Non-monotonicity of Fano factor in a stochastic model for protein expression with sequesterisation at decoy binding sites
We present a stochastic model motivated by gene expression which incorporates unspecific interactions between proteins and binding sites. We focus on characterizing the distribution of free (i.e. unbound) protein molecules in a cell. Although it cannot be expressed in a closed form, we present three...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Bulgarian Academy of Sciences, Institute of Mathematics and Informatics
2017-11-01
|
| Series: | Biomath |
| Subjects: | |
| Online Access: | http://www.biomathforum.org/biomath/index.php/biomath/article/view/1031 |
| _version_ | 1797721157788499968 |
|---|---|
| author | Michal Hojcka Pavol Bokes |
| author_facet | Michal Hojcka Pavol Bokes |
| author_sort | Michal Hojcka |
| collection | DOAJ |
| description | We present a stochastic model motivated by gene expression which incorporates unspecific interactions between proteins and binding sites. We focus on characterizing the distribution of free (i.e. unbound) protein molecules in a cell. Although it cannot be expressed in a closed form, we present three different approaches to obtain it: stochastic simulation algorithms, system of ODEs and quasi-steadystate solution. Additionally we use a large-system-size scaling to derive statistical measures of approximate distribution of the amount of free protein, such as the Fano factor. Intriguingly, we report that while in the absence of or in the excess of decoy binding sites the Fano factor is equal to one (suggestive of Poissonian fluctuations), in the intermediate regimes of moderate levels of binding sites the Fano factor is greater than one (suggestive of super-Poissonian fluctuations). We support and illustrate all of our results with numerical simulations. |
| first_indexed | 2024-03-12T09:29:39Z |
| format | Article |
| id | doaj.art-d6b8c985fbdc4ec08c2eb6c593501117 |
| institution | Directory Open Access Journal |
| issn | 1314-684X 1314-7218 |
| language | English |
| last_indexed | 2024-03-12T09:29:39Z |
| publishDate | 2017-11-01 |
| publisher | Bulgarian Academy of Sciences, Institute of Mathematics and Informatics |
| record_format | Article |
| series | Biomath |
| spelling | doaj.art-d6b8c985fbdc4ec08c2eb6c5935011172023-09-02T13:56:42ZengBulgarian Academy of Sciences, Institute of Mathematics and InformaticsBiomath1314-684X1314-72182017-11-016210.11145/j.biomath.2017.10.217687Non-monotonicity of Fano factor in a stochastic model for protein expression with sequesterisation at decoy binding sitesMichal Hojcka0Pavol Bokes1Comenius University, Bratislava, SlovakiaComenius University, Bratislava, SlovakiaWe present a stochastic model motivated by gene expression which incorporates unspecific interactions between proteins and binding sites. We focus on characterizing the distribution of free (i.e. unbound) protein molecules in a cell. Although it cannot be expressed in a closed form, we present three different approaches to obtain it: stochastic simulation algorithms, system of ODEs and quasi-steadystate solution. Additionally we use a large-system-size scaling to derive statistical measures of approximate distribution of the amount of free protein, such as the Fano factor. Intriguingly, we report that while in the absence of or in the excess of decoy binding sites the Fano factor is equal to one (suggestive of Poissonian fluctuations), in the intermediate regimes of moderate levels of binding sites the Fano factor is greater than one (suggestive of super-Poissonian fluctuations). We support and illustrate all of our results with numerical simulations.http://www.biomathforum.org/biomath/index.php/biomath/article/view/1031Gene ExpressionMaster EquationSmall Noise ApproximationStochastic Simulation |
| spellingShingle | Michal Hojcka Pavol Bokes Non-monotonicity of Fano factor in a stochastic model for protein expression with sequesterisation at decoy binding sites Biomath Gene Expression Master Equation Small Noise Approximation Stochastic Simulation |
| title | Non-monotonicity of Fano factor in a stochastic model for protein expression with sequesterisation at decoy binding sites |
| title_full | Non-monotonicity of Fano factor in a stochastic model for protein expression with sequesterisation at decoy binding sites |
| title_fullStr | Non-monotonicity of Fano factor in a stochastic model for protein expression with sequesterisation at decoy binding sites |
| title_full_unstemmed | Non-monotonicity of Fano factor in a stochastic model for protein expression with sequesterisation at decoy binding sites |
| title_short | Non-monotonicity of Fano factor in a stochastic model for protein expression with sequesterisation at decoy binding sites |
| title_sort | non monotonicity of fano factor in a stochastic model for protein expression with sequesterisation at decoy binding sites |
| topic | Gene Expression Master Equation Small Noise Approximation Stochastic Simulation |
| url | http://www.biomathforum.org/biomath/index.php/biomath/article/view/1031 |
| work_keys_str_mv | AT michalhojcka nonmonotonicityoffanofactorinastochasticmodelforproteinexpressionwithsequesterisationatdecoybindingsites AT pavolbokes nonmonotonicityoffanofactorinastochasticmodelforproteinexpressionwithsequesterisationatdecoybindingsites |