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1Physiological Laboratory, University of Cambridge, Cambridge CB2 1TN, United Kingdom; 2Division of Biophysics, Department of Physical Sciences, University of Oulu, Oulu, FIN-90014, Finland; and 3Department of Physiology and Biophysics, Dalhousie University, Halifax, Nova Scotia B3H 1X5, Canada
Submitted 4 December 2003; accepted in final form 21 January 2004
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMETHODSRESULTSDISCUSSIONACKNOWLEDGMENTSREFERENCES |
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONACKNOWLEDGMENTSREFERENCES |
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; Weckström and Laughlin 1995). Therefore understanding how specific components function within these sensory systems should benefit from using stimuli with appropriate dynamic properties. Natural visual inputs often contain strong temporal and spatial correlations, as well as large intensity fluctuations (Burton and Moorhead 1981; Field 1987; Ruderman and Bialek 1994; Srinivasan et al. 1982; Tolhurst et al. 1992) that may cause sparse, brief, intense firing events (Reinagel 2001; Vinje and Gallant 2000, 2002), and activate components such as ion channels that strongly influence neural coding. However, sensory systems are usually investigated using simpler, easily characterized stimuli, such as pulses, steps, or white noise (e.g., French 1980; Juusola and Hardie 2001; Juusola et al. 1994; Laughlin and Hardie 1978; Zettler 1969). These experiments have yielded considerable insights into sensory systems but are unlikely to predict responses to natural stimuli.
Linear systems have the property of superposition, allowing measurements from a restricted range of stimuli to predict the response to any stimulus. This is not true for nonlinear systems, including many physiological systems (Marmarelis and Marmarelis 1978). Responses of neural systems or components to one set of stimuli may not predict their responses to other inputs (Burton and Laughlin 2003; Chacron et al. 2003; Juusola and de Polavieja 2003; Lewen et al. 2001; Niven and Burrows 2003; Rieke et al. 1995; Rinberg and Davidowitz 2000; van Hateren 1997; Vickers et al. 2001). For example, responses to white noise stimulation of lateral geniculate nucleus neurons did not predict responses to naturalistic stimuli (Dan et al. 1996).
Drosophila photoreceptors provide an important system for measuring the contributions of individual neural components, such as ion channels, to overall behavior in vivo (Hardie 1991a; Hardie et al. 1991; Juusola and Hardie 2001; Niven et al. 2003a). Their membranes contain at least 3 groups of voltage-gated potassium channels, including Shaker and delayed rectifier (Hardie 1991; Hardie et al. 1991). We previously examined the role of Shaker channels on information processing in Drosophila photoreceptors using white noise stimulation (Juusola et al. 2003; Niven et al. 2003a,b) and suggested that they could significantly modulate responses to natural stimuli. To determine the contributions of light-dependent ion channels and voltage-gated K+ channels to photoreceptor responses during naturalistic stimuli, we have now recorded intracellularly from wild-type (WT) and Sh14 Drosophila photoreceptors while presenting light modulated by a natural time series of intensities (NTSIs) (van Hateren 1997; van Hateren and Snippe 2001). Sh14 flies have a missense mutation in the Shaker potassium channel core region, which generates nonfunctional channels (Kaplan and Trout 1961; Salkoff and Wyman 1981). Comparison of WT and Sh14 photoreceptor responses suggested that Shaker channels increase the response spread across the available voltage range during naturalistic stimuli. To quantify these effects, photoreceptor responses were modeled by both Volterra series and nonlinear–linear–nonlinear (NLN) cascades. These revealed that Sh14 photoreceptor responses to naturalistic stimuli were significantly different from their responses to white noise stimuli. A Hodgkin–Huxley type model was used to separate the contributions of the current through light-dependent channels [light-induced current (LIC)] and the current through voltage-activated ion channels to the total voltage response. This model showed that differences in the response nonlinearities of both WT and Sh14 photoreceptors were primarily attributed to changes in LIC, suggesting that feedback from the effects of voltage-gated ion channels to light transduction may be important for tuning photoreceptor responses during development.
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METHODS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONACKNOWLEDGMENTSREFERENCES |
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The wild-type strain was red-eyed Drosophila melanogaster Oregon Red. Mutant animals with Sh14, a missense mutation in the core region resulting in nonfunctional Shaker channels (Kaplan and Trout 1961), were also red-eyed flies. Both strains of flies were raised at 19° C in darkness.
Recording and stimulation
Recording, stimulation, and data acquisition were previously described (Juusola and de Polavieja 2003; Juusola and Hardie 2001). Photoreceptors were stimulated by a high-intensity green light-emitting diode (LED) with peak wavelength of 525 nm (Marl Optosource). Light intensity was derived from a published naturalistic stimulus time series obtained from a light detector moving through a natural environment (van Hateren 1997; van Hateren and Snippe 2001). The light stimulus was presented at a rate of 1 kHz and all the light intensity measurements were converted to dimensionless contrast units. Light intensity and photoreceptor membrane potential were sampled at 1-ms intervals during repeated presentations of naturalistic light sequences of 18-s duration. Photoreceptors were only used if their membrane potential was more negative than -55 mV and they had at least a 45-mV saturating impulse response in dark-adapted conditions.
The light source gave an approximately monochromatic, small-field stimulus, whose angle of 5.4° covered more than one ommatidium, so that stimuli delivered to different units were not statistically independent. LEDs also have compressive nonlinearities that caused the actual output to differ from the collected NTSIs. The light stimulus was presented at a rate of 1 kHz, instead of the original recording rate of 1.25 kHz, which decreased the frequency bandwidth of the stimulus. This allowed direct comparison with our previous data obtained by white noise stimulation (Juusola et al. 2003), and was justified by the relatively slow flying speeds of Drosophila (David 1978; Fry et al. 2003). Although these differences from natural outdoor spatial and chromatic light patterns must be noted, they should not affect the general validity of the analysis.
Nonlinear system identification
Identification was based on estimating the kernels of a Volterra series, K0, K1(u), K2(u, v),..., where u, v,... are time lags (French and Marmarelis 1999) with light intensity as the input x(t), as a function of time t, and receptor potential as the output y(t). Several methods have been developed for kernel estimation. Earlier methods relied on stimulating the unknown system with Gaussian white noise, but more recent methods avoid this requirement (French and Marmarelis 1999). We used a completely general approach based on a parallel cascade method (Juusola et al. 2003; Korenberg 1991), but having the linear filters of the cascades formed from Gaussian-distributed random numbers (French et al. 2001; Juusola et al. 2003). This method makes no initial assumptions about the forms of the kernels or the nature of the input or output signals and it can be applied to systems containing a relatively high order of nonlinearities. However, it is not necessary to construct all of the higher-order kernels.
Responses to 12 presentations of an 18-s sequence of naturalistic stimulus light contrast were concatenated, and the original sampling resolution of 1 ms was reduced to 2 ms by combining adjacent points to give records of 108,000 data pairs (light intensity in contrast units and receptor potential in mV). This was done both to reduce the fitting tasks and to accommodate the relative lack of high-frequency components in the NTSI. For each record, the first 50,000 data pairs were discarded to avoid any effects resulting from the onset of light stimulation. The following 40,000 data pairs were analyzed as the input and output of the unknown nonlinear dynamic system.
After kernel estimation, percentage mean square error (MSE) values (French and Marmarelis 1999) were calculated for the zeroand first-order kernels alone and for the combined, zero-, first-, second-, and third-order kernels from
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The kernel estimates were then used to predict the output of the nonlinear system to the input signal of the remaining 10,000 data pairs of each record. Therefore all predictions were based on recorded data that had not been used for system identification.
Simulation: NLN model
Nonlinear responses in Drosophila photoreceptors were simulated by an NLN (nonlinear static–linear dynamic–nonlinear static) cascade model (French et al. 1993). The two nonlinear components were polynomial functions and the linear component was the Wong and Knight photoreceptor model (Wong et al. 1980)
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are parameters to be fitted. To remove redundant parameters, only one constant term was included in the model, as an offset in the output of the linear component. Similarly, the first nonlinear component had a fixed first-order coefficient of unity. The numbers of unknown parameters were therefore: N1 - 1 (first polynomial) + 3 (Wong and Knight model plus offset) + N2 (second polynomial). The NLN cascade model was fitted to the first 9,000 data pairs (corresponding to one complete cycle through the naturalistic stimulus sequence) used for the kernel analysis. Fitting was performed by simulated annealing (Press et al. 1990). The fitting algorithms always converged satisfactorily. MSE values were again calculated using Eq. 1. Simulation: Hodgkin–Huxley photoreceptor model
A Hodgkin–Huxley type photoreceptor model was developed using MATLAB software (MathWorks, Natick, MA). Derivation and validation of the model were described previously (Niven et al. 2003a; supplementary material). The model included Shaker and delayed rectifier potassium conductances, in addition to potassium and chloride leak conductances. The voltage-dependent parameters (including time constants and steady-state functions for activation and inactivation) for the Shaker and delayed rectifier conductances were obtained from published data (Hardie 1991; Hevers and Hardie 1995; Niven et al. 2003a). Other photoreceptor membrane properties (i.e., the maximum values of the active conductances, resting potential, leak conductances, and membrane capacitance) were estimated from in vivo recordings. The voltage-dependent properties of the ion channels, the reversal potentials for each ion, and the membrane area were kept fixed in all simulations. Potassium and chloride leak conductances in the model were adjusted for each individual photoreceptor until the experimental resting potential and steady-state resistance were obtained. Maximum conductances for the Shaker and delayed rectifier channels were also adjusted to fit the experimental data.
The model allowed us to predict the current flowing through light-dependent channels (LIC) attributed to NTSI. Although the voltage-dependent properties of Shaker and delayed rectifier conductances were characterized in darkness, these properties were assumed to be insensitive to light. This was justified both by comparison of simulated voltage responses to current stimuli with experimental data (data not shown), and by experimental results from Calliphora photoreceptors (Weckström et al. 1991). The absorption of a single photon happens in all-or-none fashion, causing influx of calcium and sodium ions to a microvillus. The small microvillar volume leads to rapid changes in ionic concentrations, and a reversal potential of +10 mV for this light-induced conductance (Oberwinkler and Stavenga 2000; Reuss et al. 1997). During natural stimuli the photon flux must activate numerous microvilli, causing dynamic reversal potential fluctuations in each microvillus as it receives photons. These fluctuations were assumed to be independent and were modeled as a single average light-induced conductance input to the light-insensitive membrane. This conductance was used to drive the Hodgkin–Huxley model and its values were iterated at each sample point until the experimental voltage response was reproduced. From each simulation the individual model conductances, including Shaker, delayed rectifier and light-induced conductance, were used to calculate the corresponding currents Ii from the electrical driving force of the individual ions and their conductances gi, using Ohm's law
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Predicted LICs produced voltage responses that closely matched experimental data, except during total darkness (data not shown). This was also true for the nonlinear kernel and NLN models (Fig. 2). Experimental data contained clear afterhyperpolarizations in the WT and the mutant responses, as well as small depolarizations preceding afterhyperpolarizations in the mutant response (Fig. 2). These are caused by the Na+/K+ pump and the 3Na+/Ca2+ exchanger currents, respectively (Gerster 1997; Gerster et al. 1997; Oberwinkler and Stavenga 2000). Estimated amplitudes of these currents are about 10 times smaller than the other currents in the model (Fig. 5), indicating that they would not affect our analysis. As a further test, an NLN model was derived from the simulated voltage response of the Hodgkin–Huxley model. The components in this NLN model were identical to those derived from experimental data, confirming that the smaller currents do not cause significant errors.
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RESULTS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONACKNOWLEDGMENTSREFERENCES |
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We recorded intracellularly from WT and mutant (Sh14) photoreceptors in vivo while presenting NTSI stimuli. The naturalistic stimuli contained periods of both very low and high light intensity that were reflected in the voltage responses of both the WT and mutant photoreceptors (Fig. 1A). Although the structure of both WT and Sh14 photoreceptor responses resembled the gross structure of the naturalistic light stimulus (Fig. 1A), examination of the fine structure of the responses revealed clear differences between the 2 photoreceptor types (Fig. 1B). These differences were particularly clear during sequences of rapid transients in which WT photoreceptors closely followed the light stimulus but Sh14 photoreceptors were unable to do so. For example, in Fig. 1B light intensity fluctuations of increasing intensity were encoded by increasing responses in the WT photoreceptor but the Sh14 responses approached plateau depolarizations at lower stimulus levels, compressing their responses to bright inputs. Mutant photoreceptors produced large, fast voltage responses to large light intensity increases after dim periods, which were reduced in WT photoreceptors (Fig. 1B). During sustained periods of bright light Sh14 receptors produced smaller responses than WT (Fig. 1A). Additionally, Sh14 voltage responses repolarized more rapidly than WT voltage responses (Fig. 1A). Differences in the voltage responses over the entire stimulus sequences are shown in the response histograms (Fig. 1C), and the cumulative frequency distributions of these histograms (Fig. 1D), which show that the voltage response of WT photoreceptors was spread over a greater voltage range than the mutant.
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Measures commonly used to characterize graded neuronal responses, such as those of a photoreceptor, to Gaussian white noise stimuli cannot be used to characterize responses to natural stimuli because both stimulus and response are non-Gaussian. Therefore we used Volterra kernel series and NLN models of WT and Sh14 photoreceptor responses to NTSI sequences to characterize the effects of ion channels on natural stimulus coding (Figs. 2, 3, 4).
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First-order kernels, K1(u), derived from WT and Sh14 voltage responses to naturalistic stimuli had the same general form as flash responses in light-adapted Drosophila photoreceptors (Fig. 3A; Juusola and Hardie 2001). All of the first-order kernels had a delay of about 6 ms, but the kernels derived from Sh14 voltage responses consistently had faster time-to-peak (
3–4 ms) and narrower half-width than those from WT voltage responses (Fig. 3A). This feature corresponds with the larger and faster Sh14 voltage responses clearly visible in the voltage responses shown in Fig. 1, A and B.
We compared the kernel forms derived from voltage responses to naturalistic stimuli with those derived from Gaussian white noise stimuli (Juusola et al. 2003). Comparison of WT and Sh14 kernels from the 2 stimulus regimes revealed that the Sh14 kernel peaked later under white noise conditions. Indeed, WT and Sh14 kernels derived from white noise stimuli were indistinguishable (Fig. 3B). In addition to these changes in the timing and amplitude of the Sh14 kernels, those derived from naturalistic stimuli were less smooth than those obtained by white noise stimulation (Fig. 3, A and B; Juusola et al. 2003). One reason for this is that the selected NTSI stimulus had relatively small amplitude components at high frequencies, causing poor estimation of high frequencies and leading to increased variance in the time domain kernel estimates. Another factor is the strongly nonlinear behavior of photoreceptors to NTSI, which caused higher-order components to contaminate lower-order kernels in finite-length Volterra series.
Contamination of the linear impulse response by higher-order components in the Volterra series could potentially account for the differences in the WT and Sh14 kernels between naturalistic and white noise stimuli. To eliminate this possibility, we compared first-order kernels obtained by terminating the Volterra series at K1(u) or K3(u, v, w) (Fig. 3C). The kernel forms were similar: Sh14 first-order kernels obtained from third-order series still had larger amplitudes and faster time-to-peaks than those of WT kernels. However, the first-order kernels obtained from third-order series were significantly larger than those obtained by terminating the Volterra series at K1(u), indicating strongly nonlinear behavior, and that the second- and/or third-order kernels contain components of similar time course, but negative amplitude (Fig. 3C).
Previous analysis of WT and Sh14 voltage responses to white noise stimuli revealed negative amplitude nonlinearities on the diagonal of the second-order kernels, corresponding to a non-linear attenuation (Juusola et al. 2003). Second-order kernels, K2(u, v), derived from naturalistic stimuli, did not contain these negative nonlinearities. Instead, they had positive peaks on the diagonals having approximately the same time courses as the first-order kernels (Fig. 3, D and E). This pattern of kernel forms is characteristic of the Hammerstein nonlinear model (Korenberg and Hunter 1986) in which a linear filter is followed by a static nonlinearity. However, the second-order kernels also had many nonzero values away from the diagonals, indicating that additional, complex nonlinear interactions were significant.
NLN cascade model of phototransduction
The pattern of kernel forms derived from the first- and second-order kernels of the Volterra series suggested that the WT and Sh14 photoreceptor responses could be described by a model in which a dynamic linear filter is followed by a static nonlinearity (French and Korenberg 1989; Korenberg and Hunter 1986). This model is attractive because it may potentially correspond to the phototransduction cascade (linear filter) and the photoinsensitive membrane (static nonlinearity) of the photoreceptor. Such a model would have relatively few parameters and could be used to separate the effects of individual components of phototransduction and the photoinsensitive membrane, allowing mechanistic insights into the generation of the photoreceptor voltage responses (van Hateren and Snippe 2001). We tested several LN, NL, and NLN models to determine which model gave the best prediction of photoreceptors responses to naturalistic stimuli. The most successful of these models was an NLN model with a "Wong and Knight" or gamma function model of phototransduction (Wong et al. 1980) as the linear dynamic component surrounded by 2 static nonlinearities (Figs. 2 and 4). The first nonlinearity required a fifth-order polynomial, whereas the second polynomial was third-order, giving a total count of 10 parameters (see METHODS and Fig. 4). The NLN model captured a large part of the nonlinear photoreceptor behavior identified by the Volterra series (Fig. 2; Table 1).
Sh14 photoreceptors differed most strongly from WT photo-receptors in the second and third stages of the NLN model (Fig. 4, Table 2). The first static nonlinearity was a positive rectification, in which the response increased strongly above about 6.0 contrast units. This effect was slightly stronger in Sh14 flies. Linear components were very similar to first-order Volterra kernels, and the mutant flies again showed larger and faster responses, peaking about 2 ms before the WT. The final static nonlinearity always had a region of zero, or negative slope in the middle of an overall positive characteristic, corresponding to an intermediate region where increasing light intensity produced no change, or a slight hyperpolarization, in membrane potential. In Sh14 photoreceptors this effect occurred over a smaller stimulus range and at lower stimulus levels, corresponding to less depolarized membrane potentials.
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Although some of differences in the voltage responses of WT and Sh14 photoreceptors can be attributed directly to the Shaker channel (see DISCUSSION), it is also possible that changes in the LIC or other ionic currents could occur during development. We used a Hodgkin–Huxley model of the Drosophila photoreceptor (Niven et al. 2003a,b) to determine whether these differences in LIC or voltage-gated ion channels contribute to the observed differences between WT and Sh14 responses. This model allowed us to separate the effects of the LIC and voltage-gated currents that contributed to voltage responses.
After recording responses of Drosophila photoreceptors to naturalistic and white noise light stimuli we injected current steps to characterize the photoreceptor membrane properties (see METHODS). These membrane properties were used to construct a Hodgkin–Huxley model of the photoinsensitive membrane of each WT or Sh14 photoreceptor (Niven et al. 2003a,b). We then used this model to estimate the LIC, delayed rectifier current, and, in WT photoreceptors, the Shaker current to the same NTSI stimulus (Fig. 5, A, D, and F). There were several differences between the currents in WT and Sh14 models (other than the absence of functional Shaker channels) including an increase in the LIC and the delayed rectifier current in Sh14 photoreceptor responses (Fig. 5, C and G). The structure of both the WT and Sh14 LICs resembled both the gross structure of the naturalistic light stimulus and the photoreceptor voltage responses. Examination of the fine structure of the LICs revealed that they were more similar than the equivalent voltage responses. In particular, the WT LIC showed the same compression of signals as the Sh14 LIC during sequences of rapid transients. However, during these sequences of light pulses the WT voltage response followed the light stimulus, whereas the Sh14 did not. Additionally, many of the transients visible in the Sh14 voltage response corresponded to small, high-frequency fluctuations in the LIC.
To compare the differences in the WT and Sh14 simulated LICs with the differences in their experimental voltage responses, we calculated Volterra kernels between the naturalistic light stimulus and the LIC (Fig. 6, Table 3) and derived NLN models of the simulated LIC (Fig. 7, Table 4). There were close similarities between the time courses of the first- and second-order Volterra kernels (Fig. 6) and those derived from the WT and Sh14 voltage responses (Fig. 3), suggesting that light current dominates the dynamic response. The NLN models of the simulated LIC (Fig. 7, Table 4) also closely resembled those from the experimental data. As with the NLN model of the photoreceptor voltage responses, the NLN model consisted of a Wong and Knight function surrounded by 2 static nonlinearities. The first nonlinearity was indistinguishable between WT and Sh14 photoreceptors and reproduced the strong rectification in the first nonlinearity of the NLN model of photoreceptor voltage responses. The Wong and Knight function had a faster time-to-peak in the Sh14 LIC than in WT, which was similar to the differences between this component in the NLN model of WT and Sh14 voltage responses (Fig. 7). The main difference between the NLN model of the LIC and that of the voltage responses was in the second nonlinearity. This component was similar for both WT and Sh14 LICs (Fig. 7), unlike the same component for the voltage responses in which the WT had much larger negative slope regions at higher voltages (Fig. 4). Therefore although some of the differences between WT and Sh14 photoreceptors are directly attributed to loss of Shaker channels, there are also differences in the LIC (see DISCUSSION).
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Comparison of the delayed rectifier currents from WT and Sh14 voltage responses simulated by the Hodgkin–Huxley model revealed that in the absence of the Shaker current there was a marked increase in the delayed rectifier current (Fig. 5, D–G). Additionally, WT delayed rectifier was slower than Sh14 delayed rectifier (Fig. 5G). What contribution do these changes in delayed rectifier current have on naturalistic stimulus processing? We calculated first-order Volterra kernels between the NTSI stimulus and the voltage-gated currents of the Hodgkin–Huxley simulations (Fig. 8, Table 3). These kernels had time courses similar to those of the LICs but started 
5 ms later. In the WT photoreceptors the kernel of the Shaker current was much larger than that of the delayed rectifier. However, the amplitude of the delayed rectifier kernels in the mutant were increased in comparison to those of the WT and reflected the partial replacement of Shaker by delayed rectifier current in the mutant model. We also calculated second-order Volterra kernels to ensure that the increase in the first-order mutant delayed rectifier kernel was not the consequence of contamination by higher-order kernels. The most prominent feature of all the second-order kernels in both WT and Sh14 photoreceptors was a relatively flat valley extending about 5 ms on either side of the diagonal (Fig. 8). This time corresponds approximately to the initial delay in the rise of the light current (Figs. 6 and 7).
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DISCUSSION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONACKNOWLEDGMENTSREFERENCES |
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; Weckström et al. 1991), but the roles of these channels in shaping neuronal responses during natural stimuli remain largely unknown. We addressed this problem by comparing in vivo recordings and nonlinear models of WT and Sh14 Drosophila photoreceptors coding naturalistic stimuli. Voltage responses of Sh14 photoreceptors to naturalistic stimuli were altered compared with their WT counterparts. In particular, many of the transient responses to naturalistic stimuli in Sh14 photoreceptors were distorted, and the spread of the signal over the available voltage range was reduced in Sh14 photoreceptors (Fig. 1). Modeling the responses of both photoreceptor types as Volterra kernels or NLN cascades suggested that these differences were attributable to larger, faster and shorter responses in Sh14 photoreceptors (Figs. 3 and 4). Models obtained from naturalistic stimuli were not the same as those from white noise stimuli (Juusola et al. 2003; Niven et al. 2003a), and differences between Sh14 and WT photoreceptors could not be predicted from the white noise models, suggesting that Shaker channels behave differently under different stimulus regimes (Fig. 3). To test whether these differences were attributed to conductance changes in the photoinsensitive membrane or to changes in the current through light-dependent channels (LIC), we used a Hodgkin–Huxley simulation of Drosophila photoreceptors to calculate the LIC of both WT and Sh14 photoreceptors. Simulated LICs of the WT and Sh14 photoreceptors were more similar than their voltage responses, suggesting a significant contribution of Shaker channels to encoding of naturalistic stimuli (Fig. 5). However, the simulations indicated that differences between WT and mutant photoreceptors were not restricted to Shaker potassium channels, but included changes in both LIC and delayed rectifier channels. What causes the differences between photoreceptor responses to naturalistic and white noise stimuli?
WT photoreceptors had smaller-amplitude, longer time-to-peak, and longer half-width linear impulse responses than those of Sh14 mutants, which was also true for the linear component of the NLN model (Figs. 3 and 4). These differences between WT and Sh14 photoreceptor linear impulse responses may be explained, at least partially, by the presence or absence of functional Shaker K+ channels in the photoinsensitive membrane of the photoreceptors. Increasing light intensity depolarizes WT photoreceptors, rapidly activates Shaker K+ channels, and partially shunts the LIC through the increased membrane conductance (Niven et al. 2003a). The Shaker K+ channels then rapidly inactivate, which effectively amplifies the effect of the LIC at later times in the photoreceptor voltage response. Thus WT photoreceptor impulse responses are expected to have longer time-to-peak, smaller amplitude, and longer half-width compared with Sh14 impulse responses.
In contrast, we previously showed that WT and Sh14 photo-receptor linear kernels have similar time-to-peak, amplitude, and half-width when measured with white noise stimulation (Fig. 3B). Under these conditions, differences between WT and Sh14 photoreceptors can be seen in the second-order kernel, where WT photoreceptors show an early nonlinear amplification that is absent in the Sh14 mutants (Juusola et al. 2003). Differences between kernels derived from naturalistic and white noise stimuli are attributed to the stimulus structure. Naturalistic stimuli can contain prolonged dark periods interspersed with periods of high light intensity, evoking large fluctuations in photoreceptor voltage (van Hateren 1997), whereas dark and bright periods in band-limited Gaussian white noise stimuli of similar duration are typically brief, allowing photoreceptor responses to be modulated around a relatively constant mean voltage. Shaker K+ channels behave differently under these 2 stimulation regimes because their prominent activation and inactivation during voltage transients are reduced by maintained depolarization.
Can the differences between the WT and Sh14 photoreceptor responses to naturalistic stimuli be explained fully by the presence or absence of functional Shaker K+ channels in the photoinsensitive membrane?
In vivo intracellular recordings of Sh14 photoreceptors suggest that they have a reduced input resistance to compensate for their lack of functional Shaker K+ channels, which is accompanied by a depolarized resting potential (Niven et al. 2003a). However, it is also possible that the loss of Shaker K+ channels affects the current flowing through light-dependent channels (LIC) through one or more feedback mechanisms. Such feed-back could occur directly by changes in the voltage driving the LIC caused by changes in the numbers of different channel types in the photoinsensitive membrane. Alternatively, changes in channel populations could, through changes in membrane potential or ionic concentrations, modify the development of the components that generate the LIC. Both these possibilities must be considered.
Comparison of LIC kernels calculated from WT and Sh14 photoreceptors showed that mutant kernels were larger and faster than those of WT. Similarly, the linear Wong and Knight component of the NLN model, which may represent LIC generation, had a faster time-to-peak in mutant photoreceptors. These differences in the LIC cannot be ascribed directly to the presence or absence of Shaker K+ channels because Sh14 photoreceptors are depolarized at rest relative to WT photoreceptors (Niven et al. 2003a), effectively reducing the driving force on the LIC (Reuss et al. 1997). This suggests that differences in the light-transduction machinery of the 2 phenotypes are caused by feedback that is not simply a change in driving potential.
What changes in light transduction might be expected? In Drosophila photoreceptors (Wu and Pak 1975), as in other photoreceptors (Baylor et al. 1979; Yeandle 1985), discrete electrical events (bumps) can be recorded under dim illumination that correspond to single-photon absorptions. Although the LIC predicted by simulation is faster in Sh14 photoreceptors, in vitro recordings show that bump amplitude, quantum efficiency, and macroscopic kinetics are unaffected (Niven et al. 2003a). Therefore differences between the phototransduction cascade of WT and Sh14 photoreceptors are unlikely to be the result of differences in bump amplitude and waveform. However, individual bumps are responses to single photons, whereas the Volterra kernels and NLN model in our analysis were calculated from responses to approximately 106 photons/s or more (Juusola and Hardie 2001). As mean light intensity increases, the average bump size decreases markedly and the time course is reduced (Juusola and Hardie 2001; Wu and Pak 1978). These changes in bump waveform may be the result of Ca2+-mediated adaptation (Henderson et al. 2000), which is a feature of many invertebrate and vertebrate photoreceptors (Burns and Baylor 2001; Fain et al. 2001; Hardie and Minke 1995; Montell 1999; Pugh et al. 1999). Changes in light and dark adaptation mediated by Ca2+ have been proposed to explain differences between photoreceptor responses within an individual compound eye (Burton et al. 2001). One possibility is that Sh14 photoreceptors possess altered Ca2+ dynamics compared with WT, affecting light adaptation and the dynamics of the linear impulse response. An alternative explanation is that there are different distributions of bump latencies, such as would arise from shifting transduction to different regions of the photosensitive membrane.
The relative success of the NLN model suggests a functional analogy, in which the linear Wong and Knight component represents LIC generation. In this case, the 2 nonlinearities would occur before and after phototransduction, and could represent an early adaptation mechanism and the photoinsensitive membrane, respectively. Association of the final nonlinearity with the photoinsensitive membrane is supported by comparison of WT and Sh14 NLN models for the LIC with those of the voltage response. The final nonlinearity contains significant differences in the NLN models of the voltage response that are absent in the NLN models of the LIC. This suggests that the final nonlinearity is most affected by the properties of the photoinsensitive membrane. The first nonlinear component of the NLN models of LIC is similar for both WT and Sh14 photoreceptors, suggesting that this component cannot account for the differences in the LIC. However, the linear component is faster in Sh14 photoreceptors, supporting the idea that differences in LIC are attributed to differences in the light transduction machinery.
Interaction between Shaker and delayed rectifier K+ channels during naturalistic stimuli
The biophysical properties of Shaker and delayed rectifier channels are well characterized in Drosophila photoreceptors (Hardie 1991; Hardie et al. 1991). In WT photoreceptors Shaker channels are activated at the onset of a light impulse but inactivate rapidly, whereas delayed rectifier channels activate/inactivate more slowly (Niven et al. 2003a). The delayed rectifier current is larger in Sh14 than in WT photoreceptors (Fig. 5) because of interactions between delayed rectifier and Shaker channels. Shaker channels effectively shunt photoreceptor currents, not only reducing the overall size of delayed rectifier current but also changing the time course of activation (Niven et al. 2003a). These changes lead to a significantly smaller and slower first-order kernel for the WT delayed rectifier current compared with Sh14 (Fig. 8).
Functional significance
The change in LIC observed in Sh14 photoreceptors extends previous findings that activity of the phototransduction cascade may alter photoreceptor membrane properties (Burton 2002; Wolfram et al. 2003) by showing that these interactions may be bidirectional. Enabling photoreceptors to adjust photoinsensitive membrane properties to their LIC may ensure that photo-receptor voltage response is optimized to the prevailing light conditions. Changes in the LIC suggest that activity-dependent plasticity in Drosophila photoreceptors may occur by a feedback mechanism that is sensitive to changes in the photoreceptor membrane.
Alterations of the photoreceptor membrane, phototransduction cascade, or both represent tuning of these components to the lighting conditions experienced by the photoreceptor during development and adult life. Photoreceptor membrane properties are also thought to be tuned during evolution to the visual ecology of the insect by voltage-gated K+ and Na+ channels (for review see Weckström and Laughlin 1995). Our results suggest that individual ion channels, such as the Shaker K+ channel, may filter the LIC in different ways depending on the dynamic properties of the stimulus. Therefore to understand the precise contribution of these channels to the voltage response of a neuron it is important to assess the properties of channels under the most natural possible stimulus conditions.
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ACKNOWLEDGMENTS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONACKNOWLEDGMENTSREFERENCES |
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Present address of J. Niven: Department of Zoology, University of Cambridge, Cambridge CB2 1TN, UK.
GRANTS
This work was supported by grants from the Canadian Institutes of Health Research to A. S. French, and the Royal Society, Wellcome Trust, and Biotechnology and Biological Sciences Research Council to M. Juusola.
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FOOTNOTES |
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Address for reprint requests and other correspondence: A. S. French, Department of Physiology and Biophysics, Dalhousie University, Halifax, Nova Scotia B3H 1X5, Canada (E-mail: andrew.french{at}dal.ca).
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONACKNOWLEDGMENTSREFERENCES |
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