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Dimensionality reduction of bistable biological systems

  • Time hierarchies, arising as a result of interactions between system's components, represent a ubiquitous property of dynamical biological systems. In addition, biological systems have been attributed switch-like properties modulating the response to various stimuli across different organisms and environmental conditions. Therefore, establishing the interplay between these features of system dynamics renders itself a challenging question of practical interest in biology. Existing methods are suitable for systems with one stable steady state employed as a well-defined reference. In such systems, the characterization of the time hierarchies has already been used for determining the components that contribute to the dynamics of biological systems. However, the application of these methods to bistable nonlinear systems is impeded due to their inherent dependence on the reference state, which in this case is no longer unique. Here, we extend the applicability of the reference-state analysis by proposing, analyzing, and applying a novelTime hierarchies, arising as a result of interactions between system's components, represent a ubiquitous property of dynamical biological systems. In addition, biological systems have been attributed switch-like properties modulating the response to various stimuli across different organisms and environmental conditions. Therefore, establishing the interplay between these features of system dynamics renders itself a challenging question of practical interest in biology. Existing methods are suitable for systems with one stable steady state employed as a well-defined reference. In such systems, the characterization of the time hierarchies has already been used for determining the components that contribute to the dynamics of biological systems. However, the application of these methods to bistable nonlinear systems is impeded due to their inherent dependence on the reference state, which in this case is no longer unique. Here, we extend the applicability of the reference-state analysis by proposing, analyzing, and applying a novel method, which allows investigation of the time hierarchies in systems exhibiting bistability. The proposed method is in turn used in identifying the components, other than reactions, which determine the systemic dynamical properties. We demonstrate that in biological systems of varying levels of complexity and spanning different biological levels, the method can be effectively employed for model simplification while ensuring preservation of qualitative dynamical properties (i.e., bistability). Finally, by establishing a connection between techniques from nonlinear dynamics and multivariate statistics, the proposed approach provides the basis for extending reference-based analysis to bistable systems.show moreshow less

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Metadaten
Author:A. Zakharova, Zoran NikoloskiORCiDGND, Aneta Koseska
DOI:https://doi.org/10.1007/s11538-013-9807-8
ISSN:0092-8240 (print)
Parent Title (English):Bulletin of mathematical biology : official journal of the Society for Mathematical Biology
Publisher:Springer
Place of publication:New York
Document Type:Article
Language:English
Year of first Publication:2013
Year of Completion:2013
Release Date:2017/03/26
Tag:Bistability; Canonical correlation analysis; Dimensionality reduction; Similarity transformation; Time-scales hierarchy
Volume:75
Issue:3
Pagenumber:20
First Page:373
Last Page:392
Funder:GoFORSYS Project [0313924]; German Federal Ministry of Science and Education
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Biochemie und Biologie
Peer Review:Referiert