Fuzzy Stochastic Petri Nets for Modeling Biological Systems with Uncertain Kinetic Parameters.

Fei Liu,Ming Yang,Monika Heiner,Jérémie Bourdon

doi:10.1371/journal.pone.0149674

Abstract

Stochastic Petri nets (SPNs) have been widely used to model randomness which is an inherent feature of biological systems. However, for many biological systems, some kinetic parameters may be uncertain due to incomplete, vague or missing kinetic data (often called fuzzy uncertainty), or naturally vary, e.g., between different individuals, experimental conditions, etc. (often called variability), which has prevented a wider application of SPNs that require accurate parameters. Considering the strength of fuzzy sets to deal with uncertain information, we apply a specific type of stochastic Petri nets, fuzzy stochastic Petri nets (FSPNs), to model and analyze biological systems with uncertain kinetic parameters. FSPNs combine SPNs and fuzzy sets, thereby taking into account both randomness and fuzziness of biological systems. For a biological system, SPNs model the randomness, while fuzzy sets model kinetic parameters with fuzzy uncertainty or variability by associating each parameter with a fuzzy number instead of a crisp real value. We introduce a simulation-based analysis method for FSPNs to explore the uncertainties of outputs resulting from the uncertainties associated with input parameters, which works equally well for bounded and unbounded models. We illustrate our approach using a yeast polarization model having an infinite state space, which shows the appropriateness of FSPNs in combination with simulation-based analysis for modeling and analyzing biological systems with uncertain information.

Highlights

To achieve a system-level understanding of biological systems, modeling and simulation play a crucial role as they permit to represent, explain, analyze and predict the system behavior from a holistic point of view
We present a simulation-based analysis method for fuzzy stochastic Petri nets (FSPNs), and we can analyze the uncertainties of outputs caused by the uncertainties associated with the input parameters for both bounded or unbounded models independently of the size of the state space
Taking into account the fact that in biological systems some kinetic parameters may be uncertain due to incomplete, vague or missing kinetic data, or naturally vary, e.g., between different individuals, experimental conditions, etc., we apply FSPNs by combining the strength of SystemsPetri nets (SPNs) to model stochastic systems with the strength of fuzzy sets to deal with uncertain information

Summary

Introduction

To achieve a system-level understanding of biological systems, modeling and simulation play a crucial role as they permit to represent, explain, analyze and predict the system behavior from a holistic point of view. Stochastic modeling methods have been used, e.g., chemical master equations, stochastic differential equations [1], stochastic Pi-calculus [4], stochastic process algebra [5], or stochastic. Fuzzy Stochastic Petri Nets for Modeling Biological Systems. Petri nets (SPNs) [6]. These approaches address the stochastic aspect of biological systems and describe their behavior more accurately than deterministic approaches like ordinary or partial differential equations. SPNs have recently become a promising tool. They have been widely used for modeling and analyzing stochastic biological systems

Objectives

Conclusion