A straightforward method to compute average stochastic oscillations from data samples

Area of Science:

• Systems Biology
• Computational Biology
• Biophysics

Background:

• Biological systems often display sustained stochastic oscillations in their steady state.
• Variability in oscillation amplitude and frequency complicates assessment.
• Averaging multiple stochastic system replications can obscure oscillations, leading to incorrect conclusions of a constant steady state.

Purpose of the Study:

• To propose a straightforward and efficient method for detecting and assessing stochastic oscillations.
• To provide a new perspective on system dynamics beyond traditional Cartesian coordinate analysis.

Main Methods:

• Utilizes polar coordinates for two-species systems and cylindrical coordinates for systems with more than two species.
• Modifies coordinate systems to compute total angular distance and average Euclidean distance to a reference point.
• Enables computation of confidence intervals for average angular speed and distance from replications.

Main Results:

• The proposed coordinate transformation offers a new perspective on system dynamics.
• Mean polar trajectories reveal average circular motion, providing evidence for sustained oscillations.
• Confidence intervals for angular speed and distance can be efficiently computed.

Conclusions:

• Polar/cylindrical coordinates offer a superior method for analyzing steady-state oscillations compared to Cartesian coordinates.
• The method effectively identifies oscillations obscured by averaging, preventing erroneous conclusions.
• The coordinate transformation and confidence interval computation are computationally efficient, making it a practical tool for evaluating stochastic oscillations.