* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download PRINCIPLES OF NEUROBIOLOGY CHAPTER 6
Convolutional neural network wikipedia , lookup
Holonomic brain theory wikipedia , lookup
Neural modeling fields wikipedia , lookup
Premovement neuronal activity wikipedia , lookup
Metastability in the brain wikipedia , lookup
Neuroanatomy wikipedia , lookup
Types of artificial neural networks wikipedia , lookup
Neuroscience in space wikipedia , lookup
Psychophysics wikipedia , lookup
Optogenetics wikipedia , lookup
Mirror neuron wikipedia , lookup
Neuropsychopharmacology wikipedia , lookup
Neurotransmitter wikipedia , lookup
Chemical synapse wikipedia , lookup
Pre-Bötzinger complex wikipedia , lookup
Channelrhodopsin wikipedia , lookup
Molecular neuroscience wikipedia , lookup
Caridoid escape reaction wikipedia , lookup
Response priming wikipedia , lookup
Nonsynaptic plasticity wikipedia , lookup
Sparse distributed memory wikipedia , lookup
Single-unit recording wikipedia , lookup
Olfactory bulb wikipedia , lookup
Feature detection (nervous system) wikipedia , lookup
Olfactory memory wikipedia , lookup
Synaptic gating wikipedia , lookup
Biological neuron model wikipedia , lookup
Nervous system network models wikipedia , lookup
Efficient coding hypothesis wikipedia , lookup
PRINCIPLES OF NEUROBIOLOGY CHAPTER 6: OLFACTION, TASTE, AUDITION, AND SOMATOSENSATION JOURNAL CLUB © 2016 GARLAND SCIENCE Paper: Bhandawat V, Olsen SR, Gouwens NW, Schlief ML and Wilson RI (2007) Sensory processing in the Drosophila antennal lobe increases reliability and separability of ensemble odor representations. Nat Neurosci 10:1474–1482. Principles of Neurobiology Reading: Chapter 6. Olfaction in mammals, flies, and worms is discussed in Sections 6.1–6.16; the fly olfactory system, which is most relevant to this paper, is described in Sections 6.13–6.16. Some of the results of this paper are presented in Section 6.14. Background Although considerable effort has been directed toward developing an understanding of vertebrate olfaction (see Sections 6.1–6.10), the complexity of the vertebrate olfactory system presents many challenges. This complexity is in part due to the large number of processing channels in this system: the mouse genome encodes more than a thousand odorant receptors, and the mouse olfactory bulb has more than two thousand glomeruli (see Sections 6.4 and 6.8). The olfactory systems of insects are numerically simpler: the Drosophila genome encodes fewer than sixty olfactory receptors, and the insect analog of the olfactory bulb, the antennal lobe, has approximately fifty glomeruli. Insect and vertebrate olfactory systems are similarly organized (for instance, olfactory receptor neurons expressing a single olfactory receptor type all project to the same glomeruli in the olfactory bulb or antennal lobe in vertebrates and insects, respectively) and use similar strategies to process and represent olfactory information (see Section 6.13). These similarities, along with the numerical simplicity of insect olfactory systems compared to vertebrate olfactory systems, have made insects fruitful model organisms for understanding olfaction throughout the animal kingdom. More broadly, studies of insect olfaction have provided insight into the more general issues of how neural circuits process and represent complex sensory information. Until the 2000s, our understanding of insect olfactory system function was based principally on neurophysiological studies in locusts, moths, and bees. Because of their larger body sizes and the correspondingly larger sizes of their neurons, these insect species were more amenable to electrophysiological study than smaller species such as the fruit fly Drosophila, which has such small neuronal cell bodies that studies using patch clamp techniques (see Section 13.21 and Box 13–2) were traditionally difficult or impossible to perform. However, the genetic tools available in Drosophila (see Section 13.2) and the stereotyped identities of its neurons made it the preferred organism for developmental, anatomical, and functional imaging studies of the olfactory system and motivated the development of methods to record intracellularly from Drosophila neurons. The first patch clamp recordings from neurons in the Drosophila olfactory system were obtained by Rachel Wilson and her colleagues in the early 2000s. Since then, Wilson and her colleagues have published a series of exemplary papers examining the mechanisms and principles of information processing in the early Drosophila olfactory system. Remarkable work from numerous research groups, including Wilson’s, on the development, organization, and function of the Drosophila olfactory system, has shed light on fundamental principles and mechanisms of sensory processing. The present paper explores how olfactory information is transformed by the Drosophila antennal lobe and how this transformation may facilitate reliable and accurate representation of odors. Reading Guide p. 1474, ¶2, Response reproducibility is a central issue in sensory processing because the signal-tonoise ratio of a neural response limits the rate of information transmission by that neuron: If a neuron exhibits a consistent pattern of action potentials in response to repeated presentations of the same Page 1 of 9 stimulus, then that pattern of action potentials is considered ‘signal’: it contains information about the presence of a stimulus. On the other hand, if the firing pattern of a neuron is not dependent on the presence of a stimulus, then that neuron’s firing contains no information about the presence of the stimulus. Most sensory neurons fall in between these two extremes. In this case, a neuron’s firing patterns in response to a stimulus is partially but not perfectly reproducible across repeated presentations of the stimulus. The reproducible response of a neuron to a stimulus is the ‘signal’ carried by that neuron, while the random trial-to-trial variations of the neuron’s response to a stimulus is that neuron’s ‘noise.’ Because noise in this case is assumed to be random, it can be ‘averaged out’ over time: by monitoring a low signal-to-noise ratio neuron for a long period of time, an observer can increase her confidence that an observed spiking rate or pattern is signal and not noise. Thus, in order to be equally confident about the information represented by a low signal-to-noise ratio neuron and a high signal-to-noise ratio neuron, one would have to monitor the low signal-to-noise ratio neuron for a longer period of time than the high signal-to-noise ratio neuron. Neurons with a high signal-to-noise ratio can thus in theory faithfully transmit information at a faster rate than neurons with a low signal-to-noise ratio. p. 1474, ¶4, Here we aim to resolve these issues with a systematic analysis of the inputs and outputs of seven glomeruli in the Drosophila antennal lobe (Supplementary Fig. 1 online): Olfactory receptor neurons (ORNs) are classified into different types based on the olfactory receptor (OR) they express. ORN cell bodies in the antennae and maxillary palps have dendrites in hairlike protrusions called sensilla. Based on morphological characteristics, sensilla can be classified into multiple subclasses, each of which is found in a stereotyped position on the antennae or maxillary palps. Each type of ORN is found only within a particular sensillum subclass, and each subclass houses members of only ~2–3 ORN types. In order to perform their analyses, Bhandawat et al. had to record the activities of both projection neurons (PNs) and ORNs connecting to different glomeruli. Prior work in the fly established the glomerulus to which each ORN type sends its axons and to which each PN sends its dendrites, so the pre- and postsynaptic partner cell types for each glomerulus are known. To perform their analyses, Bhandawat et al. had to identify the ORN and PN types from which they were recoding (see Sections 6.13–6.14). To record from ORNs, they inserted extracellular recording electrodes into a sensillum, which allowed them to record action potentials from the ~2–3 ORNs that had dendrites in that sensillum. Although the action potentials produced by each ORN could often be separated using spike sorting methods (see Section 13.20), in some cases Bhandawat et al. used a genetic strategy to kill particular types of ORNs that were found paired with the ORNs they were targeting for recording; with this strategy, the dendrites from the targeted ORN would be housed alone in a sensillum. The identities of the ORNs being recorded were based on sensillum morphology and position. In addition, since the response properties of different ORNs to particular odorants and the physiological characteristics of some ORNs are known from previous studies, it was also possible to use odor tuning and physiological properties to assign identities to ORNs being recorded (see Supplemental Methods under ‘ORN recordings’). To record from PNs, Bhandawat et al. used whole-cell patch clamp methods in flies in which different subsets of PNs were labeled with GFP using GAL4 lines (see Sections 13.10 and 13.21). Since the GAL4 lines targeted multiple PN types, the identities of the recorded PNs had to be confirmed post hoc by filling cells with a compound through the patch pipette so that they could be stained; since the dendrites of a single PN all project to the same glomerulus and since each glomerulus can be identified from its stereotyped shape and position in the antennal lobe, the identity of the recorded PN could be determined based on the glomerulus to which it sent its dendrites (Fig. S1d). One limitation of whole-cell voltage clamp recordings is that diffusion between the cytoplasm and the pipette solution can change the composition of the cytoplasm and affect cellular properties; this is of particular concern when recording from neurons that have small cell bodies, such as those found in the fly (see Box 13–2). However, Bhandawat et al. found that neuronal recordings performed in cell-attached mode, in which the pipette is attached to an intact cell membrane, did not differ from those performed in whole-cell mode, in which the membrane was broken (Fig. S1e; see Box 13–2). This result suggested that changes in composition of the cytoplasm during whole-cell recordings did not affect PN response properties. Page 2 of 9 p. 1475, ¶4, Therefore, PNs act as high-pass filters that preferentially signal the rising phase of the ORN response: The PNs appear to amplify the peak ORN response more than the lower amplitude responses. For instance, in Fig. 2b, the peak ORN response in magenta is amplified several-fold in the PN; however, the PN response falls rapidly such that the firing rates of the ORN and PN during the slow decay of the response are nearly identical (that is, not amplified at all by the PN). Since they amplify higher frequency ORN activity more than lower frequency ORN activity, PNs act as high-pass filters. p. 1475, ¶6, For each glomerulus we found a statistically significant correlation between the ORN and PN response profile: For a given PN and ORN pair, Bhandawat et al. determined the average PN and ORN responses to a set of odors. If the PN response were determined by a linear scaling of the ORN response, then in a plot in which the ORN response to a given odorant is on the x axis and the PN response to that odor is on the y axis, all points (each representing different odors) would fall on a line; the correlation coefficient (r2) for a line fit to those points would be 1, indicating a perfect linear relationship between ORN and PN responses. The fact that r2 values are considerably less than 1 suggests that the PN response is not just a linear scaling of the ORN response. The plots of mean ORN response vs. mean PN response for the odor set are presented in Fig. 6a. p. 1476, ¶1, for each glomerulus, PNs are less selective than their presynaptic ORNs: This observation is apparent from Fig. 3a. In this figure, the peak firing rates of PNs and ORNs associated with the studied glomeruli (DL1, DM1, DM2, etc.) are reported for a series of odors. The spike rates are baseline-subtracted: they indicate how much the firing rate is above baseline, rather than absolute firing rate. For all glomeruli, there are a number of odors that do not evoke responses from ORNs but that do increase the firing rates of PNs above baseline. This suggests that PN responses are less selective for different odors than ORN responses. p. 1476, Fig. 3, The selectivity of each response profile is quantified as lifetime sparseness: The lifetime sparseness sL of each neuron is defined as where N is the number of odors and rj is the firing rate of the neuron to odor j. To better understand this metric, consider the extreme cases of a neuron that responds to only a single stimulus (the sparsest case) and a neuron that responds to every stimulus (the least sparse case). In the former case, if the neuron responds to a single stimulus with rate R and all other stimuli with rate 0, then and , such that . In the case of a neuron that fires at the same rate R to every stimulus, and ; therefore, . Thus, the ‘sparser’ a neuron’s responses (that is, the more selective it is for odors), the closer its lifetime sparseness is to 1, while the ‘denser’ a neuron’s responses (that is, the less selective it is for odors), the closer its lifetime sparseness is to 0. p. 1476, ¶2, Another factor that diminishes this linear correlation is that the rank order of odor preferences differs for ORNs and PNs: If a hypothetical cell is most activated by odor B, slightly less activated by odor A, and least activated by odor C, then the rank order of odor preference is 2, 1, and 3 for odors A, B, and C, respectively. If PN responses were just a linear scaling of ORN responses, then the rank orders of odor preference would be the same for a PN type and its presynaptic ORN type. In fact, if the PN response were any monotonic function of the ORN response, then the rank orders of odor preference would be the same for the PN as for the ORN. A change in the rank orders of odor preference Page 3 of 9 between a PN and its corresponding ORN would thus reduce the linear correlation between ORN and PN responses. As Bhandawat et al. note, errors in the estimation of average responses could produce large errors in the rank order of odor preferences: an error in the estimate of a neuron’s response to one odor could shift its position in the rank ordering, which would produce a corresponding shift in the positions of all the other odors. Since the sample number for each ORN, PN, and odor combination was limited, the mean response could not always be precisely estimated, resulting in errors in the rank ordering. These errors could be especially problematic for ORNs, which have a large number of near-zero responses and for which small errors in average spike rate estimates could produce large changes in rank order. To quantify the extent to which rank order differs between an ORN class and its corresponding PN class, Bhandawat et al. correlated the rank order for an individual ORN with the rank order for an individual PN. This correlation can be compared with the correlations between rank orders for two ORNs of the same class and between rank orders for two PNs of the same class; since the errors in estimating rank orders should produce similar errors in ORN–ORN and PN–PN correlations as in ORN–PN correlations, a reduction in the ORN–PN correlation relative to ORN–ORN and PN–PN correlations must not be due purely to estimation error: rather, it must be due to a true difference in the rank order preferences of the PNs and the corresponding ORNs. Since Bhandawat et al. do not have sufficient numbers of individual ORN and PN responses to robustly estimate these correlations, they produce simulated ORN and PN responses based on the mean responses for a given class. Since the mean and variability of an ORN response to a particular odor is known (and assuming that ORN responses are normally distributed), the theoretical distribution of a population of ORN responses can be determined. A large number of simulated ORN responses were then generated, such that the probability that an individual simulated ORN had a particular response to a given odor was determined from the empirically based ORN response distributions. The same process was used to generate simulated PN responses. This process of generating simulated ORN and PN responses is illustrated in Fig. 5a. The rank order of odor preference can then be determined for all simulated ORNs and PNs, and the rank order correlations can be determined for all possible ORN–ORN, PN–PN, and ORN–PN pairs within a given pair of ORN and PN classes. Fig. 5b shows the distributions of these correlations. The distribution of ORN–PN correlations is shifted to the left of the PN–PN and ORN–ORN correlations. This suggests that the rank order of odor responses for PNs and ORNs are more different than can be explained by experimental error alone. p. 1476, ¶2, The simplest explanation for this result is that the odor preferences of a PN are influenced by lateral connections between glomeruli: In addition to ORNs and PNs, the antennal lobe has local interneurons (LNs). The most common type of LNs receive input from diverse classes of ORNs and form primarily GABAergic synapses onto ORN → PN presynaptic terminals, inhibiting transmission at these synapses. Through LNs, the activities of PNs can be influenced by ORNs from classes other than its primary input class. This cross-talk between ORN–PN channels may explain the non-monotonic relationship between PN and ORN responses. p. 1477, ¶0, These functions have a similar shape for most glomeruli: they initially slope steeply, meaning that the gain of the transformation function is high for weak inputs: The ‘gain’ of the ORN–PN transformation function is equal to the slope of the function: it is the factor by which the signal from the ORN is amplified in the PN response. p. 1477, ¶1, ORNs do not use all parts of their dynamic range with equal frequency in response to our stimuli: A neuron’s ‘dynamic range’ is the range of frequencies over which it fires action potentials. In the present study, both ORNs and PNs had baseline-subtracted firing rates of ~0–200 spikes/ms. The ORN responses clustered toward the bottom end of this range (Fig. 6b, left), whereas PN responses were distributed more evenly over this range (Fig. 6b, right). p. 1477, ¶2, In this sense, PNs encode our odor stimuli more efficiently than ORNs do: The response of a neuron to each odor is distributed with some variance around a mean value. If the distributions of a neuron’s responses to two odors overlap, then the firing rate of the neuron is not completely informative about the identity of the odor: given the neuron’s firing rate, the identity of the odor cannot always be Page 4 of 9 unambiguously determined, since that firing rate could be consistent with either of the two odors. The greater the overlap between the neuron’s response distributions for two odors, the less informative the neuron is about odor identity. The overlaps between these distributions are determined both by the means of the neuron’s responses and by response variability: distributions for less variable responses will be narrower and thus exhibit less overlap, and means that are further apart from each other will exhibit less overlap. Other factors (such as response variability) aside, a neuron that has its mean responses for different odors spanning its entire dynamic range (like PNs) will thus provide more information about odor identity than a neuron that has responses clustered in one part of its dynamic range (like ORNs). p. 1478, ¶1, Third-order neurons receive convergent input from multiple PN types: PNs project to the lateral horn and the mushroom body. While PN projections to the lateral horn appear to be organized based on their responses to different types of odors, PN projections to the mushroom body appear to be random (see Section 6.16). Since third-order neurons (particularly those in the mushroom body) receive information from multiple PN types, odor coding from the perspective of the third-order neurons must be considered at the level of the PN population rather than at the level of individual PNs. p. 1478, ¶1, In the simplest case, histogram equalization in one dimension should also produce a more uniform distribution of odors in multiple dimensions: If Bhandawat et al. had determined the responses of only two PN classes to a collection of odors, then each odor could be represented in a twodimensional space: the position of the odor within this space would be determined by the response of one PN in one dimension and of the other PN in the other dimension. An odor’s position in two-dimensional ORN space could also be determined from the responses of the corresponding ORNs to the odor. If the odors were more distributed in one dimension of PN space than in the corresponding dimension of ORN space (as suggested by Fig. 6), then it is likely that the odors would be more distributed in twodimensional PN space than in the corresponding two-dimensional ORN space. However, this may not be true if the odors are less distributed in the second PN dimension than in the second ORN dimension: in this case, the more even distribution in one PN dimension is canceled out by the more clustered distribution in the second PN dimension. It may therefore be the case that, even though odors tend to be more evenly distributed across the dynamic range of individual PN classes compared with individual ORN classes, odors are not more evenly distributed in multi-dimensional PN space. Although the above discussion used two PN and two ORN dimensions as an example, Bhandawat et al. actually have seven PN and seven ORN dimensions, which they reduce to two dimensions by principal components analysis. p. 1478, ¶1, The first two principal components define the two-dimensional projection that maximizes the variance of the data: The goal of principal components analysis (PCA) is to reduce the number of dimensions in a dataset while losing the least possible amount of information. In the present example, the seven-dimensional glomerular space was reduced to just two dimensions. In order to minimize the loss of information in the transformation from seven-dimensional to two-dimensional space, the two target dimensions are selected such that they capture the greatest amount of variability in the data. To illustrate this, consider the scenario where five of the PN classes recorded maintained constant firing rates regardless of the odor. These PNs carry no information about odor identity, and the variances in their odor responses are zero. In this case, the position of an odor in seven-dimensional PN space can be reduced to a position in two-dimensional PN space by eliminating the five dimensions corresponding to the non-informative PNs. As illustrated by this example, dimensions that capture the greatest variability in the data points maximize the amount of information retained following dimensionality reduction. In the case of PCA, the dimensions in target space correspond not to two selected dimensions from the original space but rather two new dimensions produced by combining information from the original sevendimensional space. Consider an ellipsoid drawn around the data points for each odor in sevendimensional PN space. The longest axis of this ellipsoid would correspond to the first dimension in principal components space, with the value of each data point in this first dimension being determined by its projection onto this long ellipsoid axis. This dimension (or principal component) captures the greatest variability of any linear dimension in the dataset. The second principal component would correspond to Page 5 of 9 the second-longest axis of the ellipsoid. Note that Bhandawat et al. use PCA purely to visualize their data: their subsequent analyses of the dispersion of odors in coding space (Fig. 7c, d) were performed in the original seven-dimensional glomerular space rather than in the two-dimensional principal components space. p. 1478, ¶2, We quantified this by measuring Euclidean distances between odors in sevendimensional space: The Euclidean distance between two points (px, py) and (qx, qy) in (x, y) space can be determined from the Pythagorean theorem to be . For an n-dimensional space with dimensions 1…n, the Euclidean distance between p and q would be . Larger pairwise Euclidean distances would be associated with a more even distribution of points in coding space. p. 1478, ¶3, Is the separation of odors in multidimensional space larger or smaller than we would predict, based solely on the independent odor separation in each one-dimensional coding channel?: As described above (see note for p. 1478, ¶1), the distribution of odors in coding space is determined by the distributions of odors within each dimension. An expansion of the distribution as a result of the ORN → PN transformation in one dimension could be canceled out by a contraction of the distribution in a different dimension such that the overall distances between points remain unchanged. In terms of the Euclidean distance between two points p and q in n-dimensional space, a greater separation of p and q in dimension one would increase the term (q1 – p1)2 but a compensatory decrease in the separation of p and q in dimension two would decrease the term (q2 – p2)2 by the same extent such that the distance between p and q would remain unchanged. Bhandawat et al. determined whether the separation of odors by each glomerular processing channel is independent—that is, if the distribution of odors in seven-dimensional coding space is simply due to the independent separations of the odors in each individual dimension. If each glomerular channel is independent, then the separation of two odors p and q in that channel is independent of the separation in all other channels. As an example of non-independent separation in different processing channels, if p and q become widely separated by one ORN → PN channel and this channel influences other ORN → PN channels via lateral connections, then p and q might become more widely separated in other ORN → PN channels as a result. In order to test whether odor separation is independent across coding channels, Bhandawat et al. generated a simulated data set in which the distance between each odor pair p and q in each dimension is randomly chosen from the distribution of pairwise separations in that dimension; this is the same as randomly swapping the positions of odors in each dimension. In the resulting simulated datasets, the distribution of pairwise odor distances within each dimension remains the same as in the real dataset. Since the distributions of pairwise odor distances in seven-dimensional space were similar for the simulated and real datasets (Fig. 7c, d), the separation between odors in each dimension must be independent of their separation in the other dimensions. p. 1478, ¶4, the term ‘efficient coding’ has also been applied to the idea that the responses of different neurons should be maximally independent from each other: Bhandawat et al. typically use the term ‘efficient’ to refer to dispersal of stimulus representations throughout coding space to make maximal use of the coding capacity of a neuronal population. However, the term ‘efficient’ could also mean that no two neurons represent the same information. Redundancy in the information encoded by neurons implies that the number of neurons in a population could be reduced without reducing the amount of information encoded by the population; in such a system, neurons are used inefficiently. From this perspective, ‘efficient coding’ would occur when neuronal responses are maximally independent of each other so that no two neurons carry redundant information. p. 1478, ¶4, We measured the independence of different glomerular coding channels by computing the percentage of the variance in the ensemble odor responses that is captured by each of the seven principal components of the seven-dimensional ORN or PN coding space: As presented in Fig. 7, Bhandawat et al. used PCA to reduce the seven-dimensional glomerular coding space to just two principal component dimensions (see note for p. 1478, ¶1). For this analysis, Bhandawat et al. used PCA not for Page 6 of 9 dimensionality reduction but rather to determine the dimensions in coding space that account for the greatest variability in neuronal responses. To understand this, consider a simplified case of a twodimensional coding space (that is, coding by two PNs or two ORNs). If the responses of the two neurons to two different odors were perfectly linearly correlated, then the response of one neuron could be determined from the response of the other neuron, and the information encoded by the two neurons would be perfectly redundant. If the responses to a set of odors were plotted with the response of one neuron on the x axis and the response of the other neuron on the y axis, then all odor points would fall on a straight line. If PCA were performed on this two-dimensional data set, the first principal component for each point would correspond to the position of each data point along this line and would capture 100% of the variance in the data. In contrast, if there were no correlation between the two neurons, then the response of one neuron could not at all be predicted from the response of the other neuron: the information represented by the two neurons would be completely independent and non-redundant. In this case, there would exist no principal component that would capture more than 50% of the variance in the data. Bhandawat et al. describe similar cases for a seven-dimensional dataset. p. 1478, ¶4, we would need a very large odor set to discern this perfect decorrelation: To understand this point, consider the case of two neurons that have perfectly decorrelated responses to stimuli and for which responses to stimuli are uniformly distributed across each neuron’s dynamic range. In this case, the probability of an odor falling at any point in this two-dimensional space is the same for all points. However, a set of randomly chosen odors may by chance fall near a line through this space, such that it would appear as though the responses of the two neurons to the odors were linearly correlated. In this example, this is not a true correlation but rather a chance correlation due to the fact that correlation was inferred from a limited sampling of odors that just by chance happened to fall in a non-random way in coding space. A similar argument applies to seven-dimensional coding space and also to the case where the responses of each neuron are distributed in a Gaussian rather than a uniform fashion. p. 1478, ¶5, We demonstrated this by independently and randomly shuffling the odor labels on each of the seven ORN response profiles and re-computing the principal components of this simulated data set: As Bhandawat et al. note, perfect decorrelation would produce seven principal components that each account for 100/7 = ~14% of the variance in their data. However, as noted above, there may be some correlation in their data just as a matter of chance. To determine what the results of this analysis would have looked like had the responses in their dataset been completely decorrelated, they generated a simulated dataset in which odor labels were swapped independently for each neuron class. This process of shuffling odor labels produced new, simulated odor points while retaining the response distributions for each individual neuron class. By repeating the PCA on these simulated datasets, Bhandawat et al. were able to determine the variance accounted for by each resulting principal component assuming neuron responses were not correlated. p. 1479, ¶3, We performed linear discriminant analysis to identify the linear combinations of input variables that best separated all 18 odor response clusters from each other: Each odor can be represented as a point in seven-dimensional space, with its position determined by the firing rate of the ORNs (in ORN coding space) or the PNs (in PN coding space) corresponding to the seven dimensions. Linear discriminant analysis finds lines in seven-dimensional coding space that optimally separate the different odors of a ‘training’ dataset; these lines separate the space into different regions occupied by different odors. The linear discriminators can then be used to predict the identity of an unknown odor (that is, a data point not in the original training data set) given the neurons’ firing rates (that is, given the point in coding space) by determining which of these regions of coding space contain the unknown odor. Bhandawat et al. performed this analysis using firing rate data from different time bins of their recorded ORN and PN spike trains and then calculated the success of the algorithm at classifying unknown odors; the outcome of this analysis is shown in Fig. 9a. p. 1480, ¶1, This may imply an increasingly deterministic control of spike timing at high firing rates owing to intrinsic refractoriness: The refractory period is a time window following an action potential Page 7 of 9 during which the probability of initiating another action potential is decreased (see Section 2.12). ‘Refractoriness’ refers to the extent and strength of a neuron’s refractory period. In a hypothetical neuron that has no refractory period, spike times are determined purely by integration of inputs; in a real neuron that has a refractory period, spike times are determined both by the integration of inputs and also by whether or not the neuron is in a refractory period. Spike timing is likely to be strongly controlled by refractoriness particularly at high spike rates. It has been suggested that the refractory period reduces the variability of spike timing by enforcing limits on when spikes can be initiated. High spike rates may thus produce less variability in spike trains as spike timing becomes increasingly dominated by the refractory period. p. 1480, ¶2, pooling N ORN inputs should decrease the variability of the pooled average by : The variance of the sum of two independent variables is equal to the sum of the variances of each variable: . The variance of the sum of N independent variables that all have the same variance σ2 would be . The standard deviation σN of the sum of N independent variables would be . If PN responses were determined by the average of the responses of N ORN inputs, then the standard deviation of the PN response would be less than the standard deviation of the ORN responses by a factor of . Subsequent work suggested that ORN → PN connections are completely convergent: within a glomerulus, every PN receives input from every ORN. p. 1480, ¶3, This rapid accommodation might be due to any of several mechanisms, including shortterm synaptic depression at the ORN-to-PN synapse: Short-term synaptic depression is a decrease in the postsynaptic potential produced at a synapse during a series of closely spaced presynaptic action potentials (see Section 3.10). If the ORN-to-PN synapse were depressing during the course of ORN activation, then the PN response would decline over the course of ORN activation, consistent with the early decay of the PN responses (for example as shown in Fig. 2b, c). p. 1480, ¶6, If all portions of the dynamic range of a neuron are used with equal frequency, the carrying capacity of that information channel is maximized because the entropy of the neuron’s response is maximized: Entropy is a measure of information provided by an event; it was initially defined by Claude Shannon, the father of a branch of applied mathematics called ‘information theory,’ which provides a foundation for quantifying and analyzing information. The entropy of an event is related to the uncertainty of the outcome of the event. If an event always has the same outcome, it is said to have no information. In contrast, knowing the outcome of a highly uncertain event is said to contain a large amount of information. For instance, the outcome of the toss of a fair coin contains more information than the outcome of the toss of a fully loaded coin that always comes up heads. In the case of a fair coin, there is a high degree of uncertainty about the outcome of the toss—it is equally likely to come up heads and tails—and the outcome of the toss contains information. In the case of the fully loaded coin, there is no uncertainty—the coin will always come up heads—and the outcome of the toss contains no information. Likewise, the greater the uncertainty of the firing rate of a neuron, the more information the firing rate of the neuron contains. The firing rate of a neuron that is equally likely to fire at all rates within its dynamic range has the maximum amount of information that neuron could possibly contain (that is, has the greatest possible entropy). The firing rate of a neuron that is biased to fire at a rate within a limited portion of its dynamic range has comparatively less information (that is, has smaller entropy). p. 1481, ¶0, in early olfactory processing, the dimensionality of the second-order representation is the same as the dimensionality of the first-order representation: For early olfactory processing, the number of dimensions in coding space is equal to the number of ORN types or the number of PN types, which are roughly equal. p. 1481, ¶4, This result may be due to the common evolutionary origin of different Drosophila odorant receptors in gene duplication events: The 50–60 OR genes in Drosophila arose through duplication and subsequent mutation of an ancestral OR. Due to their common origin, these genes may share some structural features. Common structural features can potentially endow two different ORs with Page 8 of 9 similar odor selectivities. In other words, correlated odor selectivities may be due to correlated OR structure. Questions Question 1: Bhandawat et al. found that PNs are most strongly activated during the rising phase of the ORN response. It’s been suggested that two mechanisms contribute to this effect: (1) short-term plasticity at the ORN → PN synapse, and (2) lateral inhibition from inhibitory LNs. Explain how each of these mechanisms could result in PN responses that are strongest during the rising phase of the ORN response. Question 2: It has been argued that PNs are more broadly tuned to odors than ORNs. Do you agree with this statement? Explain your answer by reference to the Bhandawat and colleagues’ results. What neuronal circuit or synaptic mechanisms could account for this phenomenon, assuming that it’s true? Question 3: In their discussion, Bhandawat et al. write: “In a truly efficient coding scheme, neurons should efficiently encode natural stimulus distributions, not arbitrary stimulus distributions. Although our odor set is chemically diverse and relatively large, it may not be representative of the odors a wild fly would encounter.” Why would the efficiency of a coding scheme depend on the natural stimulus distribution? How do Bhandawat and colleagues’ conclusions depend on their stimulus set being representative of natural stimuli? In what ways might natural odor stimuli differ from the stimuli used by Bhandawat et al.? Question 4: The antennal lobe contains local interneurons (LN) that mediate both inhibitory and excitatory lateral connections between glomerular processing channels. Bhandawat et al. hypothesize that these lateral connections may play important roles in the transformation between ORN and PN responses. If Bhandawat and colleagues’ experiments were repeated in flies in which lateral inputs were blocked, how might their results differ from what they report in flies with intact lateral connections? Question 5: What is demonstrated by the linear discriminant analysis reported by Bhandawat et al. in Fig. 9? How well do you think Bhandawat and colleagues’ linear discriminators model neurons actually downstream of PNs (neurons in the mushroom body and lateral horn; see Section 6.16)? Question 6: What is meant by “coding efficiency”? In what ways can the encoding of information by neurons said to be efficient or inefficient? How efficient are PNs and ORNs in encoding odor identity? Why might flies have evolved an olfactory system that is not maximally efficient? Suggestions for Further Reading Wilson RI (2013) Early olfactory processing in Drosophila: mechanisms and principles. Annu Rev Neurosci 36:217–241. This review nicely summarizes the work of Bhandawat et al. along with other studies of information processing in the fly antennal lobe. Page 9 of 9