Dynamical Analysis of the MicroRNA – Mediated Protein Translation Process
Mathematical modelling of kinetic processes with different time scales allows a reduction of the governing equations using quasi-steady-state approximations (QSSA). A QSSA theorem is applied to a modified mathematical model of the microRNA-mediated protein translation process. By an appropriate norm...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Bulgarian Academy of Sciences, Institute of Mathematics and Informatics
2013-01-01
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| Series: | Biomath |
| Subjects: | |
| Online Access: | http://www.biomathforum.org/biomath/index.php/biomath/article/view/28 |
| _version_ | 1797722825273901056 |
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| author | Elena Nikolova Ivan Jordanov Nikolay Vitanov |
| author_facet | Elena Nikolova Ivan Jordanov Nikolay Vitanov |
| author_sort | Elena Nikolova |
| collection | DOAJ |
| description | Mathematical modelling of kinetic processes with different time scales allows a reduction of the governing equations using quasi-steady-state approximations (QSSA). A QSSA theorem is applied to a modified mathematical model of the microRNA-mediated protein translation process. By an appropriate normalized procedure the system of seven nonlinear ordinary differential equations is rewritten in a form suitable for model reduction. In accordance with the terminology of the QSSA theorem, it is established that two of the protein concentrations are ?fast varying’, such that the corresponding kinetic equations form an attached system. The other four concentrations are ?slow varying’, and form a degenerate system. Another variable appears to be a constant. Analytical solutions, related to the steady-state values of the fast varying concentrations and the slow varying ones, are derived and interpreted as restrictions on the regulatory role of microRNAs on the protein translation dynamics. |
| first_indexed | 2024-03-12T09:53:08Z |
| format | Article |
| id | doaj.art-3a67231cbe90445187b7f877ab2729e0 |
| institution | Directory Open Access Journal |
| issn | 1314-684X 1314-7218 |
| language | English |
| last_indexed | 2024-03-12T09:53:08Z |
| publishDate | 2013-01-01 |
| publisher | Bulgarian Academy of Sciences, Institute of Mathematics and Informatics |
| record_format | Article |
| series | Biomath |
| spelling | doaj.art-3a67231cbe90445187b7f877ab2729e02023-09-02T12:21:24ZengBulgarian Academy of Sciences, Institute of Mathematics and InformaticsBiomath1314-684X1314-72182013-01-012110.11145/j.biomath.2012.10.07144Dynamical Analysis of the MicroRNA – Mediated Protein Translation ProcessElena Nikolova0Ivan Jordanov1Nikolay Vitanov2Institute of Mechanics, Bulgarian Academy of Sciences, Sofia, BulgariaInstitute of Mechanics, Bulgarian Academy of Sciences, Sofia, BulgariaInstitute of Mechanics, Bulgarian Academy of Sciences, Sofia, BulgariaMathematical modelling of kinetic processes with different time scales allows a reduction of the governing equations using quasi-steady-state approximations (QSSA). A QSSA theorem is applied to a modified mathematical model of the microRNA-mediated protein translation process. By an appropriate normalized procedure the system of seven nonlinear ordinary differential equations is rewritten in a form suitable for model reduction. In accordance with the terminology of the QSSA theorem, it is established that two of the protein concentrations are ?fast varying’, such that the corresponding kinetic equations form an attached system. The other four concentrations are ?slow varying’, and form a degenerate system. Another variable appears to be a constant. Analytical solutions, related to the steady-state values of the fast varying concentrations and the slow varying ones, are derived and interpreted as restrictions on the regulatory role of microRNAs on the protein translation dynamics.http://www.biomathforum.org/biomath/index.php/biomath/article/view/28microRNA, protein translation, QSSA theorem, driving reactions, control parameters |
| spellingShingle | Elena Nikolova Ivan Jordanov Nikolay Vitanov Dynamical Analysis of the MicroRNA – Mediated Protein Translation Process Biomath microRNA, protein translation, QSSA theorem, driving reactions, control parameters |
| title | Dynamical Analysis of the MicroRNA – Mediated Protein Translation Process |
| title_full | Dynamical Analysis of the MicroRNA – Mediated Protein Translation Process |
| title_fullStr | Dynamical Analysis of the MicroRNA – Mediated Protein Translation Process |
| title_full_unstemmed | Dynamical Analysis of the MicroRNA – Mediated Protein Translation Process |
| title_short | Dynamical Analysis of the MicroRNA – Mediated Protein Translation Process |
| title_sort | dynamical analysis of the microrna mediated protein translation process |
| topic | microRNA, protein translation, QSSA theorem, driving reactions, control parameters |
| url | http://www.biomathforum.org/biomath/index.php/biomath/article/view/28 |
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