Data-driven inference for stationary jump-diffusion processes with application to membrane voltage fluctuations in...

Area of Science:

• Computational Neuroscience
• Stochastic Processes
• Biophysics

Background:

• Biological systems often exhibit emergent activity modeled by stochastic differential equations.
• Standard models fail when large, abrupt events (violating model assumptions) occur.
• Investigating these jump-like events is crucial for understanding system dynamics.

Purpose of the Study:

• To develop a novel, data-driven method for reconstructing jump-diffusion stochastic processes from observed data.
• To analyze neuronal membrane noise in electric fish, focusing on unexplained jump-like depolarization events.
• To understand the functional role of these events without relying on predefined biophysical models.

Main Methods:

• Reconstruction of jump-diffusion processes from stationary data with additive diffusive noise and Poisson jumps.
• Detection of jumps using threshold-crossing of time series increments.
• Iterative compensation for falsely detected jumps using probabilistic calculations and Fokker-Planck/Chapman-Kolmogorov equations.

Main Results:

• The method successfully reconstructs jump-diffusion processes from data statistics.
• Application to electric fish pyramidal neurons revealed changes in jump rate and noise intensity near spike threshold.
• Drift function and jump amplitude distribution remained constant across observed conditions.

Conclusions:

• The developed data-driven method effectively characterizes systems with jump-diffusion dynamics.
• Neuronal jump activity in electric fish is modulated by membrane potential proximity to spike threshold.
• This approach offers a powerful tool for studying the functional significance of stochastic events in biological systems.