On two diffusion neuronal models with multiplicative noise: The mean first-passage time properties

Area of Science:

• Computational Neuroscience
• Stochastic Processes
• Mathematical Biology

Background:

• Neuronal membrane depolarization between spikes is crucial for neural function.
• Diffusion processes with multiplicative noise offer a framework for modeling these dynamics.
• Understanding variability and first-passage time properties is key to neural modeling.

Purpose of the Study:

• To compare two diffusion processes with multiplicative noise for modeling neuronal depolarization.
• To investigate differences in state-dependent variabilities, asymptotic distributions, and first-passage time properties.
• To analyze the influence of model parameters on neuronal firing dynamics.

Main Methods:

• Analysis of two diffusion processes with identical deterministic parts but different stochastic components.
• Derivation of closed-form expressions for the mean first-passage time.
• Investigation of asymptotic distributions and state-dependent variabilities.
• Examination of the stationary distribution's impact on first-passage time.

Main Results:

• The study reveals that increased variability (second moment) does not invariably result in a shorter mean first-passage time.
• The shape of the stationary distribution significantly influences the first-passage time dynamics.
• Parameter analysis elucidates the role of variability and distribution in neuronal firing.
• Identified potential applications beyond neuroscience.

Conclusions:

• The relationship between variability and firing rate in neuronal models is complex and depends on the full stationary distribution.
• The findings provide insights into the biophysical mechanisms underlying neuronal excitability.
• The models and analyses can be extended to other systems exhibiting similar stochastic dynamics.