Time-dependent structural transformation analysis to high-level Petri net model with active state transition diagram

With an accumulation of in silico data obtained by simulating large-scale biological networks, a new interest of research is emerging for elucidating how living organism functions over time in cells. Investigating the dynamic features of current computational models promises a deeper understanding of complex cellular processes. This leads us to develop a method that utilizes structural properties of the model over all simulation time steps. Further, user-friendly overviews of dynamic behaviors can be considered to provide a great help in understanding the variations of system mechanisms.

We propose a novel method for constructing and analyzing a so-called active state transition diagram (ASTD) by using time-course simulation data of a high-level Petri net. Our method includes two new algorithms. The first algorithm extracts a series of subnets (called temporal subnets) reflecting biological components contributing to the dynamics, while retaining positive mathematical qualities. The second one creates an ASTD composed of unique temporal subnets. ASTD provides users with concise information allowing them to grasp and trace how a key regulatory subnet and/or a network changes with time. The applicability of our method is demonstrated by the analysis of the underlying model for circadian rhythms in Drosophila.

Building ASTD is a useful means to convert a hybrid model dealing with discrete, continuous and more complicated events to finite time-dependent states. Based on ASTD, various analytical approaches can be applied to obtain new insights into not only systematic mechanisms but also dynamics.