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Wavelet analysis of phase clusters in a distributed biochemical system

Pages: 1404 - 1412, Issue Special, September 2011

 Abstract        Full Text (468.5K)              

Andrey Yu. Verisokin - Department of Theoretical Physics, Kursk State University, Radishcheva st., 33, 305000, Kursk, Russian Federation (email)
Darya V. Verveyko - Department of Theoretical Physics, Kursk State University, Radishcheva st., 33, 305000, Kursk, Russian Federation (email)
Eugene B. Postnikov - Department of Theoretical Physics, Kursk State University, Radishcheva st., 33, 305000, Kursk, Russian Federation (email)
Anastasia I. Lavrova - Institute of Physics, Humboldt-University at Berlin, Newtonstr. 15, 12489, Berlin, Germany (email)

Abstract: The spatio-temporal dynamics of glycolysis in distributed medium have been studied both theoretically and experimentally. Different patterns such as travelling waves, standing waves and clusters have been observed in experiment. We describe pattern formation using distributed Selkov model that describes kinetics of phosphofructokinase which is a key enzyme of glycolytic reactions. We have found in numerical simulations that the varying the diffusion coefficient values within the range of 0−10$^$−$^$3 shows a large variety of phase patterns: from the birth of a hierarchy of phase clusters to their complete phase synchronization. In order to understand the mechanism phase clusters emergence and their dynamics we are using continuous wavelet transform.

Keywords:  glycolytic reaction, distributed Selkov system, reaction-diffusion, nonlinear oscillator, non-Turing bifurcations
Mathematics Subject Classification:  Primary: 58F15, 58F17; Secondary: 53C35

Received: July 2010;      Revised: March 2011;      Published: October 2011.