Download PRINCIPLES OF NEUROBIOLOGY CHAPTER 6

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
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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.
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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
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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
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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
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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
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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
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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
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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.
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