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

John R. Hetling * and David R. Pepperberg

MS 8007 Received 12 March 1998; accepted after revision 20 December 1998.

	ABSTRACT

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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 t_probe by a bright probe flash of fixed strength, and in which the probe response amplitude was determined at time t = t_probe + 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)/A_mo as a function of I_test, the test flash strength.

2. With fixed t_probe (80 t_probe 1200 ms), A(t)/A_mo was described by the saturating exponential function [1 - exp(-k_tI_test)], where k_t 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)/A_mo data were analysed in relation to the equation below, a time-generalized form of the above exponential function in which (k₈₆I_test) is replaced by the product [k₈₆I_testu(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 , an activation term 1 - exp[-(t - t_d)²]}, and a decay term
   exp(-t/):
   A(t)/A_mo = 1 - exp[-k₈₆I_testu(t)]; u(t) = {1 - exp[-(t - t_d)²]}exp(-t/)
   where t_d is a brief delay, is an exponential time constant, and characterizes the acceleration of the activation term. For I_test up to ~2·57 scotopic cd s m^-2, the overall time course of A(t) was well described by the above equation with = 2·21, t_d = 3·1 ms, = 132 ms and = 2·32 × 10^-4 ms^-2. An approximate halving of improved the fit of the above equation to ERG a-wave and A(t)/A_mo 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.

	INTRODUCTION

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The leading edge of the a-wave of the corneally recorded electroretinographic (ERG) response to a brief test flash is dominated by the massed response of the rod photoreceptors (Granit, 1933; Brown & Wiesel, 1961; Penn & Hagins, 1969). This rod contribution to the ERG is overwhelmed, or masked, at post-flash times beginning approximately between 7 and 20 ms due to intrusion by the ERG b-wave and oscillatory potentials. However, recent studies indicate that the rod response at arbitrarily long times after the test flash can be derived with the use of a bright probing flash in a paired-flash procedure (Birch et al. 1995; Lyubarsky & Pugh, 1996; Goto et al. 1996; Pepperberg et al. 1996, 1997; Robson et al. 1997).

The suitability of the mouse for studying genetically engineered changes in rod visual function (e.g. Chen et al. 1995; Goto et al. 1996; Kedzierski et al. 1997; Xu et al. 1997) raises particular interest in examining properties of the in vivo flash response in this experimental animal. The present study of normal mice of the C57BL/6J strain addresses the sensitivity and time course of the response derived using the paired-flash ERG method. The immediate foundation for this work is provided by previous ERG and single rod photocurrent studies that have developed separate mathematical descriptions of the activation and recovery phases of the rod flash response (Hood & Birch, 1990, 1993; Lamb & Pugh, 1992; Breton et al. 1994; Birch et al. 1995; Cideciyan & Jacobson, 1996; Lyubarsky & Pugh, 1996; Pepperberg et al. 1996). A specific aim of the present study was to determine whether a single algebraic expression, one incorporating features of the previously employed separate descriptions of the activation and recovery phases, can account for the full time course of both subsaturating and saturating responses. Preliminary results have been reported (Hetling & Pepperberg, 1997, 1998).

	METHODS

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Animals

C57BL/6J mice obtained from Jackson Laboratories (Bar Harbor, ME, USA) (both sexes, 5-16 weeks of age) were maintained on a light-dark cycle (12 h light : 12 h dark; ambient illumination of 2-19 lux) and dark adapted for 3 h immediately before the experiments. All procedures were in accordance with the principles embodied in the Statement for the Use of Animals in Ophthalmic and Vision Research established by the Association for Research in Vision and Ophthalmology. Under dim red light, the mouse was anaesthetized by the intraperitoneal injection of a saline solution containing ketamine and xylazine (0·15 and 0·01 mg (g body wt)^-1, respectively). A boost of anaesthetic solution (same composition but typically about 1/8 to 1/4 of the initial volume) was delivered subcutaneously 45 min after the initial dose and subsequently at about 15-20 min intervals. The pupil was dilated (2·5 % phenylephrine HCl plus 1 % tropicamide) and the cornea anaesthetized (0·5 % proparacaine HCl). The corneal surface was lubricated by the addition of an ophthalmic methylcellulose solution and kept moist during the experiment by periodic dropwise additions of distilled water at 10-15 min intervals. The anaesthetized mouse was placed on its right side on a brass plate and stabilized by a surrounding pad of foam rubber so that the visual axis of the left eye was approximately vertical. The plate was in contact with a thermoelectric module that maintained the plate temperature within the range 39·2-40·2°C. This setting of the plate temperature yielded a mouse body temperature, rectally measured, of about 38-40°C.

At the conclusion of the experiment, the mouse was allowed to recover from anaesthesia and was monitored throughout the recovery period. Typically, a given mouse was used in only one experiment. Following the experiment and the recovery period the mouse was returned to the university animal care facility.

Photic stimulation

Test flashes were provided by a flash unit (Model MVS2020; EG&G Electro-Optics, Salem, MA, USA) modified with a 72 µF, 600 V external capacitor bank. The half-height duration of the flash was approximately 20 µs. Probe flashes and conditioning flashes of half-height duration of about 1·7 ms were generated by a second flash unit (Model 2105-C flash head and 1000VR power pack; Novatron, Inc., Dallas, TX, USA). Recharge periods of the EG&G and Novatron flash units were 0·05 and 2·0 s, respectively. Light from the test flash unit passed through neutral density filters and through a Wratten 58 filter (peak transmittance near 520 nm; Eastman Kodak Co.). Light from the probe flash unit passed through an infrared attenuating filter. Separate fibre-optic guides (12 mm diameter) were used to deliver light from the two flash units to the inner surface of a plastic hemispheric dome (15 cm in diameter). A convex lens affixed to the exit of each light guide spread the light over the inner surface of the dome, which was coated with Kodak White Reflectance Coating (part 6080). The mouse was positioned with its left eye aligned approximately axially with the dome, in a plane about 2·5 cm below the dome's equatorial plane, and received diffuse, essentially full-field stimulation from the luminous surface. Strengths of the test and probe flashes were determined by photometric measurement with an integrating photometer (Model 1700, equipped with an SED033 silicon photodiode detector, radiance barrel and ZCIE scotopic filter; International Light, Inc., Newburyport, MA, USA) and are reported in units of time-integrated luminance (scotopic candela s m^-2 (sc cd s m^-2)) of the dome inner surface. Test flash strengths at defined values of neutral density attenuation were found to vary by < 8 % from the nominal values quoted in Results. Determinations of the probe flash strength yielded values within the range 316-407 sc cd s m^-2 for the routinely used unattenuated flash.

Recording

Electroretinographic (ERG) signals were recorded using a stainless-steel wire electrode placed in gentle contact with the corneal surface. The wire, 0·28 mm in diameter, was bent into a small semicircular hook of 2 mm diameter, the curved apex of which was approximately centered on the cornea. The plane defined by the hook and its shank was approximately 30 deg relative to the equatorial plane of the eye; the shank was held stationary by an adjustable manipulator. The reference electrode, a stainless-steel wire of the same diameter, was positioned in the mouth of the animal. The ground electrode was a platinum subdermal needle electrode (Model F-E2; AstroMed/Grass, Inc., West Warwick, RI, USA) inserted under the skin at the nape of the neck. The recording, reference and ground electrodes led to the respective input terminals of a differential AC amplifier (Model 511; AstroMed/Grass), where the signal was amplified 1000-fold at a bandpass (-6 dB) of 0·1-3000 Hz. Data acquisition and storage employed a Pentium computer equipped with a 3001 A/D board and DT VEE software package (Data Translation, Inc., Marlboro, MA, USA). All data were sampled at 10 kHz and mapped to a voltage range of ±1·25 V with 12-bit resolution. Successive paired-flash trials within an experiment were separated by a period of at least 2 min, to afford sufficient time for full recovery (dark adaptation) following the stimulating flashes.

Determination of the derived response

A paired-flash procedure similar to that previously described (Pepperberg et al. 1997) was used to derive a test-flash-induced response that putatively represents the massed activity of the rod photoreceptors. The method involved the recording of ERGs in a series of paired-flash trials, each of which employed the presentation of a test flash of fixed arbitrary strength (I_test) at time zero, and a bright probe flash of fixed strength at a later time, t_probe. The interflash interval t_probe was varied among trials, the family of a-wave responses to the probe flash was recorded, and the amplitude of each probe flash response was determined at a fixed near-peak time t_det, where t_det is the interval between presentation of the probe flash and determination of the probe response amplitude. The concept underlying the method is that the bright probe flash delivered at time t_probe rapidly drives the rods to saturation and thus titrates the prevailing rod circulating current. As referenced to the result obtained in the absence of a recent test flash, measurement of the probe response amplitude allows determination of the test flash's response amplitude at time t_probe + t_det. That is:

A(t) = A_mo - A_m(t); t = t_probe + t_det, (1)

where A_mo is the prevailing amplitude at time t_det of the response to the probe flash delivered alone, A_m(t) is the probe response amplitude determined in a paired-flash trial with interstimulus interval t_probe, and A(t) is the amplitude at time t of the 'derived' response to the test flash. Unless otherwise stated, determinations of A(t) were based on the measurement of probe amplitudes A_mo and A_m(t) at t_det = 6 ms after presentation of the probe flash, a time that preceded substantial intrusion by the b-wave. The reference, i.e. baseline value used for determination of the probe response amplitude was taken as the average amplitude exhibited during the interval 0·5-1·5 ms after probe flash presentation, before significant development of the response to the probe flash.

Anaesthetic treatment and corneal moistening

The experiments, which typically lasted one to several hours, involved both the repeated addition of distilled water to the corneal surface (1-2 drops per treatment) and the repeated administration of anaesthetic. The re-administration of anaesthetic was preventative, i.e. it preceded observable signs of recovery from the preceding dose; its timing was based on early determinations of the recovery period. Recording was typically begun 15 min after the initial dose of anaesthetic. The addition of water to the cornea was typically associated with an immediate slight change in the response to the probe flash delivered alone (presumably due to altered shunting of the corneally recorded signal through extraocular tissue), and with a subsequent slower change as the applied water evaporated or was absorbed. Typically, there was also a net increase in the absolute maximal excursion A_mo over the initial hour of recording. However, neither the addition of water nor treatment with anaesthetic had a substantial effect on the ratio A_m(t)/A_mo determined in paired-flash trials. Responses to the probe flash alone were routinely obtained shortly before and shortly after a given paired-flash trial. These consecutive measurements of the 'probe-alone' response (separated by 15 min) usually differed from one another by < 10 %, and the prevailing probe-alone response amplitude A_mo was taken as the time-interpolated value obtained from the two bracketing determinations. No additions of water were made during the interval between bracketing probe-alone trials. An attenuation of oscillatory potentials and b-wave contribution typically developed during the longer experiments, i.e. after 2 h of recording. However, the leading edge of the a-wave response to the probe flash, from which the amplitude data were determined, was not substantially altered.

	RESULTS

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Comparison of a-wave response with paired-flash derived amplitudes

Figure 1 compares the ERG a-wave produced by a test flash of given strength I_test with derived amplitudes to the same I_test determined in paired-flash trials. Shown by the 'test-alone' waveforms TA in Fig. 1A, C and E are normalized a-wave responses to test flashes of 0·30, 0·98 and 2·57 sc cd s m^-2, respectively. Waveform PA ('probe-alone') in each panel is the response to the probe flash delivered in the absence of a recent test flash. Waveforms labelled by numbers in each panel are the results of paired-flash trials in which the test flash (presented at time zero) was followed at time t_probe by a bright probe flash of fixed strength; labels identify the interflash intervals, t_probe, in milliseconds. If the leading edge of the test-flash-induced a-wave primarily represents the response of the rod photoreceptors, and if a probe flash presented during development of the leading edge rapidly drives the rods to saturation, the absolute peak amplitude of the resulting test-plus-probe response should be independent of the time of probe flash presentation, i.e. should approximately match that of the response to the probe flash delivered alone. The data of Fig. 1A, C and E show this to be the case with relatively short interflash intervals. That is, the paired-flash response obtained with relatively small values of t_probe exhibited a peak near that of the probe-alone waveform PA. With increasing t_probe, and with increasing I_test at a given t_probe, the peak amplitude of the test-plus-probe response progressively departed from the peak amplitude of waveform PA.

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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 1B, D and F reproduces responses TA and PA of the respective lefthand panels and shows, by open circles, the normalized derived response A(t)/A_mo determined by the paired-flash procedure. Here, as in experiments presented below, the probe flash response was analysed for amplitude at 6 ms after presentation of the probe flash to yield a paired-flash determination at time t (= t_probe + 6 ms) after the test flash (see Methods, and the results below). At each test flash strength, A(t)/A_mo corresponded closely with the normalized waveform TA at early values of t and progressively departed from this waveform with increasing t values. The relationship between the a-wave leading edge of response TA and the derived response A(t)/A_mo is consistent with the notion that both measures primarily reflect the rod photoreceptor response to the test flash, with the developing difference due to contributions from the b-wave and other post-receptor components (see e.g. Robson & Frishman, 1996; Hood & Birch, 1996).

Amplitude-intensity relationship

Figure 2 illustrates paired-flash results obtained with t_probe = 80 ms, an interflash interval that, as will be shown, yielded a near-peak amplitude of the derived response. Figure 2A shows probe flash responses obtained with variation of the test flash strength I_test over the range 0·0003-11·0 sc cd s m^-2. Increasing I_test had relatively little effect on the normalized kinetics of the rising phase of the probe flash response (Fig. 2B) but progressively reduced this response from that generated by the probe flash delivered alone (waveform PA). Data obtained in this experiment and in three others of similar type (Fig. 2C) yielded values for the normalized amplitude A(86)/A_mo. The four sets of data, individually fitted (least-squares) by the exponential relationship:

A(86)/A_mo = 1 - exp(-k₈₆I_test), (2)

where k₈₆ is a sensitivity parameter with units of (sc cd s m^-2)^-1, yielded k₈₆ = 7·0 ± 1·2 (sc cd s m^-2)^-1 (mean ± S.D.). In Fig. 2C, each data set has been shifted horizontally by a fixed small amount (< 0·15 log sc cd s m^-2) to afford a match of the individually fitted exponential curves.

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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.

In a separate experiment (not illustrated), the amplitude- intensity relationship at t_probe = 80 ms determined with the routinely used, unattenuated probe flash was compared with results obtained using a probe flash of reduced strength. Here, a neutral density filter was used to decrease the probe flash strength from 344 to 216 sc cd s m^-2, a value well below the lowest determination of the unattenuated value (316 sc cd s m^-2; see Methods). The separate fitting of eqn (2) to amplitude-intensity data obtained with the 344 and 216 sc cd s m^-2 probe flashes yielded, respectively, k₈₆ values of 7·4 and 8·2 (sc cd s m^-2)^-1. Furthermore, probe-alone responses obtained with the unattenuated and attenuated flashes were similar; these responses exhibited average peak amplitudes of 546 and 512 µV, respectively, and times to peak of 7·6 and 8·6 ms, respectively. The near-unit ratio of the two k₈₆ determinations (8·2/7·4 = 1·1) and the other results just summarized suggest little if any dependence of the normalized, weak-flash derived amplitude on the probe flash strength, when this probe strength is within the observed range of 316-407 sc cd s m^-2.

Figure 3A shows the dependence, on test flash strength, of the normalized derived response determined at fixed times after the test flash (80 t_probe 1200 ms). For each value of t_probe (data shown by identical symbols), A(t)/A_mo increased with increasing test flash strength, and the dependence on I_test was generally consistent with the relationship (smooth curves):

A(t)/A_mo = 1 - exp(-k_tI_test), (3)

where the sensitivity parameter k_t is dependent on t. In Fig. 3B the values of k_t determined by the curves in Fig. 3A were plotted against t in semilogarithmic fashion. The data obtained with t_probe 600 ms indicate an exponential decline of k_t characterized by the time constant _k = 130 ms (k_t/k₈₆ exp[-(t - 86)/_k]); those obtained with t_probe > 600 ms indicate a more gradual further decline.

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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)/Amo vs. 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 k (the time constant for e-fold decay) of 130 ms.

Time course of the derived response

Weak flash stimulation. The full time course of the derived response to a weak test flash of fixed strength was obtained by varying the interflash interval t_probe in a series of paired-flash trials. Figure 4 shows probe flash responses obtained in a representative experiment in which I_test was 0·11 sc cd s m^-2. Within the interval 30 < t < 70 ms, contributions by the b-wave and oscillatory potentials produced a rapid rate of change in the response to the test flash itself (Fig. 4A), i.e. periods in which the absolute rate exceeded 10 µV ms^-1. Figure 4B illustrates determination of the response due to a probe flash delivered 40 ms after the test flash. Here the trace labelled 40' is the raw probe flash response obtained with t_probe = 40 ms, and trace TA is the segment of the test-alone response corresponding to the same post-test-flash period. Computational subtraction of trace TA from trace 40' yielded waveform 40, the response due to the probe flash. With t_probe 80 ms, i.e. at times near and after the peak of the b-wave response to the test flash (Fig. 4A), the rate of change of the test flash response was < 10 µV ms^-1. This condition also prevailed at t_probe = 5 ms, i.e. at post-test-flash times preceding substantial intrusion by the b-wave. In all experiments, determinations of probe response amplitude were made from the raw probe flash response (i.e. response TA was not subtracted) when, at the investigated value of t_probe, the prevailing rate of change of the test-alone response was < 10 µV ms^-1. Figure 4C and D illustrates the group of probe flash responses determined with 5 t_probe 500 ms in this experiment. These data indicate a decrease and subsequent recovery of the probe response with increasing t_probe, i.e. a growth and subsequent decline of the derived response to the 0·11 sc cd s m^-2 test flash (cf. eqn (1)).

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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 5A shows mean derived response amplitudes () determined in five experiments similar in design to that of Fig. 4. The single test flash strength used in each experiment (I_test = 0·12 ± 0·02 sc cd s m^-2) yielded, at the near-peak time of 86 ms, a derived amplitude A(86) within the range 0·51-0.67A_mo; each family of derived amplitudes A(t) was normalized to the value of A(86) determined in the corresponding experiment. It is reasonable to analyse the data from these experiments as a single group, as roughly half-saturating flash responses of mammalian rods in vitro exhibit an approximate kinetic similarity with one another (Nakatani et al. 1991; Kraft et al. 1993; Xu et al. 1997). Previous studies of single rod photocurrent responses (Baylor et al. 1984; Kraft et al. 1993) and of rod responses derived from paired-flash ERGs (Pepperberg et al. 1997) show that the weak-flash response can be approximated by the multistage impulse-response function:

A(t)/A_p = {(t/t_p)exp[(t_p - t)/t_p]}^n-1, (4)

where A(t)/A_p is the response amplitude at time t normalized to its peak value, n is the number of stages and t_p is the time to peak. The fitting of eqn (4) to the experimental data, with the exponent n fixed, yielded curves a (n = 3) and b (n = 4) in Fig. 5A with peak times t_p of 80 and 77 ms, respectively. These curves generally account for the rising phase of the derived response but substantially underestimate the falling phase.

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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, ' = 1·84, ' = 3·23 × 10-4 ms-2 and ' = 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, = 2·21, = 132 ms and = n = 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 set equal to i = 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, = i = 0·97 × 10-4 ms-2, and free variation of and , yielding = 5·35 and = 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.

An alternative simple approach to describing the derived response in Fig. 5A is to model this mid-range response as the near-linear summation of elemental signals, where the time dependence of the elemental signal is represented as the product of an activation and a decay term and where the decay term largely governs the response at late post-flash times. A relationship of this type is:

A(t)/A(86) = ' [1 - exp(-'(t - t_d)²)]exp(-t/'). (5)

Here, A(t)/A(86), the derived response normalized to its near-peak value at t = 86 ms, is equated with the product of a dimensionless scaling factor ', an activation term [1 - exp(-'(t - t_d)²)] and a decay term exp(-t/'), where t_d is a brief delay, ' is an exponential time constant and ' is a parameter with units of time^-2. As shown by the thick curve in Fig. 5A, an approximation to the entire time course of the derived response is provided by eqn (5) with ' = 1·84, ' = 163 ms, t_d = 3·1 ms and ' = 3·23 × 10^-4 ms^-2. The bracketed term in eqn (5) resembles the delayed Gaussian function used by previous investigators to describe the rising phase of rod photocurrent and ERG a-wave responses (Lamb & Pugh, 1992; Breton et al. 1994; Birch et al. 1995; Goto et al. 1996; Cideciyan & Jacobson, 1996; Lyubarsky & Pugh, 1996). The brief delay t_d, which was fixed at 3·1 ms throughout the present study, is small by comparison with the eqn (5) exponential time constant '; a delay within the term exp(-t/') was omitted for simplicity.

The eqn (5) expression differs from the previously used delayed Gaussian function (Lamb & Pugh, 1992) in that it does not contain a dependence on the test flash strength I_test. It is of interest to generalize eqn (5) to incorporate an explicit dependence on I_test. Figure 2 shows that the near-peak value of the normalized derived response is described by the relationship A(86)/A_mo = 1 - exp(-k₈₆I_test) (eqn (2)). Furthermore, Fig. 3 indicates that replacing the eqn (2) parameter k₈₆ by the time-dependent variable k_t (eqn (3)), where k_t/k₈₆ declines exponentially with time, provides an approximate description of the late phase of the derived response over a large range of I_test values. These observations, the algebraic form of eqns (2) and (3), and the consistency of eqn (5) with the Fig. 5A data suggest, as a candidate description for the dependence of A(t)/A_mo on flash strength:

A(t)/A_mo = 1 - exp[-k₈₆I_testu(t)];

u(t) = {1 - exp[-(t - t_d)²]}exp(-t/), (6)

where u(t) is a unit, i.e. elemental, function analogous to the eqn (5) expression, where the parameters , and correspond functionally with the ', ' and ' of eqn (5), and where and are time independent. By analogy with earlier studies (e.g. Lamb & Pugh, 1992) we assume for the moment that is also time independent (however, see below).

In Fig. 5B the open circles replot the data of Fig. 5A normalized to the maximal excursion of A_mo relevant to each family of data. The fitting of eqn (6) to these results yields curve 1 in Fig. 5B. In this fitting procedure, t_d was fixed at 3·1 ms; k₈₆ was fixed at 7·0 (sc cd s m^-2)^-1 (Fig. 2); I_test was fixed at 0·12 sc cd s m^-2; and , and were free parameters. This fitting yielded = 2·21, = 132 ms and = 2·32 × 10^-4 ms^-2. For comparison with results below we shall define, by _n, the value of just indicated. We shall also refer to the fitted values of (= _n), and just quoted, and to the resulting curve 1 of Fig. 5B, as the 'nominal' evaluation of eqn (6). This evaluation, which exhibits a peak time t_p of 93 ms, described well the overall set of data.

Values for , and were also determined by fitting eqn (6) to results obtained within a given experiment of the group described by Fig. 5A and B. Here, the probe flash responses of a single data set were analysed for amplitude at t_det = 5 and 7 ms; the resulting determinations of derived amplitude were compared with those obtained using the standard determination time of 6 ms. Figure 5C shows derived amplitudes determined from one set of probe flash responses, and Table 1 indicates the results of fitting eqn (6) to data sets that included at least eleven values of t_probe spanning the range 10 t_probe 500 ms (four of the seven sets described in Fig. 5A and B). Varying t_det over the interval of 5-7 ms had no substantial effect on either the derived amplitudes (Fig. 5C) or the values of the eqn (6) fitted parameters (Table 1).

Table 1. Values of , and determined by fitting eqn (6) to individual sets of paired-flash data obtained with determination times (t_det) of 5, 6 and 7 ms

	tdet = 5 ms	tdet = 6 ms	tdet = 7 ms
	2·36 ± 0·85	2·00 ± 0·27	1·72 ± 0·30
(ms)	139 ± 38	141 ± 20	147 ± 31
(ms-2)	(2·81 ± 1·56) × 10-4	(2·75 ± 0·56) × 10-4	(3·18 ± 0·75) × 10-4

Initial segment of the response. The ability of eqn (6) to account for the early portion of the rod flash response was examined by comparing the nominal evaluation of this equation (curve 1 of Fig. 5B) with ERG a-wave data obtained in single-flash trials. Shown in Fig. 6A and B is a single set of normalized a-wave responses obtained with test flashes that varied over the range 0·11 I_test 27·5 sc cd s m^-2 (waveforms a-f in each panel). In Fig. 6A these responses are compared with curves 1-6, which illustrate the nominally evaluated eqn (6) for values of I_test identical to those of the correspondingly ordered waveforms. These curves significantly overestimate the a-wave responses. By contrast, a good fit to the a-wave data is provided by a delayed Gaussian function (Lamb & Pugh, 1992):

A(t)/A_mo = 1 - exp[-I_test(t - t_d)²], (7)

in which is a free parameter. This is shown by Fig. 6B, in which the lower curve within each pair 1-6 evaluates eqn (7) with t_d = 3·1 ms and = 0·0015 (sc cd s m^-2)^-1 ms^-2. The fitting of eqns (6) and (7) to a-wave data obtained in two other experiments (not illustrated) yielded results similar to the Fig. 6A and B results just described. Equation (7) is algebraically similar to the asymptotic early-time behaviour of eqn (6). That is, from eqn (6):

A(t)/A_mo 1 - exp[-k₈₆I_test(t - t_d)²]

for t << and (t - t_d)² << 1, (8)

and the similarity of eqns (7) and (8) implies an equivalence between and the product k₈₆. As illustrated by the upper curve within each pair 1-6 in Fig. 6B, eqn (6) provided a good fit to the a-wave data when in this expression was reduced from the nominal value _n (= 2·32 × 10^-4 ms^-2) to _i, where:

_i = (k₈₆)^-1 = [(2·21)^-1(7·0)^-1(0·0015)] ms^-2

= 0·97 × 10^-4 ms^-2 ½_n, (9)

and where the other parameters were fixed at their nominal values. This evaluation also improved the fit of eqn (6) to paired-flash data obtained at t about 0-20 ms (curve 2 of Fig. 5B and inset). However, with = _i = 0·97 × 10^-4 ms^-2, eqn (6) with and fixed at their nominal values or determined from a refitting of eqn (6) to the paired-flash data (free variation of and , yielding = 5·35 and = 84 ms) yielded a poor overall fit to the experimental results (curves 2-3 of Fig. 5B and inset).

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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, = 2·21, = 132 ms and = n = 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 = 0·0015 (sc cd s m-2)-1 ms-2. The upper curve of each pair plots eqn (6) with = i = 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.

The early segment of the response to a test flash was further analysed by fitting eqn (6), with and fixed at their nominal values, to a-wave responses and to paired-flash data (t_probe = 50 ms) obtained from a single animal. By analogy with the terminology used above, here the value of determined from the a-wave results (with t about20 ms or less) will be termed _i; that determined from the paired-flash results (with t at 56 ms) will be termed ₅₆. Waveforms in Fig. 7 show a-wave responses to test flashes of 0·11, 0·30, 0·98 and 2·57 sc cd s m^-2; the fitting of eqn (6) to these results (thin curves) yielded _i = 0·97 × 10^-4 ms^-2. The open circle and error bars (A(56)/A_mo = 0·36 ± 0·02) indicate the paired-flash results obtained at t = 56 ms with a 0·11 sc cd s m^-2 test flash; constraining eqn (6) to pass through the average value of A(56)/A_mo (thick curve) yielded ₅₆ = 1·85 × 10^-4 ms^-2. Results obtained in a second experiment similar to that of Fig. 7 yielded _i = 0·95 × 10^-4 ms^-2 and ₅₆ = 1·60 × 10^-4 ms^-2 (not illustrated). These results and those of Figs 5-7 indicate that the overall correspondence of eqn (6) with the experimental data is improved if the parameter , rather than being constant, increases with time about 2-fold during the rising phase of the derived response to a weak test flash.

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Figure 7. Determinations of the eqn (6) parameter 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 and fixed at their nominal values ( = 2·21; = 132 ms). The fitting yielded i = 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 and fixed at their nominal values, and with Itest = 0·11 sc cd s m-2. The fitting yielded = 56 = 1·85 × 10-4 ms-2.

Saturating test flash. Extending the test flash strength to values near and above saturation yielded the derived responses shown in Fig. 8A (0·11 I_test 27·5 sc cd s m^-2). Increasing the test flash strength progressively delayed the falling phase of the derived response, i.e. increased the period of near-saturation of A(t)/A_mo (Birch et al. 1995; Lyubarsky & Pugh, 1996). Equation (6), plotted in Fig. 8A for selected values of I_test (dotted curves), approximately described the full time course of the response, including the delayed recovery from saturation, for I_test up to 2·57 sc cd s m^-2; the delay is a direct consequence of inclusion of the term exp(-t/) within the function u(t) (Pepperberg et al. 1996). With increases in I_test above 2·57 sc cd s m^-2, the observed falling-phase kinetics were slower than predicted by this relationship.

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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 0·5 (= 140 ms) describes the T0·5 vs. logItest data obtained with Itest 2·57 sc cd s m-2. The dotted lines are linear segments of the T0·5 vs. 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.

For each set of data shown in Fig. 8A, the recovery phase was analysed by fitting a decay function of the form [c₁exp(-t/₁)], where c₁ and ₁ are free parameters, to the A(t)/A_mo data with ordinate values 0·80 (functions not illustrated). Over the range 0·11 I_test 27·5 sc cd s m^-2, the time constant ₁ increased from 108 to 1470 ms. T_0·5, defined as the post-test-flash time at which each fitted exponential curve corresponded with A(t)/A_mo = 0·5, was then determined. In Fig. 8B, T_0·5 is plotted as a function of logI_test in sc cd s m^-2 (lower horizontal axis; ). The thin continuous line in Fig. 8B was visually fitted to the T_0·5 data obtained with I_test 2·57 sc cd s m^-2; the slope of this line, equal to 140 ms per e-fold increase in I_test, defines the time parameter _0·5 referred to in Discussion. Dotted lines in Fig. 8B are the linear segments of the T_0·5 vs. log(flash strength) functions determined by Lyubarsky & Pugh (1996) in their paired-flash ERG study of rod recovery in mice. These T_0·5 data of Lyubarsky & Pugh (1996) are plotted against the logarithm of R_o* (upper horizontal axis), where R_o* is the number of test-flash-induced photoisomerizations per rod as calculated by Lyubarsky & Pugh (1996). The illustrated positioning of the logI_test and logR_o* axes in Fig. 8B, which equates 1 sc cd s m^-2 with 100 photoisomerizations per rod, provides a rough match of the present data with those of Lyubarsky & Pugh (1996).

Figure 8C shows probe flash responses recorded in one of the Fig. 8A experiments. The upper four waveforms are representative responses obtained over the range 4·37 I_test 27·5 sc cd s m^-2, and for which the values of A(t)/A_mo determined at differing post-test-flash times were within the narrow range 0·83 < A(t)/A_mo < 0·90 (horizontal arrow in Fig. 8A). The similarity of these waveforms is consistent with the idea that a given falling phase value of A(t)/A_mo produced by a saturating I_test within the investigated range is associated with an essentially fixed, i.e. I_test independent, state of rod responsiveness. The lower four waveforms in Fig. 8C are probe flash responses obtained with a fixed value of t_probe (1000 ms). As observed with weaker test flashes and with a smaller interval (80 ms) between test and probe flash presentation (Fig. 2A), variation of the test flash strength over the saturating range 4·37 I_test 27·5 sc cd s m^-2 produced changes in the overall waveform but did not substantially alter the normalized rising phase kinetics of the probe flash response.

The derived response to a saturating test flash typically exhibited a slight recovery from saturation that preceded the major phase of the recovery (Fig. 8A). The experiment of Fig. 9, which involved determinations of the derived response to a fixed test flash (I_test = 4·37 sc cd s m^-2), further describes this small early change as well as the overall recovery of A(t)/A_mo. Figure 9A and B shows probe flash responses obtained as t_probe was varied over the range of 10-1200 ms. Responses obtained with t_probe at 40 and 60 ms were essentially flat, consistent with complete saturation of the test-flash-induced response. However, a change indicative of a small departure of the test-flash-induced response from saturation was apparent in the probe response obtained with t_probe at 80 ms. The similarity of the responses obtained with t_probe at 80, 200 and 400 ms, as well as the change in wave shape that accompanied the subsequent major growth of the probe flash response, furthermore suggested near completion of the small initial recovery by about 80 ms. The qualitative similarity between these results and ERG data obtained from the human eye under rod-saturating conditions (e.g. Fig. 2A of Pepperberg et al. 1997), and the rapid time course of the initial recovery (cf. Schnapf et al. 1990; Schneeweis & Schnapf, 1995), suggest that the probe flash response determined with t_probe about 80-200 ms was mediated primarily by cone photoreceptors. Based on the small contribution of this apparent cone signal to the present determinations of A(t)/A_mo, no correction for this signal was made in the derived responses reported in this study.

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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 9C shows values of A(t)/A_mo determined using the standard analysis procedure (), in which the amplitude of the probe flash response was determined at t_det = 6 ms. The recovery time course determined by this standard method was slower, particularly in its final stage, by comparison with the time course determined using t_det = 7·5 ms, a time nearer the peak of the probe flash response (). It is unclear whether recovery of the rod response to the test flash is better approximated by the results obtained with t_det = 6 ms or by those obtained with t_det = 7·5 ms. The difference between the two sets of data is consistent with the possibility that the relatively bright test flash desensitizes the response to the subsequent probe flash, and that the resulting underdetermination of circulating current by the probe flash response (and hence, overdetermination of A(t)/A_mo) is more severe at 6 ms than at 7·5 ms. An alternative possibility is suggested by the evidence that recovery of the probe-flash-induced b-wave is incomplete even at t_probe = 1200 ms; that is, the upswing presumably reflecting b-wave intrusion in the probe flash response at t_probe = 1200 ms is less pronounced than that in the probe-alone response PA (Fig. 9B). Thus, relative to probe response amplitudes obtained with t_det = 6 ms, those obtained with t_det = 7·5 ms may overdetermine the ratio A_m(t)/A_mo and correspondingly underdetermine the derived response A(t)/A_mo.

The slowing of the falling phase of the bright-flash derived response (Figs 8 and 9) was further investigated by testing whether, during this falling phase, a slowed recovery to prevailing baseline was exhibited also by the derived response to a relatively weak test flash. The experiment employed a bright conditioning flash as the first of three stimuli delivered in a given trial. In each of these three-flash trials, the conditioning flash presented at time zero was followed by a 2·57 sc cd s m^-2 test flash at a fixed time t', and by a probe flash at time (t' + t_probe). As in the experiments described above, the variation of t_probe within a given set of trials afforded determination of the derived response to the test flash presented at time t'. Filled circles in Fig. 10 show the nominal derived response to the test flash, i.e. that obtained in trials from which the conditioning flash was omitted. Open symbols show the results of three-flash trials in which t', the interval between the conditioning and test flashes, was 10 s () and 12 s (); these data describe the normalized, combined total response to the conditioning and test flashes as determined at the indicated time after the conditioning flash. Comparison of the total derived response (open symbols) with that due to the conditioning flash alone (dotted curve; see Fig. 10 legend) shows that presentation of the test flash at an intermediate stage of recovery from the bright conditioning flash produced an incremental response of about 1 s in duration, a time scale comparable with that of the nominal response () and far shorter than that of the recovery from the conditioning flash (inset, ). The process underlying the slow recovery of the conditioning flash response was thus not rate limiting for recovery of the incremental response to the prevailing, gradually declining baseline. Similar results were obtained in a separate experiment that employed a test flash of 0·30 sc cd s m^-2 (not illustrated).

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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)/'] with T = 1·0 s and ' = 18·2 s. The dotted curve in the main figure is a segment of this exponential function.

	DISCUSSION

Top Abstract Introduction Methods Results Discussion References

The results describe the sensitivity and full time course of a test flash response derived electroretinographically from the mouse eye using a paired-flash procedure. The method is similar to that used with human subjects to derive the massed rod response to weak test flashes (Pepperberg et al. 1997). In that earlier study, isolation of the rod response required computational subtraction of a significant cone contribution to the response generated by the routinely used, short-wavelength probe flash. As the relative populations of cones in the human eye and mouse eye are of similar order (about 5 % and 3 %, respectively, of the total population of photoreceptors; Carter-Dawson & LaVail, 1979; Curcio et al. 1990), cones could in principle contribute significantly to the probe flash responses obtained in the present experiments. Because the photopigments of mouse rods and cones have similar spectral sensitivities (Jacobs et al. 1991), a cone subtraction technique based on the use of photopically matched stimuli of different wavelengths is not possible. However, several types of evidence suggest that the probe responses obtained in the present experiments on mice consist virtually entirely of signals from rods. First, the putative cone contribution to the probe flash waveform obtained shortly after a bright test flash represented only a tiny fraction of the dynamic range of the probe response amplitude (Fig. 9). Second, probe responses obtained over a wide range of stimulus conditions exhibited relatively constant normalized kinetics of the rising phase (Figs 2, 4, 8 and 9). Third, recovery from the brightest available flash was generally well described by a single exponential time constant (Fig. 10, inset), consistent with recovery of a homogenous population of photoreceptors. Fourth, the exponential saturation of the amplitude-intensity function (Fig. 2C) is most simply explained as reflecting saturation of a single type of photoreceptor signal (i.e. that from rods). If a contribution from the less sensitive cones became substantial at the higher test flash strengths, a departure from the exponential relationship of Fig. 2C would be expected. These considerations, and the general similarity of the present response to the photocurrent response of mouse rods in vitro (Sung et al. 1994; Raport et al. 1994; Chen et al. 1995; Xu et al. 1997), suggest that the ERG-derived test flash response studied here is essentially rod mediated.

That the putative cone contribution to a probe flash response is small by comparison with the peak amplitude of the probe-alone response (Fig. 9) does not rule out the possibility that the cone component represents a significant portion of the a-wave response to a flash much weaker than the probe flash, e.g. those that produced the Fig. 6 responses a-f. However, evidence against this possibility comes from the Fig. 1 results, which indicate a close correspondence between paired-flash determinations and a-wave responses at I_test = 0·30, 0·98 and 2·57 sc cd s m^-2, i.e. within the range investigated in the Fig. 6 experiment. As discussed above, there appears to be no substantial cone contribution to the paired-flash derived response. The Fig. 1 correspondence of paired-flash and a-wave data thus argues against a substantial cone contribution to the a-wave response obtained with I_test = 0·30-2·57 sc cd s m^-2.

Response kinetics

Figures 5B and 8A show that over a large range of test flash strengths, the derived response is well described by the relationship (eqn (6)):

A(t)/A_mo = 1 - exp[-k₈₆I_testu(t)];

u(t) = {1 - exp[-(t - t_d)²]}exp(-t/),

a time-generalized form of the saturating exponential function (eqn (2)) shown previously to describe the intensity dependence of near-peak amplitudes of both the single-rod photocurrent and ERG-derived rod response (Lamb et al. 1981; Baylor et al. 1984; Kraft et al. 1993; Pepperberg et al. 1997). That the nominal evaluation of (= 132 ms) determined from the Fig. 5 data is similar to _k (= 130 ms) determined in Fig. 3B is consistent with the interrelationship of the equations that define these two time constants. That is, eqn (6) predicts the response at late post-flash times (i.e. exp[-(t - t_d)²] 0) to be:

A(t)/A_mo 1 - exp[-k₈₆I_testexp(-t/)]. (10)

From comparison of eqns (3) and (10) it follows that k_t k₈₆exp(-t/). Thus _k, which by definition is the post-flash interval associated with an e-fold decline in k_t, is predicted to be equal to . The observed agreement between and _k, and the near match of and _k with the time constant _0·5 (= 140 ms) derived from the recovery data of Fig. 8B, are consistent with the validity of eqn (6) as a description of the response to both subsaturating and saturating flashes. However, recovery with a time constant of about 130-140 ms over the full excursion of the falling phase becomes a progressively poorer approximation to the data as I_test increases above 2·57 sc cd s m^-2 (Fig. 8; also cf. Birch et al. 1995; Lyubarsky & Pugh, 1996).

The function u(t) of eqn (6) models the time dependence of the presumed elemental response as the product of a delayed Gaussian activation term ([1 - exp(-(t - t_d)²)]; cf. Lamb & Pugh, 1992) and an exponential decay term exp(-t/). This construction of u(t) was chosen on the basis of simplicity, and the present study does not resolve its physical basis. The function u(t) does not explicitly model, for example, the time dependence of negative feedback processes that influence both the activation and recovery kinetics of the flash response (for a recent review see Yau, 1994). However, the consistency of eqn (6) with experimental observation implies that the product {[1 - exp(-(t - t_d)²)]exp(-t/)} approximately represents those processes that dominate the shaping of the elemental response. It is of interest in this context to note the suggestion, from the present results, of an apparent time dependence of the eqn (6) parameter . That is, the agreement of eqn (6) with ERG a-wave and paired-flash data obtained at t about 0-20 ms is improved if, for this period immediately following test flash presentation, the value of is about half the nominal value determined from fitting eqn (6) to the overall set of paired-flash data (Figs 5-7, eqns (7)-(9), and accompanying text). The apparent time dependence of could reflect merely a deficiency of eqn (6), i.e. a systematic change, with post-test-flash time, in the degree to which eqn (6) describes the response kinetics. A second possibility, one raised by the resemblance of the elemental activation term {1 - exp[-(t - t_d)²]} to the activation function investigated by Lamb & Pugh (1992), is that is an index of biochemical amplification in the phototransduction cascade and that its apparent time-dependent increase reflects a developing increase in amplification. This latter possibility is generally consistent with a recently suggested notion based on in vitro photocurrent data from amphibian rods, that of a delayed increase in the specific catalytic activity of photoactivated rhodopsin (Pepperberg, 1998).

As discussed in previous studies of the photocurrent flash response (e.g. Lamb & Pugh, 1992), the saturating exponential nature of the amplitude-intensity relationship is consistent with identification of the macroscopic (i.e. overall) response to a weak test flash as essentially the summation of elemental, or unit, responses to single photons. In the light of these findings and the present results it is reasonable to hypothesize that u(t) as defined in eqn (6), and with = (t) as discussed above, approximately describes the kinetics of a unit, i.e. single photon, response within a given rod. That is, in the limit that I_test approaches zero, A(t)/A_mo k₈₆I_testu(t). However, as [k₈₆I_testu(t)] strictly scales with flash strength, this limiting expression does not account, for example, for the observed flash dependence of the time to peak of the response observed in single-rod photocurrent data (Baylor et al. 1984; Nakatani et al. 1991; Kraft et al. 1993).

Flash sensitivity

At the near-peak time of 86 ms, the amplitude of the weak-flash derived response exhibited a mean sensitivity k₈₆ of 7·0 (sc cd s m^-2)^-1 (eqn (2) and Fig. 2). Half-saturation of the peak amplitude of the derived response thus occurs when the flash strength is about 0·1 sc cd s m^-2 [= k₈₆^-1 (ln2)]. In their paired-flash ERG study of the mouse eye, Lyubarsky & Pugh (1996) calculated the photoisomerizing strength of their flash stimuli based on the area of the dilated pupil, the retinal surface area, the transmissivity of the ocular media and retina, and the collecting area of an individual rod. The present Fig. 8B, which compares recovery data for a test flash of given strength with data obtained by Lyubarsky & Pugh (1996), shows that equating 1 sc cd s m^-2 with 100 photoisomerizations per rod provides good agreement of the results obtained in the two studies. This correspondence implies that 'R_o*_0·5', the number of photoisomerizations per rod in vivo at half-saturation, is 10. This estimate may be compared with half-saturating flash strengths determined in previous studies of mouse rods in vitro (Raport et al. 1994; Sung et al. 1994; Xu et al. 1997), although it should be noted that times to peak of weak-flash responses recorded in these studies were typically longer than that determined for the derived response examined here. Xu et al. (1997) observed half-saturation at 49 ± 3 photons (500 nm) µm^-2 in rods of wild-type mice (also cf. Raport et al. 1994; Sung et al. 1994); taking the rod collecting area as about 0·25 µm² (Raport et al. 1994; Xu et al. 1997), this photon density corresponds with R_o*_0·5 about 12. Results recently reported by Tsang et al. (1998) from C57BL/6J mouse rods (half-saturation at 112 ± 11 photons µm^-2; rod collecting area of 0·23 µm²) correspond with an average R_o*_0·5 of 26.

Recovery after bright flash

The Fig. 10 results show that the process responsible for slowed recovery after a bright conditioning flash does not retard the falling phase of the derived response to a relatively weak test flash presented during recovery; decline of the weak-flash response to the prevailing baseline proceeded on a time scale of about 1 s in both the absence and presence of the conditioning flash. This finding argues against a sluggish rate of cGMP formation as rate determining for the slow decline of the derived response to the conditioning flash, for in such a case the sluggish cGMP formation rate should similarly have retarded recovery of the weak-flash derived response to its prevailing baseline. The data suggest, rather, that the kinetics of the slow recovery are set by a process distinct from cGMP resynthesis. A possibility consistent with this conclusion and with previous paired-flash ERG results (Birch et al. 1995; Lyubarsky & Pugh, 1996; Pepperberg et al. 1996) is that the slow recovery is governed by the deactivation kinetics of a long-lived and weakly active intermediate in the bleaching pathway of rhodopsin (cf. e.g. Laitko & Hofmann, 1998).

	REFERENCES

Top Abstract Introduction Methods Results Discussion References

Baylor, D. A., Nunn, B. J. & Schnapf, J. L. (1984). The photocurrent, noise and spectral sensitivity of rods of the monkey Macaca fascicularis. The Journal of Physiology 357, 575-607	[Abstract]
Birch, D. G., Hood, D. C., Nusinowitz, S. & Pepperberg, D. R. (1995). Abnormal activation and inactivation mechanisms of rod transduction in patients with autosomal dominant retinitis pigmentosa and the pro-23-his mutation. Investigative Ophthalmology and Visual Science 36, 1603-1614	[Abstract]
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