TY - JOUR
T1 - Quantitative decomposition of dynamics of mathematical cell models
T2 - Method and application to ventricular myocyte models
AU - Shimayoshi, Takao
AU - Cha, Chae Young
AU - Amano, Akira
N1 - Funding Information:
A part of this work was supported by the Biomedical Cluster Kansai project of the Ministry of Education, Culture, Sports, Science, and Technology of Japan, and JSPS KAKENHI Grant Number 26540028.
Publisher Copyright:
© 2015 Shimayoshi et al.This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source arecredited.
PY - 2015/6/19
Y1 - 2015/6/19
N2 - 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.
AB - 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.
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U2 - 10.1371/journal.pone.0124970
DO - 10.1371/journal.pone.0124970
M3 - Article
C2 - 26091413
AN - SCOPUS:85010699631
SN - 1932-6203
VL - 10
JO - PLoS One
JF - PLoS One
IS - 6
M1 - e0124970
ER -