Integration of abduction and induction in biological networks using CF-induction

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Integration of abduction and induction in
biological networks using CF-induction

• Yoshitaka Yamamoto
• Graduate University for Advanced Studies Tokyo,
  Japan.
• Andrei Doncescu
• LAAS-CNRS Toulouse, France.
• Katsumi Inoue
• National Institute of Informatics Tokyo, Japan.

FJ07
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Our goal

• Modeling of biological systems
• Explain and predict the metabolic pathway into
  the cell
• Generic Model
• Saccharomyces Cerevisiae
• E-coli
• Inductive/Abductive Logic Programming can
  explain the biological knowledge

3
Outline

• Logical setting of abduction and induction
• CF-induction (CFI)
• Consequence finding
• Procedure of CF-induction
• Features of CF-induction
• Inhibition in metabolic networks
• Simplification of metabolic networks
• How enzymes work
• Effect on toxins
• Prediction for inhibition in metabolic networks
• Integration of abduction and induction on the
  inhibitory effect
• using CFI
• System demonstration
• Conclusion and future work

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Abduction and Induction Logical Framework

• Input
• B background theory.
• E (positive) examples / observations.
• Output
• H hypothesis satisfying that
• B ? H - E
• B ? H is consistent.
• Inverse Entailment (IE)

Computing a hypothesis H can be done deductively
by B ? ?E - ?H We use
a consequence finding technique for (IE)
computation.
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Consequence finding

• Given an axiom set, the task of consequence
  finding is to find out some theorems of interest.
  
• Theorems to find out are not given in an explicit
  way, but are characterized by some properties.
• Restricted consequence finding
• How to find only interesting conclusions? Inoue
  91
• Production field and characteristic clauses
• Production field P ltL, Cond gt
• L the set of literals to be collected
• Cond the condition to be satisfied (e.g.
  length)
• ThP(S) the clauses entailed by S which belong
  to P.
• Characteristic clause C of S (wrt P )
• C belongs to ThP(S)
• no other clause in ThP(S) subsumes C.

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IE for Abduction --- SOLAR(Nabeshima, Iwanuma
Inoue 2003)

• B full clausal theory
• E conjunction of literals (?E is a clause)
• H conjunctions of literals (?H is a clause)
• Example graph completion problem pathway
  finding
• Find an arc which enables a path from a to d.
• Axioms ?node(X), ?node(Y), ?arc(X,Y),
  path(X,Y))
• ?node(X), ?node(Y), ?node(Z), ?arc(X,Y),
  ?path(Y,Z),path(X,Z).
• node(a). node(b). node(c). node(d).
  arc(a,b). arc(c,d).
• Negated Observation ?path(a,d).
• Production_field ?arc(_,_).
• SOLAR outputs four consequences
• ?arc(a, d) , ?arc(a, c), ?arc(b, d),
  ?arc(b, c)

a c b d
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IE for Induction

• CF-induction (Inoue 2004 Yamamoto, Ray
  Inoue 2007)
• fc-HAIL (Inoue Ray 2007)
• B, E, H full clausal theory
• Note CF-induction is the only existing ILP
  system that is complete for full clausal theories.

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Principle of CF-induction
B ? ?E ? ?H (IE) ? B ? ?E ? Carc(B
? ?E, P) ? ?H . CC ? ?H where CC ?
Instances(Carc(B ? ?E, P)) . H ? F where F
is ?CC in CNF .

• Algorithm
• Compute Carc(B ? ?E , P) .
• Construct a bridge formula CC .
• Convert ?CC into CNF F .
• Generalize F to H such that
• B ? H is consistent
• H is Skolem-free.

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Outline

• Logical Setting of Abduction and Induction
• CF-induction (CFI)
• Consequence finding
• Procedure of CF-induction
• Features of CF-induction
• Inhibition in metabolic networks
• Simplification of metabolic networks
• How enzymes work
• Effect on toxins
• Prediction for inhibition in metabolic networks
• Integration abduction and induction on the
  inhibitory effect using CFI
• System demonstration
• Conclusion and future work

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Simplification of metabolic networks

• Metabolic pathway
• sequences of enzyme-catalyzed reaction steps,
  converting substrates to a variety of products to
  meet the needs of the cell.
• Mono-molecular enzymes catalyzed reactions
• mediated by enzymesproteins that encourage a
  chemical change.
• Enzymes accelerate the rate of a chemical
  reaction
• by up to three orders of magnitude

E enzyme, S substrate, P product, ES
complex, k the constant of the rate of a
chemical reaction.
S
P
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How enzymes work

• Activity of an enzyme
• the rate of the chemical reaction catalyzed by
  the enzyme.
• 1 unit (U) the amount of the enzyme for
  changing the substrate whose amount is 1 µmol to
  the product over one minute.
• proportionate to the amount of the enzyme.
• Michaelis-Menten Reaction
• the relation between the activity of
• an enzyme and the concentration of a substrate
• at steady state

Activity
Concentration of substrate
Concentration of Enzyme
V k2 ES - k-2 EP
Time T
V
Vmax
S
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Effect on toxins

• There exists chemical compounds (inhibitors)
  which control activities of enzymes.
• Higher the concentration of a inhibitor is, lower
  the activity of the enzyme controlled by the
  inhibitor becomes.

E
S
I
S
P
I
I
I
S
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Logical modeling of inhibition Tamaddoni-Nezda
et al 2006
Toxin
Inhibited
concentration(P, down) ? reaction(S, Enz, P),
inhibited(Enz, S, P).
Enz
concentration(S, up) ? reaction(S, Enz, P),
inhibited(Enz, S, P).
S
P
Toxin
Not inhibited
concentration(P, down) ? reaction(S, Enz, P),
?inhibited(Enz, S, P), concentration(S,
down).
Enz
S
P
Toxin
Not inhibited
concentration(P, up) ? reaction(S, Enz, P),
?inhibited(Enz, S, P), concentration(S, up).
Enz
S
P
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Prediction for inhibitory effect of a toxin

• The goal
• Finding inhibitions of a metabolic pathway
• Our approach
• Using IE for abduction

• Examples E
• changes (up or down) of concentrations of
  metabolites in treated cases (injected with a
  toxin)
• Background Theory B
• - chemical reactions in a metabolic networks
• - four clauses concerning the inhibitory
  effect of a toxin
• Hypothesis H
• a conjunction of literals whose predicate is
  inhibition

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Example 1/2
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Example 2/2
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Outline

• Logical Setting of Abduction and Induction
• CF-induction (CFI)
• Consequence finding
• Procedure of CF-induction
• Features of CF-induction
• Inhibition in metabolic networks
• Simplification of metabolic networks
• How enzymes work
• Effect on toxins
• Prediction for inhibition in metabolic networks
• Integration abduction and induction on the
  inhibitory effect
• using CFI
• System demonstration
• Conclusion and future work

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Prediction for intracellular fluxes

• Goals
• Predicting the concentration of metabolites
  intracellular
• Discovering inductive rules augmenting incomplete
  background theory

• Our Approaches
• Using CF-induction

• Examples E
• changes (up or down) of concentrations of
  metabolites extracelluar
• Background theory B
• - chemical reactions in a metabolic networks
• - two clauses concerning the inhibitory effect
• Hypothesis H
• - a clausal theory which consists of both
  lierals whose predicate is
• inhibition and clauses corresponding to
  inductive rules

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Metabolite Balancing

• Intracellular fluxes are determined as a function
  of the measurable extracellular fluxes using a
  stoichiometric model for major intracellular
  reactions and applying a mass balance around each
  intracellular metabolite.

v1, v2, v3, v3-, v4 unknown fluxes at the
steady state. rA, rC, rD, rE metabolite
extracellular accumulation rate.
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Example 1
B concentration(a, up). reaction(a, b).
reaction(b, d). reaction(d, e). reaction(e,
c). reaction(c, b). reaction(b, c).
?concentration(X, up) ? concentration(X, down).
concentration(X, down) ?
reaction(Y, X), ?inhibited(Y, X),
concentration(Y, down).
concentration(X, up) ? concentration(Y, up),
reaction(Y, X), reaction(X, Z),
?inhibited(Y, X), inhibited(X, Z).
E concentration(d, up). concentration(e,
down). concentration(c, down).
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Example 1 outputs of CF-induction
H1 ?inhibited(a, b). inhibited(b, c).
?inhibited(e, c). inhibited(d,
e). ?inhibited(b, d). concentration(e, down) ?
inhibited(d, e), ?inhibited(e, c).
H2 ?inhibited(a, b). inhibited(b, c).
?inhibited(b, d). inhibited(d,
e). concentration(X, down) ? concentration(Y,
up), inhibited(Y, X).
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Example 2 the real metabolic pathway (Pyruvate)

• B
• reaction(pyruvate, acetylcoa).
• reaction(pyruvate, acetaldehide).
• reaction(glucose, glucosep).
• reaction(glucosep, pyruvate).
• reaction(acetaldehide, acetate).
• reaction(acetate, acetylcoa).
• reaction(acetaldehide, ethanol).
• concentration(glucose, up).
• terminal(ethanol).
• blocked(X)?reaction(X,Z), inhibited(X,Z).
• blocked(X)?terminal(X).
• concentration(X,up) ?reaction(Y,X),
  ?inhibited(Y,X), blocked(X).
• E concentration(ethanol,up).
  concentration(pyruvate, up).

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Example 2 outputs of CF-induction

• H1
• ?Inhibited(glucosep, pyruvate).
• ?inhibited(acetaldehide, ethanol).
• inhibited(pyruvate, acetylcoa).

H2 ?inhibited(glucose, glucosep) ?Inhibited(g
lucosep, pyruvate). ?inhibited(acetaldehide,
ethanol). ?inhibited(pyruvate, acetaldehide). conc
entration(Y, up)? ?inhibited(X, Y),
concentration(X, up).
Glucose
Glucose-P
Glucose
Ethanol
Acetaldehide
Pyruvate
Glucose-P
Acetylcoa
Acetate
Ethanol
Acetaldehide
Pyruvate
Acetylcoa
Acetate
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B concentration(a, up). reaction(a, b).
reaction(b, d). reaction(d, e). reaction(e,
c). reaction(c, b). reaction(b, c).
?concentration(X, up) ? concentration(X, down).
concentration(X, down) ?
reaction(Y, X), ?inhibited(Y, X),
concentration(Y, down).
concentration(X, up) ? concentration(Y, up),
reaction(Y, X), reaction(X, Z),
?inhibited(Y, X), inhibited(X, Z).
E concentration(d, up). concentration(e,
down). concentration(c, down).
H1 ?inhibited(a, b). inhibited(b, c).
?inhibited(e, c). inhibited(d, e).
?inhibited(b, d).
concentration(e, down) ? inhibited(d, e),
?inhibited(e, c).
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Conclusion

• Introduction of inhibitions in metabolic pathways
  
• Introduction of CF-induction
• Full clausal theories (non-Horn clauses) for B, E
  and H
• Completeness of hypotheses finding
• Integration of abduction and induction on
  inhibitory effects using CF-induction.