Discretized Kinetic Models for Abductive Reasoning in Systems Biology

Abstract

The study of systems biology through inductive logic programming (ILP) aims at improving the understanding of the physiological state of the cell by reasoning with rules and relations instead of ordinary differential equations. This paper presents a method for enabling the ILP framework to deal with quantitative information from some experimental data in systems biology. The method consist in both discretizing the evolution of concentrations of metabolites during experiments and transcribing enzymatic kinetics (for instance Michaelis-Menten kinetics) into logic rules. Kinetic rules are added to background knowledge, along with the topology of the metabolic pathway, whereas discretized concentrations are observations. Applying ILP allows for abduction and induction in such a system. A logical model of the glycolysis and pentose phosphate pathways of E. Coli is proposed to support our method description. Logical formulae on concentrations of some metabolites, which could not be measured during the dynamic state, are produced through logical abduction. Finally, as this results in a large number of hypotheses, they are ranked with an expectation maximization algorithm working on binary decision diagrams.