Chaotic Dynamical Systems and Biological Applications
- 1. Chaotic Dynamical Systems and Biological Applications Stefano Sarao
- 3. The Protaganists Cdk APC Cyclin-dependent kineses Anaphase-promoting complex
- 4. • S-cyclins concentration remain high • M-cyclin gene expression is switched on • M-cyclin concentration rises S-Phase Dna Replication G1-Phase Late G1 phase: • the cell unleashes G1/S- and S-cyclin genes expression. • G1/S-Cdk activity rises immediately • CKIs destruction and APC inactivation • Start
- 5. • chromosomes alignment • spindle forming • activation of APC • cohesins destruction • Cdk inhibitor production • spindle apparatus disassembly • cytokinesis M-Phase G2-Phase • S-, M-cyclins concentration remain high • M-cyclins are activated • G2/M Checkpoint
- 13. Hill equation
- 14. First application A simple two component negative feedback system will inevitably approach a stable, intermediate state.
- 15. Tyson-Novak Model the cell-cycle mathematically
- 16. The Idea formulating the problem as physicochemical process Let’s formulate the G1/S-G2-M transition
- 17. The Idea mass dependence (m=0.6,0.9,1.2)
- 18. The Idea Those characterize a hysteresis loop 𝑝1 < 𝑝 < 𝑝2
- 19. Coming Back? The importance of A.
- 20. Coming Back? The importance of A.
- 21. Coming Back? The importance of A.
- 22. Coming Back? The importance of A.
- 23. Ingredients for a relaxation oscillator Using Michaelis-Menten:
- 24. The Results
- 25. The End