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

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:

(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.

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.

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:

(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.

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):

(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 τ_k= 130 ms (k_t/k₈₆≈ exp[-(t - 86)/τ_k]); those obtained with t_probe > 600 ms indicate a more gradual further decline.

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)).

Figure 4. Probe flash responses obtained in paired-flash trials with fixed I_test (0·11 sc cd s m⁻²).

Open in a new tab

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:

(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.

Figure 5. Time course of the weak-flash derived response.

Open in a new tab

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:

(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 γ′, an activation term [1 - exp(-α′(t - t_d)²)] and a decay term exp(-t/τ_ω′), where t_d is a brief delay, τ_ω′ is an exponential time constant and α′ 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 γ′= 1·84, τ_ω′= 163 ms, t_d= 3·1 ms and α′= 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 τ_ω′; a delay within the term exp(-t/τ_ω′) 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:

(6)

where u(t) is a unit, i.e. elemental, function analogous to the eqn (5) expression, where the parameters γ, τ_ω and α correspond functionally with the γ′, τ_ω′ and α′ of eqn (5), and where γ and τ_ω are time independent. By analogy with earlier studies (e.g. Lamb & Pugh, 1992) we assume for the moment that α 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 γ, τ_ω and α were free parameters. This fitting yielded γ= 2·21, τ_ω= 132 ms and α= 2·32 × 10⁻⁴ ms⁻². For comparison with results below we shall define, by α_n, the value of α just indicated. We shall also refer to the fitted values of α (=α_n), γ and τ_ω 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 γ, τ_ω and α 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 γ, τ_ω and α 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
γ	2.36 ± 0.85	2.00 ± 0.27	1.72 ± 0.30
τω (ms)	139 ± 38	141 ± 20	147 ± 31
α (ms−2)	(2.81 ± 1.56) × 10−4	(2.75 ± 0.56) × 10−4	(3.18 ± 0.75) × 10−4

Open in a new tab

Results were obtained from 3 mice (4 sets of probe flash responses; see text). Each entry is the mean ± s.d.

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):

(7)

in which β 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 β= 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):

(8)

and the similarity of eqns (7) and (8) implies an equivalence between β and the product γk₈₆α. 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 α in this expression was reduced from the nominal value α_n (= 2·32 × 10⁻⁴ ms⁻²) to α_i, where:

(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 α=α_i= 0·97 × 10⁻⁴ ms⁻², eqn (6) with γ and τ_ω fixed at their nominal values or determined from a refitting of eqn (6) to the paired-flash data (free variation of γ and τ_ω, yielding γ= 5·35 and τ_ω= 84 ms) yielded a poor overall fit to the experimental results (curves 2-3 of Fig. 5B and inset).

Figure 6. Comparison of eqn (6) with ERG a-wave data obtained in a single experiment.

Open in a new tab

The early segment of the response to a test flash was further analysed by fitting eqn (6), with γ and τ_ω 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 α determined from the a-wave results (with t about20 ms or less) will be termed α_i; that determined from the paired-flash results (with t at 56 ms) will be termed α₅₆. 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 α_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 α₅₆= 1·85 × 10⁻⁴ ms⁻². Results obtained in a second experiment similar to that of Fig. 7 yielded α_i= 0·95 × 10⁻⁴ ms⁻² and α₅₆= 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 α, rather than being constant, increases with time about 2-fold during the rising phase of the derived response to a weak test flash.

Figure 7. Determinations of the eqn (6) parameter α from a-wave and paired-flash (A(56)/A_mo) data obtained in the same experiment.

Open in a new tab

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 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 τ_ω (= 132 ms) determined from the Fig. 5 data is similar to τ_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[-α(t - t_d)²]≈ 0) to be:

(10)

From comparison of eqns (3) and (10) it follows that k_t≈k₈₆γexp(-t/τ_ω). Thus τ_k, which by definition is the post-flash interval associated with an e-fold decline in k_t, is predicted to be equal to τ_ω. The observed agreement between τ_ω and τ_k, and the near match of τ_ω and τ_k with the time constant τ_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(-α(t - t_d)²)]; cf. Lamb & Pugh, 1992) and an exponential decay term exp(-t/τ_ω). 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(-α(t - t_d)²)]exp(-t/τ_ω)} 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 α. 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 α 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 α 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[-α(t - t_d)²]} to the activation function investigated by Lamb & Pugh (1992), is that α 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 α=α(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).