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The Journal of Neuroscience, February 15, 1998, 18(4):1571-1582
Quantitative Analysis of a Directed Behavior in the Medicinal
Leech: Implications for Organizing Motor Output
John E.
Lewis and
William B.
Kristan Jr
Department of Biology, University of California, San Diego, La
Jolla, California 92093-0357
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ABSTRACT |
The local bend is a directed behavior produced by the leech,
Hirudo medicinalis, in response to a light touch.
Contraction of longitudinal muscles near the touched location results
in a bend directed away from the stimulus. We quantify the relationship between the location of touch around the body perimeter and the behavioral output by using video analysis, muscle tension measurements, and electromyography. On average, the direction of the behavioral output differed from the touch location by <8% of the total body perimeter. We discuss our results in the context of two contrasting behavioral strategies: a Continuous strategy, in which
the local bend is directed exactly opposite to stimulus location, and a Categorical strategy, in which there are four distinct
bend directions, each elicited by stimuli given in a single quadrant of
the body perimeter. To distinguish between these strategies, we
delivered two competing stimuli simultaneously. The resulting
behavioral output is best described by an average of the effects of
each stimulus given alone and thus provides support for the Continuous strategy. We also use a simple model, based on anatomical and physiological data, to predict the responses of the known motor neurons
to different stimulus locations. The model shows that the activation of
two of the motor neurons (D and V) is inconsistent with a Categorical
strategy. However, these neurons are known to be active during the
local bend behavior. This result, along with our experimental
observations, suggests that the local bend network uses a Continuous
strategy to encode stimulus location and produce directed behavioral
output.
Key words:
behavioral accuracy; Hirudo medicinalis; local
bend; population coding; sensorimotor transformation; touch
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INTRODUCTION |
Information processing in
sensorimotor networks often involves population codes in which the
distributed activity of broadly tuned neurons represents a specific
sensory or motor parameter. Current understanding of population coding
has resulted mainly from studies of directed behaviors
(Churchland and Sejnowski, 1992 ; Katz, 1996). Directed behaviors
transform a stimulus location in space to a directed movement in space,
with the underlying neuronal networks mapping a population-coded
stimulus representation to a population-coded motor command.
Some directed behaviors, such as orienting toward auditory cues in the
barn owl (Knudsen et al., 1979) and saccadic eye movements in primates
(Lee et al., 1988), involve a continuous mapping of a
sensory stimulus to behavioral output. Other behaviors, such as the
scratch reflex in turtles (Stein, 1989) and the tailflip escape
response in crayfish (Krasne and Wine, 1984), involve a categorical mapping, such that a range of stimuli produces
an identical behavioral response, with sharp borders between ranges of
stimuli that produce different responses. Continuous and
Categorical strategies predict differences in the
organization of motor output. A Continuous strategy could involve
population coding at all processing stages, from encoding the sensory
stimulus to encoding movement direction. Accurate transfer of
population-coded information between processing stages could result
from synaptic interactions that are governed by relatively simple rules
(Salinas and Abbott, 1995). In contrast, a Categorical strategy
requires a choice between distinct responses, so at some
processing stage, dedication to a single type of behavior must be
accomplished, perhaps by using a competitive winner-take-all
mechanism (Yuille and Grzywacz, 1989). Directly testing the predictions
made by different behavioral strategies has been difficult because of
the size and complex organization of the networks involved. In general,
it is not possible to study a single system at multiple stages of a
sensorimotor transformation. It is useful then to investigate smaller
systems and simple behaviors in which it is feasible to study the
entire transformation with single-neuron resolution.
One such behavior is the local bend behavior in the medicinal leech
(Kristan et al., 1995), which is elicited by a touch to the body wall
and results in a bend of the body directed away from the touched site
(Fig. 1A). The local
bend network resides in a single segmental ganglion and consists of
three neuronal levels (Fig. 1C). Two types of mechanosensory
neurons, T-cells and P-cells, for touch and
pressure, have overlapping receptive fields, such that a
given stimulus activates one or two P-cells and up to three T-cells
(Nicholls and Baylor, 1968; Lewis, 1997). The longitudinal motor
neurons comprise seven distinct classes, five excitatory (Fig.
1C) and two inhibitory (Stuart, 1970; Mason and Kristan,
1982), which innervate longitudinal muscle with overlapping fields.
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Figure 1.
The local bend behavior and network.
A, Illustration of three segments of the leech midbody,
producing a local bend (dorsal view, anterior is up).
Each segment consists of five annuli, and each annulus forms a ring
around the body perimeter. A touch to the lateral body wall elicits a
bend directed away from the touched site. The bend results from
shortening of longitudinal muscles near the touched site.
B, Schematic of the body perimeter in cross section
showing the convention for defining body wall location: dorsal midline
( = 0°), ventral midline ( = ±180°), right lateral ( = +90°), and left lateral ( =  90°). Shaded arrows
give two examples of different stimulus locations; the unfilled
arrow gives an example of a bend direction. C,
Schematic outline of the local bend neuronal network. Two classes of
mechanosensory neurons (T and P) connect
to a layer of interneurons (~30, with 17 identified so far; Lockery
and Kristan, 1990b), which in turn connect to five classes of motor
neurons that innervate longitudinal muscles in different regions of the
body wall: dorsal (D), dorsolateral (DL), lateral (Lat), ventrolateral
(VL), and ventral (V).
There are also two classes of inhibitory motor neurons (not
shown).
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We characterize the local bend response as a function of touch location
to determine whether this behavior uses a Continuous or Categorical
strategy. The Continuous strategy involves a different bend direction
for every stimulus location. The broadly tuned neurons in the local
bend network are well suited for such a strategy. In the Categorical
strategy one of four possible bend directions is produced, depending on
stimulus location. Each of the four responses is associated with one of
the four P-cells. The P-cell that is activated to the greatest extent
determines which response, of the four, is expressed
(winner-take-all). We provide evidence, based on
experimental and theoretical approaches, that the local bend network
uses a Continuous strategy in the sensorimotor transformation of
stimulus location to directed behavioral output.
Portions of this work have appeared previously in preliminary form
(Lewis and Kristan, 1996).
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MATERIALS AND METHODS |
The leech has a body plan consisting of 21 midbody segments
(denoted MS1-MS21) with a corresponding segmental nerve cord (one ganglion per segment). This organization is amenable to semi-intact preparations in which parts of the nervous system are exposed for
electrophysiology while most of the animal is left intact (Kristan et
al., 1974; Muller et al., 1981). Experiments were performed on 1.5-2.5
gm leeches, Hirudo medicinalis, obtained from Leeches USA
(Westbury, NY). Animals were anesthetized in ice-cold leech saline, and
surgical methods were similar to those described previously (Muller et
al., 1981). We used standard intracellular recording techniques with
sharp electrodes (20-30 M ) and the Axoclamp-2B amplifier (Axon
Instruments, Foster City, CA). Neurons were identified on the basis of
their physiology and location within the ganglion (Muller et al.,
1981). The preparations and behavioral measurement techniques used are
described in following sections. Data were collected by the Axotape 2.0 and Digidata 1200 PC-based data acquisition system (Axon Instruments).
Off-line data analyses were performed with Axotape 2.0 and Axograph 2.0 (Axon Instruments), Systat 5.2 (Systat, Evanston, IL), and Microsoft Excel (Redmond, WA).
Mechanical stimulation
We delivered mechanical stimuli (500 msec duration) to the body
wall, using a solenoid-driven push rod (Guardian, Woodstock, IL) with a
nylon filament (1.6 cm in length and 200 µm in diameter) attached to
one end. Once such filaments buckle, they exert forces that are
relatively independent of displacement (the Von Frey principle; see
Levin et al., 1978). The solenoid was controlled with a relay circuit
powered by two 9 V batteries in series and triggered by a Grass
stimulator (Grass Instruments, Quincy, MA). We positioned the stimulus
apparatus, using a micromanipulator, so that the filament tip was as
close as possible to the skin without touching (within 0.5 mm). During
a stimulus the push rod moved ~2 mm. We calibrated the filament with
a force transducer (Biocom, Culver City, CA). The mean and SD of the
force produced were 21.9 ± 0.27 mN (five trials). In addition to
this standard stimulus, one of two other nylon filaments (differing
from the standard only in length, 2.0 and 0.9 cm, 10.8 ± 0.35 and
36.6 ± 1.06 mN, respectively; mean ± SD, five trials) was
used for the experiments in which two stimuli were delivered
simultaneously. Each of these stimuli reliably elicited a local bend
response but did not activate the high-threshold nociceptive
N-cells.
Measuring motor output and behavior
We used three techniques to describe the local bend behavior.
First, we used video motion analysis in preparations consisting of four
intact midbody segments to observe the intact behavior; second, we
measured the tension generated by body wall muscle; and third, we used
electromyography (EMG). We have obtained similar results in each case,
providing reasonable evidence that our results do not depend on the
method of measurement.
Video motion analysis. We videotaped the local bend response
in a preparation consisting of four intact segments (MS8-MS11). This
was the largest number of intact segments that would not result in the
continuous generation of swimming movements (J. E. Lewis,
unpublished observations). Although this preparation may not allow for
normal internal pressures (Wilson et al., 1996), its primary advantage
is that there is normal mechanical coupling of the cylindrical body
wall within the segments tested, and thus the normal behavioral
response can be measured (mechanical coupling is compromised by the
semi-intact preparations used for the tension and EMG measurements; see
the following). One disadvantage of this preparation is that the
locations for measuring response and giving stimuli are limited to an
area around the dorsal midline. Another difference between this intact
preparation and the semi-intact preparations involves the possibility
of activating sensory neurons from segments other than the one being
tested. These cells could be activated via their secondary receptive
fields (Yau, 1976; Gu, 1991), resulting in an increased sensory input
for a given stimulus, as compared with semi-intact preparations
consisting of isolated segments. In a series of ganglion-body wall
experiments, we measured the extent to which T- and P-cells were
activated by a mechanical stimulus delivered to their secondary
receptive fields. The mechanical stimulus used in the present study
elicited no P-cell action potentials in any trial (5 animals, 10 cells, 34 trials) and in T-cells produced, at most, 10% of the number of
action potentials elicited by primary field stimulation (4 animals, 9 cells, 27 trials). Therefore, because secondary field activation
provides such a small component of the sensory input, we feel justified
in comparing results from video experiments with those using EMG and
tension measurements in which only one ganglion is present and, hence,
no secondary field innervation.
To evoke the local bend response, we gave mechanical stimuli at four
sites (S = 45°, 27°, 0°, and 27°; see Fig.
1B for definition of body perimeter coordinates)
along the central annulus of MS10. The experiments were videotaped
(Sanyo model VDC 3825) for later analysis. Figure
2A shows two video
frames corresponding to a single stimulus trial; the left frame is the
control state (before stimulation), and the right frame is the
maximally contracted state. We measured the local bend response as the
relative longitudinal length change at five locations on the body wall
perimeter ( = 45°, 27°, 0°, 27°, and 45°). The length
change at each location was measured by defining a line segment
connecting two prominent markings in the body wall pigment (denoted
schematically by unfilled circles in Fig.
2A). In every experiment it was possible to define unambiguous markings in this way, such that the length of the line
segment between two markings could be measured before and after a
stimulus. In each of five animals, five stimulus trials were given
every 2 min at each of the four stimulus locations (randomized block
trials).
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Figure 2.
Three methods of measuring the local bend
response. In each panel an icon representing the body perimeter shows
the stimulus location S (denoted by the
arrow) and the measurement location (black
rectangle). A, Video analysis. Two video frames
(before and after a stimulus trial) show a dorsal view of midbody
segment 10. The stimulator is mostly out of focus in the
top of the image; the stimulus location is denoted by a
white square. The unfilled circles drawn
on each image define the line segments used to measure the response.
B, Body wall tension. Tension is measured at one body
location for a single stimulus trial; the peak tension is indicated.
C, Electromyographic (EMG) analysis.
Shown are EMG signals from three body locations for a
single stimulus trial (S = 45°). Stimulus trace
(top) shows the time intervals
E0 and E1 (in
seconds) during which the EMG signals were analyzed (see Materials and
Methods).
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Muscle tension measurements. As in previous studies of the
local bend behavior, we used the tension produced by longitudinal muscles as another indicator of local bend response (Kristan, 1982;
Lockery and Kristan, 1991). This technique provides an easily quantified measure of the local bend behavior, but measuring the response at multiple locations is difficult. In ganglion-body wall
preparations consisting of a single innervated segment (MS9 or MS10)
from six animals, we measured muscle tension evoked by mechanical body
wall stimuli (Fig. 2B). Sutures (6-0, Ethicon, Somerville, NJ) were tied to a denervated part of the body wall at
either of two locations (90° or +90°) and attached to force transducers (Biocom). Stimuli were given at 10 different locations every 2 min (randomized block trials). The response was quantified as
the peak tension (subtracted from baseline) generated during a given
trial. The peak tension of the local bend response occurred ~1 sec
after stimulus onset. Another possible measure of the tension response
is the area under the tension-time curve; this measure varies linearly
with the peak tension (J. E. Lewis, unpublished observations).
Peak tension measurements for a given animal were normalized to the
mean value evoked for the stimulus site that resulted in the largest
response.
Electromyography (EMG). EMG recordings were made from the
body wall muscle at different locations along the body perimeter, using
methods described previously (Lewis, 1997). Briefly, EMG electrodes
consisted of a minuten pin soldered to a flexible wire; the electrodes
were insulated except for 2-3 mm at the tip and were inserted parallel
to the longitudinal axis of the body. The reference electrode was
placed in the bath, resulting in monopolar recordings. These monopolar
electrodes provided EMG recordings that were similar to those obtained
with other electrode configurations (e.g., bipolar, insulated silver
wire alone) but were much easier to insert and thus minimized damage to
the preparation. The signals were recorded with a differential
amplifier (A-M Systems, Everett, WA), bandpass-filtered (10-500 Hz),
and stored on computer for further analysis. The advantage of this
technique is that it can be used to monitor the response at many
locations in a semi-intact preparation while recording from neurons in
the local bend network. The disadvantage is that it measures electrical
activity in the muscle and does not, in a strict sense, indicate the
behavioral output.
We constructed EMG tuning curves by using the following procedure. In
ganglion-body wall preparations (MS10) from five animals, we
mechanically stimulated the body wall at seven different sites, S = ±45°, ±90°, ±135°, and 180°, and
measured the EMG responses at four body wall locations, = 45°,
90°, 135°, and 180°. In a given experiment we delivered
stimuli every 2 min in a randomized block trial paradigm, with 5 min
between blocks. Figure 2C shows EMG responses from three
locations ( = 45°, 90°, and 135°) for a single stimulus
trial (S = 45°). In another set of EMG experiments
two stimuli were delivered to different locations simultaneously. This
will be referred to as the two-stimuli protocol.
To quantify the change in EMG activity evoked by a stimulus, we
measured the area under the full-wave rectified signal over two 1.5 sec
intervals (Fig. 2C): the control period
(E0, beginning 1.5 sec before stimulus
onset) and the local bend period [E1, beginning at stimulus offset (i.e., 0.5 sec after stimulus onset)]. Then the response was quantified by
(E1/E0 1) and
referred to simply as the EMG response. We did not include the 500 msec
stimulus interval in E1 because the EMG signal
during this time is dominated by L-cell-related activity. The L-cell is
a longitudinal motor neuron with an innervation field spanning one-half
of the body wall (Stuart, 1970). In preliminary experiments we found
that the response of the L-cell to local bend stimuli is limited mostly to the duration of stimulation. The response of cell 3 can last for
many seconds after a local bend stimulus (Lockery and Kristan, 1991).
In addition, L-cell activation does not appear to depend on stimulus
location (J. E. Lewis, unpublished observations). Kristan (1982)
observed that, for dorsal stimuli, the ventral longitudinal muscle
transiently contracted before a strong ultimate relaxation response.
This transient response is attributable to the L-cell. Thus, we
conclude that the L-cell does not play a major role in the
directionality of the local bend response, the focus of this study, so
its contribution will be ignored.
Tuning curves and single-trial response curves
Tuning curves are plots of the average response of a system as a
function of some stimulus parameter (Knudsen et al., 1987; Churchland
and Sejnowski, 1992). We use tuning curves as one way of characterizing
the local bend behavior as a function of stimulus location on the body
wall perimeter. We refer to plots of EMG response (measured at a single
body wall location) versus stimulus location as EMG tuning
curves. Likewise, we refer to such curves for tension measurements
as tension tuning curves. We were not able to construct
tuning curves for video measurements because of the limited range of
stimulus locations in these experiments.
Because tuning curves are constructed by measuring the response at one
location while stimulating at many, they are particularly useful when
technical limitations make response measurements at many locations
difficult. However, because ultimately we want to characterize the
sensorimotor transformation in the local bend, we also analyzed the
response on a trial-by-trial basis. Therefore, we define a
single-trial response curve as EMG response versus electrode
location (or relative shortening vs location for video measurements).
This curve describes the response profile over the body perimeter for a
single trial and a single stimulus location.
Estimating behavioral accuracy
We define the behavioral error as the difference between
stimulus location and bend direction. To determine bend direction, we
performed the following analysis on the single-trial response curves
(EMG and video data). The single-trial response curves were bell-shaped
with a central maximum (see Fig. 5). We used the body wall location
where the maximum response occurs, max, as an
indicator of bend direction. To estimate max at a finer resolution than our measurement resolution, we used the following interpolation procedure.
The single-trial response curves were normalized so that the maximum
value in each was equal to one. Data from all trials were pooled for
each stimulus site, resulting in eight ensemble data sets
(four each for both video and EMG data). We chose a cosine function
f(), with two free parameters, A
and o, to fit the data:
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(1)
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where Ro = 1 defines the peak amplitude
of the response. The values for the parameters A and
o were determined by a regression analysis on the
ensemble data sets (thus providing a population estimate of these
parameters). Because the data at different measurement sites did not
always show uniform variance, we used a two-step weighted least-squares
method (Chatterjee and Price, 1991). The first step consisted of an
ordinary least-squares (OLS) fit to the data. The second step involved
a least-squares fit weighted by the reciprocal of the variance of the
OLS residuals. The peak locations of the individual trials were
determined by fitting the single-trial response curves to the same
function (Eq. 1) but with A fixed at the values determined
by the ensemble analysis (Table 1) so
that o was the only free parameter in this step. Again,
a weighted least-squares method was used with identical weights as for
the ensemble fits. The value of the parameter o from
these fits was taken as the value for max, the
body wall location of peak response. The quality of fit varied for the
single-trial response curves. Any trial in which the fitted curve
accounted for <65% of the variance in the data was not considered in
further analyses. This selection criterion resulted in acceptance of 94 and 65% of the trials for the video and EMG experiments, respectively. The high acceptance rate for the video trials confirms that the cosine
function is appropriate for describing the single-trial response curves
at the behavioral level. The relatively low acceptance rate for the EMG
trials could be attributable to a more variable signal at the level of
electrical activity in the muscle (that is subsequently smoothed by the
biomechanics) or to more experimental error involved in recording this
signal. For the two-stimuli protocol experiments, the single-trial
response curves were not normalized, and Ro in
Equation 1 was also a free parameter.
Statistical analysis
The data relating to stimulus location and body perimeter
location are periodic and thus were analyzed as circular data
(Batschelet, 1981). The data in Figure 6 are compared with the
predictions for each behavioral strategy by calculating the residuals
(i.e., the angular distance between a data point and the strategy
prediction for the corresponding stimulus site). Because the
predictions for the Categorical model are discontinuous at four
stimulus locations, the residuals at these locations were calculated by
a random choice of one or the other predicted value across the
discontinuity. Then the squared residuals for the different strategies
were compared with a  2 test. Variance (or angular
dispersion) in the peak response location between different stimulus
sites was compared with the Wilcoxon-Mann-Whitney U test
for circular data (Batschelet, 1981).
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RESULTS |
Tuning curves
Figure 3 shows EMG tuning curves for
four measurement locations, . In general, the EMG response is
maximal for a stimulus site equal to the EMG measurement location and
decreases for stimulus sites farther from this location. An
illustration of this trend is that for each measurement location a
cosine curve can account for >85% of the variance in the mean data
(Fig. 3A-D). If the peak of the cosine is set equal to the
measurement location, the curve can still account for >80% of the
variance in each case. This trend is evident in individual animals as
well, where on average 82% of the variance can be accounted for by a
cosine curve. Although the cosine model is quite simplistic, it appears
to capture the main features of the EMG tuning curve data. However, the
tuning curves for = 90° and = 135° appear quite
similar; in both cases the peak response in a given animal occurred at
either S = 90° or S = 135°.
Such ambiguities can result when average responses are investigated,
and we will address this issue in our investigation of individual
trials.
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Figure 3.
EMG tuning curves. Normalized EMG response at four
body locations is plotted against stimulus location. In
A, the body perimeter icon illustrates the stimulus
locations (arrows), and in all panels this icon shows
the location of EMG measurement, (small filled rectangles). A, = 45°; B,
= 90°; C, = 135°; D, = 180°. Data points show the mean ± SEM for five
animals. Also shown is the cosine curve,
b0 + b1cos
(S So), which
best fits the mean data: A,
b0 = 0.45, b1 = 0.41, So = 63°;
R2 = 0.89. B,
b0 = 0.48, b1 = 0.48, So = 113°;
R2 = 0.97. C,
b0 = 0.47, b1 = 0.47, So = 126°;
R2 = 0.92. D,
b0 = 0.48, b1 = 0.39, So = 167°;
R2 = 0.85.
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EMG activity reflects the electrical activity of the muscle and does
not necessarily reflect the resulting movement. Ideally, we could
measure tuning curves while videotaping the actual movements, but
because of technical limitations we were unable to do so (see Materials
and Methods). Instead, we compared an EMG tuning curve with one
constructed that used the evoked body wall tension (Fig. 4). The data are similar in both cases,
although the tension tuning curve appears to be slightly more narrow,
with very little response for contralateral stimuli. The best fit
cosine curve can account for 92% of the variance in the mean tension
data; the same curve (i.e., same parameter values) also can account for
90% of the variance in the mean EMG data.
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Figure 4.
Tension tuning curve. Filled
circles show the normalized peak tension measured at = 90° plotted against stimulus location (each point is
the mean ± SEM for six animals). Also plotted are the EMG data
(unfilled squares) from Figure 3B for
comparison. The cosine curve is a best fit to the peak
tension data (b0 = 0.40, b1 = 0.60, So = 104°; R2 = 0.92; see Fig. 3
legend).
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Behavioral accuracy: single-trial analysis
In both EMG and video experiments we measured the single-trial
response curves and used an interpolation procedure (see Materials and
Methods) to determine max, the body location
where the maximal response occurs. Single-trial response data were
pooled for all trials at a given stimulus location (EMG and video data
were analyzed separately). Figure
5A shows an example of such an
ensemble data set for video data (S = 0°), along with
the corresponding regression curve (Eq. 1, Ro = 1) used to obtain a population estimate of the parameter, A.
The resulting values for A are shown in Table 1. Then the
single-trial response curves were fit to the same function (Eq. 1) but
with A fixed at the ensemble values (Table 1). The only free
parameter in this step was o, for which the resulting value was taken as max. Figure 5B
shows two single-trial response curves with their corresponding curve
fits. These examples provide an idea of the range in curve fit quality;
one of the best fits is shown by the solid line (accounting for 99% of
the variance in the data), whereas one of the worst fits is shown by
the dotted line (accounting for only 42% of the variance and thus it
was not considered for further analyses; see Materials and
Methods).
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Figure 5.
Measuring single-trial response. A,
Ensemble data set. Plot shows normalized response (video analysis)
versus measurement location on the body wall. A single trial consists
of one measurement from each of the measurement locations, where the
maximal response is set to one. The solid curve shows
the cosine function that best fits the ensemble data (see Materials and
Methods). B, Single-trial response curves. Shown are a
single stimulus trial for EMG (solid squares;
S = 90°) and video (unfilled
circles; S = 0°) measurements, along with
the respective curve fits. These trials provide examples of the best
and worst fits (see Materials and Methods).
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Figure 6 shows a scatter plot for
max as a function of stimulus site. On average, the
local bend responses are centered close to the stimulus site (circular
correlation, r = 0.89; p < 0.001, Rayleigh test). The root mean-squared (RMS) difference among peak location, max, and stimulus site was 28°. In
other words, on average, the local bend network produces a behavioral
output that is directed within 8% of the stimulus location,
corresponding to an accuracy of ~1.6 mm (the perimeter of the leech
body wall is ~2 cm in length). This suggests that the local bend
behavior involves a strategy in which the response varies continuously with stimulus location (Continuous strategy). However, in the following
we show that the data are also consistent with a specific form of
Categorical strategy.
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Figure 6.
Single-trial peak response location. Shown is the
relationship between peak response location (max)
and stimulus site (S). Mean (unfilled
symbols) and single-trial data (dashes) are
shown for both EMG and video measurement techniques. Note that the
single-trial responses overlap, and thus the dashes
appear as squares. The identity line,
which is drawn for reference, also represents the predicted responses
for the Continuous strategy. The prediction for the Categorical
strategy is denoted by the shaded gray line.
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Comparing Continuous and Categorical strategies:
single-trial analysis
The Categorical strategy we considered involves four distinct
forms of the behavior (i.e., bend direction), distinguished by the
quadrant of the body wall perimeter where the stimulus is given. The
quadrants are defined by transition regions at = 0°, 90°,
180°, and 90°. These quadrants correspond approximately to the
innervation fields of the four P sensory neurons (Nicholls and Baylor,
1968; Lewis, 1997), providing a plausible physiological mechanism for
this Categorical strategy (i.e., a winner-take-all mechanism mediated
by the P-cells). This Categorical strategy makes specific predictions
about the form of the curve shown in Figure 6: there are four different
peak response locations for all possible stimulus sites, such that the
curve is piecewise constant with four steps
(gray line). The corresponding prediction for the
Continuous strategy is the identity line (i.e., where the peak location
is equal to the stimulus site). We evaluated the predicted peak
location for both strategies with the data by comparing the
distributions of the squared residuals; the Continuous strategy was a
significantly better fit to the data (p = 0.045; 2 test). Even so, the Categorical strategy
accounted for almost 80% of the variance in the data with an RMS
residual of 36°, whereas the Continuous strategy accounted for 83%
of the variance (RMS residual = 28°).
Another aspect in which the predictions of the two strategies differ is
the variance (i.e., angular dispersion) of the behavioral response. The
Continuous strategy predicts that response variance should not vary
with stimulus location. The Categorical strategy predicts that stimuli
given at the transitions between quadrants (i.e.,
S = 0°, 90°, 180°, and 90°) should produce
responses that either are distributed bimodally or are much more
variable (increased variance). There is no evidence of a bimodal
distribution for the responses at any of the stimulus sites. However,
to test the possibility that the variance was greater in the
presumptive transition regions, we calculated the angular distance
between each data point and the corresponding mean and then pooled the
data into two groups: transition zones (i.e., S = 0°,
90°, and 180°) and nontransition zones, where the two strategy
predictions are the same (S = 45° and 135°). No
significant difference was observed between these two groups
(p = 0.12).
Considering these results, it appears that the Continuous strategy best
supports our data. In both comparisons the difference between the two
strategies was fairly small, so we have considered two additional
levels of analysis, a simple model and a two-stimuli protocol, to
distinguish between the Continuous and Categorical strategies.
Predicting motor output by using a simple model
In this section we outline a simple approach for predicting the
tuning curves of the motor neurons that innervate the longitudinal body
wall muscle. These predictions are made in the context of both the
Continuous and Categorical strategies with the intent of localizing
differences between the two strategies at the level of motor output. We
then can compare these predictions with what is known about the
activation of motor neurons during a local bend.
The idealized response
So far, we have discussed the local bend response in terms of
actual movements (video), muscle tension, and EMG, but in the following
we consider a generalized local bend response. The local bend response
is a function of stimulus location, S, and the location on
the body perimeter where the response is measured, . We define an
idealized response function, R(S,), and then
fit the motor output model to this function. The form that the function
R(S,) takes is different for the Categorical
and Continuous strategies. The EMG tuning curves in Figure 3 are well
described by cosine curves, suggesting that
R(S,) should be continuous in S for
both strategies (this is a constraint imposed by the data). So we
consider R(S,) to be of the form:
![R(S, &thgr;)=0.5{1+<UP>cos</UP>[S−S<SUB><UP>max</UP></SUB>(&thgr;)]},](/content/vol18/issue4/fulltext/1571/img002.gif)
|
(2)
|
where Smax() defines the peak of the
tuning curve and differs for the two behavioral strategies. For the
Continuous strategy, Smax() = , so that
the peak of the tuning curve occurs at the body wall measurement
location, . For the Categorical strategy the function
Smax() is piecewise constant (Eq. 3) so that
the tuning curve peaks occur at one of four locations, depending on the
body location:
|
(3)
|
The response functions R(S,) for each
strategy are shown in Figure
7A. The body location and
stimulus site are represented on the vertical and horizontal axes,
respectively; the magnitude of the response is represented in gray
scale (a large response is white, and a weak response is black). A
tuning curve at a given body location, *, is a horizontal slice
through these plots intersecting *. Alternatively, a single-trial
response curve is analogous to a vertical slice through these
plots.
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Figure 7.
The basis for a model of motor output.
A, Idealized response
R(S,). The predicted responses are
shown for each behavioral strategy as a function of stimulus site
(S) and body wall measurement location (). The
response magnitude is given in gray scale, with white being the largest response. A tuning curve is a
horizontal line slice through this plot (i.e., responses
at a single location to stimuli at all locations), and a single-trial
response curve is a vertical line slice (i.e., responses
at all locations for a stimulus at one location). B,
Body wall innervation. Shown are innervation fields for the five
classes of longitudinal motor neurons considered in the model. Right
and left homologs for a given class are distinguished by different
diagonal filled patterns. Overlapping fields within the
D and V classes are shown by
cross-hatching. The discretization of the body perimeter
into 16 bins is indicated by the vertical lines.
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Anatomical constraints
There are five distinct classes of excitatory longitudinal motor
neurons, named for the area of longitudinal muscle that they innervate
(Stuart, 1970; Mason and Kristan, 1982; J. E. Lewis, unpublished
observations): dorsal (D), ventral (V), dorsolateral (DL),
ventrolateral (VL), and lateral (Lat). Figure 7B shows the approximate innervation fields for each of these classes. By dividing the body perimeter equally into 16 bins (see divisions in Figs. 7B, 8), we can define an
innervation matrix, W, where an element wij = 1 if motor neuron j innervates
the body wall at bin i, and wij = 0 otherwise. The identified motor neurons within each class are cells 3 and 4 for D and V, respectively, cell 106 for Lat, cells 5, 7, and 107 for DL, and cells 8 and 108 for VL. These motor neuron classes are
bilaterally symmetric, so each cell has a contralateral homolog. An
additional motor neuron in the Lat class is the L-cell, but we do not
consider it for the present model because its activity is transient and
its innervation field (entire hemi-segment) is not compatible with
either of the behavioral strategies most likely for the local bend (see
Materials and Methods).
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Figure 8.
Motor output model. Given is a schematic
illustration of the model used to predict motor neuron tuning. The body
perimeter is shown in conventional coordinates; the 16 bins are shown
by the dashes. The motor neurons innervating the right
body wall are shown, with the gray lines indicating
connections to a particular bin (innervation matrix). In the
box, a schematic flow of the model is provided. A
stimulus at a location S results in activation of the
different motor neurons, given by M(S). This motor
neuron activity is passed through a threshold function. The model
response Rm in a particular bin is
determined by the summed activity of all the motor neurons innervating
that bin (given by the innervation matrix,
W).
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Motor output model
We assume a simple yet plausible model for relating the activity
of a set of motor neurons,
Mj(S)
(j = 1,... ,10), and the response they
produce (Eq. 4). The motor neuron activity is passed through a
threshold function, such that only activity above zero has an effect on
the motor output response. The model response Rm
for a stimulus site Sk and a body wall location,
i, is the linear sum of the thresholded activity
of all the motor neurons that innervate i (given by the
innervation matrix, W; see Fig. 8).
|
(4)
|
where i,k = (1,... ,16) and H is
defined by H(x) = 0 if x < 0 and
H(x) = 1 if x  0 and acts as the threshold
function. The model is shown schematically in Figure 8.
Calculating the motor neuron tuning curves
The goal of this approach is to determine the functions,
Mj(S), which are the motor
neuron tuning curves. We do this by finding the
Mj(S) that minimize the
squared difference (least squares) between R and
Rm over all stimulus sites,
Sk (k = 1,... ,16), and body
wall locations, i (i = 1,... ,16). In
principle, the tuning curve for a given motor neuron can be any
function of S, with the only constraint that it is periodic
with period equal to 360°. To constrain our predictions, we assume
cosine tuning for the motor neurons, such that the
Mj(S) are of the form shown in
Equation 5:
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(5)
|
This is based on the observation that at least two motor neurons,
cells 3 and 4, exhibit cosine-like tuning (Lockery and Kristan, 1990a;
Kristan et al., 1995). We also assume right-left and dorsal-ventral
symmetry, such that the parameters Aj and
Bj are equal for D and V and are also equal for
DL and VL. This symmetry constraint was implemented for practical
reasons, but it was not necessary because the symmetry is intrinsic to
the innervation matrix, W. With these constraints the
minimization procedure is reduced to solving for the
Aj, Bj, and
Sj* for only three motor neurons, D, DL, and
Lat, with the remainder of the motor neurons specified by the results
of these three. We perform the minimization for the Continuous and
Categorical strategies by changing the form of the idealized response,
R [i.e., the choice of Smax() in
Eq. 2]. This gives a predicted set of tuning curves for both behavioral strategies. These tuning curves reflect the
effective motor neuron activation because our model does not
distinguish between the absolute level of activity of a motor neuron
and its relative efficacy in activating the muscle, nor does it
distinguish the effects of the inhibitory motor neurons. With the use
of the previous experimental data (Mason and Kristan, 1982), a more
detailed model could account for such differences between motor
neurons. However, because we were investigating the qualitative
features of motor output, our simple model was sufficient.
The model predictions
Figure 9 shows the predicted tuning
curves of the motor neurons innervating the right body wall for both
behavioral strategies. The best solution for the Continuous strategy
(RMS residual = 0.08) involves activation of all motor neurons,
with the peaks of their tuning curves distributed at six different
stimulus locations. The DL, VL, and Lat neurons are activated to a
greater extent than either the D or V neurons. The DL motor neurons
produce approximately twice the peak muscle tension as the D motor
neuron (Mason and Kristan, 1982). Our results suggest that this
difference in efficacy may be required for a continuously varying
behavioral response. However, for the Categorical strategy the D, V,
and Lat motor neurons are not activated at all: the best solution in
this case (near perfect with RMS residual  0) involves the activation
of only the DL and VL motor neurons. This is because the
single-quadrant innervation fields of these motor neurons correspond
directly to the four distinct regions of the Categorical strategy. The differential activation of any other motor neurons within these regions
would change the response within the region and thus would not satisfy
the Categorical strategy. These results suggest that activation of the
D, V, and Lat motor neurons is incompatible with the Categorical
strategy. However, the D and V neurons are known to be activated by a
local bend stimulus (Lockery and Kristan, 1990a), providing evidence
against the Categorical strategy.
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Figure 9.
Predicted motor neuron tuning curves. Model tuning
curves for each of the five classes of motor neurons (right side only) are shown for both behavioral strategies, Continuous
(A) and Categorical (B).
For the Categorical strategy (B), the
D, V, and Lat motor neurons do not respond at all (i.e., their tuning curves are
flat).
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Distinguishing between Continuous and Categorical strategies:
two-stimuli protocol
A final test of the Continuous and Categorical strategies was to
use a two-stimuli experimental protocol. Such experiments can distinguish between the two strategies because, in the Categorical strategy considered here, only one form of the behavior can be expressed for a given range of stimuli. This winner-take-all nature predicts that when two stimuli are given simultaneously, a single form
of the behavior, corresponding to one or the other stimuli, will be
expressed. Consider the stimuli, S1 and S2, that alone produce
different behaviors centered at 1 and 2, respectively. If S1 and
S2 are given simultaneously, the Categorical strategy predicts that the
behavior will be centered at either 1 or 2. If the magnitude of
S1 is greater than that of S2, the behavior centered at 1 would be
more likely. Alternatively, the Continuous strategy predicts that the
resulting behavior will be centered at some intermediate location,
3.
We performed these experiments in ganglion-body wall preparations
while measuring EMG responses at three locations ( = 90°, 180°, and 90°). Two stimuli were delivered, first individually and
then simultaneously, at locations (S1 = 135° and S2 = 135°). The stimulus S1 was of greater magnitude than S2 (see
Materials and Methods) so that one behavioral response would dominate
in a winner-take-all scenario. Figure
10, A and B,
shows the results of one experiment. Each vector represents the
location and amplitude of the peak response for a given stimulus trial.
On average, the peak responses to S1 are of greater amplitude than
those of S2 and are located at = 130°, as compared with = 101° for S2 (Fig. 10B). Also shown are the
responses to both stimuli delivered simultaneously (S1 + S2); on
average, these responses are centered at a location intermediate to the
responses to each individual stimulus. Indeed, the average peak
response location for S1 + S2 is well described by the average of the
two individual responses (i.e., vector sum). There was no evidence of a
bimodal distribution of responses, which also could result in the
observed average response. No simple relationship was observed between
the amplitude of the response caused by S1 + S2 and that predicted by a
vector sum. Figure 10C shows the predicted peak location for
both strategies versus actual peak location. The prediction for the
Continuous strategy is given by the vector sum of the responses to S1
and S2, and the prediction for the Categorical strategy is the response to S1 alone. Points that fall on the identity line in this plot correspond to perfect predictions. In all experiments the average responses were better described by the Continuous strategy. This last
piece of evidence, along with those described in previous sections,
indicates that the local bend behavior can be described best by a
strategy in which the response varies continuously with stimulus
location.
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Figure 10.
Two-stimuli protocol. A,
Single-trial responses for one experiment. The directed
lines are vectors for which the magnitude and direction are
given by the location and amplitude of the local bend EMG response to a
single stimulus trial. Three different stimuli were given:
S1 at location 135° (gray
lines), S2 at location 135° (dotted
lines), and both S1 and S2
together at their respective locations (solid black
lines). Note that the magnitude of the largest response to
S1 was slightly truncated for clarity (see the mean
value in the panel below). B, Mean values for the
responses in A: S1, gray
arrow; S2, dotted arrow;
S1 + S2, thick black arrow. Also shown is
the vector sum of the mean responses to S1 and
S2 (unfilled gray arrow). C, Comparison of the location of the
predicted and actual peak responses to two stimuli for both behavioral
strategies. The prediction for the Continuous strategy
(filled circles) is given by the vector sum of
the responses to S1 and S2, and the prediction for the Categorical strategy (unfilled
squares) is the average response to S1 alone (note that this
response does not always correspond to the ideal of 135°). The
predictions in each case are plotted against the measured mean response
(six animals, three to six trials each). A point falling
on the identity line corresponds to a perfect
prediction.
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DISCUSSION |
The local bend of the medicinal leech is a directed behavior
elicited by a touch to the body wall. The present paper quantified the
relationship between touch location and directed behavioral output. We
used a controlled mechanical stimulus to activate the mechanosensory
neurons, whereas previous studies of this behavior used direct
electrical stimulation of mechanosensory neurons to mimic a touch. By
activating these neurons in a natural way, we allow the possibility
that a realistic spike train contributes to stimulus representation and
behavioral output. We also developed methods for measuring behavioral
output on a trial-by-trial basis, allowing the behavior to be
quantified in terms of how accurately it corresponds to stimulus
location.
Behavioral accuracy
The local bend behavioral output is directed within 8% of
the stimulus location, on average. Recently, the cricket escape response to a directed wind source has been quantified in a way that
allows the estimation of a behavioral error (Tauber and Camhi, 1995).
From these data [Tauber and Camhi (1995), their Fig. 4] we estimated
the average behavioral error for an escape turn to be
~20%. For two other variants of the response, the turn and jump and the jump, the behavioral error was closer to
10%. Sound localization in barn owls is an example of a directed
behavior that is much more accurate. The form of this behavior most
relevant to the present context involves the open-loop paradigm. In
this situation the auditory stimulus is terminated before a head turn is initiated. The sound localization error can be <1% for frontal stimuli (sound source <30° to the right or left of center) and increases to ~3% for a stimulus given at 70° (Knudsen et al., 1979).
To assess the accuracy of information processing by a neuronal network,
we think that it is necessary to consider the accuracy of stimulus
representation by primary sensory neurons in the pathway. To date, it
has not been technically possible to measure accuracy at both the input
and output levels in a single system. The local bend network is a
system in which these measurements can be made (Lewis, 1997).
The local bend uses a Continuous behavioral strategy
We have cast the results of our analysis in the context of two
contrasting behavioral strategies: a Continuous strategy, in which bend
direction varies continuously with touch location, and a Categorical
strategy, in which one of four distinct bends is elicited, depending on
which body wall quadrant the touch is given. Our data describing the
input-output relationship in the local bend suggested that the
Continuous strategy is most consistent with the local bend behavior,
but to strengthen this argument, we performed two additional analyses.
First we investigated a simple model, based on the known anatomy and
physiology of the identified longitudinal motor neurons and their
muscle innervation patterns. This analysis showed that the activation
of the D, V, and Lat classes of motor neurons was incompatible with the
Categorical strategy. However, both the D and V motor neurons (cells 3 and 4) are known to be activated substantially by a local bend stimulus (Lockery and Kristan, 1990a).
Second, we performed a series of two-stimuli experiments to
test the prediction of the Categorical strategy, that the response to
both stimuli would be the same as that produced by either one of the
stimuli given individually (i.e., one response would win). The experiment showed that the responses to two stimuli was better described by an average of the responses to the individual stimuli. This result is consistent with the Continuous strategy. Taken together,
our results suggest that the local bend behavioral output varies
continuously with touch location.
Population coding for Continuous and Categorical behaviors
Several systems can be related directly to the discussion of
Continuous and Categorical behavioral strategies. The turtle scratch
reflex (Stein, 1989) also can be considered Categorical, in that one of
three distinct forms of the behavior is elicited, depending on the
stimulus location (touch to the body surface). This is not strictly
true, because there are transition regions where stimuli can
evoke blends of the different behavioral forms (Mortin et
al., 1985). Directed saccadic eye movements in primates clearly are
governed by a Continuous strategy (Lee et al., 1988). The strategy used
to produce wind-evoked escape responses in crickets and cockroaches
(Miller et al., 1991; Tauber and Camhi, 1995) is more difficult to
determine. Many studies of the behavior have been aimed at the problem
of right-left discrimination, a categorical task (Levi and Camhi,
1996). Tauber and Camhi (1995) characterized the behavioral responses
to a broader range of wind directions, but the variability in the
response makes its difficult to distinguish between Categorical and
Continuous strategies. At the level of the interneurons, sufficient
information about wind direction is encoded to enable a Continuous
strategy (Theunissen and Miller, 1991).
In each of these systems, interneurons involved in the behavior are
broadly tuned to the stimulus input (Miller et al., 1991; Berkowitz and
Stein, 1994), suggesting that the stimulus is represented as a
population code. Microstimulation and inactivation of neurons in the
superior colliculus produce effects on saccadic eye movements that
provide direct evidence for population coding in this system (Lee et
al., 1988). Similarly, in the local bend network, the mechanosensory
neurons are broadly tuned to touch location (Nicholls and Baylor, 1968;
Lewis, 1997). Electrophysiological studies also have revealed broad
tuning and distributed synaptic organization of the local bend
interneurons (Lockery and Kristan, 1990b). This suggests that the local
bend network also uses population coding. It is an open question, in
all of these systems, how the population-coded sensory stimulus is
translated into the appropriate motor command.
Choosing between behaviors
The choice of behavioral form in Categorical behaviors
implies that at some level in the sensorimotor pathway population-coded information must be channeled into appropriate categories. This process
could involve the nervous system, where some competitive mechanism
(e.g., mutual inhibition) between the subnetworks underlying each
behavior was present. Alternatively, this process could be attributable
to biomechanical constraints (see Levi and Camhi, 1996). A simple
example of behavioral choice by non-neural mechanisms is suggested in
Figure 9B of the present study. If a system were constructed
as in this example, the motor neurons could be broadly tuned to a
stimulus, but a categorical response would be produced because of the
pattern in which these motor neurons innervate the
muscle.
A standard approach in the study of behavioral choice is to
deliver a stimulus that alone elicits one specific behavior, along with
a conflicting stimulus that alone produces another behavior. The
response to such two-stimuli protocols depends on the underlying organization of the behaviors in question. In some cases, one or the
other behavior will dominate (Shaw and Kristan, 1997), corresponding to
a pure Categorical strategy. In other cases, a dominant behavior is not
always evident. For example, in the turtle scratch reflex, the
two-stimuli protocol occasionally produced blends of two behavioral
forms (Stein et al., 1986); the most common response in these
experiments, however, was one or the other behavior. This suggests a
modular organization in the networks underlying scratching,
with each module acting independently but not always in a
mutually exclusive manner. The results we present here for the
two-stimulus protocol eliminate the possibility that the local bend is
a pure categorical behavior. However, we cannot discount a model
consisting of four independent modules that can act together to form
blends. Indeed, for the local bend, such a modular
organization could form a cartesian representation of motor output and
thus could be a simple way to produce a continuously varying
response.
In conclusion, the local bend network solves two interesting problems
from the perspective of neural computation. First, the mechanosensory
neurons form an accurate representation of touch location. Second, the
subsequent neuronal levels compute the transformations that result in
behavioral output that varies continuously with touch location. These
processes apparently involve neuronal population coding; however, the
detailed cellular and network mechanisms are not known. This study
provides a necessary context for further work aimed at elucidating
these mechanisms. The relative simplicity of the local bend behavior
and its underlying neuronal networks, as well as the experimental
accessibility of the system, provides a unique opportunity to
investigate sensorimotor transformations in a detailed and quantitative
manner.
| |
FOOTNOTES |
Received July 29, 1997; revised Nov. 19, 1997; accepted Nov. 25, 1997.
This work was supported by National Research Service Award Predoctoral
Fellowship MH10677 (J.E.L.), National Institutes of Health Training
Grant GM08107 (J.E.L.), and National Institutes of Health Research
Grant MH43396 (W.B.K.). We thank R. J. A. Wilson for many
helpful discussions.
Correspondence should be addressed to Dr. William B. Kristan Jr,
Department of Biology 0357, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA, 92093-0357.
Dr. Lewis's present address: Cellular and Molecular Medicine,
University of Ottawa, Ottawa, Ontario, Canada K1H-8M5.
| |
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E. E. Thomson and W. B. Kristan
Encoding and decoding touch location in the leech CNS.
J. Neurosci.,
July 26, 2006;
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8009 - 8016.
[Abstract]
[Full Text]
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R. Levi, P. Varona, Y. I. Arshavsky, M. I. Rabinovich, and A. I. Selverston
The Role of Sensory Network Dynamics in Generating a Motor Program
J. Neurosci.,
October 19, 2005;
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[Abstract]
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S. M. Baca, E. E. Thomson, and W. B. Kristan Jr.
Location and Intensity Discrimination in the Leech Local Bend Response Quantified Using Optic Flow and Principal Components Analysis
J Neurophysiol,
June 1, 2005;
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[Abstract]
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A. Mazzoni, E. Garcia-Perez, D. Zoccolan, S. Graziosi, and V. Torre
Quantitative Characterization and Classification of Leech Behavior
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[Abstract]
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J. Jing and R. Gillette
Directional Avoidance Turns Encoded by Single Interneurons and Sustained by Multifunctional Serotonergic Cells
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April 1, 2003;
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[Abstract]
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C. L. Cleland and R. E. Bauer
Spatial Transformations in the Withdrawal Response of the Tail in Intact and Spinalized Rats
J. Neurosci.,
July 1, 2002;
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[Abstract]
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D. Zoccolan and V. Torre
Using Optical Flow to Characterize Sensory-Motor Interactions in a Segment of the Medicinal Leech
J. Neurosci.,
March 15, 2002;
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[Abstract]
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G Pinato and V Torre
Coding and adaptation during mechanical stimulation in the leech nervous system
J. Physiol.,
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[Abstract]
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R. Levi and J. M. Camhi
Wind Direction Coding in the Cockroach Escape Response: Winner Does Not Take All
J. Neurosci.,
May 15, 2000;
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[Abstract]
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J. E. Lewis and W. B. Kristan Jr.
Representation of Touch Location by a Population of Leech Sensory Neurons
J Neurophysiol,
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[Abstract]
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Top
Abstract
Introduction
