Exact analysis of the subthreshold variability for conductance-based neuronal models with synchronous synaptic...

Area of Science:

• Computational neuroscience
• Theoretical neuroscience

Background:

• Neocortical neurons display significant spiking variability, even with identical stimuli, suggesting operation in the asynchronous state.
• While asynchronous models explain spiking variability, their ability to account for subthreshold membrane potential variability remains unclear.

Approach:

• Developed a novel analytical framework using exchangeability theory to model input synchrony via jump-process-based synaptic drives.
• Performed a moment analysis on a conductance-based neuron model with all-or-none conductances, neglecting post-spiking reset.
• Derived exact closed-form expressions for the first two stationary moments of membrane voltage, dependent on synaptic parameters and synchrony.

Key Points:

• Realistic subthreshold voltage variability in biophysical models is achieved with a limited number of strong synapses (e.g., thalamic input).
• Dense cortico-cortical inputs require weak, non-zero input synchrony to produce realistic subthreshold variability.
• Absence of synchrony leads to vanishing neural variability in scaling limits, irrespective of balanced state hypotheses.

Conclusions:

• The asynchronous state model's ability to explain subthreshold variability is conditional on specific input characteristics.
• Input synchrony plays a crucial role in shaping subthreshold voltage variability in neural networks.
• Findings challenge the theoretical underpinnings of mean-field theories for the asynchronous state in neural computation.