Neslihan AvcuNihal PekerginFerhan PekerginCüneyt Güzeliş2025-10-06201815579964, 154559631545-596310.1109/TCBB.2017.2699177https://www.scopus.com/inward/record.uri?eid=2-s2.0-85048310411&doi=10.1109%2FTCBB.2017.2699177&partnerID=40&md5=c0903a9da39906c1f25b2fcab9e74fa9https://gcris.yasar.edu.tr/handle/123456789/9562This paper proposes aggregation-based three-stage algorithms to overcome the numerical problems encountered in computing stationary distributions and mean first passage times for multi-modal birth-death processes of large state space sizes. The considered birth-death processes which are defined by Chemical Master Equations are used in modeling stochastic behavior of gene regulatory networks. Computing stationary probabilities for a multi-modal distribution from Chemical Master Equations is subject to have numerical problems due to the probability values running out of the representation range of the standard programming languages with the increasing size of the state space. The aggregation is shown to provide a solution to this problem by analyzing first reduced size subsystems in isolation and then considering the transitions between these subsystems. The proposed algorithms are applied to study the bimodal behavior of the lac operon of E. coli described with a one-dimensional birth-death model. Thus the determination of the entire parameter range of bimodality for the stochastic model of lac operon is achieved. © 2018 Elsevier B.V. All rights reserved.EnglishAggregation, Bimodality, Cme, Lac Operon, Agglomeration, Escherichia Coli, Genes, Probability Distributions, Problem Oriented Languages, Stochastic Systems, Bimodality, Chemical Master Equation, Gene Regulatory Networks, Lac Operon, Mean First Passage Time, Standard Programming Language, Stationary Distribution, Stochastic Behavior, Stochastic Models, Algorithm, Biological Model, Biology, Gene Regulatory Network, Genetics, Lactose Operon, Markov Chain, Procedures, Algorithms, Computational Biology, Gene Regulatory Networks, Lac Operon, Models Biological, Stochastic ProcessesAgglomeration, Escherichia coli, Genes, Probability distributions, Problem oriented languages, Stochastic systems, bimodality, Chemical master equation, Gene regulatory networks, Lac operon, Mean first passage time, Standard programming language, Stationary distribution, Stochastic behavior, Stochastic models, algorithm, biological model, biology, gene regulatory network, genetics, lactose operon, Markov chain, procedures, Algorithms, Computational Biology, Gene Regulatory Networks, Lac Operon, Models Biological, Stochastic ProcessesArticle