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Morphological and F’unctional Identifications of Catfish Retinal Neurons. III. Functional Identification KEN-ICHI NAKA, Divisions of Applied Pasadena, California PANOS 2. MARMARELIS, Science and Biology, 91109 TWO MAIN QUESTIONS arise naturally CaZifornia for publication April 8, 1974. RAYMOND Institute Y. CHAN of Technology, input does. In practice, of course, the system is tested with a great variety of inputs (instead of all), because of the finite duration of the experiment, and the resulting functional characterization is a statistically averaged one. Thus, in this sense, a whitenoise stimulus becomes the universal probe for testing and identifying a system functionally, and the resulting characterization is global, as it describes the system over its entire stimulus-response function space. In spite of the power and generality of the white-noise “universal” experiment, no attempts except one (39) were made to apply it to biological systems until recently, when we made an extensive study on the application of the theory (properly formulated and extended) to the systematic description of the dynamic characteristics of certain neuron chains in the vertebrate retina (16, 18-21). In that series of studies we concluded that the theory could be successfully applied to the functional identification of neuron chains and that the resulting characterizations could predict the nonlinear response of these neuron chains with a good degree of accuracy. Inasmuch as the major objective of these studies was the exploration of the potentialities of the “white-noise methods,” the biological scope of these studies was limited. Accordingly, the application of the methods was confined to the horizontal cell responses (a slow potential) and the spike discharges of the ganglion cells (a discrete signal), thus examining the two representative classesof neural signals. Although the great advantages of the method, especially when applied to intracellular recording, were recognized at this earlier stage of the development, we also realized that for such a functional Downloaded from http://jn.physiology.org/ by 10.220.33.3 on June 18, 2017 in the study of neural systems: “What does the system do?” and its logical companion and does the system do this?” sequel, “How Answering the first question involves the ability to predict the system response to any stimulus, and it is therefore usually carried out through the performance of suitable stimulus-response experiments. As this endeavor is directed to the discovery of the system function (in its processing of stimuli signals into response signals), we term it functional identification of the system. In this series of papers (parts I, II, and III) we attempt to answer both of these questions for the neural systems in the catfish retina. While part I (24) dealt with answering the structural question and part II (28) dealt with answering the functional question by traditional methods, part III (this paper) concentrates on answering the functional question with the white-noise analysis technique and with pooling the results of parts I, II, and III for the comprehensive identification of the vertebrate retinal neurons. Twenty years ago, approximately, Wiener (49) proposed that a nonlinear system could be identified functionally by stimulating it with a Gaussian white-noise input, i.e., a random signal containing all frequencies within the system bandwidth with equal power (and whose amplitude is distributed in Gaussian fashion). Wiener’s proposal was based on the idea that, since the principle of superposition does not hold for nonlinear system, we would need to test such a system exhaustively with all possible inputs; this is exactly what a white-noise Received AND WHITE-NOISE identification to be of much biological significance it had to be conducted together with the structural identification of the neural system. It is to this latter task that part I (24) of this study is directed-structural characterization. Part II (28) attempts to correlate these findings with traditionally oriented functional studies. In this paper (part III of the series) we apply the nonlinear analysis technique (through white-noise stimulation of the re- Y3 it morphologically. The best such example is the argument presented to identify a class of neurons as “amacrine cells” by observing their responses (11, 12, 44, 47, 48). We will conclude that I) the nonlinearanalysis technique can be applied successfully to the intracellular responses of the retinal neurons; 2) their nonlinear responses can be predicted by a small set of characterizing kernels which may include, for some neuron types, up to the third-order nonlinear kernel; 3) identification of the horizontal and bipolar cells (as classes of neurons) is straightforward; 4) it is not possible to classify the neurons in the proximal layers into two distinct classes, namely, amacrine and ganglion cells; and 5) instead, we propose to classify them into three functional types, types N, C, and Y, which have no strict correspondence (but rather a loose one) to morphologically established classes. Finally, in the APPENDIX we attempt a preliminary classification analysis of the neurons in this vertebrate retina to assess the objectivity and validity of the classification we propose in this paper. METHODS Experimental The retina of the channel catfish, Ictalurus $~nctatus, in eye cup preparation, was used for the experiments. The apparatus used and the general experimental conditions have been described previously (18, 26, 27). In this experiment the moist oxygen was not supplied as in the previous series but we did not find any adverse effects (compare with results in part II (28)). The optical bench used in previous experiments (26) was modified by placing glow modulator tubes (R-l l?llC, Sylvania Electric) in appropriate places in the apparatus. The glow tubes were driven by amplifiers with large negative feedback in order to linearize the current through them. The spectral composition of the light produced by the glow modulators remains unchanged for the range of intensities used in the experiments of this study (18). The white-noise signals were generated digitally and converted into analog form by a D/A converter and appropriate low-pass filtering. Subsequently, these signals were stored on analog magnetic tape to be used in the experiments, to modulate the glow-tube light sources. The resulting white-noise signals have an amplitude dynamic range of about 40 to 1 and a flat power spectrum from 0 to 60 Hz. In the experiments Downloaded from http://jn.physiology.org/ by 10.220.33.3 on June 18, 2017 ceptive-field components) to the intracellular responses of the vertebrate neurons. Following the white-noise test, dye is intracellularly injected into the unit being tested. The objective is to identify both functionally and structurally the classes of neurons in the catfish retina. When applied to intracellular responses, the white-noiseanalysis technique has distinct advantages in that a) it allows us to gather a large amount of diverse stimulus-response data in a short span of time; and b) unwanted contaminating noise, such as may arise from the electrode, can be eliminated (because of the cross-correlating process employed (18, 21)). These are important factors to be considered when one tries to record intracellular responses from retinal neurons and, at the same time, tries to establish the morphological type of the neuron through intracellular dye injection. Particularly, in this part, we will attempt to correlate the functional characteristics of the neurons, as derived from the nonlinear white-noise analysis, to their morphological characteristics which we have described in parts I and II: a series of kernels (18,2 1) will define functionally the neurons, and a majority of these neurons will also be identified morphologically by Procion dye injection. The central theme of this paper is to answer the question, “Can we reconcile the morphological classification of neurons with the classification of similar neurons based on their functional traits?” So far it has been commonly assumed that there is a oneto-one correspondence between a morpholog ical class of neurons and a characteristic class of responses. That is, it is commonly asserted that a given class of morphologically defined neurons gives rise to characteristic responses or, conversely, that knowing the response of a given neuron one can identify ANALYSIS 94 NAKA, MARMARELIS, Analytical For a time-invariant system with input x(t) and o utput y(t), both of which are functions of SPOT ANNULUS FIELD i i tc- 5.0+ FIG. 1. Sketches of the approximate shape size of the three standard stimulus* patterns throughout this experiment, spot, annulus, and stimulations. In two-input experiments both and annulus of lights were given together. and used field spot CHAN time t only, Wiener (49) showed that the relationship between y(t) and x(t) can be written as a series where {Gi} is a complete set of orthogonal functionals with respect to a Gaussian white-noise input x(t). The first four functionals in the series are: G,P,~ WI = h, G,[h,, x(t)] = j&(x)x@ - x)dt 0 h,(t,, t2)x(t - +(t G,[h,, x(t)] = Jl - Z2)dtIdtz - P s”h2(t, z)dz 0 G&9 x(t)] = J 7 J h&9 X2’Z&q - zJx(t - z2)x 0 (t - t3)dtldt2dt3 - 31’7 h3(tl, z2, z2)x(t - QdTldt, (2) 0 where P is the power level of the white-noise stimulus; i.e., P = @,,(f) (where f is the frequency in hertz) and Q&(f) is the power spectrum of the stimulus white noise. In practice, of course, Q,,(f) becomes less than P for frequencies much higher than the system bandwidth. The system is characterized functionally by the set of kernels {h,, h,(x), h2(t1, TV), h&r, z2, .}. That is, if we have knowledge of these kernel functions, we are able to describe quantitatively the system response to any stimulus x(t) by carrying out the integration indicated by equation 2 and summing. Each kernel is a symmetric function of its arguments. Kernel ho, a constant, indicates the DC response value to the white-noise stimulus signal and it plays a significant role in the signal processing by the retinal neurons, as we will see later. Kernel h,(z) is the “impulse response” if the system is approximated as a linear system. That is, for example, if the system is linear, the response to a brief flash of light (at the mean intensity level of the white-noise signal) would be given exactly by h,(z) as a function of time t. Similarly, the nonlinear kernels [h2(z1,z2), h& z2, zs) . . .I “crosstalk“ between difquantify the nonlinear ferent portions of the past history of the stimulus as it affects the system response at the present; i.e., how much the response to (two, three . . .) $)’ l l Downloaded from http://jn.physiology.org/ by 10.220.33.3 on June 18, 2017 described here, two light-stimulus patterns were used; a spot of light (0.30 mm in diameter) placed at the center of the receptive field of the neural unit under study, and a concentric annulus of light (0.35-mm inner diameter and 5.0mm outer diameter). Three kinds of stimulation (experiments) were utilized: 1) the spot area and stimulated by annulus area were simultaneously separate light sources whose intensities were modulated by separate, statistically independent, white-noise signa ls; 2) the spot area alon .e was stimulated light signal while bY a white-noise the ann ulus area was kept at dark; and 3) the annulus area alone was stimu lated bY a whitenoise light signal while the spot area-is kept at dark. In addition, in a particular series of experiments, a single input “field” (spatially uniform) stimulus, covering nearly two-thirds of the entire retinal surface, was used (Fig. 1). In this case, the maximum intensity of the light input was similar to that of the spot input and decreased by neutral-density filters. In all two-input experiments the intensity of the annular light was dimmer by about 0.8 log units than the spot light. In some experiments the intensities of two inputs were decreased by interposing neutral-density filters after the two were combined in to one. After the functional identification experiment (through white noise), Procion yellow dye (M4RAN) was injected iontophoretically into the cell by pulses of current (about 10 nA and duty cycle of 0.5) for 30 s. In the earlier part of these experiments the sections were made according to the method described by Matsumoto and Naka (Z?), but later the flat-mount method developed and described in part II was used to detect injected neurons. All pictures of Procion neurons shown in this paper were from radially or tangentially sectioned prepara tions. AND WHITE-NOISE different impulses deviates from the superimposed responses due to each impulse separately. For example, for a second-order nonlinear system (i.e., h, = 0, K > S), kernel h,(t, t - to) denotes this deviation, at time t, from linear superposition (for t > to) between an impulse input at t = 0 and an impulse at t = to. Thus this kernel, in some cases, can be interpreted to signify effects such as saturation, facilitation, refractoriness, etc. Lee and Schetzen (15) showed that the kernels {hi} can be readily obtained through the use of cross-correlation techniques. Specifically, the n thorder kernel would be given by l . . on) = - E n!Pn n- - 1 m= 1 z YW K G,Jh,, 0 x(t)] x(t - 01> . l l x(t - a,) 95 where Pa, Pu, are the power levels of (independent) white-noise inputs x(t) and u(t), respectively. Kernels h&tl, h2e&l, t2) and h2&r1, zZ) z2) (we call them self-kernels) along with h,,(z) and h&), are symmetric functions of their arguments, while h22u(tl, h2,&, t2) (we call a cross kernel) is, in general, asymmetric with respect to its arguments. The cross kernel describes the (second order) nonlinear interaction of the two inputs as it affects the system response, while the self-kernels describe the individual nonlinear contribution of each input to the response. These kernels can be estimated through the use of cross-correlation techniques. They are given by the following equations, where z(t) is either x(t) or u(t) and it has zero mean (18, 21): >(3) where x(t) is the Gaussian white-noise stimulus, y(t) is the corresponding system response, P is the stimulus power level, and E{.) signifies a statistical average over the entire record length, i.e., statistical “expected value” of the quantity inside the brackets. The method was extended to systems with more than one input and output (18, 21). This extension alleviates greatly some of the persistent difficulties in dealing with neural systems, such as the short lives of the experimental preparations over which the identification process must be carried out. As an example, let us consider a system with two inputs, x(t) and u(t), and one output y(t). The two inputs used for the identification are statistically independent Gaussian white-noise processes. Then, hO = ECYW h&j = wP,)E~Ywt h&l h&!&$9 $1 $1 == (1 (1 /q2Y3 /q2Y3 - 41 [r(t) [r(t) - h()W - QP - $)) h&&p 02) Because = (w&p{Yw(t - o&G - 62)) P-9 of the orthogonality of the terms of 5 and the independence of the inputs, it is possible to describe the transfer characteristic due to each input separately. Thus, a twoinput identifying experiment provides the inr(t) = I?4 G,Kh>,~ w 491 (4) formation of two one-input experiments and, in addition, the information about the interaction 7Z=0 between the two inputs. In consideration that where {h}, is the set of kernels of degree n. experimental life times are very limited in the Terms of different degrees as well as those that case of neural systems (in particular in this arise from each input exclusively are mutually study, where both intracellular recording and orthogonal and normalized. The first three terms dye injection are done on the same unit) the of this series are given by two-input characterization through white-noise stimulation is critically efficient. Thus, the sysG,KhlO~x(t), WI = h, tem response to two inputs can be “separated” G,[{h},, x(t), u(t)] = 7 h,&)x(t - t)dt into three components, two of them each de0 scribing the effect of each input to the response 00 and the third describing the interaction between + J h,&)u(t - t)dt 0 the two inputs. This is easily seen from equation 4 and 5 as follows. Without loss of generality we assume that inputs x(t) and u(t) have zero from means (i.e., these signals are measured their average values). Then, if we set u(t) = 0 (i.e., u(t) is constant at its average value) we - pm7 &(t, t)dt easily see from equations 4 and 5 that 0 equation Downloaded from http://jn.physiology.org/ by 10.220.33.3 on June 18, 2017 1 h&r1 ANAM& NAKA, 96 MARMARELIS, 00 Y#) = $h&)x(t - tldz 0 Y,(9 = J h,&>u(t 0 + s”s h2&1’ 0 - ddt QJP - z2)dt,dt, - Q+ - Pu 7 h2&, z)dt (8) 0 Subtracting r,(t) and mu from the total response r(t) we can obtain the interaction signal between inputs x(t) and u(t): v,(t) = r(t) -Y,(t) -Y,(t) which is a measure of the dynamic nonlinear crosstalk between the two inputs x(t) and u(t) (note that this term depends on the product of x(t) and u(t)). In all the catfish two-input (spot and concentric annulus) experiments this term was very small, signifying that there is no dynamic interaction between these two inputs. However, the self-kernels for each input (component) were different for one-input experiments (in which the complementary component is totally absent) and two-input experiments (in which the complementary component is present but equal to a constant, unmodulated DC value). This indicates that there is interaction between the two receptive-field components (as excited by the spot and annulus stimuli) but that this interaction takes place only for DC or very low frequencies. Computational Prior to the execution of a white-noise experiments several preliminary measurements and analyses must be made in order to achieve an optimal functional identification. These include a) choice of the stimulus mean level and amplitude range, b) choice of the stimulus white-noise bandwidth so as to minimize undesirable effects but still evaluate the system over its entire bandwidth, c) measurement of the system “memory” (settling time) to be used in estimating the times up to which the system kernels should be evaluated, d) the number of terms (kernels) to be identified for a desirable accuracy of the system characterization, e) the length of the identifying experiment required by the types of noise, the specific system features (nonlinearities, etc.), and other issues. All these preliminary steps have been described in detail and the experimental and analytical procedures to deal with them established (18, 21). In addition, the effect on the kernel estimates of many types of contaminating noise as well as stimulus deviations from gaussianness and whiteness has been analyzed. For the present studies, a series of preliminary experiments and analyses were made and these parameters were settled and fixed for all subsequent experiments. The mean intensity level in the two-input experiments was about 5 X 10-S pW/mm2 for the spot input and 0.56 X 10-s pW/mrn” for the annular input without attenuation. In the oneinput experiments the mean intensity level without attenuation was the same as the spot input. Generally the mean intensity level of whitenoise inputs was attenuated by interposing the appropriate neutral density filter (Kodak type M carbon), the value of which is given in the text. Naturally the depth of modulation remained constant throughout the experiment. The amplitude range of the input in each case was about 40 to 1. The white-noise bandwidth extended flat from DC to about 100 Hz. The first-order kernels h,(z) were measured up to at least z = 0.4 s and the second-order kernels up to at least z1 = z2 = 0.32 s. For most neural systems the kernels only up to and including the second order were measured. For some neurons the third-order (nonlinear) kernels were also measured, as they contributed significantly to the response. The length of the white-noise experiments varied, depending on conditions, from 10 to 50 s. The data were initially stored on magnetic tape and subsequently transmitted through a special-purpose multichannel A/D converter onto the disc memory of a digital computer (IBM 370/ 135). The large spike discharges present in the recording from ganglion cells were filtered out by selecting appropriate low-pass filters but, as will be seen from the computed kernels, it was not possible to eliminate completely these spike components. The signals (white-noise stimuli and recorded responses) were sampled at 0.00% or 0.004-s intervals, depending on the frequency-response characteristics of each neural system. Subsequently, the stimulus-response data were processed and the Downloaded from http://jn.physiology.org/ by 10.220.33.3 on June 18, 2017 where we have also subtracted the average value of the response (h,) from the data. Thus we obtain by equation 7 the contribution of input x(t) to the response when input u(t) is held at zero (i.e., its constant average value). Similarly we obtain the contribution *of input u(t) to the response AND CHAN WHITE-NOISE system kernels were computed following procedures outlined above (equations 3 and 6) and discussed elsewhere (ref 18, Fig. 3). Evaluation of functional identification 00 Y#) = J h,(dx(t - 4dz 0 is computed (with x(t) the white-noise signal used in the experiment) and its mean square deviation from the experimental response is measured and normalized in the same units. This number gives a measure of goodness of the linear representation of the system as a percentage (since the error of the zeroth-order model is 100 units). The smaller this number, the better is the agreement. Subsequently, the second-order nonlinear response term is computed and the mean square deviation from the experimental response of this nonlinear model Y#) + Y# is computed and normalized in the same units. Thus, a quantitative measure of the system nonlinearity is obtained by comparing this reduction in MSE with that due to the linear kernel alone, in addition to assessing the predictability of the characterization at each (linear, nonlinear) stage. 97 A similar process of MSE measurement is carried out for the case of a two-input system. In this case, in addition to assessing the predictability of the model, the MSE gives an indication of the relative contribution of each input component. For example, with knowledge of MSE for the spot and annular inputs to a bipolar cell, it is possible to assess the relative contribution of each input to the bipolar cell responses (in percent). This is, of course, in reference to the MSE of the zeroth-order model. The MSE (or more exactly the difference between the MSEs of the linear and nonlinear models) is again used to indicate the degree of nonlinearity involved in the generation of responses from a given class of neurons. The spectral density functions (or power spectra) for the inputs and various responses (linear, nonlinear, experimental, etc.) were computed by estimating the autocorrelation function and Fourier transforming it following the various numerical procedures discussed in Blackman and Tukey (4). The spectral density function is a measure of the energy present at each frequency (Hz) in the signal. The relationship between input x(t) and output r(t) and transfer function H(jj of a linear system is where Q(fl and a&f) are the spectral density functions of response r(t) and input x(t), respectively. Since, in our case, the input x(t) is broadband white noise, a,&) = 1 over all frequencies of interest. Then, and therefore the power spectrum of the response is a direct measure of the linear system transfer function. Scaling of kernels Due to computational requirements the input and response signals were multiplied by an arbitrary constant factor, thus scaling the kernel amplitude by a certain constant. However, for a given series of experiments this multiplying factor remains the same so that the relative contribution from each input component (spot or annulus) can be compared. We feel that in the intracellular recordings from smaller neurons in the retina, the absolute amplitude of the kernel is a far less reliable indicator of the neuron functional characteristics than, say, its latency or peak response time. Nevertheless for the linear neurons, the amplitude of the kernels is such that the response was calculated to range between 5 and 15 mV, depending on the class of neurons and recording conditions. Downloaded from http://jn.physiology.org/ by 10.220.33.3 on June 18, 2017 The “model” responses (linear, nonlinear, due to a particular input, etc.) were computed by estimating the integrals depicted by equations 4, 5, 7, 8, and 9 and using the measured kernels. Wiener (49) showed that two systems are equivalent if and only if they respond identically to white-noise input. Consequently, the criterion of “goodness” of the functional identification and predictability of the measured kernels is how well the model response mimics the actual experimental response to the same whiteThis comparison of the noise stimulus. and functional model system experimental (manifested by the measured system kernels) is carried out, in this study, by quantizing the agreement in waveshape of the two responses in terms of the mean square deviation. Consider, for example, the case of a one-input system. The zero-order model (h,) is a constant equal to the average value of the response over the entire record. The mean square error (MSE) for this model is computed and normalized to 100 (arbitrary) units. Subsequently the response, as predicted by h,(z), i.e., ANALYSIS NAKA, 98 Definition MARMARELIS, of terms For the efficient presentation of the results the f&lowing notation and terms are used: h,(t) Orh, h,(t,* t2) Orh, h,(t,, t2, t3>or h, his* h2s %ash2a h2,/a h la/s' h2,/s LM,, LMa NM,, NM, or MR monotonic receptive field biphasic receptive field CHAN underdamped overdamped complementary component (of receptive field) cutoff frequency band pass low pass high-frequency asymptote exhibiting overshoots or undershoots (in response) exhibiting no overshoots or undershoots (in response) “other” of two components (e.g., complementary component of spot is annulus) frequency at which system response starts to attenuate rapidly system response attenuates significantly for both low and high frequencies sys tern response attenuates significantly only for high frequencies and remains rather unchanged for low frequencies rate of attenuation of system response for high frequencies (in dB/octave) RESULTS In this series of experiments, the vertebrate retinal neurons were functionally identified through white-noise stimulation and the subsequent estimation of a small set of kernels for each neuron; in addition, these neurons, in the majority of cases, were also identified morphologically through intracellular dye injection. To avoid any possible bias from morphological clues we classified responses (neurons) based solely on only) functional traits, such as waveform and respectively, nonlinear, linear, polarity of kernels, frequency response and model responses for spot compower contribution of each component, ponent (or annulus component) in two-input (spot and annulus) degree of nonlinearity involved, and preby experiments as predicted dictability of model responses. From these h Is/a and LhIe/a and h2s/al Or functional clues it was possible to classify h and [hl /s and h2a/J about 75a/, of the neurons (responses), extl?%onlinear qnteraction model cept the receptors, into five distinct types: response as predicted by has in a two-input experiment two of them were identified as the horiresponse in a onetotal model zontal and bipolar cells while the remaining or two-input experiment (i.e., three could not be correlated to well-desum of NM,/,,NM,,,, and fined morphological types. To avoid any N"aJ mean square error deviation of structural implications we will refer to model iesponse (cf. section on them simply as types N, C, and Y responses evaluation of functional identi(neurons). All these three types were refication) corded from neurons in the proximal parts receptive field of a neuron for of the retina. which a stimulus anywhere in field evokes rethe receptive As discussed in METHODS, the functional sponses of same polarity in cell identification of each neuron by a two-input potential (e.g., receptive field of (spot and concentric annulus) white-noise horizontal cells) experiment results in a set of six kernels for receptive field of a neuron for which center (spot) and surthis neuron: ho, h Is/a(t)9 h2s/a( h, t2)9 hla/f3(t)p round (annulus) stimulation h2a,s(tl, t2), and h,(tI, tz>. These kernels evoke responses of opposite poare interpreted as: kernel ho (the zerolarization in cell potential (e.g., order kernel) is simply the average value receptive field of bipolar cells) Downloaded from http://jn.physiology.org/ by 10.220.33.3 on June 18, 2017 h Is/a DC or zero-order kernel linear or first-order kernel quadratic or second-order kernel or second-order nonlinear kernel cubic or third-order kernel or third-order nonlinear kernel first- and second-order kernels in one-input experiments with spot only stimulus first- and second-order kernels in one-input experiments with annulus only stimulus firstand second-order (self) kernels for spot component in two-input experiments and second-order (self) firstkernels for annular component in two-input experiments crosstalk in two-input experiments representing dynamic interaction between two spot and annulus inputs linear model response (as preexdicted by h, in one-input periments) (LM, for spot only, LM, for annulus only) nonlinear model response (as predicted by h, and h2) in oneinput experiments (NM, for annulus spot only, NM, - for AND WHITE-NOISE P- h,,,,.,(t), if linear h,,,(t) +bs/a if nonlinear (1,,1), hrojs (11, if linear -;1,AVERAGE ---m-e--t DARK I J t- h,/,(t) + b,,r(trt), if nonlinear FIG. 2. Schematic representation of the two-input white-noise experiment in which the set of kernels predicts the r&ponse of the system to an impulse input which is superposed on the DC i .nput whose amplitude corresponds to the average mean intensity input, while the 0th .er input of the white-noise is held at a DC level which corresponds to the average mean intensity level of the other white-noise input. 99 indicates that there is interaction between these two receptive-field components but that this interaction takes place only for DC or very low-frequency signals. Naturally, because of the limited duration of a white-noise experiment (and record) the kernels do not reflect this very low-frequency behavior. The average length of the white-noise records analyzed in this experiment were 15-25 s for horizontal, bipolar, and type N neurons and 2045 s for types C and Y neurons. Although longer records were desirable for a more accurate kernel computation, the need for performing three sets of white-noise input experiments and injection of the dye into the same neuron limited the practical length of each white-noise experiment. Horizontal cells In part I of this study (24) we showed that there are three subclasses of horizontal cells in the catfish retina: external, intermediate, and internal All these three subclasses of horizontal cells produced slow, hyperpolarizing responses to photic stimuli. Examples of Procion dye-injected horizontal cells are shown in Fig. 3, in which the external and intermediate horizontal cells are shown in radial sections and the internal cell in a semitangential section. As we have already mentioned in part I, the three horizontal cells share morphological features common to those found in other fish (11, 14, 40). In this part, the analysis will be limited to the external and internal horizontal cells because the frequency response of the intermediate horizontal cell is so slow that within the normal length of 15-25 s of the white-noise test, the power content in the low frequencies was so limited that this neuron seemed to produce only sustained (DC responses (cf. ref 14)). A typical response of an internal horizontal cell to a two-input (spot and concentric annulus), white-noise stimulus is shown in Fig. 4 in which record A is by a white-noise input of unit average intensity (0 log), while record B is by a similar input whose average intensity and also depth of modulation are decreased by 0.8 log units. Some of the nonlinear characteristics of Downloaded from http://jn.physiology.org/ by 10.220.33.3 on June 18, 2017 (DC) of the response to the white-noise stimuli. Kernel hlSia (the linear spot kernel in the presence of an annular white-noise input) is the impulse response of the best linear system approximation if an impulse is delivered to the spot input while the annular input is kept constant (unmodulated) at its average value, as shown schematically in the upper diagram in Fig. 2. In other words, it denotes the linear responses of the neuron if a brief flash of light is given on top of the average intensity of the spot white-noise signal, while the annulus of light is kept at a constant value equal to the average intensity of the annulus white-noise signal. Similarly, the annular first-order kernel is the best linear response of the system to a brief flash of light superposed on the constant input in the presence of similar spot input, as shown in the lower diagram in Fig. 2. The nonlinear crosstalk kernel, h,,, for all the two-input (spot and concentric annulus) experiments in the catfish retina was of the model very small; i.e., improvement performance by the interaction (model) response, NM,,, was always less than 3%. This signifies that, for this stimulus configuration, there is no dynamic interaction because of changing signals between these two receptive-field components as excited by the spot and annulus of light. However, the “self-kernels” for each input were quite different for one-input experiments (in which the complementary input stimulus is totally absent or kept at dark), and twoinput experiments (in which the complementary input is present but equal to a constant, unmodulated, DC value). This ANALYSIS 100 NRKA, MARMARELIS, the external and internal horizontal cells have been described previously (19, 20). There, it was shown that these cells are fairly linear and act essentially as low-pass filters. In this paper we describe the response characteristics of the horizontal cells in order to facilitate a comparison with similar responses from other types ot neu- CHAN rons in the retina. Specifically, tile analysis has been pcr-lorrnctl on all cells which were identifietl morphologically through intracellular dye injection. As seen frorn records in Fig. 4, the horizontal cell responses were characterized by a large IX component on which modulation due Co white-noise was superposed; the horizontal cells were responding mainly to the rnagnitutle and less to the faster changes of the level of input signal. As already noted, the horizontal cells are essentially low-pass filter devices wllicli detect the DC level of the input signal. This characteristic of the horizontal cells, together with the fact that they form a monotonic receptive field, enabled Naka and Kushton (30) to derive the log-stimulus intensity versus resl)orise-;~~~l~~lit~~~fe curves (V-log I curve) and show that the relationship between these two quantities is the tanh-log curve. ‘I‘his relationship has since been found as a general stimulus-response transfer characleristic in the horizontal and receptor cells, which equally exhibited the low-pass filter characteristics (1, 3, 6). However, as will be discussed lacer, any conclusion drawn from a similar analysis on neuron responses exhibiting a bandpass frequency charactcrislic (a transient response) must be interpreted carefully. The four first-order (linear) kernels shown in Fig. 5 wcrc computed from the data shown in Fig. 4 which were obtained from an internal horizontal cell; curves 1 and 2 are hIr,:, and h,:,,, at 0 log mean intensity, while curves 3 and 4 arc the corresponding kernels from the same neuron at -0.8 log units rnean intensity. From these kernels we observe the following traits of the horizontal cell responses: I) The annular response component, as exhibited by lilt,,,, is much larger than the spot component L/w a fact which can be predicted from the assumption that the horizontal cells form a laminar layer (or S space) of low intercellular resistivity (17, 30, 37). However, the relative amplitude of the spot. component was larger in the external cells than in the internal cells due to a difference in spatial decay characteristics of the two types of cells (17, 37). 2) The annular kernels are slightly underdamped. 3) The latency and peak response time become shorter as the average intensity of the in- Downloaded from http://jn.physiology.org/ by 10.220.33.3 on June 18, 2017 FIG. 3. Procion dye-injected horizontal cells seen in the radially sectioned preparations. A: external; B: intermediate; C: internal horizontal cells. In C the section was at some angle to the radial plane to show the larger part of the cell. Responses shown in Fig. 4 were recorded from the cell shown in C in this figure. R, receptors; EH, external horizontal cells; IH, internal horizontal cells; and ISL, inner synaptic layer. AND WHITE-NOISE ANALYSIS 101 put signal is increased; i.e., at higher intensities the response becomes faster. At 0 log average intensity the latency was 25 ms and the peak response time was 70 ms. At a given intensity and under similar adaptation conditions those parameters of the horizontal cell h, were surprisingly consistent and they did not differ significantly from cell to cell, a conclusion which is consistent with our hypothesis that the horizontal cells form a laminar layer, a structure which would tend to minimize individual cell differences (see APPENDIX). This observation is in contrast with the responses from other types of cells which showed a large variation in the response parameters although all responses were recorded under similar experimental conditions. Two sets of horizontal cell response power spectra from the same unit are shown in Fig. 6, one obtained at 0 log (A) and the other at -0.8 log (I?) average intensity. These spectra were calculated from the responses ihown in Fig. 4 and the kernels of Fig. 5. In the figure are shown the power Frequency 5. First-order kernels from the horizontal cell response in Fig. 4. Trace 1 for h,s,a and trace * for hl,El are for 0 log unit, while trace 3 for h,s,a and trace 4 for hra,s are for -0.8 long units mean in tensi ty level. Ordinates are for volts/(photons/ mm2). Upward deflection is for hyperpolarization of the membrane potential. The amplitude of the kernels with log filters was scaled down by the value corresponding to the optical density of the filter? FIG. (Hz) FIG. 6. Power spectra of the horizontal cell responses shown in Fig. 4. Power spectra in A are for the upper record A in Fig. 4, and power spectra in B are for the lower record B in the figure. Curves are so scaled that the power level of the system response, R, in A is approximately at 0 dB. R, system response; MR, model response; LM, and NM,, linear and nonlinear model responses for the annular input; and LMs and NMS, linear and nonlinear model responses for the spot input. For definition of terms refer to the text, Downloaded from http://jn.physiology.org/ by 10.220.33.3 on June 18, 2017 FIG. 4. Oscilloscope recording of the response from the internal horizontal cell to two-input white-noise stimulation. Record A was by 0 log unit and B by -0.8 log units average mean intensity. In this and all subsequent oscilloscope recordings the lower traces are the white-noise signals for spot and annular inputs. Amplitude of the response in A was about 40 mV. Upward deflection is for hyperpolarization of the membrane potential. NAKA, 102 MARMARELIS, spectra of a> the system experimental response, R; b) the system model response, MR, as predicted by hlB,B, h18,s, h2a,s, and h 2s/a; c) the model response of the annular component:linear (LM,) by hl,,, and nonlinear (NM,) by hl,,, and haa,s; and d) the model response of the spot components: linear (LM,) by hl,,a and nonlinear NM, by b/a and h29/a. CHAN more direct experiments turtle retina (3, 10). Bipolar reported in the cells As already described in part II (28), the catfish bipolar cells produce only slow potentials, an observation similar to that already made in other vertebrate retinas (11, 12, 22, 43, 46, 48). In contrast with the horizontal cells, which have a monotonic receptive field, the catfish bipolar cells form a field which is referred to as a biphasic receptive field; i.e., the spot and concentric _ annulus of light give rise to responses of opposite polarity (part II). Responses from two bipolar cells to twoinput white noise are shown in Fig. 7 in which one produced a hyperpolarizing, Bb (A>, and the other a depolarizing response, Ba (B). The former cell is apparently what is known as an off-center bipolar cell and the latter cell an on-center bipolar cell (11, 12, 43). As in the horizontal cells: bipolar cell responses have a DC response component on which modulation due to the whitenoise input is superposed. In some bipolar cells we observed a large on-transient due to the response of the cell to a sudden increase in the level of input, practically the same on-response having been observed with a step input. In others these initial transient responses were less prominent (Fig. 7A), while in still others no such initial transient l FIG. 7. 2 set I Oscilloscope recordings of responses from two bipolar cells to white-noise inputs. One off center cell response in A and the other on-center response in B were recorded from the bipolar cells shown in Fig. 1OF and H, respectively. In B the bandwidth of the white-noise inputs is limited to 10 Hz. The amplitude of the response in both A and B is approximately 10 mV. Upward deflection is for hyperpolarization of the membrane potential. Average mean intensity, -0.8 log units. Downloaded from http://jn.physiology.org/ by 10.220.33.3 on June 18, 2017 A decrease of the average mean intensity level by 0.8 log units resulted in a decrease of the response power level by 10 dB and the cutoff frequency shifted from 12 to 8 Hz. At the same average mean intensity level, the common response characteristics as seen from these power spectra are that: I) Agreement between experimental and model power spectra is extremely good (MSE of about 10%) indicating the small amount of noise present in the system. 2) The system is a low-pass filter and has a highfrequency attenuation at about 24 dB/octave of frequency; for the stimulus of less than 3 Hz the system gain is almost constant. 3) The responses are dominated by the annular component as seen by close agreement between the power spectra of the total response and those of the annular component. These observations, made on the horizontal cell power spectra, augment as well as confirm the similar observations made on the system response (Fig. 4) and the system kernels (Fig. 5). Practically the same results have been obtained from the external horizontal cells even though the gain of the spot component increased in the presence of the annular input as already described in a previous paper. This analytical study suggests that such an increase in the gain of the spot component is due to an increase in the space decay constant of the potential in the laminar structure formed by the external horizontal cells (17). Another feature of the horizontal cell response is the speeding up of the spot component in presence of the annular input (20). We have hypothesized that this is due to the feeding of the horizontal cell potential back to the receptors in order to improve the frequency response of these initial stages in the processing of the visual signal. This hypothesis is in accord with results of AND WHITE-NOISE FIG. 8. First-order kernels from the bipolar cell which is shown in Fig. 1OC. One set of kernels are from two-input and the other set are from oneinput white-noise stimulation performed on the cell under the same experimental conditions. Trace 1 is h la,s; trace 2, h,,,,; trace 3, hlB; and trace 4, h,,. Average mean intensity level is - 0.8 log units. All four records are scaled by the same factor and ordinates are for volts/(photons/mm2). Upward deflection is for hyperpolarization of the membrane potential., 103 presence of a constant spot input). These four kernels, obtained under the same experimental conditions, indicate the following characteristics of the catfish bipolar cell responses: I) The hl’s are only slightly underdamped, suggesting that bipolar cells, like the horizontal cells, detect mainly the level of the stimulus signal. 2) The annular kernels (Fig. 8, traces 1 and 4) have both longer latency (40 ms for annular response versus 24-30 ms for spot response) and longer peak response time (80 versus 70 ms). 3) In the presence of an annular input, both the latency and peak response time of the spot hI (Fig. 8, trace 2 versus trace 3) becomes shorter but no such speed up of the annular kernel is observed in the presence of the spot input. 4) The amplitude (and, therefore, the dynamic gain) of both the spot and annular kernels becomes larger in the presence of the complementary member of these two inputs (Fig. 8, trace 1 for annulus and trace 2 for spot). 5) The amplitude of the spot kernels (traces 2 and 3) is comparable to that of the annular kernels (traces 1 and 4) but the polarity is opposite, an observation which is characteristic of the bipolar cell kernels and which is in sharp contrast with the horizontal cell kernels for which the amplitude of the spot hl is much smaller than that of the annular hl, but of the same polarity (Fig. 5). The response power spectra of one of the slower bipolar cells are shown in Fig. 9. They are the power spectra of the experimental response (R), of the spot NM,,, and annular NM,,, components in the two-input experiment and of the spot and annular experimental responses in the one-input experiments. In a large number of spectra obtained from bipolar cells we note the following frequency-response characteristics of the bipolar cells: 1) Some have a low-pass characteristic while others exhibit a band-pass characteristic (corresponding, respectively, to the “slow” and “fast” bipolar cells) but they do not segregate into two well-defined groups. 2) Both the spot and annular response components increase their gain in the presence of the complementary member of these two inputs. 3) In the presence of the annular input, the frequency response of the spot component t Downloaded from http://jn.physiology.org/ by 10.220.33.3 on June 18, 2017 be observed (Fig. 7B). In some of the published records from bipolar cells a similarly large transient response could be seen (cf. Fig. 2, ref 43). The response characteristics of the catfish bipolar cells are not at all consistent and a considerable variability was observed: some bipolar cells had very fast-frequency responses (as judged from the latency of h1 and the cutoff frequency of their response power spectra), while others were very slow. Although the most obvious explanation is that the former responses are from the smaller (cone) bipolar cells and the latter ones are from the larger (rod) bipolar cells, the dye-injection results could not confirm or deny this possibility. In part II (28) we have shown that all the catfish bipolar cells had a biphasic receptive-field organization in which a spot of light and concentric annulus of light produced responses of opposing polarity. It further was observed that when the two inputs were given together, the DC response level was set somewhere between the two DC response levels produced either by a spot or by an annulus of light alone (part II, Fig. 1C). Toyoda (43) reported a similar observation in a teleost retina, that of the carp. The first-order (linear) kernels of a bipolar cell, as evaluated from these stimulusresponse data, are shown in Fig. 8. They are: h,, (spot stimulus alone), hl, (annulus stimulus alone), hlgia (spot component in the presence of a constant, DC, annular input), and l&/s (annular component in the could ANALYSIS NAKA, FIG. 9. responses. are shown Hz Power spectra for the bipolar cell Power sp&tra of the white-n&se inputs as annular and spot and are flat up to 5o IGo Itspot + annulus’ Rspor and RanIlulus indicate the system responses to three stimulus modes, spot and annulus &en together (two input) or spot or annulus given alone (one input). NMa and NM8 responses for the annular and are nonlinear model spot inputs in two-input experiments. Notice the appreciable increase in the power levels of the spot and annular responses in two-input experiments compared with the power levels of the two responses in one-input experiments. For definition of terms see the tekt. Curies are all scaled by the same factor so that the power level for the two-input system response is close to 0 dB. shows an im provemen t; a similar effect is not observed for the annular corn ponent. @Ve have already reached the same conclusion by observing the first-order kernels.) 4) In the particular bipolar cells analyzed in Fig. 9 the difference in the power levels of the spot and annular components is about 4 dB at 5 Hz, while in the horizontal cells the corresponding difference is about 12 dB. 5) The bipolar response power spectra have a steep asymptote (about 2430 dB/octave) and no high-frequency component is present. Of the observations made above the most interesting is the increase in the dynamic gain of each component response in the presence of the complementary member of the two-input stimulus; no other types of retinal neurons showed such a mutual enhancement of the two components. In the horizontal cells, Marmarelis and Naka (17) have observed an increase in the gain of the spot component in the presence of an annular input, but not vice versa, and in other neurons, as will be described later, mutual depression was commonly observed. AND CHAN In part II (28) we showed that, in the catfish bipolar cells, the step responses to (low intensity) spot and annulus inputs had opposite polarities and that when two inputs were given simultaneously, the DC level of the resulting response was settled somewhere between the two opposi te-polarity DC levels resulting from stimulation by each input alone (part II, Fig. 1C). In interpreting the self-kernels (hl,/B, hl,,,, etc.) of the two-input white-noise experiments we noted that the complementary input (e.g., the spot for hl,,,) can be treated (as seen from the other input) as a DC input whose amplitude is the average mean intensity level of this particular input, a fact illustrated in Fig. 2. This is a direct consequence of the orthogonality of the response terms arising from the two inputs. For example, hl,,, is the annular (linear) kernel describing the dynamics of the annulus contribution to the response resulting from modulation at the mean intensity level of the annular white-noise signal, while the input to the spot is a constant (DC) light equal to the mean intensity of the spot white-noise signal. Thus, in the bipolar cells, the effect of the complementary input (due to the presence of white-noise stimulation) in the two-input experiments, is to bring the DC level of the cell potential closer to the resting (dark) level. We also note that the bipolar cell response to a spot or an annulus of light, when given alone, has a very small dynamic range and the response shows an amplitude saturation even with a small increase in the stimulus intensity (13, 45, 46). The increase of the dynamic response gain in the two-input experiments can best be interpreted as due to a shift of the operating point (DC response level) of the bipolar cell from points near the saturation level back toward the middle of the range (near the dark level). By analyzing the ganglion cell discharges resulting from extrinsic polarization of the horizontal cells, Naka and Nye (27) and Naka and Witkovsky (31) have concluded that both catfish and dogfish bipolar cells must be comparing two signals, a local signal coming from the spot (center of receptive field) and an integrating signal coming from the annulus (surround of receptive field). Similarly, Marmarelis and Naka (17) Downloaded from http://jn.physiology.org/ by 10.220.33.3 on June 18, 2017 Frequency, MARMARELIS, IVHITE-NOISE 105 teristic of the bipolar cells With their dendrites in the outer synaptic layer and with their axons in the inner synaptic layer. We also note that some of the bipolar cells have their smaller and round somata in the proximal layer of the inner nuclear layer while some others had their larger vaseshaped somata in the proximal layer of the inner nuclear layer. So far, we have not been able to correlate such morphological subclasses to functional subclasses. The results obtained from the bipolar cells lead us to conclude that those neurons with biphasic receptive-field organizations FIG. 10. Examples of Procion dye-injected bipolar cells on which white-noise analysiswas performed. All neurons are seen in the radial section. In E, a receptor, probably a cone, is also stained although injection was limited to the bipolar cell. Letters D and A are for dendrites and axons. Downloaded from http://jn.physiology.org/ by 10.220.33.3 on June 18, 2017 have concluded from white-noise analysis of the horizontal and ganglion (spike) cell responses that the following relationship must exist: (bipolar cell response) E (horizontal cell input) - (receptor cell input). Thus, the present results of the nonlinear analysis on the bipolar cells give further and more direct evidence to support this conclusion drawn in previous studies. Examples of Procion dye-injected neurons of the type classified functionally as bipolar cells (from the functional traits described above) are shown in Fig. 10. We note that these neurons exhibit a geometry charac- ANALYSIS 106 NAKA, MARMARELIS, in which the two subfield components are mutually enhancing, are the class of ncurons known as bipolar cells, and that those neurons which do not exhibit such functional characteristics are not bipolar cells. This conclusion is substantiated further by the results we described in part II (28) of this series. AND CI-TAN Neurons whicll l~orlucetl this type of rcsponse generally had their somata in the proximal region of the inner nuclear layer (INL) and a principal dendrite descended down lo the inner synaptic layer (ISL) where longer dendrites were seen spreading laterally through the layer (Fig. 11). In some Downloaded from http://jn.physiology.org/ by 10.220.33.3 on June 18, 2017 11~. 11, Protion tl!e-idcntilictl cvamplcs of type N ncuxon~ scrn in radial srctions. A, IS, and C are typical type N neurons with their somata in the INL with a descending principal dcndritc from which $plcatl the holirontal dcndritcs. Although the flat-mount views arc not axailablr, the shapes of the principal dendrites suggest that A and C arc probably the starbmst type\ and B, a thick spaghetti type in part I (24). Neuron I; has its soma in the INL, but its principal tlcndritc i? much thinner and a lateral process takes off directly from the soma. Neuron D has its soma in the ISI,. Neuron I; is classified as type N from white-noise analysis but its morphological trait is that of a spindle-shaped ganglion cell. Among this nemon ‘L\BS the only cxccption. 25 type N nrulons identified by dye injection, WHITE-NOISE B Oscilloscope recordings of responses FIG. 12. from types Na, shown in A, and Nb, shown in B, neurons to two-input white-noise stimulation. Amplitudes of both responses are about 15 mV. Upward deflection is for hyperpolarization of the membrane potential. Average mean intensity, 0 log unit. 107 , 0.1 set , FIG. 13. First-order kernels from type Na shown in A and Nb shown in B neurons which are shown in Fig. 11B and F, respectively. Two sets of kernels, one set from two-input experiment and the other set from two one-input experiments, are from the responses recorded under the same conditions. In A traces 1 and 3 are hla/s and h,,, and traces 2 and 4 are hls,a and hrs. Note the complete suppression of his in the presence of the annular input. In B, traces 1 and 3 are hla,a and hr8, and traces 2 and 4 are hlR/8 and h,,. In both records responses are scaled by the same factor with ordinates as volts/(photons/mmz). Upward deflection is for hyperpolarization of the membrane potential. Average mean intensity, 0 log unit. form and amplitude of the annular kernels are little affected by the presence of the spot input. The spot kernels, on the other hand, are slower latencywise and peak response timewise and they are overdamped. In the type Na neurons, the presence of the annular input completely depresses the spot response component, as shown by curve 2, h Is/a, in Fig. 13A; while in the type Nb response, the presence of the annular component increases slightly the spot response, as shown by curve 3 in Fig. 13B. The latenties of the annular and spot responses are 25 and 35 ms and peak response times are 65 and 85 ms, respectively. The MSEs of Na and Nb model responses, as predicted by the system kernels in Fig. 13, are tabulated in Table 1. They indicate: 1) Types Na and Nb responses are linear either for one- or for two-input Downloaded from http://jn.physiology.org/ by 10.220.33.3 on June 18, 2017 neurons the principal dendrite was very short and in others it was long. The latter type of neurons corresponds to those classified as the spaghetti type (part I (24), Fig. 6E-H) and the former to the starburst type (part I, Fig. 5). However, exceptions could be found and some of those neurons classified as type N had their somata in the ISL with their lateral dendrites spreading throughout the layer (see part II (28), Fig. 4) . Responses from the type N neurons are always depolarizations (type Na) or hyperpolarizations (type Nb) of the membrane potentials. Examples of types Na and Nb responses are shown in Fig. 12 in which we observe that the responses, regardless of their polarity, are composed of a small DC component on which modulations due to the white-noise input are superposed. Lack of a high-frequency component in the response indicates that spike activities or regenerative slow potentials are absent in this system. Thus the responses from type N neurons are strikingly similar to those from the bipolar cells shown in Fig. 7. In part II we have already noted that the step responses of the type N neurons were very similar to those from the bipolar cells. Figure 13 shows the four first-order kernels of types Na and Nb neuron responses; hl,, hlsr hla,s, and hl,,, were obtained by the three standard white-noise stimulus modes. We note that the annular kernel, whether obtained by single or twoinput stimulation, are either depolarizing or hyperpolarizing and underdamped. This suggests that the annular component of this system responds to changes in the annular signal (slightly differentiating). The wave- ANALYSIS 108 NAKA, MARMARELIS, AND CHAN TABLE 1. MSEs for model responses predicted from Na and Nb neurons by sets of kernels Two-Input Annulus and Spot One-Input N”da and Na Nb Values are L”s/a L”a/f3 99 86 35 31 percentages. For spot MR NMa/t3 definitions terms 2 Summary of MSES for see the 18 29 Type C neurons (response) In part II (28) of these series, it was shown that, in the catfish retina, there is a class of neurons which give rise to transient in this paper Improvement and External horizontal Internal horizontal Ba Bb Na Nb C Y Values 90 k 6 95 & 3 57 2 47 t 91 & 94*3 92 z!z 92 t are percentages. 2 12 5 4 7 15 t MR L”Zl,S 6 20 28 power spectra of these responses, as shown in Fig. 14. We note, in addition to the points made above, the following: I) In the two-input experiment the system exhibits a low-pass characteristic with a small peak at 4 Hz. 2) In the one-input experiments the annular response shows something of a band-pass characteristic, while the spot response shows a low-pass characteristic (Fig. 14B). 3) In the presence of the annular input the power level of the spot response is depressed to nearly 20 dB below the level of the response to a spot input alone (Fig. 14A, NM, and B, RPOt). Thus, in summary, the functional traits of the type N neuron (response) are in marked contrast with those of the bipolar cells in which the annular and spot components have opposite polarity (biphasic receptive-field organization), and these two components are mutually enhancing. catfish neurons obtained L”a/B 18 32 text. L”S,a L”8/a MR L”a 12 2 4 11+5- 9&3 lo&3 12 62 k 2 68 + 8 31 ;8 27 2 6 91+5 57-t-11 25 + 25 : 30 2 26 & 84 + 51211 6 7 6 6 5 -+ 1924 20 + 2725 23 2 46k 33 & bY h, 2 4 6 12 8 No. of Neurons 1 7 6 4 3 3 38 18 5 20 8 11 13 37 7 -2 -- Downloaded from http://jn.physiology.org/ by 10.220.33.3 on June 18, 2017 stimulation because of the improvement in the performance of the model response by the introduction of the second-order model response (computed from h,‘s) is less than 6%. 2) In the two-input experiment the response is largely due to the annular component, particularly in the type Na response. 3) The introduction of the interaction term (NM,,) or the difference in MSES between (NM,,, + NM,,, and MR) improves the predictability by less than 3%, indicating the absence of any significant dynamic interaction between the two inputs. As seen in Tables 1 and 2, the MSEs of the model responses from the type N neurons, therefore, are comparable to those of the linear and more distally located neurons, such as the bipolar and horizontal cells. It is interesting that neurons which belong to the ISL have a linear characteristic, a strong indication of the absence of any regenerative activity. The functional traits of the type Na response, as observed from the first-order kernels and also from the performance of the model responses, are confirmed in the TABLE 16 35 24 of MR L”s 28 30 25 Annulus WHITE-NOISE I 2 FIG. 14. Power System responses terns, one two-input bY R4qmt + annulus’ 5 IO Frequency 0-k) 20 50 spectra from a type Na neuron. to three standard stimulus patand two one-inputs, are shown Rf3pot’ and Rannulus* MR* mode1 response; NM,, nonlinear model response for the annular component in two-input experiment. NMR, similar model response for the spot component. Responses are scaled by the same factor to bring the power level of the system response to two-input stimulation close to 0 dB. Note the absence of any high-frequency component as seen from the steep asymptotic slope and also the depression of the spot component in the two-input experiment. on-off responses very similar to those obtained from a class of neurons identified as amacrine cells in the mudpuppy (47, 48), carp, and goldfish (11, l&44). In a majority of cases, the somata of those neurons giving rise to type C responses could be found in the proximal regions of the INL. In part II we reported that this response originated from the spindle-type neurons (part II, Fig. 6). Examples of Procion dye-injected type C neurons are shown in Fig. 15 in which three neurons (A, 23, and C) fit the morphological critera proposed in part II for the neurons which produced transient depolarizing responses. Two examples of type C responses to 109 white-noise input are shown in Fig. 16 in which A shows the response including the initial transient and B is a part of the response from another unit. We observe that the response is composed of high-frequency transients and no DC component. We also notice that some of the transients are much larger in their amplitudes relative to others, suggesting a strong nonlinearity in the system. In the type C neurons, spike discharges can be seen occasionally to superpose on the depolarizing phase of the response, but such cases are the exception rather than the rule. Although not so conspicuous, a closer observation of B in Fig. 16 reveals the presence of spike discharges of very small amplitude. Type C responses produce consistently very small and noisy h,‘s and two such examples are shown in Fig. 17. These noisy first-order (linear) kernels indicate that the response is highly nonlinear (as we have already noted from the records in Fig. 16) and that this type of neuron is responding to more complex stimulus parameters than those taken care of by a linear transformation., On the other hand, the type C responses produce consistent and characteristic nonlinear kernels h,; four such examples are shown in Fig. 18. We note that the secondorder (nonlinear) kernels of type C neurons have a large negative peak on the diagonal at about 65 ms and two off-diagonal positive peaks at t1 = 65 ms, and t2 z 130 ms. In consideration that hI is very small, the second-order kernel is interpreted as follows: two pulses of light given in close succession (within 50 ms) would produce, 65 ms later, a negative (depolarizing) response, whereas, if the two pulses are separated by about 65 ms, they would produce, 65 ms after the occurrence of the second pulse, a positive (hyperpolarizing) response. Strictly speaking, of course, these responses due to h2 are in addition to the responses (to the two pulses) due to h, (but h1 is very small in this case, as we have seen). Although the positions of the peaks in h2 are slightly different among type C neurons, the number, size, extent, and relative locations of the peaks are very consistent and can be used as a reliable functional identifier (a signature) of type C neurons (responses). The responses from a type C neuron to annular white-noise inputs, together with Downloaded from http://jn.physiology.org/ by 10.220.33.3 on June 18, 2017 B ANALYSIS 110 NAKA, MARMARELIS, AND CHAN the predicted model responses, are shown in Fig. 19, in which are also shown photographic records from a part of the response from the same neuron (but not the same L 2 set I Oscilloscope recordings of the type C responses to two-input white-noise stimulation. Neuron A did not produce any spike discharges but neuron 13 had small spike discharges. Record B is a portion of an experiment approximately 10 s after the beginning of the white-noise stimulation. In both records the largest transient peak is about 20 mV. IJpward deflection is for hyperpolarization of the membrane potential. Average mean intensity, 0 log unit. FIG. 16. portion). As we have already mentioned, the response of the type C neuron is characterized by the presence of large, discrete de- FIG. 17. First-order kernels from two type C neurons; one of them, B, is from the same neuron which is shown in Fig. 19. Traces 1 through 4 are h la/s’ hld hls,a’ The scaling of kernels is and his. such that their amplitude is expanded approximately 10 times compared with kernels from other neurons such as those shown in Figs. 8 or 13. All traces are scaled by the same factor with the ordinates for volts/(photons/mmz). Upward deflection is for hypcrpolarization of the membrane potential. Average mean intensity, 0 log unit. Downloaded from http://jn.physiology.org/ by 10.220.33.3 on June 18, 2017 Procion dye-identified examples of the type C neurons. Neurons A and B arc seen in the radial FIG. 15. sections. Note that in A the soma has a shape of a fish with a descending process, P, giving the neuron a bistratified dendritic field. Neuron B showed a descending dendrite arising from its soma. In C and D neurons are vicwcd in tangential sections (not in flat mount). Neuron C has the characteristic spindleshaped soma, but that of neuron D is more round. In both neurons the dendrites extend horizontally from the somata which are in the INL. Due to the tangential sectioning, any possible bistratified dendritic structure is not seen. WHITE-NOISE oy + ANALYSIS T, (msec) $4 + 158 + I?2 o + 111 T, (msec) 6,4 58 + + ‘9? + 226 B l 1 -0 6? + l 128 + ~ 192 + Of + 6,4 + ‘2+8 + 19+2 + 2?6 1921 Type FIG. 18. Four second-order positive peaks which are seen axes are in milliseconds with ANNUAL SYSTEM RESPONSE hl, MODEL h2 CH?DER MODEL hl, h2,h3 CRT h, (T,,T~) Note the characteristic from type C neurons. Kernels are for annular input in two-input scaled by volts/(photons/mm2)? INPUT 2nd ORDER 3td (self) kernels in the kernel. units of ha’s C response: RECORD System and model responses from a type FIG. 19. C neuron to annular white-noise input. Model responses are computed from sets of kernels shown in the figure. For detail see the text. Upward deflection is for hyperpolarization of the membrane potential. The oscilloscope recording is from the same neurons but not from the same portion of the record used Peaks of the response are for white-noise analysis. about 20 mV. negative experiments and and polarizing responses which are evident in the records shown in this figure. The linear model (predicted by h,) of the type C neurons performed poorly, as expected from the noisy first-order kernels, two examples of which are shown in Fig. 17, and the MSE of such a model is of the order of SO-90% (for average figures see Table 2). The introduction of the secondorder nonlinear term improved the predictability of the model considerably (with a MSE of about 45%); still the performance of the second-order model is not satisfactory when compared with the system response (Fig. 19). The addition, however, of the third-order nonlinear term reduced the MSE of the model response to 15-20%, the main improvement seen as a sharpening of the large depolarizing transient peaks which are characteristic of the type C response (Fig. 19). The fact that a third-order nonlinear term has to be introduced to describe the Downloaded from http://jn.physiology.org/ by 10.220.33.3 on June 18, 2017 256 112 NAKA, MARMARELIS, Type 1’ neurons (responses) Neurons (responses) classified functionally as type Y exhibit the following characteristics: 1) they produce well-defined linear kernels, and 2) they have a large secondorder nonlinearity. Those responses classified as type Y, based on these two criteria, originate from neurons of various morphological types (as could be expected from the great morphological variation of neurons in the proximal region of the retina). Examples of typical type Y neurons in the Procion preparation are shown in Fig. 20 in which we observe that the somata of the type Y neurons lie close to the inner limiting membrane or in the layer of the classical ganglion cells. Some of the type Y neurons are observed having round somata in the flat-mount preparations, suggesting that they correspond to one of the polar (ganglion) cells described in part I (24); other type Y neurons have elongated and more complex somata. Oscilloscope recordings of the type Y responses are shown in Fig. 21 in which three examples are shown; in the first example, shown in A, the neuron produces a spike discharge of large amplitude (about 30 mV); in the second example, shown in B, the amplitude of the spike discharges are less than the amplitudes of the postsynaptic potentials; and in the third example, shown in C, the amplitude of the spike discharge is very small and barely visible in the record. It was often observed that penetration of the electrode resulted in a gradual loss of the spike activity without any apparent effect on the slow potential activity of the CHAN impaled neuron. Rarely did we encounter type Y responses without any trace of spike activity. As we have already discussed in parts I and II, the amplitude and/or time course of the spike discharge is not thought to be an indication of the type of neurons, but rather depends on such incidental factors as the distance between the spike-generating site and tip of recording electrode. In part I, we showed that in some neurons the axons took off from one of the principle dendrites, some distance away from the soma. In Fig. 21 we also notice that the slow potentials (synaptic or generator potentials) look as if they are half-wave rectified and that no appreciable DC component is present in the response. The type Y responses produce well-defined but somewhat noisy first-order kernels (probably because of the presence of the spike discharges which could not be filtered out completely due to the overlap in the frequency ranges of the spike discharges and the slow synaptic potentials). In Fig. 22 are shown two such sets of hl’s, one producing depolarizing (type Y,) and the other producing hyperpolarizing (type Yb) responses. Although the polarity is reversed, the two sets of kernels are, otherwise, very similar and display common features: 1) The annular kernels hl, are overdamped and faster than the spot kernels latencywise and frequency responsewise. 2) The spot kernels, hl,, are underdamped and slower latencywise and frequency responsewise. 3) In the two-input experiments the presence of the annular input depresses completely the spot compo,nent, hr,,a, while the presence of the spot component either depresses or enhances the annular components, hlalfi, although such changes are not as drastic as in the case of the spot component. Thus, the interaction between the spot and annular components is rather unilateral for type Y responses, while in the bipolar cells such an interaction is mutual. In analyzing the spike discharges in the catfish retina, Marmarelis and Naka (20) reported that the annular input gave rise to a slow, overdamped kernel and that the faster component depressed the slower component. In fact the set of kernels (derived from spike discharges) shown in Fig. 7 of Marmarelis and Naka’s paper corresponds exactly to Downloaded from http://jn.physiology.org/ by 10.220.33.3 on June 18, 2017 sharp peaks is probably an indication of some threshold mechanism followed bv a regenerative slow potential. The time scale of the response is about 30 ms and this does not warrant us the description of this phenomenon as a “spike” and, as we have already shown, fast spike discharges are clearly present in the type C neurons in addition to the transient depolarization. It is conceivable that in large neurons, such as those found in the catfish retina, the need for a regenerative slow potential might arise if signals are to be transmitted over a large distance without involving spike generation. AND WIII’I‘E-NOISE ANALYSIS 113 those in Fig. 22 shown here. If we assume that the frequency of the spike discharge is proportional to the amplitude of the depolarizing (intracellular) slow potentials, the close agreement between the results of the two analyses (one, on the spike discharges and the other, on the intracellular slow potentials) is what one could expect if both responses are recorded from the same class of neurons. Although indirect in approach, it might thus be possible to identify morphologically the origin of the extraccllularly recorded spike discharges by comparison with the intracellular recordings in which morphological identification is possible through the intracellular dye-injection technique. For example, the set of kernels shown in Fig. 22B were recorded from a three-polar ganglion cell, and the fact that this set of kernels is very similar to those shown in Fig. 7 of Marmarelis and Naka (20) suggests that the extracellular spikes observed in their experiment might have originated Downloaded from http://jn.physiology.org/ by 10.220.33.3 on June 18, 2017 FIT.. 20. Examples of Procion dye-itlcntified type Y nwrons seen in the radial (‘4 through II) ant1 tangential (E and F) sections. Neurons A through U are probably the polar neurons in part I (24), to judge from their round somata. Neuron D is apparently a spindle type, while neurons E and F are two-polar and kite-type ganglion cells, respectively. Optic fiber bundle is shown by “on.” 114 NAKA, MARMARELIS, CHAN from a neuron of similar morphologicd origin. A second-order kernel obtained from a type Y response is shown in Fig. 23; it is for the annular component in a two-input experiment (the corresponding spot kernel is not shown since it is almost zero). The kernel has three peaks; one at the diagonal at t, = t2 = 64 ms, and the other two off the diagonal at tl = 64 ms ad t2 = 128 ms. The general features of the second-order kernel of type C neurons bear very close resemblance to those from the !qnglion cell discharges (rcf 19, 20) and those from type Y respoiiscs (although the type C secondorder kernels were always less noisy than the type Y second-order kernels). Typical response power spectra of the type Y neurons are shown in Fig. 24. We observe the following: I) The spectra have some characteristics of band-pass filter. 2) The spectra have large high-frequency components as seen from the slower asymptote at frequencies 2040 Hz and the secondary peaks at very high frequencies. 3) The discrepancy between the system response and model response (computed from 11, and Ii,) or between tile linear and nonlinear annular model responses becomes larger at the higher frequency range, intlicaling the pres- T, (msec) I28 64 OP , O.Isec ’ + ’ * ’ 192 + + 256 ’ , 1 I(.. 22. 1 ilst-order hcinelc fion~ typri Yb, shown in ‘4, ant1 Ya, \hou n in B, neurons. In both sets of kclnrl\, traces 1 and 3 ale h,n,s and hl,, and trace? 4 and 2 are Ir15,T and h,\. All trace5 a;e xalcd by the same factor ;\ith ortlilrate5 f’or volt\/(photon\/ mmz). A lowpa\s hltcr WI\ 11w1 to \uppre~s the higll-frcclw~~~y components tluc to the spike di\thargra. IJpr\ard deflection is fol 1iypcrpolarir;rtiorI of the mcmbiatlc potential. Alciagc mean inlcnGly, 0 log unit. Type Annul<w SC( olltl-Ol a type Y rrcurc~n are shown in Fig. 22.1. ant1 units of h, arc scaled 11.):,,s’ from kcr&ls :ccontls lIlf112j”. Y response h, (r,, tlnr (wlr) 7‘2) kc1 nrl, Ivhosc first-order Axes are in milliby volts/(photons/ Downloaded from http://jn.physiology.org/ by 10.220.33.3 on June 18, 2017 Ix. 21. Samplr responw from type Y neurons obt.~inctl by IT\O illput !\hitc noise stimulations. In A the :Implitmle of the spike tlischargc i* about 30 m\‘, arltl ilr 11 and C amplitutlrs of the synaptic potential5 al c about 10 ml’. Notice the difference in heights of spike distllargcs and alto the half-wake rectified qnaptic potentials. IJpwartl deflection is for hypelpolari/ation of the mcmlnanc potential. ,\I crage mc’d~~ intensity, 0 log unit. AND WHITE-NOISE 0 ANALYSIS r 2 5 100 FIG. 24. Power spectra of responses from a type Y neuron. R, system response; MR, model response, LMB and NM,, linear and nonlinear model responses from the spot input; and LM, and NM,, linear and nonlinear model responses from the annular input. Responses are so scaled that the pourer level of the system response is close to 0 dB. Notice the presence of the high-frequency component. ence of high-frequency components in the response. Such high-frequency components seem to originate from two sources: one, the intracellular slow potentials and the other, the remnant of the spike discharges left unfiltered. However, it is worth mentioning here that despite the presence of the high-frequency component, the model response based on hI and h2 can predict the system response with reasonable accuracy, in contrast with the type C response in which h3 had to be introduced to predict the system response with comparable accuracy (see Table 2). Com,pa rison of responses retinal neurons from catfish In the preceding sections we ha ve described the function al traits of the catfish retinal neurons as revealed by morphological (through intracellular dye injection) and functional (through white-noise analysis) experimen ts, and classified identification the responses into five major categories based on a few selected ex.amples which we believed to be typical of a given class of neurons. As we will amplify in the APPENDIX, such a traditional classification aPpreach fails to indicate how objective the classification is or how clearly each cla ss of response is separated from the rest. To overcome partially this difficulty and also to give some objectivity to the classification scheme which we propose for the catfish retinal neurons, the responses from about 100 neurons on which two-input whitenoise analysis have been performed are classified into five types based on their functional (mainly through the kernels) and morphological characteristics, and the MSEs for each class of neurons are tabulated in Table 2. In the table are shown five sets of values: MSE for LM,,,, LMa,s, LM,,, -ILM,/S? and MR, and the difference between the last two MSEs or the improvement in the model performance by the addition of the second-order terms predicted by hS’s. In the table we notice that both the external and internal horizontal cells (which were identified by dye injection) are linear because the introduction of the secondorder term improves the MSE of the external cells by 1% and worsens the MSE of the internal cells by 2%. Such worsening of the model response by the addition of the second-order term is due to the fact that the term is composed mainly of the high-frequency noise because of the nearperfect fit of the annular linear model (MSE of 9%). This fact also indicates that in the horizontal cells the total response MR is almost entirely due to the annular inputs, a fact which is predictable from our assumption that the horizontal cells form a laminar layer (17, 30, 37). The bipolar cells, both types Ba and Bb, are linear, but less so than the horizontal cells, as the second-order model showed an improvement in the MSE of about 5% over the linear model. However, contrary to what we have seen in the horizontal cells, the MSEs for the spot and the annular linear models are quite comparable, indicating almost equal contribution to the total response from the two inputs. Together with the fact that the polarities of the spot and annular h,‘s are opposite, this table indicates that the bipolar cells form a biphasic receptive field. We notice that in the bipolar cells the MSEs for the total MR models are about 20%, while in the horizontal cells it is about 10%. To judge from the absence of the high-frequency components in the bipolar cell of the responses, the poor predictability second-order model seems to reflect more Downloaded from http://jn.physiology.org/ by 10.220.33.3 on June 18, 2017 Freqiky -I 20 (Hz) 115 116 NAKA, MARMARELIS, CHAN sponses to step inputs. In this study they showed that the relationship between the amplitude of the light input and the amplitude of the resulting horizontal cell response (V-log I) could be fitted by a tanh-log curve. In some other retinas, such as those of the carp and mudpuppy, similar curves were constructed for the responses arising from neurons other than the horizontal cells (13, 4547). However, such a relationship can be unambiguously established only if the system under study shows a constantgain low-pass frequency response; i.e., if the system detects only the magnitude of the stimulus. Otherwise it is a strong function of frequency. Another condition for the meaningful interpretation of such a static V-log I curve is a monotonic receptivefield organization; if the receptive fields are organized in a more complex fashion, such as those found in the bipolar cells, the interpretation of the resulting V-log I curves becomes problematic. In the catfish retina the analysis performed so far has shown that, except for the horizontal cells and probably also the receptors, the retinal neurons have complex receptive-field organizations and, often, strong band-pass characteristics. Therefore, their input-output relationships must be established based on the dynamics of their responses, preferably by the use of two-input white-noise analysis, so that both receptive-field components are accounted for. This is due to the fact that the dynamics of a given system can be efficiently described in terms of a small set of kernels and that the two-input analysis technique is capable of separating the responses from the two components. In the present study, however, we limit our analysis to one-input experiments which could, although not as completely as twodescribe the dynamic input experiments, response range of the catfish retinal neuDynamic response ranges of catfish rons. In this study we confine the stimulus retinal neurons to field illumination (Fig. l), which covered Thus far the study of the relationship about two-thirds of the entire retinal surexisting between input and output in the face and whose average mean intensity level neurons in vertebrate retinas has been ex- was controlled by interposing neutral denplored mainly through stimulating the sys- sity filters (while keeping the modulation tem by step or sinusoidal functions. The depth constant). To make interpretation most ubiquitous relationship found so far easier, the analysis was performed on the was originated in Naka and Rushton’s (29) linear neurons in which the magnitude of treatment of the tenth horizontal cell ‘re- the first-order kernels can be taken as an Downloaded from http://jn.physiology.org/ by 10.220.33.3 on June 18, 2017 difficult recording conditions rather than the presence of the higher order terms. The second-order nonlinearity in the type N neurons is also small; an improvement in the model performance of 3% is seen by the addition of the second-order term. In the type N neurons the annular linear model predicts the system response with a MSE of about 30%, while a similar spot model predicts the system response with a MSE of 90%, thus indicating that in the type N neurons, as in the horizontal cells, the total response mainly arises from the annular input. The type C neurons are characterized by the fact that the first-order models perform very poorly, thus indicating the highly nonlinear characteristics of the neuron. The improvement of the model response by the introduction of the second-order term is about 40%, the largest in the catfish retinal neurons, a fact which further substantiates the high nonlinearity in the type C response. We have already mentioned that the addition of the third-order term improves the predictability of the model response by nearly 20%. In the type Y responses the improvement in the MSE by an addition of the secondorder term is IS%, a value halfway between the similar improvements in the linear (horizontal and bipolar cell) and in the highly nonlinear (type C) responses. Under the present experimental conditions the type Y responses are largely due to the annular inputs and only a small part is due to the spot inp ut. Those observations we made in Table 2 agree fully and augment further the classification scheme we proposed earlier of the catfish retinal neuronsA and also the conclusions we have drawn on the functional traits of each class of neurons. AND WHITE-NOISE 0.8 log units step , IOOmsec 113 cussed later. However, all types of neurons show a common feature: a shorter peak response time as the mean intensity level is increased and a similar decrease in latency (although the latter cannot be seen as clearly as the former). Clearly, the response range (or sensitivity) of a neural system, unless it shows a constant-gain low-pass characteristic, is a function of the stimulus frequency. Therefore, a natural way to study this matter is through the response (to white noise) power spectra, which in effect measures the power (or amplitude) of the response at each frequency. These spectra, of course, would have to be measured for different mean intensity levels (while the modulation depth is kept constant). Incidentally, such an approach to measuring the dyna .mic response range of a neuron circumvents the problems of nonlinearity as these are also accounted for in the spectrum. One such&attempt is shown in Fig. 26 in which are shown the power spectra of bipolar cell responses recorded at two different mean intensity 1evels, one at 0 log and the other at -0.8 log units. From the re- , 25. First-order kernels from horizontal, A, two bipolar, B and C, and type N, 0, neurons obtained white-noise input. Curves marked 1 are obtained by inputs with average mean level at 0 log unit. For subsequent curves marked 2 through 5 the average intensity levels are decreased by 0.8 log unit steps by interposing neutral-density filters. Upward deflection is for hyperpolarization of the membrane potentials. The amplitude of kernels with log filters was scaled down by the factor corresponding to the optical density of the filter. FIG. by field Downloaded from http://jn.physiology.org/ by 10.220.33.3 on June 18, 2017 indication of their dynamic sensitivity. In Fig. 25 are shown results from one horizontal (A), two bipolar (B and C), and one type 3J (D) cells; those records marked 1 were obtained by inputs whose average intensity level was 0 log units (without any neutraldensity filter) and for the records 2 through 5, the average intensity levels were decreased by a decrement of 0.8 log units. In the figure we notice that the amplitude of the horizontal cell h1 decreases rapidly as the level of mean intensity is decreased and such a decrease is roughly proportional to the decrease in b; i.e., the DC component of the response. Thus the dynamic range of the horizontal cell is comparable to the response range when it is explored by step inputs. The response from the other types of neurons, however, has a much larger dynamic range and a decrease in the mean intensity level by one or two log units does not produce a marked change in the amplitudes of the first-order kernels (cf. Fig. 25). In some cases a decrease in the mean intensity level results in an increase in the dynamicgain of the system. A possible explanation for this observation will be dis- ANALYSIS NAKA, MARMARELIS, CHAN due to the annular component; 2) as the mean intensity level is decreased the system becomes overdamped, due to predominance of the response by the spot component; and 3) decreases in the level of intensity result in a faster decrease in the power level of the spot than the annular component. Similar characteristics have been observed consistentIy in the power spectra of the linear neurons and they were not confined to the bipolar cell responses. We conclude that the dynamic response range of the horizontal cells (and probably the receptors) is the smallest (for the range of intensities used) and is comparable to the static V-log I relationship of these cells, while other proximal neurons such as the bipolar cells, have much larger dynamic ranges, well over 34 log units, although their static response range, as probed by the step inputs, is reportedly very limited (13, 45). DISCUSSION Classification Frequency (Hz) FIG. 26. Bipolar cell power spectra obtained at two mean intensity levels, A at 0 log and B at -0.8 log units. R, system response to two-input white-noise; MR, model response; LMa and NMa, linear and nonlinear model responses for the annular input; LMS and NM,, linear and nonlinear model responses for the spot input. In both records responses are scaled by the same factor so that the power level of the system response at 0 log in tensi ty is close to 0 dB. sults of each two-input experiment six power spectra are computed for each set: the power spectra of the system experimental response, R, of the model response, MR, the nonlinear annular-component, NM,, the linear annular-component, LM,, the nonlinear spot-component, NM,, and the spot linear component, LM,. In addition to the features we have already described these power spectra show that 1) there is a very close agreement between model and system responses, and 2) a similar close agreement exists between the linear and nonlinear model responses. Comparing sets of power spectra, we notice 1) at higher mean intensity, the system exhibits a band-pass characteristic which is mainly of neurons During the late 19th and early 20th century, vertebrate retinal neurons were classified into taxonomical sets based on such morphological traits as the degree of dendritic expansion, location of somata, or the presence or absence of axons. As already recognized by Ramon y Cajal (5), such a morphological classification was necessarily tentative, as any class of neurons requires functional as well as structural definition. The introduction of the intracellular dyeinjection technique, particularly of Procion dyes, offers now the possibility of testing the validity of the classical classification of the retinal neurons. Pioneering studies by Dowling and Werblin (7, 48) and especially, Kaneko (1 l), followed by Matsumoto and Naka (22), have shown that intracellular recordings, as well as dye injection, can be performed in the vertebrate retinal neurons. Although these studies have brought forth valuable information, they were unsatisfactory in four respects: 1) No appreciable effort was made to establish the classical morphology of the neurons in the retina in which intracellular dye injection was attempted. For successful structural identification of a class of neurons through intracellular dye injection, Downloaded from http://jn.physiology.org/ by 10.220.33.3 on June 18, 2017 B AND WHITE-NOISE 119 distal layers of the retina agrees fully with the conclusions reached in the earlier studies, our identifications of the neurons in the proximal layers deviate from the previously accepted views. However, we also realize that our identification of the proximal neurons is not yet complete, and to circumvent any further complications, we have assigned them the noncommital designations, types N, C, and Y neurons, reflective of their response characteristics. A more quantitative categorization procedure, such as the one attempted in the APPENDIX, might be able to establish a more definitive classification of these neurons. Functional identification The functional identification of a neural system involves the complete determination of the input (stimulus) versus output (response) dynamic relationship of the system in the form of a compact mathematical representation. For a linear system the identification procedure is simple and well established; a step or a series of sinusoidal stimuli of different frequencies are well suited for this purpose because the principle of superposition holds for these systems. Except for a few cases where certain linearization techniques have been used (38), a step or sinusoidal stimulus has been used almost exclusively to identify functionally the response characteristics of a given neuron. Here we mention an attempt by Schellart and Spekreijse (35) to study the dynamics of the retinal ganglion cells by cross correlating the noise input and the resulting spike discharges. When applied to the study of sensory systems, testing (in order to identify functionally) by these traditional inputs is very disadvantageous in that such stimuli are unnatural, inefficient in gathering data over a short period of time and, most of all, unsuitable for the nonlinear quantitative description of the system stimulus-response behavior. In a series of studies we have successfully applied Wiener’s theory (49) of nonlinear analysis to the horizontal and ganglion (spike) cell responses from the catfish retina and have shown that this method is applicable and well suited to the study of the retinal ne ural systems. Specifically, the white-noise method of testing Downloaded from http://jn.physiology.org/ by 10.220.33.3 on June 18, 2017 the classical morphology has to be established through the Golgi silver-impregnation and/or the methylene blue vital-staining technique. The apparently premature identification of amacrine cells by Toyoda et al. (44) exemplifies the danger inherent in basing conclusions on incomplete data. As already pointed out by Stell (40), a considerable amount of variation in the morphology of the retinal neurons exists even among the teleost retinas. 2) The histological procedure employed by the earlier investigators reduced the number of recovered neurons, due to the tedious sectioning involved, and eliminated virtually any characterization of the neurons based on the lateral spread of their dendrites. We have already shown in part I (24) that morphological classification of retinal neurons in radial section (or side view) is of limited value in the catfish retina; some of the drawings by Ramon y Cajal (ref 5, plate III, Fig. 4e) indicate the importance of viewing the neurons in flatmount preparation. 3) The scope of the functional identification of the neurons was severely restricted by being based only on the responses to step (pulse) input. In part II (28) of this series we have already described the difficulties involved when such step inputs are used as a functional probe. 4) Due to the diversity in shape and size of the retinal neurons (cf. ref 5, 24, 40), morphological and functional identifications have to be performed on the same neurons; any conclusion on the correlation between structure and function must be statistically based on the results of a large number of such dual identification experiments. Unfortunately, in the intracellular dye-injection experiments so far carried out in the vertebrate retina, such conditions have not been fully met, except for the excellent studies on the turtle horizontal cells (23, 34, 37). In this series of studies we have avoided these obstacles found in the earlier attempts to correlate structure and function in the vertebrate retina. Moreover, each paper in this series was developed independently, so that results from one part would not bias any conclusion drawn from any other parts. While our analysis of the neurons in the ANALYSIS 120 NAKA, MARMARELIS, CHAN white-noise analysis of spike discharges requires a recording time of 5-10 times longer than for slow potentials (in order to achieve similar statistical accuracy) and produces less satisfactory results. Horizontal cells The morphological and functional identification of the horizontal cells is straightforward. The horizontal cells, both external and internal, have independent monotonic receptive fields (cf. ref 17, 30, 37). As shown above, their dynamic as well as static range of responses to the light stimulus is limited. The horizontal cells have a large DC response component (h,) which together with the first-order kernels is sufficient to describe the response of the cell with very good accuracy. Although there is a certain dynamic, “small signal” nonlinearity associated with the cell, i.e., asymmetric rising and falling phases, besides the usual saturating nonlinearity, the horizontal cell is, with the depth of modulation used, essentially a linear device with a constant-gain, low-pass filter characteristic. The results of the nonlinear analysis so far performed on the cell, as well as those from other mathematical analyses (17, 30, 37), lead to the conclusion that the cell’s function is simply to detect the magnitude of the input signal and integrate it by means of its laminar structure. We have also noted a remarkable consistency in the responses from horizontal cells, a feature easily attributable to a group of cells acting as a syncytium (see APPENDIX). Bipolar cells The identification of the bipolar cells as a class of neurons did not pose any difficulty, morphologywise (part I (24)) or functionwise (part II (28)). However, the patterns of responses from individual cells encompassed a large range in which certain response parameters varied continuously (see APPENDIX). Thus, it was not possible from the present analysis to classify them into two classes which might correspond to the smaller and larger bipolar cells. Such classification of the bipolar cells can perhaps be obtained in the near future by an experiment in which the diameter of Downloaded from http://jn.physiology.org/ by 10.220.33.3 on June 18, 2017 a sensory neural system (in order to identify it functionally) has four major advantages over the traditional methods of testing by pulses and/or sinusoidal inputs: 1) It allows a concise quantitative description of the dynamics and nonlinearities of the system. 2) The white-noise stimulus, by its nature, nearly maximizes the rate of information gathering about the stimulus-response behavior of the system as compared with a sinusoidal stimulation or a brief pulse given once in a few seconds. This is a very important point in the study of the vertebrate retina (or any other part of the central nervous system), where stable intracellular recording time is limited to less than a few minutes, during which a given neuron must be identified morphologically (through dye injection) as well as functionally. 3) Most types of unwanted, contaminating noise are eliminated through either the cross-correlation process involved or the orthogonali ty of the white-noise characterization. This is also important in intracellular recordings from smaller neurons where noise is indeed a problem. 4) When expanded to multi-input systems, necessary because of the biphasic or concentric nature of retina1 receptive fields, the whitenoise analysis allows us to identify the dynamics of each field component separately as well as their interaction in a single experiment. For example, we have shown that a 20. to 40-s-long experiment on a bipolar cell is sufficient to give information on the contributions to the total response from each compnent, spot or annular, and also on the nature of their mutual dynamic interaction (which was found to be rather small in all the catfish retina1 neurons). Moreover, the effect of each receptive-field component on the other is manifested clearly and completely by the change of the kernels from the one-input experiments to t.he two-input experiments (e.g., the change of hl, and hZa to hl,,, and h2a,s). Thus white-noise analysis is an ideal tool to identify functionally the retinal neurons which have either concentric, biphasic, or monotonic receptive-field organizations (in which the spot and annular stimuli play important roles) and which transmit signals primarily through analog potentials. As we have discussed elsewhere (18, 2 1) the AND WHITE-NOISE I 121 cell predicts nicely the increase in the dynamic gain of each component observed in the two-input experiments: we have shown that the horizontal cells have a large DC response component; the results obtained in the receptors of other retinas indicate a similarly large DC component must exist in the catfish receptor signal (1, 3, 6, 41, 48). With only one input active, such a large DC component easily saturates the cell driven at the next stage (bipolar cell), thus limiting the dynamic gain of the system. Steeper V-log I curves were seen in the mudpuppy bipolar cells (45, 46) and in the presumed carp bipolar cells (13). However, if both inputs are active with similar DC components but of opposite polarity (as in the case here), the bipolar cell potential is set to an intermediate level in its range from which it can be swung over a large rangea characteristic of a comparator or differential amplifier. This is clearly evidenced by the larger gain of hIa,s and h Is/a? respectively (see Fig. S), since in the former case the system is “biased” nearer the middle of its range. The analysis so far made, directly and indirectly, on the function of the catfish bipolar cell still supports the original contention (27) to the effect that its main function is to compare two signals, one local (center) and the other integrating (surround.) Neurons in proximal layers The functional and morphological identifications of neurons in the proximal layers of the catfish retina were far more difficult and ambiguous than for the neurons in the distal layers. This is due to the complexity of the response patterns as well as the diverse morphology of the neurons in the former lavers. Based on their functional traits obtained through white-noise analysis, we have classified the neurons (responses) into three types, N, C, and Y. However, such a classification cannot be taken as unique nor every neuron (response) classified into one of these three categories without any ambiguity. We rather feel that the neurons in the proximal layers constitute a continuous spectrum, structurewise and functionwise, and that the three neuron types (or any other classification scheme), Downloaded from http://jn.physiology.org/ by 10.220.33.3 on June 18, 2017 the spot of light as well as its intensity are modulated in white-noise fashion. The DC response component was very large in some of the bipolar cells and small in others. Within the depth of modulation used in these experiments the bipolar cells behaved linearly and the firstorder (linear) model describes the system response with a fair degree of accuracy. The addition of the second-order (nonlinear) kernels improves the MSE only slightly (about 5%). An interesting feature of the bipolar cell kernel is that the annular component always had both longer latency and the frePeak response time, al though quency response of this corn .ponent was faster than that of the spot compon .ent. We have also noticed that ihe spot componen t became faster frequencywise and that the latency and peak response time of the component became shorter in the presence of the annular input. From results of previous experiments in which current was injected into the horizontal cells (of dogfish and catfish retinas) it has been proposed that a bipolar cell receives two inputs: one representing the local signal and coming directly from a small number of receptors and the other realizing the integrating signal by the horizontal cells and reflecting the average intensity level of the visual environment (26, 27, 31). As both the receptors and horizontal cells hyperpolarize in the dogfish and catfish retinas, while the bipol& cell hyperpolarizes for one of these inputs and depolarizes for the other, it was further argued that one of these two inputs must invert its polarity. Marmarelis and Naka (19) have further stipulated that when a large number of receptors are activated, as in the case of a field or annular input, the resulting horizontal cell activity is fed negatively back to the receptors in order to improve (speed frequency response. Such a up) t .heir speedup of the receptor response must also result in a faster spot response in the bipolar cells, while the longer latency and peak response times of the annular bipolar cell response can be attributed to the delay involved in the three-stage transmission of the annular input as compared with the two-stage transmission of the spot input. The function proposed for the bipolar ANALYSIS 122 NABA, MARbdARBLiS, represent only the peaks in a mountain range formed by the entire population of the neurons. The degree of complexity of any classification scheme depends simply on the level of threshold set to separate the (imaginary) individual peaks in such a continuous range. CilAN apses) must be based solely on the hyper- or depolarization of the potential, since this is the only available information at this stage about the origin (spot or annulus) of the signal. A .lternatively, if type N respon ses are produced by inputs from the two different types of bipolar cells there must be a “switching” mechanism such that the inputs from the bipolar cells always produce either a depolarization or hyperpolarization response. The fact that both bipolar cell and type N responses are linear seems to exclude the possibility of a complex signal transmission between the two cells. -Here we recall that the horizontal cells form a monotonic receptive field giving rise to responses of the same polarity to any form of inputs. In consideration of the fact that the internal horizontal cells and the neurons giving rise to the type N responses face each other directly at the junction of the inner nuclear layer and inner synaptic layer, the possibility cannot be excluded that there is a direct-signal transmission between these two classes of neurons. However, they are distinguished from one another functionally by different response patterns: 1) although both neurons form monotonic receptive fields, the spot response is not depressed by an annular input in the horizontal cells, while in the type Na neurons the presence of an annular stimulus completely depresses the spot response component; and 2) the dynamic gain of the type N response covers a far larger range than the horizontal cell response. Type C responses The type C response, evoked by step inputs, is a transient depolarization at the on- and offset of the stimulus. Similar depolarizing transient responses have been seen in the mudpuppy and goldfish retinas by Werblin and Dowling (48) and by Kaneko (11, 12), who ascribed them as originating from amacrine cells. Procion dye injection performed concurrently with white-noise analysis has revealed that the majority of the type C responses was produced by a class of neurons referred to as the spindle-type (ganglion) neuron in part I (24) of this series; the observations made in part II (28) substantiate this conclusion. The most striking feature of the type C Downloaded from http://jn.physiology.org/ by 10.220.33.3 on June 18, 2017 Type N responses Procion dye injection performed concurrently with white-noise analysis has revealed that the majority of type N responses originated from neurons with their mitershaped somata in the proximal layer of the INL. In part I (24) of this series these neurons were referred to as starburst or spaghetti, the latter neurons being characterized by their thick dendrites which expanded nearly 1 mm through the ISL. Identification of the type N neurons in this paper agrees well with the identification through the step inputs in part 11 (28) in which these neurons produced sustainedtype responses. A morphological correspondence (not necessarily functional) of type N neurons can be found in Ramon y Cajal’s amacrine cells (such as those in the perch retina; ref 5, plate I, Fig. 5), in the frog (plate II, Fig. 3), in the green lizard (plate III, Fig. 4), and in the chick (plate V, Figs. 7 and 8). Ramon y Cajal never located axons associated with these neurons; we are still not sure, however, that in fact these cells do not possess any. Al though their en tire dendri tic spread lies in the ISL, type N neurons have linear responses and lack any higher frequency components. Their functional traits are very similar to those of the horizontal or bipolar cells. However, in type N neurons (responses) both the spot and annular inputs give rise either to depolarizing (Na) or hyperpolarizing (Nb) responses, while in all the bipolar cells these stimuli produce responses of opposing polarity. If type N neuron responses result from inputs coming from one type of bipolar cell, then the signal due to one of these two inputs must be inverted somewhere along the chain of processing. However, it should be noted that the “decision” (for the inversion of this signal) by an observer sitting at the output of the bipolar cell (which must be the site of the decision by the type N neuron syn- AND WHITE-NOISE Type Y responses Responses were classified as type Y based on two criteria: a noisy but well-defined first-order kernel and a large second-order nonlinearity. These were produced by a large variety of neurons which fit best the definition of “classical” ganglion cells. In 123 the methylene blue preparations it was always possible to find a group of neurons with axons which had a close morphological resemblance to the Procion neurons which gave rise to type Y responses. Apparently, neurons which produce type Y responses constitute .a large population of neurons which may include many morphological as well as functional subclasses. In one of the companion papers (part I (24)) we showed that the morphology of the ganglion cells encompasses a whole gamut of structural variation. A further study has to be undertaken to correlate the rich variety of morphological shapes with the response characteristics of these neurons; for example, it is interesting to compare the dynamics of simpler (or more primitive) neurons, such as one-polar cells, to those of more complex (or more advanced) neurons, such as- the multipolar cells. Probably spacewise whitenoise input, combined with quantitative morphological identification, holds the key to the classification of the type Y neurons. It has been reported that ganglion cell discharges showed a strong rectifying nonlinearity which was commonly believed to be simply a manifestation of the fact that there are no “negative” spike discharges (38). However, in a recent paper Marmarelis and Naka (18, 19) have suggested that such rectification takes place at the ganglion cell stage, probably at the ganglion-bipolar cell synapses, and the results of more direct observations made in this study on the intracellular potentials have shown that this rectification takes place when the signals are transmitted from bipolar or type N cells to types Y and C neurons. Apparently in the catfish retina, then, initiation of spike discharges is not the main site of rectification. Morphological and functional characteristics of the catfish retinal neurons studied in this trilogy are summarized in Table 3. Comparison with results obtained other retinas in The morphological and functional identification of the horizontal cells agrees fully with the results in earlier studies (11, 14, 40). Although the identification of bipolar cells as a class of neurons is largely in accord with the conclusions drawn in other earlier Downloaded from http://jn.physiology.org/ by 10.220.33.3 on June 18, 2017 response is the absence of well-defined firstorder (linear) kernels, suggesting the existence of a high nonlinearity involved in the response. Another characteristic feature of the response is the large, spikelike depolarization which apparently is produced by some thresholdlike mechanism. This feature requires the introduction of the third-order nonlinear kernel in order to describe the response with a reasonable degree of accuracy. Similar depolarizing (regenerative) slow potentials which bear close resemblance to the type C response were seen in the turtle photoreceptors (ref 10, Fig. 9; ref 33, Fig. 3). It has been shown in the catfish retina that some neurons have very large dendritic fields, reaching nearly 1 mm in diameter, and it is conceivable that some sort of a regenerative mechanism is set up in order to transmit signals over such a large distance. In the horizontal cells this type of problem is overcome by the formation of a laminar layer in which the potential decays much more slowly than in a simple tubular structure (cf. ref 17, Fig. 2). In their studies on the discharge patterns of the catfish ganglion cells Naka and Nye (26, 27) have reported that these cells form concentric receptive fields in which a spot and an annulus of light produce responses of opposing modes; i.e., transient versus sustained discharges. We have found that the pattern of the type C response to a large extent is invariant of the stimulus parameters (part 11). Therefore there are two possibilities: a) Naka and Nye failed to record spikes from a class of ganglion cells, if indeed the type C neurons are ganglion cells; or b) type C neurons feed signals into the ganglion cells or type Y neurons. However, the fact that type C neurons do not exhibit any clearly defined first-order kernels indicates that the noisy but well-defined first-order kernels seen in type Y neurons are likely due to signals from other neurons, such as type N or bipolar cells. ANALYSIS 124 TABLE catfish NAKA, MARMARELIS, 3. Summary of morphological retinal neurons AND CHAN and functional characteristics of Response Response polarity Classification Part I Part II Part III Spot AnnuIus Receptive field Characteristics spotannulus in teraction Degree of Types nonlinof eari ty, nonlineari ty % Set of kernel Model Horizontal DYHYPer Monotonic Synergic Biphasic Enhancing h h 0' 2 1 namic asymmetry saturation Laminar DC de tection Bipolar Ba Bb On-center Off -center Amacrine Starburst Depol Hyper Depol HYP- hor hl h 1' 6 0 DYnamic asymmetry Comparison DC subtraction sustained DeNa Nb Depol HYper Monotonic pressing h Laminar? 1 Or: none Spaghet ti sustained Re- Spindle Transien t C Depol h,, h, 45 On-off gener slowpotential Ganglion On-ten Off-center ter 1 -polar P-polar 3polar 4-polar Multipolar Kite Ya HYPer (Concentric) Spiking Yb An tagonis tic hl’ h2 25 Rectification Spike production Depol studies (11, 12, 43, 48) there are important points of variance to be mentioned: 1) Kaneko (11) in the goldfish, Matsumoto and Naka (22) in the frog retinas reported that some of the dye-identified bipolar cells showed monotonic receptivefield organizations, while in the catfish retina all of the dye-identified bipolar cells in parts 11 (28) and III (this paper) had bi- phasic receptive-field organizations. In the mudpuppy retina, Nelson (32) reported a group of neurons referred to as depolarizing bipolars in which a surround antagonism was not seen. Three explanations are possible to account for this discrepancy: a) in the catfish we failed to detect such bipolar cells, b) as already mentioned by Kaneko and also by Matsumoto and Naka the stim- Downloaded from http://jn.physiology.org/ by 10.220.33.3 on June 18, 2017 External Intermediate Internal WHITE-NOISE 125 longer than the center (or spot) response only by 20-30 ms. Together with the results in part II (28) we conclude that the operating modes of bipolar cells in these two retinas are radically different. EnrothCugell and Pinto (8) obtained evidence to show that in some of the cat retinal ganglion cells the center-surround interaction could be expressed in terms of algebraic sum of two pure responses, i.e., the responses elicited by the center or surround signal alone. If the cat ganglion cell response reflected the bipolar cell activity, their results are what we would expect from the model we proposed for the catfish bipolar cell. Werblin and Dowling (48) were the first to designate as amacrine cells a class of neurons which gave rise to depolarizing transient potentials with or without spikes superimposed on them, although similar transient depolarizations had been previously seen in the frog retina by Naka et al. (25) and were referred to as type II responses by Tomita et al. (42). Werblin and Dowling’s identification was supported by Kaneko (11) who recorded from and injected Procion dye into goldfish neurons he classified as amacrine cells because of their transient depolarizing responses. However, we note that Kaneko’s amacrine cell (ref 11, plate 5) had a round soma and thick dendrites, which are characteristic of the catfish type N neurons. Furthermore, Matsumoto and Naka (22) qualified their reference to the origin of the transient depolarizations in the frog retina as assumed amacrine cells. Schwartz (36) was surprised to find, in the turtle retina, somata of a class of neurons which gave rise to on-off discharges in the ganglion cell layer as well as in the INL. To complicate the issue, Toyoda et al. (44) claimed to have recorded from the carp amacrine cells a variety of responses, including those with clear spontaneous spike discharges, although their criteria for distinguishing amacrine cells were questionable at best. Curiously, no report is available to indicate the presence of the type N response in other retinas, although neurons very similar, structurally, to type N neurons were seen by Ramon y Cajal in many animals, including lizards (ref 5, plate IV, Fig. 9\ Downloaded from http://jn.physiology.org/ by 10.220.33.3 on June 18, 2017 ulus parameters were inadequate in their experiments, or c) those bipolar cells with monotonic receptive fields are type N neurons in the catfish or vice versa. 2) In the catfish retina, illumination of the receptive-field surround (by annular light) gives rise either to depolarizing (type Bb bipolar cell) or hyperpolarizing (type Ba bipolar cell) responses, as reported in the goldfish by Kaneko (12) and in the frog by Matsumoto and Naka (22), while in the mudpuppy retina, illumination of the surround does not produce any response in the bipolar cells (45, 46, 48). Simultaneous presentation of two stimuli, a spot and a concentric annulus of light, enhances the dynamic gain of each component (seen in all bipolar cells identified). Thus the surround functions, not to produce an inhibitory influence, as commonly assumed, but to provide an integrating signal from the horizontal cells to the bipolar cells, as originally proposed by Naka and Nye (26). Toyoda (43) in his study on the carp bipolar cells observed an increase in the depolarizing response evoked by a step input in the presence of an annular illumination; in the carp retina, however, the reverse was not true. In his recent study on the mudpuppy retina, Werblin (45, 46) concluded that the presence of a background (annular) illumination brought forth a lateral shift of the bipolar cell V-log I curve toward a lower sensitivity. In the catfish bipolar cells a simultaneous presentation of the center (through a spot of light) and surround (through an annulus of light) stimuli resulted in a mutual enhancement of the dynamic gain of the two receptive-field components. If the presence of an annular input brought forth a lateral shift of the V-log I curve to increase the dynamic gain of the spot component, a similar shift for the annular component must take place by the presence of a spot input, a situation hard to visualize. Therefore, the observations we made in this paper cannot be explained by a simple shift of V-log I curves. In the mudpuppy it was further shown that effects of surround illumination were seen 250 ms after the onset of the center response (46), while in the catfish bipolar cells the latency of the surround (or annular) response was ANALYSIS 126 NAKA, MARMARELIS, Dynamics of catfish retinal neurons In the cat as well as in the goldfish retinas it was observed that the ganglion cell responses (as represented by their spike discharges) changed from a strictly low-pass filter to a band-pass filter when the intensity of the background illumination was increased (9, 35). Catfish retinal neurons show exactly the same characteristic when the average mea .n in tensi ty level is increased; this is reflected by a transformation of the overdamped hl at low-intensity levels into the under-damped hl at high-intensity levels (Fig. 25). In the cat ganglion cells the low-frequency cutoff (i.e., the band-pass characteristics) was proved to be due not to lateral inhibition from the surround but to the nonlinear feedback in which the controlled transhorizon .tal ccl 1 potential mission from the receptors to the bipolar CHAN cells (9). Schellart and Spekreijse (35) have also suggested that spatial summation played an important role in the shift to higher values of the cutoff frequencies. Marmarelis and Naka (20) suggested that the speedup of the horizontal cell responses at higher mean intensity levels could be explained conveniently if the horizontal cell potentials (integrating signal) were assumed to feed negatively back to the receptors. The results of analysis on other retinal neurons give support to this assump tion. Kaneko and Hashimoto (13) were the first to note that the neurons in the INL had steeper V-log I curves; their observations were later confirmed by Werblin (45, 46). As we have already mentioned in RESULTS, the static V-log I curve plotted in their experiments serves as a measure of sensitivity only and only if the system under study has a constant-gain low-pass characteristic (i.e., if it is not a function of frequency for frequencies within the system bandwidth). The horizontal cell response (generated by a single class of receptors) is the only neuron, except for the receptors, which partially satisfies such a condition. As we have shown in RESULTS, the dynamic range of the catfish retinal neurons (except for the horizontal cell and possibly the receptors) is much larger than what was predicted by the static V-log I curves. The fact that such a large dynamic range is seen first in the bipolar cells gives further support to our hypothesis that the cell acts essentially as a comparator of two signals, each with a large DC bias, one from the receptor and the other from the horizontal cells. CONCLUSIONS A number of (about 150) white-noise experiments have been performed on the catfish retina; the stimulus consists of light intensities exciting the center (by a spot of light) and surround of the receptive field (by a concentric annulus) and modulated by independent white-noise signals. The elici ted response is measured intracellularly from neurons throughout the retina. For each two-input experiment a set of five functions (kernels) is computed from these stimulus-response data., This set of kernels describes completely the nonlinear dynamic Downloaded from http://jn.physiology.org/ by 10.220.33.3 on June 18, 2017 In the catfish retina we have shown conclusively in parts II (28) and III (this paper) that the majority of neurons which fit Ram&r y Cajal’s description (5) of amacrine cells produced on 1y the type N response any (1inear, sustained response without high-frequency component), whi .e depolarizing on-off responses (type C responses) were recorded from a class of neurons with the characteristic spindle-shaped cell body. In part II it was further shown that each of these type C neurons had a characteristic process which descended down to the ganglion cell layer. Here we recall our definition of type C responses as those which lack well-defined first-order kernels, necessitating a thirdorder term to describe their responses. When tested by step inputs, the resulting responses are transient depolarizations at the on- and offset of pulses. Some ganglion cells (type Y neurons) produce similar transient on-off depolarizations in response to step inputs (26, 27), but such responses are modeled with reasonable accuracy with the first- and second-order terms (18-20). Clearly, these transient depolarizations from amacrine cells published so far are not well documented in terms of their functional and morphological characteristics and, therefore, we are not in a position to resolve the di screpancy between the results in the catfish and other animals. AND WHITE-NOISE 127 ulations give rise to responses which are synergistic. The static and dynamic ranges of the cells are limited, and the system is essentially a low-pass filter which detects mainly the amplitude of the input signal. The functional significance of the cells is twofold; first, they integrate the signal over the entire retinal area and then transmit it to the bipolar cells, and second, the same signal is fed back to the receptors to improve their frequency response (and, consequently, that of the subsequent stages). 2) Bipolar cells. There are two opposing subtypes, one on-center and the other offcenter bipolar cells, both of which are linear (within the depth of modulation) and show characteristics of a low-pass to band-pass filter. The functional parameters of bipolar cells cover a large range, as evidenced by the loose clusters in the scattergram in the APPENDIX. In the bipolar cells, stimulation by a spot of light produces an overdamped kernel, which is transformed in the presence of an annular input into an underdamped kernel, accompanied also by a shortening of the latency and the peak response time. The annular response has always longer latency and peak response time, but is faster frequencywise, than the spot response. In the bipolar cells two receptivefield components, one a local signal activated by a spot input and the other an integrating signal derived from the horizontal cell, are mutually enhancing. All evidence obtained so far supports the original contention by Naka and Nye (26) that the bipolar cells act as a comparator of the two signals. 3) Type N neurons. There are two types, Na which depolarizes and Nb which hyperpolarizes, to any form of input. The neurons are linear, within the depth of modulation used and show characteristics of a low-pass to band-pass filter without any highfrequency components. Morphologically, these neurons correspond to most of the amacrine cells described by Ramon y Cajal (3, including the giant amacrine cells in lizards. 4) Type C neurons. This neuron is highly nonlinear, requiring a third-order term to model the response with a reasonable degree of accuracy. It does not produce any welldefined first-order kernels but has a charac- Downloaded from http://jn.physiology.org/ by 10.220.33.3 on June 18, 2017 behavior of each neuron. In still other experiments a single white-noise stimulus is used (a field or spot or annulus only) and a similar set of characterizing kernels is measured. The method allows us to describe separately (in the two-input experiments) the contributions (linear as well as nonlinear) of each input to the response. Furthermore, as applied to intracellular recordings, it allows us nearly to maximize the amount of diverse stimulus-response data we can obtain over a limited amount of time and it greatly alleviates the problems caused by unwanted noise. Besides these advantages, the universal nature of the white-noise signals results in a global functional identification of each neuron (i.e., over its entire operational range) and the characterization in terms of the kernels is given in a canonical form (i.e., in the same fixed format for all neurons). These three features of the method, in turn, allow us to proceed in an objective and efficient way with the functional classification of the retinal neurons. We have correlated the morphology of the catfish retinal neurons with their (nonlinear) dynamic characteristics as derived from white-noise stimulation. From such combined structural and functional studies we propose to revise the classical classificcation of the retinal neurons, at least in the catfish retina, based on the functional properties of each class of neurons as repres$ted by a small set of kernels. : In our scheme the neurons are classified as horizontal, bipolar, and types N, C, and Y neurons, the latter three types encompassing cells otherwise known as amacrine and ganglion cells. The objectivity of this categorization system and the degree of separation among the types of neurons (or the clusters formed by classes of neurons) are shown in a scatter-gram in the APPENDIX, in which morphologically identified neurons are grouped according to their common function al features. The characteristics of the five types of catfish neurons are: 1) Horizontal cells. Both the external and internal (and probably the intermediate, cells form independent too) horizontal monotonic receptive fields through the S space, in which center and surround stim- ANALYSIS 128 NAKA, MARMARELIS, APPENDIX As discussed, the white-noise stimulus is a type of universal probe with which to test a system. The resulting characterization of the system in terms of a set of kernels is therefore a global picture of the system functional characteristic and it is given in a canonical form; i.e., it describes the system behavior over its entire operational range and it is always given in terms of a set of kernels of fixed format. It is exactly these three features, i.e., the stimulus, the the white-noise universality of globality of the functional characterization, and the canonicity of the kernels, together with the fact that for all our experiments in the retina a fixed geometric configuration (a spot and a concentric annulus) is employed, that lead us naturally to the following intriguing questions: If the kernels of all the retinal neurons are grouped into categories according to their features, a) Do they form distinct groups (clusters)? b) If yes, do these clusters correspond, on a one-to-one basis, to clusters formed by grouping the neurons according to morphological features? c) Can we associate each cluster with a particular class of neurons (e.g., horizontal cells, bihow many distinct polar cells, etc.). 7 d) Finally, classes of neurons are there in the vertebrate retina, and what are their average functional and morphological characteristics? Relying on the results of the two-input white- CHAN noise experiments of the present study, we have performed a limited preliminary anaiysis in an attempt to answer these questions. We consider all the two-input white-noise experiments we have performed so far on the vertebrate retina for which experimental conditions were approximately the -same, such conditions as levels of the spot and annulus mean lights, length of experiment, equal bandwidth white-noise signals, and the like. For all these experiments, each performed on a different unit, we have computed kernels (hls,a, hla,B, h2s,a, h 2a,s, h,,) as well as their responses to white-noise, reductions in MSE, power spectra, etc. (as described previously). The number of these experiments (or neural units) is 147. The set of kernels for each unit constitutes a “signature” of the neuron. Imagine, now, each set of kernels as a point in an n-dimensional space, the position (coordinates) of this point depending on the features of all these kernels. Then, different (functional) classes of neurons will form different clusters of these points in this space. Clearly, then, such a “PlO t” of the kernels will allow us to give definite answer to questions a through d above. more complete functional signature of the neuron should include also the oneinput kernels, hrs, hZs, hIa, and h,,. In this preliminary study, we consider only two indirect features of the kernels and plot them in a two-dimensional space. Both these features are estimated from the MSE reduction. The first one simply measures how nonlinear the neuron is. The second one measures the relative contribution to the response of each receptive-field component (spot and annulus). Both these measures are positive quantities. One addi tional piece of information is plot ted on this plane, the direction of polarization thYperor de-) for each input (spot and annulus). The latter is simply accomplished by utilizing the four quadrants of the plane (if hl,s,a and hl,,* both hyperpolarize, the point is plotted in quadrant I. depolarizes and hla,a hyperpolarizes, the point is plotted in quadrant II, etc.). The indexes of nonlinearity and relative input contribution for each neuron are estimated as follows. Let the MSE of model response LMs,a be El9 and LMa 8 be E,,. Let the MSE of the linear model, i.e., t h e sum of responses LMEI,a and LM,,B, be E,. Let the MSE of the total model response MR (computed from all linear and nonlinear kernels) be E,. Then, we define the index of nonlinearity In gr each neuron to be 100 - E, In = 100 - E, That is, the ratio of MSE reduction of the nonlinear representation divided bY the MSE reduction of the linear representation. Th us, the larger In is, the larger is the nonlineari linear tY* For a perfectly neuron In = 1. The index of relative con tri bu tion Ire of each input (spot and annulus) is defined as E 1s -1 (100 - EJ - (100 - E& E, -Ire = = -Ela (100 - EJ - (100 - El,) M If hlf3/a --1 El Downloaded from http://jn.physiology.org/ by 10.220.33.3 on June 18, 2017 teristic second-order kernel which can be used as a signature to identify the neuron. Morphologically, the type C neuron corresponds to those neurons with a spindleshaped soma, commonly found in the INL. Type C response may or may not be accompanied by spike discharges. 5) Type Y neurons. This neuron is characterized by a noisy but well-defined first-order kernel and fits more closely the description of the classical ganglion cells. The response is normally accompanied by spike discharges, the amplitudes of which vary from neuron to neuron. This neuron type is probably composed of a large variety of subtypes. Type Y neurons produce either sustained or transient responses to step inputs. In conclusion, the results obtained in this series of papers indicate that the relation of the function of a type of neurons to the underlying morphology is not as simple or homologous as hitherto assumed, and any such correlation at the present time must be statistical rather than a discrete one-to-one correspondence. The application of the intracellular dye-injection technique to the neurons in the central nervous system for identification purposes must be conducted with prudence. AND WHITE-NOISE ANALYSIS of the Note that (100 - EJ is the MSE reduction total linear representation, (100 - El*) is the reduction of the spot component, and (100 - El,) is the reduction of the annulus component. In general, (100 - EJ + (100 - ErJ + (100 - Er,) II !2 I z 3 In The following observation can be made at first glance: 1. For neurons exhibiting high degrees of nonlinearity, the response contributions of the spot (s) and annulus (a) are about equal, i.e., Ire is always near 1. 2) The nonlinear neurons are concentrated in quadrants I and III. That is, for the nonlinear neurons in the retina, the spot and annular inputs produce polarizations of the same direction, i.e., either both hyperpolarize (quadrant I) or both depolarize (quadrant III). In this scattergram dotted lines are drawn to indicate clusters of neurons with similar functional and morphological characteristics, as described in RESULTS. We note: 1) The type C neurons form a well-distinguished cluster in the III quadrant. The polarity of the h, was arbitrarily chosen in the depolarizing direction (because of the noisy h, from type C neurons it was not possible to indicate clearly its polarity). The choice of depolarizing direction is based on the fact that the response of the neuron is depolarizing transients. Type C neurons are highly nonlinear. 2) The type N neurons form one well-distinguished cluster for Na in the III quadrant and one cluster for Nb in the I quadrant. In type N neurons In is small, while Ire is large; their linear responses are largely due to annular inputs. 3) There are two classes of bipolar cells (Ba and Bb) in quadrants II and IV. However, their clusters are not well defined and are rather expansive, indieating a large degree of variation in their response parameters. This may be due to the various sizes I a:hyp s:dep a : hyp s : hyp a: dep s:dep a : dep s : hyp e Ire Ire* ID m In 0 BIPOLAR 0 -- * $-, - .-&- -,--L-f (cx3 3 93 .--- 0 Ba _ --. - - \> \ 0 larger annular [a] Ya NEURONS=?‘1 =------------ bI contribution [a] /c--N //I14 o’, \ 19 cl ’\ II G ,cl II I larger [SI annular e contribution C NEURONS FIG. 27. Scattergram for functional classification of the catfish retinal neurons. For details see the text. Downloaded from http://jn.physiology.org/ by 10.220.33.3 on June 18, 2017 of the spot and If Els = Ela, i.e., the contributions annular inputs are equal, the Ire = 1. If Ire > 1 then the contribution of the annular signal is greater than the contribution of the spot signal, i.e., in a sense, the annular stimulus is more effective in eliciting a response from the neuron. The reverse holds (spot is more effective) if Ire < 1. For all the neurons in the catfish retina for which two-input white-noise experiments were performed, indexes In and Ire were computed. There are 14’7 of them corresponding to the number of experiments. Each experiment (neuron) is plotted on the plane according to its In and Ire indexes (as coordinates). Both of these indexes are positive numbers. However, one of the four quadrants is chosen in each case according to the direction of polarization of the cell potential for spot and annulus stimuli: quadrant I: h, ,a hyperpolarizes, hIa,* hyperPJ arizes quadrant II: h,,/, depolarizes, hla,g hyperpolarizes quadrant III: hlg,a depolarizes, h1a,s depolarizes quadrant IV: hIala hyperpolarizes, hla,B depolarizes The plot of the neuron labels is shown in Fig. 27. 129 130 NAKA, MARMARELIS, CHAN belong either to one of the other clusters or, properly, form a new separate cluster. As noted earlier, this is only a preliminary analysis of the clustering of the retinal neurons according to their functional traits (as reflected by their sets of kernels). Although it is obviously limited-since it considers only two parameters (degree of nonlinearity and relative contribution of each receptivefield component) plus the polarizations-the results seem to be impressive in two aspects: a) this analysis is congruent to our subjective classification scheme presented in RESULTS and b) it could classify to a satisfactory degree 75% of all the neurons analyzed. Considering the difficulties involved in our experiments, which encompassed white-noise analysis and Procion dye injection, we think this is a very favorable score. A more complete study of “clustering” of these neurons according to their functional traits (kernels) would have to take into account a host of other features reflecting the response dynamics of each neuron (e.g., latency, peak response time, damping, forms of nonlinear kernels, etc.). It might alto be possible to produce a similar scattergram of these neurons according to their morphological traits and correlate in a more quantitative (and objective) fashion the structure of a given class of neurons to their functional traits. ACKNOWLEDGMENTS The Service research Grants was supported by NS 10628, EY 00898, Public Health and NB 19234. REFERENCES 1. BAYLOR, D. A. AND FUORTES, M. G. F. Electrical responses of single cones in the retina of London 207: 77-92, 1970. the turtle. J. Physiol., 2. BAYLOR, D. A., FUORTES, M. G. F., AND O’BRYAN, P. M. Receptive fields of single cones in the retina of the turtle. J. Physiol., London 214: 265-294, 1971. 3. BAYLOR, D. A. AND HODGKIN, A. L. Detection and resolution of visual stimuli by turtle photo163-198, receptors. J. Physiol, London 234: 1973. 4. BLACKMAN, R. B. AND TUKEY, J. W. The Measurement of Power Spectra. New York: Dover, 1958. 5. CAJAL, RAM~N Y, S. The Structure of the Retina, translated by S. A. Thorpe and M. 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Whitenoise analysis of a neuron chain: an application Downloaded from http://jn.physiology.org/ by 10.220.33.3 on June 18, 2017 of dendritic expansion or varying degree of contributions from different receptors. 4) The horizontal cells, both internal and external, form very close clusters indicating a very small difference in the response parameters seen in the cells. As we have already mentioned, this is probably due to the fact that they form a syncytium (or laminar layer) in which responses from individual cells are pooled and averaged (S space of Naka and Rushton, ref SO). I) The type Y neurons tend to be rather diffuse in this plane, giving credence to our impression from the functional and structural studies that these neurons encompass a whole spectrum of functional and structural characteristics. However, they tend to have intermediate values of In (around 1.5-2) and intermediate values of Ire. There are two subclasses of type Y neurons: one, type Ya, in the III quadrant and the other, Yb, in the I quadrant. These two types of Y neurons are seen in Fig. 22 in which A is for type Yb and B is for type Ya. 111 are classified into 8 6) Out of 147 neurons, clusters; 36 neurons (or 25 %) are left unclassified, due to a failure either by us to identify them positively in Procion preparations and/or by them to meet the functional criteria of a given class of neurons. Those unclassified neurons between the two clusters Yb and Nb are morphologically unidentified, but functionally they could possibly be included in either one of the two nearby clusters. Those in quadrant I close to the origin of the axes do not fit any of the functional criteria used to classify neurons in this study; it is possible that they AND WHITE-NOISE of Wiener’s 1972. 17. theory. Science 175: 1276-1278, 32. MARMARELIS, 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 131 NELSON, R. 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