Exact Analysis of the Subthreshold Variability for Conductance-Based Neuronal Models with Synchronous Synaptic Inputs

Area of Science:

• Computational Neuroscience
• Systems Neuroscience
• Theoretical Neuroscience

Background:

• Neocortical neuron activity displays significant variability, even with identical stimuli.
• The asynchronous state hypothesis suggests independent neuronal firing, minimizing synchronous synaptic input.
• Existing models explain spiking variability but not subthreshold membrane potential variability.

Purpose of the Study:

• To develop an analytical framework for quantifying subthreshold voltage variability in conductance-based neurons.
• To investigate the impact of synaptic input synchrony on neuronal variability.
• To determine conditions for realistic subthreshold variability in neural networks.

Main Methods:

• Utilized the theory of exchangeability to model input synchrony using jump-process-based synaptic drives.
• Performed a moment analysis on the stationary response of a simplified neuronal model (all-or-none conductances, neglecting postspiking reset).
• Derived exact, closed-form expressions for the first two stationary moments of membrane voltage.

Main Results:

• The asynchronous regime produces realistic subthreshold variability (4-9 mV²) only with a limited number of strong synapses, consistent with thalamic input.
• Achieving realistic variability with dense cortico-cortical inputs necessitates incorporating weak, non-zero input synchrony.
• Neural variability diminishes to zero without synchrony in scaling limits with vanishing synaptic weights, irrespective of balanced state hypotheses.

Conclusions:

• Subthreshold voltage variability in neocortical neurons is sensitive to synaptic input characteristics, including synchrony.
• Realistic subthreshold variability may depend on specific network structures (e.g., strong thalamic drive) or weak input synchrony.
• The findings challenge the theoretical underpinnings of mean-field theories for the asynchronous state in neural networks.