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First published online August 31, 2007
Journal of Experimental Biology 210, 3199-3208 (2007)
Published by The Company of Biologists 2007
doi: 10.1242/jeb.006726
Fast-scale adaptive changes of directional tuning in fly tangential cells are explained by a static nonlinearity
Applied Vision Research Centre, City University, Northampton Square, London EC1V 0HB, UK
e-mail: pn{at}white.stanford.edu
Accepted 8 July 2007
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Summary |
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We modelled the data using elementary operators (linear filters and threshold nonlinearities). A satisfactory account of the results is obtained when an early static nonlinearity acts on the outputs of multiple front-end filters that are subsequently pooled in a spatially restricted manner by the tangential cell. In line with recent studies, these findings emphasize the importance of testing simple nonlinear models before attempting more elaborate interpretations of fast-scale adaptive phenomena in single neurons. We discuss a potential neural implementation of the model based on medullar projections to the lobula plate.
Key words: temporal dynamics, motion-sensitive neurons, static nonlinearity
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Introduction |
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TOPSummaryIntroductionMaterials and methodsResultsDiscussionReferences |
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), which
integrate directional signals according to flow patterns occurring during
flight (Krapp and Hengstenberg,
1996). This class of neurons, named tangential cells after their
anatomy, represents an ideal system for developing and testing models of
motion detection and adaptation (Egelhaaf
et al., 2002). This article focuses on two important spiking
tangential cells, H1 and V1.
H1 is known to modify its response characteristics depending on previous
stimulation history, both over short and long time scales
(Fairhall et al., 2001). The
focus of this paper is on relatively short time scales and brief adaptors [for
a characterization of adaptive responses to longer lasting adaptors, see Neri
and Laughlin (Neri and Laughlin,
2005)]. When the time scale is short, adaptive effects are
sometimes referred to as `temporal dynamics' in the literature
(Perge et al., 2005a). We use
these two descriptions interchangeably in this paper, because the effects we
report here can be accounted for without truly adaptive changes in system
parameters.
We were interested in how the neuronal response to a local directional
signal is affected by signals that are presented immediately before, and
whether the effect of the preceding signals depend on their spatial location
within the receptive field. Our stimulus consisted of a stream of two
simultaneous patches that appeared at different locations and changed
direction independently. By analyzing the neuronal response conditional upon
the occurrence of selected combinations of directions at specific locations
and time points, we could derive detailed descriptors of how the temporal and
spatial interaction of two directional signals affect firing rate at scales of
200 ms and 20° of visual angle.
We measured highly reproducible, spatially local temporal dynamics that
appear to satisfy expectations from mechanisms with adaptive utility [e.g.
redundancy reduction (Barlow,
2001)]. We wished to establish whether active changes in the
parameters specifying the system were required to account for the observed
results. Our simple computational schemes demonstrate that these effects are
largely explained by models that do not involve any adaptive change, but
rather very early nonlinear operations acting before signals are further
integrated by the tangential cell. We propose a physiological interpretation
of these models based on the connectivity between medulla and lobula plate
(Douglass and Strausfeld,
1995). Because the effects we observe are closely related to those
reported for macaque middle temporal (MT) area
(Perge et al., 2005a;
Perge et al., 2005b) and cat
posteromedial lateral suprasylvian (PMLS) region
(Vajda et al., 2006), we
speculate that a substantially similar modeling scheme may apply to both
vertebrate and invertebrate motion pathways. This speculation is supported by
recent computational work on primates
(Rust et al., 2006).
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Materials and methods |
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TOPSummaryIntroductionMaterials and methodsResultsDiscussionReferences |
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) (see V1 neuron
example in Fig. 2A). The
monitor (ViewSonic PT795, Walnut, CA, USA) was driven by a VSG graphics card
(Cambridge Research Systems, Kent, England) at 180 Hz, covered roughly
78°x74° (width x height) and was typically centred at
40°/5° azimuth/elevation. Results on simultaneously presented patches
from these experiments were presented previously
(Neri, 2006). The same dataset
has been analyzed for the present study, but the analysis herein does not
overlap with the preceding analysis and presents results that cannot be
derived from the earlier work (Neri,
2006). With the exception of the preliminary tests with wide-field
gratings to identify the neurons (see above), which we repeated only a small
number of times (e.g. the directional tuning curve in
Fig. 2A shows the mean ±
s.e.m. of 4 repetitions), all other measurements come from a large number of
repetitions. More specifically, s.e.m. values for
Fig. 2C were computed from an
average of 273 repeats per data point. Data points and
s.e.m./Z-scores for Fig.
2D–K were computed from 68 repeats on average per data
point, those in Fig. 3 from 125
on average per data point. Fig.
4B shows mean ± s.e.m. from an average of 302 repeats per
data point, and each point on the surfaces in
Fig. 6A was computed from 2150
repeats.
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;
Neri, 2006) applied to a
stream of multiple patches moving in random directions at a constant speed of
23° s–1 (Fig.
1A, leftmost frame). Each patch subtended roughly
19°x18° (100% contrast on a 38 cd m–2 mean
luminance background, carrier spatial frequency 0.1 cycles
deg.–1, s.d. of Gaussian envelope 4°) and moved for 220
ms in one of eight possible directions at cardinal and diagonal axes. After
inspection of the vector map for the entire receptive field, we chose two
highly responsive locations (see Fig.
4 for a quantitative assessment of responsiveness) and stimulated
them in pairs (Fig. 1A). When
possible, we tested more than 1 pair for the same neuron.
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Data analysis
Analysis and modeling (below) are presented here using compact notation. A
smoother, more intuitive and descriptive account is provided in the first
section of Results. The direction of the patch at location x as a
function of time t is Dx(t), where 0 is
downward (
). The time-locked neuronal firing is F(t)
(firing was computed by binning every 1 patch duration). The vector
(
)={t1,t2,...tn}
is the subset of time points for which the expression is satisfied.
For example, (D1=0) is the subset of time points at
which patch 1 was moving . The relevant descriptors in this study are
captured by the expression
Sx,y(d1,d2)=
F{[Dx(t)=d1
Dy(t–
t)=d2]}
t,
where t=1 patch duration. For example, the surface plot in
Fig. 1E (patches at same
location) was obtained for x=y=1, the one in
Fig. 1F (patches at different
locations) for x=1 and y=2, and that in
Fig. 1D for x=1,
y=2 and t=0. Fig.
2H,I were obtained from Fig.
2E,F by subtracting
Sx,y(d1,d2)d1
from Sx,y(d1,d2)
for every d2 to obtain
.
Fig. 2J,K were obtained from
Fig. 2H,I by further
subtracting
from
for every d1 to obtain
[for a related analysis procedure, see Felsen et al.
(Felsen et al., 2002)]. In
Figs 3 and
6, `same' surface plots were
obtained by averaging
and
,
while `different' plots were obtained by averaging
and
.
Modelling
For the model in Fig. 1C the
response at time t from the filter at location x is
rx(t)=cos[Dx(t)]+cos[Dx(t–t)]+2,
i.e. tuning is sinusoidal (peaking at ) and temporal integration is over
two patch presentations. The final output is
f(r1+r2)–1/10 (the
subtractive term allows the output to be negative, thus simulating inhibition
via firing rates below baseline), where f is the
Naka–Rushton equation
f(r)=rß/(rß+
ß)
with =rt and ß=2. The output of
the basic linear model (Fig.
6B) is simply (r1+r2). For
the model in Fig. 1D the final
output is
f(r1)+f(r2). For the
model in Fig. 1E, the response
from location x is
where the four front-end filters
are shifted versions of rx with preferred directions
, =2, and the weighting function
w=cos( )+
. The final output is
R1+R2.
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t. The preceding
signal could be delivered at the same location 1 (broken white circle) or at a
different spatial location 2 (broken red circle), and we analyzed these two
conditions separately. Fig. 2
shows how we obtained the two corresponding descriptors for an example V1
neuron. As typical for V1, this cell responded most vigorously to a full-field
grating moving downwards (Fig.
2A). Correspondingly, its vector map within the frontolateral
visual field shows multiple locations with downward directional tuning
(Fig. 2B; the map was obtained
using a vector white noise reverse correlation technique, see Materials and
methods). We selected the two locations within the receptive field indicated
by coloured circles. Directional tuning at these locations, as tested using
single patches restricted to the individual locations, was consistent with
that indicated by the map (Fig.
2C).
We then stimulated the two locations simultaneously using two Gabor patches
moving in random directions (Fig.
1A). At any given time t, the response to two
simultaneous patches is very close to that expected from quasi-linear
summation across all possible combinations of different directions
[Fig. 2D; for a detailed
analysis of responses to two simultaneous patches, see Neri
(Neri, 2006)]. As shown in
Fig. 1B, we performed the
analysis for two patches that followed one another within the streaming
sequence. The surface plot in Fig.
2E reports the intensity of the response to a patch presented at
location 1 (whose direction is on the x axis) when preceded by a
patch at the same location (whose direction is on the y axis).
Fig. 2F reports the results of
a similar analysis, but performed in relation to the preceding patch that
appeared at the other location 2. The two surfaces clearly differ. In
Fig. 2F (patches at different
locations) the direction of the preceding patch is virtually irrelevant (the
surface shows little variation along the y axis), the response being
modulated predominantly by the patch that is currently moving when the
response is recorded at time t (the surface varies along the
x axis as expected from the directional tuning at location 1). In
Fig. 2E (patches at same
location) the response is reduced when the preceding patch was moving in the
same direction as the current patch (darker pixels along the diagonal), on top
of a large modulation in response to the current patch that is similar to
Fig. 2F.
To bring out these effects more clearly, we factored out the expected
response to both the current patch (time t) and the preceding patch
(time t–t) in the assumption that they are
integrated linearly by the neuron. This can be achieved by simply subtracting
the directional response to each patch after averaging along the direction of
the other patch (see Materials and methods). A similar procedure was used by
Felsen et al. for experiments with same-location oriented patches in cat area
17 (Felsen et al., 2002). In
simple terms, this procedure consists of taking the average across different
columns (thus obtaining a directional response for the patch at time
t–t regardless of the direction of the patch at
time t) and subtracting this average from each column in the surface
matrix. The outcome of the subtraction is shown in
Fig. 2H,I. This leaves us with
the response to the patch at time t conditional upon the direction of
the patch at time t–t, but without
contamination from the delayed response that is simply expected from the
stimulation provided by the patch at time t–t
on its own. Fig. 2G shows
slices across Fig. 2H (along
the rows indicated by the coloured rectangles), showing the effect whereby the
response is reduced by a preceding patch moving in the same direction as the
patch at time t.
The second subtraction is for the expected response to the patch at time
t regardless of the direction of the patch at time
t–t, which is obtained by averaging and
subtracting across rows rather than columns. The outcome of this subtraction
is shown in Fig. 2J,K. For
purely linear summation of the responses to the two individual patches, we
expect this surface to be completely flat. This prediction is confirmed when
the two patches occupy different locations
(Fig. 2K), but not when they
are at the same location (Fig.
2J). In the latter case we observed a clear pattern with negative
modulations along the central diagonal (blue) and nearby positive modulations
(red). In the rest of the paper we only focus on the two descriptors at
Fig. 2J,K, because they
encapsulate sequential effects for patches at same (J) and different (K)
locations.
Consistency of results across neuronal types and sample
Fig. 3 shows `same' and
`different' plots (analogous to Fig.
2J,K) for six more neurons, including H1, V2 and H3 as well as V1.
Although noisy, these surface plots show that the main observation in
Fig. 2, i.e. that strong
modulations are only observed for same-location patches and not for
different-locations patches, holds true for all the other neurons we recorded
from. Moreover, the diagonal structure of negative and positive modulations is
present in all `same' location plots. In the following we demonstrate the
validity of these two claims for the entire population, one at a time.
Preliminary to that, however, it is necessary to establish that the two
regions we selected for testing were responsive enough to ensure that the
observed lack of any effects for the `different' descriptor did not simply
result as a consequence of one region being unresponsive.
Fig. 4A plots the distribution
for the difference in preferred direction between the two patches. For 96% of
our tests the difference did not exceed 45°, and the majority of the tests
involved locations with matched directional preference (peak at 0). In
Fig. 4B each point plots the
response ranges of the two locations that were paired in a given test, one
against the other on the two axes (the largest response range within a pair
was assigned to the x axis). Response range was defined as the
difference between largest and smallest responses on the directional tuning
curve. For a location that is not directionally selective or that is
unresponsive, response range (although positive by definition) should not be
significantly different from 0. It is clear from
Fig. 4B that no such
unresponsive locations were included in our dataset, as all response ranges
are significantly greater than 0. Moreover, the responsiveness of the two
locations within a pair was highly correlated (r2=0.94),
meaning that the two locations we selected for testing were not only similar
in directional preference but also in overall responsiveness. On average, the
response range of the less responsive location within a pair was 72% of the
response range of the more responsive location.
To assess whether surfaces like those shown in Fig. 3 present strong modulations, we determined the percentage of pixels that reaches statistical threshold (|Z|>2) for all double-patch tests individually. Fig. 5A plots this quantity for the `same' surfaces (on the y axis) versus `different' surfaces (on the x axis) for all neurons and tests. All points lie above the unity line, demonstrating that `same' surfaces modulated far more significantly than `different' surfaces (paired t-test for `same' versus `different' returns P<10–10; when restricted to the V1 population P<0.002, to the H1 population P<0.001). We wished to determine whether the few modulations that reached significance in the `different' surfaces were consistent across tests and neurons. For this purpose, we computed the pixel-wise correlation between all possible pairs of surfaces for the H1 and V1 populations separately. Fig. 5B plots correlations for `same' surfaces (on the y axis) versus `different' surfaces (on the x axis), for both V1 (solid circles) and H1 (open circles). Correlations were all positive for `same' surfaces (t-test P<10–40 for both V1 and H1), but not different from 0 on average for the `different' surfaces (P=0.08 for V1, P=0.63 for H1). This result demonstrates that the few significant modulations within `different' surfaces were not consistent across tests/neurons, confirming our claim that `different' surfaces were essentially featureless. Below we therefore focus on `same' surfaces.
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We wished to determine whether the diagonal structure suggested by the
`same' surface plot in Fig. 2J
was consistently observed across the entire sample. As a starting point, we
report that the modulation at the pixel indexed by the preferred direction on
both axes ( on x and on y in
Fig. 2J) was invariably
negative (P<10–11) for `same' surfaces, but not
different from 0 for `different' surfaces (P=0.82). We then studied
the 4 immediately surrounding pixels along the diagonals, indicated by circles
in Fig. 6D. If no diagonal
structure is present (as is the case for the left-hand surface plotted in
Fig. 6D), we expect similar
modulations at the positions indicated by black circles when compared with the
modulations at the positions indicated by white circles. If, however, the
structure of the surface is diagonal, with a negative modulation along the
central negative diagonal and positive modulations along the nearby parallel
diagonals (as suggested by the surface plot in
Fig. 2J), we expect negative
modulations at the white positions and positive modulations at the black
positions. Fig. 5C plots the
modulation at the white positions (averaged between the two positions) on the
y axis versus the modulation at the black positions on the
x axis for all tests and neurons. Clearly the pattern conforms to the
diagonal structure discussed earlier.
To further support our claim that we did observe a consistent diagonal structure across our entire dataset, we computed Fourier power spectra for all surfaces individually, and extracted power at different orientations. The presence of a diagonal structure in the surface should be reflected in the presence of larger power at the corresponding orientation in the power spectrum. Fig. 5D plots power for the orientation corresponding to the negative diagonal (on the y axis) versus power for the orientation corresponding to the positive diagonal (on the x axis). For `same' surfaces (solid symbols) the former is larger than the latter (paired t-test P<10–7), as we expect from the diagonal structure that was already uncovered by Fig. 5C. No such difference is observed for `different' surfaces (open symbols, P=0.17). Similar results were obtained when we considered power at vertical and horizontal orientations, which did not differ from the positive diagonal. In summary, both Fig. 5C and Fig. 5D concur to demonstrate that the diagonal structure suggested by Fig. 2J was consistent across our entire sample and set of tests.
Fig. 6A shows `same' and
`different' surfaces averaged across the entire neuronal population after
realigning the preferred direction of each neuron to downward. No modulation
is observed when the two patches are at different locations, but a clear
pattern is observed when they are at the same location, in line with the
population results at Fig.
5A,B. Specifically, in the latter case the modulation resembles a
diagonally tilted Gabor function (notice the additional negative ripples
within the bottom-left and top-right portions of the surface), as already
demonstrated by the population analysis at
Fig. 5C,D. This result is
closely related to that obtained by Perge et al. for MT neurons when tested
with same-location patches [compare fig. 8A in Perge et al.
(Perge et al., 2005a) with the
left-hand surface plot in Fig.
6A here]. In a separate study, Perge et al. also tested different
locations within the centre and surround of MT neurons' receptive fields
(Perge et al., 2005b).
Although they did not explore inter-patch temporal dynamics to the same degree
that was done here, their results were consistent with ours (see
Discussion).
We emphasize that, although the averaging procedure used to obtain the surfaces in Fig. 6A relies on the assumption that the different neurons we tested can be lumped into one descriptor, this assumption is not necessary for our claims on the structure of `same' and `different' surfaces, which motivated our choice of modeling schemes described in the next section. The logic behind our modeling strategy is driven by two observations about the structure of `same' and `different' surfaces: (1) that only `same' surfaces showed consistent modulations and (2) that these modulations conformed to a diagonal structure along the negative diagonal, with a central negative modulation surrounded by positive modulations. We demonstrated the validity of both observations across our neuronal population without assuming that data from different neurons could be averaged together, so this assumption is not necessary for our conclusions. In Fig. 6A we present the grand average for reference purposes only, so that the modeling results can be directly compared to an average descriptor. We also note that our analysis could not discern any difference across neuronal types in relation to the metrics that are relevant for this study.
Modeling with early nonlinearities
As a first step, we attempted to simulate the results in
Fig. 6A using the very minimal
model that we could design as a potential candidate for this process. This
model simply consists of two linear filters applied to the two different
patches (see Materials and methods). Each filter has a directional tuning
curve that resembles V1, and integrates across two patch presentations
(temporal integration window=2 patch durations). The responses from the two
filters are summed to generate the output from the neuron (this is the same as
using just one filter). This model is like that cartooned in
Fig. 1C, but without the late
nonlinearity (red) before the output. As we expected from the way in which we
computed the two surfaces in Fig.
6A, they show no modulation for a simple linear model of this kind
(Fig. 6B).
We then introduced a basic nonlinearity directly borrowed from standard spike-output nonlinear transducers (see Materials and methods). The nonlinearity was initially placed very late in the model, right before the sum from the two filters was converted into the final output (Fig. 1C). This simple nonlinearity generated clear modulations at the level of the two surfaces in Fig. 6C. The most conspicuous discrepancy with respect to the experimental results is that this simulation shows no difference between same-location and different-location conditions. This outcome is expected because the model in Fig. 1C integrates the responses from the two patches before, not after, the nonlinearity. At the level of the nonlinearity there is no distinction between the two locations.
We remedied to this failure of the simulations by simply placing the
nonlinearity at an earlier stage in the model. More specifically, the
responses to the two patches are now separately subjected to the nonlinear
transducer before, rather than after, they are summed
(Fig. 1D). This simple
modification eliminated all modulations from the `different' surface, without
affecting the result obtained earlier for the `same' surface
(Fig. 6D). However, the outcome
of this model still falls short of providing an account for the experimental
results in Fig. 6A. More
specifically, the surface in Fig.
6D is not oriented diagonally. This is an important failure of the
model, as demonstrated by the following example. If the patch at time
t is moving down to the right and it was preceded by a patch at time
t–t that was moving in the same direction
(right-most white circle in Fig.
6D), the model predicts a negative modulation that is identical to
when the preceding patch at time t–t was moving
down to the left (right-most black circle in
Fig. 6D), i.e. orthogonally to
the patch at time t. This is clearly not the case for the real
neurons: as a consequence of the diagonal structure in the experimental data,
the modulations associated with these two conditions are very different in
Fig. 6A (see also
Fig. 5C,D, where we showed that
this result holds across the entire dataset).
We were able to capture this aspect of our data by simply placing the nonlinearity at an even earlier stage in the model, before the two linear filters corresponding to the two patch locations (Fig. 1E). We introduced a bank of four front-end linear filters with different directional tuning, one for each cardinal direction. The output of each front-end filter was nonlinearly transduced individually, after which the four outputs were summed using weights that conformed to the V1-like linear filter used in the previous models (i.e. the front-end filter preferring downward was weighed more than the other three). Although there is still room for improvement, this model does generate a diagonally oriented structure for the same-location condition. It also simulates directional preference for individual patches (Fig. 2C) and patches presented simultaneously (Fig. 2D) (simulations not shown).
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),
macaque (Priebe and Lisberger,
2002; Priebe et al.,
2002; Perge et al.,
2005a) and cat (Vajda et al.,
2006) neurons. Particularly relevant to this study are the results
of Perge et al. (Perge et al.,
2005a). They showed that neurons in macaque MT respond to a
sequence of moving patches presented at the same location within the receptive
field in a manner that is very similar to what we observed here for fly
tangential cells (compare their fig. 8A with the left-hand surface in
Fig. 6A) (see also
Priebe et al., 2002). Vajda et
al. found similar results for neurons located in cat PMLS
(Vajda et al., 2006).
Related results have also been reported for orientation tuning in monkey
(Müller et al., 1999) and
cat (Dragoi et al., 2000;
Dragoi et al., 2001;
Dragoi et al., 2002;
Felsen et al., 2002) primary
visual cortex, where exposure (even brief) to an adapting stimulus causes the
preferred orientation of the cell to shift away from the adapting orientation.
This repulsive effect was also present in our data, as demonstrated in
Fig. 2G (blue and red traces
show that preferred direction shifts away from the preceding direction,
indicated by the colour-coded arrows).
Perge et al. (Perge et al.,
2005a) did not provide quantitative simulations of their results,
which they interpreted as deriving from a mixture of static nonlinearities and
fast-scale adaptation. More specifically, they recognized that the reduced
response to a patch preceded by another patch moving in the same direction
could result as a consequence of a simple compressive nonlinearity acting on a
sluggish temporal integrator (model in Fig.
1C), but speculated that positive modulations away from the
central diagonal (warm-coloured streaks in
Fig. 6A) may reflect specific
network interactions before or within MT [p. 2114 of Perge et al.
(Perge et al., 2005a)]. In a
general sense this intuition was correct, because the model in
Fig. 1E could be described as a
small network that performs simple nonlinear processing before feeding signals
to the tangential cell where spikes were recorded. Our simulations provide a
computable model for implementing this idea quantitatively.
Adaptive properties of simple nonlinear models
Apparently complex phenomena can unexpectedly be accounted for by extremely
simple nonlinear models. A recent example in the fly literature is provided by
the modeling work of Borst et al. (Borst et
al., 2005), who offered a simple explanation for some fast-scale
adaptive effects that had been previously reported
(Fairhall et al., 2001) in H1
(see also Brenner et al.,
2000). Borst et al. showed that the basic Reichardt model displays
quasi-instantaneous velocity gain control, and that it can explain H1
behaviour without any adaptive change in its internal parameters
(Borst et al., 2005). Some
effects happen on a longer timescale
(Fairhall et al., 2001) and
are likely to involve adaptive parameter changes.
The temporal interactions we measured in spiking tangential cells may
appear to fulfill an adaptive role. For example, the reduced response to a
stimulus moving in the same direction and the enhanced response to a change in
stimulus direction, both of which are implied by the surface in
Fig. 6A, can be interpreted
within the framework of redundancy reduction and enhanced signaling of novel
events (Barlow, 2001). However,
similar to Borst et al.'s modeling work, our simulations show that these
adaptation-like effects need not imply that the system is adaptively modifying
its internal structure in response to its stimulation history. The model in
Fig. 1E is static, i.e. its
parameters do not vary depending on previous stimulation. Nevertheless it
provides an adequate description of the data
(Fig. 6E).
It is also interesting to note that the model in
Fig. 1E shares similarities
with a modeling framework that has recently been proposed for plaid
selectivity in MT (Rust et al.,
2006). Plaids involve the spatial superposition of two directional
signals, which differs from the stimuli we and others have used to study
temporal interactions between different patches. However the response
properties of MT neurons to this class of stimuli can be characterized by
surface plots similar to those in Fig.
3, where x and y axes refer to the directions of
the two signals that generate the plaid [see
fig. 1 in Rust et al.
(Rust et al., 2006)]. The
experimental surfaces are consistent with a model involving a bank of
front-end filters, each subjected to a nonlinear operation (gain control
normalization), followed by a weighted pooling stage and finally a spike
converter [see fig. 3a in Rust
et al. (Rust et al., 2006)].
The structure of this model is clearly related to
Fig. 1E, despite the fact that
the two models refer to different stimuli and neuronal types.
Spatial specificity
Because our stimuli consisted of multiple patches at different locations
within the receptive field, we were able to study temporal interactions
between patches that appeared at the same as well as at different locations.
We only observed interactions for patches that appeared at the same location
and one immediately after the other (we performed our analyses for
t>1 patch duration and found no effects). This result may
not apply to macaque MT neurons, which show some rapid adaptation across
different locations within the receptive field
(Priebe and Lisberger, 2002).
A related difference between fly and macaque motion-sensitive cells has been
reported for long-lasting adaptors: in this case MT neurons adapt only locally
(Kohn and Movshon, 2003),
whereas fly neurons display some degree of global adaptation
(Neri and Laughlin, 2005).
These studies are not entirely comparable, however, not only because of
species differences but also because the effect of adaptation was often
measured using different metrics and stimuli; e.g. use of directional gain
(Neri and Laughlin, 2005)
rather than contrast gain (Kohn and
Movshon, 2003).
The directional effects (or lack thereof) that we report here for patches
at different locations within the receptive field have not been studied
extensively in other species. As mentioned previously, these experiments were
performed for patches that appeared at the same location and the results
obtained were very similar to ours (Perge
et al., 2005a; Vajda et al.,
2006). Perge et al. (Perge et
al., 2005b) conducted experiments in which different spatial
regions were stimulated separately, but they focused on the comparison between
the classical receptive field and the so-called `surround'. Surround responses
are very different from those obtained within the classical receptive field,
as there is convincing evidence that the former are controlled by mechanisms
that differ from those that support responses within the receptive field
(Huang et al., 2007). Perge et
al. (Perge et al., 2005b) also
briefly discuss interactions between patches that were both within the centre
of the receptive field. They report nonlinear interactions for differently
located patches that appeared at the same time (t=0), but no
nonlinear interaction when presented successively (t=26 ms).
These authors only tested two directions (preferred and anti-preferred) and
did not report detailed data as to the consistency of this result across their
sample (this question was not central to their article), but this last
observation is certainly in agreement with ours [see last paragraph of their
results section, p. 2056 (Perge et al.,
2005b)]. In conclusion, although more data on MT is required to
confirm Perge et al.'s analysis, their observations indicate that a successful
simulation of their data would require the two separate pooling stages that
are implemented by the model in Fig.
1E, in the same way that this modeling scheme was necessary to
explain our results.
It seems reasonable to expect that, had we made our patches significantly
smaller, we would have observed some interaction across different locations.
The model in Fig. 1E implies
that the receptive field is subdivided into regions that pool signals from the
preceding stages in a spatially localized fashion. If the stimuli are
sufficiently small to place the two patches within the receptive field of the
front-end filters, then clearly the two patches will interact as if they had
been presented at the same location. This prediction also applies to the local
effects demonstrated by Kohn and Movshon
(Kohn and Movshon, 2003), as
well as to the original H1 study (Maddess
and Laughlin, 1985) (see also
de Ruyter van Steveninck et al.,
1986); however, these previous studies have not tested it. We
attempted to reduce patch size on a few occasions, but this required us to
increase the spatial frequency of the carrier in order to preserve enough
detail within the patch to confer it directional properties (as the envelope
of the Gabor is reduced to approach the spatial period of the carrier, the
patch turns into a blob). This resulted in suboptimal spatial frequencies for
the neuron, combined with stimuli that only excited a very small portion of
the receptive field. Even at 100% contrast, we failed to find stimulus
parameters that drove the cell with sufficient reliability to carry out an
extensive investigation of temporal interactions between pairs of very small
patches. We hope to resolve this limitation in future studies.
Potential physiological interpretations
All the building components of our models are basic standard operators in
computational modeling, their physiological plausibility being
straightforward. The question remains, however, as to whether the particular
way in which they are assembled in Fig.
1E is interpretable in the context of the anatomy and physiology
of the fly lobula plate.
For V1, a potential interpretation may be that the front-end filters
represent the VS system, which is known to feed onto V1
(Kurtz et al., 2001;
Haag and Borst, 2004).
Although VS neurons convey information predominantly via graded
potentials rather than spiking, their response is nonlinear in several
respects (Farrow et al., 2005;
Farrow et al., 2006), so the
early nonlinearity in Fig. 1E
may be implemented at the level of the VS system. There are several problems
with this interpretation, however. First, the VS system is preferentially
selective for downward motion, whereas the front-end layer in
Fig. 1E consists of units with
different directional selectivity. Despite the fact that VS receptive fields
are heterogeneous in directional preference, it seems unlikely that the VS
system would be able to support an extensive multi-directional input like that
in Fig. 1E at every point in
the receptive field of a V1 neuron. Second, VS receptive fields are very
large, certainly larger than the patches we used in our stimuli. The spatial
selectivity we demonstrated in Fig.
6A seems hard to reconcile with such extensive spatial pooling.
Third and most importantly, a VS-like interpretation may apply to V1 but not
H1, which receives direct retinotopic input from the medulla
(Hausen, 1984). An
interpretation based on intra-lobula network connectivity seems unlikely for
H1. Because we observed very similar effects for both V1 and H1, our data
argue against this class of interpretations.
An altogether different possibility is that the front-end stage in
Fig. 1E is implemented at the
level of the medulla, where directional selectivity has been documented
(Douglass and Strausfeld, 1995)
and receptive fields only represent small fractions of the visual space
covered by H1 and V1 (Strausfeld and Lee,
1991). These receptive fields are typically smaller than our
patches of 20°x20°
(Strausfeld and Gilbert,
1992). The most likely candidates are bushy T-cells (particularly
T5), small retinotopic neurons with bushy dendrites extending across a few
neighbouring columns within the medulla
(Douglass and Strausfeld,
1995). These neurons leave the inner medulla and supply inputs
onto lobula plate tangentials (Strausfeld
and Lee, 1991). The spatially separate pooling of front-end
signals in Fig. 1E would
correspond to different compartments within the dendritic arborization of the
tangential cell, which is plausible given the massive extent of these
arborizations. This interpretation is consistent with previous modeling work
on the emergence of directional selectivity across the medulla–lobula
plate projection (Melano and Higgins,
2005). Specifically, Melano and Higgins placed the relevant
nonlinearity between T5 and subsequent pooling by the tangential cell [see
their fig. 1b, where the
nonlinearity is labeled `POS' (Melano and
Higgins, 2005)].
In summary, our results on the temporal dynamics and interactions of
directional signals within the receptive fields of spiking tangential cells
support a simple and physiologically plausible scheme where an early
nonlinearity between medulla and lobula plate generates response properties
that may serve a fast-scale adaptive role. These properties, however, arise as
a consequence of static nonlinearities, without requiring truly adaptive
changes in the system. A similar demonstration of adaptive phenomena mediated
by static nonlinearities in the fly has been recently provided for velocity
gain control in H1 (Borst et al.,
2005). Further work is needed to identify the exact components of
this simple model, and to refine its structure in relation to empirical
results that are not captured by its formulation in
Fig. 1E.
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Acknowledgments |
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References |
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(comparable to Z score) for
100 simulations of each model. For N values, see Materials and
methods.
, V1; 
, H1; 
, V2;
, H3. +ve, positive; –ve, negative.