Experimental and theoretical cumulative probability distribution functions (CDF) <i>P</i>(<i>C</i>) of dimensionless odorant concentration <i>C/</i><<i>C</i>> (concentration divided by the total mean concentration).

<p>(A) Experimental CDF (solid) as measured at 75 m from a propylene (passive tracer) source and its best exponential fit (dashed) plotted on a logarithmic scale (taken from <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000053#pcbi.1000053-Mylne2" target="_blank">[19]</a>). The intermittency is included in the plots in the non-zero value of <i>P</i>(<i>C</i>) for zero concentrations (see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000053#s4" target="_blank">Methods</a>). The experimental data clearly follow the exponential CDF, except close to <i>C</i> = 0, which is caused by technical issues in the measurement process <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000053#pcbi.1000053-Mylne2" target="_blank">[19]</a>. The relatively high value of measured intermittency (close to 47%) is caused mainly by initial data processing <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000053#pcbi.1000053-Mylne2" target="_blank">[19]</a>. (B) CDF predicted by the pheromone reception model together with its best exponential fit, the scales correspond to panel (A) After correcting (see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000053#s4" target="_blank">Methods</a>) for the fact that the intermittency predicted by the pheromone reception model (20%) is lower than that measured in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000053#pcbi.1000053-Mylne2" target="_blank">[19]</a> (as explained in the <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000053#s3" target="_blank">Discussion</a>), the predictions correspond well to the measured data in (A), except at very high values of <i>L</i>_air where they are less frequent than expected. Since this deviation is apparent only for events occurring with probability <i>P</i><0.01, it can be considered as non-significant.</p

Response properties of the olfactory reception model.

<p>(A) Temporal properties. Inset: concentration of activated receptors, <i>R</i>^*(<i>t</i>), as a function of time for single pulses of pheromone of fixed duration (0.4 s) and different intensities <i>L</i>_air (1, 5, 10 and 20 nM). The maximum of <i>R</i>^*(<i>t</i>) is reached slightly after the end of the stimulation. The prolongation of the falling time with increasing intensities is quantified by the half-fall time, <i>τ</i>, as a function of <i>R</i>^* at the end of stimulation. (B) Stimulus-response function <i>R</i>^*(<i>L</i>_air) for single pulses of the same duration as in (A). This curve depends on the temporal resolution and the choice of the response intensity. (C) Optimal cumulative distribution function of the responses, <i>F_R</i>(<i>R</i>^*), determined by maximizing the information transfer per average half-time (see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000053#s4" target="_blank">Methods</a>). The functions <i>R</i>^*(<i>L</i>_air) and <i>F_R</i>(<i>R</i>^*) were used for calculating the optimal stimulus probability distribution (shown in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000053#pcbi-1000053-g005" target="_blank">Figure 5B</a>).</p

Visualization of a pheromone plume.

<p>The figure is extracted and adapted from a digitized image of a smoke plume filmed in a wind tunnel 1 m across and 2 m long with source on the left side <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000053#pcbi.1000053-Belanger1" target="_blank">[43]</a>. Though the average pheromone concentration in the air decreases with distance, high pheromone concentrations can be found relatively far from the source due to the imperfect mixing of odorant with air. The signal detected by both moving and stationary detectors is therefore always intermittent, consisting of pulses of relatively undiluted pheromone.</p

Parameters of the perireceptor and receptor model.

<p>From <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000053#pcbi.1000053-Kaissling1" target="_blank">[25]</a>,<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000053#pcbi.1000053-Kaissling2" target="_blank">[26]</a>.</p

Determination of the optimal Lagrange multiplier <i>λ</i> giving the optimal response probability distribution.

<p>(A) Mutual information for the pheromone reception model in dependence on <i>λ</i> (Equation 21). (B) Mean half-fall time in dependence on <i>λ</i> (Equation 19). (C) Information transferred per average half-time representing the balance between the reactivity of the system and information transferred (Equation 20). Maximum occurs for <i>λ</i>≈6.</p

Amount of information transferred by a neuron in the case where all response states are equiprobable.

<p>(A) Stimulus-response function. The amount of transferred information is limited by the finite range of possible response states. Due to the non-linearity of the stimulus-response function, each response state encodes different relative changes in stimulus intensity. (B) Corresponding probability density function (pdf). Maximum information is transferred if all response states are used equally, i.e., if the area under the stimulus pdf is equal for each response state, as shown. In the limit of vanishingly small response states, the optimal stimulus CDF corresponds to the (normalized) stimulus-response function (adapted from <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000053#pcbi.1000053-Laughlin1" target="_blank">[2]</a>).</p

Qualitative comparison of reconstructed optimal pheromone stimulations <i>L</i>_air with experimentally-measured fluctuations in concentration of tracers (in arbitrary units), at various time scales.

<p>10 s (A), 50 s (B) and 350 s (C). Temporal positions of pulses in experiments and simulations do not need to coincide. Quantitative comparisons are done in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000053#pcbi-1000053-g005" target="_blank">Figures 5</a> and <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000053#pcbi-1000053-g006" target="_blank">6</a> and in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000053#pcbi-1000053-t002" target="_blank">Table 2</a>. (A) Ion signal measured using Langmuir probe in the field, 2.5 m from the source (top, from <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000053#pcbi.1000053-Murlis2" target="_blank">[17]</a>); theoretical prediction (bottom) shows reasonable correspondence: the temporal resolution Δ<i>t</i> = 0.4 s is sufficient to capture the main bursts of pheromone. (B) Ion signal, averaged over 330 ms, distance up to 30 m from the source (top, from <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000053#pcbi.1000053-Murlis3" target="_blank">[39]</a>); the predicted signal (bottom) captures the overall character of the natural stimulation. (C) Propylene source, 67 m from the source (top, from <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000053#pcbi.1000053-Mylne1" target="_blank">[18]</a>); the longest pauses (over 1 minute) are caused by the global meandering of the plume: they are absent in the prediction (bottom) because moths are assumed to stay within the pheromone plume.</p

Spectral density functions of the predicted fluctuations in time of pheromone concentration.

<p>Several spectral density functions were calculated from the predicted optimal pheromone stimulations (such as shown in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000053#pcbi-1000053-g004" target="_blank">Figure 4</a>, bottom panels), for different initial random seeds. Calculated spectral shapes are usually almost flat from 0.02 Hz to 0.2 Hz, although exceptions are sometimes observed at lower frequencies, which are also found in experimental data <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000053#pcbi.1000053-Mylne2" target="_blank">[19]</a>. Above 0.2 Hz there is a decreasing slope close to −2/3. Flat spectrum up to 0.2 Hz and true −2/3 slope beyond are shown for comparison (thick line). Spectra from experimental measurements (not shown) on propylene plume obtained close to the source are reported to exhibit a similar flat region followed by −2/3 slope <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000053#pcbi.1000053-Mylne2" target="_blank">[19]</a>.</p

Comparison of statistical characteristics of optimal and actual plumes.

a<p>The mean concentration, standard deviation and their ratios are calculated from the complete stimulus course, including parts of zero concentration (see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000053#s4" target="_blank">Methods</a>).</p>b<p>Based on a simulated sample 4000 s long.</p

Interaction of cellular and network mechanisms for efficient pheromone coding in moths

Sensory systems, both in the living and in machines, have to be optimized with respect to their environmental conditions. The pheromone subsystem of the olfactory system of moths is a particularly well-defined example in which rapid variations of odor content in turbulent plumes require fast, concentration-invariant neural representations. It is not clear how cellular and network mechanisms in the moth antennal lobe contribute to coding efficiency. Using computational modeling, we show that intrinsic potassium currents (IA and ISK) in projection neurons may combine with extrinsic inhibition from local interneurons to implement a dual latency code for both pheromone identity and intensity. The mean latency reflects stimulus intensity, whereas latency differences carry concentration-invariant information about stimulus identity. In accordance with physiological results, the projection neurons exhibit a multiphasic response of inhibitionexcitationinhibition. Together with synaptic inhibition, intrinsic currents IA and ISK account for the first and second inhibitory phases and contribute to a rapid encoding of pheromone information. The first inhibition plays the role of a reset to limit variability in the time to first spike. The second inhibition prevents responses of excessive duration to allow tracking of intermittent stimuli