Neural circuitry underlying linear representation of wind information in a nonspiking local interneuron of the cockroach

In the cercal system of the cockroach Periplaneta americana, primary sensory interneurons exhibiting a sharp directional sensitivity respond to wind in a linear manner whereas those exhibiting an omnidirectional sensitivity respond nonlinearly. For example, the wind-evoked response in an identifiable, nonspiking local interneuron, 101, which responds preferentially to wind from the left versus the right, is characterized exclusively by a differential first-order (linear) kernel. However, the slow potential response in a cercal giant interneuron, GI-1, is omnidirectional, and characterized by a second-order (nonlinear) kernel with an elongated depolarizing peak on the diagonal with two off-diagonal valleys. We here examined the neural circuitry underlying the linear and nonlinear representations of wind information by the deprivation of inputs from particular sets of cercal hair afferents. Electrical stimulation of the ipsilateral (related to the soma) cercal nerve elicited a depolarizing potential in 101, which was followed by delayed hyperpolarization. A continuous flow of 10^–4 M picrotoxin, which selectively blocked this delayed hyperpolarization, resulted in a significant change in the 101 response from linear to nonlinear. Because no frequency-doubling response was observed, the nonlinearity is due to signal compression (or rectification) that reflects the mechanical property of cercal afferents. This is consistent with the hypothesis that the linear representation in 101 is based on a subtraction process between two subsets of particular column hairs, whose best optimal directions are opposite to each other.Abbreviations GABA -aminobutyric acid - GI(s) giant interneuron(s) - GI-1, GI-2, GI-3, GI-4 giant interneuron 1,2,3,4 - ipsi ipsilateral - cont contralateral - MSE(s) mean square error(s)     

White noise analysis of a chromatic type horizontal cell in the Xenopus retina

The dynamics of color-coded signal transmission in the light-adapted Xenopus retina were studied by a combination of white noise (Wiener) analysis and simultaneous recordings from two types of horizontal cells: chromatic-type horizontal cells (C-HCs) are hyperpolarized by blue light and depolarized by red light, whereas luminosity-type horizontal cells (L-HCs) are hyperpolarized by all wave-lengths. The retina was stimulated by two superimposed fields of red and blue light modulated by two independent white noise signals, and the resulting intracellular responses were decomposed into red and blue components (first-order kernels). The first-order kernels predict the intracellular responses with a small degree of error (3.5-9.5% in terms of mean square error) under conditions where modulated responses exceeded 30 mV in amplitude peak-to-peak, thus demonstrating that both red and blue modulation responses are linear. Moreover, there is little or no interaction between the red- and blue-evoked responses; i.e., nearly identical first-order kernels were obtained for one color whether the other color was modulated or not. In C-HCs (but not L-HCs), there were consistent differences in the dynamics of the red and blue responses. In the C-HC, the cutoff frequency of the red response was higher than for the blue (approximately 12 vs 5 Hz), and the red kernel was more bandpass than the blue. In the L-HC, kernel waveform and cutoff frequencies were similar for both colors (approximately 12 Hz or greater), and the time-to-peak of the L-HC kernel was always shorter than either the red or blue C-HC kernel. These results have implications for the mechanisms underlying color coding in the distal retina, and they further suggest that nonlinear phenomena, such as voltage-dependent conductances in HCs, do not contribute to the generation of modulation responses under the experimental conditions used here.     

White-noise analysis of nonlinear behavior in an insect sensory neuron: Kernel and cascade approaches

A functional expansion was used to model the relationship between a Gaussian white noise stimulus current and the resulting action potential output in the single sensory neuron of the cockroach femoral tactile spine. A new precise procedure was used to measure the kernels of the functional expansion. Very similar kernel estimates were obtained from separate sections of the data produced by the same neuron with the same input noise power level, although some small time-varying effects were detectable in moving through the data. Similar kernel estimates were measured using different input noise power levels for a given cell, or when comparing different cells under similar stimulus conditions. The kernels were used to identify a model for sensory encoding in the neuron, comprising a cascade of dynamic linear, static nonlinear, and dynamic linear elements. Only a single slice of the estimated experimental second-order kernel was used in identifying the cascade model. However, the complete second-order kernel of the cascade model closely resembled the estimated experimental kernel. Moreover, the model could closely predict the experimental action potential train obtained with novel white noise inputs.     

Nonlinear analysis of the human visual evoked response

Using time-domain correlation techniques, the first- and second-order Wiener kernels have been calculated for the system mediating the human visual evoked response. The first-order kernels indicate the linear element is a resonant one, with a natural frequency near 20 Hz, and a memory of approximately 250 ms. The transport delay associated with this element is approximately 56 ms. The second-order kernels indicate a quadratic nonlinear element with a memory less than 20 ms. The analytic form of this element can be approximated by a parabola shifted to the right of the origin. A close correspondance between the spectrum of the first-order kernel and the spectrum of the main diagonal of the second-order kernel suggests the nonlinear element preceeds the linear one. Tests of reproducibility on the first-order kernel and the main diagonal of the second-order kernel suggest they are reliable describing functions for the system mediating the human visual evoked response.     

Dynamics of cockroach ocellar neurons

The incremental responses from the second-order neurons of the ocellus of the cockroach, Periplaneta americana, have been measured. The stimulus was a white-noise-modulated light with various mean illuminances. The kernels, obtained by cross-correlating the white-noise input against the resulting response, provided a measure of incremental sensitivity as well as of response dynamics. We found that the incremental sensitivity of the second-order neurons was an exact Weber-Fechner function; white-noise-evoked responses from second-order neurons were linear; the dynamics of second-order neurons remain unchanged over a mean illuminance range of 4 log units; the small nonlinearity in the response of the second-order neuron was a simple amplitude compression; and the correlation between the white-noise input and spike discharges of the second-order neurons produced a first-order kernel similar to that of the cell's slow potential. We conclude that signal processing in the cockroach ocellus is simple but different from that in other visual systems, including vertebrate retinas and insect compound eyes, in which the system's dynamics depend on the mean illuminance.     

Spike discharges of skeletomotor neurons during random noise modulated transmembrane current stimulation and muscle stretch

 Spike discharges of skeletomotor neurons innervating triceps surae muscles elicited by white noise modulated transmembrane current stimulation and muscle stretch were studied in decerebrated cats. The white noise modulated current intensity ranged from 4.3 to 63.2 nA peak-to-peak, while muscle stretches ranged from 100 μm to 4.26 mm peak-to-peak. The neuronal responses were studied by averaging the muscle length records centered at the skeletomotor action potentials (peri-spike average, PSA) and by Wiener analysis. Skeletomotor spikes appeared after a sharp peak in PSA of the injected current, preceded by a longer-lasting smaller wavelet of either depolarizing or hyperpolarizing direction. The PSA amplitude was not related to the injected current amplitude nor showed any differences related to the motor unit type. The PSA amplitudes were virtually independent of the stretching amplitude σ, after an initial increase with stretching amplitudes in the range of 15–40 μm (S.D.), or 100–270 μm peak-to-peak.Analyses of cross-spectra indicated a small or absent increase in gain with frequency in response to injected current, but about 20 dB/decade in the range 10–100 Hz in response to muscle stretch. The peaks of both Wiener kernels in response to current injection appear to decrease with the amplitude of injected current, but this decrease was not statistically significant. The narrow first-order kernels suggest that the transfer function between the current input and spike discharge is lowpass with a wide passband, i.e. there is very little change in dynamics. The values of the second-order kernels appear to be nonzero only along the main diagonal. This is characteristic of a simple Hammerstein type cascade, i.e. a zero memory nonlinearity followed by a linear system. Small values of second-order kernels away from the origin and narrow first-order kernels suggest that the linear cascade contributes very little to the overall dynamic response.In contrast to Wiener kernels found in response to current injection, the Wiener kernels in response to stretch showed a decreasing trend with stretch amplitude. The size of the second-order kernels decreased to a somewhat larger extent with input amplitude than that of the first-order kernels, indicating an amplitude-dependent nonlinearity. Overall, the transformation between length and spike output was described as an LNNL cascade with second-order nonlinearities. Received: 1 April 1993/Accepted in revised form: 24 March 1994     

Dynamics of the ganglion cell response in the catfish and frog retinas

Responses were evoked from ganglion cells in catfish and frog retinas by a Gaussian modulation of the mean luminance. An algorithm was devised to decompose intracellularly recorded responses into the slow and spike components and to extract the time of occurrence of a spike discharge. The dynamics of both signals were analyzed in terms of a series of first-through third-order kernels obtained by cross-correlating the slow (analog) or spike (discrete or point process) signals against the white-noise input. We found that, in the catfish, (a) the slow signals were composed mostly of postsynaptic potentials, (b) their linear components reflected the dynamics found in bipolar cells or in the linear response component of type-N (sustained) amacrine cells, and (c) their nonlinear components were similar to those found in either type-N or type-C (transient) amacrine cells. A comparison of the dynamics of slow and spike signals showed that the characteristic linear and nonlinear dynamics of slow signals were encoded into a spike train, which could be recovered through the cross-correlation between the white-noise input and the spike (point process signals. In addition, well-defined spike correlates could predict the observed slow potentials. In the spike discharges from frog ganglion cells, the linear (or first-order) kernels were all inhibitory, whereas the second-order kernels had characteristics of on-off transient excitation. The transient and sustained amacrine cells similar to those found in catfish retina were the sources of the nonlinear excitation. We conclude that bipolar cells and possibly the linear part of the type-N cell response are the source of linear, either excitatory or inhibitory, components of the ganglion cell responses, whereas amacrine cells are the source of the cells' static nonlinearity.     

White noise analysis of Phycomyces light growth response system. I. Normal intensity range.

The Wiener-Lee-Schetzen method for the identification of a nonlinear system through white gaussian noise stimulation was applied to the transient light growth response of the sporangiophore of Phycomyces. In order to cover a moderate dynamic range of light intensity I, the imput variable was defined to be log I. The experiments were performed in the normal range of light intensity, centered about I0 = 10(-6) W/cm2. The kernels of the Wierner functionals were computed up to second order. Within the range of a few decades the system is reasonably linear with log I. The main nonlinear feature of the second-order kernel corresponds to the property of rectification. Power spectral analysis reveals that the slow dynamics of the system are of at least fifth order. The system can be represented approximately by a linear transfer function, including a first-order high-pass (adaptation) filter with a 4 min time constant and an underdamped fourth-order low-pass filter. Accordingly a linear electronic circuit was constructed to simulate the small scale response characteristics. In terms of the adaptation model of Delbrück and Reichardt (1956, in Cellular Mechanisms in Differentiation and Growth, Princeton University Press), kernels were deduced for the dynamic dependence of the growth velocity (output) on the "subjective intensity", a presumed internal variable. Finally the linear electronic simulator above was generalized to accommodate the large scale nonlinearity of the adaptation model and to serve as a tool for deeper test of the model.     

Filter characteristics of cercal afferents in the cockroach

Summary The response dynamics of cercal afferents in the cockroach, Periplaneta americana, were determined by means of a cross-correlation technique using a Gaussian white noise modulation of wind as a stimulus. The white noise stimulus could evoke sustained firing activity in most of the afferents examined (Fig. 1). The spike discharges were unitized and then cross-correlated with the stimulus to compute 1st- and 2nd-order Weiner kernels. The Ist-order kernels from a total of 28 afferents were biphasic and closely matched the time differential of a pulse (Figs. 1, 3 and 4). The amplitude and waveform of the kernels depended on the stimulus angle in such a way that the kernels were the mirror image of those on the polar opposite side (Figs. 2 and 3). The 2nd-order kernels were also differential. They had 2 diagonal peaks and 2 off-diagonal valleys in a 2-dimensional plot with 2 time axes (Figs. 1, 5 and 6). This 4-eye configuration was basically invariant irrespective of the stimulus angle, although the kernels varied in amplitude when the stimulus angle was changed. The time between the peak and a following trough of the 1st-order kernel was constant and had a mean of 4.6±0.1 ms, whereas the time between 2 diagonal peaks of the 2nd-order kernels was 4.7±0.1 ms (Figs. 4 and 6), suggesting that wind receptors (filiform sensilla) on cerci act as a band-pass filter with a peak frequency of about 106 Hz. The peak time, however, varies from 2.3 to 6.9 ms in both kernels, which may reflect the spatial distribution of the corresponding hairs on the cercus. The summation of the 1st- (linear) and 2nd-order (nonlinear) models precisely predicted the timing of the spike firing (Fig. 8). Thus, these 2 lower-order kernels can totally characterize the response dynamics of the wind receptors. The nonlinear response explains the directional sensitivity of the sensory neurons, while the differentiating 1st-order kernel explains the velocity sensitivity of the neurons. The nonlinearity is a signal compression in which one of the diagonal peaks of the 2nd-order kernel always offsets the downward phase of the 1st-order kernel (Fig. 7) and obviously represents a half-wave rectification property of the wind receptors that are excited by hair movement in only one direction and inhibited by hair movement in the polar opposite direction.     

Stimulus coding in crayfish antennal mechanoreceptors estimated by noise analysis

Two different kinds of mechanoreceptive hairs (smooth and feathered) on the second antennae of the freshwater crayfish, Orconectes virilis, have been investigated for their stimulus coding propertics. These mechanoreceptors show a great deal of non-linear behaviour both in threshold and in directionality. An effective appraoch for the investigation of such systems is noise analysis in the frequency domain. This method has been used here to calculate zero-, first- and second-order kernels. Sensory cells reveal different first- and second-order kernels, depending on which type of hair is being stimulated. The first-order kernel has a pronounced peak in the frequency response at 110 Hz if a feathered hair is stimulated and at 60 Hz if a smooth hair is stimulated. The second-order kernel shows a number of pronounced peaks in the frequency response between 40 and 110 Hz, but only if a feathered hair is stimulated. Smooth hair stimulation results in less sharp peaks but in higher gain for the same range of stimulus frequencies.     

Cartesian representation of stimulus direction: Parallel processing by two sets of giant interneurons in the cockroach

The cockroachPeriplaneta americana responds to wind puffs by turning away, both on the ground and when flying. While on the ground, the ventral giant interneurons (ventrals) encode the wind direction and specify turn direction, whereas while flying the dorsal giant interneurons (dorsals) appear to do so. We report here on responses of these cells to controlled wind stimuli of different directions. Using improved methods of wind stimulation and of positioning the animal revealed important principles of organization not previously observed.All six cells of largest axonal diameter on each side respond preferentially to ipsilateral winds. One of these cells, previously thought to respond non-directionally (giant interneuron 2), was found to have a restricted directional response (Fig. 3). The organization of directional coding among the ventral giant interneurons is nearly identical to that among the dorsals (Fig. 2). Each group contains, on each side, one cell that responds primarily to wind from the ipsilateral front, another primarily in the ipsilateral rear, and a third responding more broadly to ipsilateral front and rear.These results are discussed in terms of the mechanisms of directional localization by the assembly of giant interneurons.Abbreviations GI giant interneuron - vGI ventral giant interneuron - dGI dorsal giant interneuron - CF 5-carboxyfluorescein - A6 6th abdominal ganglion - TI thoracic interneuron - BED best excitatory direction     

Modelling of the control of heart rate by breathing using a kernel method

The process of the breathing (input) to the heart rate (output) of man is considered for system identification by the input-output relationship, using a mathematical model expressed as integral equations. The integral equation is considered and fixed so that the identification method reduces to the determination of the values within the integral, called kernels, resulting in an integral equation whose input-output behaviour is nearly identical to that of the system. This paper uses an algorithm of kernel identification of the Volterra series which greatly reduces the computational burden and eliminates the restriction of using white Gaussian input as a test signal. A second-order model is the most appropriate for a good estimate of the system dynamics. The model contains the linear part (first-order kernel) and quadratic part (second-order kernel) in parallel, and so allows for the possibility of separation between the linear and non-linear elements of the process. The response of the linear term exhibits the oscillatory input and underdamped nature of the system. The application of breathing as input to the system produces an oscillatory term which may be attributed to the nature of sinus node of the heart being sensitive to the modulating signal the breathing wave. The negative-on diagonal seems to cause the dynamic asymmetry of the total response of the system which opposes the oscillatory nature of the first kernel related to the restraining force present in the respiratory heart rate system. The presence of the positive-off diagonal of the second-order kernel of respiratory control of heart rate is an indication of an escape-like phenomenon in the system.     

Contrast gain control in the lower vertebrate retinas [published erratum appears in J Gen Physiol 1995 Aug;106(2):following 388]

Control of contrast sensitivity was studied in two kinds of retina, that of the channel catfish and that of the kissing gourami. The former preparation is dominantly monochromatic and the latter is bichromatic. Various stimuli were used, namely a large field of light, a spot- annulus configuration and two overlapping stimuli of red and green. Recordings were made from horizontal, amacrine, and ganglion cells and the results were analyzed by means of Wiener's theory, in which the kernels are the contrast (incremental) sensitivity. Modulation responses from horizontal cells are linear, in that the waveform and amplitude of the first-order kernels are independent of the depth of modulation. In the N (sustained) amacrine and ganglion cells, contrast sensitivity was low for a large modulation input and was high for a small modulation input, providing an example of contrast gain control. In most of the cells, the contrast gain control did not affect the dynamics of the response because the waveform of the first-order kernels remained unchanged when the contrast sensitivity increased more than fivefold. The signature of the second-order kernels also remained unchanged over a wide range of modulation. The increase in the contrast sensitivity for the second-order component, as defined by the amplitude of the kernels, was much larger than for the first-order component. This observation suggests that the contrast gain control proceeded the generation of the second-order nonlinearity. An analysis of a cascade of the Wiener type shows that the control of contrast sensitivity in the proximal retinal cells could be modeled by assuming the presence of a simple (static) saturation nonlinearity. Such a nonlinearity must exist somewhere between the horizontal cells and the amacrine cells. The functional implications of the contrast gain control are as follows: (a) neurons in the proximal retina exhibit greater sensitivity to input of lower contrast; (b) saturation of a neuronal response can be prevented because of the lower sensitivity for an input with large contrast, and (c) over a large range of modulation depths, the amplitude of the response remains approximately constant.     

Dynamics of turtle cones

The response dynamics of turtle photoreceptors (cones) were studied by the cross-correlation method using a white-noise-modulated light stimulus. Incremental responses were characterized by the kernels. White-noise-evoked responses with a peak-to-peak excursion of greater than 5 mV were linear, with mean square errors of approximately 8%, a degree of linearity comparable to the horizontal cell responses. Both a spot (0.17 mm diam) and a large field of light produced almost identical kernels. The amplitudes of receptor kernels obtained at various mean irradiances fitted approximately the Weber-Fechner relationship and the mean levels controlled both the amplitude and the response dynamics; kernels were slow and monophasic at low mean irradiance and were fast and biphasic at high mean irradiance. This is a parametric change and is a piecewise linearization. Horizontal cell kernels evoked by the small spot of light were monophasic and slower than the receptor kernels produced by the same stimulus. Larger spots of light or a steady annular illumination transformed the slow horizontal cell kernel into a fast kernel similar to those of the receptors. The slowing down of the kernel waveform was modeled by a simple low-pass circuit and the presumed feedback from horizontal cells onto cones did not appear to play a major role.     

System analysis of Phycomyces light-growth response with sum-of-sinusoids test stimuli.

The light-growth response of Phycomyces has been studied with the sum-of-sinusoids method of nonlinear system identification (Victor, J.D., and R.M. Shapley, 1980, Biophys. J., 29:459). This transient response of the sporangiophore has been treated as a black-box system with one input (logarithm of the light intensity, I) and one output (elongation rate). The light intensity was modulated so that log I, as a function of time, was a sum of sinusoids. The log-mean intensity was 10(-4) W m-2 and the wavelength was 477 nm. The first- and second-order frequency kernels, which represent the linear and nonlinear behavior of the system, were obtained from the Fourier transform of the response at the appropriate component and combination frequencies. Although the first-order kernel accounts for most of the response, there remains a significant nonlinearity beyond the logarithmic transducer presumed to occur at the input of the sensory transduction chain. From the analysis of the frequency kernels, we have derived a dynamic nonlinear model of the light-growth response system. The model consists of a nonlinear subsystem followed by a linear subsystem. The model parameters were estimated from a combined nonlinear least-squares fit to the first- and second-order frequency kernels.     

The dynamic nonlinear behavior of fly photoreceptors evoked by a wide range of light intensities.

Fly photoreceptor cells were stimulated with steps of light over a wide intensity range. First- and second-order Volterra kernels were then computed from sequences of combined step responses. Diagonal values of the second-order Volterra kernels were much greater than the off-diagonal values, and the diagonal values were roughly proportional to the corresponding first-order kernels, suggesting that the response could be approximated by a static nonlinearity followed by a dynamic linear component (Hammerstein model). The amplitudes of the second-order kernels were much smaller in light-adapted than in dark-adapted photoreceptors. Hammerstein models constructed from the step input/output measurements gave reasonable approximations to the actual photoreceptor responses, with light-adapted responses being relatively better fitted. However, Hammerstein models could not account for several features of the photoreceptor behavior, including the dependence of the step response shape on step amplitude. A model containing an additional static nonlinearity after the dynamic linear component gave significantly better fits to the data. These results indicate that blowfly photoreceptors have a strong early gain control nonlinearity acting before the processes that create the characteristic time course of the response, in addition to the nonlinearities caused by membrane conductances.     

Response dynamics and receptive-field organization of catfish ganglion cells [published erratum appears in J Gen Physiol 1995 Aug;106(2):following 388]

Responses from catfish retinal ganglion cells were evoked by a spot or an annulus of light and were analyzed by a procedure identical to the one used previously to study catfish amacrine cells (Sakai H. M., and K.-I. Naka, 1992. Journal of Neurophysiology. 67:430-442.). In two- input white-noise experiments, a response evoked by simultaneous stimulation of the center and surround was decomposed into the components generated by the center and surround through a process of cross-correlation. The center and surround responses were also decomposed into their linear and nonlinear components so that the response dynamics of the linear and nonlinear components could be measured. We found that the concentric organization of the receptive field was determined by linear components, i.e., the first-order kernels generated by the center and surround were of opposite polarity. Both the center and surround generated second-order kernels with similar signatures, i.e., the second-order components formed a monotonic receptive field. The peak response time of the first- and second-order kernels from the surround was longer by approximately 20 ms than that of the center. Except for the DC potential present in the intracellular responses, almost identical first- and second-order kernels for the center and surround were obtained from both the intracellular response and spike discharges. Thus, information on concentric organization of a receptive field is translated into spike discharges with little loss of information. A train of spike discharges carries, simultaneously, at least four kinds of information: two linear and two nonlinear components, which originate in the receptive field center and the surround. A spike train is not a simple signaling device but is a carrier of complex and multiple signals. Victor, J. D., and R. M. Shapley (1979. Journal of General Physiology. 74:671-687.) discovered similarly that, in the cat retina, static second-order nonlinearity is encoded into spike trains. Results obtained in this study support the thesis that signals generated by the preganglionic cells are translated into spike discharges without major modification and that those signals can be recovered from the spike trains (Sakuranaga, M., Y. Ando, and K.-I. Naka. 1987. Journal of General Physiology. 90:229-259.; Korenberg, M. J., H. M. Sakai, and K.-I. Naka. 1989. Journal of Neurophysiology. 61:1110-1120.). Current injection studies have shown that such signal transmission is possible (Sakai, H. M., and K.-I. Naka, 1988a. Journal of Neurophysiology. 60:1549-1567.; 1990. Journal of Neurophysiology. 63:105-119.).     

White noise analysis of Phycomyces light growth response system. II. Extended intensity ranges.

By means of white gaussian noise stimulation, the Wiener kernels are derived for the Phycomyces light growth response for a variety of intensity conditions. In one experiment the intensity I, rather than log I, is used as the input variable. Under the very limited dynamic range of that experiment, the response is fairly linear. To examine the dependence of the kernels on dynamic range, a series of experiments were performed in which the range of log I was halved and doubled relative to normal. The amplitude of the kernels, but not the time course, is affected strongly by the choice of dynamic range, and the dependence reveals large-scale nonlinearities not evident in the kernels themselves. In addition kernels are evaluated for experiments at a number of absolute intensity levels ranging from 10(-12) to 10(-3) W/cm2. The kernel amplitudes are maximal at about 10(-6) W/cm2. At 10(-12) W/cm2, just above the absolute threshold, the respond is very small. The falloff at high intensity, attributable to inactivation of the photoreceptor, is analyzed in the framework of a first-order pigment kinetics model, yielding estimates for the partial extinction coefficient for inactivation epsilonI455 = (1.5 +/- 0.2) X 10(4) liter/mol-cm and a regeneration time constant of tau = (2.7 +/- 0.6) min. A model is introduced which associates the processes of adaptation and photoreceptor inactivation. The model predicts that the time constants for adaptation and pigment should be identical. This prediction is consistent with values in this and the preceding paper. The effects of pigment inactivation are simulated by a linear electronic analog circuit element, which may be cascaded with the linear simulator circuit in the preceding paper.     

The Intrinsic Electrophysiological Characteristics of Fly Lobula Plate Tangential Cells: III. Visual Response Properties

In this last paper in a series (Borst and Haag, 1996; Haag et al., 1997) about the lobula plate tangential cells of the fly visual system (CH, HS, and VS cells), the visual response properties were examined using intracellular recordings and computer simulations. In response to visual motion stimuli, all cells responded mainly by a graded shift of their axonal membrane potential. While ipsilateral motion resulted in a graded membrane potential shift, contralateral motion led to distinct EPSPs. For HS cells, simultaneous extracellular recorded action potentials of a spiking interneuron, presumably the H2 cell, corresponded to the EPSPs in the HS cell in a one-to-one fashion. When HS cells were hyperpolarized during ipsilateral motion, they mainly produced action potentials, but when they were hyperpolarized during contralateral motion only a slight increase of EPSP amplitude, could be observed. Intracellular application of the sodium channel blocker QX 314 abolished action potentials of HS cells while having little effect on the graded membrane response to ipsilateral motion. HS and CH cells were also studied with respect to their spatial integration properties. For both cell types, their graded membrane response was found to increase less than linearly with the size of the ipsilateral motion pattern. However, while for HS cells various amounts of hyperpolarizing current injected during motion stimulation led to different saturation levels, this was not the case for CH cells. In response to a sinusoidal velocity modulation, CH cells followed pattern motion only up to 10 Hz modulation frequency, but HS cells still revealed significant membrane depolarizations up to about 40 Hz.In the computer simulations, the compartmental models of tangential cells, as derived in the previous papers, were linked to an array of local motion detectors. The model cells revealed the same basic response features as their natural counterparts. They showed a response saturation as a function of stimulus size. In CH-models, however, the saturation was less pronounced than in real CH-cells, indicating spatially nonuniform membrane resistances with higher values in the dendrite. As in the experiments, HS models responded to high-frequency velocity modulation with a higher amplitude than did CH models.