Knowledge-Guided Identification of Petri Net Models of Large Biological Systems
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To date, the most expressive, and understandable dynamic models of biological systems identified by ILP have employed qualitative differential equations, or QDEs. The QDE representation provides a direct and simple abstraction of quantitative ODEs. However, the representation does have several limitations, including the generation of spurious behaviour in simulation, and a lack of methods for handling concurrency, quantitative information or stochasticity. These issues are largely absent in the long-established qualitative representation of Petri nets. A flourishing area of Petri net models for biological systems now exists, which has almost entirely been concerned with hand-crafted models. In this paper we show that pure and extended Petri nets can be represented as special cases of systems in which transitions are defined using a combination of logical constraints and constraints on linear terms. Results from a well-known combinatorial algorithm for identifying pure Petri nets from data and from the ILP literature on inverting entailment form the basis of constructing a maximal set of such transition constraints given data and background knowledge. An ILP system equipped with a constraint solver is then used to determine the smallest subset of transition constraints that are consistent with the data. This has several advantages over using a specialised Petri net learner for biological system identification, most of which arise from the use of background knowledge. As a result: (a) search-spaces can be constrained substantially using semantic and syntactic constraints; (b) we can perform the hierarchical identification of Petri models of large systems by re-use of well-established network models; and (c) we can use a combination of abduction and data-based justification to hypothesize missing parts of a Petri net. We demonstrate these advantages on well-known metabolic and signalling networks.
KeywordsBackground Knowledge Incidence Matrix Inductive Logic Programming Constraint Solver Input Place
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