| HOME | HELP | FEEDBACK | SUBSCRIPTIONS | ARCHIVE | SEARCH | TABLE OF CONTENTS |
|
|
|
|||||||
|
|||||||||
Department of Neuroscience, University of Pennsylvania School of Medicine, Philadelphia, Pennsylvania
Submitted 23 August 2006; accepted in final form 15 June 2007
 |
ABSTRACT |
|---|
 TOP ABSTRACT INTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSREFERENCES |
|---|
|
INTRODUCTION |
|---|
|
TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSREFERENCES |
|---|
Although this approach has contributed greatly to our understanding of visual receptive fields, and the relationship between stimulus and response, it does not consider the multitude of coding schemes these neurons might use. This is because firing rate measurements are based on the assumption that only the number of action potentials elicited by a neuron is important to downstream neurons. An alternative method would be to assess neural activity using multiple metrics and to use these statistics together when formulating the role of a neuron.
Recently, progress has been made in examining higher-order parameters of spike trains in retina (Berry and Meister 1998
; Berry et al. 1997; Chichilnisky and Kalmar 2003; Passaglia and Troy 2004; Reich et al. 1997; Uzzell and Chichilnisky 2004), lateral geniculate nucleus (LGN) (Dan et al. 1996; Liu et al. 2001; Reich et al. 1997; Reinagel and Reid 2000, 2002), and primary visual cortex (V1) (Mainen and Sejnowski 1995; Reich et al. 2000; Tolhurst 1989; Victor and Purpura 1998; Vinje and Gallant 2002; Weliky et al. 2003). These studies, done both in vitro and in vivo, have demonstrated that measurements of precision, reliability, and information rates provide deeper insight into neuronal responses than firing rate alone. Unfortunately, because the experiments used different stimuli, the results of these studies are difficult to reconcile.
In one study, Reinagel and Reid (2000) showed that cat LGN neurons fire with high temporal precision and reliability in response to a large, spatially homogeneous stimulus whose luminance varies rapidly (128 Hz) and randomly. They also found that these responses are highly conserved within cell classes (e.g., all ON-centered LGN X-cells), suggesting that, under these circumstances, thalamic input to layer IV simple cells is highly synchronous. However, it is unlikely a priori that layer IV simple cells will respond to this stimulus due to the approximate balance of excitation and inhibition elicited by spatially homogeneous stimuli (Ferster 1988; Hirsch et al. 1998; Hubel and Wiesel 1962).
To compare the spike trains elicited by LGN relay cells and their layer IV simple cell targets while maintaining the temporal richness of Reinagel and Reid's approach, we modified the spatial organization of the stimulus to increase the likelihood that cortical cells would respond. For both LGN and cortical cells, we presented a stochastic, contrast-modulated Gabor patch. This permitted measurement and comparison of the precision, reliability, and information content of spike trains elicited from LGN cells and layer IV simple cells.
We found that layer IV simple cells were as precise but not as reliable as their principal thalamic afferents (LGN X-cells), and that this precision was greater than predicted from the synchronous activation of the LGN inputs. We also calculated the information-theoretic content of our neurons using the "direct method" (Strong et al. 1998) and found that simple cell responses 1) encoded less information per second than LGN X-cells; 2) did not encode information using temporal patterns, unlike LGN neurons; and 3) used their total information capacity more efficiently than their primary inputs. In all cases, spike trains from LGN Y-cells exhibited greater precision, reliability, and information rates than either LGN X-cells or layer IV simple cells. We discuss the implications of these findings and how they relate to the function of layer IV simple cells.
|
METHODS |
|---|
|
TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSREFERENCES |
|---|
Animals were prepared for single-unit recording as described in detail elsewhere (Nolt et al. 2004). Adult male cats were anesthetized with 3–4% halothane in a 30:70 mixture of O2 and N2O. Catheters were placed in each femoral vein, gas anesthesia was discontinued, and the animal was maintained on intravenous sodium thiopental (Pentothal) as needed throughout the remainder of the surgery. A tracheotomy was performed and the animal was placed in a stereotaxic frame. The animal was paralyzed with an injection of gallamine triethiodide (Flaxedil, 60 mg) and maintained on positive-pressure ventilation adjusted so as to hold the end-expired CO2 at 3.8%. Two venous catheters were used so that anesthetic (2–8 mg·kg–1·h–1 sodium thiopental) and paralytic (15 mg/h gallamine triethiodide) could be infused throughout the experiment at independent rates. Cortical electroencephalogram (EEG) was monitored continuously throughout the experiment and the rate of anesthetic infusion regulated so as to maintain the animal in a state similar to light sleep characterized by frequent bursts of 7- to 10-Hz waves (spindles). Body temperature was also monitored and maintained at 38°C. A small craniotomy was made at either Horsley–Clarke A6.0, L8.5 for LGN experiments or Horsley–Clarke P4.0, L1.0 for area 17 experiments; LGN and area 17 experiments were not performed in the same cat. Neutral, gas-permeable contact lenses (Lancaster Contact Lens) were placed in each eye and spectacle lenses added so as to bring the reflection of retinal vessels into sharp focus on the screen of a CRT mounted in front of the cat. Biprisms were also placed in front of each eye to allow approximate superposition of the lines of sight. Independently controlled shutters were placed in front of the biprisms, allowing us to study cells monocularly. Pupils were dilated with 1% ophthalmic atropine and the nictitating membranes were retracted with 1% phenylephrine hydrochloride. Animals were given intramuscular (im) injections of atropine (0.1 mg im once per day) to minimize secretions, dexamethasone (0.4 mg im once per day) to minimize cerebral edema, and ampicillin (10 mg/kg im) to prevent infection on a 12-h schedule. Most experiments lasted 2 days. At the conclusion of each experiment, animals were given a lethal injection of sodium pentobarbital. This protocol was approved by the University of Pennsylvania's Institutional Animal Care and Use Committee and conforms to guidelines recommended in Preparation and Maintenance of Higher Mammals during Neuroscience Experiments (National Institutes of Health Publication 91–3207).
Recording and data acquisition
All recordings were made extracellularly with tungsten-in-glass electrodes. Signals were amplified, conditioned, and routed to an oscilloscope, an audio monitor, and a spike sorter (Alpha Omega, Nazareth, Israel). The latter performed on-line template matching of action potentials and produced TTL pulses that were detected at the computer interface during clock interrupt service routines every 100 or 1,000 µs, depending on the application. The electrode was advanced with a Burleigh Inchworm (Burleigh Instruments, Victor, NY). Penetrations were limited to layers A and A1 of the LGN or layer IV of area 17 based on electrophysiological criteria. In particular, layer IV was identified by electrode depth (
700 µm normal to cortical surface), the presence of strong, modulated, multiunit activity (hash) to drifting gratings, and the abundance of simple cells. Because histology was not performed, we cannot reject the possibility that some cells may have been recorded from layer III. Due to limited electrode depth (no >1,200 µm), and the emergence of layer V complex cells, we are confident layer VI simple cells were not sampled. All receptive fields were limited to the central 10° of the visual field with the vast majority within 5°. Only single-unit data were collected and analyzed.
The responses of each cell were thoroughly characterized before any experimental procedures. Initially, computer-assisted hand-plotting procedures were used to approximate the optimal receptive field properties of each cell (Jones and Palmer 1987). Next, the parameters of the receptive field were refined by obtaining the spatial frequency tuning curve, the contrast-response function, and the spatial summation tuning curve for LGN neurons in response to drifting gratings. In addition, orientation tuning curves to drifting gratings and spatial phase tuning curves to stationary, counter-phased gratings were also generated for cells in area 17. The spatial position of the receptive field was determined by systematically moving a patch of a drifting grating. The position that generated the maximal F1 response was used as the receptive field center coordinate. LGN neurons were classified as X or Y and lagged or nonlagged according to a set of standard criteria (see Wolfe and Palmer 1998); only nonlagged LGN cells were studied because lagged LGN cells failed to respond to our stimuli. In layer IV of area 17, only simple cells were studied (F1 > DC; see Skottun et al. 1991).
Stimulus presentation
Visual stimuli were presented on an Image Systems multisynch monochrome monitor at a frame rate of 125 Hz by means of a VSG-2/3 board (Cambridge Research Systems, Cambridge, UK). Mean luminance was 80 cd/m2 and lookup tables were linearized for contrasts in the range of ±100%. The monitor was situated 24.7 cm from the eye such that 1 cm represents 2.3° of visual space. The screen subtended 36° horizontally and 27° vertically. Stimuli were presented with a resolution of 22 pixels/degree. An identical monitor driven in series was situated at the experimenter's console.
A Gabor patch of optimal orientation, spatial frequency, spatial phase, and size was centered on the receptive field of a neuron. An example of the stimulus for an even-symmetric layer IV simple cell is shown in Fig. 1C (right column). For LGN neurons, an orientation of 0° and an even spatial phase (0°) was used. Contrast of the Gabor patch was randomly drawn from a normal distribution (µ = 0% contrast, 
= 31% contrast) every 8 ms (125 Hz).
|
The mean and SD of the contrast distributions were selected to ensure our stimulus had a temporal entropy greater than the encoding ability of our neurons. Although there are many distributions that would satisfy these requirements, we chose one that approximates naturalistic distributions (Tadmor and Tolhurst 2000; van Hateren 1997). The stimulus entropy per trial was calculated as
 |
Precision of the response
For each cell, we binned the responses to repeated stimulus sets at 1-ms resolution and generated a peristimulus spike-time histogram (PSTH). The histogram was then convolved with a 10-ms boxcar filter to smooth the data. Minima of the convolved histogram were extracted and used as the boundaries for events (Fig. 3A). All further analysis used the original, nonsmoothed data. Only event periods that contained values of 5% of the maximum value of the PSTH were analyzed. This eliminated statistically insignificant peaks that may have been caused by factors unrelated to our stimulus. For each valid event period, two sets of data were generated: one using the first spike present on each trial and the other using all the spikes present on each trial. The interquartile range of spike times within each event was then used to estimate the spread, or temporal jitter, of spike times. For each event, we divided the distribution of spike times into two halves based on the median spike time. The difference in the median values of each half was taken as the interquartile range. For all events, a frequency distribution of temporal jitter was generated and the median temporal jitter was calculated. We define this value as the precision of the response to our stimulus.
|
|
For each population of neurons, we binned the responses of each cell to repeated stimulus sets at 1-ms resolution and generated normalized PSTHs (i.e., normalized such that the autocorrelation of each PSTH at zero lag was 1). Next, we performed cross-correlations between all pairwise combinations of normalized PSTHs. For each cross-correlation, we calculated the peak correlation coefficient 
and the absolute value of the temporal offset of the peak value |
|. Identical spike trains would have a peak normalized correlation of 100% and an offset of 0 ms.
Reliability of the response
To assess the reliability of a neuron's response to repeated stimuli, we used a method described by Schreiber et al. (2003). First, rasters of the responses to the repeated stimulus were generated at 100-µs resolution and each trial was converted into a binary vector (where ones represented the occurrence of a spike and zeros represented the absence of a spike). Because this time bin was smaller than the refractory period of the neuron, we were guaranteed a maximum of only one spike per bin. All spike train vectors were then smoothed by convolving them with a Gaussian of mean of zero and SD equal to the neuron's minimal interspike interval (ISI); the average minimal ISIs were: LGN X-cells: 1.8 ms; LGN Y-cells: 1.5 ms; and simple cells: 1.9 ms. This Gaussian approximates the temporal region in the spike train where only one spike might occur. The reliability of the response was defined as the mean normalized inner product of all pairwise combinations of these smoothed spike trains. It was calculated according to
 |
i is the smoothed spike train vector and Trials represents the number of repeated trials. A reliability value of 100% would indicate that, across all trials, all spike trains were exactly the same. Fano factor
We calculated the event variability of the responses to repeated stimulus sets by calculating the mean Fano factor of the neural events within the response. First, the responses to repeated stimulus sets were binned at 1-ms resolution and processed according to the event-identification method described earlier (see Precision of the response). For each cell, we calculated the mean Fano factor according to
 |
Information-theoretic measurements
To calculate the mutual information between the stimulus and the response, the total entropy and the noise entropy of the neural response are needed. Simply put, the total entropy is a measure of how many different neural states a response can encode, whereas the noise entropy is a measure of the inherent variability of the response. By subtracting the noise entropy from the total entropy, we can calculate the mutual information between the stimulus and response. We binned the responses to repeated and unique stimuli at 1-ms resolution. Spike-time histograms for each trial were generated and converted into binary vectors. The data from unique stimuli were used to calculate the total entropy, whereas the data from repeated stimuli were used to calculate the noise entropy of the neural response.
Total entropy calculation
The first step in calculating the total entropy of the response was to convert the unique binary vectors into word vectors. A word W is a concatenation of adjacent bins. Starting at the beginning of our binary vector, we used the first L bins to form a word. That word became the first element of our word vector. We then shifted the origin by one bin and used the next L bins to create the second element of our word vector. This was repeated throughout the entire binary vector and repeated for all 25 unique trials. The result was a collection of 25 word vectors consisting of (N – L + 1) elements, where N is the total number of 1-ms bins in one binary vector. We searched these vectors for all possible words of length L and constructed a probability distribution function PL(W). Finally, we calculated the entropy rate (bits/s) of our probability distribution according to
 |
t is the bin width in seconds, and PL(W) is the probability of a particular word W. Optimally, one would prefer an unlimited number of trials to prevent underestimation of the total entropy. Although this was not feasible, we tested if we acquired sufficient data for our analysis (Juusola and de Polavieja 2003; Koch et al. 2004; Reinagel and Reid 2000). Briefly, we repeated our entropy calculation multiple times, each time using a smaller subset of our data. We fit these multiple points to the following second-order polynomial
 |
 |
Noise entropy calculation
Similarly, the first step in calculating the noise entropy of the response was to convert the binary vectors from repeated trials into word vectors. We then used our collection of word vectors to calculate the probability distribution function PL(W|t), of a particular word W, of word length L, at time t, relative to the start of our vectors. The entropy rate (bits/s) of each of our probability distributions was calculated according to the following
 |
t is the bin size resolution in seconds; and PL(W|t) is the probability of a particular word W, at a time t. The expected value of these entropies, 
HL(R|t)
, was used as our noise entropy, HL(R|S). As with our total entropy calculations, we extrapolated our data to estimate the noise entropy of the response at infinite data size, and infinite word length using the same inverse quadratic method. All further analyses used this extrapolated noise entropy as the actual noise entropy of the data set. Z-value
The Z-value (Reinagel and Reid 2000) allows one to assess the influence of temporal correlation on the mutual information of a neuron's response. It is calculated according to
 |
is the mutual information calculated using words of infinite length and MI1 is the mutual information calculated using words of unit length. Because words of unit length do not contain temporal correlations between spike times, by definition, they have a pattern length of zero. Conversely, words of infinite length have a pattern length of infinity. Encoding efficiency
Encoding efficiency E(S, R) is defined as the percentage of the neural response that is encoded as information according to
 |
Spike-triggered average
We calculated the spike-triggered average (STA) of the stimulus contrast using reverse correlation (DeAngelis et al. 1993; Jones and Palmer 1987). For each cell, the responses to repeated stimuli sets were binned at 1-ms resolution. The STA was calculated as the average 1,000 ms of the stimulus preceding each spike. Stimuli presented >500 ms before the spike were unlikely to be correlated with the response; thus this region was used to determine the mean and SD of the noise of the STA. On the other hand, stimuli presented <300 ms before the spike were correlated with the response and thus this region was used to calculate the slope and the peak time of the STA and the integration time of the cell. The slope was measured between the point when the STA was >2 SDs above the noise and the point when the STA equaled 90% of its maximum value. Only the slope of the STA immediately before the peak value was used. The integration time of the cell was measured between the point when the STA rose >2 SDs out of the noise to when it fell back within 2 SDs of the noise.
Data analysis
A total of 46 LGN X-cells, 24 LGN Y-cells, and 50 layer IV simple cells from a total of 41 adult cats were studied. For all cells, the first 150 ms of the responses were ignored because spikes during this period may have been elicited by stimuli from previous trials. Mean population values are reported as ±1 SD. For nonparametric distributions, a median value is given. All P values correspond to a two-tailed, two-sample t-test of unequal variances between the populations listed, unless otherwise noted.
|
RESULTS |
|---|
|
TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSREFERENCES |
|---|
Before we tested simple cells with Gabor patches, we confirmed our a priori hypothesis that simple cells in area 17 do not respond to stochastic, spatially homogeneous stimuli (full-field flicker). Every 8 ms, we randomly selected a new screen luminance from a normal distribution (µ = 80 cd/m2, = 31%; Fig. 1B, right column). The rest of this stimulus paradigm was identical to the stochastic Gabor patches (see METHODS). Rasters of the responses from a typical layer IV simple cell to repeated stimuli (top, left column) and unique stimuli (top, middle column) are given in Fig. 1B, along with the associated PSTHs below. We found that simple cells responded poorly to this type of stimulus. In fact, the stimulus elicited so few spikes that higher-order quantitative analysis was not possible. In contrast, the same simple cell responds precisely and reliably to a stochastic, contrast modulated Gabor patch (Fig. 1C). All further analysis used only the responses of neurons to stochastic Gabor patch stimuli.
LGN and layer IV simple cells have similar responses to stochastic Gabor patches
In Fig. 2, we show the typical responses of an LGN X-cell (Fig. 2B), an LGN Y-cell (Fig. 2C), and a layer IV simple cell (Fig. 2D) to the repeated (left column) and unique (right column) stimulus sets (Fig. 2A). For clarity, only a 2-s section of the entire response is shown. The sequence of repeated stimuli was identical for all three cells. For each cell type, we show spike-time rasters of the responses to repeated and unique stimuli (top) along with associated PSTHs (bottom). The rasters and PSTHs were generated at 1-ms resolution, which is less than the minimal ISI of our cells. These rasters and PSTHs demonstrate that LGN cells fire with highly reproducible responses to our repeated stimulus set. Layer IV simple cells also responded very well to our repeated stimuli set, in spite of the speed at which our stimulus was changing (125 Hz). Although simple cells did not respond with firing rates as high as those of the LGN neurons (average firing rate of simple cells was 4.40 ± 3.17 vs. 16.15 ± 7.77 spikes/s for X-cells and 23.66 ± 10.01 spikes/s for Y-cells), most of the peaks in the simple cell's PSTH had widths comparable to those of LGN neurons. This suggests that simple cells have temporal precision similar to that seen in LGN neurons. Qualitatively, LGN Y-cells tended to have narrower and taller peaks than LGN X-cells or layer IV simple cells. This suggests that LGN Y-cells have greater temporal precision and response reliability to our stimulus than LGN X-cells and simple cells. Quantitatively, we will subsequently show that these insights are correct.
LGN X-cells and layer IV simple cells respond with similar precision
As seen in the rasters and PSTHs in Fig. 2, LGN and simple cells respond at specific times relative to the start of the stimulus set. We can use the PSTHs to estimate the precision of the neural response to our stimuli because the peaks represent neural events (i.e., periods of highly reproducible activity). Associated with each of these events is a probability distribution that the neuron will fire within a particular time period relative to the start of the event. Neural precision is a metric of the width of that distribution—the wider the probability distribution, the less precise the response. Because these events were not always Gaussian, we measured the precision of each event as the interquartile range of the spike times, a nonparametric measure of the spread of the distribution. Examples of the distributions of temporal jitters for each cell type are given in Fig. 3, B–D. On average, across all LGN and simple cells, our median values were <5% different from our mean values, indicating a near-symmetric distribution of temporal jitters.
To eliminate the influence of multiple spikes per event (i.e., patterned responses) on the precision measurement, we examined precision using only the first spike per event. In response to our stochastic Gabor patches, the precision of LGN Y-cells was greater than either LGN X-cells or layer IV simple cells (P < 0.001, both). However, the precision of layer IV simple cells was statistically indistinguishable from that of their primary afferents, LGN X-cells (P = 0.60; Fig. 3E). Mechanisms that might account for this remarkable precision will be suggested in the DISCUSSION. When all of the spikes per event were considered, the precision of spike timing of all three cell types decreased significantly (P < 0.001). Specifically, the temporal jitter of spike timing increased by 16, 30, and 11% in X-, Y-, and simple cells, respectively (P < 0.001 for all; paired, two-tailed t-test). Similar to our finding using only the first spike, the precision of the responses of LGN Y-cells was greater than that of either LGN X-cells (P < 0.001) or layer IV simple cells (P < 0.001), whereas the precision of the responses of simple cells was statistically indistinguishable from the precision of LGN X-cells (P = 0.68; Fig. 3E). Specifically, the first-spike precision values were: LGN X-cells: 8.12 ± 2.21 ms, LGN Y-cells: 3.91 ± 1.28 ms, and simple cells: 8.35 ± 1.97 ms; the all-spike precision values were: LGN X-cells: 9.43 ± 2.10 ms, LGN Y-cells: 5.09 ± 1.18 ms, and simple cells: 9.25 ± 2.09 ms.
All LGN cells of the same type respond similarly to the same stimulus sequence
Cells of a given class (e.g., ON-centered LGN X-cells) responded with remarkable similarity even when compared across cats. This is similar to the results of Reinagel and Reid (2002), even though our stimulus was spatially structured rather than homogeneous. This assessment was made in 26 LGN X-cells and 15 LGN Y-cells, which were studied using the same sequence of repeated stimuli. In Fig. 4A, the rasters of responses of ON- and OFF-centered LGN X- and Y-cells to our repeated stimuli sequences are shown. Each row represents one trial (100 total trials per cell), and each cell is separated by a black line. Qualitatively, the similarity between the responses of same-type neurons is remarkable. We quantified this similarity by computing all pairwise, normalized cross-correlations of the PSTHs generated from the response to repeated sequences, binned at 1-ms resolution. The mean maximum correlation value is a measure of the similarity of LGN responses within a cell class, whereas its associated absolute temporal offset || is a measure of the temporal jitter between the responses of same-type LGN neurons. The main difference when compared with our precision measurement is that this measurement assesses the jitter between the average responses of multiple cells, whereas our precision calculation looks at the temporal jitter of spike times within individual events of a single cell.
|
This high degree of similarity cannot be explained by firing rate alone. The probability that both spike trains contain a spike in a given time bin will be higher when the firing rates of the two neurons are high than when they are low. This rationale assumes a Poisson-like generation of spikes, where the probability of each spike is independent of spike history and is dependent on firing rate alone. To estimate this similarity due to firing rate, the bins of the PSTHs were temporally shuffled. This eliminated the dependence of the response on the stimulus but retained each response's overall firing rate and reliability. The average similarities of our shuffled PSTHs were less than half of the similarities found using unshuffled PSTHs (Fig. 4B). This suggests that the high level of similarity between LGN neurons was not due to firing rate alone. Specifically, the similarities of the shuffled PSTHs were: 31.7% for ON-centered LGN X-cells, 28.6% for OFF-centered LGN X-cells, and 20.5% for both ON- and OFF-centered LGN Y-cells.
Last, we examined each LGN subpopulation's temporal offsets at peak correlation. In Fig. 4C, we show that the median absolute temporal offsets of OFF-centered LGN neurons were greater than those of ON-centered LGN neurons, within both X- and Y-cell populations (P < 0.01, Kruskal–Wallis test). The temporal offsets for a given LGN population were not greater than the population's mean temporal jitter (Fig. 3). This suggests that, on average, there is greater spike timing variability within the response of a neuron to our stimulus than the spike timing variability between the average responses of any two neurons of the same type. Furthermore, our data suggest that all LGN afferents driving bright subregions of simple receptive field are synchronously activated by our stimulus. Likewise, all the LGN afferents driving the dark subregions of a simple receptive field are synchronously activated.
ON-Centered LGN responses are similar to OFF-centered LGN responses to inverted stimuli
The spatial structure of our stimulus, an optimal Gabor patch, ensures that one of the following two circumstances will occur for a simple cell for any nonzero contrast: 1) simultaneous activation of ON-centered LGN inputs to bright subregions and OFF-centered LGN inputs to dark subregions or 2) the inverse, that is, simultaneous activation of OFF-centered LGN inputs to bright subregions and ON-centered LGN inputs to dark subregions. Circumstance (1) will excite the simple cell, whereas (2) will inhibit it. Because of the simultaneous excitation in circumstance (1), we investigated the similarity of responses of ON-centered LGN X-cells to the repeated contrast sequence [normal sequence (NS)] with responses of OFF-centered LGN X-cells to the inverse sequence (IS; i.e., all contrasts multiplied by –1). For completeness, we also compared the responses of OFF-centered cells to the normal sequence with ON-centered cells to the inverse sequence.
The responses of all LGN X-cells to our random, repeated-stimulus sequence are remarkably similar as long as the comparison is made between sequences that excite the center (i.e., the NS for an LGN cell and IS for an LGN cell of the opposite center sign). In Fig. 5, we show the responses of an ON-centered LGN X-cell to our normal, repeated sequence (Fig. 5A) and the responses of an OFF-centered X-cell to the inverse sequence (Fig. 5B). The similarity of these two responses is obvious. In Fig. 5C, we show the concatenated spike-time rasters of 17 ON-centered NS LGN X-cells and six OFF-centered IS LGN X-cells (left) as well as nine OFF-centered NS LGN X-cell and eight ON-centered IS LGN X-cells (right). As before, we quantified this similarity with the mean maximal normalized correlation taken pairwise between a subset of ON- and OFF-centered cells for which inverse sequence data were available (Fig. 5D). ON-Centered NS/OFF-centered IS LGN X-cells showed 71.16 ± 6.48% similarity and OFF-centered NS/ON-centered IS LGN X-cells showed 75.00 ± 8.62% similarity. For each cell type, the similarity between NS and IS LGN spike trains was indistinguishable from the similarity seen within NS LGN spike trains (P > 0.05). Furthermore, the similarity seen between a given set of NS and IS LGN neurons was more than twice that expected from firing rate alone. Specifically, shuffling the time bins of our PSTHs reduced the mean similarity to about 30%.
|
Our finding that layer IV simple cells and LGN X-cells have identical precision of spike timing in their events may therefore follow from the synchronous activation of all X-cell afferents under our stimulus conditions. To test this hypothesis, the following was performed. First, because layer IV simple cells are estimated to receive input from 20 to 30 LGN afferents (Alonso et al. 2001), the PSTHs of all the ON-centered NS LGN X-cells and OFF-centered IS LGN X-cells were summed (Fig. 5F). Then, the median temporal jitter (using the first spike per event) of the summed PSTH was calculated (see METHODS). This precision of spike timing approximates the precision of the input to a typical layer IV simple cell. If the precision of the input and output of a simple cell is different, it would argue against the notion that a simple cell derives its spike-time precision solely from its inputs. We found this to be the case (Fig. 5G). Summed PSTHs of ON-centered NS/OFF-centered IS LGN X-cells showed a median temporal jitter of 11.12 ms, which is about 33% (P < 0.001; two-tailed, one-sample t-test) greater than the observed temporal jitter of simple cells. We also performed this test with OFF-centered NS/ON-centered IS LGN X-cells and found a similar result (i.e., a median temporal jitter of 10.47 ms; an increase of 25%; P < 0.001). These results suggest that the precision of spike timing seen in layer IV simple cells is not a straightforward consequence of the precision and similarity of the spike trains elicited by our stimulus in the LGN afferents. They argue that additional cortical mechanisms operate to ensure the precision of spike timing in simple cells.
Layer IV simple cells are not as reliable as LGN neurons to stochastic stimuli
We define reliability as the trial-to-trial reproducibility of a spike train. Unlike precision, reliability assesses how often a spike occurs within a particular time window regardless of the exact timing of that spike. Although there are multiple ways to compute reliability (Berry et al. 1997; Mainen and Sejnowski 1995), the method used by Schreiber et al. (2003) is the least influenced by temporal jitter and bin size selection. We calculated the reliability of the response as the mean normalized inner product of all pairwise combinations of Gaussian-smoothed spike trains (see METHODS), and found the reliabilities of each cell population to be: LGN Y-cells: 35.7 ± 11.2%, LGN X-cells: 20.0 ± 9.8%, and layer IV simple cells: 11.5 ± 7.4% (Fig. 6). This demonstrates that LGN Y-cells have spike trains that are 78% more reliable than LGN X-cell spike trains (P < 0.001) and 210% more reliable than simple cell spike trains (P < 0.001). Correspondingly, the reliability of LGN X-cell spike trains was 74% greater than that of simple cell spike trains (P < 0.001).
|
Event reliability
The trial-to-trial neural reliability described earlier examined the reproducibility of an entire spike train, irrespective of the variability of individual neural events within that spike train. Additionally, the reliability of a neuron's response using only significant events was examined, thus reducing the influence of spontaneous activity on our measurement. This was done by calculating the mean Fano factor of all neural events (see METHODS).
In Fig. 7, we plot the variance of the number of spikes versus the mean number of spikes per event for a typical LGN X-cell (Fig. 7A), LGN Y-cell (Fig. 7B), and layer IV simple cell (Fig. 7C). For each graph, the dashed line of unit slope represents the expected Fano factor for a Poisson process. Neural events of LGN X- and Y-cells generally fall below the unity line (i.e., more reliable than what is expected for a Poisson process). Conversely, the neural events of simple cells lay above the unity line, suggesting a highly unreliable response in terms of spike count. Population results are provided in Fig. 7D. On average, LGN X-cell and LGN Y-cell responses had Fano factors less than what is expected from a Poisson process (0.74 ± 0.27 and 0.41 ± 0.23, respectively). On the other hand, layer IV simple cells had Fano factors greater than a Poisson process (1.54 ± 0.53). Thus simple cells were far less reliable than either LGN X-cells or LGN Y-cells (P < 0.001, both). Unlike the normalized reliability measure derived from the entire spike train, LGN X-cell responses during neural events were less reliable than LGN Y-cell responses (P < 0.001).
|
, the reliability of LGN neurons and simple cells is similar to a Poisson process when using a small time window (1 ms). Because the responses were analyzed with larger time windows, the mean Fano factors of LGN neurons decreased, whereas those of simple cells increased. The counting window size that produced the smallest Fano factor was: LGN X-cells: 100 ms (Fano factor: 0.84), LGN Y-cells: 300 ms (Fano factor: 0.37), and simple cells: 2 ms (Fano factor: 0.98). Unlike the reliability of simple cells to drifting gratings (Kara et al. 2000), the mean Fano factors of the responses of simple cells to our temporally rich stimuli were generally much greater than that expected from a Poisson process. As the counting window became very large (>200–300 ms), the mean Fano factor of LGN response increased. The source of this phenomenon is unclear, but we speculate it may be caused by a lack of stationarity in the firing rate within this time window. In addition to having Fano factors lower than that of simple cells, both LGN X- and Y-cells responded with twice as many significant events when the same stimulus was used. Because a simple cell is thought to be driven by multiple LGN inputs, we also compared a summed LGN response (ON-centered NS/OFF-centered IS LGN X-cells) to a typical simple cell response (Fig. 8A). The number of events isolated in the summed LGN response was greater than that found in simple cells (P < 0.001; Fig. 8B). Although not all LGN events resulted in a simple cell event, all simple cell events were aligned with an LGN event. The mechanism responsible for determining which simple cell events were conserved and which were dropped will be discussed in the following text. Specifically, we found the numbers of events in each population were: LGN X-cells: 70.9 ± 11.3 events, LGN Y-cell: 74.5 ± 13.2 events, summed ON-centered NS/OFF-centered IS LGN X-cells: 71 events, summed OFF-centered NS/ON-centered IS LGN X-cells: 62 events, and layer IV simple cells: 35.0 ± 11.2 events.
|
Neural responses to repeated and unique stimuli were characterized by information-theoretic analysis using the "direct" method (Strong et al. 1998). Unlike other methods (reviewed in Borst and Theunissen 1999) that provide upper and lower bounds, the "direct" method allows one to directly estimate the mutual information between the stimulus and the neural response. This value represents the number of neural states a response can reliably encode about a given stimulus. Because the exact mechanisms that LGN and cortical neurons use to generate their responses are unclear, we believe an unbiased measure of neural activity such as mutual information is preferential to other measures (e.g., mean firing rate). By using information-theoretic measures, we can compare neural activity across neurons that may use different encoding mechanisms. Last, this form of analysis allows one to examine whether temporal patterning plays a role in conveying information.
To perform this calculation, both the total entropy of the response (i.e., the number of neural responses given all possible stimuli) and the noise entropy of the response (i.e., the number of neural responses given the same stimulus) were estimated. By subtracting the noise entropy from the total entropy, we estimated the mutual information encoded in the responses of LGN X-cell, LGN Y-cell, and layer IV simple cell populations (Fig. 9A). On average LGN Y-cell responses encoded 49.04 ± 18.14 bits/s, LGN X-cell responses encoded 25.35 ± 14.17 bits/s, and layer IV simple cells encoded 10.36 ± 5.63 bits/s. LGN Y-cells encoded about twice as much information per second as LGN X-cells, and LGN X-cells encoded more than twice as much information per second as layer IV simple cells (P < 0.001, both). As with our reliability measurement, this was expected because information rate is bound by firing rate (Koch et al. 2004; Zador 1998) and LGN neurons respond with greater firing rates to our stimuli than do cortical neurons. To compensate for changes in firing rate, we calculated the information density of each cell's response by dividing the information rate (bits/s) of each cell by its firing rate (spikes/s). LGN Y-cell responses encoded 2.12 ± 0.35 bits/spike, LGN X-cell responses encoded 1.61 ± 0.53 bits/spike, and simple cell responses encoded 2.82 ± 1.21 bits/spike to our stimulus (Fig. 9A, inset). All three cell types showed significantly different levels of encoding, with simple cells encoding, on average, 33% more information per spike than LGN Y-cell responses and 76% more information per spike than LGN X-cell responses. Likewise, LGN Y-cells encoded 32% more information per spike than LGN X-cells (P < 0.001, for all).
|
This effect was quantified by calculating the Z-value (Reinagel and Reid 2000), the percentage of mutual information gained or lost when taking into account temporal patterns (i.e., a temporally correlated response, where the occurrence of a spike depends on the recent activity of the neuron). A positive Z-value indicates that the estimate of mutual information calculated by ignoring temporal patterns underestimates the actual information encoded in the response. This suggests that some information is encoded in the temporal patterning of spikes. Conversely, a negative Z-value indicates that the estimate of mutual information calculated by ignoring temporal patterns overestimates the actual information encoded in the response. This would be the case when some of the information encoded in the response is temporally redundant.
Population data are given in Fig. 9B. LGN X-cell responses contained 16.14 ± 11.33% of their information in the form of temporal patterns, whereas LGN Y-cell responses contained only 7.09 ± 12.89% of their information as patterns. On average, simple cells did not significantly encode any information in the form of patterns (2.70 ± 19.85%). LGN X-cell responses showed significantly different distributions of Z-values when compared with Y-cells (P < 0.001) and simple cells (P < 0.001). The differences in Z-value between Y-cells and simple cells was not significant (P > 0.05). This result, combined with our previous finding that LGN X-cell responses contain the least information per spike, suggests that LGN X-cells are using a patterned response at the cost of more spikes.
Finally, we examined the encoding efficiency of our neural responses to our stimulus. Encoding efficiency is defined as the percentage of the neural response encoded as mutual information. LGN neurons and layer IV simple cells have less than one third encoding efficiency to our stochastic stimuli (LGN Y-cells: 32.50 ± 5.33%, LGN X-cells: 21.51 ± 6.93%, and simple cells: 30.55 ± 9.56%; Fig. 9C). Although we did not observe significant differences between LGN Y-cell and simple cell populations (P = 0.30), LGN X-cells were less efficient than either LGN Y-cells (P < 0.001) or simple cells (P < 0.001).
Comparison of temporal statistics with physiological measures
Finally, we compared the precision, reliability, and information rates of thalamocortical neurons to physiological measures. First, we binned the responses of our neurons to the repeated stimulus set at 1-ms resolution. The choice of stimulus set used did not significantly affect the results (i.e., the analysis based on the repeated set alone, the unique set alone, and the combination of the repeated and unique sets did not differ significantly). Next, we calculated the spike-triggered average (STA) of the stimulus contrast for each neuron using reverse correlation (see METHODS). The STA is an estimate of the temporal impulse response that captures the linear part of the transformation between the stimulus and response. Based on the STA, we measured the change in contrast of the stimulus preceding each spike (slope) and the integration time of the cell. An example of an STA for a simple cell along with an illustration of the extracted measures is provided in Fig. 10A. The slope and integration times were then systematically compared with our temporal statistics for all three cell types (Fig. 10B).
|
|
DISCUSSION |
|---|
|
TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSREFERENCES |
|---|
Reinagel and Reid showed that cat LGN cells respond with high precision to rapid (128 Hz), random luminance variation of a homogeneous area many times larger than their receptive fields (Reinagel and Reid 2000) and that all LGN cells of the same type are activated synchronously by this stimulus (Reinagel and Reid 2002). We have shown that cortical simple cells fail to respond to this stimulus and attribute this lack of response to the synchronous activation of excitatory and inhibitory inputs that subserve subregions within the simple cell's receptive field. Subregions that are excited by bright stimuli are inhibited by dark and vice versa (Ferster 1988; Hirsch 2003; Hirsch and Martinez 2006), and this "push–pull" arrangement causes synaptic events to spatially homogeneous stimuli to cancel.
On the other hand, layer IV simple cells responded well to Gabor patches whose contrast was modulated randomly at a similar temporal frequency (125 Hz). This also follows from the push–pull model: half the time, the contrast provides excitation from all subregions within the receptive field, thus producing a vigorous cortical response. This makes the modulated Gabor patch an excellent stimulus for comparing responses of LGN and V1 neurons.
Precision and reliability of geniculate responses
We examined the temporal properties of LGN neurons and found that LGN Y-cell responses were substantially more precise and reliable than LGN X-cell responses. This was not surprising given that LGN Y-cells tend to have shorter refractory periods and higher temporal frequency resolutions than those of LGN X-cells (Frishman et al. 1983; Lehmkuhle et al. 1980; but see Saul and Humphrey 1990). Previous studies have shown that the precision and reliability of neural responses are linked to the cell's refractory period (Berry and Meister 1998; Kara et al. 2000; Liu et al. 2001). Although the refractory period can enhance the precision of neural output by regularizing the spike output, it cannot account for the difference observed between the "first-spike" precision of LGN X- and Y-cell responses; most events were separated by periods of inactivity much longer than the estimated refractory period. Whether the refractory period played a significant role in the precision of an entire event is less clear. For both LGN cell types, most of the "all-spike" precision of the response could be accounted for by the "first-spike" precision. The refractory period may have helped regularize subsequent spikes, which explains why the "all-spike" temporal jitter increased only 16–30% over the "first-spike" jitter even with two to four times as many spikes being included (see Fig. 7, A and B).
Models of early visual responses have also shown that the refractory period plays a significant role in determining the reliability of a neuron's response (Berry and Meister 1998; Kara et al. 2000; Liu et al. 2001). This is difficult to reconcile with our finding that, as a population, the overall reliability of LGN Y-cell responses was greater than that of LGN X-cells even though both LGN populations had similar ISI distributions and estimated refractory periods (data not shown). Furthermore, the differences in these reliabilities could be explained by differences in firing rate (Fig. 6, inset). One possibility is that LGN X-cells have a refractory recovery function similar to that of LGN Y-cells but a much lower free firing rate (Berry and Meister 1998), resulting in lower firing rates and a reduced overall reliability.
Precision and reliability of layer IV simple cell responses
Although anatomical studies show that cat area 17 receives Y- as well as X-cell input from the LGN (Ferster and LeVay 1978; Freund et al. 1985a,b; Peters and Payne 1993), functional studies (Ferster 1990a,b) have failed to identify any signature of the Y-cell input. Accordingly, the most appropriate comparison is between the precision of spike timing of LGN X-cells and simple cells in layer IV of area 17. It is quite astonishing that the jitter in the spike timing of these two groups of cells is virtually identical. This is even more remarkable given that simple cells are estimated to receive convergent input from about 30 X-cells (Alonso et al. 2001) in addition to recurrent excitatory and inhibitory inputs from other cortical cells both within and outside of layer IV.
Several factors must contribute to this maintained precision in simple cells. First, it is known that geniculocortical synapses of layer IV cells are far less variable than those from other sources (Ahmed et al. 1994; Stratford et al. 1996). Another contributing factor is the high reproducibility of LGN responses to our stimuli across cells studied in different cats. Spike trains elicited by ON- and OFF-centered cells are also highly synchronous, provided that each is driven by the normal sequence or its inverse. This means that under our stimulus conditions, all of the geniculate inputs to a given simple cell are discharging with extraordinary synchrony.
These facts alone, however, cannot fully account for the precision of simple cell respon
) and from our summed OFF-centered NS/ON-centered IS LGN X-cell population (
) are shown to the left of the LGN X-cell bar.
