A Quantitative Description of the Dynamics of Excitation and Inhibition in the Eye of <i>Limulus </i>

Knight, Bruce W.; Toyoda, Jun‐Ichi; Dodge, F. A.

doi:10.1085/jgp.56.4.421

Cited by 110 publications

(92 citation statements)

References 17 publications

(21 reference statements)

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“…Furthermore, similar work has been presented for both retinular and eccentric cells in Limulu (Knight, Dodge & Toyoda, 1970;Dodge, Knight & Toyoda, 1968;Pinter, 1966) and locust and cricket (Pinter, 1972).…”

Section: Introductionsupporting

confidence: 55%

Linear and non‐linear performance of transducer and pupil in Calliphora retinula cells.

Leutscher-Hazelhoff¹

1975

The Journal of Physiology

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SUMMARY1. Intracellular recordings have been made from the blowfly (Calliphora erythrocephala) retinula cell; apart from the transducer mechanism, these cells also feature a pupil mechanism.2. At several mean intensity levels, within the apparently linear range of response, frequency characteristics of amplitude and phase and responses to 'delta '-flashes and 'delta '-flash pairs have been obtained.3. Fourier methods have shown these responses to be mutually compatible, confirming linearity in these circumstances.4. Non-linear behaviour can be made to appear at the lower frequencies when the modulation depth is increased.5. Non-linearities can also appear through application of the superposition test: a low frequency sine wave, modulated so as to elicit an apparently linear response, and a high frequency sine wave which does not give rise to non-linearity even at the highest modulation depths can, when superimposed, yield a greater response to the latter when situated at the minima of the former than at its maxima.6. At frequencies above approximately 1 Hz these superposition nonlinearities are attributed to the transducer mechanism gain control. Below this frequency the pupil mechanism takes part considerably in the retinula cell's total observed gain control: its characteristics remain yet to be cleared up.7. The transducer's linear and non-linear properties fit in closely with those of the Fuortes-Hodgkin model which couples increases in gain and time constants. 8. The Fuortes-Hodgkin model will probably require some quantitative modifications in the originally treated case of LimulUs, on account of its pupil.9. Finally, the merits of Veringa's diffusion model, and the possibility of eventually joining this model with the Fuortes-Hodgkin one are pointed out briefly.

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Section: Introductionsupporting

confidence: 55%

Linear and non‐linear performance of transducer and pupil in Calliphora retinula cells.

Leutscher-Hazelhoff¹

1975

The Journal of Physiology

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“…Stimulus presentation and control were identical to those described by Knight et al (1970). The stimulus waveform was generated by adding together constant voltages with time-varying voltages generated by a waveform generator (Hewlett-Packard 3300A).…”

Section: Stimulus and Stimulus Controlmentioning

confidence: 99%

“…The important mechanism to understand, in connection with this problem, is the process which produces the impulse rate from depolarization. Knight et al (1970) have shown that this process acts like a linear transducer for small modulated signals; in other words, it can be characterized by its frequency response, S(f). S(f) is defined as the relative modulation (peak to peak divided by the average) of the impulse rate divided by the relative modulation of the driving current at the frequency f.…”

Section: Frequency Response Of the Current-to-firing Rate Processmentioning

confidence: 99%

“…These results implied that the randomness in the generator potential, which is probably due to randomness in photon arrival and absorption , was responsible for the impulse rate fluctuations. Because the impulse-firing mechanism can be treated as a linear filter for modulated stimuli (Dodge, 1968;Knight et al, 1970), I have used the theory for the linear filtering of stochastic processes to show how fluctuations in impulse rate arise from the generator potential "noise" (Shapley, 1969).…”

Section: Introductionmentioning

confidence: 99%

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Fluctuations of the Impulse Rate in Limulus Eccentric Cells

Shapley

1971

The Journal of General Physiology

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Fluctuations in the discharge of impulses were studied in eccentric cells of the compound eye of the horseshoe crab, Limulus polyphemus. A theory is presented which accounts for the variability in the response of the eccentric cell to light. The main idea of this theory is that the source of randomness in the impulse rate is "noise" in the generator potential. Another essential aspect of the theory is that the process which transforms the generator potential "noise" into the impulse rate fluctuations may be treated as a linear filter. These ideas lead directly to Fourier analysis of the fluctuations. Experimental verification of theoretical predictions was obtained by calculation of the variance spectrum of the impulse rate. The variance spectrum of the impulse rate is shown to be the filtered variance spectrum of the generator potential.

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“…An early system-analytic study of the crayfish stretch-receptor by Borsellino, Poppele, and Terzuolo [7] has led to a comparative study by Fohlmeister, Poppele and Purple [16,17] of nerve-impulse generating transducers. The linear frequency response of the lateral eye of the horseshoe crab Limulus was given early investigation by Pinter [40], by Biederman-Thorson and Thorson [5,52], and by Dodge, Knight and Toyoda [14,26,43], Over the past decade a very detailed and predictively accurate linear system-analytic model has evolved for the visual neurophysiology of Limulus [8,9,44], There now have been a substantial number of experimental forays unto applying methods of nonlinear system identification, in the general spirit of Wiener's proposal, to biological transducers [15, 19, 20, 28, 30, 32, 33, 35-37, 45, 46, 53, 55, 57], Concurrently, the theoretical state of the subject has continued to advance. It was recognized before 1963 by Barrett [2] that Wiener's white-noise approach is just one member of a wide class of analytic procedures, each based on its own particular ensemble of input test signals.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear analysis with an arbitrary stimulus ensemble

Victor¹,

Knight²

1979

Quart. Appl. Math.

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113

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Abstract.A family of Wiener-type methods is discussed in a general context. These methods share the concept of expansion of an unknown transducer as an orthogonal series. The terms of the series are drawn from a hierarchy of subspaces of transducers that are orthogonal with respect to a particular stimulus ensemble. Choices of specific stochastic ensembles lead to previously described analytical methods, including the classical one of Wiener.It is proposed that a sum of incommensurate or nearly incommensurate sinusoids forms a signal that leads to a useful orthogonal expansion. The family of orthogonal subspaces are presented explicitly. Projection of an unknown transducer into an orthogonal subspace amounts to isolation of Fourier components of the output of the unknown transducer at certain harmonics and combination frequencies of the input frequencies. Practical advantages of this technique include i) the ease of computation of the higherorder kernels, and ii) the opportunity for digital filtering of the response, which enhances the signal-to-noise ratio.Finally, it is shown that the kernels obtained using a sum-of-sinusoids signal approach the Fourier transforms of the Wiener kernels as the number of sinusoids grows without bound. Thus, the sum-of-sinusoids technique retains a major theoretical advantage of the Wiener white-noise method: the kernels of simple model transducers have simple analytic forms.

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A Quantitative Description of the Dynamics of Excitation and Inhibition in the Eye of Limulus

Cited by 110 publications

References 17 publications

Linear and non‐linear performance of transducer and pupil in Calliphora retinula cells.

Linear and non‐linear performance of transducer and pupil in Calliphora retinula cells.

Fluctuations of the Impulse Rate in Limulus Eccentric Cells

Nonlinear analysis with an arbitrary stimulus ensemble

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