S–R relation of an ORN in normal-Ca²⁺ solution. (A) (Upper) Response family with 300 μM cineole and duration of 100–200 ms. Traces are averages of 10–100 stimulus trials. (Lower) Corresponding S–R relation at transient peak of response, with a prominent supralinearity in the overall foot. Solid curve is the best-fit power-law relation with an exponent of 3.05. (B) Same cell as in A, but with cineole durations of 20–100 ms. The S–R relation is linear up to about 40-ms duration (or ∼0.5 pA response), beyond which it becomes supralinear. Each trace is average of >100 trials. The downward deflection immediately after the odorant pulse is a small movement artifact detectable only at high gain. For clarity, response traces for 80- to 100-ms odorant durations are not shown. Black line in lower panel is a least-squares linear fit to the first three datapoints. Red curve is same as in A, to indicate that the detailed foot of the S–R relation does not strictly follow a simple power law.

Comparison of olfactory responses in low (20 μM)-Ca²⁺ and normal (1 mM)-Ca²⁺ solutions. (A–C) Different cells, with cineole as stimulus at 500, 300, and 50 μM respectively. For each cell, the different responses were elicited by different stimulus durations beginning at time 0. The traces are color-coded according to stimulus duration (black, 20 ms; red, 30 ms; green, 40 ms; blue, 50 ms). The initial linear segment of the S–R relation in low-Ca²⁺ solution is mirrored also in normal-Ca²⁺ solution (Right), but the response is much smaller in the latter (magnified in Inset in extreme right), with the ratio (slope ratio) indicated. Traces in low-Ca²⁺ solution are averages of 2–10 trials each, and in normal-Ca²⁺ solution averages of ≥50 trials each. For clarity, not all response traces corresponding to datapoints in the right panels are shown. Small downward deflection visible in some traces in normal-Ca²⁺ solution is a movement artifact detectable only at high gain.

Effect of external Ca²⁺ concentration on olfactory response. (A) Sample traces showing responses of an ORN to a fixed, weak cineole pulse (300 μM, 50 ms) delivered at time 0 in different low-Ca²⁺ solutions. Cell was exposed to a given low-Ca²⁺ solution for 2–3 s before stimulation with odorant dissolved in the same solution. (B) Amplitude at transient peak of response plotted against external Ca²⁺ concentration, normalized with respect to value at 0.1 μM Ca²⁺. Collected data, with each point representing average from at least five cells.

Direct estimate of unitary-response amplitude in normal-Ca²⁺ solution by fluctuation analysis in linear range of S–R relation. (A and B) Two different cells, stimulated by cineole at 300 and 500 μM, respectively, of increasing durations. Note the large increase in variance as the response intrudes into the supralinear range of the S–R relation. (Upper, Inset) The foot of the variance plot expanded. (Lower, Inset) Similar time courses of the mean response [m(t)] and the standard deviation [σ(t)] of the response (see text) at one illustrative stimulus strength in the linear range (for the stimulus strength of 60-ms duration in A and 70-ms duration in B). (C) Collected σ²/m values from multiple cells. Note that σ²/m does not depend on m. The mean is 0.032 pA (±0.013 pA, SD). More than 50 trials per stimulus intensity for each cell.

Estimate of physical-domain size of unitary response. (A) S–R relations from four cells (cineole as stimulus in all cases at concentrations between 300 μM and 1 mM and of varied durations), plotted as number of equivalent unitary responses (y axis) against number of successful binding events (x axis). As such, data from different cells can be compared and fitted by the same mathematical function. In each panel, the smooth curve is the best-fit by Eq. 3 with the indicated w/L and α values. (B) Various fittings of data from Upper Right of A to indicate unique w/L and α values required for fit. Four quite different w/L values were successively adopted (leftmost column), and best-fit was then made with α as the only free variable. The same was repeated with different arbitrarily chosen α values (rightmost column in B) and w/L as the free variable. Black curve is same as in A, Upper Right; all other fits, which are not as good, are in red.

Probability of action-potential generation as a function of number of successful odorant-binding events. (A–C) Data from same cell. (A) Sample traces low-pass filtered at 500 Hz to show occasional spikes in response to a repeated, weak cineole pulse (300 μM and 20-ms duration) delivered at time 0 (indicated by arrow). (B) Superposed responses (black) from 151 stimulus trials in the experiment shown in A, together with mean response (red), low-pass filtered at 20 Hz to highlight the slow receptor current. (C) Probability of firing during a 1-s time interval following odorant stimulation of different strengths (same odorant concentration but pulse duration varied between 20 and 125 ms, respectively) plotted against number of successful binding events. The probability in the case of zero binding events (i.e., control with no odorant stimulation) was derived from a 1-s interval before odorant stimulus. (D) Data similar to C from five other cells, shown by different colored symbols.