A High-Level Petri Net Framework for Genetic Regulatory Networks

Abstract

Summary 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, however, at present they have limited formal analysis techniques and tools. We present a flexible formal framework for modelling and analysing multi-valued genetic regulatory networks using high-level Petri nets and logic minimization techniques. 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 multivalued model to a corresponding Boolean model and consider their formal relationship.

Abstracting Asynchronous Multi-Valued Networks: An Initial Investigation

“…Note that as it stands, the decision procedure is inefficient; work is on going to refine this procedure and to use it as a basis of a tool for abstraction checking. Such a tool will provide the support needed to carry out more complex case studies, for example supporting the work currently underway to investigate abstractions for the relatively complex MVN model of the carbon starvation response in E. coli presented in [3].…”

“…This approach seems to be complimentary to the one developed here and we are currently investigating combining these ideas. Another possible abstraction approach would be to make use of results on modelling MVNs using Petri nets [11,3,4,8] and to then apply Petri net abstraction techniques (see for example [31,19,38]). Such an approach appears promising from an analysis point of view but problematic in that the resulting Petri net abstraction may not be interpretable as an MVN and so force the modeller to explicitly use a different modelling formalism.…”

“…MVNs can therefore discriminate between the strengths of different activated interactions, something which Boolean networks are unable to capture. MVNs have been extensively studied in circuit design (for example, see [25,20]) and successfully applied to modelling biological systems (for example, see [35,7,28,3]).…”

“…Multi-valued networks (MVNs) [25,34,35] are an expressive qualitative modelling approach for biological systems (for example, see [35,7,28,3]). They extend the well-known Boolean network [17,18] approach by allowing the state of each regulatory entity to be within a range of discrete values instead of just true or false.…”

Several supplementary concepts for applied category-theoretical states over an extended Petri net using an example relating to genetic coding: Toward an abstract algebraic formulation of molecular/genetic biology

“…Invented by Carl Adam Petri [10], it is used as a language or a tool in designing or visualizing a parallel, discrete, asynchronous, distributed and dynamical system. In practice, the classical PN, as well as various types of extended PNs, have been applied to various fields such as the dynamics of molecular biological systems [7−33], genetic activity [34,35], biological and flexible manufacturing systems [36,37], multi-valued genetic regulatory networks [38], the algebraic application of Boolean differential calculus [39], programming languages [40], artificial intelligence [41], fuzzy PNs [42,43], and quantum computation using quantum PNs [44,45]. §2-3.…”