Introducing Time Delays in Process Hitting Framework of Biological Regulatory Networks

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 the constraints associated with the evolution of expression levels of biological entities of BRN is not possible. In this thesis, we propose a Hybrid Process Hitting scheme for introducing time delays in Process Hitting Framework for dynamical modelling and analysis of Large Biological Regulatory Networks. It will provide 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, it was possible to perform goal-oriented reduction of the BRN and also determine the constraints on time delays characterizing the evolution (dynamics) of the reduced BRN. The proposed Hybrid Process Hitting methodology is applied to a considerably large BRN of Apoptosis Pathway comprising of 90 entities for obtaining the dynamical properties of this pathway. The determination of constraints on time delays corresponding to the evolution of entities for the reduced BRN (entities involving feedbacks) was successfully computed using the new methodology. The chemical reactions as well as the biological interactions are all stochastic in nature and could, therefore, assume any rate of change within the range of delays determined through Hybrid Modeling. The same has thus been extended to Stochastic Modeling using Stochastic Petri Nets (SPNs) in which the random delay in firing of the transitions x Abstract aptly captures the stochastic behaviour of changes in expression levels of genes. The proposed scheme was found to be more efficient than existing methodology and less computationally intensive. It was applied to the mucus production in Pseudomonas Aeruginosa BRN and results obtained from Stochastic Petri Nets are in agreement with the Hybrid Modeling results which establishes the accuracy of this approach as well as provide more insight in the dynamical behaviour of BRNs through simulation.