Figure 1.
Ca2+ imaging shows that each pheromone component activates a single glomerulus in the MGC.
(A) The main pheromone component activates the cumulus only. (B, C) The two secondary components activate two neighboring glomeruli. (D) The blend of the 3 components in the behaviorally most efficient ratio 4∶1∶4 activates the whole MGC. Outlines of antennal lobe (AL), antennal nerve (AN) and the 3 main subdivisions of MGC are shown.
Figure 2.
Pheromone-evoked spiking activities are qualitatively and quantitatively different in ORNs and PNs.
In this and all following figures ORNs are shown in blue and PNs in red. (A) Phasic-tonic activity in a single ORN at various doses C of Z7-12∶Ac from -1 to 4 log ng (bar: stimulus duration, 200 ms). Schematic representation based on spike sorting. Hexane (hex) used as control. Vertical line at Tt = 180±13 ms (mean ± SD) indicates mean time of arrival of stimulus on antenna. (B) Multiphasic activity in a PN at doses from -3 to 1 with repetitions. Same representation as in (A). (C) Instantaneous firing rates estimated with a 50 ms Gaussian kernel (see Methods) of spike trains shown in (A). (D) Instantaneous firing rates of the trains shown in (B). (E) Comparison of average instantaneous firing rates of ORNs and PNs recorded at doses -1, 0 and 1 log ng. (F) Firing rate F versus latency L pairs from the same pheromone-evoked response for all ORNs (blue) and PNs (red) recorded at dose C = −1 log ng (responses significantly different shown as filled circles; all other figures show only responses significantly different from spontaneous activity).
Figure 3.
Spontaneous activity in PNs is higher than in ORNs and depends on ORN spontaneous activity.
(A) Total number of spontaneous spikes Nsp fired from time 0 to ti (firing time of ith spike) plotted as a function of ti in 4 ORNs (blue) and 4 PNs (red). The mean spontaneous firing rate is the slope of the regression line of Nsp vs. t. (B) Spontaneous activity of a PN before and after sectioning the antennal nerve (black cross); same representation as in (A). Top curve: first 3 min with sectioning marked with cross; slope of regression line before sectioning = 32 AP/s. Bottom curve: same neuron from 5 to 8 min after sectioning (slope = 5.6 AP/s). (C) Distribution of spontaneous firing rates in ORNs (blue) and PNs (red), with empirical cumulative distribution functions (CDFs, staircase), fitted lognormal CDFs (dashed curve) and corresponding probability distribution functions (PDFs, dotted curve). Parameters of these distributions are given in S2 Table.
Figure 4.
Distributions of firing rates (top row) and latencies (bottom row) at single pheromone doses are dose-dependent.
(A) Comparison in ORNs of raw firing rates Fraw (not corrected from control stimulations) for control stimulations (green) and for pheromone doses −1, 0, 1, 2, 3, 4 log ng (blue, from left to right). Fraw at C = −1 log ng not significantly different from control (Kolmogorov-Smirnov test, p = 0.43). (B) Comparison in ORNs of latencies L for same stimuli and doses (from right to left) as in (A). (C) Comparison in PNs of firing rates Fraw for control stimulations (green) and for pheromone doses −3, −2, −1, 0, 1 log ng (red), same representation as in (A). Fraw at C = −3 log ng not significantly different from control (Kolmogorov-Smirnov test, p = 0.43) but significantly different from Fraw at C = −2 (p<10−4). (D) Comparison in PNs of latencies L for same stimuli and doses as in (C). (E, G) Comparison of firing rates F (corrected from control stimulation) in ORNs (blue) and PNs (red) at the same doses −1, 0 (in E) and 1 log ng (in G). For C≤1, the mean firing firing rates of ORNs is smaller than that of PNs. (F–H) Comparison of latencies, same representation as in (E, G). At all doses, the mean firing latency of ORNs is larger than that of PNs. At C≥1, the shortest ORN latencies become almost as short as the shortest PN latencies.
Figure 5.
Firing rates and latencies at single pheromone doses are normally distributed with standard deviations related to means.
(A) Empirical CDFs of firing rates F (corrected from control stimulations) for ORN significant responses (staircases) from C = −1 (left) to 4 log ng (right) and fitted Gaussian distributions (dashed lines) of means Fμ and standard deviations σTr. (B) Same as (A) for ORN latencies. (C) Same as (A) for PNfiring rates. (D) Same as (A) for PN latencies. (E) Response heterogeneity plot of σTr versus Fμ as determined in (A) for ORNs (blue dots) and in (C) for PNs (red dots), with regression lines σTr ≈0.331 Fμ AP/s for C = −1 to 1 log ng (ORNs, dose indicated in blue) and −3 to −1 (PNs, in red) and σTr ≈35 AP/s for C>1 (ORNs) and> −1 (PNs). (F) Response heterogeneity plot of σTr versus Lμ for ORNs (blue) and PNs (red) based on (B, D).
Figure 6.
Firing rates are Hill functions of dose with different parameter values in each neuron.
(A) Measured firing rate F (dots) of 3 ORNs fitted to Hill functions (eq. 4; solid curves) showing parameters FM and C1/2 and characteristic C0 and Cs for F0 = 5 AP/s. (B) All (N = 38) Hill curves fitted to ORNs. (C) Hill curves of 3 PNs. (D) All (N = 37) PN curves successfully fitted to Hill functions. (E) Distribution of maximum firing rates FM in the ORN (blue, N = 38) and PN (red, N = 37) populations. Each empirical CDF (staircase) with its fitted normal CDF (dotted curve) and corresponding PDF (dashed curve). (F) Distributions of dynamic ranges ΔC (related to n), same N and representation as in (E) except fitted distribution is lognormal for ORNs.
Figure 7.
Latencies are linear functions of pheromone dose with different parameter values in each neuron.
(A) Measured latency L (dots) of 3 ORNs fitted to decreasing lines (eq. 8; solid curve) showing minimum latency Lm and maximum latency LM at threshold C0 given from Fig. 6A. (B) All (N = 38) fitted ORN dose-latency curves. (C) Three examples of PN latency curves. (D) All (N = 44) fitted PN dose-latency curves. (E) Maximum latencies LM at threshold dose C0 fitted to lognormal CDFs; same N's as in (B, D) and representation as in Fig. 6E. (F) Minimum latencies Lm fitted to normal CDFs; same N and representation as in (E). A few zero latencies arise in PNs from variability on pheromone transport time Tt.
Figure 8.
Dose-response curves of PNs are shifted to left of ORN curves and explain ORN-to-PN transfer functions.
(A) Medians (circles) and quantiles 10% and 90% (vertical dashed lines) of all F measured at a given dose, as shown in Fig. 5. Dose-firing rate curves of ORN (blue) and PN (red) populations reconstructed from parameters of individual C–F curves shown in Fig. 6, based on median (solid), 10% most responsive neurons (dashed, based on quantiles 90% for FM and 10% for C1/2, n) and 90% less responsive neurons (dash-dotted). (B) Dose-latency curves of ORNs (blue) and PNs (red) based on median, 90% and 10% quantiles. Same representations as in (A) based either on pooled L (Fig. 5) or on parameters of C-L curves (Fig. 7). (C) Median transfer function for firing rates (solid, eq. 9); it can be approximated by FPN = 62.5/(1+ (1.5/FORN)1.15); inset: detail of most nonlinear part from threshold to ED50 of ORNs. Transfer function for the 10% most responsive neurons (dashed, derived from (A) by coupling most responsive ORNs and PNs) and for the 10% least responsive ones (dash-dotted). (D) Median transfer function for latencies running from right (low doses) to left (high doses) (solid, eq. 12); inset: linear part from threshold to ED50 of ORNs. Transfer functions for the 10% fastest neurons (dashed) and for the 10% slowest neurons (dash-dot). (E) Distributions of thresholds C0 in ORNs (blue, N = 38) and PNs (red, N = 37); empirical CDFs (staircases) with fitted normal CDF (solid curve) and corresponding PDF (dashed curve); maximum contrast at C0Δ = −1.9 log ng (dashed vertical line) with 17% ORNs and 85% PNs activated. (F) Distributions of ED50 C1/2, same N's and representation as in (E); maximum contrast at C1/2Δ = 0 log ng (dashed vertical line) with 2% of ORNs and 98% of PNs above their C1/2.
Figure 9.
Model of a large ORN population converging on a small PN population.
(A, B) Example at dose C = 1 log ng of cumulated distributions of modelled firing rates (A) and latencies (B) of ORNs and comparison with experimental data. Distributions of experimental values (N = 32, same as in Fig. 5A, B) shown as staircase graphs (solid line) with 95% confidence intervals (green lines). Distributions of modelled F and L shown as smooth curves (in blue) based on N = 5 000 drawings. Firing rates in the model obey eq. 4 and latencies eq. 8 with parameters L0, ln(λ), Lm, FM, C1/2, ln(n) drawn from a multinormal distribution with their observed means, SDs and correlations (S5 Table). The modelled and experimental distributions are not significantly different (Kolmogorov–Smirnov tests at level 1%). (C) Examples of 5 simulated ORN responses with interspike interval 1/F and latency L at C = 1 log ng for 5 parameter drawings; 7000 such responses are summated to simulate the whole ORN population). (D) Simulated spontaneous activity of the whole ORN population (based on the lognormal distribution with μ = 1.23 and σ = 0.71 shown in Fig. 3E); the firing rate fluctuates around a stationary value ∼270 AP/10 ms. (E) Proportion of ORNs that respond with a shorter latency than the typical PN (with all 6 parameters equal to their median values; solid line), than a slow and insensitive PN (parameters equal to their 75% quantiles, dotted), and than a fast and sensitive PN (parameters equal to their 25% quantiles; dashed) at doses C0, C1/2 and Cs. (F) PSTH of the total number of spikes fired per 10 ms at doses from −8 to −2 log ng by a simulated population of 7000 NROs. The summated firing rate close to detection threshold (dotted line, 275 APs per 10 ms, see text) is reached for C≈−4.5 log ng at time ∼200 ms.