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2011, 2011(Special): 1404-1412. doi: 10.3934/proc.2011.2011.1404

Wavelet analysis of phase clusters in a distributed biochemical system

Andrey Yu. Verisokin 1, , Darya V. Verveyko 1, , Eugene B. Postnikov 1, and  Anastasia I. Lavrova 2,

1. 

Department of Theoretical Physics, Kursk State University, Radishcheva st., 33, 305000, Kursk, Russian Federation, Russian Federation, Russian Federation
2. 

Institute of Physics, Humboldt-University at Berlin, Newtonstr. 15, 12489, Berlin, Germany

Received  July 2010 Revised  March 2011 Published  October 2011

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, nonlinear oscillator, non-Turing bifurcations, distributed Selkov system, reaction-diffusion.
Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.
Citation: Andrey Yu. Verisokin, Darya V. Verveyko, Eugene B. Postnikov, Anastasia I. Lavrova. Wavelet analysis of phase clusters in a distributed biochemical system. Conference Publications, 2011, 2011 (Special) : 1404-1412. doi: 10.3934/proc.2011.2011.1404
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