Type-dependent stochastic Ising model describing the dynamics of a non-symmetric feedback module
We study an alternative approach to model the dynamical behaviors of biological feedback loop, that is, a type-dependent spin system, this class of stochastic models was introduced by Fernández et. al [13], and are useful since take account to inherent variability of gene expression.We analyze a non...
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AIMS Press
2016-06-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2016026 |
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| author | Manuel González-Navarrete |
| author_facet | Manuel González-Navarrete |
| author_sort | Manuel González-Navarrete |
| collection | DOAJ |
| description | We study an alternative approach to model the dynamical behaviors of biological feedback loop, that is, a type-dependent spin system, this class of stochastic models was introduced by Fernández et. al [13], and are useful since take account to inherent variability of gene expression.We analyze a non-symmetric feedback module being an extension for the repressilator, the first synthetic biological oscillator, invented by Elowitz and Leibler [7]. We consider a mean-field dynamics for a type-dependent Ising model, and then study the empirical-magnetization vector representing concentration of molecules. We apply a convergence result from stochastic jump processes to deterministic trajectories and present a bifurcation analysis for the associated dynamical system. We show that non-symmetric module under study can exhibit very rich behaviours, including the empirical oscillations described by repressilator. |
| format | Article |
| id | doaj-art-862bd2b6f19c4b4b8b896d6cee7a7158 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2016-06-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-862bd2b6f19c4b4b8b896d6cee7a71582025-01-24T02:36:57ZengAIMS PressMathematical Biosciences and Engineering1551-00182016-06-0113598199810.3934/mbe.2016026Type-dependent stochastic Ising model describing the dynamics of a non-symmetric feedback moduleManuel González-Navarrete0Institute of Mathematics and Statistics, Universidade de São Paulo, Rua do Matão, 1010, CEP 05508-090, São PauloWe study an alternative approach to model the dynamical behaviors of biological feedback loop, that is, a type-dependent spin system, this class of stochastic models was introduced by Fernández et. al [13], and are useful since take account to inherent variability of gene expression.We analyze a non-symmetric feedback module being an extension for the repressilator, the first synthetic biological oscillator, invented by Elowitz and Leibler [7]. We consider a mean-field dynamics for a type-dependent Ising model, and then study the empirical-magnetization vector representing concentration of molecules. We apply a convergence result from stochastic jump processes to deterministic trajectories and present a bifurcation analysis for the associated dynamical system. We show that non-symmetric module under study can exhibit very rich behaviours, including the empirical oscillations described by repressilator.https://www.aimspress.com/article/doi/10.3934/mbe.2016026bifurcation analysis.type-dependent ising modelcontinuous-time jump processesdynamical systemfeedback loopsrepressilator |
| spellingShingle | Manuel González-Navarrete Type-dependent stochastic Ising model describing the dynamics of a non-symmetric feedback module Mathematical Biosciences and Engineering bifurcation analysis. type-dependent ising model continuous-time jump processes dynamical system feedback loops repressilator |
| title | Type-dependent stochastic Ising model describing the dynamics of a non-symmetric feedback module |
| title_full | Type-dependent stochastic Ising model describing the dynamics of a non-symmetric feedback module |
| title_fullStr | Type-dependent stochastic Ising model describing the dynamics of a non-symmetric feedback module |
| title_full_unstemmed | Type-dependent stochastic Ising model describing the dynamics of a non-symmetric feedback module |
| title_short | Type-dependent stochastic Ising model describing the dynamics of a non-symmetric feedback module |
| title_sort | type dependent stochastic ising model describing the dynamics of a non symmetric feedback module |
| topic | bifurcation analysis. type-dependent ising model continuous-time jump processes dynamical system feedback loops repressilator |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2016026 |
| work_keys_str_mv | AT manuelgonzaleznavarrete typedependentstochasticisingmodeldescribingthedynamicsofanonsymmetricfeedbackmodule |