Toward a unified model of vertebrate rod phototransduction.

Recently, we introduced a phototransduction model that was able to account for the reproducibility of vertebrate rod single-photon responses (SPRs) (Hamer et al., 2003). The model was able to reproduce SPR statistics by means of stochastic activation and inactivation of rhodopsin (R*), transducin (G alpha ), and phosphodiesterase (PDE). The features needed to capture the SPR statistics were (1) multiple steps of R* inactivation by means of multiple phosphorylations (followed by arrestin capping) and (2) phosphorylation dependence of the affinity between R* and the three molecules competing to bind with R* (G alpha, arrestin, and rhodopsin kinase). The model was also able to account for several other rod response features in the dim-flash regime, including SPRs obtained from rods in which various elements of the cascade have been genetically disabled or disrupted. However, the model was not tested under high light-level conditions. We sought to evaluate the extent to which the multiple phosphorylation model could simultaneously account for single-photon response behavior, as well as responses to high light levels causing complete response saturation and/or significant light adaptation (LA). To date no single model, with one set of parameters, has been able to do this. Dim-flash responses and statistics were simulated using a hybrid stochastic/deterministic model and Monte-Carlo methods as in Hamer et al. (2003). A dark-adapted flash series, and stimulus paradigms from the literature eliciting various degrees of light adaptation (LA), were simulated using a full differential equation version of the model that included the addition of Ca2+-feedback onto rhodopsin kinase via recoverin. With this model, using a single set of parameters, we attempted to account for (1) SPR waveforms and statistics (as in Hamer et al., 2003); (2) a full dark-adapted flash-response series, from dim flash to saturating, bright flash levels, from a toad rod; (3) steady-state LA responses, including LA circulating current (as in Koutalos et al., 1995) and LA flash sensitivity measured in rods from four species; (4) step responses from newt rods ( Forti et al., 1989) over a large dynamic range; (5) dynamic LA responses, such as the step-flash paradigm of Fain et al. (1989), and the two-flash paradigm of Murnick and Lamb (1996); and (6) the salient response features from four knockout rod preparations. The model was able to meet this stringent test, accounting for almost all the salient qualitative, and many quantitative features, of the responses across this broad array of stimulus conditions, including SPR reproducibility. The model promises to be useful in testing hypotheses regarding both normal and abnormal photoreceptor function, and is a good starting point for development of a full-range model of cone phototransduction. Informative limitations of the model are also discussed.

Kinetics of synaptic transfer from rods and cones to horizontal cells in the salamander retina.

We examined synaptic transmission between rods or cones and horizontal cells, using perforated patch recording techniques in salamander retinal slices. Experimental conditions were established under which horizontal cells received nearly pure rod or pure cone input. The response-intensity relation for both photoreceptors and horizontal cells was described by a Michaelis-Menten function with an exponent close to 1. A dynamic model was developed for the transduction from photoreceptor voltage to postsynaptic current. The basic model assumes that: (i) photoreceptor light-evoked voltage controls Ca2+ entry according to a Boltzmann relation; (ii) the rate of glutamate release depends linearly on the voltage-gated Ca2+ current (ICa) in the synaptic terminal; (iii) glutamate concentration in the synaptic cleft reflects the balance of release and reuptake in which reuptake obeys first order kinetics; (iv) the binding of glutamate to its receptor and channel gating are fast compared with glutamate kinetics in the synaptic cleft. The good fit to the model confirms that these are the key features of synaptic transmission from rods and cones. The model accommodated changes in kinetics induced by the glutamate uptake blocker, dihydrokainate. The match between model and response was not improved by including an estimate of alpha-amino-3-hydroxy-5-methylisoxazole-4-propionic acid (AMPA) receptor desensitization or by making glutamate uptake voltage dependent.

Multiple steps of phosphorylation of activated rhodopsin can account for the reproducibility of vertebrate rod single-photon responses.

Single-photon responses (SPRs) in vertebrate rods are considerably less variable than expected if isomerized rhodopsin (R*) inactivated in a single, memoryless step, and no other variability-reducing mechanisms were available. We present a new stochastic model, the core of which is the successive ratcheting down of R* activity, and a concomitant increase in the probability of quenching of R* by arrestin (Arr), with each phosphorylation of R* (Gibson, S.K., J.H. Parkes, and P.A. Liebman. 2000. Biochemistry. 39:5738-5749.). We evaluated the model by means of Monte-Carlo simulations of dim-flash responses, and compared the response statistics derived from them with those obtained from empirical dim-flash data (Whitlock, G.G., and T.D. Lamb. 1999. Neuron. 23:337-351.). The model accounts for four quantitative measures of SPR reproducibility. It also reproduces qualitative features of rod responses obtained with altered nucleotide levels, and thus contradicts the conclusion that such responses imply that phosphorylation cannot dominate R* inactivation (Rieke, F., and D.A. Baylor. 1998a. Biophys. J. 75:1836-1857; Field, G.D., and F. Rieke. 2002. Neuron. 35:733-747.). Moreover, the model is able to reproduce the salient qualitative features of SPRs obtained from mouse rods that had been genetically modified with specific pathways of R* inactivation or Ca2+ feedback disabled. We present a theoretical analysis showing that the variability of the area under the SPR estimates the variability of integrated R* activity, and can provide a valid gauge of the number of R* inactivation steps. We show that there is a heretofore unappreciated tradeoff between variability of SPR amplitude and SPR duration that depends critically on the kinetics of inactivation of R* relative to the net kinetics of the downstream reactions in the cascade. Because of this dependence, neither the variability of SPR amplitude nor duration provides a reliable estimate of the underlying variability of integrated R* activity, and cannot be used to estimate the minimum number of R* inactivation steps. We conclude that multiple phosphorylation-dependent decrements in R* activity (with Arr-quench) can confer the observed reproducibility of rod SPRs; there is no compelling need to invoke a long series of non-phosphorylation dependent state changes in R* (as in Rieke, F., and D.A. Baylor. 1998a. Biophys. J. 75:1836-1857; Field, G.D., and F. Rieke. 2002. Neuron. 35:733-747.). Our analyses, plus data and modeling of others (Rieke, F., and D.A. Baylor. 1998a. Biophys. J. 75:1836-1857; Field, G.D., and F. Rieke. 2002. Neuron. 35:733-747.), also argue strongly against either feedback (including Ca2+-feedback) or depletion of any molecular species downstream to R* as the dominant cause of SPR reproducibility.

Population density methods for large-scale modelling of neuronal networks with realistic synaptic kinetics: cutting the dimension down to size.

Population density methods provide promising time-saving alternatives to direct Monte Carlo simulations of neuronal network activity, in which one tracks the state of thousands of individual neurons and synapses. A population density method has been found to be roughly a hundred times faster than direct simulation for various test networks of integrate-and-fire model neurons with instantaneous excitatory and inhibitory post-synaptic conductances. In this method, neurons are grouped into large populations of similar neurons. For each population, one calculates the evolution of a probability density function (PDF) which describes the distribution of neurons over state space. The population firing rate is then given by the total flux of probability across the threshold voltage for firing an action potential. Extending the method beyond instantaneous synapses is necessary for obtaining accurate results, because synaptic kinetics play an important role in network dynamics. Embellishments incorporating more realistic synaptic kinetics for the underlying neuron model increase the dimension of the PDF, which was one-dimensional in the instantaneous synapse case. This increase in dimension causes a substantial increase in computation time to find the exact PDF, decreasing the computational speed advantage of the population density method over direct Monte Carlo simulation. We report here on a one-dimensional model of the PDF for neurons with arbitrary synaptic kinetics. The method is more accurate than the mean-field method in the steady state, where the mean-field approximation works best, and also under dynamic-stimulus conditions. The method is much faster than direct simulations. Limitations of the method are demonstrated, and possible improvements are discussed.

A population density approach that facilitates large-scale modeling of neural networks: extension to slow inhibitory synapses.

A previously developed method for efficiently simulating complex networks of integrate-and-fire neurons was specialized to the case in which the neurons have fast unitary postsynaptic conductances. However, inhibitory synaptic conductances are often slower than excitatory ones for cortical neurons, and this difference can have a profound effect on network dynamics that cannot be captured with neurons that have only fast synapses. We thus extend the model to include slow inhibitory synapses. In this model, neurons are grouped into large populations of similar neurons. For each population, we calculate the evolution of a probability density function (PDF), which describes the distribution of neurons over state-space. The population firing rate is given by the flux of probability across the threshold voltage for firing an action potential. In the case of fast synaptic conductances, the PDF was one-dimensional, as the state of a neuron was completely determined by its transmembrane voltage. An exact extension to slow inhibitory synapses increases the dimension of the PDF to two or three, as the state of a neuron now includes the state of its inhibitory synaptic conductance. However, by assuming that the expected value of a neuron's inhibitory conductance is independent of its voltage, we derive a reduction to a one-dimensional PDF and avoid increasing the computational complexity of the problem. We demonstrate that although this assumption is not strictly valid, the results of the reduced model are surprisingly accurate.

Modeling corticofugal feedback and the sensitivity of lateral geniculate neurons to orientation discontinuity.

We model feedback from primary visual cortex to the dorsal lateral geniculate nucleus (dLGN). This feedback makes dLGN neurons sensitive to orientation discontinuity (Sillito et al., 1993; Cudeiro & Sillito, 1996). In the model, each dLGN neuron receives retinotopic input driven by layer 6 cortical neurons in a full set of orientation columns. Excitation is monosynaptic, while inhibition is through perigeniculate neurons and dLGN interneurons. The stimulus consists of drifting gratings,k one within and the other outside a circular region centered over the receptive field of the model dLGN relay neuron we study. They appear as a single grating when they are aligned with equal contrast. The model reproduces experimental results showing an increasing inhibitory effect of feedback on the firing rate of dLGN neurons as the two gratings move towards the aligned position. Moreover, enhancement of dLGN cell center-surround antagonism by feedback is revealed by measuring the responses to drifting gratings inside a circular window, as a function of window radius. This effect is related to the observed length tuning of dLGN cells. Sensitivity to orientation discontinuity could be mediated in the model by feedback from either simple or complex cells. The model puts constraints on the feedback synaptic footprint and shows that its elongated shape does not play a crucial role in sensitivity to orientation discontinuity. The inhibitory component of feedback must predominate overall, but the feedback signal from a cortical neuron to a dLGN neuron with the same or nearby receptive-field center can be dominated by excitation. Predictions of the model include (1) robust stimuli for layer 6 cortical neurons give pronounced nonlinearities in the responses of dLGN neurons; (2) the sensitivity to orientation discontinuity at low contrast is twice that at high contrast.

A population density approach that facilitates large-scale modeling of neural networks: analysis and an application to orientation tuning.

We explore a computationally efficient method of simulating realistic networks of neurons introduced by Knight, Manin, and Sirovich (1996) in which integrate-and-fire neurons are grouped into large populations of similar neurons. For each population, we form a probability density that represents the distribution of neurons over all possible states. The populations are coupled via stochastic synapses in which the conductance of a neuron is modulated according to the firing rates of its presynaptic populations. The evolution equation for each of these probability densities is a partial differential-integral equation, which we solve numerically. Results obtained for several example networks are tested against conventional computations for groups of individual neurons. We apply this approach to modeling orientation tuning in the visual cortex. Our population density model is based on the recurrent feedback model of a hypercolumn in cat visual cortex of Somers et al. (1995). We simulate the response to oriented flashed bars. As in the Somers model, a weak orientation bias provided by feed-forward lateral geniculate input is transformed by intracortical circuitry into sharper orientation tuning that is independent of stimulus contrast. The population density approach appears to be a viable method for simulating large neural networks. Its computational efficiency overcomes some of the restrictions imposed by computation time in individual neuron simulations, allowing one to build more complex networks and to explore parameter space more easily. The method produces smooth rate functions with one pass of the stimulus and does not require signal averaging. At the same time, this model captures the dynamics of single-neuron activity that are missed in simple firing-rate models.

Recovery of cable properties through active and passive modeling of subthreshold membrane responses from laterodorsal tegmental neurons.

The laterodorsal tegmental nucleus (LDT) is located in the dorsolateral pontine reticular formation. Cholinergic neurons in the LDT and the adjacent pedunculopontine tegmental nucleus (PPT) are hypothesized to play a critical role in the generation of the electroencephalographic-desynchronized states of wakefulness and rapid eye movement sleep. A quantitative analysis of the cable properties of these cells was undertaken to provide a more detailed understanding of their integrative behavior. The data used in this analysis were the morphologies of intracellularly labeled guinea pig LDT neurons and the voltage responses of these cells to somatic current injection. Initial attempts to model the membrane behavior near resting potential and in the presence of tetrodotoxin (TTX, 1 microM) as purely passive produced fits that did not capture many features of the experimental data. Moreover, the recovered values of membrane conductance or intracellular resistivity were often very far from those reported for other neurons, suggesting that a passive description of cell behavior near rest was not adequate. An active membrane model that included a subthreshold A-type K+ current and/or a hyperpolarization-activated cation current (H-current) then was used to model cell behavior. The voltage traces calculated using this model were better able to reproduce the experimental data, and the cable parameters determined using this methodology were more consistent with those reported for other cells. Additionally, the use of the active model parameter extraction methodology eliminated a problem encountered with the passive model in which parameter sets with widely varying values, sometimes spanning an order of magnitude or more, would produce effectively indistinguishable fits to the data. The use of an active model to directly fit the experimentally measured voltage responses to both long and short current pulses is a novel approach that is of general utility.

Gain of rod to horizontal cell synaptic transfer: relation to glutamate release and a dihydropyridine-sensitive calcium current.

We related rod to horizontal cell synaptic transfer to glutamate release by rods. Simultaneous intracellular records were obtained from dark-adapted rod-horizontal cell pairs. Steady-state synaptic gain (defined as the ratio of horizontal cell voltage to rod voltage evoked by the same light stimulus) was 3.35 +/- 0.60 for dim flashes and 1.50 +/- 0.03 for bright flashes. Under conditions of maintained illumination, there was a measurable increment of horizontal cell hyperpolarization for each light-induced increment of rod hyperpolarization over the full range of rod voltages. In separate experiments we studied glutamate release from an intact, light-responsive photoreceptor layer, from which inner retinal layers were removed. Steady light reduced glutamate release as a monotonic function of intensity; spectral sensitivity measures indicated that we monitored glutamate release from rods. The dependence of glutamate release on rod voltage was well fit by the activation function for a high-voltage-activated, dihydropyridine-sensitive L-type calcium current, suggesting a linear dependence of glutamate release on [Ca]i in the synaptic terminal. A simple model incorporating this assumption accounts for the steady-state gain of the rod to horizontal cell synapse.

Background contrast modulates kinetics and lateral spread of responses to superimposed stimuli in outer retina.

Surround enhancement (sensitization) is a poorly understood form of network adaptation in which the kinetics of the responses of retinal neurons to test stimuli become faster, and absolute sensitivity of the responses increases with increasing level of steady, surrounding light. Surround enhancement has been observed in all classes of retinal neurons in lower vertebrates except cones, in some primate retinal ganglion cells, and in human psychophysical studies. In theory, surround enhancement could be mediated by two broad classes of mechanisms, which are not mutually exclusive: one in which the kinetics of the transduction linking cone voltage to postsynaptic current in second-order neurons is modulated, and another in which the transformation of postsynaptic current to membrane voltage is modulated. We report here that both classes of mechanism play a role in surround enhancement measured in turtle horizontal cells (HCs). We stimulated the retina by modulating sinusoidally the illuminance of a bar placed at various positions in the HC receptive field. The bar was surrounded by either equally luminant or dim, steady light. Interpretation of responses in the context of a model for the cone-HC network led to the conclusion that the speeding up of response kinetics--due to selective increase in response gain at high temporal frequencies--by surround illuminance is almost completely accounted for by the change in the kinetics of the transduction linking cone membrane potential to HC postsynaptic current. However, surround illuminance also had an additional, surprising effect on the transformation between postsynaptic current and voltage: the space constant for signal spread in the HC network for the dim-surround condition was roughly twice as large as that for the bright-surround condition. Thus, increasing surround illuminance had analogous effects in the spatial and temporal domains: it restricted the time course and the spatial spread of signal. Both effects were dependent on the contrast between the mean bar illuminance and that of the surround, rather than on overall light level. When the stimulus with the bright surround was dimmed uniformly by a neutral density filter, the space constant did not increase, and response gain at high temporal frequencies did not decrease. Pharmacological experiments performed with dopamine and various agonists and antagonists indicated that, although exogenous dopamine can influence surround enhancement, endogenous dopamine does not play an important role in surround enhancement. We conclude that contrast in background light modulates the spatiotemporal properties of signal processing in the outer retina, and does so by a non-dopaminergic mechanism.

Modulation of synaptic transfer between retinal cones and horizontal cells by spatial contrast.

We studied the influence of steady annular light on the kinetics and sensitivity of horizontal cell (HC) responses to modulation of the intensity of small concentric spots in the turtle retina. As shown by previous investigators, when the intensity of the annulus was equal to the mean spot intensity, spot response kinetics were the same as those for the modulation of spatially uniform light. Turning off the annulus attenuated dramatically high-frequency flicker sensitivity and enhanced somewhat low-frequency sensitivity. This phenomenon reflects a modulation of synaptic transfer between cones and second-order neurons that is mediated by cones, and it will be referred to as cone-mediated surround enhancement (CMSE). Our main results are as follows: (a) The change in test-spot response sensitivity and kinetics upon dimming a steady surrounding annulus is a consequence of the change in spatial contrast rather than change in overall light level. (b) Introduction of moderate contrast between the mean spot intensity and steady surrounding light intensity causes a marked change in spot response kinetics. (c) The dependence of spot response kinetics on surrounding light can be described by a phenomenological model in which the steady state gain and the time constant of one or two single-stage, low-pass filters increase with decreasing annular light intensity (d) The effect of surrounding light on spot responses of a given HC is not determined by change in the steady component of the membrane potential of that cell. (e) Light outside the receptive field of an HC can affect that cell's spot response kinetics. (f) In an expanding annulus experiment, the distance over which steady annular light affects spot response kinetics varies among HCs and can be quite different even between two cells with closely matched receptive field sizes. (g) The degree of CMSE is correlated with HC receptive field size. This correlation suggests that part of the enhancement mechanism is located in the HC. Taken together, our results suggest the involvement of the inner retina in CMSE.

Origin of the apparent tissue conductivity in the molecular and granular layers of the in vitro turtle cerebellum and the interpretation of current source-density analysis.

1. We determined the origin of the apparent tissue conductivity (sigma 2) of the turtle cerebellum in vitro. 2. Application of a current with a known current density (J) along the longitudinal axis of a conductivity cell produced an electric field in the cerebellum suspended in the cell. The measured electric field (E) perpendicular to the cerebellar surface indicated a significant inhomogeneity in sigma a (= J/E) with a major discontinuity between the molecular layer (0.25 +/- 0.05 S/m, mean +/- SD) and granular layers (0.15 +/- 0.03 S/m) (n = 39). 3. This inhomogeneity was more pronounced after anoxic depolarization. The value of sigma a decreased to 0.11 +/- 0.03 and 0.040 +/- 0.008 S/m in the molecular and granular layers, respectively. The ratio of sigma a S in the two layers increased from 1.67 in the normoxic condition to 2.75 after anoxic depolarization. 4. This difference in sigma a across the two layers was present within the range of frequencies (DC to 10 kHz) studied where the phase of sigma a was small (less than +/- 2 degrees) and therefore sigma a was ohmic. 5. The inhomogeneity in sigma a was in part due to an inhomogeneity in the extracellular conductivity (sigma e) as determined from the extracellular diffusion of ionophoresed tetramethylammonium. Like sigma a, the value of sigma e was also higher in the molecular layer (0.165 S/m) than in the granular layer (0.097 S/m). The inhomogeneity in sigma e was due to a smaller tortuosity and a larger extracellular volume fraction in the molecular layer compared with the granular layer. 6. sigma a was, however, consistently higher, by approximately 50%, than sigma e. A core conductor model of the cerebellum indicated that these discrepancies between sigma a and sigma e were attributable to additional conductivity produced by a passage of the longitudinal applied current through the intracellular space of Purkinje cells and ependymal glial cells, with the glial compartment playing the dominant role. Cells with a long process and a short space constant such as the ependymal glia evidently enhance the effective "extracellular" conductivity by serving as intracellular conduits for the applied current. The result implies that the effective sigma e may be larger than sigma e for neuronally generated currents in the turtle cerebellum because the space constant for Purkinje cells is several times greater than that for the ependymal glia and consequently Purkinje cell-generated currents travel over a long distance relative to the space constant of glial cells.(ABSTRACT TRUNCATED AT 400 WORDS)

Membrane currents of horizontal cells isolated from turtle retina.

1. Membrane currents of horizontal cells isolated from the retina of the turtle, Pseudemys, were characterized by the whole-cell patch-clamp technique. 2. Four membrane currents were identified: an anomalous rectifier blocked by barium, a transient A-current, a sustained L-type calcium current enhanced by Bay K 8644, and a fast, tetrodotoxin-sensitive sodium current. Each of these four currents was found in both horizontal cell somata and axon terminals. 3. The current-voltage relations of axon terminals and somata were similar, but, in the normal operating range of the cell (-30 to -50 mV), the mean slope resistance of the axon terminal was higher (1.38 G omega) than that of the soma (0.26 G omega). 4. Exposure to either glutamate, kainate, or quisqualate induced a sustained inward current in horizontal cell axon terminals. The reversal potential for this current was -3 mV when tested with voltage steps and +9.1 mV when measured by a voltage ramp. The same horizontal cells were insensitive to N-methyl-D-aspartate. 5. A continuum model was developed to compute the degree of signal transfer between a horizontal cell body and its axon terminal. The model consisted of a network of electrically coupled somata that communicates with a network of electrically coupled axon terminals through the connecting axons. The specific membrane resistances used for the model derived from the patch-clamp measures. 6. We computed the voltage change elicited in either the layer of somata or of axon terminals by a static light stimulus of arbitrary dimensions. The amplitude of a spot response as a function of its radius was given by the weighted sum of two Bessel functions with different space constants. 7. The computed responses of the cell body were dominated by the Bessel function with the smaller space constant, whereas those of the axon terminal depended primarily on the Bessel function with the larger space constant. 8. The model predicts that, in contrast to the findings in teleost retina, there is little signal transfer between the somata and axon terminals of horizontal cell in the turtle retina.

Light adaptation in turtle cones. Testing and analysis of a model for phototransduction.

Light adaptation in cones was characterized by measuring the changes in temporal frequency responses to sinusoidal modulation of light around various mean levels spanning a range of four log units. We have shown previously that some aspects of cone adaptation behavior can be accounted for by a biochemical kinetic model for phototransduction in which adaptation is mediated largely by a sigmoidal dependence of guanylate cyclase activity on the concentration of free cytoplasmic Ca2+, ([Ca2+]i) (Sneyd and Tranchina, 1989). Here we extend the model by incorporating electrogenic Na+/K+ exchange, and the model is put to further tests by simulating experiments in the literature. It accounts for (a) speeding up of the impulse response, transition from monophasic to biphasic waveform, and improvement in contrast sensitivity with increasing background light level, I0; (b) linearity of the response to moderate modulations around I0; (c) shift of the intensity-response function (linear vs. log coordinates) with change in I0 (Normann and Perlman, 1979); the dark-adapted curve adheres closely to the Naka-Rushton equation; (d) steepening of the sensitivity vs. I0 function with [Ca2+]i fixed at its dark level, [Ca2+]i dark; (Matthews et al., 1988, 1990); (e) steepening of the steady-state intensity-response function when [Ca2+]i is held fixed at its dark level (Matthews et al., 1988; 1990); (f) shifting of a steep template saturation curve for normalized photocurrent vs. light-step intensity when the response is measured at fixed times and [Ca2+]i is held fixed at [Ca2+]i dark (Nakatani and Yau, 1988). Furthermore, the predicted dependence of guanylate cyclase activity on [Ca2+] closely matches a cooperative inhibition equation suggested by the experimental results of Koch and Stryer (1988) on cyclase activity in bovine rods. Finally, the model predicts that some changes in response kinetics with background light will still be present, even when [Ca2+]i is held fixed at [Ca2]i dark.

Light adaptation in the primate retina: analysis of changes in gain and dynamics of monkey retinal ganglion cells.

The responses of monkey retinal ganglion cells to sinusoidal stimuli of various temporal frequencies were measured and analyzed at a number of mean light levels. Temporal modulation tuning functions (TMTFs) were measured at each mean level by varying the drift rate of a sine-wave grating of fixed spatial frequency and contrast. The changes seen in ganglion cell temporal responses with changes in adaptation state were similar to those observed in human subjects and in turtle horizontal cells and cones tested with sinusoidally flickering stimuli; "Weber's Law" behavior was seen at low temporal frequencies but not at higher temporal frequencies. Temporal responses were analyzed in two ways: (1) at each light level, the TMTFs were fit by a model consisting of a cascade of low- and high-pass filters; (2) the family of TMTFs collected over a range of light levels for a given cell was fit by a linear negative feedback model in which the gain of the feedback was proportional to the mean light level. Analysis (1) revealed that the temporal responses of one class of monkey ganglion cells (M cells) were more phasic at both photopic and mesopic light levels than the responses of P ganglion cells. In analysis (2), the linear negative feedback model accounted reasonably well for changes in gain and dynamics seen in three P cells and one M cell. From the feedback model, it was possible to estimate the light level at which the dark-adapted gain of the cone pathways in the primate retina fell by a factor of two. This value was two to three orders of magnitude lower than the value estimated from recordings of isolated monkey cones. Thus, while a model which includes a single stage of negative feedback can account for the changes in gain and dynamics associated with light adaptation in the photopic and mesopic ranges of vision, the underlying physical mechanisms are unknown and may involve elements in the primate retina other than the cone.

Photoreceptor to horizontal cell synaptic transfer in the Xenopus retina: modulation by dopamine ligands and a circuit model for interactions of rod and cone inputs.

1. In the Xenopus retina, the effects of selective D1 and D2 dopamine ligands on photoreceptor to horizontal cell transfer were studied by intracellular recording from horizontal cell axons. Rod and cone inputs to the horizontal cell were estimated by adjusting the intensities of red and green flashes to elicit equal rod tails. The resultant waveforms were digitized and subtracted, and their difference was taken to reflect solely cone input to the horizontal cell. 2. It was found that both D1 (SKF 38393) and D2 (LY 171555) agonists increased the amplitude and quickened the kinetics of cone-to-horizontal cell transfer; they also depolarized the horizontal cell by 8-10 mV. In contrast, either D1 or D2 agonists reduced the rod input to the horizontal cell without altering its kinetics. 3. Type D2 antagonists reduced and slowed the cone input and hyperpolarized the horizontal cell. D2 antagonists increased the rod input but left its kinetics unchanged. 4. Although both D1 and D2 agonists elicited qualitatively similar effects, the D1 agonist evoked a greater increase in the amplitude and a greater acceleration of the kinetics of the cone input than did the D2 agonist. Moreover, the action of the D1 agonist was blocked by SCH 23390 but not by spiroperidol or metoclopramide, whereas the reverse was true for the D2 agonist. These data indicate that D1 and D2 agonists probably act at different sites. 5. The pharmacologic findings are interpreted to indicate that dopamine ligands act primarily through the cone pathway and that rod-to-horizontal cell transfer is shunted to a variable degree. 6. An equivalent circuit model was developed for a spine-bearing portion of a horizontal cell axon of the Xenopus retina. Anatomic study shows that such spines branch, making contact with both rod and cone photoreceptor bases. Thus there are two conductance pathways in parallel for rod-to-horizontal cell and cone-to-horizontal cell transmission. The model is used to test the hypothesis that mutual shunting in the two pathways can account for the physiological effects observed. 7. The values of the purely resistive elements of the pathway are based on their dimensions. Membrane resistance was taken to be 5,000 omega/cm2 and axial resistance 200 omega/cm. The photoreceptor-to-horizontal cell synaptic battery was taken to be composed of glutamate-sensitive channels, with unitary channel conductance of 6 pS. Channel density was estimated from freeze-fracture data at 5,000 microns-2. A potassium battery and a glycine-sensitive synaptic input from an interplexiform cell were modeled to exist in parallel with the light-sensitive battery. 8. Dopamine was assumed to increase the conductance of the cone-to-horizontal cell synapse, but not to affect the conductance of the rod-to-to-horizontal cell synapse, consistent with physiological measures.(ABSTRACT TRUNCATED AT 400 WORDS)

Phototransduction in cones: an inverse problem in enzyme kinetics.

Phototransduction is a process which links the absorption of photons by a rod or cone to the modulation of voltage across the cell membrane. An important feature of many vertebrate photoreceptors is a mechanism that adjusts the sensitivity and dynamics of the response to light according to the level of illumination. We construct a system of ordinary differential equations that models what are currently thought to be the important molecule mechanisms involved in phototransduction: this includes consideration of both intracellular enzyme kinetics and the properties of light-insensitive and light-sensitive conductances in the cone membrane. The system contains negative feedback whose functional form is determined by constraining the steady-state behaviour of the system. Despite the highly nonlinear nature of the system of ordinary differential equations, our methods permit us to derive an analytic expression for the first-order frequency response parametric in the steady-state value of only one dynamic variable, the light input. Various unknown kinetic parameters are found by fitting the model to experimental data on the first-order frequency response of cones measured at several mean light levels spanning a range of four log units. Good fits are obtained to the data, and the computed shape of the feedback function agrees qualitatively with recent experiment. Moreover, the model accounts for the dramatic speeding up of the response kinetics and the decrease in response gain with increasing light level.

Light adaptation in the turtle retina: embedding a parametric family of linear models in a single nonlinear model.

A method for constructing nonlinear models for light adaptation in the retina is introduced. The components of the models are linear filters and static (instantaneous) nonlinear elements configured in a feedback arrangement. The signals in the models are combined through algebraic addition or multiplication. We apply the method to model light adaptation measured in turtle horizontal cells. Given a particular wiring diagram for the components, the functional forms of the static nonlinearities and frequency responses of the linear filters are determined by constraining the model to give temporal frequency responses (linear regime behavior) consistent with a family of linear feedback models which has been shown to provide a good description of adaptation in these cells. Two particular models, quite different in structure, are presented. Each model responds to perturbations around a mean light level as a feedback circuit in which the gain (strength) of feedback is adjusted to be proportional to the mean light level, but neither model has a separate pathway for measuring the mean light level. Thus, each of these nonlinear models embeds an entire family of linear models parametric in mean light level. Harmonic distortion in the responses of these models to sinusoidal input is found to be qualitatively consistent with physiological data. An alternative class of nonlinear models in which feedback gain is set by a separate slow pathway which tracks the mean light level is ruled out on the basis of its incorrect steady-state input-output behavior. The methods presented can be used to develop specific physical models for light adaptation based on the chemical kinetics of phototransduction or on nonlinear neural feedback. The relevance of the nonlinear models and construction techniques to modeling phototransduction is discussed.