Oscillatory synchronization requires precise and balanced feedback inhibition in a model of the insect antennal lobe

In the insect olfactory system, odor-evoked transient synchronization of antennal lobe (AL) projection neurons (PNs) is phase-locked to the oscillations of the local field potential. Sensory information is contained in the spatiotemporal synchronization pattern formed by the identities of the phase-locked PNs. This article investigates the role of feedback inhibition from the local neurons (LNs) in this coding. First, experimental biological results are reproduced with a reduced computational spiking neural network model of the AL. Second, the low complexity of the model leads to a mathematical analysis from which a lower bound on the phase-locking probability is derived. Parameters involved in the bound indicate that PN phase locking depends not only on the number of LN-evoked inhibitory postsynaptic potentials (IPSPs) previously received, but also on their temporal jitter. If the inhibition received by a PN at the current oscillatory cycle is both perfectly balanced (i.e., equal to the mean inhibitory drive) and precise (without any jitter), then the PN will be phase-locked at the next oscillatory cycle with probability one.