Quantitative Decomposition of Dynamics of Mathematical Cell Models: Method and Application to Ventricular Myocyte Models.
Mathematical cell models are effective tools to understand cellular physiological functions precisely. For detailed analysis of model dynamics in order to investigate how much each component affects cellular behaviour, mathematical approaches are essential. This article presents a numerical analysis...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Public Library of Science (PLoS)
2015-01-01
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| Series: | PLoS ONE |
| Online Access: | http://europepmc.org/articles/PMC4474442?pdf=render |
| _version_ | 1818064762460700672 |
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| author | Takao Shimayoshi Chae Young Cha Akira Amano |
| author_facet | Takao Shimayoshi Chae Young Cha Akira Amano |
| author_sort | Takao Shimayoshi |
| collection | DOAJ |
| description | Mathematical cell models are effective tools to understand cellular physiological functions precisely. For detailed analysis of model dynamics in order to investigate how much each component affects cellular behaviour, mathematical approaches are essential. This article presents a numerical analysis technique, which is applicable to any complicated cell model formulated as a system of ordinary differential equations, to quantitatively evaluate contributions of respective model components to the model dynamics in the intact situation. The present technique employs a novel mathematical index for decomposed dynamics with respect to each differential variable, along with a concept named instantaneous equilibrium point, which represents the trend of a model variable at some instant. This article also illustrates applications of the method to comprehensive myocardial cell models for analysing insights into the mechanisms of action potential generation and calcium transient. The analysis results exhibit quantitative contributions of individual channel gating mechanisms and ion exchanger activities to membrane repolarization and of calcium fluxes and buffers to raising and descending of the cytosolic calcium level. These analyses quantitatively explicate principle of the model, which leads to a better understanding of cellular dynamics. |
| first_indexed | 2024-12-10T14:41:09Z |
| format | Article |
| id | doaj.art-5694129cc66d454b8c3e026d2c8274a2 |
| institution | Directory Open Access Journal |
| issn | 1932-6203 |
| language | English |
| last_indexed | 2024-12-10T14:41:09Z |
| publishDate | 2015-01-01 |
| publisher | Public Library of Science (PLoS) |
| record_format | Article |
| series | PLoS ONE |
| spelling | doaj.art-5694129cc66d454b8c3e026d2c8274a22022-12-22T01:44:41ZengPublic Library of Science (PLoS)PLoS ONE1932-62032015-01-01106e012497010.1371/journal.pone.0124970Quantitative Decomposition of Dynamics of Mathematical Cell Models: Method and Application to Ventricular Myocyte Models.Takao ShimayoshiChae Young ChaAkira AmanoMathematical cell models are effective tools to understand cellular physiological functions precisely. For detailed analysis of model dynamics in order to investigate how much each component affects cellular behaviour, mathematical approaches are essential. This article presents a numerical analysis technique, which is applicable to any complicated cell model formulated as a system of ordinary differential equations, to quantitatively evaluate contributions of respective model components to the model dynamics in the intact situation. The present technique employs a novel mathematical index for decomposed dynamics with respect to each differential variable, along with a concept named instantaneous equilibrium point, which represents the trend of a model variable at some instant. This article also illustrates applications of the method to comprehensive myocardial cell models for analysing insights into the mechanisms of action potential generation and calcium transient. The analysis results exhibit quantitative contributions of individual channel gating mechanisms and ion exchanger activities to membrane repolarization and of calcium fluxes and buffers to raising and descending of the cytosolic calcium level. These analyses quantitatively explicate principle of the model, which leads to a better understanding of cellular dynamics.http://europepmc.org/articles/PMC4474442?pdf=render |
| spellingShingle | Takao Shimayoshi Chae Young Cha Akira Amano Quantitative Decomposition of Dynamics of Mathematical Cell Models: Method and Application to Ventricular Myocyte Models. PLoS ONE |
| title | Quantitative Decomposition of Dynamics of Mathematical Cell Models: Method and Application to Ventricular Myocyte Models. |
| title_full | Quantitative Decomposition of Dynamics of Mathematical Cell Models: Method and Application to Ventricular Myocyte Models. |
| title_fullStr | Quantitative Decomposition of Dynamics of Mathematical Cell Models: Method and Application to Ventricular Myocyte Models. |
| title_full_unstemmed | Quantitative Decomposition of Dynamics of Mathematical Cell Models: Method and Application to Ventricular Myocyte Models. |
| title_short | Quantitative Decomposition of Dynamics of Mathematical Cell Models: Method and Application to Ventricular Myocyte Models. |
| title_sort | quantitative decomposition of dynamics of mathematical cell models method and application to ventricular myocyte models |
| url | http://europepmc.org/articles/PMC4474442?pdf=render |
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