GAP d FDP v v dt FDP d P G v v v dt P G d X v dt GLC d X ACE GLC dt X d

ACS ACK ACK PTA GAPDH ALDO ALDO PFK PDH G PFK PTS PTS ex ex ex

                          2 6 6 ,

6

Glycolise

Glycolysis is a series of reactions that and extract energy from glucose by splitting it into two three-carbon molecules called pyruvates. Glycolysis is an ancient metabolic pathway, meaning that it evolved long ago, and it is found in the great majority of organisms alive today

Pathways (KEGG)

Graph: G=(V,E)

Biological Networks

Glycolysis Pathway

 

 

 

 

                                                             

ACE v v dt ACE d ACP v v dt ACP d GOX v v dt GOX d OAA v v v v dt OAA d MAL v v v v dt MAL d FUM v v v dt FUM d SUC v v v dt SUC d KG v v dt KG d ICIT v v v dt ICIT d AcCoA v v v dt AcCoA d PYR v v v v dt PYR d PEP v v v v v dt PEP d GAP v v dt GAP d FDP v v dt FDP d P G v v v dt P G d X v dt GLC d X ACE GLC dt X d

                                                                             

2 2 2 6 6 ,

Analytical Solution ?

• E. Montseny, A. Doncescu:

Operatorial Parametrizing of Dynamic Systems. 17th IFAC World Congress, July 6-11, 2008, Seoul, Korea.

Time Scalling Transformation

• The causalities:

1.con(A,up,ti) react(A,B) act(A,B) react(B,C) ¬act(B,C) → con(B,up,ti+1) 2.con(A,up,tj) react(A,B) ¬act(A,B) react(B,C) act(B,C) → con(B,down,tj+1) 3.con(A,down,tk) react(A,B) act(A,B) → con(B,down, tk+1)

Where :

• con(X, up/down,tx): the concentration of A is increase/decreased at time tx.
• act(A,B): metabolite A is consumed for the production of B
• ¬act(A,B): A is not consumed during B production

Knowledge Representation in System Biology

Automated hypothesis-finding in Systems Biology

(Doncescu ILP ‘09)

• 1.00E-01

Hypothesis Finder

SOLAR

Hypothesis Evaluator

BDD-EM

Observations Background Knowledge Best Hypotheses Hypotheses Pathway Model

(Qualitative / Kinetic)

Pathway Data

(from lab + KEGG)

Pathway Analysis

B H |= O

discretization hypothesis ranking

Best Student Paper Award Certificate : International Conference on Bioinformatics Models, Methods and Algorithms, January 26-29, 2011 Rome Italy, pour le papier : « Kinetic Models and Qualitative Abstraction for Relational Learning in System Biology »

• G. Synnaeve, K.Inoue, A. Doncescu, T. Sato.

Causal Graphs Solution of Biological Systems Representation

Network motifs in Genetics

5 4 1 2 3

Incoherent feed-forward double path 3-switch Incoherent double loop Negative regulon Positive regulon

• U. Alon Nature Rev. Genetics (2007)

Biological Networks

• Gene regulatory network: two genes are connected if

the expression of one gene modulates expression of another one by either activation or inhibition

• Protein interaction network: proteins that are

connected in physical interactions or metabolic and signaling pathways of the cell;

• Metabolic network: metabolic products and

substrates that participate in one reaction and/or metabolic pathway;

Machine Learning applications in Molecular Biology

18

Scientific Reasoning

Hypothesis Generation Prediction Observation

Deduction Verification Abduction

Evidential reasoning effect/cause Causal Reasoning cause/effect Simulation

In Machine Learning 3 criteria have been traditionally used to compare And select hypothesis : consistency, completeness and simplicity

Causal Reasoning

Abduction reciprocal of Deduction

Abduction is often viewed as inference to the “best explanation”

The computation has the following basic form : extract from the given theory T a hypothesis and check this for consistency

Abduction: logical framework

Input:

B : background theory G : observations Γ : possible causes (abducibles)

Output:

H : hypothesis satisfying that

• B  H ╞ G
• B  H is consistent
• H is a set of instances of literals from Γ.

Inverse Entailment (IE) Computing a hypothesis H can be done deductively by: B ￢ G ￢ H We use a consequence finding technique for IE computation.

B H

Abductive engine

G

Consequence finding

Given an axiom set, the task of consequence finding is to find out some theorems of interest.

• How to find only interesting conclusions?
• Production field and characteristic clauses
• Production field P = <L, Cond >

– L : the set of literals to be collected – Cond : the condition to be satisfied (e.g. length) ThP(Σ) : the clauses entailed by Σ which belong to P.

• Characteristic clause C of Σ (wrt P ):

– C belongs to ThP(Σ) ; – no other clause in ThP(Σ) properly subsumes C. Carc(Σ, P) : the characteristic clauses of Σ wrt P.

SOL-resolution (Siegel 1988)

■ Computing Carc(Σ，P) where Σ is a given axiom set and

P is a production field

■ Composed of three operations Skip, Reduction, Extension

(An extension of SLD-resolution with Skip operation)

■ Preserving the soundness and completeness for finding characteristic

clauses． Suppose an axiom set Σ and a production field P as follows． Σ = B ¬E = { g ← c1 e1, c2 ← c1, e2 ← c2 , c3 ← c2 e2 , ¬g }, P = < {¬c1, ¬e1, c3}, max_length =2 >.

SOLAR: SOL tableau (Inoue 1992)

• Generating a tableau where the root is labeled by a clause in the axiom

set

• Extending the tableau using those three operations

¬g ¬c1 g ¬e1

*

skipped skipped ¬c1 skipped skipped c2 e2 ¬c2

* *

¬e2 c3 ¬c2 reduction

*

Σ = B ¬E = {g ← c1 e1, c2 ← c1, e2 ← c2 , c3 ← c2 e2 , ¬g} P = < {¬c1, ¬e1, c3}, max_length =2 >

The characteristic clause false← c1 e1is found. Another clause c3 ← c1is found

Hypothesis finding with SOL-resolution

B = { g ← c1 e1, c2 ← c1, e2 ← c2 , c3 ← c2 e2 }, E = { g }.

• 1. Construct an intermediate formula CC1.

Let CC1 be a clausal theory {← c1 e1}．

• 2. Translate ￢CC1 (DNF) into a CNF formula F1.

F1 = {c1, e1}.

■ In the case of H2 = {c1, e1←c3}

■ In the case of H1 = { c1, e1 }

• 1. Construct an intermediate formula CC2.

CC2 = {← c1 e1 , c3 ← c1}

• 2. Translate ￢CC1 (DNF) into a CNF formula F2.

F2 = {c1, c1 ← c3 , c1 e1 , e1 ← c3}

c1 e2 g c2 e1 c3

and and

Redundant clauses

• Default Logic: Ray Reiter 1980 (le papier le plus cité

en A.I.)

• Circumscription : McCarthy 1980
• Preferential approach
• Answer sets ….

Nonmnotonic Reasoning

 Défaut semi-normal : Si A(X) est » vérifié » et il est possible que B(X) et C(X) soient VRAIE, Alors infère C(X).

D  A X

  : B(X)C X  

C X

 

prérequis justification conséquence

Biological Knowledge Representation using Defaults

26/35

 Défaut sans prérequis  Défaut Normal sans prérequis :  L’hypothèse du monde clos exprimée en Logique des Défauts :

D  : B(X) C X

 

D  :C(X) C X

  TRUE :Ø Ø

Raisonnement par Default

27/35

 Exception Rule:  Activation :

a : Øb g activation(X,Y,T): Øinhibition(X,T 1) activation(X,Y,T 1)

Biological Knowledge Representation using Defaults

28/35

 Entrée : E = W; (extension E). calcul_extension(E) : { (1) tant que a un défaut non inspecté (2) Selection du defaut d D, (3) Verification que A W (4) Verification que ¬Bi W (i = 1..n) (5) Ajouter C à W (6) End tant que (7) Fin du calcul d’extension.

}

Logique des Défauts: Calcul des Extensions de la Théorie de Défauts Normaux Δ=(W,D)

29/35

Abduction Problem: How cancer could be blocked using a candidate RhoB ?

X

UV

cancer p53 A B Mdm2

Defaults D:

 d1 = UV : cancer / cancer  d2 = UV : p53 / p53  d3 = p53 : A / A  d4 = p53 Mdm2: B / B  d5 = B : ¬A / ¬A  d6 = A : ¬cancer / ¬cancer  d7 = C : ¬B / ¬B

d8 = Y : X /X ;

• ù Y

{UV, Mdm2} Et d9 = Z X: C / C; où Z {UV, Mdm2, p53, A, B} Défauts généraux:

W={uv,mdm2,X}

UV

cancer p53 A B Mdm2 X

New Knowledge : Knots and Links

UV

cancer p53 A B X Mdm2 C

Default Abduction

UV

cancer p53 A B X Mdm2 C

Extensions (18) ont un sens : uv -> p53 p53 -> a uv -> x joint(p53,x) -> c c -> -b a -> -cancer

Bloque B (p21 ?)

Reactivation of suppressed RhoB is a critical step for inhibition of anaplastic thyroid cancer growth Laura A. Marlow,1 Lisa A. Reynolds,1 Alan S. Cleland,2 Simon J. Cooper,1 Michelle L. Gumz,1,+ Shinichi Kurakata,3 Kosaku Fujiwara,3 Ying Zhang,1 Thomas Sebo,4,8 Clive Grant,5,8 Bryan McIver,6,8 J. Trad Wadsworth,7 Derek C. Radisky,1 Robert C. Smallridge,2,8,* and John A. Copland1,*

Validation Biologique

Defaults for System Biology

• Rules with exceptions :

a : Øb g activation(X,Y,T): Øinhibition(X,T 1) activation(X,Y,T 1)

An example of Discrete Time System: Cancer Inhibition at time t0, t1, t2 UV

cancer p53 A B X Mdm2

t0 t0 t1 t2 t1 t2

How can we block the cancer using X?

P53 Model improved by Default Abduction

• Ultraviolets (UV) either

activate cancer or P53.

• P53 activate a protein A

which blocks cancer but p53 binds mdm2 and together will activate B which blocks A

• How is it possible to

block cancer by inhibiting B?

Defaults D:

• d1 = UV : cancer / cancer
• d2 = UV : p53 / p53
• d3 = p53 : A / A
• d4 = p53

Mdm2: B / B

• d5 = B : ¬A / ¬A
• d6 = A : ¬cancer / ¬cancer
• d7 = C : ¬B / ¬B

d8 = Y : X /X ; où Y {UV, Mdm2} Et d9 = Z X: C / C; où Z {UV, Mdm2, p53, A, B} Défauts généraux:

W={uv,mdm2,X}

UV

cancer p53 A B Mdm2 X

37/35

Génération Automatique de la carte de la Cassure double-brin de l’ADN

38/35

Black – binding interaction ; Blue – Protein modification ; Green – enzymatic processes Red – inhibitions Purple – activation/inhibition by transcription

Pommier Y. and all. Chk2 Molecular Interaction Map and Rationale for Chk2 Inhibitors Clin Cancer Res. 2006 May 1;12(9):2657-61..

Black – binding interaction ; Blue – Protein modification ; Green – enzymatic processes Red – inhibitions Purple – activation by transcription

Symbols : (a) Proteins A and B could link, the knot represents the binding A:B ; (b) Multimolecular Complex binding ; (c) Covalent Modification of A ; (d) Degradation of A ; (e) Enzymatic stimulation in transcription ; (f) Autophosphorylation (g) General Stimulation; (h) Necessity ; (i) Inhibition ; (j) Activation of transcription ; (k) Inhibition of transcription

Légende Réaction

Interaction de liaison : binding Modification covalente de la Protéine Processus Enzymatique Inhibition Activation/Inhibit ion de la Transcription

Carte génomique de la cassure Double-brin de l’ADN 206 reactions 63 proteines

41/35

Symbols : (a) Protéines A et B peuvent se lier, le nœud représente la liaison A:B (b) Liaison complexe multi-protéique (c) Modification covalente de A (d) Dégradation de A (e) Stimulation enzymatique de la transcription (f) Auto-phosphorylation (g) Stimulation générale; (h) Nécessité (i) Inhibition (j) Activation de transcription (k) Inhibition de transcription

42/35

Automatic Map using Defaults: 206 rules

• rule(Blabla, Type, Prerequisite —> Consequent, Time, Weight)
• - Blabla : commentaries.
• - Type : hard (sure rule) / def (default) / exc (mutual exclusion)
• - Prerequisite : set of literals, Consequent : literal
• - Weight : weight of the rule (extensions having weghts)
• - Time : (1, T+4, …
• rule(blabla, def, [ (product(mdm2_p53), 1) ] —>(phosphorylation(atr,mdm2_p53) ,1), T+1, 5)
• * The Hard rules are Horn clauses.
• The hard rules with empty prerequisite vide, are elementary facts.
• Except exception, they don’t contain variables.
• rule (1, hard, [] —> (product(p53),1), 1, 1)
• The literals are couples ( action(objet) , state ).
• - The actions are : product, binding, stimulation, phosphorylation, dissociation, transcription activation
• - The objects are the proteins p53, mdm2,..
• - The state is 1 (active) ou -1 (not active).

Dynamic Knowledge Base : revision of the knowledge

• A. Doncescu, P. Siegel, “DNA Double-Strand Break–Based Non Monotonic

Logic", Emerging Trends in Computational Biology, Bioinformatics, and Systems Biology", Morgan Kauffman, Print Book ISBN :9780128025086 2015.

• A. Doncescu, P.Siegel, Utilisation de la logique des

hypothèses pour la modélisation des voies de signalisation dans la cellule, Cinquièmes Journées de l'Intelligence Artificielle Fondamentale (JIAF) Juin 8- 10 2011, Lyon , France.

Génération Automatique de la carte Génomique

Découverte ? : Réduction de Kinase et p73 ne stimule pas l’apoptose Chk2 Molecular Interaction Map and Rationale for Chk2 Inhibitors (Pommier 2006)

44/35

Conclusion

Hypothèse vraie

• u fausse ?

Test

Hypothèse vraie

• u fausse ?

Théorie de Défauts Modèles complétés Gestion de conflit Calcul d’extensions

Découverte de connaissances biologiques et plus …

Ajout d’hypothèses Calcul d’extensions

MERCI !