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规范非线性模型中的时间层次结构与模型简化

Time Hierarchies and Model Reduction in Canonical Non-linear Models.

作者信息

Löwe Hannes, Kremling Andreas, Marin-Sanguino Alberto

机构信息

Specialty Division for Systems Biotechnology, Technische Universität München Garching, Germany.

出版信息

Front Genet. 2016 Sep 21;7:166. doi: 10.3389/fgene.2016.00166. eCollection 2016.

DOI:10.3389/fgene.2016.00166
PMID:27708665
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC5030239/
Abstract

The time-scale hierarchies of a very general class of models in differential equations is analyzed. Classical methods for model reduction and time-scale analysis have been adapted to this formalism and a complementary method is proposed. A unified theoretical treatment shows how the structure of the system can be much better understood by inspection of two sets of singular values: one related to the stoichiometric structure of the system and another to its kinetics. The methods are exemplified first through a toy model, then a large synthetic network and finally with numeric simulations of three classical benchmark models of real biological systems.

摘要

分析了一类非常一般的微分方程模型的时间尺度层次结构。已将模型简化和时间尺度分析的经典方法应用于这种形式体系，并提出了一种补充方法。统一的理论处理表明，通过检查两组奇异值可以更好地理解系统的结构：一组与系统的化学计量结构有关，另一组与系统的动力学有关。这些方法首先通过一个简单模型进行举例说明，然后是一个大型合成网络，最后是对三个真实生物系统的经典基准模型进行数值模拟。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a2fc/5030239/1ad8de70e757/fgene-07-00166-g0014.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a2fc/5030239/9f987bec141e/fgene-07-00166-g0001.jpg
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https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a2fc/5030239/eb80ee7eb04d/fgene-07-00166-g0009.jpg
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https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a2fc/5030239/45459ab164da/fgene-07-00166-g0011.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a2fc/5030239/5db12d3cfa49/fgene-07-00166-g0012.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a2fc/5030239/e708b100bad5/fgene-07-00166-g0013.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a2fc/5030239/1ad8de70e757/fgene-07-00166-g0014.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a2fc/5030239/9f987bec141e/fgene-07-00166-g0001.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a2fc/5030239/2c8a780cd465/fgene-07-00166-g0002.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a2fc/5030239/5baef5d459b8/fgene-07-00166-g0003.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a2fc/5030239/aae6dadb3b41/fgene-07-00166-g0004.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a2fc/5030239/ffe3ee421c3a/fgene-07-00166-g0005.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a2fc/5030239/7823ce1f8369/fgene-07-00166-g0006.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a2fc/5030239/012c36779336/fgene-07-00166-g0007.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a2fc/5030239/78b1886b15e6/fgene-07-00166-g0008.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a2fc/5030239/eb80ee7eb04d/fgene-07-00166-g0009.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a2fc/5030239/14416094101c/fgene-07-00166-g0010.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a2fc/5030239/45459ab164da/fgene-07-00166-g0011.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a2fc/5030239/5db12d3cfa49/fgene-07-00166-g0012.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a2fc/5030239/e708b100bad5/fgene-07-00166-g0013.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a2fc/5030239/1ad8de70e757/fgene-07-00166-g0014.jpg

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