Incorporating Time Delays in Process Hitting Framework for Dynamical Modeling of Large Biological Regulatory Networks

Modeling and simulation of molecular systems helps in understanding the behavioral mechanism of biological regulation. Time delays in production and degradation of expressions are important parameters in biological regulation. Constraints on time delays provide insight into the dynamical behavior of a Biological Regulatory Network (BRN). A recently introduced Process Hitting (PH) Framework has been found efficient in static analysis of large BRNs, however, it lacks the inference of time delays and thus determination of their constraints associated with the evolution of the expression levels of biological entities of BRN is not possible. In this paper we propose a Hybrid Process Hitting scheme for introducing time delays in Process Hitting Framework for dynamical modeling and analysis of Large Biological Regulatory Networks. It provides valuable insights into the time delays corresponding to the changes in the expression levels of biological entities thus possibly helping in identification of therapeutic targets. The proposed framework is applied to a well-known BRNs of Bacteriophage λ and ERBB Receptor-regulated G1/S transition involved in the breast cancer to demonstrate the viability of our approach. Using the proposed approach, we are able to perform goal-oriented reduction of the BRN and also determine the constraints on time delays characterizing the evolution (dynamics) of the reduced BRN

Reduction of Qualitative Models of Biological Networks for Transient Dynamics Analysis

International audienceQualitative models of dynamics of signalling pathways and gene regulatory networks allow to capture temporal properties of biological networks while requiring few parameters. However, these discrete models typically suffer from the so-called state space explosion problem which makes the formal assessment of their potential behaviours very challenging. In this paper, we describe a method to reduce a qualitative model for enhancing the tractability of analysis of transient reachability properties. The reduction does not change the dimension of the model, but instead limits its degree of freedom, therefore reducing the set of states and transitions to consider. We rely on a transition-centered specification of qualitative models by the mean of automata networks. Our framework encompass usual asynchronous Boolean and multi-valued network, as well as 1-bounded Petri nets. Applied to different large-scale biological networks from the litterature, we show that the reduction can lead to drastic improvement for the scalability of verification methods