Probabilistic polynomial dynamical systems for reverse engineering of gene regulatory networks

The enormous accumulation of experimental data on the activities of the living cell has triggered an increasing interest in uncovering the biological networks behind the observed data. This interest could be in identifying either the static network, which is usually a labeled directed graph describing how the different components of the network are wired together, or the dynamic network, which describes how the different components of the network influence each other. Identifying dynamic models for gene regulatory networks from transcriptome data is the topic of numerous published articles, and methods have been proposed within different computational frameworks, such as continuous models using differential equations [1,2], discrete models using Boolean networks [3], Petri nets [4-6], or Logical models [7,8], and statistical models using dynamic Baysein networks [9,10], among many other methods. For an up-to-date review of the state-of-the-art of the field, see, for example [11,12]. Most of these methods identify a particular model of the network which could be deterministic or stochastic. Due to the fact that the experimental data are typically noisy and of limited amount and that gene regulatory networks are believed to be stochastic, regardless of the used framework, stochastic models seem a natural choice [9,13,14]. Furthermore, discrete models where a gene could be in one of a finite number of states are more intuitive, phenomenological descriptions of gene regulatory networks and, at the same time, do not require much data to build. These models could actually be more suitable, especially for large networks [15].The discrete modeling framework for gene regulatory networks that has received the most attention is Boolean networks, which was introduced by Kauffman [3]. They have been used successfully in modeling gene regulatory and signaling networks; see, for example [16-18]. Many reverse engineering methods have been developed to infer such networks, see, for