Accurate population models are needed to build very large-scale neural models, but their derivation is difficult for realistic networks of neurons, in particular when nonlinear properties are involved, such as conductance-based interactions and spike-frequency adaptation. Here, we consider such models based on networks of adaptive exponential integrate-and-fire excitatory and inhibitory neurons. Using a master equation formalism, we derive a mean-field model of such networks and compare it to the full network dynamics. The mean-field model is capable of correctly predicting the average spontaneous activity levels in asynchronous irregular regimes similar to in vivo activity. It also captures the transient temporal response of the network to complex external inputs. Finally, the mean-field model is also able to quantitatively describe regimes where high- and low-activity states alternate (up-down state dynamics), leading to slow oscillations. We conclude that such mean-field models are biologically realistic in the sense that they can capture both spontaneous and evoked activity, and they naturally appear as candidates to build very large-scale models involving multiple brain areas.

We report a transition from asynchronous to oscillatory behaviour in balanced inhibitory networks for class I and II neurons with instantaneous synapses. Collective oscillations emerge for sufficiently connected networks. Their origin is understood in terms of a recently developed mean-field model, whose stable solution is a focus. Microscopic irregular firings, due to balance, trigger sustained oscillations by exciting the relaxation dynamics towards the macroscopic focus. The same mechanism induces in balanced excitatory-inhibitory networks quasi-periodic collective oscillations.

How does the brain link visual stimuli across space and time? Visual illusions provide an experimental paradigm to study these processes. When two stationary dots are flashed in close spatial and temporal succession, human observers experience a percept of apparent motion. Large spatiotemporal separation challenges the visual system to keep track of object identity along the apparent motion path, the so-called "correspondence problem." Here, we use voltage-sensitive dye imaging in primary visual cortex (V1) of awake monkeys to show that intracortical connections within V1 can solve this issue by shaping cortical dynamics to represent the illusory motion. We find that the appearance of the second stimulus in V1 creates a systematic suppressive wave traveling toward the retinotopic representation of the first. Using a computational model, we show that the suppressive wave is the emergent property of a recurrent gain control fed by the intracortical network. This suppressive wave acts to explain away ambiguous correspondence problems and contributes to precisely encode the expected motion velocity at the surface of V1. Together, these results demonstrate that the nonlinear dynamics within retinotopic maps can shape cortical representations of illusory motion. Understanding these dynamics will shed light on how the brain links sensory stimuli across space and time, by preformatting population responses for a straightforward read-out by downstream areas.