Four-Variable Model of an Enzymatic Oscillator Based on Trypsin |
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Authors: | Sergey N. Semenov Alar Ainla Ekaterina V. Skorb Sjoerd G. J. Postma |
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Affiliation: | 1. Department of Chemistry and Chemical Biology, Harvard University, 12 Oxford Street, MA, 02138 USA;2. INL – International Iberian Nanotechnology Laboratory, Avenida Mestre José Veiga s/n, 4715-330 Braga, Portugal;3. SCAMT Laboratory, ITMO University, St. Petersburg, 197101 Russian Federation;4. Institute for Molecules and Materials, Radboud University Nijmegen, Heyendaalseweg 135, 6525 AJ Nijmegen, The Netherlands |
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Abstract: | This paper describes a four-variable model for an enzymatic oscillator based on trypsin. Variables in this model are concentrations of the essential proteins (trypsin and trypsinogen) and small molecules (masked and active inhibitors of trypsin) within the network. Importantly, to simplify the model, non-essential side reactions are neglected and essential reactions are assumed to follow first or second order kinetics. Numerical solutions of this reduced model semi-quantitatively reproduce experimentally determined periods, amplitudes, and phase shifts of oscillations in the concentrations of several species in the network. Moreover, linear stability analysis shows that oscillations in the trypsin oscillator emerge and disappear through Hopf bifurcation. The model will be helpful in situations where simplicity is necessary such as detailed analysis of dynamics and modeling of reaction-diffusion systems. |
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Keywords: | Chemical Oscillator Trypsin Reaction Networks Linear Stability Analysis |
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