Analysing the Influence of the Spontaneous Aneuploidy Frequency on the Cell Population System Cultivation
<p>The paper provides a qualitative analysis of M.S. Vinogradova's nonlinear model for dynamics of the cell population system. This system describes the stem cells cultivation in vitro under resource constraints. The system consists of two populations, namely: population of normal cells a...
| Main Authors: | , |
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| Format: | Article |
| Language: | Russian |
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MGTU im. N.È. Baumana
2015-01-01
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| Series: | Matematika i Matematičeskoe Modelirovanie |
| Subjects: | |
| Online Access: | http://mathm.elpub.ru/jour/article/view/18 |
| _version_ | 1819237195668520960 |
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| author | G. A. Nefedov S. B. Tkachev |
| author_facet | G. A. Nefedov S. B. Tkachev |
| author_sort | G. A. Nefedov |
| collection | DOAJ |
| description | <p>The paper provides a qualitative analysis of M.S. Vinogradova's nonlinear model for dynamics of the cell population system. This system describes the stem cells cultivation in vitro under resource constraints. The system consists of two populations, namely: population of normal cells and population of abnormal cells. Resource constraints are considered as linear dependences of mitosis parameters on the normalized densities of each population.<br />One of the key parameters that effects on the realization of the system evolution scenarios is a parameter that determines a share of the normal cells, which pass, when dividing, into population of the abnormal cells. The paper analyses both the existence conditions of the rest points and the changes of the evolution scenarios of population system with changing abovementioned parameter and other system parameters held fixed. It is shown that there is a saddle-node bifurcation in the system; the bifurcation value of the parameter is found. The paper shows the interval of parameter values in which the favorable scenarios of population system evolution are implemented. It also presents results of mathematical modeling.</p> |
| first_indexed | 2024-12-23T13:16:28Z |
| format | Article |
| id | doaj.art-02b72ca1a4224d4ab0d40b55ced1932e |
| institution | Directory Open Access Journal |
| issn | 2412-5911 |
| language | Russian |
| last_indexed | 2024-12-23T13:16:28Z |
| publishDate | 2015-01-01 |
| publisher | MGTU im. N.È. Baumana |
| record_format | Article |
| series | Matematika i Matematičeskoe Modelirovanie |
| spelling | doaj.art-02b72ca1a4224d4ab0d40b55ced1932e2022-12-21T17:45:35ZrusMGTU im. N.È. BaumanaMatematika i Matematičeskoe Modelirovanie2412-59112015-01-0103162617Analysing the Influence of the Spontaneous Aneuploidy Frequency on the Cell Population System CultivationG. A. Nefedov0S. B. Tkachev1Bauman Moscow State Technical University, RussiaBauman Moscow State Technical University, Russia<p>The paper provides a qualitative analysis of M.S. Vinogradova's nonlinear model for dynamics of the cell population system. This system describes the stem cells cultivation in vitro under resource constraints. The system consists of two populations, namely: population of normal cells and population of abnormal cells. Resource constraints are considered as linear dependences of mitosis parameters on the normalized densities of each population.<br />One of the key parameters that effects on the realization of the system evolution scenarios is a parameter that determines a share of the normal cells, which pass, when dividing, into population of the abnormal cells. The paper analyses both the existence conditions of the rest points and the changes of the evolution scenarios of population system with changing abovementioned parameter and other system parameters held fixed. It is shown that there is a saddle-node bifurcation in the system; the bifurcation value of the parameter is found. The paper shows the interval of parameter values in which the favorable scenarios of population system evolution are implemented. It also presents results of mathematical modeling.</p>http://mathm.elpub.ru/jour/article/view/18mathematical modelingstem cellspopulation dynamicsbifurcationdevelopment scenariosrest points |
| spellingShingle | G. A. Nefedov S. B. Tkachev Analysing the Influence of the Spontaneous Aneuploidy Frequency on the Cell Population System Cultivation Matematika i Matematičeskoe Modelirovanie mathematical modeling stem cells population dynamics bifurcation development scenarios rest points |
| title | Analysing the Influence of the Spontaneous Aneuploidy Frequency on the Cell Population System Cultivation |
| title_full | Analysing the Influence of the Spontaneous Aneuploidy Frequency on the Cell Population System Cultivation |
| title_fullStr | Analysing the Influence of the Spontaneous Aneuploidy Frequency on the Cell Population System Cultivation |
| title_full_unstemmed | Analysing the Influence of the Spontaneous Aneuploidy Frequency on the Cell Population System Cultivation |
| title_short | Analysing the Influence of the Spontaneous Aneuploidy Frequency on the Cell Population System Cultivation |
| title_sort | analysing the influence of the spontaneous aneuploidy frequency on the cell population system cultivation |
| topic | mathematical modeling stem cells population dynamics bifurcation development scenarios rest points |
| url | http://mathm.elpub.ru/jour/article/view/18 |
| work_keys_str_mv | AT ganefedov analysingtheinfluenceofthespontaneousaneuploidyfrequencyonthecellpopulationsystemcultivation AT sbtkachev analysingtheinfluenceofthespontaneousaneuploidyfrequencyonthecellpopulationsystemcultivation |