Automated verification of living organism models allows us to gain previously unknown knowledge about underlying biological processes. In this paper, we show the benefits to use parametric time Petri nets in order to analyze precisely the dynamic beh
avior of biological oscillatory systems. In particular, we focus on the resilience properties of such systems. This notion is crucial to understand the behavior of biological systems (e.g. the mammalian circadian rhythm) that are reactive and adaptive enough to endorse major changes in their environment (e.g. jet-lags, day-night alternating work-time). We formalize these properties through parametric TCTL and demonstrate how changes of the environmental conditions can be tackled to guarantee the resilience of living organisms. In particular, we are able to discuss the influence of various perturbations, e.g. artificial jet-lag or components knock-out, with regard to quantitative delays. This analysis is crucial when it comes to model elicitation for dynamic biological systems. We demonstrate the applicability of this technique using a simplified model of circadian clock.
The stochastic dynamics of biochemical reaction networks can be accurately described by discrete-state Markov processes where each chemical reaction corresponds to a state transition of the process. Due to the largeness problem of the state space, an
alysis techniques based on an exploration of the state space are often not feasible and the integration of the moments of the underlying probability distribution has become a very popular alternative. In this paper the focus is on a comparison of reconstructed distributions from their moments obtained by two different moment-based analysis methods, the method of moments (MM) and the method of conditional moments (MCM). We use the maximum entropy principle to derive a distribution that fits best to a given sequence of (conditional) moments. For the two gene regulatory networks that we consider we find that the MCM approach is more suitable to describe multimodal distributions and that the reconstruction is more accurate if conditional distributions are considered.
The classical problem of moments is addressed by the maximum entropy approach for one-dimensional discrete distributions. The numerical technique of adaptive support approximation is proposed to reconstruct the distributions in the region where the main part of probability mass is located.
