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How information encoded in neuronal spike trains is used to guide sensory decisions is a fundamental question. In olfaction, a single sniff is sufficient for fine odor discrimination but the neural representations on which olfactory decisions are based are unclear. Here, we recorded neural ensemble activity in the anterior piriform cortex (aPC) of rats performing an odor mixture categorization task. We show that odors evoke transient bursts locked to sniff onset and that odor identity can be better decoded using burst spike counts than by spike latencies or temporal patterns. Surprisingly, aPC ensembles also exhibited near-zero noise correlations during odor stimulation. Consequently, fewer than 100 aPC neurons provided sufficient information to account for behavioral speed and accuracy, suggesting that behavioral performance limits arise downstream of aPC. These findings demonstrate profound transformations in the dynamics of odor representations from the olfactory bulb to cortex and reveal likely substrates for odor-guided decisions.
Active sampling is an important component of sensory processing that can result in chunking of information into short, discrete epochs of a fraction of a second, as exemplified by visual fixations. In olfaction, rodents exhibit rapid stereotyped respiration at theta frequency (called sniffing) during active exploration (Wachowiak, 2011; Welker, 1964). Behavioral experiments have shown that a single rapid sniff can support accurate odor discrimination (Uchida and Mainen, 2003; Wesson et al., 2008), suggesting that each sniff generates a relatively complete “snapshot” of an olfactory world, and constitutes a unit of odor coding (Kepecs et al., 2006). Despite these observations, however, how sensory information is represented in this timescale and how it is transformed in the brain to ultimately control behavior remain unclear.
Studies in the olfactory bulb, the first relay in the olfactory neural pathway, have shown that odor stimulation triggers diverse temporal patterns of activity at the level of the olfactory nerve inputs and mitral/tufted cells, the exclusive outputs of the olfactory bulb (Cang and Isaacson, 2003; Friedrich and Laurent, 2001; Hamilton and Kauer, 1989; Junek et al., 2010; Macrides and Chorover, 1972; Margrie and Schaefer, 2003; Meredith, 1986; Spors and Grinvald, 2002; Wehr and Laurent, 1996; Wellis et al., 1989). During sniffing, spiking activity of mitral/tufted cells show diverse and reliable temporal patterns at the resolution of tens of milliseconds (Carey and Wachowiak, 2011; Cury and Uchida, 2010; Shusterman et al., 2011). These dynamic response patterns, in particular, those in the initial portion of the response (~100 ms), convey substantial odor information compared to the total spike counts contained in the entire period of a theta sniff cycle (Cury and Uchida, 2010), suggesting that timing of spikes plays a critical role in rapid and accurate odor coding in the olfactory bulb.
Compared to the olfactory bulb, relatively little is known about how odor information is coded by neurons in the olfactory cortex. Neurons in the olfactory bulb project broadly to the cortex without apparent topography (Ghosh et al., 2011; Miyamichi et al., 2011; Nagayama et al., 2010; Ojima et al., 1984; Sosulski et al., 2011) and odor stimulation activates widely distributed neurons in the cortex again without apparent topography (Illig and Haberly, 2003; Rennaker et al., 2007; Stettler and Axel, 2009), suggesting that the olfactory cortex might use a different mechanism for odor coding than the olfactory bulb. To elucidate coding principles in the olfactory cortex that underlie rapid olfactory decisions, here we examined (1) how active sniffing shapes neural responses, (2) whether spike times or rate carry more information and (3) the nature of odor coding at the ensemble level. We show that odor inhalation triggers a transient burst of spikes time-locked to inhalation onset. In contrast to the olfactory bulb, timing of spikes conveyed little additional information compared to the total spike counts, demonstrating a profound transformation of coding mechanisms between the olfactory bulb and cortex. Furthermore, odor stimulation dramatically reduced correlated noise among neurons, which facilitated the efficiency of population code.
We recorded spiking activity of olfactory cortical neurons in rats while simultaneously monitoring their sniffing and performance in a two-alternative choice odor mixture categorization task (Uchida and Mainen, 2003) (Figure 1A). The stimuli consisted of three or four odor pairs with each delivered either alone (100/0, 0/100) or in mixtures (68/32, 32/68) (Figure 1B). All stimuli were randomly interleaved and one odor of each pair was assigned to the right and the other to the left choice port, with mixtures rewarded according to the dominant component. One set of subjects (n = 5) performed a reaction time version of the task, taking one to two sniffs between odor onset and response initiation (1.71 ± 0.01; Figure S1B) (Uchida and Mainen, 2003). A second set of subjects (n = 3) was trained to wait for a tone (Rinberg et al., 2006) at 700 ms delay from odor valve onset in order to enforce a longer odor sampling period (Figure 1C) and more sniffs (3.84 ± 0.03, P < 0.05 compared to reaction time paradigm; Figure S1B). In both paradigms, rats sniffed at theta frequency during odor sampling (7.18 ± 0.29 and 6.35 ± 0.27 s−1 respectively; Figure 1C). Task performance accuracy was higher for pure than mixture stimuli across all pairs, but was independent of the training paradigm and of the number of sniffs taken within a given paradigm (Figure 1D, Figures S1C, D). Thus, as previously reported (Uchida and Mainen, 2003), a single sniff was sufficient for maximal performance by rats in this odor mixture categorization task.
We recorded from ensembles of up to 21 neurons (9.4 ± 4.7, mean ± S.D.) in the anterior piriform cortex (aPC) using chronically-implanted tetrodes during performance of the above tasks (see Experimental Procedures for details). From a total of 460 well-isolated single neurons, 179 neurons recorded using a fixed panel of 6 odorants formed the primary data set for the subsequent analyses. Given the similarity of behavioral performance in reaction-time and go-signal paradigms data from these experiments was pooled (91 neurons from the reaction time paradigm and 88 neurons from the go-tone paradigm).
Previous studies have noted relatively brief, burst-like responses in PC (McCollum et al., 1991; Wilson, 1998) but these studies did not explicitly compare neural responses with respiration. We found that odor responses in aPC consisted typically of a transient burst of spikes time-locked to the onset of odor inhalation. Aligning spike times relative to the onset of the first sniff after odor onset revealed a much tighter temporal organization than was apparent by aligning on odor valve opening (Figures 2A–C). Indeed some responses were detectable only using sniff-locking (Figures S2A, B). Responses peaked rapidly (Tpeak: 99 ± 45 ms from the first inhalation onset, median ± S.D.; Figure 2D) and returned to baseline rapidly (full-width at half max: 32 ± 24 ms, median ± S.D.; Figure 2E). Thus, odor-evoked transients lasted approximately one sniff cycle (158.1 ± 40.2 ms, mean ± S.D.).
Single neurons in aPC showed robust and stimulus-specific responses to odor stimuli (Figure 3A). Relatively little selectivity for spatial choices (left vs. right) or reward outcomes was observed (Figure 3B). As a population, 45% of aPC neurons were activated by at least one of the six odors tested while 28% were activated by two or more (Figures 3C, D, S3) (P<0.05, Wilcoxon rank sum test). Conversely, each odor caused significant responses in 16.5 ± 3.1% of aPC neurons (mean ± S.D., n = 6 odors, 10.3% excitatory; 6.2% inhibitory). The probability of response of a piriform neuron to an odor was well-fit by a binomial distribution with an extra allowance for non-responding neurons (Figure 3D). We calculated a population sparseness of 0.41 and a lifetime sparseness of 0.61 (see Experimental Procedures), somewhat lower than previously observed in aPC of anesthetized rats (Poo and Isaacson, 2009). Therefore, aPC responses were observed in broadly distributed, moderately sparse neural populations, largely consistent with previous studies (Poo and Isaacson, 2009; Rennaker et al., 2007; Stettler and Axel, 2009; Zhan and Luo, 2011).
The latency and peak timing of aPC responses varied across neurons and odors, raising the possibility that these parameters may carry odor information (Cury and Uchida, 2010) (Figures 4A, B). However, both of these timing parameters were anti-correlated with spike counts (Figures 4C, D), suggesting that the information conveyed by these variables might be redundant. In order to quantify the amount of information carried by different response variables (i.e. latency, peak timing and spike counts), we performed a decoding analysis to ask how accurately could an ideal observer classify each individual trial as belonging to one of six odor stimuli. By comparing decoding accuracy using vectors consisting of different variables derived from aPC responses, we compared the relative importance of each coding strategy. As decoders (ideal observers), we used linear classifiers including perceptrons and support vector machines with linear kernels. These decoders essentially calculate a weighted sum of inputs followed by a threshold and therefore resemble a biophysical decoding of aPC information that might actually be implemented in downstream areas.
Input codes based on the total number or rate of spikes in a sniff cycle provided the most reliable performance in odor classification, whereas codes based on first spike latency or peak timing performed significantly worse (Figure 4E). Furthermore, combining latency or peak timing with rate failed to improve decoding accuracy. Although it has been postulated that spike times may provide a more rapid coding mechanism (Cury and Uchida, 2010; Gollisch and Meister, 2008; Thorpe et al., 2001), we found that decoders using spike count actually performed faster than those based on spike latency or peak timing (Figure 4F), demonstrating that spike counts can convey information in a more reliable manner. Furthermore, decoding based on complete temporal patterns of activity in a sniff cycle did little to improve decoding accuracy (Figure 4G).
Finally, using phase of spike occurrence with respect to sniffing cycle instead of absolute time did not improve the decoding accuracy (Figure 4H). Together, these results suggest that spike rates or counts are the predominant carrier of olfactory information in the aPC, and that the dependence of odor coding on spike timing is greatly reduced compared to the olfactory bulb (Cury and Uchida, 2010).
We next compared the performance of aPC populations decoded using linear classifiers to the performance of the animal. Decoding based on total spike counts in the first sniff using the entire 179 neurons gave nearly perfect performance on pure odors (Figures 5A, B). For both pure and mixture stimuli, the accuracy of the classifier reached a level comparable to that of the animal using only about 70 neurons (Figure 5A). Analysis of the time course of decoding using a short sliding time window showed that the maximum information could be read out from the initial burst of activity within 100 ms after the first inhalation onset and that the rate of information dropped thereafter (Figure 5B, C). Comparing the first and second sniff separately, spikes in the first sniff gave significantly higher accuracy than those in the second sniff or the last sniff before odor port exit (Figure 5D; P<0.05, χ2 test), and using both the first and second sniff cycles resulted in only a small increase in accuracy (Figure 5D). Therefore spike counts in ensembles of aPC neurons appear to be sufficient to explain both the speed and accuracy of decisions in an odor mixture discrimination task.
If firing rates across ensembles of aPC neurons are used by the brain to form behavioral responses, and if sensory uncertainty reduces performance accuracy, as in the mixture trials, then we ought to observe trial-by-trial correlations between decoding based on these neural representations and the animals’ choices. To test this idea, we first compared neuronal firing rates on correct and error choices for a given stimulus, a measure analogous to “choice probability”, a measure that has been used previously to test the role of a neural representation in behavior (Britten et al., 1996; Cury and Uchida, 2010; Parker and Newsome, 1998). We found a low average correlation between the firing rates of individual neurons and subjects’ choices (Avg. choice prob. = 0.51 ± 0.011; Figures 5E, F). This correlation was somewhat smaller than those found in previous observations in visual cortex (0.53–0.7; Britten et al., 1996; Cohen and Newsome, 2009; Dodd et al., 2001; Uka and DeAngelis, 2004). However, if the information for choices is distributed across a large number of uncorrelated aPC neurons such that the contribution of single neurons is diluted (Cohen and Newsome, 2009), then we reasoned that the accuracy of decoding based on simultaneously recorded ensembles may be correlated on a trial-by-trial basis with behavioral choices. Indeed, we found that patterns of spike counts across aPC neurons in correct trials provided significantly higher decoding accuracy than patterns in error trials (Figure 5G, P=0.030, Wilcoxon test). In contrast, decoding using peak timing or latency did not show a significant difference between correct and error trials (Figures 5H, I, P>0.05, Wilcoxon test). Therefore, the spike rates in aPC not only carry substantial stimulus information, they are also correlated at an ensemble level with the behavioral choices of the animal.
The above results indicate that odor information is coded by a large number of neurons in aPC. A critical feature of information coding in neuronal ensembles is the structure and magnitude of correlated fluctuations in firing, which can affect the ability of downstream neurons to decode the information. A simple example of ensemble decoding is population averaging or pooling. By this strategy, neuronal noise can, in principle, be eliminated by averaging the activity of a large number of neurons. However, if noise is not random across neurons, that is, when neural activity co-fluctuates across neurons, the benefit of pooling can be significantly curtailed (Cohen and Kohn, 2011; Zohary et al., 1994). The choice probability analysis suggested that aPC neurons are actually very weakly correlated. To test more directly whether such correlations affect representations of odors in the olfactory cortex, we analyzed the “noise correlations” between pairs of simultaneously recorded aPC neurons (see Experimental Procedures). Noise was defined as the trial-to-trial variability of spike counts in a sniff cycle (40–160 ms after the first sniff onset) around the mean response under a given stimulus condition. Noise correlation was defined as the correlation coefficient between the noise of two neurons to multiple presentations of a given odor stimulus. We found surprisingly low noise correlations amongst aPC neurons (0.0046 ± 0.0988; mean ± S.D.; N=936 pairs, Figures 6A, S5). In fact, both the mean and the standard deviation of noise correlations of the aPC data were similar to trial-shuffled data in which all correlations are removed (0.00011 ± 0.0870; Figures S5C–F) suggesting that deviations from zero were mostly due to the effect of finite sample size (Ecker et al., 2010). Moreover, we observed no dependence of the magnitude of noise correlations on the number of evoked spikes over a range of rates < 5 to > 100 spikes·s−1 (Figure S5A, B). Therefore, near-zero noise correlations in aPC were not a consequence of low firing rates (Cohen and Kohn, 2011; de la Rocha et al., 2007; Kohn and Smith, 2005).
In the neocortex, neighboring neurons with similar stimulus tuning tend to exhibit correlated trial-by-trial fluctuations in firing rate (Bair et al., 2001; Cohen and Kohn, 2011; Zohary et al., 1994), thought to arise from common inputs, and it has been postulated that these “structured” or “limited-range” correlations are particularly detrimental to the efficiency of population coding (Averbeck et al., 2006; Sompolinsky et al., 2001). We therefore examined whether aPC noise correlations are low even when odor tuning is similar. To quantify the similarity of odor tuning between pairs of neurons, we calculated the correlation coefficient of the mean odor responses across all 12 stimuli used (i.e. signal correlation). This analysis showed that signal correlations were low both for aPC neurons recorded on the same tetrode and for those recorded on different tetrodes (P > 0.05, Wilcoxon rank sum test; Figure 6B). Similarly, noise correlations were near-zero regardless of whether neurons were recorded on the same or different tetrodes (P > 0.05, Wilcoxon rank sum test; Figure 6C). Most importantly, the noise correlations of pairs of aPC neurons were independent of their signal correlations (regression slope: 0.0156 ± 0.0090, not significantly different from zero, P > 0.05; Figure 6D). These results suggest that, during odor stimulation, aPC neurons act largely as independent encoders regardless of their distance or the similarity of their odor tuning.
Neuronal variability and noise correlation are not static, but can be modulated by attentional state (Cohen and Maunsell, 2009; Mitchell et al., 2009), perceptual learning (Gu et al., 2011) and stimulus input (Bhandawat et al., 2007; Churchland et al., 2010; de la Rocha et al., 2007; Kazama and Wilson, 2009). Therefore, in order to gain insight into how near zero noise correlations arise in aPC, we tested how trial-to-trial correlations across neurons are modulated during the course of events in a trial. For this analysis, since odor stimuli were not always present, we calculated the correlation coefficients of spike counts without subtracting the mean responses of each stimulus condition (see Experimental Procedures for more details). We found that when rats begin active sampling (sniffing) in anticipation of odor presentation, the aPC population was globally activated, with the mean population firing rate increasing by around 30% (Figure 7A). Surprisingly, during the same period the mean pairwise correlation across the entire population dropped, implying a possible positive impact on population coding (Zohary et al., 1994). However, correlations between similarly tuned pairs increased (Figures 7B–D, S6A–C; regression slope: 0.0916 ± 0.0092, significantly different from zero, P < 0.01), implying a possible negative impact on population coding (Sompolinsky et al., 2001). In order to estimate the net effect, we performed decoding analysis using simulated data in which spike counts obtained during odor stimulation were trial-shuffled to generate noise correlation structures with different means and signal correlations while preserving the mean odor response profile of individual neurons (see Experimental Procedures for details). We found that correlations of the type observed during the pre-odor sampling period, had they persisted into the odor sampling period, would have significantly eroded the efficacy of decoding, reducing classifier performance by more than 5–10% (P < 0.01, t-test)(Figures 8A–C, S7). We calculated that 2–3 times more neurons would have been required to achieve the same level of decoding performance had pre-odor correlation levels been maintained (Figure 8D). The simulation also indicated that the effects would be even larger with larger ensembles. We also found that trial-to-trial variability in spike count, as measured by the Fano factor and the coefficient of variation, was significantly reduced by odor onset (Figures S6D, E). Thus, potentially deleterious population correlations are increased during the period of high sniffing preceding odor onset but these correlations are quenched during the arrival of the stimulus (Churchland et al., 2010).
Together with recent studies of neural coding in the olfactory bulb (Carey and Wachowiak, 2011; Cury and Uchida, 2010; Shusterman et al., 2011), this study demonstrates that odor representations are profoundly transformed between the bulb and the aPC. While these studies show that odor responses in the olfactory bulb exhibit complex temporal patterns carrying stimulus information, here, we show that those in the aPC consist primarily of a simple burst of firing, locked to respiration. Furthermore, the baseline firing rates are higher in the olfactory bulb compared to the piriform cortex (12.9 ± 6.4 Hz in the olfactory bulb; 6.15 ± 9.01 Hz in the aPC; mean ± S.D.; Cury and Uchida, 2010 and the present study). As the consequence, whereas in the olfactory bulb extracting information from mitral/tufted cells requires decoding of temporal patterns (Cury and Uchida, 2010), in the aPC most odor information can be read out using only spike counts of neurons.
Why might the olfactory bulb and cortex areas use different strategies for odor coding? One important consideration is the substantial anatomical differences between the two areas: while a relatively small number of neurons (20–50 mitral cells) transmit odor information from each of the approximately 1000 input channels (glomeruli) in the olfactory bulb, this information is broadcast to an olfactory cortex that contains an estimated two orders of magnitude more neurons (Shepherd, 2004). Because of this expansion in coding space the necessity to maximize the rate of information transmitted per neuron and per unit time in the olfactory bulb will be much greater than in the aPC. The cortex can therefore better afford to employ a rate-based coding strategy based on a larger number of neurons and a widely-distributed code. One significant advantage of rate-based code over temporal code is that downstream areas can more readily read out such a code or combine it with other kinds of information encoded in rates. This might then facilitate proposed functions of the piriform cortex such as forming associative memories (Franks et al., 2011; Haberly, 2001).
The mechanism of the temporal-to-rate transformation remains to be determined. In insects, temporally dynamic responses in the antennal lobe (AL, considered equivalent to the olfactory bulb) are transformed into sparse responses in the mushroom body (MB, considered equivalent to the PC). Various mechanisms have been proposed to underlie this process, including (1) oscillatory spike synchronization, (2) short membrane time constants of MB neurons, (3) feedforward inhibition and (4) highly convergent connectivity between the AL and MB (Perez-Orive et al., 2004; Perez-Orive et al., 2002). In zebrafish, different mechanisms appear to shape the responsiveness of cortical neurons: neurons in the dorsal telencephalon (Dp) effectively discard information about synchronous firing in the olfactory bulb due to cortical neurons’ slow membrane time constants and relatively weak feedforward inhibition (Blumhagen et al., 2011). It will be important to examine whether PC neurons in mammals are tuned to temporal patterns of activity in the olfactory bulb (Carey and Wachowiak, 2011; Cury and Uchida, 2010; Shusterman et al., 2011), and if so, which aspects of temporal patterns are important.
Our findings bear on the relationship between psychophysical limits and neuronal representations, a central subject in sensory physiology (Parker and Newsome, 1998). We found that, by monitoring spikes from as few as 50–100 aPC neurons, a simple decoder based on firing rates could extract more than enough information in a single sniff cycle to account for the behavioral accuracy of rats in the odor categorization task. We also found that while single neuron activity was not on average different between correct and error trials (low average “choice probability”), population activity-based decoders performed significantly better on correct compared to error trials. Rate information peaked within 100 ms during the first sniff, and aggregating information over longer periods in multiple sniff cycles failed to significantly augment decoding performance, providing an explanation for the rapid speed of olfactory discrimination performance and the lack of speed-accuracy tradeoff over longer periods (Uchida and Mainen, 2003). Therefore, these observations provide substantial evidence linking a rate-based population code to behavioral performance.
We found that an optimal linear decoder of aPC neurons can reach levels of performance superior to the animal itself using < 100 neurons out of the estimated population of around 106 neurons (Shepherd, 2004). The aPC clearly contains an extremely robust representation of odor identity. What then ultimately limits behavioral accuracy? While similar observations in the visual system have been attributed to the reduced efficiency of pooling in the actual network of neurons due to ensemble correlations (Shadlen et al., 1996; Zohary et al., 1994), this appears not to be the case in the aPC. During odor stimulation, aPC networks have near zero mean noise correlation, more than one order of magnitude lower than that generally reported in the neocortex (0.05–0.2; Cohen and Kohn, 2011; Gawne and Richmond, 1993; Lee et al., 1998; Zohary et al., 1994) (Figure 6A), similar to that reported in the primary auditory cortex of anesthetized rats (Renart et al., 2010) and area V1 of awake monkeys (Ecker et al., 2010). More importantly, aPC neurons also lack the positive relationships between signal and noise correlations that are typically observed (Bair et al., 2001; Gu et al., 2011; Zohary et al., 1994). However, the absence of such correlations is not simply due to the distributed connectivity of the olfactory cortex: Such structured correlated activity can and does emerge prior to odor onset and simulations demonstrated that such correlations would have substantially reduced the efficiency of population coding. However, we found when driven by odor stimulation, these pre-stimulus correlations are quenched. While we cannot rule out the possibility that additional correlations that we were unable to measure with this data set might affect decoding, behavioral performance in the odor mixture categorization task appears to be limited neither by the level of noise of the sensory representation nor by correlated fluctuations amongst the population of neurons. We therefore conclude that the limits of performance must be set either by the ability of downstream circuits to accurately read out of these representations or by other non-sensory sources of variability.
Whether prolonged odor sampling can improve the accuracy of odor discrimination has been controversial. Some studies have suggested that the accuracy of odor discrimination can be improved with longer odor sampling over 500 ms (Rinberg et al., 2006) or more (Friedrich and Laurent, 2001). It has been suggested that the accuracy of discrimination of highly similar odor pairs might depend on the refinement of odor representations through temporal evolution of neural activity (Friedrich and Laurent, 2001) or through temporal integration of sensory evidence. However, the result of the present study suggests that these processes are unnecessary. These findings indicate, instead, that performance accuracy is affected not only by stimulus information but additionally by other task parameters that may affect the ability of the animal to choose accurately based on olfactory stimulus representations (Zariwala et al., 2005). It remains to be seen whether similar conclusions can be drawn in different olfactory tasks such as odor detection, discrimination at low concentrations, or more complex tasks. The present study indicates that neuronal recording in animals performing these behavioral tasks will be a critical step toward addressing these fundamental questions.
All procedures involving animals were carried out in accordance with NIH standards and approved by the Cold Spring Harbor Laboratory and Harvard University Institutional Animal Care and Use Committee (IACUC). All values were represented by mean ± S.E.M unless otherwise noted.
Rats were trained and tested on a two-alternative choice odor mixture categorization task where water was used as a reward as described previously (Cury and Uchida, 2010; Uchida and Mainen, 2003). Odor delivery was controlled by a custom made olfactometer (Cury and Uchida, 2010; Uchida and Mainen, 2003). Three rats (two of them trained with go-signals) were tested on a standardized stimulus set of three odor pairs: (1) caproic acid and citralva, (2) ethyl 3-hexenoate and 1-hexanol, and (3) dihydroxy linalool oxide vs. cumin aldehyde (Figure 1B). Each of these odors was diluted 1:10 in mineral oil, and further diluted by filtered air by 1:20 (1:200 total).
After each animal reached an asymptotic performance in behavioral training, each rat was implanted with a custom-made multielectrode drive (Cury and Uchida, 2010) in the left hemisphere in the aPC (3.5 mm anterior to bregma, 2.5 mm lateral to midline) and a bipolar stimulating electrode in the olfactory bulb (Kashiwadani et al., 1999; Schoenbaum and Eichenbaum, 1995) under anesthesia. Extracellular recordings were obtained using six independently adjustable tetrodes. To monitor sniffing, during drive implantation, a temperature sensor (thermocouple) was implanted in one nostril (Cury and Uchida, 2010; Uchida and Mainen, 2003).
We are grateful to Haim Sompolinsky for stimulating discussions on population coding. We thank John Maunsell, Markus Meister, Alex Pouget and Rachel Wilson for their valuable comments on the manuscript. We also thank Kevin Cury, Rafi Haddad, Gabriel Kreiman, Eran Mukamel, Alice Wang and other members of the Uchida lab for discussions. This work was supported by: National Institutes of Health Grant DC006104, Cold Spring Harbor Laboratory and Champlimaud Foundation (Z.F.M.); Swartz Foundation, Smith Family New Investigator Award, Alfred Sloan Foundation, Milton Fund and start-up funding from Harvard University (N.U.).
AUTHOR CONTRIBUTIONSN.U. and Z.F.M. designed the experiments and wrote the paper. N.U. performed the experiments. K.M. performed the data analysis and helped writing the paper. N.U. and Z.F.M. helped the data analysis.
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