The Switch in a Genetic Toggle System with Lévy Noise

Area of Science:

• Systems Biology
• Biophysics
• Stochastic Processes

Background:

• Bistable toggle switches are fundamental biological models.
• Previous studies focused on Gaussian noise, which doesn't capture biological burst phenomena.
• Real biological systems often exhibit non-Gaussian noise characteristics.

Purpose of the Study:

• To investigate the impact of non-Gaussian Lévy noise on bistable toggle switch dynamics.
• To analyze how Lévy noise affects coherent and on/off switching behaviors.
• To compare the system's response to Lévy noise versus Gaussian noise.

Main Methods:

• Analysis of steady-state probability density.
• Examination of joint steady-state probability density.
• Calculation of mean first passage times.
• Modeling with non-Gaussian Lévy noise to account for large protein bursts.

Main Results:

• Lévy noise can induce coherent switches at lower intensities compared to Gaussian noise.
• The stability index and skewness parameter of Lévy noise significantly influence on/off switching and stable state preference.
• Mean first passage times exhibit complex behaviors under Lévy noise conditions.
• Lévy noise fundamentally alters the escape mechanism from stable states.

Conclusions:

• Non-Gaussian Lévy noise provides a more realistic model for biological toggle switches, especially concerning burst events.
• The characteristics of Lévy noise offer new ways to control and understand switching dynamics in biological systems.
• This work highlights the importance of considering non-Gaussian noise in biological modeling.