A High-Level Petri Net Framework for Multi-Valued Genetic Regulatory Networks

To understand the function of genetic regulatory networks in the development of cellular systems, we must not only realise the individual network entities, but also the manner by which they interact. Multi-valued networks are a promising qualitative approach for modelling such genetic regulatory networks, providing an interesting compromise between the simplicity of Boolean models and more detailed quantitative models. However, at present multi-valued networks lack the formal analysis techniques and tools required to comprehensively investigate a genetic regulatory model. This is compounded by the fact that little appears to be known about the relationship between multi-valued models and their more abstract Boolean counterparts. We present a flexible formal framework for modelling and analysing multi-valued genetic regulatory networks using high-level Petri nets. We propose an approach for translating a multi-valued model in to a corresponding compact high-level Petri net model using logic minimization techniques and consider coping with the problem of incomplete data that often occurs in practice. We demonstrate our approach with a detailed case study in which part of the genetic regulatory network responsible for the carbon starvation stress response in Escherichia coli is modelled and analysed. We then compare and contrast this multi-valued model to a corresponding Boolean model and present an initial investigation into the formal relationship between these two modelling approaches.