The variance of phase-resetting curves

Area of Science:

• Computational Neuroscience
• Nonlinear Dynamics
• Biophysics

Background:

• Phase resetting curves (PRCs) quantify oscillator sensitivity to perturbations.
• Environmental noise introduces significant variability into observed PRCs.
• Accurate characterization of this variability is crucial for understanding noisy oscillatory systems.

Purpose of the Study:

• To develop a theoretical framework for computing the mean and variance of PRCs in noisy environments.
• To introduce an analytical method for estimating phase-dependent variance.
• To compare the accuracy of this new method against existing techniques and experimental data.

Main Methods:

• Application of perturbation theory to derive analytical expressions for PRC mean and variance.
• Fitting theoretical curves to experimental data and simulation results.
• Comparison with an ad-hoc method for variance estimation.
• Simulation of a dual-cell network to validate predictions.

Main Results:

• The derived analytical method accurately predicts the mean and variance of PRCs for limit cycle oscillators under small noise conditions.
• The phase-dependent variance estimation significantly outperforms an ad-hoc method in fitting experimental and simulation data.
• Dual-cell network simulations align well with the theoretical predictions.

Conclusions:

• The novel analytical approach provides a more accurate and robust estimation of phase-dependent variance in noisy PRCs.
• This method enhances the understanding of oscillatory dynamics in biological systems, such as neuronal networks.
• The findings offer insights into noise-induced phenomena like neuronal entrainment.