Efficient Finite-Difference Estimation of Second-Order Parametric Sensitivities for Stochastic Discrete Biochemical Systems
Biochemical reaction systems in a cell exhibit stochastic behaviour, owing to the unpredictable nature of the molecular interactions. The fluctuations at the molecular level may lead to a different behaviour than that predicted by the deterministic model of the reaction rate equations, when some rea...
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2024-12-01
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| author | Fauzia Jabeen Silvana Ilie |
| author_facet | Fauzia Jabeen Silvana Ilie |
| author_sort | Fauzia Jabeen |
| collection | DOAJ |
| description | Biochemical reaction systems in a cell exhibit stochastic behaviour, owing to the unpredictable nature of the molecular interactions. The fluctuations at the molecular level may lead to a different behaviour than that predicted by the deterministic model of the reaction rate equations, when some reacting species have low population numbers. As a result, stochastic models are vital to accurately describe system dynamics. Sensitivity analysis is an important method for studying the influence of the variations in various parameters on the output of a biochemical model. We propose a finite-difference strategy for approximating second-order parametric sensitivities for stochastic discrete models of biochemically reacting systems. This strategy utilizes adaptive tau-leaping schemes and coupling of the perturbed and nominal processes for an efficient sensitivity estimation. The advantages of the new technique are demonstrated through its application to several biochemical system models with practical significance. |
| format | Article |
| id | doaj-art-c50a22d790464bbf942c538b9bb0fb9c |
| institution | Kabale University |
| issn | 1300-686X 2297-8747 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematical and Computational Applications |
| spelling | doaj-art-c50a22d790464bbf942c538b9bb0fb9c2024-12-27T14:38:28ZengMDPI AGMathematical and Computational Applications1300-686X2297-87472024-12-0129612010.3390/mca29060120Efficient Finite-Difference Estimation of Second-Order Parametric Sensitivities for Stochastic Discrete Biochemical SystemsFauzia Jabeen0Silvana Ilie1Department of Mathematics, Toronto Metropolitan University, Toronto, ON M5B 2K3, CanadaDepartment of Mathematics, Toronto Metropolitan University, Toronto, ON M5B 2K3, CanadaBiochemical reaction systems in a cell exhibit stochastic behaviour, owing to the unpredictable nature of the molecular interactions. The fluctuations at the molecular level may lead to a different behaviour than that predicted by the deterministic model of the reaction rate equations, when some reacting species have low population numbers. As a result, stochastic models are vital to accurately describe system dynamics. Sensitivity analysis is an important method for studying the influence of the variations in various parameters on the output of a biochemical model. We propose a finite-difference strategy for approximating second-order parametric sensitivities for stochastic discrete models of biochemically reacting systems. This strategy utilizes adaptive tau-leaping schemes and coupling of the perturbed and nominal processes for an efficient sensitivity estimation. The advantages of the new technique are demonstrated through its application to several biochemical system models with practical significance.https://www.mdpi.com/2297-8747/29/6/120stochastic simulation algorithmstochastic models of biochemical kineticssensitivity analysistau-leaping methodvariable time stepping |
| spellingShingle | Fauzia Jabeen Silvana Ilie Efficient Finite-Difference Estimation of Second-Order Parametric Sensitivities for Stochastic Discrete Biochemical Systems Mathematical and Computational Applications stochastic simulation algorithm stochastic models of biochemical kinetics sensitivity analysis tau-leaping method variable time stepping |
| title | Efficient Finite-Difference Estimation of Second-Order Parametric Sensitivities for Stochastic Discrete Biochemical Systems |
| title_full | Efficient Finite-Difference Estimation of Second-Order Parametric Sensitivities for Stochastic Discrete Biochemical Systems |
| title_fullStr | Efficient Finite-Difference Estimation of Second-Order Parametric Sensitivities for Stochastic Discrete Biochemical Systems |
| title_full_unstemmed | Efficient Finite-Difference Estimation of Second-Order Parametric Sensitivities for Stochastic Discrete Biochemical Systems |
| title_short | Efficient Finite-Difference Estimation of Second-Order Parametric Sensitivities for Stochastic Discrete Biochemical Systems |
| title_sort | efficient finite difference estimation of second order parametric sensitivities for stochastic discrete biochemical systems |
| topic | stochastic simulation algorithm stochastic models of biochemical kinetics sensitivity analysis tau-leaping method variable time stepping |
| url | https://www.mdpi.com/2297-8747/29/6/120 |
| work_keys_str_mv | AT fauziajabeen efficientfinitedifferenceestimationofsecondorderparametricsensitivitiesforstochasticdiscretebiochemicalsystems AT silvanailie efficientfinitedifferenceestimationofsecondorderparametricsensitivitiesforstochasticdiscretebiochemicalsystems |