Knowledge-Guided Identification of Petri Net Models of Large Biological Systems

Abstract

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.