Dimensionality Reduction of Bistable Biological Systems
- 447 Downloads
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 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.
KeywordsBistability Time-scales hierarchy Similarity transformation Canonical correlation analysis Dimensionality reduction
A.Z., Z.N., and A.K. are financially supported by the GoFORSYS Project No. 0313924 funded by the German Federal Ministry of Science and Education.
- Conradi, C., Saez-Rodriguez, J., Gilles, E.-D., & Raisch, J. (2005). Using chemical reaction network theory to discard a kinetic mechanism hypothesis. In IEE proc. systems biology, December 2005 (Vol. 152, pp. 243–248). Google Scholar
- Conradi, C., Saez-Rodriguez, J., Gilles, E.-D., & Raisch, J. (2006). Chemical reaction network theory: a tool for systems biology. In Proceedings of the 5th MATHMOD, 2006. Google Scholar
- Conradi, C., Flockerzi, D., & Raisch, J. (2007b). Saddle-node bifurcations in biochemical reaction networks with mass action kinetics and application to a double-phosphorylation mechanism. In 2007 American control conference, New York City, USA, July 11–13, 2007 (pp. 6103–6109). CrossRefGoogle Scholar
- del Rio, G., Koschützki, D., & Coello, G. (2009). How to identify essential genes from molecular networks? BMC Syst. Biol., 3(102). Google Scholar
- Feinberg, M., & Ellison, P. (2000). The chemical reaction network toolbox. www.chbmeng.ohio-state.edu/~feinberg/crnt, version 1.1a. Accessed October 2007.
- Fell, D. A. (1992). Metabolic control analysis: a survey of its theoretical and experimental development. Biochem. J., 286, 313–330. Google Scholar
- Flach, E. H., & Schnell, S. (2006). Use and abuse of the quasi-steady-state approximation. IEE Proc. Syst. Biol., 153, 187–191. Google Scholar
- Gustin, M. C., Albertyn, J., Alexander, M., & Davenport, K. (1998). Map kinase pathways in the yeast Saccharomyces cerevisiae. Microbiol. Mol. Biol. Rev., 62, 1264–1300. Google Scholar
- Kim, T. Y., Kim, H. U., & Lee, S. Y. (2009). Metabolite-centric approaches for the discovery of antibacterials using genome-scale metabolic networks. Metab. Eng. Google Scholar
- Mendenhall, M. D., & Hodge, A. E. (1998). Regulation of Cdc28 cyclin-dependent protein kinase activity during the cell cycle of the yeast Saccharomyces cerevisiae. Microbiol. Mol. Biol. Rev., 62, 1191–1243. Google Scholar
- Palsson, B. O., Palsson, H., & Lightfoot, E. N. (1984). Mathematical modeling of dynamics and control in metabolic networks: II. Simple dimeric enzymes. J. Theor. Biol., 303–321. Google Scholar
- Palsson, B. O., Palsson, H., & Lightfoot, E. N. (1985). Mathematical modeling of dynamics and control in metabolic networks: III. Linear reaction sequences. J. Theor. Biol., 231–259. Google Scholar
- Surovtsova, I., Simus, N., Huebner, K., Sahle, S., & Kummer, U. (2012). Simplification of biochemical models: a general approach based on the analysis of the impact of individual species and reactions on the systems dynamics. BMC Syst. Biol., 6(14). Google Scholar