Learning Metabolic Network Inhibition using Abductive Stochastic

Logic Programming

Jianzhong Chen, Stephen Muggleton, José SantosImperial College, London

Florence, 2nd August 2007

Summary

•Background: Metabolic networks, ILPs and SLPs•Problem: Learning Metabolic Network Inhibition•Modeling: Abductive SLPs•Results: Improvement by extracting probabilistic examples•Conclusions and Discussion

Metabolic Network

Metabolites interact with each other in a complex metabolic network with enzymes catalyzing the transformation of one metabolite into another.

Metabolites are the nodes and enzymes are the arcs of this graph.

The metabolic network data was taken from the Kyoto Encyclopedia of Genes and Genomes (KEGG).

Excerpt of the rat metabolic network

Introducing ILP

Inductive Logic Programming is an expressive machine learning technique which receives a description of a problem in a logic program.

This description is divided in background knowledge (i.e. facts, rules and constraints about the domain) and observations.

Induction and Abduction

Induction: Inference of a general theory that entails as many observations as possible (the observations are causes)

Abduction: Inference of the hypothesis that best explain available observations (the observations are consequences)

Problem

Build a model to predict enzyme inhibition due to a toxin (hydrazine) injection.

MotivationPredicting the inhibitory effects of a drug is crucial in drug development to understand the possible side effects of the drug in the metabolic system of the recipient.

Experiment setting

Our dataset consists of 2 groups with 10 rats each. The control group was injected with a placebo and the case group was injected with 30mg of hydrazine.

The injection of hydrazine changes the metabolite concentration in the rats. The level of change was measured comparing to the control rats.

Important point

It is not possible to directly observe the inhibitory effects of the drug (i.e. which enzymes it inhibited). We can know, however, the metabolite concentrations at certain hours after the drug injection.

We abduce the inhibited status by observing the metabolite concentrations

Background knowledge

concentration(X, down, T):- reactionnode(X, Enz, Y),

inhibited(Enz, Y, X, T).

concentration(X, down, T):- reactionnode(X, Enz, Y),

noninhibited(Enz, Y, X, T),

concentration(Y, down, T).

concentration(X, up, T):- reactionnode(Y, Enz, X),

inhibited(Enz, X, Y, T).

concentration(X, up, T):- reactionnode(X, Enz, Y),

noninhibited(Enz, Y, X, T),

concentration(Y,up,T).

:- concentration(M, up, T), concentration(M, down, T)

:- inhibited(Enz, From, To, T), noninhibited(Enz, From, To, T).

Background knowledge- partial network

reactionnode('l-2-aminoadipate','2.6.1.39', '2-oxo-glutarate').reactionnode('2-oxo-glutarate','2.6.1.39', 'l-2-aminoadipate').reactionnode('2-oxo-glutarate', '1.1.1.42', 'isocitrate').reactionnode('isocitrate', '1.1.1.42', '2-oxo-glutarate').reactionnode('2-oxo-glutarate','2.3.1.61', 'succinate').reactionnode('succinate','2.3.1.61', '2-oxo-glutarate').reactionnode('isocitrate','4.2.1.3', 'citrate').reactionnode('citrate','4.2.1.3', 'isocitrate').reactionnode('isocitrate','4.2.1.3', 'trans-aconitate').reactionnode('trans-aconitate','4.2.1.3', 'isocitrate').reactionnode('citrate','4.2.1.2', 'fumarate').reactionnode('fumarate','4.2.1.2', 'citrate').reactionnode('succinate','1.3.99.1', 'fumarate').reactionnode('fumarate','1.3.99.1', 'succinate').reactionnode('succinate','1.13.11.16', 'hippurate').reactionnode('hippurate','1.13.11.16', 'succinate').reactionnode('citrate','2.6.1.-', 'taurine').reactionnode('taurine','2.6.1.-', 'citrate').

Observations after 8 hours of injection

concentration('citrate',up,8).

concentration('2-oxo-glutarate',down,8).

concentration('succinate',up,8).

concentration('l-2-aminoadipate',up,8).

concentration('creatine',down,8).

concentration('creatinine',down,8).

concentration('hippurate',up,8).

concentration('beta-alanine',down,8).

concentration('lactate',up,8).

concentration('methylamine',up,8).

concentration('trans-aconitate',down,8).

concentration('formate',down,8).

concentration('taurine',up,8).

concentration('acetate',down,8).

concentration('nmna',down,8).

concentration('nmnd',up,8).

concentration('tmao',down,8).

concentration('fumarate',up,8).

concentration('l-as',up,8).

concentration('glucose',down,8).

Discovered abducibles

noninhibited('1.13.11.16',succinate,hippurate,8).noninhibited('2.1.1.1',fumarate,nmnd,8).noninhibited('2.1.1.7',fumarate,nmna,8).noninhibited('1.1.99.8',formaldehyde,formate,8).inhibited('2.6.1.39','l-2-aminoadipate','2-oxo-glutarate',8).inhibited('4.2.1.3',isocitrate,'trans-aconitate',8).inhibited('4.2.1.2',fumarate,citrate,8).inhibited('1.3.99.1',fumarate,succinate,8).inhibited('2.6.1.-',taurine,citrate,8).inhibited('4.3.2.1','l-as',arginine,8).inhibited('2.1.1.2',ornithine,creatine,8).inhibited('3.5.1.59',sarcosine,creatinine,8).inhibited('1.4.99.3',methylamine,formaldehyde,8).inhibited('4.1.2.32',tmao,formaldehyde,8).inhibited('4.2.1.54',lactate,'acryloyl-coA',8).inhibited('4.3.1.6','beta-alanine','acryloyl-coA',8).inhibited('2.7.1.69',glucose,pyruvate,8).inhibited('6.2.1.1',acetate,acetylCoA,8).

Introducing SLPs

ILP has a great modeling power, however more can be done if probabilities are attached to the background knowledge rules.

Attaching probabilities to rules is, in brief, the idea of Stochastic Logic Programs (SLPs)

Reformulating the problem

In our SLP modeling we started with the logic program just like in the ILP case, including the abducibles as part of the model.

The difference is that probabilities were attached to the inhibited/4 and noninhibited/4 predicates as well as in the concentration/3 rules.

The SLP system has to discover the probability values that maximize the likelihood of observing the given concentrations.

Significance of this approach

In real world problems the status of entities is rarely just two folds (on/off). Most problems are better modeled if the modelling system allows for a certain degree of fuzzyness.

Also, the rules previous discovered may not be all equally important and we leave to the SLP system the responsibility of determining the best relative weighting.

Novelty of our work

We divided SLP modeling in two, Categorical SLP (CSLP) and Probabilistic SLP (PSLP), the only difference between the two is that the latter uses probabilistic examples to learn (confidence for being up or down) rather than categorical (totally up/down)

The problem now is how to derive these confidences from the dataset.

Extracting Probabilistic Examples from Scientific Data

Pnorm(1.72, 0,1)=0.9573

Concentration Empirical Prob CSLP PSLP

citrate down 0,9843 0,69 0,686

2-og down 1,000 0,568 0,69

succinate down 0,9368 0,259 0,297

l-2-aa up 0,9962 0,658 0,828

creatine down 0,5052 0,307 0,443

creatinine down 0,5798 0,322 0,493

hippurate down 0,7136 0,303 0,166

beta-alanine up 0,9659 0,567 0,686

lactate up 0,9503 0,54 0,516

methylamine up 1,000 0,301 0,525

trans-aconitate down 0,6488 0,392 0,441

formate down 0,9368 0,392 0,423

taurine up 0,7362 0,65 0,81

acetate up 0,6727 0,556 0,539

nmna up 0,5239 0,489 0,492

nmnd up 0,6414 0,489 0,499

tmao up 0,5166 0,31 0,112

fumarate up 0,697 0,297 0,502

l-as up 0,6748 0,504 0,507

glucose up 0,8096 0,557 0,531

Average accuracy 68,34% 72,75%

P-value 4,12%

Prediction accuracy of CSLP vs PSLP

Default accuracy and ILP accuracy= 60%

Abductive SLP model

Learned metabolic network with Probabilistic SLP

Conclusions and Discussion

•This kind of problems is almost impossible to model without a rich machine learning framework like logic programs.

•SLPs produce a richer description of the underneath biological reality compared to ILP.

•Additionally, learning SLPS from probabilistic examples leads to an statistically significant improvement in predictive accuracy.