How noise can generate calcium spike-type oscillations in deterministic equilibrium modes

Area of Science:

• Computational Neuroscience
• Theoretical Biophysics
• Nonlinear Dynamics

Background:

• The Li-Rinzel model describes calcium dynamics and neuronal excitability.
• Deterministic versions of such models can exhibit stable equilibria, lacking oscillatory behavior.
• Stochastic influences are crucial for understanding biological system dynamics.

Purpose of the Study:

• To investigate noise-induced spiking oscillatory regimes in the Li-Rinzel model.
• To analyze the probabilistic mechanisms behind large-amplitude oscillations in excitable systems.
• To explore the phenomenon of coherence resonance in this context.

Main Methods:

• Numerical simulations of the Li-Rinzel model under stochastic conditions.
• Analytical investigation using the confidence domain method and stochastic sensitivity analysis.
• Statistical description of interspike intervals.

Main Results:

• Demonstrated noise-induced generation of large-amplitude oscillations in previously stable regions.
• Identified key parametric zones for stochastic excitability.
• Showcased the role of separatrices (stable manifolds of saddle equilibria) in governing noise effects.

Conclusions:

• Stochastic excitability is a significant phenomenon in the Li-Rinzel model, enabling oscillations via noise.
• Coherence resonance may play a role in tuning the system's response to noise.
• The interplay between noise, model parameters, and separatrices dictates the emergence of spiking activity.