  It is known that if odors are presented to an olfactory receptor neuron (ORN)
in a sub-threshold concentration -- i.e., when the average value of the number
of the ORN bound receptor proteins (RPs) is insufficient for the generation of
spikes, but such a generation is still possible due to fluctuations around the
average value -- the ORN selectivity can be higher than the selectivity at
higher concentrations and, in particular, higher than the selectivity of the
ORN's RPs. In this work, the optimal odorant concentration providing the
highest ORN selectivity is found in the framework of a simplified ORN model,
and the dependence of the highest selectivity on the total number of RPs in the
ORN, $N$, and its threshold value $N_{0}$ is derived. The effect of enhanced
selectivity in the sub-threshold regime is best manifested, if $N_{0}$ is close
to either unity or $N$. It is also more pronounced at large $N$-values.
