Quadrature subunits in directionally selective simple cells: spatiotemporal interactions.

I explore here whether linear mechanisms can explain directional selectivity (DS) in simple cells of the cat's striate cortex, a question suggested by a recent upswing in popularity of linear DS models. I chose a simple cell with a space-time inseparable receptive field (RF), i.e. one that shows gradually shifting latency across space, as the RF type most likely to depend on linear mechanisms of DS. However, measured responses of the cell to a moving bar were less modulated, and extended over a larger spatial region than predicted by two different popular "linear" models. They also were more DS in exhibiting a higher ratio of total spikes for the preferred direction. Each of the two models used for comparison has a single "branch" with a single spatiotemporally inseparable linear filter followed by a threshold, hence, a- "1-branch" model. Nonlinear interactions between pairs of bars in a 2-bar linear superposition test of the cell also disagreed in time-course with those of the 1-branch models. The only model whose 1-bar and 2-bar predictions matched the measured cell (including a complete "4-branch" motion energy model that matches complex cells) has two branches that differ in phase by about 90 deg, i.e. in quadrature. Each branch has its own threshold that helps define the preceding spatiotemporal unit as a subunit even after the outputs of the two branches are summed. As subunit phases differ by only 90 deg, flashing bar responses of the 2-subunit model are similar to those of the 1-subunit model. Therefore, the number of subunits is hidden from view when testing with a conventional stationary bar. In summary, movement responses and nonlinear interactions between pairs of bars in the measured cell matched those of the 2-subunit model, while they disagreed with the popular 1-subunit model. Thus, multiple nonlinear subunits appear to be necessary for DS, even in simple cortical cells.

Quadrature subunits in directionally selective simple cells: counterphase and drifting grating responses.

Here we examine further the basis for directional selectivity (DS) in simple cells of the cat's striate cortex. We use a distinctly different input stimulus and different analysis of the output signal for the same type of space-time inseparable receptive field (RF) that was measured with flashing bars in the companion paper (Emerson, 1997). As in the companion paper, we have mimicked a popular "linear" model with a single "branch" that consists of a linear spatiotemporal filter followed by a soft threshold, which should mimic any simple cells that have a single subunit. Counterphase sinusoidal measurements of such a configuration always generate elliptically shaped polar plots of amplitude versus temporal phase, often pinched along the minor axis because of a high threshold. However, for many spatiotemporal frequencies, such polar phase plots, as measured in simple cells by others, show a consistent rotational phase skew. Here we apply counterphase analysis to the same 2-branch model as developed in the companion paper. We show that the model accounts for the skew as the summation of signals from linear filters separated spatially and temporally by approximately 90 deg (i.e. in spatiotemporal phase quadrature), each separated from the output stage by a soft-threshold nonlinearity. We also prove conclusively that such skew cannot be generated by a single-subunit configuration. This demonstration supports the proposed two-subunit structure for DS simple cells, such as in the example from the companion paper, which has strong linear contributions from its inseparable RF. The presence of at least two nonlinear subunits appears to be an obligatory concomitant of DS in all visual cortical cells. The primary function of these subunits may be to enhance the strength of responses to images moving in the preferred direction, as in complex cells. However, subunits may also aid in identifying the moving object through overcoming, at least partially, the phase-concealing properties of the neuron's threshold by generating a steady signal that effectively decreases the threshold for the preferred direction.

Directionally selective complex cells and the computation of motion energy in cat visual cortex.

We applied a set of 1- and 2-bar tests to directionally selective (DS) complex cells in the cat's striate cortex, and compared the responses with those predicted by two computational models. Single-bar responses and 2-bar interactions produce distinctive patterns that are highly diagnostic. The observed responses are quite similar to those predicted by a basic (non-opponent) motion-energy model [Adelson & Bergen (1985) Journal of the Optical Society of America A, 2, 284-299]. However, they are not consistent with an opponent combination of energy models, nor are they consistent with any stage of the classic Reichardt model. In particular, the Reichardt model (as well as opponent combinations of energy models) predicts a separable space-time symmetry in the 2-bar interaction that is not observed in our measurements, while the non-opponent energy model predicts an inseparable, oriented interaction very similar to the measured cortical responses. Comparisons between model and measurements suggest possible mechanisms of spatial receptive-field organization and of nonlinear transformations.

Identification of complex-cell intensive nonlinearities in a cascade model of cat visual cortex.

Complex cells in the cat's visual cortex show nonlinearities in processing of image luminance and movement. To study mechanisms, initially we have represented the chain of neurons from retina to cortex as a black-box model. Independent information about the visual system has helped us cast this "Wiener-kernel" model into a dynamic-linear/static-nonlinear/dynamic-linear (LNL) cascade. We then use system identification techniques to define the nature of these transformations directly from responses of the neuron to a single presentation of a stimulus composed of a sequence of white-noise-modulated luminance values. The two dynamic linear filters are mainly low-pass, and the static nonlinearity is mainly of even polynomial degree. This approximate squaring function may be effected in the animal by soft-thresholding each of the linear ON- and OFF-channel signals and then summing them, which account for "ON-OFF" responses and for the squaring operation needed for computation of "motion energy", both observed in these neurons.

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

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

ON-OFF units in the mustached bat inferior colliculus are selective for transients resembling "acoustic glint" from fluttering insect targets.

Of 311 single units studied in the central nucleus of the inferior colliculus (ICC) in 18 mustached bats (Pteronotus parnelli), a small but significant population (13%) of cells with on-off discharge patterns to tone bursts at best frequency (BF) was found in the dorsoposterior division. In contrast to units with the same BF's but other discharge patterns, the majority of ON-OFF units were unresponsive to sinusoidally amplitude-modulated tone bursts (SAM). To define the contribution of linear and nonlinear components to the responses of ICC neurons to amplitude modulation, we tested some of these neurons with a long, seamlessly repeating pseudorandom sequence of ternary amplitude-modulated tones at BF. Wiener-like kernels were subsequently derived from cross-correlation of spikes with acoustic events in the sequence. These kernels provided estimates of neural impulse responses that proved unusual in SAM-unresponsive ON-OFF units. First, their estimated impulse response had no linear component. Second, the predicted second-order impulse responses to both increments and decrements in stimulus intensity were long (about 20 ms) and nearly identical in shape: triphasic, with the positive phase bounded by leading and trailing negative periods. The similar shape of responses to increments and decrements in these neurons suggests a full-wave rectifier. The triphasic, initially negative second-order prediction of the impulse response accounted for an unusual result in experiments measuring the recovery cycle of ON-OFF units using a pair of identical stimulus pulses separated by various time delays. This recovery cycle can be related to their response to amplitude modulation. As the delay between two brief, near-threshold BF tone bursts decreased, the response to the first tone diminished, rather than to the second. The second-order prediction of this experiment derived from impulse responses obtained with pseudorandom noise suggests that, at short interpulse intervals, the initial negative phase of the response to the later stimulus cancels the positive phase of the response to the first. Such cancellation at short interpulse intervals may help explain why the majority of ON-OFF units are unresponsive to SAM. The unusual properties of these ON-OFF units make them ideally suited to respond selectively to infrequent acoustic transients superimposed on an ongoing background of modulation. Such patterns are commonly encountered by mustached bats foraging in cluttered habitats for small, fluttering insects, which generate "acoustic glints" upon a background of modulated echoes from the surroundings (Schnitzler et al. 1983; Henson et al. 1987).

Nonlinear measurement and classification of receptive fields in cat retinal ganglion cells.

Originally, modeling of ganglion-cell responses in cat was based mainly on linear analysis. This is satisfactory for those cells in which spatial summation of excitation is approximately linear (X-cells) but it fails for Y-cells, where summation has strong nonlinear components. Others have shown the utility of using sinusoidal analysis to study harmonic and intermodulation nonlinearities in the temporal frequency domain. We have used Wiener-kernel analysis to obtain directly both temporal and spatial impulse responses and their nonlinear interactions. From these, we were able to predict accurately the responses that a counterphase modulated grating elicited in both X-cells and Y-cells. In addition, we show that the first-order responses can measure the two-dimensional spatial features of the receptive field with high resolution. Thus, nonlinear analysis of responses to white-noise stimuli may be sufficient to both classify and measure the receptive fields of many different types of ganglion cells.

A linear model for symmetric receptive fields: implications for classification tests with flashed and moving images.

The purpose of this study was to explore the effects of spatial and temporal properties on the expected responses of visual neurons that have linear receptive fields (RFs), particularly those having a mirror symmetric distribution of spatial subregions. Receptive fields that are symmetric in at least one spatial dimension occur in neurons of the retina, the lateral geniculate nucleus (LGN), and the visual cortex of mammals. Responses to flashing bars, moving bars, and moving edges were studied for different configurations of an analog RF model in which spatial and temporal aspects were varied independently. Responses of the model at intermediate stimulus speeds were found to agree with responses in the literature for X and Y units of the LGN and often for simple units of the visual cortex. In particular, having separated regions of response to light and dark edges, an identifying property of simple cells, was found to be a linear consequence of RF regions responding inversely to stimuli of opposite polarity. Model differences from responses of cortical complex units show that a linear model cannot mimic their responses, and imply that complex units employ major nonlinearities in coding image polarity (light vs dark), which signifies a nonlinearity in coding intensity. Because sudden flux changes inherent in flashing bars test mainly temporal RF properties, and slowly moving edges test mainly spatial properties, these two tests form a useful minimal set with which to describe and classify RFs. The usefulness of this set derives both from its sensitivity to spatial and temporal variables, and from the correlation between the linearity of a cell's processing of stimulus intensity and its RF classification.

Nonlinear directionally selective subunits in complex cells of cat striate cortex.

1. We have analyzed receptive fields (RFs) of directionally selective (DS) complex cells in the striate cortex of the cat. We determined the extent to which the DS of a complex cell depends on spatially identifiable subunits within the RF by studying responses to an optimally oriented, three-luminance-valued, gratinglike stimulus that was spatiotemporally randomized. 2. We identified subunits by testing for nonlinear spatial RF interactions. To do this, we calculated Wiener-like kernels in a spatial superposition test that depended on two RF positions at a time. The spatial and temporal separation of light and dark bars at these two positions varied over a spatial range of 8 degrees and a temporal range of +/- 112 ms in increments of 0.5 degree and 16 ms, respectively. 3. DS responses in complex cells cannot be explained by their responses to single light or dark bars because any linear superposition of responses whose time course is uniform across space shows no directional preference. 4. Nonlinear interactions between a flashed reference bar that is fixed in position and a second bar that is flashed at surrounding positions help explain DS by showing multiplicative-type facilitation for bar pairs that mimic motion in the preferred direction and suppression for bar pairs that mimic motion in the null direction. Interactions in the preferred direction have an optimal space/time ratio (velocity), exhibited by elongated, obliquely oriented positive domains in a space-time coordinate frame. This relationship is inseparable in space-time. The slope of the long axis specifies the preferred speed, and its negative agrees with the most strongly suppressed speed in the opposite direction. 5. When the reference bar position is moved across the RF, the spatiotemporal interaction moves with it. This suggests the existence of a family of nearly uniform subunits distributed across the RF. We call the subunit interaction, as averaged across the RF, the "motion kernel" because its spatial and temporal variables are those necessary to specify the velocity, the only parameter that distinguishes a moving image from a temporally modulated stationary image. The nonlinear interaction shows a spatial periodicity, which suggests a mechanism of velocity selectivity for moving extended images.(ABSTRACT TRUNCATED AT 400 WORDS)

White noise analysis of cortical directional selectivity in cat.

We studied spatiotemporal interactions in cat cortical receptive fields by presenting a stimulus composed of 16 narrow bars whose luminances were randomly modulated. Conventional stimuli were also presented to classify receptive field properties. A white noise estimate of the cell's response to a stepwise moving bar stimulus was calculated from responses to the spatiotemporal random stimulus. The white noise estimate captured the most important feature of the receptive field demonstrated by conventional stimuli, i.e. directional selectivity. In addition, the white noise analysis; (1) made visible inhibitory response phases that are usually below threshold; (2) subdivided the response into its linear and non-linear estimates; (3) further subdivided the non-linear estimate into spatial and temporal interactions; and (4) allowed estimation of responses to stimuli that were never explicitly presented.

Does image movement have a special nature for neurons in the cat's striate cortex?

The question of whether a moving image is especially effective for stimulating visual neurons was studied in the striate cortex of the cat. Receptive fields (RFs) of simple and complex neurons were stimulated with optimally oriented bright and dark bars that either moved smoothly or were presented statically at an array of positions across the RF. A linear prediction of responses to the smooth movement was calculated by superposition of the responses to stationary presentation of these bar stimuli. A comparison between responses to actual movement and their prediction showed that the relative effectiveness of a moving stimulus decreases with speed. Effects of "conditioning" stimuli and nitrous oxide anesthesia were also studied. Both simple and complex units exhibited on average slightly lower than predicted responses for both bright and dark bars, even when they moved in the preferred direction of the unit. Movement in the opposite direction usually elicited even lower response levels, suggesting nonlinear suppression. These results imply that a moving image has no special efficacy for visual neurons but rather that it has a special propensity to elicit suppression when it moves in the nonpreferred (null) direction of a neuron.

Spatial sampling by dendritic trees in visual cortex.

Kittens were reared in vertically or horizontally striped cylinders. After rearing exposures of 400-500 h, responses of single neurons were determined as a function of orientation of a square wave grating stimulus. These data suggest that the rearing environment did alter orientation preference in some of the kittens. The visual cortices of the stripe-reared kittens and of control kittens were impregnated according to a Golgi-Cox method. Dendrites of layer IV stellate cells were tracked and analyzed in three dimensions by a computer-microscope. Four methods of analyzing the spatial distribution of dendrites are described and discussed. Two methods previously described in the literature were not sufficiently sensitive to detect any differences among kittens exposed to vertical or horizontal stripes or to a control environment. Two newly developed methods were able to provide initial evidence for rearing effects on dendritic trees in visual cortex. The more detailed of these new methods describes the angular location of dendritic segments, with respect to standard brain axes, as a function of distance from the cell body. Data obtained by means of this method of dendritic angular distribution (DAD) plots suggests a number of conclusions. Rearing animals in a striped environment may influence the way in which dendrites of layer IV stellate cells of visual cortex distribute themselves in the neuropil. The effect of selective rearing on dendritic distribution does not appear to extend back to those portions of the dendritic tree closest to the cell body. This influence of rearing in a selective environment may be explained by hypothesizing that during development dendrites distribute themselves in ways that tend to maximize the effects of spatiotemporal summation for the postsynaptic neurons.

Simple striate neurons in the cat. I. Comparison of responses to moving and stationary stimuli.

1. Peristimulus time (PST) histograms of simple striate responses to static presentations of narrow bright and dark bars in an array of receptive-field (RF) positions have demonstrated one to four response regions with distinct response properties. 2. There is a high degree of correlation of these responses with PST histograms of responses to the same stimuli moving smoothly ("dynamic" stimuli) in a direction perpendicular to the long axis of the RF. 3. Trailing responses to smoothly moving bar stimuli usually occur as the stimulus leaves an apparently inhibitory (for that stimulus) RF region. 4. Spatially leading responses to smoothly moving stimuli occur just as a bar stimulus enters an excitatory RF region, and may be based on certain gradient-detecting properties of neurons. 5. Close agreement in peak firing rates and in positions of responses for statically and dynamically elicited responses in units that are not strongly directionally selective suggests the possibility that in most respects smooth movement responses may be the sequential linear superposition of static responses. A quantitative superposition of static responses from two units supports this conclusion. 6. The dependence on a steady background for sustained responses to static presentation of dark bars illustrates the significance of steady illumination in the RF and raises questions about the efficacy of using edge stimuli as elemental visual probes.

Simple striate neurons in the cat. II. Mechanisms underlying directional asymmetry and directional selectivity.

1. Directionally asymmetric (DA) units respond preferentially to one direction of image movement. If that preferred direction is independent of stimulus contrast then the DA unit is considered directionally selective (DS). We have analyzed receptive-field (RF) properties of striate units with these properties by presenting bar-shaped stimuli that are moved in a stepwise sequence. Short interstimulus durations for certain ranges of step size elicit DA responses similar to those from smooth movement, while still allowing identification of on- and off-components of the response. 2. We have been able to isolate three mechanisms underlying DA and DS. The simplest, superposition, explains the dependence of preferred direction on stimulus contrast found in some DA units. It relies completely on asymmetries in static RF regions to provide an advantage for one direction of image motion by means of the simultaneity of image elements leaving an apparently inhibitory region and entering an excitatory one. 3. For all DA and DS units we have encountered forward inhibition of otherwise excitatory influences that reduces the responsiveness in the antipreferred direction. The spatial specificity of inhibitory target RF regions and the nonlinearity of the effect suggest that lateral inhibition may be transmitted via sequence-detecting subunits. 4. Units that do not show superposition in the preferred direction exhibit forward facilitation of responses in a nonlinear and target-specific way which suggests that facilitation may also be transmitted via sequence-detecting subunits. 5. Each of these mechanisms depends on short-lived influences that are laterally transmitted between 0.125 and 0.5 degrees in visual space. These spatial and temporal values are appropriate for the analysis of smooth movement by the visual system. 6. Stepwise movement sequences using dark bars on a bright background demonstrate for some DA units exactly the same mechanisms as demonstrated using bright-bar sequences in other units or, in the case of DS units, in the same units. In such DS units, which do not normally exhibit strong stationary RF asymmetries, differential sensitivity of the nonlinear DS mechanisms to stimulus elements of either contrast will yield an effective preferred movement direction for complex stimuli.