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. 1999 Apr 15;516 ( Pt 2)(Pt 2):593-609.
doi: 10.1111/j.1469-7793.1999.0593v.x.

Sensitivity and kinetics of mouse rod flash responses determined in vivo from paired-flash electroretinograms

J R Hetling  1 , D R Pepperberg
Affiliations

Sensitivity and kinetics of mouse rod flash responses determined in vivo from paired-flash electroretinograms

J R Hetling et al. J Physiol. .

Abstract

1. Electroretinograms (ERGs) were recorded corneally from C57BL/6J mice using a paired-flash procedure in which a brief test flash at time zero was followed at time tprobe by a bright probe flash of fixed strength, and in which the probe response amplitude was determined at time t = tprobe + 6 ms. Probe responses obtained in a series of paired-flash trials were analysed to derive A(t), a family of amplitudes that putatively represents the massed response of the rod photoreceptors to the test flash. A central aim was to obtain a mathematical description of the normalized derived response A(t)/Amo as a function of Itest, the test flash strength. 2. With fixed tprobe (80 <= tprobe <= 1200 ms), A(t)/Amo was described by the saturating exponential function [1 - exp(-ktItest)], where kt is a time-dependent sensitivity parameter. For t = 86 ms, a time near the peak of A(t), k86 was 7.0 +/- 1.2 (scotopic cd s m-2)-1 (mean +/- s. d.; n = 4). 3. A(t)/Amo data were analysed in relation to the equation below, a time-generalized form of the above exponential function in which (k86Itest) is replaced by the product [k86Itestu(t)], and where u(t) is independent of the test flash strength. The function u(t) was modelled as the product of a scaling factor gamma, an activation term 1 - exp[-alpha(t - td)2]), and a decay term exp(-t/tauomega): A(t)/Amo = 1 - exp[-k86Itestu(t)]; u(t) = gamma(1 - exp[-alpha(t - td)2](exp(-t/tauomega) where td is a brief delay, tauomega is an exponential time constant, and alpha characterizes the acceleration of the activation term. For Itest up to approximately 2.57 scotopic cd s m-2, the overall time course of A(t) was well described by the above equation with gamma = 2.21, td = 3.1 ms, tauomega = 132 ms and alpha = 2.32 x 10-4 ms-2. An approximate halving of alpha improved the fit of the above equation to ERG a-wave and A(t)/Amo data obtained at t about 0-20 ms. 4. Kinetic and sensitivity properties of A(t) suggest that it approximates the in vivo massed photocurrent response of the rods to a test flash, and imply that u(t) in the above equation is the approximate kinetic description of a unit, i.e. single photon, response.

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Figures

Figure 1
Figure 1. Comparison of the ERG a-wave and the derived response to a test flash
All data were obtained in a single experiment. A, waveform TA, ‘test-alone’ response to a test flash of strength Itest= 0·30 sc cd s m−2, delivered at time zero. Waveform PA, ‘probe-alone’ response to the bright probe flash delivered at time zero. Numbered waveforms, probe flash responses obtained in paired-flash trials with Itest= 0·30 sc cd s m−2. Numbers indicate the interflash interval, tprobe, in milliseconds. Waveforms TA and PA are averages of 2 records; numbered waveforms are single records. Waveforms are plotted as normalized responses r(t)/rmax with the peak amplitude of waveform PA taken as rmax. Here and in later illustrated families of waveforms, responses are vertically shifted for alignment and are scaled by the ratio of the prevailing PA response (see Methods) to the illustrated PA response. B shows waveforms TA and PA reproduced from A.^, normalized derived amplitudes A(t)/Amo determined from the paired-flash data of A. Probe response amplitudes were determined at 6 ms after probe flash presentation, after correction for excursion of the test-alone response. Time t, the abscissa value of each paired-flash data point, is equal to tprobe+ 6 ms. In C-F, the format is similar to that of A and B, with Itest= 0·98 sc cd s m−2 (C and D) and 2·57 sc cd s m−2 (E and F). Absolute peak amplitudes of waveforms PA are 406 μV (A and B), 440 μV (C and D) and 430 μV (E and F).
Figure 2
Figure 2. Amplitude-intensity relationship determined at t= 86 ms (interflash interval tprobe= 80 ms)
A, probe flash responses obtained with test flashes of varying strength, Itest. Values of Itest (in sc cd s m−2) were, from top to bottom: 11·0, 0·98, 0·30, 0·17, 0·11, 0·06, 0·03 and 0·0003. Waveform PA, probe-alone response. Vertical arrow, time of determination of the probe response amplitude (6 ms after probe flash presentation). All illustrated waveforms are single records. B, selected probe flash responses from A, labelled with the test flash strength in sc cd s m−2. The responses are scaled to produce a match of amplitudes at 6 ms after probe flash presentation. C, normalized derived amplitudes A(86)/Amo plotted in relation to logItest (sc cd s m−2). Results from 4 experiments. Data obtained within a given experiment (identical symbols) are shifted horizontally by a fixed amount (see text). Continuous curve, eqn (2) with k86= 7·0 (sc cd s m−2)−1.
Figure 3
Figure 3. Relationship between the normalized derived response A(t)/Amo and flash strength Itest (0·05 ≤Itest≤ 27·5 sc cd s m−2) determined at fixed values of the interflash interval, tprobe
Data were obtained in 3 experiments. A,A(t)/Amovs. logItest obtained with tprobe= 160 (^), 200 (•), 300 (▵), 400 (▴), 500 (□), 600 (▪), 800 (⋄), 1000 (♦) and 1200 (×) ms. Dotted curve, eqn (2) (tprobe= 80 ms), with k86= 7·0 (sc cd s m−2)−1, replotted from Fig. 2C Continuous curves, eqn (3) fitted separately to the data obtained with 160 ≤tprobe≤ 1200 ms. B shows the relationship (^) between kt and t determined by fitting eqn (3) to the results shown in A. The line fitted (least-squares) to the semilogarithmic data obtained with tprobe≤ 600 ms exhibits a slope τk (the time constant for e-fold decay) of 130 ms.
Figure 4
Figure 4. Probe flash responses obtained in paired-flash trials with fixed Itest (0·11 sc cd s m−2)
Data were obtained in a single experiment. A, ERG response to the test flash alone (average of 3 responses). B, waveform PA, probe-alone response. Waveform 40′, raw response to the probe flash presented 40 ms after the test flash. Waveform TA, segment of the test-alone response of A corresponding with the period illustrated for waveform 40′. Waveform 40 was obtained by subtraction of trace TA from trace 40′. Each waveform is the average of 3-4 records. C and D show waveform 40 reproduced from B, and raw probe flash responses (single records) obtained with tprobe= 5, 80, 170, 300 and 500 ms (as labelled). Waveform PA is the probe-alone response reproduced from B. The lower scale bars apply to B-D.
Figure 5
Figure 5. Time course of the weak-flash derived response
Data were obtained from experiments on 5 mice (a total of 7 sets of data, each of which included results at 4-19 values of tprobe). A shows the derived response normalized to A(86), the near-peak value (^). Error bars are ±s.d. for multiple determinations. The single Itest used in each experiment (0·11 ≤Itest≤ 0·15 sc cd s m−2) yielded A(86)/Amo within the range 0·51-0·67. Curves a and b plot n-stage impulse-response functions (eqn (4)) with n= 3 (a) and n= 4 (b). The thick curve plots eqn (5), with td= 3·1 ms, γ′= 1·84, α′= 3·23 × 10−4 ms−2 and τω′= 163 ms. Here and in B, curves were determined by fitting to the ensemble of data contained in the 7 sets. B shows data from A normalized to the prevailing probe-alone amplitude Amo. Curve 1 plots eqn (6), with k86= 7·0 (sc cd s m−2)−1, td= 3·1 ms, γ= 2·21, τω= 132 ms and α=αn= 2·32 × 10−4 ms−2 (‘nominal’ evaluation). The value of Itest used for this fitting was 0·12 sc cd s m−2, the average flash strength used in these experiments. Curve 2 plots eqn (6), with α set equal to αi= 0·97 × 10−4 ms−2, and other parameters as in curve 1. Curve 3 shows results obtained by fitting eqn (6) with td and k86 fixed at the nominal values, α=αi= 0·97 × 10−4 ms−2, and free variation of γ and τω, yielding γ= 5·35 and τω= 84 ms. The inset to B shows experimental data and curves 1-3 on an expanded time scale. C, derived amplitudes A(t)/Amo obtained using different determination times tdet for the analysis of probe flash responses. Results were obtained in a single experiment (a single family of probe flash responses, representing one of the 7 sets of data described in A and B). ⋄, □ and ▵, results obtained with tdet= 5, 6 and 7 ms, respectively.
Figure 6
Figure 6. Comparison of eqn (6) with ERG a-wave data obtained in a single experiment
Values of Itest for the a-wave responses a-f shown in each panel were, respectively, 0·11, 0·98, 2·57, 6·61, 17·4 and 27·5 sc cd s m−2. Waveform PA, probe-alone response. The a-wave responses r(t) are normalized to rmax, the peak amplitude of response PA (503 μV). Waveform PA is the average of 2 records; responses a-f are single records. In A, curves 1-6 plot eqn (6) with k86= 7·0 (sc cd s m−2)−1, td= 3·1 ms, γ= 2·21, τω= 132 ms and α=αn= 2·32 × 10−4 ms−2 (nominal evaluation, identical to that of curve 1 in Fig. 5B). In B, the lower curve of each pair 1-6 results from visual fitting of eqn (7) to the ensemble of a-wave data (td fixed at 3·1 ms), yielding β= 0·0015 (sc cd s m−2)−1 ms−2. The upper curve of each pair plots eqn (6) with α=αi= 0·97 × 10−4 ms−2 and other parameter values as in A. Values of Itest used to determine curves 1-6 in A and B are identical to those that yielded the correspondingly ordered waveforms.
Figure 7
Figure 7. Determinations of the eqn (6) parameter α from a-wave and paired-flash (A(56)/Amo) data obtained in the same experiment
The waveforms are normalized a-wave responses to test flashes of strengths (from top to bottom): 0·11, 0·30, 0·98 and 2·57 sc cd s m−2. Waveform PA, probe-alone response. Waveform PA is the average of 4 records; other waveforms are averages of 2 records. Thin curves were obtained by visually fitting eqn (6) to the a-wave data, with γ and τω fixed at their nominal values (γ= 2·21; τω= 132 ms). The fitting yielded αi= 0·97 × 10−4 ms−2. ^, average ±s.d. for 6 determinations of A(56)/Amo, with Itest= 0·11 sc cd s m−2. The thick curve was obtained by constraining eqn (6) to pass through the average A(56)/Amo determination, with γ and τω fixed at their nominal values, and with Itest= 0·11 sc cd s m−2. The fitting yielded α=α56= 1·85 × 10−4 ms−2.
Figure 8
Figure 8. Derived responses A(t)/Amo obtained with Itest near and above saturation
A, time course of the derived response. Test flash strengths (Itest) in sc cd s m−2 were: 0·11 (^), 0·30 (•), 0·50 (▵), 0·98 (▴), 2·57 (□), 4·37 (▪), 11·0 (⋄), 17·4 (♦) and 27·5 (×). Data were obtained in 3 experiments. Error bars, ±s.d. for multiple determinations. Dotted curves 1-8 plot eqn (6) evaluated for Itest= 0·11, 0·30, 0·50, 0·98, 2·57, 4·37, 11·0 and 27·5 sc cd s m−2, respectively. B shows the post-flash period T0·5 required for half-recovery of the derived response, determined from exponential decay functions fitted to the data in A (see text). ^, values of T0·5 plotted against logItest (sc cd s m−2; lower horizontal axis). The thin continuous line labelled by the visually determined slope τ0·5 (= 140 ms) describes the T0·5vs. logItest data obtained with Itest≤ 2·57 sc cd s m−2. The dotted lines are linear segments of the T0·5vs. log(flash strength) functions determined by Lyubarsky & Pugh (1996) (data from 5 mice; their Fig. 7), with flash strength represented in units of photoisomerizations per rod (Ro*) (upper horizontal axis). C, probe flash responses obtained during recovery from saturating test flashes. All responses are single records. Results were obtained in one of the experiments shown in A. Each label identifies, sequentially, the relevant values of Itest (sc cd s m−2) and tprobe (ms). The horizontal arrow in A identifies approximate values of the normalized derived response A(t)/Amo relevant to the upper 4 waveforms (0·83 < A(t)/Amo < 0·90). The vertical arrow in A identifies the post-test-flash time t relevant to the lower 4 waveforms.
Figure 9
Figure 9. Rapid and slow phases of recovery following a saturating test flash (Itest= 4·37 sc cd s m−2)
A and B, probe flash responses obtained in paired-flash trials. For numbered waveforms, tprobe= 10, 20, 40, 60, 80, 200 and 400 ms. For unlabelled waveforms (top to bottom), tprobe= 500, 600, 800, 1000 and 1200 ms. Waveform PA, probe-alone response. Waveform PA is the average of 6 records; other responses are single records. Vertical arrows show the determination times 6 and 7·5 ms after probe flash presentation. C,A(t)/Amo obtained by analysis of probe flash responses at tdet= 6 ms (^) and tdet= 7·5 ms (0).
Figure 10
Figure 10. Derived response to a test flash (Itest= 2·57 sc cd s m−2) presented during recovery from a bright conditioning flash
•, normalized derived response A(t)/Amo to the test flash determined in the absence of the conditioning flash. ⋄ and □, results of 3-flash trials involving presentation of the conditioning flash at time 0, the test flash at time t′ and the probe flash at time (t′+tprobe). Determination of each probe response amplitude was at time (t′+tprobe+ 6 ms). Data points indicate the normalized, combined derived response due to the conditioning flash and test flash, with t′= 10 s (⋄) or 12 s (□). The inset shows A(t)/Amo, the derived response to the conditioning flash determined in paired-flash trials (no test flash) (▴). Each probe response amplitude was determined at time t (=tprobe+ 6 ms) after the conditioning flash. The continuous curve in the inset plots the expression exp[-(t - T)/τ′] with T= 1·0 s and τ′= 18·2 s. The dotted curve in the main figure is a segment of this exponential function.
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