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

Area of Science:

• Computational neuroscience
• Neural dynamics
• Mathematical modeling

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.

Approach:

• Developed a novel analytical framework to quantify subthreshold variability in conductance-based neurons.
• Utilized exchangeability theory to model input synchrony using jump-process-based synaptic drives.
• Performed moment analysis on a simplified neuronal model (all-or-none conductances, neglecting post-spiking reset).

Key Points:

• Derived exact, closed-form solutions for the first two stationary moments of membrane voltage.
• Showed that realistic subthreshold variability (4-9mV^2) in the asynchronous regime requires a limited number of strong synapses (e.g., thalamic input).
• Demonstrated that dense cortico-cortical inputs necessitate weak but non-zero synchrony for realistic subthreshold variability.

Conclusions:

• The asynchronous state alone may not fully explain subthreshold voltage variability.
• Input synchrony plays a crucial role in shaping neural variability, especially for cortico-cortical networks.
• Findings challenge the theoretical underpinnings of mean-field theories for the asynchronous state in neural networks.