Journal
SYSTEMS & CONTROL LETTERS
Volume 60, Issue 6, Pages 373-382Publisher
ELSEVIER
DOI: 10.1016/j.sysconle.2011.03.003
Keywords
Gene-protein regulatory networks; Matrices with cyclic structure; Robust stability; Generalized frequency variable
Funding
- Ministry of Education, Culture, Sports, Science and Technology in Japan [19656104, 21656106]
- Ministry of Education, Science and Technology [2010-0010720]
- National Research Foundation of Korea [2010-0010720] Funding Source: Korea Institute of Science & Technology Information (KISTI), National Science & Technology Information Service (NTIS)
- Grants-in-Aid for Scientific Research [21246067, 11J09203, 19656104, 21656106] Funding Source: KAKEN
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This paper investigates analytic robust stability criteria for large-scale cyclic gene-protein regulatory network systems consisting of genes with heterogeneous dynamics combined with parametric or unstructured uncertainties from a control-theoretic viewpoint. We first consider a class of gene expressions, which is described as an uncertain linear transcription-translation model (LTTM) with feedback loops from translation products to transcription. Next, we show that such a model belong to a class of large-scale dynamical linear network systems with a generalized frequency variable. Then, we derive robust stability criteria systematically for the following two types of biological uncertain LTTM: (i) LTIMs consisting of heterogeneous gene dynamics with parametric uncertainties and (ii) LTTMs consisting of homogeneous nominal gene dynamics with unstructured uncertainties. These criteria provide fairly simple analysis methodologies, which can be readily applied to the analysis for large-scale genetic regulatory networks and give some biological insight. (C) 2011 Elsevier B.V. All rights reserved.
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