A dynamical feedback model for adaptation in the olfactory transduction pathway

Abstract

Olfactory transduction exhibits two distinct types of adaptation, which we denote multipulse and step adaptation. In terms of measured transduction current, multipulse adaptation appears as a decrease in the amplitude of the second of two consecutive responses when the olfactory neuron is stimulated with two brief pulses. Step adaptation occurs in response to a sustained steplike stimulation and is characterized by a return to a steady-state current amplitude close to the prestimulus value, after a transient peak. In this article, we formulate a dynamical model of the olfactory transduction pathway, which includes the kinetics of the CNG channels, the concentration of Ca ions flowing through them, and the Ca-complexes responsible for the regulation. Based on this model, a common dynamical explanation for the two types of adaptation is suggested. We show that both forms of adaptation can be well described using different time constants for the kinetics of Ca ions (faster) and the kinetics of the feedback mechanisms (slower). The model is validated on experimental data collected in voltage-clamp conditions using different techniques and animal species.

Figure 1

The pathway and its feedback loops. (A) Representation of the entire olfactory transduction pathway in the cilia of OSNs. Modified from Pifferi et al. (38), with permission. The shaded part is not considered in this study. A detailed description of the pathway is provided in the Supporting Material. (B) Scheme of the basic reactions and feedback mechanisms included in our model. Pointed arrows mean positive regulation, stopped arrows mean negative feedbacks, dashed arrows degradations. The three bidirectional arrows represent reversible reactions. The two feedback loops are represented in red and green.

Figure 2

Response to odorant. (A) Response reductions by a conditioning pulse and their recovery time course in newt OSN (blue) and the corresponding fit of the model (red). (The blue traces above the fit of the data represent the timing of the odorant stimulations.) The amplitude of each response was normalized to the response to the first conditioning pulse. Two identical odorant stimuli of amyl acetate of 200-ms duration were applied separated by a time interval Δt of 2.5, 4.5, and 6.5 s. Experimental data drawn from Kurahashi and Menini (7) with permission from Macmillan Publishers. (B) The response of a salamander OSN to an odorant stimulus sustained for 43.5 s. Experimental data adapted from Menini et al. (15) with permission from Macmillan Publishers. (C) Corresponding simulated input, normalized state variables, and output currents (with the two components I_CNG and I_Cl) for the pulse pair with Δt = 2.5 s shown in panel A. (D) Simulated input, normalized state variables, and output currents (I_CNG and I_Cl) for a sustained stimulus of 43.5 s in duration.

Figure 3

Response to photorelease of caged cyclic nucleotides. Response reductions by a conditioning pulse and their recovery time course in OSNs. (Color online: the experimental data are shown in blue, the response of the model in red.) Above each panel, the experimental input is shown (see Fig. S3 for the simulated input). In each panel, the amplitudes of the responses were normalized to the response to the first conditioning pulse. (A) Responses of a newt OSN to photorelease of cAMP by two identical 100-ms ultraviolet flashes, separated by increasing time intervals Δt of 2.3, 4.3, and 6.3 s. Experimental data adapted from Kurahashi and Menini (7) with permission from Macmillan Publishers. (B) Responses of a mouse OSN to photorelease of 8-Br-cAMP obtained with two identical ultraviolet-light flashes of 1.5 ms separated by time intervals of 2.5, 4, and 6.8 s. Experimental data from Boccaccio et al. (20), reproduced with permission.

Figure 4

Response to IBMX. Responses of salamander OSNs to IBMX. (On-line color version: blue) Experimental data; (red) response of the model. Above each panel, the experimental input is shown (see Fig. S4 for the simulated input). (A) Responses to repeated applications of IBMX pulses of 20 ms applied to the cell at time intervals Δt of 6, 10, and 15 s. (B) Response to an IBMX stimulus applied for 24 s. (C) Responses to two subsequent prolonged IBMX stimuli of 8 s duration with interpulse interval of 20 and 28 s. IBMX was applied through a glass pipette controlled by a pressure ejection system. The concentration of IBMX in the pipette was 0.1 mM. Both kinds of adaptation are observed in the experiments and reproduced by the model: decline of the peak and convergence to a new adapted steady state within each stimulation, and peak amplitude modulation depending on the interstimuli lag time.