Fig. 1. Responses of a neuron in the basal optic nucleus (BON) recorded in vitro to electrical (A, C) and visual stimulation (B). The shape of the raw EPSP responses (shown in panels B and C as voltage traces) were quantified based on their amplitude and rise time and displayed as scatterplots in panels A and B. (A) Responses to electrical stimulation using 100 μs current pulses (black dots), compared to miniature synaptic events (mEPSPs; gray dots). Within the scatterplot is a drawing of a ventral view of the preparation, showing the brainstem below with its midline, cut oculomotor nerves and pipette in the BON. The top of the drawing shows the contralateral eyecup, with its optic disc and retinal visual streak. The circle drawn on the retinal surface corresponds to the neuron's receptive field, within which the retina was stimulated by current pulses via a bipolar electrode. The stimulus intensity (180 μA) was set just above threshold to evoke a unitary EPSP in the BON neuron (due to a spike response from the single nearest retinal ganglion cell). (B) Responses to visual stimulation. To the left is a scatterplot of amplitude versus rise time. Within the scatterplot is a drawing showing a checkerboard pattern that stimulating the entire retinal eyecup in 12 different directions. To the right is a polar plot demonstrating the directional selectivity of the neuronal response, measured as the area above baseline during each of the 4.5-s image movements. Dashed arrow is an estimate of the preferred direction. Two insets show the initial responses during motion in the preferred and null directions. The centered circle indicates the response amplitude measured during a stationary image. (C) 100 superimposed voltage traces before, during and after Cd²⁺ application. For display purposes, the mean voltage of the portion of each trace just prior to the postsynaptic response was subtracted from the entire trace so that the response amplitudes can be compared visually. (D) Histograms of postsynaptic response amplitudes for each condition in panel C. On each histogram, a Gaussian curve was fit using the mean and standard deviation of the amplitudes. Note that many bins deviate substantially from the Gaussian curve, suggesting either that the responses are quite variable or that response amplitude is not simply a random process. Q, the mean amplitude of each retinal quanta, was estimated for this BON cell to be 0.97 mV (cell I of Table 1). Bin width = 0.2 mV.

Fig. 2. Peak amplitudes of mEPSPs and unitary EPSPs relative to noise. (A) Expanded voltage scale showing 100 superimposed traces recorded prior to stimulation (NOISE) and during spontaneous miniature events (MINIS) detected in the absence of retinal stimulation. These traces are displayed at a high magnification to show that the noise was less variable than the mEPSPs. Amplitudes were measured between the vertical dotted lines and displayed on an expanded voltage scale in panel B as histograms for noise (gray bars) and mEPSPs (black bars). The unfilled bars indicate amplitude values of the gray traces of suspected non-mini responses that were excluded from further analysis (see Experimental procedures). Panels C and D display traces and histograms at a voltage scale smaller than panels A and B. (C) Noise, mEPSPs and responses (EPSPs) evoked by retinal current pulses (280 μA, 100 μs), and (D) their corresponding histograms. Note that mEPSPs have amplitudes much lower than the control evoked unitary EPSPs (CTRL) yet not much smaller than the unitary EPSPs evoked during the maximal effect of Cd²⁺ application (Max Cd²⁺, lowest row). Note that the EPSPs of the control and Cd²⁺ effect (Cd²⁺) can be seen to cluster at discrete voltages, which are seen as peaks in the histograms. Histograms are formatted as in Fig. 1 except bin width = 0.4 ms. Q, the amplitude of a quantal response, was estimated for this cell to be 0.75 mV (cell D of Table 1).

Fig. 3. Two quantal models applied to a single response histogram from cell B of Table 1. Superimposed on the histograms are curves of thin lines (‘Quanta’) that indicate the probability distribution of response amplitudes expected from a certain multiple of synaptic vesicles. Above those curves is a single thick line (‘Fit’) that is the sum of the individual distributions. Within each panel are the values of bin width, number of measured responses, χ², degrees of freedom (dof) and the significance measured as α′. The criterion for this study was α > 0.05.

Fig. 4. Effect of bin width on shape of histograms and the statistical significance of two fitting approaches. (A) Response histograms were generated from a single data set but using four different bin widths. Arrows point to the peak of the mini probability distribution and the three next convolutions. (B, D) Plots of the α′ value as a function of bin width for two models. (C, E) Response histograms as in panel A using 0.32 mV bin width, as selected from the α′ value plots at the bin width marked by asterisks (B, D). Unitary EPSPs were in response to 70-μA, 100-μs retinal pulses using cell H of Table 1.

Fig. 5. Time course of effect of Cd²⁺. Sequential histograms of unitary EPSP peak amplitudes recorded before (A), during (B, C) and after (D, E) the Cd²⁺ application, using the same neuron analyzed in Fig. 4. Histograms were fit with the Independent convolutions model (curves of thin lines). Quantal clusters in the amplitude histograms were most apparent in panel B after 5 min of Cd²⁺ and in panel D after 15 min of cadmium washout. After 10 min of Cd²⁺ (C), just after the solution was switched back to control, the maximal effect was recorded, and partial recovery was observed 40 min later.

Fig. 6. Quantal fits of single response histograms from eight different neurons. These examples exhibited statistically significant fits with the Independent convolutions model (curves of thin lines). In most cases, significant fits were only achieved during a substantial effect of Cd²⁺ application that uncovered the quantal events.

Statistical analysis of two quantal models

Q: amplitude of a quantal response; Q_vm: Q based on Variance–Mean analysis (using cvQ = 0.5–0.1); M: mean quantal number of the best fit data set; α′-value of the best fit file (α′ > 0.5 is statistically significant); M during Cd²⁺: mean of quantal numbers from all Cd²⁺ files that fit statistically: M^*: CTRL response/Q.