(A) Hypothetical physiological processes underlying the olfactory transduction pathway and spike generation. The integral feedback (IFB) motif is built on the assumption that inhibitory feedback modulates the activity of the odorant receptor, as was proposed in the adult fly (Nagel and Wilson, 2011). This motif appears to be essential to olfactory transduction in vertebrates (De Palo et al., 2013). The incoherent feed-forward (IFF motif) relies on the hypothetical existence of a delayed inhibitory effect, as was proposed for the transduction cascade of C. elegans (Kato et al., 2014). (B) Biophysical model of the olfactory transduction pathway. (Bi) Circuit elements combining the IFF and IFB motifs described in panel A. Variable x represents the stimulus intensity, u, the activity or concentration of the intermediate variable and y, the firing rate of the OSN. Pathway (3) is specific to the IFB motif (light blue). (Bii) ODE system providing a phenomenological description of the reaction scheme outlined in panel A for the combination of the IFF and IFB regulatory motifs. The three pathways regulating the activity of u are outlined by numbers (1)–(3). Reaction (1) corresponds to a ‘production’ of u through the IFF branch; (2) corresponds to a first-order ‘decay’ of u; (3) corresponds to a ‘production’ of u through the IFB branch. (C) Simulated activity of u (green, middle) and firing rate y (blue, bottom) in response to an 8-s linear odor ramp (magenta, top). Numerical simulations were achieved by integrating the ODE system described in panel Bii with the parameter values listed in Table 1. (D) Decomposition of the predicted activity of individual pathways contributing to the regulation of u for the linear odor ramp displayed in panel C. Activity computed from the terms (1)–(3) outlined in panel B for the feed-forward activation by the stimulus (IFF, 1), first-order decay (2) and coupling of the firing rate with the intermediate variable through the negative feedback (IFB, 3). Notably, the contribution of the reaction specific to the IFB motif (3) is dominated by the reaction specific to the IFF motif (1). (E) Fit of the solution of the ODE model for three linear stimulation ramps introduced in Figure 3A,B and produced with odor (middle) and light (bottom). (Top) Stimulus intensity given as odor concentration (μM). The time derivative of the concentration profile (gray lines) is given according to the y-axis shown on the right side of the graph. The derivative was computed after mild smoothening of the stimulus time course. The same (idealized) profile was used for the light stimulation with an intensity ranging between 15 W/m2 and 207 W/m2. (Middle) Comparison of the outcome of the model featuring a pure IFF motif (green) and a combination of the IFF and IFB motifs (blue). The parameters of both models were obtained independently through a Simplex optimization procedure (‘Materials and methods’). For the pure IFF model, parameter α3 was artificially set to 0. (Bottom) Comparison of the outcome of the experimental PSTH and the model's predictions based on a pure IFF motif (green) for light stimulation. Parameter optimization shows that the IFB motif does not contribute to the light-evoked OSN dynamics. (F) Fit of the solution of the ODE model for three nonlinear stimulation ramps generated with odor and light. (Middle) Results of the model compared to the odor-evoked OSN activity. Close-up view of the 8-s linear ramp highlighting the differences between the behavior of the pure IFF (green) and combined IFF+IFB (blue) circuit motifs for odor stimulation. (Bottom) Comparison of the outcome of the experimental PSTH and model based on a pure IFF motif (green) for light stimulation. For all conditions shown in the figure, PSTHs were computed on a pool of a minimum of 10 recordings obtained from a minimum of 10 preparations.