A spatiotemporal white noise analysis of photoreceptor responses to UV and green light in the dragonfly median ocellus

Adult dragonflies augment their compound eyes with three simple eyes known as the dorsal ocelli. While the ocellar system is known to mediate stabilizing head reflexes during flight, the ability of the ocellar retina to dynamically resolve the environment is unknown. For the first time, we directly measured the angular sensitivities of the photoreceptors of the dragonfly median (middle) ocellus. We performed a second-order Wiener Kernel analysis of intracellular recordings of light-adapted photoreceptors. These were stimulated with one-dimensional horizontal or vertical patterns of concurrent UV and green light with different contrast levels and at different ambient temperatures. The photoreceptors were found to have anisotropic receptive fields with vertical and horizontal acceptance angles of 15 degrees and 28 degrees, respectively. The first-order (linear) temporal kernels contained significant undershoots whose amplitudes are invariant under changes in the contrast of the stimulus but significantly reduced at higher temperatures. The second-order kernels showed evidence of two distinct nonlinear components: a fast acting self-facilitation, which is dominant in the UV, followed by delayed self- and cross-inhibition of UV and green light responses. No facilitatory interactions between the UV and green light were found, indicating that facilitation of the green and UV responses occurs in isolated compartments. Inhibition between UV and green stimuli was present, indicating that inhibition occurs at a common point in the UV and green response pathways. We present a nonlinear cascade model (NLN) with initial stages consisting of separate UV and green pathways. Each pathway contains a fast facilitating nonlinearity coupled to a linear response. The linear response is described by an extended log-normal model, accounting for the phasic component. The final nonlinearity is composed of self-inhibition in the UV and green pathways and inhibition between these pathways. The model can largely predict the response of the photoreceptors to UV and green light.     

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     

Nonlinear mechanisms for gain adaptation in locust photoreceptors.

Intracellular membrane potential responses were recorded from locust photoreceptors under two stimulus conditions: pairs of flashes to dark-adapted receptors, and white-noise modulated light at a range of background intensities from 500 to 15,000 effective photons per second. Nonlinear analysis of the input-output relationships were performed by estimating the Volterra and Wiener kernels of the system. The Volterra kernels obtained from the double-flash experiments were similar to the Wiener kernels obtained from the white-noise experiments, except for a change of time scale. The structure of the second-order kernels obtained with either method gave evidence for a gain control mechanism acting at an early stage of the cascade. Both feedforward and feedback nonlinearities could account for the observed system behavior at any one background level. The differences in amplitude between the kernels obtained at different background levels could be accounted for by an adaptation process which further decreased the gain of the system, acting on a slower time scale, also at some early stage of the cascade.     

Light adaptation in Drosophila photoreceptors: II. Rising temperature increases the bandwidth of reliable signaling

It is known that an increase in both the mean light intensity and temperature can speed up photoreceptor signals, but it is not known whether a simultaneous increase of these physical factors enhances information capacity or leads to coding errors. We studied the voltage responses of light-adapted Drosophila photoreceptors in vivo from 15 to 30 degrees C, and found that an increase in temperature accelerated both the phototransduction cascade and photoreceptor membrane dynamics, broadening the bandwidth of reliable signaling with an effective Q(10) for information capacity of 6.5. The increased fidelity and reliability of the voltage responses was a result of four factors: (1) an increased rate of elementary response, i.e., quantum bump production; (2) a temperature-dependent acceleration of the early phototransduction reactions causing a quicker and narrower dispersion of bump latencies; (3) a relatively temperature-insensitive light-adapted bump waveform; and (4) a decrease in the time constant of the light-adapted photoreceptor membrane, whose filtering matched the dynamic properties of the phototransduction noise. Because faster neural processing allows faster behavioral responses, this improved performance of Drosophila photoreceptors suggests that a suitably high body temperature offers significant advantages in visual performance.     

Principal dynamic mode analysis of action potential firing in a spider mechanoreceptor

The encoding of mechanical stimuli into action potentials in two types of spider mechanoreceptor neurons is modeled by use of the principal dynamic modes (PDM) methodology. The PDM model is equivalent to the general Wiener–Bose model and consists of a minimum set of linear dynamic filters (PDMs), followed by a multivariate static nonlinearity and a threshold function. The PDMs are obtained by performing eigen-decomposition of a matrix constructed using the first-order and second-order Volterra kernels of the system, which are estimated by means of the Laguerre expansion technique, utilizing measurements of pseudorandom mechanical stimulation (input signal) and the resulting action potentials (output signal). The static nonlinearity, which can be viewed as a measure of the probability of action potential firing as a function of the PDM output values, is computed as the locus of points of the latter that correspond to output action potentials. The performance of the model is assessed by computing receiver operating characteristic (ROC) curves, akin to the ones used in decision theory and quantified by computing the area under the ROC curve. Three PDMs are revealed by the analysis. The first PDM exhibits a high-pass characteristic, illustrating the importance of the velocity of slit displacement in the generation of action potentials at the mechanoreceptor output, while the second and third PDMs exhibit band-pass and low-pass characteristics, respectively. The corresponding three-input nonlinearity exhibits asymmetric behavior with respect to its arguments, suggesting directional dependence of the mechanoreceptor response on the mechanical stimulation and the PDM outputs, in agreement to our findings from a previous study (Ann Biomed Eng 27:391–402, 1999). Differences between the Type A and B neurons are observed in the zeroth-order Volterra kernels (related to the average firing), as well as in the magnitudes of the second and third PDMs that perform band-pass and low-pass processing of the input signal, respectively.     

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.     

Implementation of an elaborated neuromorphic model of a biological photoreceptor

We describe here an elaborated neuromorphic model based on the photoreceptors of flies and realised in both software simulation and hardware using discrete circuit components. The design of the model is based on optimisations and further elaborations to the mathematical model initially developed by van Hateren and Snippe that has been shown to accurately simulate biological responses in simulations under both steady-state and limited dynamic conditions. The model includes an adaptive time constant, nonlinear adaptive gain control, logarithmic saturation and a nonlinear adaptive frequency response mechanism. It consists of a linear phototransduction stage, a dynamic filter stage, two divisive feedback loops and a static nonlinearity. In order to test the biological accuracy of the model, impulses and step responses were used to test and evaluate the steady-state characteristics of both the biological (fly) and artificial (new neuromorphic model) photoreceptors. These tests showed that the model has faithfully captured most of the essential characteristics of the insect photoreceptor cells. The model showed a decreasing response to impulsive stimuli when the background intensity was increased, indicating that the circuit adapted to background luminance in order to improve the overall operating range and better encode the contrast of the stimulus rather than luminance. The model also showed the same change in its frequency response characteristics as the biological photoreceptors over a luminance range of 70,000 cd/m², with the corner frequency of the circuit ranging from 10 to 90 Hz depending on the current state of adaptation. Complex naturalistic experiments have also further proven the robustness of the model to perform in real-world scenario. The model showed great correlation to the biological photoreceptors with an r ² value exceeding 0.83. Our model could act as an excellent platform for future experiments that could be carried out in scenarios where in vivo intracellular recording from biological photoreceptors would be impractical or impossible, or as a front-end for an artificial imaging system.     

A nonlinear cascade model for action potential encoding in an insect sensory neuron.

Action potential encoding in the cockroach tactile spine neuron can be represented as a single-input single-output nonlinear dynamic process. We have used a new functional expansion method to characterize the nonlinear behavior of the neural encoder. This method, which yields similar kernels to the Wiener method, is more accurate than the latter and is efficient enough to obtain reasonable kernels in less than 15 min using a personal computer. The input stimulus was band-limited white Gaussian noise and the output consisted of the resulting train of action potentials, which were unitized to give binary values. The kernels and the system input-output signals were used to identify a model for encoding comprising a cascade of dynamic linear, static nonlinear, and dynamic linear components. The two dynamic linear components had repeatable and distinctive forms with the first being low-pass and the second being high-pass. The static nonlinearity was fitted with a fifth-order polynomial function over several input amplitude ranges and had the form of a half-wave rectifier. The complete model gave a good approximation to the output of the neuron when both were subjected to the same novel white noise input signal.     

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.     

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 identification of nonlinear biological systems: Wiener and Hammerstein cascade models

Systems that can be represented by a cascade of a dynamic linear subsystem preceded (Hammerstein cascade model) or followed (Wiener cascade model) by a static nonlinearity are considered. Various identification schemes that have been proposed for the Hammerstein and Wiener systems are critically reviewed with reference to the special problems that arise in the identification of nonlinear biological systems. Examples of Wiener and Hammerstein systems are identified from limited duration input-output data using an iterative identification scheme.     

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.     

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.).     

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 nonlinear pathway of Y ganglion cells in the cat retina

Retinal ganglion cells of the Y type in the cat retina produce two different types of response: linear and nonlinear. The nonlinear responses are generated by a separate and independent nonlinear pathway. The functional connectivity in this pathway is analyzed here by comparing the observed second-order frequency responses of Y cells with predictions of a "sandwich model" in which a static nonlinear stage is sandwiched between two linear filters. The model agrees well with the qualitative and quantitative features of the second-order responses. The prefilter in the model may well be the bipolar cells and the nonlinearity and postfilter in the model are probably associated with amacrine cells.     

Neural response mechanisms in the photoreceptive pineal organ of goldfish

In order to classify the different cell types involved in signal transmission of the photoreceptive pineal organ of the goldfish, Carassius auratus, intra- and extracellular electrical responses were recorded from photoreceptors and second-order neurons. Photoreceptor responses to light consisted of hyperpolarizing potentials up to 30 mV. The responses were graded with intensity and their voltage-intensity relation followed the hyperbolic function V/Vmax = In/In + sigma n. Latencies varied between 500 msec for responses near threshold and 60 msec for supersaturating flashes. The response duration increased up to 60 sec for flashes 2 log units above the saturation level. Action spectra of individual photoreceptors peaked at lambda max = 530 nm and corresponded to measurements of extracellular slow mass potentials or spike potentials. Slow mass potentials exhibited similar characteristics as intracellular recorded photoreceptor potentials with respect to latency, voltage-intensity curves and spectral sensitivity. Ganglion cells showed maintained discharges under conditions of steady illumination. The discharge rate changed inversely with the logarithm of steady illumination over a range of 8 log units. The response to light flashes was purely achromatic and consisted of inhibition of the maintained discharge. The physiological properties demonstrate that the pineal organ of the goldfish is an effective functional photoreceptor organ operating both in dim and in bright light. The light-induced hyperpolarization of photoreceptors lead to an inhibition of the nervous discharge of ganglion cells. The direct flow of information from photoreceptors to ganglion cells is the basic channel of data processing in the goldfish pineal.     

Linear and non-linear contrast coding in light-adapted blowfly photoreceptors

The response properties of R1–6 type photoreceptors of the blowfly (Calliphora vicina) were investigated using 1- to 600-ms light steps with contrasts from -1.00 to +1.12 at different adapting backgrounds. To prevent activation of voltage-dependent K⁺-channels, some photoreceptors were treated with ionophoretically injected tetraethylammonium. The linearity and time-course of the photoresponses depended on the adapting background and the duration of the contrast stimulus. At low backgrounds photoresponses were approximately linear regardless of the contrast step duration. However, at higher backgrounds photoreceptors produced, with long contrast steps of opposite polarities, larger and slower hyperpolarizing responses than depolarizing ones, but linear responses with equal time-courses to transient (2ms) contrast changes. The early rising phases of photoresponses were independent of the contrast signal duration, deviated to the same extent from the steady-state potential and steepened as the value of contrast was increased. The photoreceptor contrast gain increased with the background, but its value depended on the duration, the magnitude, and the polarity of the contrast step. Tetraethylammonium linearised the photoreceptor membrane, increased and delayed photoresponses probably by blocking the shunting of the outwardly rectifying potassium channels. These effects did not strongly influence on the photoreceptors' characteristic non-linear contrast dependence on light adaptation.Abbreviations LED light emitting diode - TEA tetraethylammonium ion     

Sinusoidal and delta function responses of visual cells of the Limulus eye

Dynamic responses of visual cells of the Limulus eye to stimuli of sinusoids and narrow pulses of light superimposed on a nonzero mean level have been obtained. Amplitudes and phase angles of averaged sinusoidal generator potential are plotted with respect to frequency of intensity modulation for different mean levels of light adaptation. At frequencies above 10 CPS, generator potential amplitudes decrease sharply and phase lag angle increases. At frequencies below 1 CPS, amplitude decreases. A maximum of amplitude in the region of 1 to 2 CPS is apparent with increased mean intensity. The generator potential responses are compared with those of differential equation models. Variation of gain with mean intensity for incremental stimuli is consistent with logarithmic sensitivity of the photoreceptor. Frequency response of the photoreceptor derived from narrow pulses of light predicts the frequency response obtained with sinusoidal stimuli, and the photoreceptor is linear for small signals in the light-adapted state.