AUTHOR=Sheikh Iftikhar Ali , Ahmad Jamil , Magnin Morgan , Roux Olivier 

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

JOURNAL=Frontiers in Physiology

VOLUME=Volume 10 - 2019

YEAR=2019

URL=https://www.frontiersin.org/journals/physiology/articles/10.3389/fphys.2019.00090

DOI=10.3389/fphys.2019.00090

ISSN=1664-042X

ABSTRACT=Modelling and simulation of molecular systems helps in understanding the behavioural 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 behaviour 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 biological entities of BRN is not possible. In this paper we propose a \textit{Hybrid Process Hitting} scheme for introducing time delays in Process Hitting Framework for dynamical modelling and analysis of Large Biological Regulatory Networks. The proposed framework is applied to a well-known BRNs of \textit{Bacteriophage $ \lambda $} 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 characterising the evolution (dynamics) of the reduced BRN.