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Demonstrating the importance of dynamical systems theory

Date:
June 27, 2011
Source:
Rockefeller University Press
Summary:
Two new papers demonstrate the successes of using bifurcation theory and dynamical systems approaches to solve biological puzzles.

Properties of two successive action potentials within a burst at 8 mM Glucose. (Top) Time-dependent changes of the instantaneous equilibrium or "lead" potential VL (red) and Vm (black). (Bottom) Time-dependent changes in contributions (c) of ICaV, IKDr, IKCa(BK) and INaCa. The c of other currents were also plotted in the diagram, but are barely visible because of their minor contributions. The time scale of the x-axis is 40 s.
Credit: Cha, C.Y., et al. 2011. J. Gen. Physiol. doi:10.1085/jgp.201110611.

Two new papers demonstrate the successes of using bifurcation theory and dynamical systems approaches to solve biological puzzles.

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The articles appear online in the Journal of General Physiology on June 27.

In companion papers, Akinori Noma and colleagues from Japan first present computer simulations of a model for bursting electrical activity in pancreatic beta cells, and then use bifurcation diagrams to analyze the behavior of the model. In his Commentary accompanying the articles, Arthur Sherman (National Institutes of Health) proposes that the methods demonstrated in these two papers have broader implications and demonstrate the increasingly important role of dynamical systems approaches in the field of biology.

Mathematical modeling is an important tool in understanding complex cellular processes. Unlike time-based simulations of models, which test only one set of parameter values, bifurcation diagrams analyze the solutions of the governing equations as a function of critical parameters. Such bifurcation scenarios are a powerful tool for dissecting complex systems by subdividing them into parameter regions that underlie distinct behavioral patterns, Sherman explains. He proposes that dynamic modeling will become a more prominently used tool for biologists as live cell-imaging techniques continue to reveal greater complexity and more cell-signaling mechanisms.


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The above story is based on materials provided by Rockefeller University Press. Note: Materials may be edited for content and length.


Journal References:

  1. Chae Young Cha, Yasuhiko Nakamura, Yukiko Himeno, Jianwu Wang, Shinpei Fujimoto, Nobuya Inagaki, Yung E. Earm, Akinori Noma. Ionic mechanisms and Ca2 dynamics underlying the glucose response of pancreatic β cells: a simulation study. Journal of General Physiology, 2011; 138 (1): 21-37 DOI: 10.1085/jgp.201110611
  2. Chae Young Cha, Enrique Santos, Akira Amano, Takao Shimayoshi, Akinori Noma. Time-dependent changes in membrane excitability during glucose-induced bursting activity in pancreatic β cells. Journal of General Physiology, 2011; 138 (1): 39-47 DOI: 10.1085/jgp.201110612
  3. Arthur Sherman. Dynamical systems theory in physiology. Journal of General Physiology, 2011; 138 (1): 13-19 DOI: 10.1085/jgp.201110668

Cite This Page:

Rockefeller University Press. "Demonstrating the importance of dynamical systems theory." ScienceDaily. ScienceDaily, 27 June 2011. <www.sciencedaily.com/releases/2011/06/110627122935.htm>.
Rockefeller University Press. (2011, June 27). Demonstrating the importance of dynamical systems theory. ScienceDaily. Retrieved October 31, 2014 from www.sciencedaily.com/releases/2011/06/110627122935.htm
Rockefeller University Press. "Demonstrating the importance of dynamical systems theory." ScienceDaily. www.sciencedaily.com/releases/2011/06/110627122935.htm (accessed October 31, 2014).

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