Browsing by Author "Pekergin, Ferhan"

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Citation - WoS: 1
Citation - Scopus: 2
Aggregation for Computing Multi-Modal Stationary Distributions in 1-D Gene Regulatory Networks
(IEEE COMPUTER SOC, 2018) Neslihan Avcu; Nihal Pekergin; Ferhan Pekergin; Cuneyt Guzelis; Pekergin, Nihal; Pekergin, Ferhan; Avcu, Neslihan; Guzelis, Cuneyt
This 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.
Citation - WoS: 6
Citation - Scopus: 7
Discriminant-based bistability analysis of a TMG-induced lac operon model supported with boundedness and local stability results
(Tubitak Scientific & Technological Research Council Turkey, 2016) Levent Cavas; Neslihan Avcu; Hakan Alyuruk; Güleser Kalaycı Demir; Cüneyt GÜZELİŞ; Ferhan PEKERGİN; Pekergin, Ferhan; Demir, Güleser Kalayci; Guzelis, Cuneyt; Kalayci Demir, Guleser; Cavas, Levent; Avcu, Neslihan; Alyuruk, Hakan
This paper presents the results of a theoretical and numerical study on the analysis of bistable behavior of the most studied gene regulatory network the lac operon in terms of the model parameters. The boundedness of the state variables for the considered model are demonstrated the parameter values providing the existence of the multiple equilibria and thus the bistable behavior are determined and a local stability analysis of the equilibria is performed. The parameter region yielding the existence of multiple equilibria is determined in an algebraic way based on discriminants. The model given in the state equation form is defined by the ordinary differential equations with the rational right-hand sides constituted within Hill and Michaelis Menten approaches based on enzyme kinetics. The presented method can also be used in the parametric studies of other gene regulatory and metabolic networks given by state equations with rational right hand sides.