Design Issues for Qualitative Modelling of Biological Cells with Petri Nets

Abstract

Abstract. Petri nets are a widely used formalism to qualitatively model concurrent systems such as a biological cell. We present techniques for modelling biological processes as Petri nets for further analyses and insilico experiments. Instead of extending the formalism with ,,colours" or rates, as is most often done, we focus on preserving the simplicity of the formalism and developing an execution semantics which resembles biology -we apply a principle of maximal parallelism and introduce the novel concept of bounded execution with overshooting. A number of modelling solutions are demonstrated using the example of the wellstudied C. elegans vulval development process. To date our model is still under development, but first results, based on Monte Carlo simulations, are promising.

Synchronous Balanced Analysis

“…This semantics describes totally asynchronous behaviour, which does not capture the concurrent nature of cellular behavior, where all reactions can happen in parallel. A better suited semantics, proposed in [7], and which we adapt in this paper, is presented below.…”

“…The max-parallel execution semantics can be informally described as "execute greedily as many transitions as possible in one step" [7]; we formalize this description in Def.3.…”

“…A mathematical cell model that respects the resource trade-offs experienced by cells is built in [4]. The concept of maximally parallel execution already appears in the literature on P-systems [5], and in Levy's family reductions [6], while in [7], the authors use it to develop a Petri Net execution semantics that resembles biology. The scheduling policy of cells is also tackled in [8], where the notion of bounded asynchrony is introduced.…”

What Can Formal Methods Bring to Systems Biology?

“…Weighted arcs connect places and transitions. In [13] we explained a method to represent biological knowledge as a Petri net. As explained before, places represent genes and protein species, i.e., bound and unbound, active and inactive, or at different locations, while transitions represent biological processes.…”

“…Therefore, in [13] we advocate to use what is called maximal parallelism [3]. A fully asynchronous approach would allow one part of the network to deploy prolonged activity, while another part of the network shows no activity at all.…”