On the Use of Stochastic Petri Nets in the Analysis of Signal Transduction Pathways for Angiogenesis Process

Abstract

Abstract. In this paper we consider the modeling of a selected portion of signal transduction events involved in the angiogenesis process. The detailed model of this process contains a large number of parameters and the data available from wet-lab experiments are not sufficient to obtain reliable estimates for all of them. To overcome this problem, we suggest ways to simplify the detailed representation that result in models with a smaller number of parameters still capturing the overall behaviour of the detailed one.Starting from a detailed stochastic Petri net (SPN) model that accounts for all the reactions of the signal transduction cascade, using structural properties combined with the knowledge of the biological phenomena, we propose a set of model reductions.

Petri Net modelling approach for analysing the behaviour of Wnt/ ‐catenin and Wnt/ Ca 2+ signalling pathways in arrhythmogenic right ventricular cardiomyopathy

“…An SPN is especially suitable for modelling of bio‐molecular networks [29 ]. Several studies have comprehensively described in sufficient details the inherent stochasticity of different bio‐molecular systems including gene regulation, signalling pathways and other biochemical reactions and we refer our readers to them for more insights [23, 36 ].…”

“…Petri net is a very dynamic mathematical formalism for modelling of real systems initially utilised for the biochemical systems in 1939 [21]. After that many biological systems have been modelled using petri net approach on the basis of its simplicity and flexibility (some recent examples are [10,12,[23][24][25]). These models facilitate us to present the dynamic behaviour of time-dependent systems.…”

An Integrated Qualitative and Quantitative Biochemical Model Learning Framework Using Evolutionary Strategy and Simulated Annealing

“…Preliminary quantitative analysis of biochemical systems has been very difficult to perform, due to the inherent complexity of biochemical processes [ 25 , 57 ]. Biochemical systems have been modelled by employing Petri nets theory [ 44 ], including enzymatic cascades and synergistic binding of ligands to enzymes [ 3 , 38 , 45 ]. In primary research, the issues of quantitative analysis of metabolic pathways have been studied by Reddy et al [ 58 , 59 ].…”

Simulative Model Checking of Steady State and Time-Unbounded Temporal Operators

“…This Petri net models a part of the signal transduction pathway involved in the angiogenetic process and was originally published in [21]. The stochastic Petri net SPN AN G comprises 39 places and 64 transitions connected by 185 arcs.…”