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.
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