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The Journal of Neurophysiology Vol. 80 No. 2 August 1998, pp. 762-770
Copyright ©1998 by the American Physiological Society
1 University of California, Davis Center for Neuroscience and Section of Neurobiology, Physiology and Behavior, Davis, 95616; and 2 Howard Hughes Medical Institute and Department of Neurobiology, Stanford University School of Medicine, Stanford, California 94305
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ABSTRACT |
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 Abstract
 Introduction
Methods
Results
Discussion
References
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Britten, Kenneth H. and William T. Newsome. Tuning bandwidths for near-threshold stimuli in area MT. J. Neurophysiol. 80: 762-770, 1998. It is not known whether psychophysical performance depends primarily on small numbers of neurons optimally tuned to specific visual stimuli, or on larger populations of neurons that vary widely in their properties. Tuning bandwidths of single cells can provide important insight into this issue, yet most bandwidth measurements have been made using suprathreshold visual stimuli, whereas psychophysical measurements are frequently obtained near threshold. We therefore examined the directional tuning of cells in the middle temporal area (MT, or V5) using perithreshold, stochastic motion stimuli that we have employed extensively in combined psychophysical and physiological studies. The strength of the motion signal (coherence) in these displays can be varied independently of its direction. For each MT neuron, we characterized the directional bandwidth by fitting Gaussian functions to directional tuning data obtained at each of several motion coherences. Directional bandwidth increased modestly as the coherence of the stimulus was reduced. We then assessed the ability of MT neurons to discriminate opposed directions of motion along six equally spaced axes of motion spanning 180°. A signal detection analysis yielded neurometric functions for each axis of motion, from which neural thresholds could be extracted. Neural thresholds remained surprisingly low as the axis of motion diverged from the neuron's preferred-null axis, forming a plateau of high to medium sensitivity that extended ~45° on either side of the preferred-null axis. We conclude that directional tuning remains broad in MT when motion signals are reduced to near-threshold values. Thus directional information is widely distributed in MT, even near the limits of psychophysical performance. These observations support models in which relatively large numbers of signals are pooled to inform psychophysical decisions.
Two contrasting ideas have dominated inquiry concerning the relationship between perception and the activity of sensory neurons in the CNS. According to Horace Barlow's classic single neuron doctrine (Barlow 1972 These data were obtained from area MT of two adult, female rhesus monkeys (Macaca mulatta). The general methods are similar to those used in previous studies and will be described only briefly. Before recording, each monkey was equipped with a head post for restraint, a scleral search coil to monitor eye position, and a recording cylinder implanted over the occipital cortex to allow microelectrode access to area MT from a posterior direction, 20° above horizontal in a parasagittal plane. This equipment was secured to the skull using a dental acrylic implant, and this procedure was performed under deep surgical anesthesia. The monkeys were given at least 2 wk to recover from surgery before recording. For recording experiments, the monkeys were removed from their home cages and seated in a primate chair in front of the cathode ray tube (CRT) screen on which the stimuli were displayed. They were required to fixate within 0.75-1.2° of a small spot projected on the screen; no discrimination was required. Successfully completed fixation trials were rewarded with a drop of water or juice; broken fixations were followed by a brief time-out period. All procedures complied with the National Institutes of Health and United States Department of Agriculture guidelines for the care and use of laboratory animals and had been approved by the Stanford University Animal Care and Use Committee.
Visual stimuli
The computer presented, via a fast D/A converter, streams of dots on the face of a vector display CRT (Xytron A21, P4 phosphor). These dots could either be replotted randomly on each iteration, or with a specified spatiotemporal offset, which determined the direction and speed of the apparent motion signal. In practice, the temporal interval between replottings of the signal dots was held fixed at 45 ms, and the speed of motion was varied by adjusting the spatial interval. The proportion of dots replotted in this way was determined by a parameter we term the coherence of the display. This parameter controlled the signal-to-noise ratio of the display and thus the salience of the motion. The coherence corresponds approximately linearly to total motion energy in the specified direction (Britten et al. 1993 Data analysis
Data were stored digitally as times of spike arrivals (1 ms resolution), and these were converted to spike counts by integrating over the entire 1-s stimulus period. Two different analyses were performed on these data. First, we performed bandwidth analysis to characterize the breadth of directional tuning of our cells as a function of coherence. For this purpose, the response-versus-direction data were fit with Gaussian functions of the form
INTRODUCTION
Abstract
Introduction
Methods
Results
Discussion
References
, 1995), a cortical neuron is tuned along a number of stimulus dimensions so that only a small, highly specific set of stimuli can excite the cell optimally. Furthermore, the optimal stimulus for each neuron is likely to differ given the large number of stimulus dimensions along which neurons can be tuned. From this point of view, each individual neuron acts as a highly specific detector ("cardinal cell") for its optimal stimulus and thus wields substantial signaling power concerning the presence of this stimulus in the visual environment. According to this view, simple perceptual judgments would ideally be based on activity in a very small number of cortical neurons best tuned to the stimulus at hand. A key advantage of such "sparse coding" models is that they increase the efficiency of the representation by reducing statistical dependence among individual elements.
; Britten et al. 1992; Maunsell and Van Essen 1983a; Newsome and Paré 1988; Orban et al. 1995; Pasternak and Merigan 1994; Salzman et al. 1992; Schiller 1993; Schiller and Lee 1994; Zeki 1974). We measured the directional tuning of MT neurons for both near-threshold and suprathreshold stimuli. Our visual stimuli were stochastic random dot patterns in which we could vary the signal-to-noise ratio of the directional motion signal. Using these stimuli, we found that directional tuning of MT cells remains broad even near behavioral threshold. In addition, neuronal thresholds for signaling direction remained fairly low even for stimuli quite far removed from their preferred directions. These observations suggest that information remains broadly distributed across a cortical map, even near threshold, consistent with the notions of coarse coding. Considered together with our prior experimental and modeling studies (Britten et al. 1992, 1996; Shadlen et al. 1996), the present data suggest that directional judgments under our experimental regime are influenced by a population of MT neurons having a wide range of preferred directions.
METHODS
Abstract
Introduction
Methods
Results
Discussion
References
) and were inserted through the dura using local anesthetic if necessary. On recording days, parylene-coated tungsten microelectrodes (Micro Probe) were introduced through the guide tube, and neural signals from these were amplified, filtered, and displayed using standard methods. Spikes were isolated using a time-amplitude window discriminator (Bak Electronics) and were fed as transistor-transistor logic pulses to the computer controlling the experiment. The electrode was advanced until a single-unit signal could be isolated, and appropriately moving dot patterns or moving bars were used as search stimuli. Once a single unit was isolated, the receptive field was mapped using hand-held stimuli, typically moving bars of light. Random dot stimuli were restricted to the classical receptive field (RF) in subsequent experiments.
) and is independent of the average luminance as well as the specified motion parameters. The display was stochastic; the replotting of each dot was independent of all others and of its own history. Accordingly, the directional signal was randomly distributed both in space and in time, varying around a uniform mean. Each stimulus was 1 s in duration, and dots were presented at a rate of 6.67 kHz. The average luminance of the stimulus was 0.67 cd/M2, and the contrast of each dot was very nearly 100% (background of 0.01 cd/M2).
where A is response amplitude (i.e., dynamic range), µ specifies the center of the function,
(1)
the bandwidth, and B is the baseline response at directions far from preferred (this need not be equal to the maintained activity, because of inhibition in the null direction). The present analysis focuses on the bandwidth parameter, ; we have previously characterized the amplitudes of response in preferred and null direction (approximated by the parameters A and B) as a function of coherence (Britten et al. 1993).
; Britten et al. 1992; Tolhurst et al. 1983; Vogels and Orban 1990). For each cell, axis of motion, and coherence level, we measured the discriminative capability of the cell using ROC analysis (Green and Swets 1966). The area under a ROC curve forms an unbiased, distribution-free estimator of the capability of the cell to discriminate between the two opposite directions along a given axis of motion. For each cell and axis, ROC area was plotted as a function of stimulus coherence to form a neurometric function relating performance to stimulus strength. We fitted each of these with a Quick function (Quick 1974) of the form
where P is the probability of a correct decision by the ideal observer, c is the coherence of the stimulus,
![<IT>p</IT>= 1 − 0.5 {exp [−(<IT>c</IT>/α)<SUP>β</SUP>]}](/content/vol80/issue2/fulltext/762/img002.gif)
(2)
is the threshold (82% correct point), and 
is a unitless parameter characterizing the steepness of the relationship. In previous work (Britten et al. 1992), we established that this function is a good description of neurometric data from MT cells' responses measured along the preferred-null axis. Note that in Eq. 2, the asymptotic performance is assumed to be unity; this assumption is similar to the one we have tested previously for optimal stimuli (Britten et al. 1992). We maintained this assumption in the present analysis even though nonoptimal axes of motion frequently yielded imperfect performance at the highest coherence level (ROC area < 1.0). We adopted this procedure so that neural thresholds measured along the various axes could be fairly and quantitatively compared. Allowing the asymptote to vary as a free parameter would preclude such a comparison because the threshold parameter is defined relative to the asymptote. We emphasize that the thresholds reported in this study reflect the same absolute level of neuronal performance (i.e., 82% correct) irrespective of the axis of motion.
). The log likelihood for each fit (which is distributed approximately as 
2) was calculated both for the fit with more parameters (2 for the Quick function and 4 for the Gaussian), and also for the fit to the mean alone. The difference of these log likelihoods is also distributed approximately as 2, and the associated degrees of freedom is the difference in the number of free parameters in each fit. This statistic tests the null hypothesis that there is no significant improvement in fit by the full function. Conditions for which the null hypothesis could be rejected (P < 0.05) were retained for quantitative analysis. Inspection of the fits "by eye" suggested that this test was fairly stringent, and all of the retained fits were of high quality. For both types of fit, there was no indication that the fit parameters in the unreliable cases were biased.
Histology
During recording, cells were identified as being within MT according to reliable physiological landmarks, including 1) consistently directional responses, 2) reasonable RF size, with the diameter being approximately equal to the eccentricity, 3) appropriate depth from the opercular surface, 4) systematic progressions in preferred direction (Albright 1984), and 5) shifts of RF location with electrode movement corresponding to the expected retinotopy of MT. After the experiments, the monkeys were anesthetized with ketamine hydrochloride, killed with an overdose of pentobarbital sodium, then perfused with normal saline followed by a 10% Formalin fixative solution. The brains were removed, blocked, and postfixed in 10% Formalin containing 30% sucrose. After equilibrating in sucrose, they were sectioned at 40 µm thickness on a horizontal freezing microtome. Alternate series of sections at 0.5-mm intervals were stained for Nissl substance and myelin (Gallyas 1979). MT was easily identified as a myelin-dense region on the posterior bank of the superior temporal sulcus (Allman and Kaas 1971; Ungerleider and Mishkin 1979; Van Essen et al. 1981). In both cases, the interval between recording and histological reconstruction prevented the use of marking lesions, but the overall region of intensive recording was easily visible from guide tube damage posterior to area MT. In both cases, this area corresponded well to the myeloarchitectonic boundaries of area MT.
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RESULTS |
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Abstract
Introduction
Methods
Results
Discussion
References
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These results were obtained from 52 cells in 2 monkeys. Data from two representative MT neurons are shown in Fig. 1. The neuron shown in A and B is broadly tuned for direction, whereas the neuron illustrated in C and D is more narrowly tuned. Figure 1, A and C, depicts firing rate as a function of direction for several coherence levels, and it is clear that the responses increase systematically as a function of coherence within the excitatory portion of each tuning curve. Figure 1, B and D, depicts the same data following normalization to the range of response in each tuning curve. The normalized tuning curves superimpose nicely. These example data illustrate two important points. First, the responses increase monotonically and approximately linearly as a function of coherence for every direction tested. This extends the observations of Britten et al. (1993) to stimulus directions other than the preferred and null. Second, the normalized plots on the right show that the shape of the direction tuning functions are not strongly influenced by the coherence of the stimulus. In Fig. 1D, there is a slight suggestion that the direction tuning functions become somewhat broader at lower coherence, because the dashed line curves tend to lie outside the solid line curve representing 100% coherence.
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Bandwidth analysis
To parameterize the shape of the direction tuning functions and their dependence on the coherence of the stimulus, we fit each direction tuning curve with a Gaussian function (Eq. 1). Figure 2 illustrates Gaussian fits to data from two coherence levels. The mean ± SD (±1 ) of the two Gaussians, indicated by the vertical lines, are in good agreement for the two functions despite the substantial difference in the amplitudes. Thus the two functions are largely scaled replicas of each other.
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ROC analysis
We analyzed each neuron's ability to discriminate opposed directions of motion using the method of ROC analysis, in a manner similar to our previous work (for details, see Britten et al. 1992
The results of this study confirm and extend numerous studies of tuning properties of MT neurons (Albright 1984 Relationship with previous work
This result may be compared with measurements made using other classes of stimuli in other cortical areas. In primary visual cortex of cats, tuning bandwidths for orientation and spatial frequency are largely invariant with stimulus contrast (Albrecht et al. 1984 Stimulus effects
The manipulation of stimulus strength employed in the present work is complex because it changes the distribution of motion energy in the stimulus without changing the total energy in the stimulus (Britten et al. 1993 Coarse or sparse coding in MT?
The principal result of this work is that the distribution of information on the map of direction in MT is very broad, even for weak motion signals near psychophysical threshold. This appears to contrast with the predictions of sparse coding schemes. One way of visualizing these predictions is to picture a "hill" of activity on the map of direction in MT, and then to imagine how it changes as the stimulus is made weaker. If one imagines such a hill "sinking" past some threshold, then as performance limits are reached, only the very tip of the hill would be visible, and useful information would become highly localized within MT. Thus a representation that appeared coarsely coded at high stimulus intensities could be quite sparsely coded near threshold. A variety of nonlinearities in the pathway leading to MT could produce such effects. However, our results argue against such a picture: as the stimulus is made weaker, the hill simply scales down in height without changing its shape. If anything, the peak of activity becomes a little broader, not narrower. Thus the ideal observer charged with the job of extracting information from this representation would not change strategy for weaker stimuli.
The authors thank J. Stein for expert technical assistance. We also thank M. N. Shadlen and B. A. Olshausen for helpful discussion.
This work was supported by National Eye Institute Grants EY-05603 to W. T. Newsome and EY-10562 to K. H. Britten. W. T. Newsome is an Investigator of the Howard Hughes Medical Institute.
Address for reprint requests: K. H. Britten, UC Davis Center for Neuroscience, 1544 Newton Ct., Davis, CA 95616. Received 14 October 1997; accepted in final form 14 April 1998.
0.131. This relationship was not significant (P = 0.17), although there is a weak trend toward larger bandwidths at lower coherence values. This effect, if real, is clearly modest in magnitude, because it predicts only a 14% change in bandwidth across the range of 0-100% coherence.
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FIG. 3.
Relationship between tuning bandwidth and stimulus coherence for all cells. A data set was included only if the fitted Gaussian function met a strict goodness of fit criterion (see METHODS). The line shows the simple regression relationship derived from the 95 data sets that passed this test.
0.21, again suggesting a modest negative relationship between bandwidth and coherence. The mean of this distribution is significantly <0 (2-tailed t = 2.18, P = 0.034). Thus, analyzed on a per cell basis, the weak relationship seen in Fig. 3 becomes statistically significant. This is only evident after pooling; in only 2/52 cases was the individual correlation significant (P < 0.05), because the number of coherence values contributing to each was small. As seen previously, the relationship is not strong, predicting only modest changes in bandwidth across the full range of possible stimulus strengths. Because of the uncertainty in the individual slope estimates, the resulting mean slope should be interpreted with caution.
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FIG. 4.
Relationship between bandwidth and coherence, analyzed on a per-cell basis. For each cell, a simple regression was performed, and the slope value was taken from this relationship. The resulting slopes were compiled into the histogram, whether or not they were individually significant. The arithmetic mean of the slope values is indicated above the arrow.
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FIG. 5.
Residuals from the Gaussian fits. For each coherence employed between 6.4 and 100%, we plot the average (across cells), normalized residual as a function of direction. Data were aligned to the peak of the best-fit Gaussian, and a running 15-point arithmetic mean was computed for each coherence (solid curves). All individual residuals were scaled to the amplitude parameter for the Gaussian fit for that cell and coherence value before averaging; this gives all observations equal weight despite differences in firing rate or dynamic range. The curves were offset from each other vertically for graphic clarity.
). This method extracts a performance estimate from the two distributions of spike counts obtained for the two opposed directions of motion along a particular axis. If these distributions are similar, the performance estimate (ROC area) will be close to chance (0.5, or 50% correct). If the response distributions are nonoverlapping; however, the performance estimate will be perfect (1.0, or 100% correct). In effect, the ROC area estimates the performance of an ideal observer who is trying to deduce the stimulus from the spike rate of the cell. For 43 neurons with adequate data sets (data collected for all 6 axes of motion), we computed ROC areas for each axis of motion and coherence level tested. The contour plot in Fig. 6 illustrates average neuronal performance (ROC area) as a function of axis of motion and coherence level. The preferred direction was defined as the peak of the Gaussian fit to the data at the highest coherence used.
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FIG. 6.
Average performance of 43 MT cells, calculated using receiver operating characteristic analysis, as a function of coherence and direction of the stimuli. The gray level and the contours both depict the average ROC estimate of performance, and the bold contour shows performance of 82% correct, a value we have defined as threshold performance. Directional data were binned for averaging in 15° bins, and all coherences between 6.4 and 100% were included. As indicated by the calibration bar to the right, lighter gray values correspond to better performance (ROC areas nearer to 1.0).
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FIG. 7.
Neurometric thresholds plotted as a function of axis of motion for the same cells illustrated in Fig. 1. The axis of motion is given in degrees of polar angle relative to the preferred-null axis. Along each axis, data from opposed directions were used to calculate a neurometric function from which neural thresholds were derived. 
, statistically unreliable threshold estimates (see METHODS).
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FIG. 8.
Neurometric thresholds as a function of axis of motion for all cells for which sufficient data were obtained. The axis of motion is given in degrees relative to the preferred direction, defined as the peak of the Gaussian function fit to the highest coherence stimulus. Large circles indicate statistically reliable threshold measurements; small circles represent cases that failed our goodness of fit test (see METHODS). Thirty-four extreme values have been removed from this latter group. Solid curve corresponds to a running 9-point boxcar geometric mean of only the reliable threshold estimates. These data are subject to 2 sources of noise not present in previous work from this laboratory (Britten et al. 1992 ): smaller number of trials per coherence and smaller number of coherence levels presented. Both were necessary compromises because of the number of directions presented, but neither should in principle be a source of bias.
DISCUSSION
Abstract
Introduction
Methods
Results
Discussion
References
; Lagae et al. 1993; Maunsell and Van Essen 1983b; Snowden et al. 1992). We find broad tuning for direction, both with high and low coherence stimuli. Bandwidths became significantly broader at low coherences, but this effect was small. Additionally, analysis of neuronal discrimination thresholds showed that MT neurons maintained differential sensitivity to opposed directions for axes of motion quite far removed from the preferred-null axis. Thus large numbers of neurons carry signals appropriate for performing the task, even near psychophysical threshold. This pattern of results appears consistent with coarse coding models of the representation of stimulus direction in MT.
; Sclar and Freeman 1982). This comparison is particularly interesting because contrast-response functions frequently saturate, whereas coherence-response functions rarely do (Britten et al. 1993). Contrast saturation might be expected to change the shape of tuning functions, because it would broaden the top of these functions, as the high rates near the center of the function reach the saturating response. The modest effects of coherence on bandwidth in our results are unexpected on these grounds, because coherence-response functions are linear on average. However, these effects are small, affecting bandwidth by 15-30% at most, and the general finding appears to be that tuning functions are largely invariant with changes in stimulus strength. This, of course, is highly desirable from a theoretical point of view, because it stabilizes the representation of image features against changes in viewing conditions or the addition of noise.
, 1996; Newsome and Paré 1988; Shadlen et al. 1996). The task involved discrimination of opposed directions of motion using the same family of stochastic motion stimuli employed in the current study. We now consider the import of the current results for models of how directional signals in MT mediate performance on this task. The relevance of the current results for other motion discrimination tasks is less clear (e.g., Orban et al. 1995; Pasternak and Merigan 1994; Snowden et al. 1992), and we therefore have little to say about them.
). Initially, this led us to suggest that perhaps very small numbers of MT neurons were involved in any particular task configuration (Newsome et al. 1989). However, consideration of two other measurements [shared noise between neurons and the correlation of neuronal discharge with choice (Britten et al. 1996; Zohary et al. 1992)] subsequently led us to favor models in which much larger pools of neurons are involved in such a direction discrimination task. Simulations showed that larger pools can produce behavioral thresholds consistent with those we observed, even if the pools include additional neurons whose sensitivity to direction is an order of magnitude worse than those we actually measured. Our simulations suggest, in fact, that such insensitive neurons must be included in the sensory pool to reconcile the complete set of physiological and psychophysical data (Shadlen et al. 1996). In our computational analysis, we simulated these "insensitive" neurons by an arbitrary linear scale factor because we had never measured the responses of nonoptimally tuned neurons. The present measurements allow us to ground this modeling work in the actual responses of nonoptimally tuned neurons in MT.
; Shadlen et al. 1996), the neurons would be formed into two broad pools, each one centered around one of the two opposed directions of motion in a particular discrimination between opposed alternatives.
; Raiguel et al. 1995), suggesting that a stimulus need not overlap the RF by much to generate a useful directional signal in the cell. Second, the RFs of MT neurons are large, with diameters roughly equal to their eccentricity (Maunsell and Van Essen 1983a; Zeki 1974). Together these observations suggest that the pool of available signals in MT is very large, and that a substantial fraction of MT neurons might carry signals useful for any given configuration of our task.
). As coherence is reduced, a broad region of increased motion energy forms, including velocities near but not identical to the specified motion signal. Thus, at low coherence levels, the somewhat larger directional bandwidths we observe might result from changes in the stimulus itself, rather than changes in the neuronal representation per se. To explore this possibility, we have performed computer simulations similar to those we have reported in previous work (Britten et al. 1993). We designed motion-energy filters whose spatiotemporal characteristics resembled those of MT cells, and we simulated their responses to random dot stimuli like those in the present work. Across a wide range of model parameter values, direction tuning bandwidths were completely unaffected by the coherence of the stimuli. Thus we believe that the modest increase in bandwidth observed in our experiments arises from the biology of the system, rather than being a trivial consequence of the distribution of motion energy in our stimuli.
). Although MT appears more specialized than many cortical areas, it probably still represents at least six stimulus dimensions (2 dimensions of space, 2 of velocity, 1 of stereoscopic depth, and possibly orientation, spatial scale, and surround velocity as well). Thus the representation along any single dimension (such as direction of motion) can appear quite redundant, if the test stimuli were optimized along the other relevant dimensions. In our experiments, we attempted to optimize along only a subset of these stimulus dimensions (2 of space and 2 of velocity), yet the representation still appears coarsely coded and thus not highly "efficient." As suggested by Barlow (Barlow and Tripathy 1997), this might reflect the advantage of averaging out noise in the image or its representation by pooling across inputs, each representing somewhat different values along some dimension. An inescapable consequence of such averaging is the broadening of tuning functions, and a concomitant decrease in the "sparseness" of the representation. Given that noise is most limiting near threshold, it would be advantageous to maintain a coarse code for such stimuli. By pooling broadly across available signals, one maintains sensitivity to the presence and rough identity of stimuli nearly lost in noise.
ACKNOWLEDGEMENTS
FOOTNOTES
REFERENCES
Abstract
Introduction
Methods
Results
Discussion
References
0022-3077/98 $5.00 Copyright ©1998 The American Physiological Society
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, data for 100% coherence stimuli;