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Delay-induced degrade-and-fire oscillations in small genetic circuits
William Mather1, Matthew R Bennett, Jeff Hasty
1Department of Bioengineering, University of California San Diego, La Jolla, California, 92093, USA.
Physical Review Letters
|March 5, 2009
Summary
A small time delay in synthetic gene networks with feedback loops can cause robust, nonlinear oscillations. The period of these oscillations can exceed the delay time, with variability influenced by molecular fluctuations.
Area of Science:
- Synthetic biology
- Systems biology
- Biophysics
Background:
- Synthetic gene networks with coupled positive and negative feedback loops exhibit robust oscillations.
- Understanding the dynamics of these networks is crucial for designing biological circuits.
Purpose of the Study:
- To investigate the impact of time delays on oscillations in synthetic gene networks.
- To characterize the resulting nonlinear dynamics and their dependence on network parameters.
Main Methods:
- Deterministic and stochastic modeling approaches were employed.
- Analysis focused on networks with coupled positive and negative feedback loops and incorporated time delays.
Main Results:
- A small time delay can induce strongly nonlinear oscillations, termed "degrade-and-fire" dynamics.
- Oscillation periods can significantly exceed the delay time when strong activation and tight repression are present.
- Period variability is sensitive to fluctuations at low molecular counts near oscillatory minima.
Conclusions:
- Time delays are a critical factor in generating complex oscillatory behavior in synthetic gene networks.
- The "degrade-and-fire" mechanism provides a framework for understanding these oscillations.
- Network parameter tuning and stochastic effects are key determinants of oscillatory characteristics.
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