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.     

The mapping of visual space by identified large second-order neurons in the dragonfly median ocellus

In adult dragonflies, the compound eyes are augmented by three simple eyes known as the dorsal ocelli. The outputs of ocellar photoreceptors converge on relatively few second-order neurons with large axonal diameters (L-neurons). We determine L-neuron morphology by iontophoretic dye injection combined with three-dimensional reconstructions. Using intracellular recording and white noise analysis, we also determine the physiological receptive fields of the L-neurons, in order to identify the extent to which they preserve spatial information. We find a total of 11 median ocellar L-neurons, consisting of five symmetrical pairs and one unpaired neuron. L-neurons are distinguishable by the extent and location of their terminations within the ocellar plexus and brain. In the horizontal dimension, L-neurons project to different regions of the ocellar plexus, in close correlation with their receptive fields. In the vertical dimension, dendritic arborizations overlap widely, paralleled by receptive fields that are narrow and do not differ between different neurons. These results provide the first evidence for the preservation of spatial information by the second-order neurons of any dorsal ocellus. The system essentially forms a one-dimensional image of the equator over a wide azimuthal area, possibly forming an internal representation of the horizon. Potential behavioural roles for the system are discussed.     

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.     

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.     

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.     

System analysis of Phycomyces light-growth response. Wavelength and temperature dependence.

The light-growth response of the Phycomyces sporangiophore was studied further with the sum-of-sinusoids method of nonlinear system identification. The first- and second-order frequency kernels, which represent the input-output relation of the system, were determined at 12 wavelengths (383-529 nm) and 4 temperatures (17 degrees, 20 degrees, 23 degrees, and 26 degrees C). The parametric model of the light-growth response system, introduced in the preceding paper, consists of nonlinear and linear dynamic subsystems in cascade. The model parameters were analyzed as functions of wavelength and temperature. At longer wavelengths, the system becomes more nonlinear. The latency and the bandwidth (cutoff frequency) of the system also vary significantly with wavelength. In addition, the latency decreases progressively with temperature (Q10 = 1.6). At low temperature (17 degrees C), the bandwidth is reduced. The results indicate that about half of the latency is due to physical processes such as diffusion, and the other half to enzymatic reactions. The dynamics of the nonlinear subsystem also vary with wavelength. The dependence of various model components on wavelength supports the hypothesis that the light-growth response, as well as phototropism, are mediated by multiple interacting photoreceptors.     

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.     

Synchronization of wing beat cycle of the desert locust, Schistocerca gregaria, by periodic light flashes

Studies on the generation of rhythmic motor patterns have shown that peripheral sensory input may contribute substantially to the rhythm generating network. A prominent example is the wing beat frequency of desert locusts, which can be entrained to rhythmic mechanosensory input, but also to the frequency of periodic light flashes. To further analyze the entrainment by light, tethered flying locusts were presented with periodic light flashes, while the position of the forewing was filmed. We show that entrainment of wing beat occurs both in the UV and green range of light. Animals maintained a characteristic phase relationship to the light stimulus with the most elevated wing position occurring at the end of the dark phase. Speed and time course of entrainment varied greatly and ranged from the duration of a single wing beat cycle to several seconds. To identify the visual system mediating entrainment, synchronization to UV light was tested after cutting the optic stalks to the optic lobes/compound eyes or the ocellar nerves. The results show that light entrainment of the locust flight pattern is largely and perhaps exclusively mediated via the fast ocellar pathway and may have a role to stabilize flight with respect to the horizon.     

The effects of temperature on signalling in ocellar neurons of the desert locust, <Emphasis Type="Italic">Schistocerca gregaria</Emphasis>

In Schistocerca gregaria ocellar pathways, large second-order L-neurons use graded potentials to communicate signals from the ocellar retina to third-order neurons in the protocerebrum. A third-order neuron, DNI, converts graded potentials into axonal spikes that have been shown in experiments at room temperature to be sparse and precisely timed. I investigated effects of temperature changes that a locust normally experiences on these signals. With increased temperature, response latency decreases and frequency responses of the neurons increase. Both the graded potential responses in the two types of neuron and the spikes in DNI report greater detail about a fluctuating light stimulus. Over a rise from 22 to 35°C the power spectrum of the L-neuron response encompasses higher frequencies and its information capacity increases from about 600 to 1,700 bits/s. DNI generates spikes more often during a repeated stimulus but at all temperatures it reports rapid decreases in light rather than providing a continual measure of light intensity. Information rate carried by spike trains increases from about 50 to 185 bits/s. At warmer temperatures, increased performance by ocellar interneurons may contribute to improved aerobatic performance by delivering spikes earlier and in response to smaller, faster light stimuli.     

Photoreceptor processing speed and input resistance changes during light adaptation correlate with spectral class in the bumblebee, Bombus impatiens

Colour vision depends on comparison of signals from photoreceptors with different spectral sensitivities. However, response properties of photoreceptor cells may differ in ways other than spectral tuning. In insects, for example, broadband photoreceptors, with a major sensitivity peak in the green region of the spectrum (>500 nm), drive fast visual processes, which are largely blind to chromatic signals from more narrowly-tuned photoreceptors with peak sensitivities in the blue and UV regions of the spectrum. In addition, electrophysiological properties of the photoreceptor membrane may result in differences in response dynamics of photoreceptors of similar spectral class between species, and different spectral classes within a species. We used intracellular electrophysiological techniques to investigate response dynamics of the three spectral classes of photoreceptor underlying trichromatic colour vision in the bumblebee, Bombus impatiens, and we compare these with previously published data from a related species, Bombus terrestris. In both species, we found significantly faster responses in green, compared with blue- or UV-sensitive photoreceptors, although all 3 photoreceptor types are slower in B. impatiens than in B. terrestris. Integration times for light-adapted B. impatiens photoreceptors (estimated from impulse response half-width) were 11.3 ± 1.6 ms for green photoreceptors compared with 18.6 ± 4.4 ms and 15.6 ± 4.4 for blue and UV, respectively. We also measured photoreceptor input resistance in dark- and light-adapted conditions. All photoreceptors showed a decrease in input resistance during light adaptation, but this decrease was considerably larger (declining to about 22% of the dark value) in green photoreceptors, compared to blue and UV (41% and 49%, respectively). Our results suggest that the conductances associated with light adaptation are largest in green photoreceptors, contributing to their greater temporal processing speed. We suggest that the faster temporal processing of green photoreceptors is related to their role in driving fast achromatic visual processes.     

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.     

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.).     

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.     

White noise analysis of temporal properties in simple receptive fields of cat cortex

We studied the linear and nonlinear temporal response properties of simple cells in cat visual cortex by presenting at single positions in the receptive field an optimally oriented bar stimulus whose luminance was modulated in a random, binary fashion. By crosscorrelating a cell's response with the input it was possible to obtain the zeroth-, first-, and second-order Wiener kernels at each RF location. Simple cells showed pronounced nonlinear temporal properties as revealed by the presence of prominent second-order kernels. A more conventional type of response histogram was also calculated by time-locking a histogram on the occurrence of the desired stimulus in the random sequence. A comparison of the time course of this time-locked response with that of the kernel prediction indicated that nonlinear temporal effects of order higher than two are unimportant. The temporal properties of simple cells were well represented by a cascade model composed of a linear filter followed by a static nonlinearity. These modelling results suggested that for simple cells, the nonlinearity occurs late and probably is a soft threshold associated with the spike generating mechanism of the cortical cell itself. This result is surprising in view of the known threshold nonlinearities in preceding lateral geniculate and retinal neurons. It suggests that geniculocortical connectivity cancels the earlier nonlinearities to create a highly linear representation inside cortical simple cells.This work comprises a portion of a PhD thesis submitted by the first author. This study was supported in part by NIH Grant EY04630 and EY06679 to R.C.E., and EY01319 (Core Grant) to the Center for Visual Science     

Crumbs regulates polarity and prevents light-induced degeneration of the simple eyes of Drosophila, the ocelli

The evolutionary conserved transmembrane protein Crumbs (Crb) regulates morphogenesis of photoreceptor cells in the compound eye of Drosophila and prevents light-dependent retinal degeneration. Here we examine the role of Crb in the ocelli, the simple eyes of Drosophila. We show that Crb is expressed in ocellar photoreceptor cells, where it defines a stalk membrane apical to the adherens junctions, similar as in photoreceptor cells of the compound eyes. Loss of function of crb disrupts polarity of ocellar photoreceptor cells, and results in mislocalisation of adherens junction proteins. This phenotype is more severe than that observed in mutant photoreceptor cells of the compound eye, and resembles more that of embryonic epithelia lacking crb. Similar as in compound eyes, crb protects ocellar photoreceptors from light induced degeneration, a function that depends on the extracellular portion of the Crb protein. Our data demonstrate that the function of crb in photoreceptor development and homeostasis is conserved in compound eyes and ocelli and underscores the evolutionarily relationship between these visual sense organs of Drosophila. The data will be discussed with respect to the difference in apico-basal organisation of these two cell types.     

Nonlinear signal transmission between second- and third-order neurons of cockroach ocelli

Transfer characteristics of the synapse made from second- to third-order neurons of cockroach ocelli were studied using simultaneous microelectrode penetrations and the application of tetrodotoxin. Potential changes were evoked in second-order neurons by either an extrinsic current or a sinusoidally modulated light. The synapse had a low-pass filter characteristic with a cutoff frequency of 25-30 Hz, which passed most presynaptic signals. The synapse operated at an exponentially rising part of the overall sigmoidal input/output curve relating pre- and postsynaptic voltages. Although the response of the second-order neuron to sinusoidal light was essentially linear, the response of the third-order neuron contained an accelerating nonlinearity: the response amplitude was a positively accelerated function of the stimulus contrast, reflecting nonlinear synaptic transmission. The response of the third-order neuron exhibited a half-wave rectification: the depolarizing response to light decrement was much larger than the hyperpolarizing response to light increment. Nonlinear synaptic transmission also enhanced the transient response to step-like intensity changes. I conclude that (a) the major function of synaptic transmission between second- and third-order neurons of cockroach ocelli is to convert linear presynaptic signals into nonlinear ones and that (b) signal transmission at the synapse between second- and third-order neurons of cockroach ocelli fundamentally differs from that at the synapse between photoreceptors and second-order neurons of visual systems so far studied, where the synapse operates in the midregion of the characteristic curve and the transmission is essentially linear.     

System analysis of Phycomyces light-growth response: madC, madG, and madH mutants.

The light-growth response of Phycomyces has been studied further with the sum-of-sinusoids method in the framework of the Wiener theory of nonlinear system identification. The response was treated as a black box with the logarithm of light intensity as the input and elongation rate as the output. The nonlinear input-output relation of the light-growth response can be represented mathematically by a set of weighting functions called kernels, which appear in the Wiener intergral series. The linear (first-order) kernels of wild type, and of single and double mutants affected in genes madA to madG were determined previously with Gaussian white noise test stimuli, and were used to investigate the interactions among the products of these genes (R.C. Poe, P. Pratap, and E.D. Lipson. 1986. Biol. Cybern. 55:105.). We have used the more precise sum-of-sinusoids method to extend the interaction studies, including both the first- and second-order kernels. Specifically, we have investigated interactions of the madH ("hypertropic") gene product with the madC ("night blind") and madG ("stiff") gene products. Experiments were performed on the Phycomyces tracking machine. The log-mean intensity of the stimulus was 6 x 10(-2) W m-2 and the wavelength was 477 nm. The first- and second-order kernels were analyzed in terms of nonlinear kinetic models.(ABSTRACT TRUNCATED AT 250 WORDS)     

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.     

The role of ocelli in circadian singing rhythms of crickets

ABSTRACT. . There is a direct quantitative relationship between the free-running period (r) of the circadian stridulation rhythm of male Australian field crickets, Teleogryllus commodus (Walker), and the intensity of the constant light conditions. Both T. commodus and the house cricket, Acheta domesticus (L.), show free-running periods of the singing rhythm of c. 24 h when the light intensity is 0.00025 lux. In both species the severance of the three ocellar nerves significantly slows the circadian period which is indicative of a reduced perception of the available light intensity. To test whether this period reduction is a peripheral or a central effect, electro-retinograms (ERGs) were recorded from compound eyes of male T. commodus with the ocelli fully functional, then occluded, and then uncovered. The size of the compound eye ERG is reduced by 20% with ocellar occlusion and can subsequently be fully restored to the intact level, which indicates that the ocellar effect is a peripheral one. Intensified CoCl₂ fills reveal one neurone in A. domesticus and two in T. commodus which travel from the lateral ocellar nerve out into the ipsilateral optic lobe of the compound eye. These neurones all terminate in or distal to the lobular neuropile. The data are interpreted to indicate a role for ocelli in modulating the light intensity perception of the compound eye. The final effect of the ocellar afferents is at a peripheral level prior to the input of the visual information to the optic lobe circadian pacemaker. Hence ocelli play an indirect role in circadian rhythmicity, augmenting the sensitivity of the primary photoreceptors to better perceive photic entrainment signals.     

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