 |
|||||
|
|||||
|
|||||
|
|||||
|
|||||
The Journal of Neuroscience, July 30, 2003, 23(17):6681-6689
Previous Article | Next Article
Temporal Resolution of Ensemble Visual Motion Signals in Primate Retina
E. J. Chichilnisky andR. S. Kalmar Systems Neurobiology, The Salk Institute and University of California, San Diego, La Jolla, California 92037
Abstract
Top
Abstract
Introduction
Recent studies have examined the temporal precision of spiking in visual system neurons, but less is known about the time scale that is relevant for behaviorally important visual computations. We examined how spatiotemporal patterns of spikes in ensembles of primate retinal ganglion cells convey information about visual motion to the brain. The direction of motion of a bar was estimated by comparing the timing of responses in ensembles of parasol (magnocellular-projecting) retinal ganglion cells recorded simultaneously, using a cross-correlation approach similar to standard models of motion sensing. To identify the temporal resolution of motion signals, spike trains were low-pass filtered before estimating the direction of motion. The filter time constant that resulted in most accurate motion sensing was in the range of 10-50 msec for a range of stimulus speeds and contrasts and approached a lower limit of10 msec at high speeds and contrasts. This time constant was, on average, comparable to the length of interspike intervals. These findings suggest that cortical neurons could filter their inputs on a time scale of tens of milliseconds, rather than relying on the precise times of individual input spikes, to sense motion most reliably.
Key words: motion; retinal ganglion cell; retina; primate; coding; temporal; cortex; precision
Introduction
Ensembles of neurons encode information in spatiotemporal patterns of spikes. A fundamental aspect of this encoding is its temporal resolution (Bialek et al., 1991; de Ruyter van Steveninck et al., 1997
Here we develop an approach to determine the time scale relevant for sensing the direction of visual motion. Motion sensing is an important test case because it is behaviorally significant and relies entirely on the temporal pattern of spikes in a population of neurons. Primate RGCs that transmit visual information to the cortex via the magnocellular layers of the lateral geniculate nucleus are not individually selective for the direction of motion; instead, motion is represented in the spatiotemporal pattern of activity in many RGCs. Thus, direction-selective cortical neurons must compare the timing of spikes from multiple non-direction-selective inputs to sense motion. For this comparison to be reliable, it must be performed at a temporal resolution matched to input spiking statistics. If moving stimuli induce spike trains in nearby RGCs that are precisely and reliably timed relative to one another, cortical neurons could extract the highest-fidelity representation of visual motion by comparing the arrival times of spikes from different inputs at fine temporal resolution. Conversely, if RGC spike trains induced by moving stimuli are not precisely and reliably timed relative to one another, cortical neurons could most accurately sense motion by discarding fine temporal structure and comparing the timing of their inputs at a coarser resolution. These considerations suggest that there is an optimal temporal resolution for reading out ensemble visual motion signals in RGCs.
Because the activity of nearby RGCs is not statistically independent (Mastronarde, 1983
Materials and Methods
Recordings. Eyes were obtained from terminally anesthetized macaque monkeys (Macaca mulatta; Macaca radiata) used by other experimenters, in accordance with institutional guidelines for the care and use of animals. Immediately after enucleation, the anterior portion of the eye and vitreous were removed in room light, and the eye cup was placed in bicarbonate-buffered Ames solution (Sigma, St. Louis, MO) and stored in darkness for at least 20 min before dissection. Under infrared illumination, pieces of retina 2-4 mm in diameter were cut from regions 20-50° from the fovea and placed flat against a planar array of 61 extracellular microelectrodes that were used to record action potentials from retinal ganglion cells (Meister et al., 1994Retinal eccentricity was measured with a precision of 1-2 mm. Eccentricity was converted to a temporal equivalent value, because the contours of constant RGC density (and thus presumably dendritic- and receptive field size) in the macaque monkey retina are approximately semicircular in the temporal half of the retina, but elliptical with an aspect ratio of 0.61 in the nasal half (Perry and Cowey, 1985
. A location X mm temporal and Y mm superior (or inferior) to the fovea was assigned an equivalent eccentricity of
. Visual angle (A) in degrees was computed from temporal equivalent eccentricity (E) in millimeters using the following relation: A = 0.1 + 4.21 E + 0.038 E2 (Perry and Cowey, 1985
Spikes were digitized at 20 kHz (Meister et al., 1994
Stimuli. The preparation was stimulated with the optically reduced (1.3 mm diameter) image of a cathode ray tube (CRT) computer display refreshing at 120 Hz, focused on the photoreceptor layer by a microscope objective, and centered on the 480 µm-diameter electrode array. Stimuli were attenuated to low photopic light levels using neutral-density filters. In isolated retina experiments, the stimulus was delivered from the photoreceptor side. In experiments in which the RPE was attached, the retina was stimulated from the ganglion cell side through the mostly transparent electrode array. In the latter case, the shadows cast by the platinized (black) electrode tips (5 µm in diameter and spaced 60 µm apart) had a minimal influence on the intensity or spatial pattern of the stimulus, because they occupied
All stimuli were presented as modulations around a mean gray background. The background photon absorption rates for the long-, middle-, and short-wavelength-sensitive cones were approximately equal to the absorptions that would have been caused by spatially uniform monochromatic lights of 561, 530, and 430 nm wavelength and 9000, 9000, and 5000 photons · µm-2 · sec-1 intensity, respectively, incident on the photoreceptors.
RGCs were characterized and classified on the basis of their responses to a white-noise stimulus presented for 15-30 min (Sakai et al., 1988
Analysis of responses to moving stimuli was restricted to a class of commonly recorded cells whose receptive field tiling and density, spectral sensitivity, response kinetics, and contrast gain obtained from the STA were consistent with those of the anatomically defined parasol cells of the retina of the macaque (Chichilnisky and Kalmar, 2002
Moving bars of different positive and negative contrasts and speeds were presented in randomly interleaved trials. The bar length (orthogonal to direction of motion) covered the entire area recorded and the bar width (parallel to direction of motion) was 118 µm. For comparison, the mean receptive field diameter for the putative parasol cells recorded in each of the three preparations was 164, 96, and 100 µm, respectively. Receptive field diameter was defined as the geometric mean of the major and minor axes of the 1 SD boundary of the center Gaussian fit to the STA spatial profile (see above) (Chichilnisky and Kalmar, 2002
Data from three preparations are presented in Results, with cells, speeds, contrasts, and number of trials as follows: retina 1, 6 ON, 4 OFF; speeds, 14.7, 29.4, and 58.7 deg · sec-1; contrasts, ±96%; 80 trials; retina 2, 6 ON, 14 OFF; speeds 3.6, 7.1, 14.2, and 28.4 deg · sec-1; contrasts, ±12, 24, 48, and 96%; 50 trials; retina 3, 11 ON, 5 OFF; speeds, 3.6, 7.1, 14.2, and 35.5 deg · sec-1; contrasts, ±12, 24, 48, and 96%; 20 trials.
Analysis. In each trial, the temporal pattern of responses from multiple RGCs was used to compute a net motion signal. The sign of the net motion signal provided an estimate of the direction of motion of the bar from the spike trains. The net motion signal was computed as follows. Let sA(t) and sB(t) represent the spike counts as a function of time recorded from cells A and B, respectively, represented in bins of size 0.05 msec (see Fig. 2). These responses were convolved with a low-pass filter to create filtered responses, rA(t) = sA(t) * f(t) and rB(t) = sB(t) * f(t), where f(t) = e-t/
for t
0 and f(t) = 0 for t < 0 (see Fig. 2), and represented using bins of size
. The filter width, or time constant
2 was used, and the value of
t, multiplying pointwise by the filtered response of cell B, and summing the result: R =
t rA(t -
View larger version (20K):
[in this window]
[in a new window]
Figure 2. Opponent detector for motion readout. The procedure for reading out the direction of motion from ensemble RGC activity is depicted schematically, operating on hypothetical spike trains (black vertical ticks) obtained from two cells in response to a bar moving from left to right. Each spike train is low-pass filtered in time (gray smooth traces superimposed on spike trains). For a rightward detector, the filtered response from cell A is delayed by a fixed amount and multiplied pointwise by the filtered response from cell B. The result is summed over time to yield a rightward motion signal. A leftward motion signal is obtained by delaying the response from cell B instead. The difference between rightward and leftward motion signals is the net signal used to estimate the direction of motion. In the case shown, the rightward motion signal is larger than the leftward motion signal, so the net motion signal is positive.
View larger version (20K):
[in this window]
[in a new window]
Figure 4. Dependence of the SNR on temporal filtering. SNR is shown as a function of filter width (time constant) for three stimulus speeds (shown inset) in one preparation. SNR was computed from the pooled distribution of net motion signals obtained in trials with leftward and rightward motion, with the sign of the signal on leftward trials inverted. A, Six ON cells (bar contrast, 96%). B, Four OFF cells (bar contrast, -96%).
View larger version (24K):
[in this window]
[in a new window]
Figure 3. Net motion signals for moving bars. A, Net motion signals obtained from six ON cells in response to 80 trials of a leftward (rightward)-moving bar are shown in the histogram on the left (right). Filter time constant (
Motion detectors were constructed with an explicit delay, although delay lines have not been observed in the mammalian visual system (but see Mastronarde et al., 1991
The pairwise computation of the net motion signal described above is equivalent to an approach that combines responses of all of the cells simultaneously. For the ith cell, let
(1)
(2)
(3) Because summation is over all of the times t and delayed responses are circularly shifted, the first terms in R and L are equal. This leaves the difference N consisting of the remaining cross terms, which is exactly twice the motion signal obtained from the summed pairwise product of delayed spike trains used above. Thus, the pairwise motion sensing algorithm is equivalent to an algorithm that integrates responses of all of the cells simultaneously.
(4) Motion sensing algorithms can also be defined on the basis of other measures of response alignment. One approach evaluated in Results is based on principal components analysis. The fraction of the variance of a collection of responses explained by the first principal component defines an index of alignment. If the index is 1, then all of the responses differ by at most a scale factor. If the index is small, then the response waveforms differ. The index of alignment was obtained by creating a matrix composed of one row for the response of each cell, computing the singular value decomposition of this matrix, and dividing the square of the first singular value by the sum of the squares of all of the singular values. The net motion signal was defined as the difference between the index of alignment obtained from right-delayed responses, ri(t -
Optimal filter width for each condition was estimated by computing the signal-to-noise ratio (SNR) as a function of filter width (see Fig. 4) for filter widths between 0.25 and 0.25 sec in logarithmic steps of
2, fitting the results with an eighth order polynomial, and extracting the peak of the fit. Conditions with peak SNR of <0.674 (75% correct for a Gaussian distribution; 27 of 140 conditions) or with optimal filter width of >100 msec (1 of 140 conditions) were excluded, because in these conditions, the peaks of the SNR versus filter width curves were poorly defined.
Results
Ensemble responses to moving stimuli
Visual responses of multiple RGCs were recorded simultaneously from a region of peripheral primate retina stimulated with a moving bar superimposed on a photopic background. Analysis was restricted to a single functionally defined class of cells whose spatial and temporal properties have been examined in detail previously (Chichilnisky and Kalmar, 2002An example of the ensemble activity elicited by a moving bar is shown in Figure 1. Figure 1A shows the receptive field outlines of a mosaic of six ON cells (presumed parasol) measured using white-noise stimulation and reverse correlation (see Materials and Methods). Figure 1B shows the spike trains obtained from these cells in a single trial in which a vertically oriented white bar drifted from right to left across the receptive fields of all six cells. As the bar crossed the receptive field of each cell in sequence, it elicited spikes in excess of background activity. Responses to a bar moving from left to right are shown in Figure 1C; as expected, the order of the stimulus-elicited responses in this condition was reversed. Because individual RGCs are not direction selective, the relative timing of spikes in sparse, noisy spike trains such as these carries all of the information available to the visual system about the direction of motion.
View larger version (26K):
[in this window]
[in a new window]
Figure 1. Responses of a collection of RGCs to moving bars. A, The mosaic of receptive fields of six ON cells (presumed parasol) recorded simultaneously. Scale bar, 250 µm (1.25°). Ellipses indicate the 1.5 standard deviation boundary of the best fitting two-dimensional Gaussian sensitivity profile. B, Spikes recorded from these cells in a trial in which a white bar (contrast, 96%; speed, 29.4 deg·sec-1) moved to the left on a gray background. C, Same as B, but for rightward motion. D, Top panels show spike trains from the leftward trial in A shifted to compensate for leftward or rightward stimulus motion. Bottom panels show spike trains filtered with a time constant of 10 msec. E, Same as D, but for rightward motion.
Direction estimation and temporal filtering
The following considerations suggest that motion sensing may be improved by temporally filtering retinal spike trains. Estimating the direction of motion (left or right) involves evaluating which direction is most consistent with the pattern of evoked activity. This amounts to determining whether the evoked activity in different cells is more aligned when shifted to compensate for time delays expected from rightward or leftward motion. Figure 1D shows the spike trains obtained with a leftward-moving bar from B. On the left side, each spike train has been delayed by an amount equal to the time that it would take for a leftward moving bar to travel from the center of the receptive field of each cell to a fixed, arbitrary reference location. On the right side, each spike train has been delayed by an amount equal to the time that it would take for a rightward-moving bar to move from the center of the receptive field of each cell to a reference location. Visual inspection suggests that an assumption of leftward motion results in more aligned spike trains (i.e., that the spike trains are more consistent with leftward motion). The reverse is true for the data obtained with a rightward-moving bar (Fig. 1E).However, the alignment of individual spike times in different cells is not exact, so temporal filtering of the spike trains would be required for motion-sensitive neurons in the brain to accurately sense the direction of motion. Low-pass-filtered responses are shown in Figure 1, D and E, bottom. Because filtering transforms the approximate alignment of discrete spike trains into measurable overlap, it may improve the accuracy of motion sensing. This is examined quantitatively below.
Motion readout from ensemble activity
To assess the fidelity with which the direction of motion is encoded by the retina, a standard motion sensing algorithm that extracted an estimate of the direction of motion from the ensemble RGC activity (Reichardt, 1961This motion readout approach was applied to all pairs of recorded cells of like sign (ON or OFF), with a delay equal to the bar speed divided by the distance between the centers of the receptive fields of the cells, yielding a detector tuned for the correct stimulus speed. ON and OFF cells were treated separately because of their distinct response kinetics (Chichilnisky and Kalmar, 2002
Temporal resolution of motion readout
To determine the effective temporal resolution of motion signals in RGCs, the SNR of the motion signal was examined as a function of the width of the filter used to smooth each spike train. If the relative timing of spikes in different cells is precise, and all of the cells fire reliably, then a narrow filter can be used to exploit the alignment of spikes, suppressing spurious alignment caused by maintained discharge and yielding a high-fidelity motion signal. If the relative timing of spikes is imprecise, or the cells fire unreliably, a wider filter will be required to sense the approximate alignment of spikes. These considerations lead to the prediction that there exists an optimal filter width that is appropriate for the temporal alignment of spike trains from different cells relative to one another.A test of this prediction is given in Figure 3, which shows the distributions of motion signals obtained with filter widths of 1, 10, and 100 msec. The fidelity of the motion signal obtained with 10 msec filtering (Fig. 3B) was higher than that obtained with 1 msec or 100 msec filtering (A,C): its sign indicated the correct direction on every trial, and the SNR was significantly higher. Figure 4A, middle, shows SNR as a function of filter width for the same cells and stimuli. Consistent with the pattern of results in Figure 3, the filter width that yielded the highest SNR was
Temporal resolution was measured in ON and OFF cells in three preparations tested with a range of bar speeds and contrasts. Each point in Figure 5A shows optimal filter width and peak SNR for a single condition (speed, contrast, and ON and OFF cells) in one preparation. The median optimal filter width obtained this way for all of the conditions in three preparations was 21 msec; the 10th and 19th percentiles were 10 and 53 msec, respectively. In many conditions (e.g., lower speeds in Fig. 4), the peak SNR was much greater than 1 (i.e., the direction of motion was easily discriminable from ensemble RGC activity). Discriminability depended on stimulus contrast and speed (see below), the number of cells recorded, and other factors, but the data in Figure 5A show that, on average, optimal filter width varied little with discriminability.
View larger version (25K):
[in this window]
[in a new window]
Figure 5. Dependence of optimal filter width on SNR, contrast, and speed (three preparations). A, Each point shows the peak SNR (see Materials and Methods) and the filter width that yielded the peak SNR, for a single condition. A total of 112 points are shown. B, Each point shows the peak SNR and the absolute value of contrast, averaged across ON and OFF cells and all of the speeds tested in a single preparation. Because of variation with speed (below), error bars indicate 1 SD. Nine points and an inverse relationship are shown (see Eq. 5). C, Each point shows peak SNR and speed, averaged across ON and OFF cells and all of the contrasts tested in a single preparation. Because of variation with contrast (above), error bars indicate 1 SD. Eleven points and an inverse relationship are shown (see Eq. 5). D, Each point shows the peak SNR and the product of speed and contrast, averaged across ON and OFF cells in a single preparation. Error bars indicate 1 SEM. Eighteen points and an inverse relationship are shown (see Eq. 5).
Factors affecting temporal resolution
Temporal resolution varied with stimulus contrast, as might be expected from increases in firing rate with contrast. Each point in Figure 5B shows the mean optimal filter width across all of the conditions in a single preparation with common absolute value of stimulus contrast. Mean optimal filter width declined approximately twofold as contrast increased from 12 to 96%, apparently approaching a limit at high contrasts.Temporal resolution also varied with stimulus speed, as might be expected: resolution could be finer at higher speeds, because faster moving bars enter the receptive field more abruptly, but resolution could be coarser, because faster moving bars elicit sparser and less reliable spike trains. Each point in Figure 5C shows optimal filter width obtained a single speed, averaged across ON and OFF cells and all of the contrasts tested in a single preparation. Mean optimal filter width declined approximately threefold as speed increased from 3 to 60 deg · sec-1, apparently approaching a limit at high speeds. The constancy of optimal filter width at high speeds can also be seen in the positions of the peaks of the SNR versus filter width curves from a single preparation shown in Figure 4.
The trends in Figure 5, B and C, suggest a functional approximation in which mean optimal filter width (w) depends inversely on the product of speed (s) and contrast (c):
Here, w
(5) is the asymptotic optimal filter width for high speed and contrast, and
is a constant. These parameters were selected to minimize the squared error between log10(w) and the prediction from Equation 5, for pooled data from three preparations. The data and fit are shown superimposed in Figure 5D. The asymptotic optimal filter width w
Temporal resolution and interspike intervals
The optimal filter width can be used to obtain a meaningful measure of the number of spikes that typically convey the elementary motion signal. If the interspike interval (ISI) is always much larger than the filter width, optimal motion sensing preserves the distinction between sequential spikes, and motion information is effectively conveyed by individual spike times. Conversely, if the ISI is always much smaller than the filter width, optimal motion sensing integrates over many spikes, and motion information is effectively conveyed by variations in firing rate. The ratio of ISI to optimal filter width was accumulated across all of the spike trains from all conditions in three preparations; its distribution is shown in Figure 6. The modal ratio was
View larger version (9K):
[in this window]
[in a new window]
Figure 6. Ratio of ISI to optimal filter width (
Technical considerations
Estimates of temporal resolution could be artificially coarse if the delays used in computing motion signals (Fig. 2) differed from the true time differences in responses of different cells to the moving bar. This could result from error in estimated receptive field location (see Materials and Methods), receptive field microstructure not captured by a Gaussian model (Chichilnisky and Baylor, 1999bThe coarse temporal resolution observed was not attributable to artificially low evoked firing rates in the in vitro preparation. In the three preparations examined, peak firing rates measured in 25 msec bins for 96% contrast bars at intermediate speeds were 121 ± 18, 116 ± 24, and 93 ± 19 Hz, respectively (mean ± SD across cells). A previous in vivo study of macaque RGCs (Kremers et al., 1993
In addition, randomly subsampling half of the spikes from each cell (10 iterations) on each trial of the moving stimulus yielded median optimal filter width of 28 msec across all conditions; 10th and 19th percentiles were 13 and 63 msec, respectively. Asymptotic filter width was 17 msec. Because evoked firing rates were within a factor of 2 of what would be expected in vivo (see above), this suggests that the optimal filter widths that would apply to parasol cells in vivo are similar to the values reported here.
The observed temporal resolution was not restricted to the specific functional form of the filter used. This was determined by estimating SNR as a function of the width (standard deviation) of a Gaussian filter applied to spike trains. The median optimal filter width obtained this way was 17 msec; 10th and 19th percentiles were 8 and 41 msec, respectively. Asymptotic filter width was 10 msec.
The observed temporal resolution was not dependent on the pairwise construction of the cross-correlation algorithm used to read out the direction of motion. This can be seen by noting that the algorithm is mathematically equivalent to a multicell computation in which the left and right motion signals are created by appropriately delaying responses from each cell, summing and squaring all of the responses pointwise, and integrating the result over time (see Materials and Methods).
Temporal resolution on the order of tens of milliseconds was also observed using the following alternative algorithm for motion sensing. If responses from different cells were identical up to an overall scaling of response amplitude, then the first principal component would explain all of the variance in the time course of response across cells. The fraction of the total variance explained by the first principal component therefore provides an index of the alignment of the responses of different cells. This was applied to motion sensing by temporally filtering responses of all cells in each trial, then computing the difference between the index of alignment obtained for responses delayed according to leftward and rightward motion. This value was used to discriminate direction of motion, and the SNR of its distribution across trials was examined as a function of filter width, as above. The median optimal filter width across all conditions was 28 msec; 10th and 19th percentiles were 16 and 59 msec, respectively. Asymptotic filter width was 18 msec.
Discussion
The present results indicate that direction of motion can be most accurately extracted from primate RGC spike trains by temporally filtering by 10-50 msec, effectively interpolating the gaps between spikes, before comparing the timing of responses in different cells. This defines the time scale for reading the population code, assuming readout based on linear filtering and cross-correlation. Despite the fact that direction sensing relies entirely on spike timing, the millisecond precision that is sometimes observed in RGC spike trains is of little consequence in this task. Indeed, the results suggest that motion-sensitive neurons in the visual cortex could filter their inputs coarsely in time at the synapse, rather than relying on the precise times of individual input spikes, to sense motion most reliably.Time scales of neural signals
Numerous studies have examined whether the precise times of individual spikes, rather than slowly varying firing rates, are used to transmit information in the visual system and other areas of the brain (Abeles et al., 1993Of course, aspects of visual performance outside the scope of this study may demand finer or coarser filtering than is optimal for direction sensing. A filter width of 1 msec on average yields a direction discrimination SNR that is only 53% as high as that obtained with a filter width of 10 msec (Fig. 4), but this reduction in SNR could be acceptable if retaining precise temporal information served other purposes. For example, a finer filter would narrow the speed tuning of motion detectors. Also, the precise times of spikes could be used by the brain for other visual tasks such as determining the time of stimulus onset.
Temporal resolution and spike timing precision
The temporal resolution observed in this study was approximately an order of magnitude coarser than the finest temporal precision of spiking observed in individual RGCs of salamander and rabbit (Berry et al., 1997First, previous reports emphasized the maximum precision observed in spike trains that display both low and high precision. It seems unlikely that direction-selective neurons in the brain use only the most precise segments of input spike trains to compute motion and selectively exclude other informative spikes (but see Usrey et al., 1998
Second, RGC spike trains exhibit unreliability (spike count variability) that is typically factored out in estimates of spike timing precision. Unreliability in sparse spike trains demands coarser temporal filtering by postsynaptic neurons to obtain an accurate estimate of input activity. This is particularly important for computations such as motion sensing that involve comparing the activity of two or more inputs, because most or all of the inputs must be active to perform the comparison.
Third, previous studies examined responses to full-field stimuli, which may elicit precisely timed spikes by simultaneously activating many synapses, bringing membrane potential to threshold too rapidly to be significantly affected by voltage fluctuations. The tapering receptive field profile of RGCs could make the onset of responses to moving stimuli more gradual and more variable. Full-field stimuli may elicit maximal precision, but moving bars may be more representative of naturally occurring stimuli of behavioral importance.
Finally, heterogeneity in the receptive field profiles of different cells (Chichilnisky and Baylor, 1999b
Stimulus dependence
Temporal resolution declined with speed and contrast but was 10-50 msec for a wide range of conditions and approached a limit ofAt speeds lower than a few degrees per second, temporal resolution approached values in excess of 50 msec. However, this is probably not functionally significant given that the preferred speeds of neurons in area MT fall mostly in the range 8-64 deg · sec-1 and always in the range 2-512 deg · sec-1 (Maunsell and Van Essen, 1983
Models of motion readout
Temporal resolution was analyzed by reading out retinal motion signals using low-pass filtering followed by cross-correlation as a computational tool. Motion sensing in the visual cortex is undoubtedly different in detail, but perhaps not in essential structure. Filtering and cross-correlation are the core elements in computational models of motion sensing in the brain (Reichardt, 1961The principal difference between a motion energy sensor and the readout approach adopted here is that the latter is directly applicable to spike trains. Motion energy computations begin with noiseless, linear filtering of the visual scene. This is at best a crude approximation of retinal processing: responses of primate parasol RGCs are nonlinear (Benardete and Kaplan, 1999
The coarse temporal resolution observed was not restricted to motion readout based on pairwise cross-correlation: an approach that used the responses of all of the cells simultaneously was shown to be formally identical to the pairwise approach (see Materials and Methods). Also, motion readout using principal-components analysis instead of cross-correlation exhibited similar temporal resolution. However, the main readout approach examined—linear filtering followed by cross-correlation—is not guaranteed to be optimal or biologically accurate, and it is possible that other approaches would exhibit significantly different temporal resolution. The results reported here apply to a restricted but important class of motion sensing models.
Motion detectors were assumed to be tuned to the correct stimulus speed for simplicity. Neurons in area MT, which has an important role in motion sensing (Albright, 1984
Implications for motion sensing in visual cortex
The timing of spikes in MT neurons elicited by moving stimuli can be reproducible to within a few milliseconds (Bair and Koch, 1996
Footnotes
Received Feb. 28, 2003; revised Apr. 28, 2003; accepted May. 27, 2003.This work was supported by National Institutes of Health Grant EY-13150, a Sloan Research Fellowship, a McKnight Scholar's Award (E.J.C.), and a University of California, San Diego, Undergraduate Research Scholarship (R.S.K.). We thank E. Callaway for providing access to tissue; T. Albright, E. Callaway, S. duLac, G. Horwitz, R. Krauzlis, F. Rieke, and E. Shrader-Frechette for valuable input; A. Litke and colleagues for technology development; J. French for experimental and analysis assistance; and S. Barry for technical assistance.
Correspondence should be addressed to Dr. E. J. Chichilnisky, Systems Neurobiology, The Salk Institute, 10010 North Torrey Pines Road, La Jolla, CA 92037. E-mail: ej{at}salk.edu.
Copyright © 2003 Society for Neuroscience 0270-6474/03/236681-09$15.00/0
References
Abeles M, Bergman H, Margalit E, Vaadia E (1993) Spatiotemporal firing patterns in the frontal cortex of behaving monkeys. J Neurophysiol 70: 1629-1638.
[Abstract/Free Full Text] Adelson EH, Bergen JR (1985) Spatiotemporal energy models for the perception of motion. J Opt Soc Am A 2: 284-299.[Web of Science][Medline]
Albright TD (1984) Direction and orientation selectivity of neurons in visual area MT of the macaque. J Neurophysiol 52: 1106-1130.
[Abstract/Free Full Text] Bair W, Koch C (1996) Temporal precision of spike trains in extrastriate cortex of the behaving macaque monkey. Neural Comput 8: 1185-1202.[Web of Science][Medline]
Benardete EA, Kaplan E (1999) The dynamics of primate M retinal ganglion cells. Vis Neurosci 16: 355-368.[Web of Science][Medline]
Berry MJ, Meister M (1998) Refractoriness and neural precision. J Neurosci 18: 2200-2211.
[Abstract/Free Full Text] Berry MJ, Warland DK, Meister M (1997) The structure and precision of retinal spike trains. Proc Natl Acad Sci USA 94: 5411-5416.
[Abstract/Free Full Text] Bialek W, Rieke F, Steveninck RR, Warland D (1991) Reading a neural code. Science 252: 1854-1857.
[Abstract/Free Full Text] Brown SP, He S, Masland RH (2000) Receptive field microstructure and dendritic geometry of retinal ganglion cells. Neuron 27: 371-383.[Web of Science][Medline]
Buracas GT, Zador AM, DeWeese MR, Albright TD (1998) Efficient discrimination of temporal patterns by motion-sensitive neurons in primate visual cortex. Neuron 20: 959-969.[Web of Science][Medline]
Chichilnisky EJ (2001) A simple white noise analysis of neuronal light responses. Network 12: 199-213.[Web of Science][Medline]
Chichilnisky EJ, Baylor DA (1999a) Synchronized firing by ganglion cells in monkey retina. Soc Neurosci Abstr 25: 1042.
Chichilnisky EJ, Baylor DA (1999b) Receptive-field microstructure of blue-yellow ganglion cells in primate retina. Nat Neurosci 2: 889-893.[Web of Science][Medline]
Chichilnisky EJ, Kalmar RS (2002) Functional asymmetries in ON and OFF ganglion cells of primate retina. J Neurosci 22: 2737-2747.
[Abstract/Free Full Text] Dacey DM, Petersen MR (1992) Dendritic field size and morphology of midget and parasol ganglion cells of the human retina. Proc Natl Acad Sci USA 89: 9666-9670.
[Abstract/Free Full Text] de Ruyter van Steveninck RR, Bialek W (1988) Real-time performance of a movement-sensitive neuron in the blowfly visual system: coding and information transfer in short spike sequences. Proc R Soc Lond B Biol Sci 234: 379-414.
[Abstract/Free Full Text] de Ruyter van Steveninck RR, Lewen GD, Strong SP, Koberle R, Bialek W (1997) Reproducibility and variability in neural spike trains. Science 275: 1805-1808.
[Abstract/Free Full Text] Emerson RC, Bergen JR, Adelson EH (1992) Directionally selective complex cells and the computation of motion energy in cat visual cortex. Vision Res 32: 203-218.[Web of Science][Medline]
Kraft TW (1988) Photocurrents of cone photoreceptors of the golden-mantled ground squirrel. J Physiol (Lond) 404: 199-213.
[Abstract/Free Full Text] Kremers J, Lee BB, Pokorny J, Smith VC (1993) Responses of macaque ganglion cells and human observers to compound periodic waveforms. Vision Res 33: 1997-2011.[Web of Science][Medline]
Litke AM (1999) The retinal readout system: a status report. Nucl Instrum Methods Phys Res A 435: 242-249.
Liu RC, Tzonev S, Rebrik S, Miller KD (2001) Variability and information in a neural code of the cat lateral geniculate nucleus. J Neurophysiol 86: 2789-2806.
[Abstract/Free Full Text] Mastronarde DN (1983) Interactions between ganglion cells in cat retina. J Neurophysiol 49: 350-365.
[Free Full Text] Mastronarde DN, Humphrey AL, Saul AB (1991) Lagged Y cells in the cat lateral geniculate nucleus. Vis Neurosci 7: 191-200.[Web of Science][Medline]
Maunsell JH, Van Essen DC (1983) Functional properties of neurons in middle temporal visual area of the macaque monkey. I. Selectivity for stimulus direction, speed, and orientation. J Neurophysiol 49: 1127-1147.
[Abstract/Free Full Text] Meister M, Pine J, Baylor DA (1994) Multi-neuronal signals from the retina: acquisition and analysis. J Neurosci Methods 51: 95-106.[Web of Science][Medline]
Meister M, Lagnado L, Baylor DA (1995) Concerted signaling by retinal ganglion cells. Science 270: 1207-1210.
[Abstract/Free Full Text] Newsome WT, Wurtz RH, Dursteler MR, Mikami A (1985) Deficits in visual motion processing following ibotenic acid lesions of the middle temporal visual area of the macaque monkey. J Neurosci 5: 825-840.[Abstract]
Perry VH, Cowey A (1985) The ganglion cell and cone distributions in the monkey's retina: implications for central magnification factors. Vision Res 25: 1795-1810.[Web of Science][Medline]
Polyak SL (1941) The retina. Chicago: University of Chicago.
Reich DS, Victor JD, Knight BW, Ozaki T, Kaplan E (1997) Response variability and timing precision of neuronal spike trains in vivo. J Neurophysiol 77: 2836-2841.
[Abstract/Free Full Text] Reichardt W (1961) Autocorrelation, a principle for the evaluation of sensory information by the central nervous system. In: Sensory communication (Rosenblith WA, ed), pp 303-317. Cambridge, MA: MIT.
Reinagel P, Reid RC (2000) Temporal coding of visual information in the thalamus. J Neurosci 20: 5392-5400.
[Abstract/Free Full Text] Reinagel P, Reid RC (2002) Precise firing events are conserved across neurons. J Neurosci 22: 6837-6841.
[Abstract/Free Full Text] Rieke FM, Warland D, Steveninck RR, Bialek W (1997) Spikes: exploring the neural code, Ed 1. Cambridge, MA: MIT.
Rodieck RW (1998) The first steps in seeing, Ed 1. Sunderland, MA: Sinauer.
Sakai HM, Naka K, Korenberg MJ (1988) White-noise analysis in visual neuroscience. Vis Neurosci 1: 287-296.[Web of Science][Medline]
Salzman CD, Britten KH, Newsome WT (1990) Cortical microstimulation influences perceptual judgements of motion direction. Nature 346: 174-177.[Medline]
Schnapf JL, Nunn BJ, Meister M, Baylor DA (1990) Visual transduction in cones of the monkey Macaca fascicularis. J Physiol (Lond) 427: 681-713.
[Abstract/Free Full Text] Shadlen MN, Newsome WT (1998) The variable discharge of cortical neurons: implications for connectivity, computation, and information coding. J Neurosci 18: 3870-3896.
[Abstract/Free Full Text] Simoncelli EP, Heeger DJ (1998) A model of neuronal responses in visual area MT. Vision Res 38: 743-761.[Web of Science][Medline]
Softky WR, Koch C (1993) The highly irregular firing of cortical cells is inconsistent with temporal integration of random EPSPs. J Neurosci 13: 334-350.[Abstract]
Troy JB, Lee BB (1994) Steady discharges of macaque retinal ganglion cells. Vis Neurosci 11: 111-118.[Web of Science][Medline]
Usrey WM, Reppas JB, Reid RC (1998) Paired-spike interactions and synaptic efficacy of retinal inputs to the thalamus. Nature 395: 384-387.[Medline]
Van Essen DC (1985) Functional organization of primate visual cortex. In: Cerebral cortex, Vol III (Peters A, Jones EG, eds), pp 259-327. New York: Plenum.
Watanabe M, Rodieck RW (1989) Parasol and midget ganglion cells of the primate retina. J Comp Neurol 289: 434-454.[Web of Science][Medline]
Watson AB, Ahumada AJ (1985) Model of human visual-motion sensing. J Opt Soc Am A 2: 322-341.[Web of Science][Medline]
This article has been cited by other articles:
Y. S. Liu, C. F. Stevens, and T. O. Sharpee
Predictable irregularities in retinal receptive fields
PNAS, September 22, 2009; 106(38): 16499 - 16504.
[Abstract] [Full Text] [PDF]
G. M. Ghose and I. T. Harrison
Temporal Precision of Neuronal Information in a Rapid Perceptual Judgment
J Neurophysiol, March 1, 2009; 101(3): 1480 - 1493.
[Abstract] [Full Text] [PDF]
C. Sekirnjak, P. Hottowy, A. Sher, W. Dabrowski, A. M. Litke, and E. J. Chichilnisky
High-Resolution Electrical Stimulation of Primate Retina for Epiretinal Implant Design
J. Neurosci., April 23, 2008; 28(17): 4446 - 4456.
[Abstract] [Full Text] [PDF]
B. G. Borghuis, C. P. Ratliff, R. G. Smith, P. Sterling, and V. Balasubramanian
Design of a Neuronal Array
J. Neurosci., March 19, 2008; 28(12): 3178 - 3189.
[Abstract] [Full Text] [PDF]
R. D. Kumbhani, M. J. Nolt, and L. A. Palmer
Precision, Reliability, and Information-Theoretic Analysis of Visual Thalamocortical Neurons
J Neurophysiol, November 1, 2007; 98(5): 2647 - 2663.
[Abstract] [Full Text] [PDF]
R. Narayan, G. Grana, and K. Sen
Distinct Time Scales in Cortical Discrimination of Natural Sounds in Songbirds
J Neurophysiol, July 1, 2006; 96(1): 252 - 258.
[Abstract] [Full Text] [PDF]
B. Roska, A. Molnar, and F. S. Werblin
Parallel Processing in Retinal Ganglion Cells: How Integration of Space-Time Patterns of Excitation and Inhibition Form the Spiking Output
J Neurophysiol, June 1, 2006; 95(6): 3810 - 3822.
[Abstract] [Full Text] [PDF]
D. Tadin, J. S. Lappin, and R. Blake
Fine temporal properties of center-surround interactions in motion revealed by reverse correlation.
J. Neurosci., March 8, 2006; 26(10): 2614 - 2622.
[Abstract] [Full Text] [PDF]
J. L. McKinstry, G. M. Edelman, and J. L. Krichmar
A cerebellar model for predictive motor control tested in a brain-based device
PNAS, February 28, 2006; 103(9): 3387 - 3392.
[Abstract] [Full Text] [PDF]
E. S. Frechette, A. Sher, M. I. Grivich, D. Petrusca, A. M. Litke, and E. J. Chichilnisky
Fidelity of the Ensemble Code for Visual Motion in Primate Retina
J Neurophysiol, July 1, 2005; 94(1): 119 - 135.
[Abstract] [Full Text] [PDF]
Z. N. Aldworth, J. P. Miller, T. Gedeon, G. I. Cummins, and A. G. Dimitrov
Dejittered Spike-Conditioned Stimulus Waveforms Yield Improved Estimates of Neuronal Feature Selectivity and Spike-Timing Precision of Sensory Interneurons
J. Neurosci., June 1, 2005; 25(22): 5323 - 5332.
[Abstract] [Full Text] [PDF]
V. J. Uzzell and E. J. Chichilnisky
Precision of Spike Trains in Primate Retinal Ganglion Cells
J Neurophysiol, August 1, 2004; 92(2): 780 - 789.
[Abstract] [Full Text] [PDF]
This Article Abstract 
Full Text (PDF) Submit an eLetter Alert me when this article is cited Alert me when eLetters are posted Alert me if a correction is posted Citation Map Services Email this article to a friend Similar articles in this journal Similar articles in Web of Science Similar articles in PubMed Alert me to new issues of the journal Download to citation manager 
Citing Articles Citing Articles via HighWire Citing Articles via Web of Science (23) Citing Articles via Google Scholar Google Scholar Articles by Chichilnisky, E. J. Articles by Kalmar, R. S. Search for Related Content PubMed PubMed Citation Articles by Chichilnisky, E. J. Articles by Kalmar, R. S.
|
|
|
|
 |
|