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Oscillations in a model of repression with external control
J M Mahaffy1, D A Jorgensen, R L Vanderheyden
1Department of Mathematical Sciences, San Diego State University, CA 92182.
Journal of Mathematical Biology
|January 1, 1992
Summary
This study models nutrient uptake, revealing how active transport can trigger cellular oscillations or stable states. These findings suggest a potential mechanism for morphogenesis, impacting biological pattern formation.
Area of Science:
- Mathematical Biology
- Biophysics
- Systems Biology
Background:
- Extracellular substances regulate cellular processes through repression.
- Active nutrient transport is crucial for cell function and can lead to complex dynamics.
Purpose of the Study:
- To develop a mathematical model for control by repression, incorporating diffusion and time delays.
- To investigate how active nutrient transport influences cellular responses (oscillatory or stable).
Main Methods:
- Developed a mathematical model for repression control with diffusion and time delays.
- Reduced the system to delay differential and linear Volterra equations.
- Performed local stability analysis and numerical studies on the linearized system.
Main Results:
- The model demonstrates that active nutrient transport can yield either oscillatory or stable cellular responses.
- Stability analysis reveals potential for Hopf bifurcations and asymptotic stability based on parameter values.
- Numerical simulations show intracellular biochemical oscillations with increasing extracellular nutrient concentrations.
Conclusions:
- The model provides insights into how extracellular substances and nutrient transport can regulate cellular dynamics.
- Oscillatory behaviors identified may serve as a trigger mechanism for morphogenesis.
- The study highlights the importance of diffusion, time delays, and active transport in biological pattern formation.