Delays induce novel stochastic effects in negative feedback gene circuits

Area of Science:

• Systems Biology
• Computational Biology
• Molecular Systems Biology

Background:

• Stochastic models are crucial for understanding gene expression dynamics.
• Ignoring transcriptional and translational delays in these models can lead to inaccurate results.
• Delay-induced effects like stochastic oscillations remain underexplored.

Purpose of the Study:

• To systematically investigate the influence of delays and negative feedback on gene expression dynamics.
• To analyze periodicity and multimodality in a simple gene circuit with negative feedback.
• To compare deterministic and stochastic frameworks regarding bifurcation analysis.

Main Methods:

• Developed a simple gene circuit model with negative feedback incorporating transcriptional and translational delays.
• Analyzed dynamics using both deterministic and stochastic simulation approaches.
• Investigated the impact of feedback strength and delay duration on oscillatory and multimodal behaviors.

Main Results:

• An oscillatory regime emerges via Hopf bifurcation in both deterministic and stochastic models.
• Stochastic Hopf bifurcations shift compared to deterministic ones, indicating model inaccuracies.
• Noise in oscillations decreases with increased transcriptional delays and moderate feedback.
• Strong feedback can trigger oscillations via bursts.
• Explicitly including delays increases accessible states in the multimodal regime and introduces excitable system features.

Conclusions:

• Accounting for delays is critical for accurate stochastic modeling of gene expression.
• Delays can induce novel phenomena like stochastic oscillations and excitable dynamics.
• Deterministic bifurcation analysis can be misleading when delays are present.