Analysis of a Simple Model for Dual Inhibition in the Olfacotry Bulb

The olfactory bulb (OB) is the first stage of olfactory sensory processing in the brain, receiving olfactory receptor neuron (ORN) input from the periphery and transmitting a processed signal to the rest of the brain via mitral/tufted cells (MTCs). The purpose of this study is to determine how changes in odorant concentration are encoded and transformed by processing within the OB. In vivo measurements have revealed four general classes of MTC output response over a range of odorant concentrations: those that increase monotonically, those that decrease monotonically, those that increase and then decrease at higher input levels, and those that decrease and then increase. While network models of OB processing have been developed previously and computer simulations performed, their complexity greatly limited detailed analysis. Here, we developed a simple mathematical model that is amenable to rigorous investigation. The model demonstrates that experimental MTC response patterns across varying odorant concentrations can emerge from ORN input properties combined with concurrent OB inhibitory processes - primarily feed-forward and lateral inhibition. We also demonstrated how the different response types are situated in the parameter space for the two key ORN parameters; the half-maximum and Hill coefficient.

Relevance to Life Sciences - Processing of odor information begins at the olfactory bulb, where input from receptor neurons is transformed and integrated through two mechanisms: inhibition local to individual glomeruli and inhibition that spans glomeruli. This study shows how the two forms of inhibition transform the monotonic concentration-response curves of receptor neurons into distinct classes of non-monotonic outputs in mitral/tufted cells.

Mathematical Content - We demonstrated mathematically that the effects of ORN and MTC parameters are separable, offering both conceptual and practical consequences. Bifurcation analysis was then used to construct maps depicting which concentration-response category of MTC would result as the parameters that shape the ORN response to odorants, the half-maximum value and Hill coefficient, were varied. Model predictions motivated a re-examination of Ca2+ imaging data, uncovering two new classes of MTC responses. Overall, we demonstrate how the two types of OB inhibition can impact MTC concentration-response output relationships, and form predictions about ORN parameter regions that lead to each class of response.