chaotic dynamical systems and biological applications
TRANSCRIPT
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Chaotic Dynamical Systems and Biological Applications
Stefano Sarao
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The Cell Cycle
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The Protaganists
Cdk APCCyclin-dependent kineses Anaphase-promoting complex
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• S-cyclins concentration remain high
• M-cyclin gene expression is switched on
• M-cyclin concentration rises
S-PhaseDna Replication
G1-PhaseLate G1 phase:
• the cell unleashes G1/S- and S-cyclin genes expression.
• G1/S-Cdk activity rises immediately
• CKIs destruction and APC inactivation
• Start
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• 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
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Concentrations
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Stimulus-Response
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Biological Oscillator
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Biological Oscillator
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Classical Chemical LawsBriefly
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Michaelis-Menten equation
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Goldbeter-Koshland equation
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Hill equation
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First application
A simple two component negative feedback system will inevitably approach a stable, intermediate state.
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Tyson-Novak Modelthe cell-cycle mathematically
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The Idea
formulating the problem as physicochemical process
Let’s formulate the G1/S-G2-M transition
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The Idea
mass dependence (m=0.6,0.9,1.2)
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The Idea
Those characterize a hysteresis loop
𝑝1 < 𝑝 < 𝑝2
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Coming Back? The importance of A.
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Coming Back? The importance of A.
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Coming Back? The importance of A.
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Coming Back? The importance of A.
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Ingredients for a relaxation oscillator
Using Michaelis-Menten:
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The Results
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The End