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Dual-Color Fluorescence Cross-Correlation Spectroscopy to Study Protein-Protein Interaction and Protein Dynamics in Live Cells
Published on: December 11, 2021
Dynamic properties of a delayed protein cross talk model.
Svetoslav Nikolov1, Julio Vera, Vladimir Kotev
1Institute of Mechanics and Biomechanics-BAS, Acad. G. Bonchev Str., Bl. 4, 1113 Sofia, Bulgaria.
Bio Systems
|August 22, 2007
Summary
Time delay significantly impacts the Jacob-Monod model dynamics, influencing beta-galactosidase synthesis regulation in E. coli. A critical time delay value can induce stable oscillations and all-or-nothing responses, depending on end-product repression features.
Area of Science:
- Systems Biology
- Biophysics
- Mathematical Biology
Background:
- The Jacob-Monod model describes gene regulation, specifically beta-galactosidase synthesis controlled by the lac repressor protein in E. coli.
- Understanding the impact of time delays on biological system dynamics is crucial for accurate modeling.
Purpose of the Study:
- To investigate how time delays affect the dynamical properties of the Jacob-Monod model.
- To analyze the consequences of time delay on the system's dynamics and identify critical parameters.
Main Methods:
- Hopf's theorem and Lyapunov-Andronov's theory were applied to analyze the mathematical model.
- Analytical calculations and numerical simulations were used to study the system's behavior.
Main Results:
- Time delay acts as a key bifurcation parameter, with a critical value analytically established.
- Exceeding this critical time delay can lead to the emergence of stable limit cycles (self-sustained oscillations).
- End-product repression features, particularly cooperativity, influence the characteristics of these oscillations, potentially causing all-or-nothing responses.
Conclusions:
- Time delay is a critical factor in the dynamics of the Jacob-Monod model.
- The presence and characteristics of time delays can lead to complex oscillatory behaviors and distinct response patterns in gene expression regulation.
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