Related Experiment Videos
Formation of a regular dissipative structure: a bifurcation and non-linear analysis
J Chattopadhyay1, P K Tapaswi, D Mukherjee
1Embryology Unit, Indian Statistical Institute, Jadavpur University, Calcutta.
Bio Systems
|January 1, 1992
Summary
This study presents a non-linear reaction diffusion model for epigenetic control. Negative cross-diffusion is crucial for forming stable patterns in biological systems.
Area of Science:
- Systems Biology
- Mathematical Biology
- Epigenetics
Background:
- Epigenetic mechanisms regulate gene expression without altering DNA sequence.
- Feedback control systems are essential for cellular processes like mitosis.
- Reaction-diffusion models are used to study spatial patterns in biological systems.
Purpose of the Study:
- To develop a non-linear reaction diffusion model for a negative feedback epigenetic control system.
- To investigate the role of intercellular diffusion in pattern formation.
- To analyze the stability and dynamics of the epigenetic system.
Main Methods:
- Developed a non-linear reaction diffusion model.
- Incorporated synthesis of mitotic proteins and intercellular diffusion.
- Performed bifurcation analysis on the diffusive system.
- Applied Liapunov's direct method for stability analysis.
Main Results:
- Demonstrated the importance of negative cross-diffusion for creating regular dissipative structures.
- Conducted bifurcation analysis, concluding that bifurcation is supercritical.
- Proved global asymptotic stability of the evolved pattern using Liapunov's direct method.
Conclusions:
- Negative cross-diffusion is key for pattern formation in this epigenetic model.
- The system exhibits supercritical bifurcation and globally stable patterns.
- The model provides insights into the dynamics of epigenetic regulation.