Modelling the signal delivered by a population of first-order neurons in a moth olfactory system

A statistical model of the population of first-order olfactory receptor neurons (ORNs) is proposed and analysed. It describes the relationship between stimulus intensity (odour concentration) and coding variables such as rate and latency of the population of several thousand sex-pheromone sensitive ORNs in male moths. Although these neurons likely express the same olfactory receptor, they exhibit, at any concentration, a relatively large heterogeneity of responses in both peak firing frequency and latency of the first action potential fired after stimulus onset. The stochastic model is defined by a multivariate distribution of six model parameters that describe the dependence of the peak firing rate and the latency on the stimulus dose. These six parameters and their mutual linear correlations were estimated from experiments in single ORNs and included in the multidimensional model distribution. The model is utilized to reconstruct the peak firing rate and latency of the message sent to the brain by the whole ORN population at different stimulus intensities and to establish their main qualitative and quantitative properties. Finally, these properties are shown to be in agreement with those found previously in a vertebrate ORN population

Odour transduction in olfactory receptor neurons

International audienceThe molecular mechanisms that control the binding of odorant to olfactory receptors and transduce this signal into membrane depolarization are reviewed. They are compared in vertebrates and insects for interspecific (allelochemicals) and intraspecific (pheromones) olfactory signals. Attempts to develop quantitative models of these multistage signalling networks are presented. Computational analysis of olfactory transduction is still in its infancy and appears as a promising area for future developments

Low-amplitude, high-frequency electromagnetic field exposure causes delayed and reduced growth in <em>Rosa hybrida</em>

International audienceIt is now accepted that plants perceive high-frequency electromagnetic field (HF-EMF). We wondered if the HF-EMF signal is integrated further in planta as a chain of reactions leading to a modification of plant growth. We exposed whole small ligneous plants (rose bush) whose growth could be studied for several weeks. We performed exposures at two different development stages (rooted cuttings bearing an axillary bud and 5-leaf stage plants), using two high frequency (900 MHz) field amplitudes (5 and 200 V m(-1)). We achieved a tight control on the experimental conditions using a state-of-the-art stimulation device (Mode Stirred Reverberation Chamber) and specialized culture-chambers. After the exposure, we followed the shoot growth for over a one-month period. We observed no growth modification whatsoever exposure was performed on the 5-leaf stage plants. When the exposure was performed on the rooted cuttings, no growth modification was observed on Axis I (produced from the elongation of the axillary bud). Likewise, no significant modification was noted on Axis II produced at the base of Axis I, that came from pre-formed secondary axillary buds. In contrast, Axis II produced at the top of Axis I, that came from post-formed secondary buds consistently displayed a delayed and significant reduced growth (45%). The measurements of plant energy uptake from HF-EMF in this exposure condition (SAR of 7.2 10(-4) W kg(-1)) indicated that this biological response is likely not due to thermal effect. These results suggest that exposure to electromagnetic field only affected development of post-formed organs

Distributions of firing rates (top row) and latencies (bottom row) at single pheromone doses are dose-dependent.

<p>(<b>A</b>) Comparison in ORNs of raw firing rates <i>F</i>_raw (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). <i>F</i>_raw at <i>C</i> = −1 log ng not significantly different from control (Kolmogorov-Smirnov test, <i>p</i> = 0.43). (<b>B</b>) Comparison in ORNs of latencies <i>L</i> for same stimuli and doses (from right to left) as in (A). (<b>C</b>) Comparison in PNs of firing rates <i>F</i>_raw for control stimulations (green) and for pheromone doses −3, −2, −1, 0, 1 log ng (red), same representation as in (A). <i>F</i>_raw at <i>C</i> = −3 log ng not significantly different from control (Kolmogorov-Smirnov test, <i>p</i> = 0.43) but significantly different from <i>F</i>_raw at <i>C</i> = −2 (<i>p</i><10⁻⁴). (<b>D</b>) Comparison in PNs of latencies <i>L</i> for same stimuli and doses as in (C). (<b>E, G</b>) Comparison of firing rates <i>F</i> (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 <i>C</i>≤1, the mean firing firing rates of ORNs is smaller than that of PNs. (<b>F–H</b>) 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 <i>C</i>≥1, the shortest ORN latencies become almost as short as the shortest PN latencies.</p

Latencies are linear functions of pheromone dose with different parameter values in each neuron.

<p>(<b>A</b>) Measured latency <i>L</i> (dots) of 3 ORNs fitted to decreasing lines (eq. <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003975#pcbi.1003975.e008" target="_blank">8</a>; solid curve) showing minimum latency <i>L</i>_m and maximum latency <i>L</i>_M at threshold <i>C</i>₀ given from <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003975#pcbi-1003975-g006" target="_blank">Fig. 6A</a>. (<b>B</b>) All (<i>N</i> = 38) fitted ORN dose-latency curves. (<b>C</b>) Three examples of PN latency curves. (<b>D</b>) All (<i>N</i> = 44) fitted PN dose-latency curves. (<b>E</b>) Maximum latencies <i>L</i>_M at threshold dose <i>C</i>₀ fitted to lognormal CDFs; same <i>N</i>'s as in (B, D) and representation as in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003975#pcbi-1003975-g006" target="_blank">Fig. 6E</a>. (<b>F</b>) Minimum latencies <i>L</i>_m fitted to normal CDFs; same <i>N</i> and representation as in (E). A few zero latencies arise in PNs from variability on pheromone transport time <i>T</i>_t.</p

Spontaneous activity in PNs is higher than in ORNs and depends on ORN spontaneous activity.

<p>(<b>A</b>) Total number of spontaneous spikes <i>N</i>_sp fired from time 0 to <i>t_i</i> (firing time of <i>i</i>th spike) plotted as a function of <i>t_i</i> in 4 ORNs (blue) and 4 PNs (red). The mean spontaneous firing rate is the slope of the regression line of <i>N</i>_sp vs. <i>t</i>. (<b>B</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). (<b>C</b>) 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 <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003975#pcbi.1003975.s006" target="_blank">S2 Table</a>.</p

Ca²⁺ imaging shows that each pheromone component activates a single glomerulus in the MGC.

<p>(<b>A</b>) The main pheromone component activates the cumulus only. (<b>B, C</b>) The two secondary components activate two neighboring glomeruli. (<b>D</b>) 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.</p

Firing rates are Hill functions of dose with different parameter values in each neuron.

<p>(<b>A</b>) Measured firing rate <i>F</i> (dots) of 3 ORNs fitted to Hill functions (eq. <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003975#pcbi.1003975.e004" target="_blank">4</a>; solid curves) showing parameters <i>F</i>_M and <i>C</i>_1/2 and characteristic <i>C</i>₀ and <i>C</i>_s for <i>F</i>₀  =  5 AP/s. (<b>B</b>) All (<i>N</i>  =  38) Hill curves fitted to ORNs. (<b>C</b>) Hill curves of 3 PNs. (<b>D</b>) All (<i>N</i>  =  37) PN curves successfully fitted to Hill functions. (<b>E</b>) Distribution of maximum firing rates <i>F</i>_M in the ORN (blue, <i>N</i> = 38) and PN (red, <i>N</i> = 37) populations. Each empirical CDF (staircase) with its fitted normal CDF (dotted curve) and corresponding PDF (dashed curve). (<b>F</b>) Distributions of dynamic ranges <i>ΔC</i> (related to <i>n</i>), same <i>N</i> and representation as in (E) except fitted distribution is lognormal for ORNs.</p

Dose-response curves of PNs are shifted to left of ORN curves and explain ORN-to-PN transfer functions.

<p>(<b>A</b>) Medians (circles) and quantiles 10% and 90% (vertical dashed lines) of all <i>F</i> measured at a given dose, as shown in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003975#pcbi-1003975-g005" target="_blank">Fig. 5</a>. Dose-firing rate curves of ORN (blue) and PN (red) populations reconstructed from parameters of individual <i>C</i>–<i>F</i> curves shown in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003975#pcbi-1003975-g006" target="_blank">Fig. 6</a>, based on median (solid), 10% most responsive neurons (dashed, based on quantiles 90% for <i>F</i>_M and 10% for <i>C</i>_1/2, <i>n</i>) and 90% less responsive neurons (dash-dotted). (<b>B</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 <i>L</i> (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003975#pcbi-1003975-g005" target="_blank">Fig. 5</a>) or on parameters of <i>C-L</i> curves (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003975#pcbi-1003975-g007" target="_blank">Fig. 7</a>). (<b>C</b>) Median transfer function for firing rates (solid, eq. <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003975#pcbi.1003975.e009" target="_blank">9</a>); it can be approximated by <i>F</i>_PN  = 62.5/(1+ (1.5/<i>F</i>_ORN)^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). (<b>D</b>) Median transfer function for latencies running from right (low doses) to left (high doses) (solid, eq. <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003975#pcbi.1003975.e012" target="_blank">12</a>); 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). (<b>E</b>) Distributions of thresholds <i>C</i>₀ in ORNs (blue, <i>N</i> = 38) and PNs (red, <i>N</i> = 37); empirical CDFs (staircases) with fitted normal CDF (solid curve) and corresponding PDF (dashed curve); maximum contrast at <i>C</i>_0Δ  = −1.9 log ng (dashed vertical line) with 17% ORNs and 85% PNs activated. (<b>F</b>) Distributions of ED50 <i>C</i>_1/2, same <i>N</i>'s and representation as in (E); maximum contrast at <i>C</i>_1/2Δ  = 0 log ng (dashed vertical line) with 2% of ORNs and 98% of PNs above their <i>C</i>_1/2.</p

Pheromone-evoked spiking activities are qualitatively and quantitatively different in ORNs and PNs.

<p>In this and all following figures ORNs are shown in blue and PNs in red. (<b>A</b>) Phasic-tonic activity in a single ORN at various doses <i>C</i> 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 <i>T</i>_t = 180±13 ms (mean ± SD) indicates mean time of arrival of stimulus on antenna. (<b>B</b>) Multiphasic activity in a PN at doses from -3 to 1 with repetitions. Same representation as in (A). (<b>C</b>) Instantaneous firing rates estimated with a 50 ms Gaussian kernel (see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003975#s4" target="_blank">Methods</a>) of spike trains shown in (A). (<b>D</b>) Instantaneous firing rates of the trains shown in (B). (<b>E</b>) Comparison of average instantaneous firing rates of ORNs and PNs recorded at doses -1, 0 and 1 log ng. (<b>F</b>) Firing rate <i>F</i> versus latency <i>L</i> pairs from the same pheromone-evoked response for all ORNs (blue) and PNs (red) recorded at dose <i>C</i> = −1 log ng (responses significantly different shown as filled circles; all other figures show only responses significantly different from spontaneous activity).</p