A small neural net simulates coherence and short-term memory in an insect olfactory system

We present a simple neural network model which simulates the experimental action potentials measured by Laurent and coworkers from single local (LN) and projection neurons (PN) in the olfactory system of an insect, the locust. Our recurrent network consists of one LN and 80 PNs where the individual units (neurons) are described by the Hodgkin–Huxley model. Bifurcation diagrams for the isolated neurons are calculated, where the PNs are oscillatory whereas the LN is treated as a non-oscillatory steady state neuron. The PN–PN and PN–LN synapses are excitatory. Inhibitory synaptic coupling between the LN and all 80 PNs causes all PNs to fire coherently generating a local field potential which precedes the LN by a small phase-shift. The LN and the PNs receive a scaled antennal nerve current from the olfactory receptor neurons (ORNs) where the receptors bind odor molecules with specific binding constants in a simple “ open” binding process. We assume, that the odor-bound receptors exist in two states; an active state (R1) and an inactive state (R2) leading to adaptation where R1 is assumed to be proportional to the antennal nerve current. All synaptic strengths are augmented by small increments for each successive odor presentation. Thus, the short-term memory effect which has been measured by Stopfer and Laurent (M. Stopfer and G. Laurent, Nature, 1999, 402, 664) in 10 repeated presentations of the same odor, is successfully simulated: the PN action potentials decrease in intensity, successive signatures simplify and the PN-coherence increases. High PN-frequencies (>50 Hz) abolish the coherence in the range 20–50 Hz. A previously augmented synaptic strength is retained after 10 trials and a 30 s resting period to produce coherence in a “naive” part of the antenna in a subsequent trial.