Patterns of interval correlations in neural oscillators with adaptation

Area of Science:

• Computational Neuroscience
• Neural Dynamics
• Mathematical Biology

Background:

• Neural firing patterns are shaped by intrinsic properties and external inputs.
• Adaptation currents are key mechanisms providing negative feedback in neurons.
• These currents can introduce dependencies between successive neuronal events (spikes).

Purpose of the Study:

• To analytically investigate interval correlations in noisy neural oscillators with spike-triggered adaptation.
• To establish a general relationship between interval correlations and the neuron's phase-response curve (PRC).
• To identify factors governing the qualitative patterns of these correlations.

Main Methods:

• Development of a weak-noise theory for neural oscillators.
• Analytical derivation of interval correlations based on the phase-response curve (PRC).
• Stochastic simulations of various integrate-and-fire neuron models with adaptation.

Main Results:

• A general relation between interval correlations and the PRC was established.
• Anti-correlations between adjacent spike intervals were proven for type I PRC neurons.
• A single order parameter was identified to predict correlation patterns.
• Correlation structures (decaying or oscillating) linked to post-spike voltage dynamics and phase plane geometry.

Conclusions:

• Spike-triggered adaptation significantly shapes neural spike train statistics.
• The phase-response curve (PRC) is a crucial determinant of interval correlations.
• Understanding these correlations is vital for interpreting neural coding and network dynamics.