Ken-Ichi Naka

White-noise analysis of a neuron chain: an application of the Wiener theory.

The Wiener theory of nonlinear system identification was applied to a three-stage neuron chain in the catfish retina in order to determine the functional relationship between the artificial polarization of the horizontal cell membrane potential and the resulting discharge of the ganglion cell. A mathematical model was obtained that can predict quantitatively, with reasonable accuracy, the nonlinear, dynamic behavior of the neuron chain. The applicability of the method is discussed. We conclude that this is a very powerful method in the analysis of information transfer in the central nervous system.

Identification of Multi-Input Biological Systems

The Wiener theory of nonlinear system identification is extended to multi-input-output systems and experimentally applied. The experimental applicability of the method is discussed with regard to biological systems. It is shown that the method is well suited for the treatment of the idiosyncratic features of such systems: nonlinearities, short lifetimes of experimental preparations, and high noise content. A preliminary analysis is outlined, taking into account the characteristics of the system under study, which results in the determination of the parameters of the identifying experiment. An error analysis is made which can be used to increase the accuracy of the derived model within certain constraints. Several examples are given of the experimental application of the method to certain neural networks in a vertebrate retina (the catfish, Ictalurus punctatus, retina was used for these experiments). In addition to functional identification through white-noise stimulation, these same retinal neurons are identified morphologically through intracellular dye injection. The performance of the derived functional models, as compared to the physical system, is evaluated through a variety of tests and it is found to be very satisfactory.

The horizontal cells.

Abstract The catfish retina (as well as other teleost retinas) is equipped with unique structures called horizontal cells which functionally form a laminar layer ( S -space) extending over entire retina. A potential change arising inside the S -space, whether caused by light through receptors or by extrinsic current injection, can spread passively more than 2 mm and is still effective in inducing a response from retinal ganglion cells. The S -space forms one of the lateral transmission mechanisms within the retina and it provides the surround of the catfish receptive field.

Receptive Field Mechanism in the Vertebrate Retina

In the catfish retina there are two types of ganglion cells: in one type (type A cell) a spot of light at the center of its receptive field gives rise to a sustained discharge whereas an annulus gives rise to a transient response, and in the other type (type B cell) the response pattern is reversed for a spot and an annulus. Current injected into the horizontal cell induces spike discharges of the ganglion cell very similar to that elicited by a spot of light or by an annulus. In both types of receptive fields, depolarization of the horizontal cell gives rise to a response of the ganglion cell similar to that elicited by a spot of light, whereas hyperpolarization of the cell gives rise to a response of the ganglion cell similar to that elicited by an annulus. Current through a single injecting electrode could drive two types of cells simultaneously. Interaction between a spot of light and an annulus can also be simulated by replacing one light stimulus by current of the proper polarization injected into the horizontal cells. Results suggest that interactions among three neuronal structures, the receptor, the horizontal cell, and the bipolar cell, produce the basic receptive field organization in the channel catfish.

An attempt to analyze multi-unit recordings

Abstract In neurophysiological experiments it is sometimes desirable or inevitable to record signals from several units simultaneously with a single electrode. In either case, one wishes to separate the recorded spike potentials with regard to their sources. A “single” unit must be defined either on the basis of spike wave form, or on an operational basis by means of recurring patterns in spike discharge. The first approach can be and has been pursued by means of special electronic equipment. The second approach usually requires a search for a meaningful operational criterion, and can be aided materially by the use of an appropriate computer system. This note illustrate the use of a computer system in two attempts to analyze complex data in which spike potentials from several neurons were involved. If spike potentials from several units are recorded simultaneously with a single electrode, digital computers with graphic display facilities may be used to advantage to separate the signals from the various units rapidly. Two simple methods for separation are discussed, one using the wave shape, the other using operational criteria. These methods are illustrated by applications to research in the fly and cat central nervous systems.

The dynamics of inhibitory interaction in a frog receptive field: A paradigm of paracontrast

Abstract Neurons in the frog retina, that generate on responses when the central regions of their receptive fields are stimulated and that are inhibited by a peripheral light, have been illuminated with a central and peripheral stimulus in varying time sequence. If a light is allowed to fall on the periphery of a receptive field as much as 160 msec after the onset of the central stimulus, the number of impulses produced by a cell is reduced. The time course of the interaction can be recorded in detail and indicates a possible physiological site for the psychophysical phenomenon of para-contrast.

The modes of chromatic interactions in the retina.

Abstract The multi-input Wiener analysis technique has been used to evaluate the modes of chromatic interactions in the turtle retina using intracellular recording and staining. Receptor, horizontal and bipolar cells displayed linear chromatic interactions. More proximal neurons have predominantly nonlinear responses and displayed nonlinear chromatic interactions. These observations make it clear that there are chromatic interactions at the inner plexiform layer of the retina in addition to those of the outer plexiform layer and that modes of chromatic interaction at the two synaptic layers are significantly different.

Experimental analysis of a neural system: Two modeling approaches

The retinal neural system in the catfish which transforms light intensity temporal variations into the horizontal cell potential is experimentally analyzed and modeled by two distinct methods. The first method involves testing the system with gaussian white-noisemodulated light intensity and the subsequent derivation of a mathematical model in terms of a Wiener functional series. The second method involves testing of the system by step and sinewave stimuli and the postulation of a set of nonlinear differential equations which are designed to fit these stimulus-response data. In this latter approach, the differential equations describe the usually assumed dynamic behavior of the component subsystems, such as photoreceptor and horizontal cell membranes in terms of properties of membrance resistance and capacitance. The system behavior is found to exhibit certain “small signal” nonlinearities such as dynamic asymmetry in the response as well as certain “large signal” nonlinearities. The two modeling approaches and the resulting models are compared and it is found that the functional model derived from the white-noise experiment, while it does not attempt to describe the underlying system structure as the differential equation does, produced, in general, more satisfactory results as far as the input-output behavior of the system is concerned. It is suggested that combination of the two approaches could be very fruitful in modeling a particular system.

Effects of temperature change on the catfish S-potentials

Abstract Effects of temperature change on the resting (dark) level and light-induced potential ( S-potential ) of the catfish S-space or horizontal cells were observed. The rise and decay time of the S-potential were found most sensitive to temperature change while the resting level was least affected by change in temperature of preparation ranging from 5 to nearly 30°. Though change in temperature resulted in marked change in the wave form of S-potentials , the fit of the amplitude vs . log intensity relation to the logistic function was reasonably good from about 7 to nearly 30°. However, the slope of the curve became less steep when the temperature of the preparation was less than 7°.

Mimetic Model of Retinal Network in Catfish

Abstract Nonlinear analysis through single and two-input white-noise stimulation is performed on the catfish retinal neurons; the receptor, horizontal, bipolar, amacrine and ganglion cells. The results are correlated to the morphological and functional structure of this retina, as it pertains to the concentric receptive-field organization. The derived models can predict the neuron responses with good accuracy Conclusions are drawn on the functional role of the various neuron chains, within the retina, in realizing the receptive-field response components and processing light information. A preliminary functional model of the catfish retina is presented.