Partitioning non-linearities in the response of honey bee olfactory receptor neurons to binary odors

In many organisms, of which honey bees are one example, a general (i.e., non-pheromonal) olfactory receptor neuron may respond to some odorants by increasing its firing rate and to others by decreasing its firing rate. In the latter case, this decrease will be with respect to a background firing rate determined by intrinsic (internal noise) and extrinsic (background odors) factors. To analyse receptor neurons of this complexity, we extend Beidler's model of receptor protein activation dynamics to account for the competition between depolarizing and hyperpolarizing pathways and couple the model to a phenomenological description of the non-linear relationship between the proportion of activate membrane receptors and the receptor cell spike generation rates. We then examine the implications of this theory for predicting the response of receptor neurons to odor mixtures based on their response to pure odorants at concentrations matched to the mixture. We derive inequalities that must be satisfied under our normative model, and propose that deviations from the model be designated as synergisms and inhibitions, depending on the direction in which various equalities and inequalities are violated. We then apply our inequalities to identifying synergisms and inhibitions in data analysed in a different way elsewhere (Akers, R.P. and Getz, W.M. Response of olfactory receptor neurons in honey bees to odorants and their binary mixtures. J. Comp. Physiol. (in press)). In these data regarding the response of honey bee placode sensilla to a number of odorants and their binary combinations, we demonstrate the presence of synergisms and inhibitions--that is, elevated or repressed responses that are not due to competitive interactions of mixture component odorants for receptor sites or Beidler (Beidler, L.M., 1962. Taste receptor stimulation. Prog. Biophys. Biophys. Chem. 12, 107-151) saturation mechanisms.