Gatsby Unit, UCL, London, United Kingdom
Cortical neurons are driven by both excitatory and inhibitory sources, and an increasing amount of evidence suggests that this excitation and inhibition is tightly balanced. Can such a balance be explained by simple, static mechanisms, as predicted by models of random networks? A recent in vivo-study (Okun & Lampl, Nat. Neurosci. 11, 535-537, 2008) found almost instantaneous correlations of excitation and inhibition in pairs of cortical neurons, seemingly contradicting random models and calling for continuous control with millisecond precision. Motivated by insights from mean-field theory, we investigated the question whether the dynamics observed in cortex are compatible with simple models of random networks.
We simulated a minimal model of an unstructured cortical column consisting of two populations, one excitatory and one inhibitory, and excitatory input from an external source. We chose the quadratic integrate-and-fire neuron model with conductance-based synaptic dynamics. Neurons were connected randomly with 10% connection probability and synaptic strengths were chosen within a physiologically realistic range.
When the model network was left without external input apart from brief bursts of variable strengths, we observed excitatory and inhibitory dynamics similar to those reported in the in vivo-study.
Specifically, both the size of the cross-correlations and the time-lag between excitation and inhibition were in close agreement with experimental values. In our model network, as in cortex, inhibition lags excitation by several milliseconds when measured via the position of the peak in the cross-correlogram. We find that the position of this peak is insensitive to the size of the synaptic time constants, while the width of the cross-correlation increases with increasing synaptic time constants.
Our results demonstrate that instantaneous correlations of excitation and inhibition in cortical networks do not require precisely timed control mechanisms. Rather than invalidating models of random networks, as previously suggested, recent data obtained from intracellular pair-wise recordings in vivo provide additional support to the notion that simple random models can capture essential aspects of cortical dynamics. Since entirely random networks do not support functional roles, our results highlight the fact that precise timing does not constitute evidence for temporal coding mechanisms.