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The Journal of Neuroscience, July 15, 2000, 20(14):5516-5525
Timing Mechanisms in the Cerebellum: Testing Predictions of a
Large-Scale Computer Simulation
Javier F.
Medina,
Keith S.
Garcia,
William L.
Nores,
Nichole M.
Taylor, and
Michael D.
Mauk
W. M. Keck Center for the Neurobiology of Learning and Memory
and Department of Neurobiology and Anatomy, University of Texas Medical
School, Houston, Texas 77030
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ABSTRACT |
We used large-scale computer simulations of eyelid conditioning to
investigate how the cerebellum generates and makes use of temporal
information. In the simulations the adaptive timing displayed by
conditioned responses is mediated by two factors: (1) different
sets of granule cells are active at different times during the
conditioned stimulus (CS), and (2) responding is not only amplified at
reinforced times but also suppressed at unreinforced times during the
CS. These factors predict an unusual pattern of responding after
partial removal of the cerebellar cortex that was confirmed using
small, electrolytic lesions of cerebellar cortex. These results are
consistent with timing mechanisms in the cerebellum that are similar to
Pavlov's "inhibition of delay" hypothesis.
Key words:
LTD; LTP; eyelid conditioning; Pavlov; timing; simulation; cerebellum
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INTRODUCTION |
The timing displayed by Pavlovian
eyelid responses represents an opportunity to examine how a brain
system generates and makes use of temporal coding. Pavlovian eyelid
conditioning involves repeated presentations of an initially neutral
conditioned stimulus (CS) often a tonepaired with a reinforcing
unconditioned stimulus (US)such as periorbital electrical
stimulation. With this training the animal not only learns to close its
eye in response to the tone but also learns to time or to delay these
conditioned responses to achieve maximum eyelid closure when the US
arrives (Schneiderman et al., 1962 ; Mauk and Ruiz, 1992). Previous
studies have shown that lesions of the cerebellar cortex permanently
abolish this adaptive timing, yielding conditioned responses with short
and relatively fixed latencies (Perrett et al., 1993; Garcia and Mauk, 1998). Although these studies indicate that the cerebellar cortex is
necessary for adaptive timing of conditioned response, the present
studies attempt to address the mechanisms involved.
Pavlov (1927) first proposed in his "inhibition of delay"
hypothesis that the timing of conditioned responses could be delayed appropriately via differential conditioning within each trial. In
Pavlov's view, adaptive timing could be achieved with a brain mechanism able to discriminate the latter part of the tone, which is
reinforced by the US, from early periods during the tone, which are not
reinforced. Thus, the ability to respond at the right time would result
from learning to suppress the response early in the tone as well as
learning to respond later in the tone. Here we show that large-scale
computer simulations of the cerebellum are able to learn adaptively
timed responses in part via a variant of Pavlov's within-trial
differential conditioning mechanism. Our simulations suggest that this
mechanism is mediated by differential modification of synapses in the
cerebellar cortex dependent on whether they are active early or late in
the CS. The simulations reproduced previous empirical observations by
producing short-latency responses when the cerebellar cortex was
removed, but they also predicted a novel and unusual pattern of results
with partial removal of the cerebellar cortex.
To test this prediction we examined the effects that small,
electrolytic lesions of the cerebellar cortex have on the timing of
conditioned responses. In the simulations the initial effect of a
partial lesion is to produce conditioned eyelid responses with both
short-latency and properly timed components. With additional postlesion
training the well timed component persists, whereas the short-latency
component diminishes or disappears completely. We present data from a
group of rabbits in which we observed this pattern of effects after
making electrolytic lesions of the anterior lobe of the cerebellar
cortex. These results are compatible with a timing mechanism that
actively learns to suppress the conditioned response early in the CS,
consistent with Pavlov's inhibition of delay hypothesis.
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MATERIALS AND METHODS |
Computer simulations. The simulations were intended
to capture the synaptic organization and physiology of the cerebellum (Eccles et al., 1967; Ito, 1984) and the way in which its inputs are
engaged by eyelid conditioning (Fig. 1;
Table 1). Converging evidence from a
number of laboratories suggests that (1) the CS is conveyed to the
cerebellum via the mossy fiber input (Steinmetz et al., 1985, 1988;
Lewis et al., 1987), (2) the US is conveyed by the climbing fiber input
(McCormick et al., 1985; Mauk et al., 1986), and (3) increases in the
activity of cerebellar output cells in the anterior interpositus
nucleus drive the expression of the conditioned eyelid response
(McCormick and Thompson, 1984). Because of the straightforward manner
in which CS and US map onto the afferent pathways to the cerebellum,
eyelid conditioning can be relatively easily represented in our
simulations. Adding a constant depolarizing pulse to the membrane
potential of the climbing fiber simulates the presence of the US during
acquisition trials (Sears and Steinmetz, 1991) (Fig. 1, CLIMBING
FIBER INPUTS), whereas transiently altering the activity of the
mossy fiber input as initially described by Aitkin and Boyd (1978)
represents the CS (Fig. 1, MOSSY FIBER INPUTS). Increases in
simulated nucleus cell activity can then be taken as a measure of the
conditioned response (Fig. 1, NUCLEUS CELL
OUTPUT).
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Figure 1.
A schematic representation of the cerebellar
simulation (middle) as well as its inputs
(left) and outputs (right). The close
correspondence of the simulation to biology is made possible by the way
in which eyelid conditioning engages the inputs and output of the
cerebellum. The tone CS is emulated by activation of tonic- and
phasic-firing mossy fiber inputs, whereas the puff US is emulated by
the phasic activation of climbing fibers. Because output from the
cerebellar interpositus nucleus drives the expression of conditioned
responses, the activity of nucleus cells represents the output of the
simulation. The simulation itself is comprised of layers of
integrate-and-fire neurons interconnected following the well known
synaptic organization of the cerebellum (see Appendix). To simulate
presentation of the CS, 4% of the mossy fibers changed their activity
according to the recordings by Atkin and Boyd (1978). During
presentations of pure tones, these authors found a 3:1 ratio of mossy
fibers that were activated phasically compared with tonically. The
peristimulus histograms of Atkin and Boyd are shown to the
left of the peristimulus histograms of inputs presented
to the simulation. Raster plots of actual inputs for one phasic and one
tonic mossy fiber are also shown. As shown in these raster plots, each
individual response is different, representing the natural degree of
noise or variability in neural responses. Similar histograms and raster
plots for climbing fiber inputs are also shown. Here, the activity is
based on the recordings of Sears and Steinmetz (1991). The activity of
six nucleus cells represents the output of the simulation. Histograms
taken before and after training show the learned and well timed
increase in nucleus cell responding produced by the simulation and are
compared with the data of McCormick and Thompson (1984).
NUC, Nucleus cell; PURK, Purkinje cell;
B/S, basket and stellate cells.
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The key assumption of our simulations is that two sets of synapses in
the cerebellum can undergo changes in strength during motor learning.
On the basis of evidence that supports this assumption (Robinson, 1976;
Perrett et al., 1993; Raymond et al., 1996; Mauk, 1997), we have
implemented a plasticity rule that specifies that the synapses that
granule cells make with Purkinje cells (gr Pkj) decrease in
strength when active in the presence of a climbing fiber input and
increase in strength when active in the absence of a climbing fiber
input (Sakurai, 1987; Hirano, 1990; Salin et al., 1996). On the basis
of indirect evidence (Perrett and Mauk, 1995; Medina and Mauk, 1999)
that mossy fiber plasticity is controlled by Purkinje cell activity,
the simulations also implement plasticity at mossy fiber synapses onto
the cerebellar nucleus (mfnuc) so that their strength decreases when
they are active during periods of strong inhibition from Purkinje cells and increases during pauses in this inhibition. Although these synapses
contain NMDA receptors (Cull-Candy et al., 1998) and there is one
report of mossy fiber plasticity under rather nonphysiological stimulating conditions (Racine et al., 1986), the results did not
depend on the precise plasticity implementation as long as conditioning
strengthened mossy fiber synapses activated by the CS.
Animals. Data were obtained from nine male New Zealand
albino rabbits (Oryctolagus cuniculus), weighing 2.5-3.0 kg
each. The animals were individually housed and given food and water
ad libitum. Treatment of the animals and surgical procedures
were in accordance with an approved animal welfare protocol.
Surgical preparation. All animals were first prepared with a
head bolt cemented to the skull and electrodes implanted in the anterior lobe of the cerebellar cortex (5.7 mm anterior, 4.9 mm left
lateral, and 14.0 mm ventral to lambda). A large craniotomy was drilled
to accommodate the electrode assembly and covered with bone wax. After
placement, the electrode assembly and head bolt were secured to the
skull with dental acrylic, and the skin was sutured. Two stainless
steel stimulating electrodes were chronically implanted in the
periorbital muscles rostral and caudal to the eye. Antibiotics,
intravenous fluids, and analgesics were administered after surgery as
needed, and animals were allowed ~1 week to recover.
Conditioning procedures. The standard training session
involved a Pavlovian conditioning delay protocol with a 500 msec
interstimulus interval. Each training session consisted of 12 nine-trial blocks. Each block was comprised of eight paired
presentations of the CS and US and one presentation of the CS only. The
CS (a 1 kHz, 85 dB tone) was presented for 550 msec during CS-alone
trials and coterminated with a 50 msec train of constant-current pulses (200 Hz; 1 msec pulse width; 1-2 mA) delivered to the periorbital electrodes during paired trials. Trials were separated by a fixed 30 sec intertrial interval. Animals were conditioned to an asymptotic rate
of responding with at least 10 standard training sessions. Lesions were
then made by passing 2.0 mA of direct current through one or more of
the electrodes for ~1 min. The timing of conditioned responses was
assessed over six postlesion training sessions.
Stimulus presentation and data acquisition were controlled by a
computer using custom software. Movement of the unrestrained eyelid was
recorded by measuring the reflectance of an infrared light-emitting
diode aimed at the eyelid. Voltage responses were determined to be
linearly related to eyelid movement and were calibrated for each animal
daily. Digitized responses (1 point per msec) were analyzed using
custom software to determine onset and peak latencies.
Histology. After training, the location of the lesion was
determined for each animal using standard histological procedures. Animals were killed with an overdose of sodium pentobarbital and perfused intracardially with 1.0 l of 10% formalin. The brains were removed and stored in 10% formalin for several days. Brains were
embedded in an albumin-gelatin mixture. To assess the extent of the
lesions, we sectioned the cerebellum parasagittally using a freezing
microtome (80 µm sections). This plane of sectioning best illustrated
the degree to which tissue damage involved each lobule of cerebellar
cortex. Tissue was mounted, stained with cresyl violet, and
counterstained with Prussian blue.
Data analysis. For rabbit data, peak response amplitude,
onset latency, and peak latency were calculated by custom software. Digitized sweeps corresponded to the 200 msec before and 2300 msec
after the CS onset. After being calibrated, peak amplitude was measured
relative to an average of the 200 msec baseline collected before CS
onset. To be counted as a conditioned response, onset latency had to
follow CS onset, and the movement amplitude had to reach 0.3 mm before
US onset during paired trials. This criterion was relaxed for CS-alone
trials in which movements were counted as conditioned responses if they
reached a 0.3 mm amplitude at any time after CS onset. Trials in which
there was >0.3 mm of movement during the baseline were excluded from
further analysis. Onset latency was determined by calculating the point
at which the response reached criterion. For simulation data, the
activity of the nucleus cells had to increase by 10 spikes/sec over
background levels to reach criterion. This increase corresponds to 5%
of the maximum rate of activity for the nucleus cells and thus is similar to the 0.3 mm criterion used for rabbit data (i.e., 0.3 mm is
~5% of the maximum conditioned response amplitude).
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RESULTS |
Simulations learn appropriately timed conditioned responses
The architecture of the simulations was based on three fundamental
properties (see Appendix for details). First, neurons were represented
as single-compartment, leaky integrate-and-fire elements. This standard
representation is based on the idea that the summation of inputs
(excitatory and inhibitory) and leak currents determines a neuron's
membrane potential. A spike occurs whenever the membrane potential
exceeds a threshold level, and the refractive period is
achieved by elevating the threshold immediately after a spike and
allowing it to decay back to its original value. Second, layers of
these integrate-and-fire neurons were interconnected in ways consistent
with the known numeric ratios of cells, the geometry of the
projections, and the divergence/convergence ratios of connections between cell types (Fig. 1) (Eccles et al., 1967; Ito, 1984). When
known, the individual properties of each type of simulated neuron and
its synapses were based on their cerebellar counterparts (Table 1)
(Shinoda et al., 1987; Midtgaard, 1992; Barbour, 1993; Gould et al.,
1993; Llano and Gerschenfeld, 1993; Puia et al., 1994; D'Angelo et
al., 1995; Mouginot and Gahwiler, 1995; Virginio et al., 1995; Lang et
al., 1996; Simpson et al., 1996; Vincent and Marty, 1996; Dieudonne,
1998; Kim et al., 1998). Third, on the basis of empirical evidence, two
classes of synapses were modifiable according to specific,
activity-dependent plasticity rules. The grPkj synapses
decreased in strength [long-term depression (LTD)] when active
during a climbing fiber input to the Purkinje cell and increased in
strength [long-term potentiation (LTP)] when active in the absence of
a climbing fiber input (Sakurai, 1987; Hirano, 1990; Salin et al.,
1996). As first suggested by Miles and Lisberger (1981), and supported
by theoretical work (Medina and Mauk, 1999), the second site of
plasticity involves LTD of mfnuc synapses during strong inhibitory
input from Purkinje cells and LTP during pauses in this strong
inhibition. However, for the present results, the specific rule
governing plasticity in the nucleus is not crucial as long as mossy
fiber synapses by themselves are strong enough to permit responding
during the expected decrease in Purkinje cell inhibition associated
with a lesion of the cerebellar cortex. Interestingly, although
evidence of LTP and LTD of these mossy fiber synapses is almost
nonexistent in the literature (Racine et al., 1986), a recent report
(Aizenman and Linden, 2000) has shown increases in the intrinsic
excitability of nucleus cells after repeated mossy fiber stimulation.
The results presented here would not be expected to differ if this form
of nonsynaptic plasticity were implemented, assuming that conditioning can lead to an increase in the excitability of the nucleus cells.
Events occurring during the simulations were based on the well
characterized relationship between the synaptic organization of the
cerebellum (Eccles et al., 1967; Ito, 1984) and Pavlovian eyelid
conditioning (Thompson, 1986; Thompson and Krupa, 1994; Mauk and
Donegan, 1997) (Fig. 1). Previous studies have demonstrated that
information about the CS and US is conveyed to the cerebellum via mossy
fiber (Steinmetz et al., 1985, 1988; Lewis et al., 1987) and climbing
fiber (McCormick et al., 1985; Mauk et al., 1986) inputs, respectively,
and that output of the cerebellum via the interpositus nucleus is
necessary for the expression of the conditioned responses (McCormick
and Thompson, 1984). This correspondence between eyelid conditioning
and cerebellar input-output pathways permits a relatively
straightforward representation of Pavlovian conditioning in a
simulation (Fig. 1). Presentation of the CS was simulated by altering
the background activities of a small number of mossy fibers inputs
(~4%) according to published recording data (Aitkin and Boyd, 1978)
(Fig. 1, MOSSY FIBER INPUTS). Similarly, applying a
transient excitatory input to the climbing fiber input simulated the
observed activation of these fibers in response to the presentation of
the US (Sears and Steinmetz, 1991) (Fig. 1, CLIMBING FIBER
INPUTS). Finally, based on evidence that stimulation of the
interpositus nucleus elicits eyelid movements and that these neurons
display increases in activity that precede and closely resemble the
eyelid response (McCormick and Thompson, 1984), increases in simulated
nucleus cell activity during the CS were taken as a measure of the
amplitude and timing of conditioned eyelid responses (Fig. 1,
NUCLEUS CELL OUTPUT).
Similar to what is observed during standard eyelid conditioning, when
trained in this way the simulations gradually acquired appropriately
timed conditioned responses over several hundred trials (see
Figs. 2, 4a). As observed in chronic recordings during eyelid conditioning in rabbits, nucleus cell activity did not increase
immediately after the onset of the CS; rather, the peak in activity
occurred just before the presentation of the US regardless of the
CS-US interval that was used during training (Fig.
2). As described in detail below, these
appropriately timed responses were produced in the simulation by a
combination of plasticity in both the cerebellar cortex and cerebellar
nucleus, which is consistent with results from previous studies on
eyelid conditioning and vestibulo-ocular reflex adaptation (Robinson,
1976; Perrett et al., 1993; Raymond et al., 1996; Mauk, 1997). The
simulations also produced extinction of conditioned responses when the
CS was presented in the absence of the US (data not shown).
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Figure 2.
Simulated response timing under different CS-US
intervals. The three traces show the average nucleus
activity for the last 100 trials of a 1000-trial simulation trained
with a CS-US interval of either 250 msec (black
trace), 500 msec (dark gray
trace), or 750 msec (light gray
trace). The timing is adaptive because regardless of the CS-US
interval being simulated, the peak of the response always occurs at the
time of presentation of the US (depicted by respective
color squares above each
trace).
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Although no unwarranted features were added to the simulations to
ensure that they learn with appropriate timing, they necessarily contain inaccuracies and omissions. Thus, rather than a precise emulation of the cerebellum, the simulations can be considered the
equivalent of a detailed and precisely specified working hypothesis of
cerebellar mechanisms that contribute to eyelid conditioning. Like all
hypotheses, the value of the simulation rests primarily with its
ability to generate empirically testable predictions. Next we examine
how the simulations accomplish response timing and then present results
from a lesion experiment that tests a corresponding prediction.
Within-trial differential conditioning sharpens
response timing
Response timing in the simulations arises from the following three
features: (1) the activity of granule cells varies throughout the
presentation of the CS such that the subsets of grPkj synapses that
are active at the beginning of the CS are somewhat different from those
active at the end (Fig. 3), (2)
conditioning results in increased inhibition of the nucleus cells by
Purkinje cells during the early parts of the CS, and (3) conditioning
also reduces the inhibitory action of the Purkinje cells during the
latter parts of the CS. Figure 4,
b and c, illustrates that as training proceeded,
simulated Purkinje cells acquired the ability to decrease their
activity late in the CS and to increase it early in the CS. The learned
decrease was caused by the induction of LTD in grPkj synapses active
late in the CS, during the US-related climbing fiber input to the
Purkinje cells. Similarly, the increase in Purkinje cell activity in
the simulation was produced by the induction of LTP in grPkj
synapses active during the early parts of the CS, when the reinforcing
climbing fiber input was not present. Interestingly, recent
recording studies from Purkinje cells during classical conditioning
have demonstrated the same unusual pattern of early-increase and
late-decrease in activity shown by our simulated Purkinje cells
(Hesslow and Ivarsson, 1994).
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Figure 3.
Sample histograms for simulated granule cells
during 500 presentations of a 1 sec CS (black
vertical bars). For reference, the
activity of each cell during the 100 msec preceding the CS is also
shown (gray vertical
bars). Some simulated granule cells showed increased
activity at some point during the presentation of the CS (ON
column). Other granule cells showed decreased activity
(OFF column). The histograms are arranged from
top to bottom and left to
right approximately according to the latency of the
maximum (ON column) or minimum (OFF
column) rate of activity. The ability of simulated granule
cells to fire at different times is a consequence of the dynamic
interactions between mossy fibers, granule cells, and Golgi cells that
produce complex patterns of granule cell excitation and/or inhibition
during the CS. These time-varying patterns of granule cell activity are
crucial in producing well timed conditioned responses because they
allow for differential learning at different times during the CS.
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Figure 4.
Changes in nucleus and Purkinje cell activity
during acquisition. a, Averaged responses from 10 100-trial training sessions are shown. The responses are depicted as
average nucleus cell activity during each 100-trial session. CS
presentation is indicated by the long
horizontal bar at the
bottom, with the US occurring at the end of the
CS. Over the course of 200-300 trials, the simulation acquires
the ability to elicit well timed responses. b, Example
activity of a simulated Purkinje cell during the acquisition of
responses is shown. The numbers on the
left indicate the training session from which the
response was taken. The short and long bars at
the bottom indicate presentation of the US and CS,
respectively (with the early and late periods used for the graph in
c indicated). The simulated cell's spontaneous activity is
~60 Hz, and before training it is relatively unchanged by a CS
presentation. As training proceeded, the Purkinje cells learned to
decrease their activity late in the CS and increase it early in the CS.
c, Training produced a gradual increase in Purkinje cell
activity early in the CS and a decrease late in the CS.
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Because Purkinje cells inhibit the nucleus cells that are responsible
for producing conditioned responses, our simulations suggest a way in
which the observed Purkinje cell activity could account for response
timing. The conditioned responses permitted by disinhibition of the
nucleus cells during the latter parts of the CS would be preceded by
periods in which conditioned responses are actively suppressed by
increases in simulated Purkinje cell activity. To examine further the
role played by increases in Purkinje cell activity during the early
parts of the CS, simulations were run under the artificial circumstance
in which LTP of grPkj synapses was disengaged during the CS. As
shown in Figure 5a, these
simulations learned at a comparable rate, but response timing was
abnormally broad because the simulated Purkinje cells could only learn
to decrease activity during the CS (Fig. 5b,c). Thus, these
simulation data suggest the hypothesis that the strong inhibition of
nucleus cells that results from learned increases in Purkinje activity suppresses responding early in the CS, thereby sharpening conditioned response timing.
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Figure 5.
The effects of training with LTP at the grPkj
synapses disengaged. The data shown parallel that of Figure 4.
a, As with the normal situation, the simulation learns
to respond, but the timing of the responses is inappropriately broad.
This reflects the inability to suppress responses early in the CS.
b, Activity in the simulated Purkinje cells reflects the
ability to acquire decreases in activity late in the CS without the
ability to increase responding early in the CS. c,
Average activity of the Purkinje cells during the early and late
periods of the CS is shown. The increase in activity early in the CS is
absent.
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Plasticity at mfnuc synapses is responsible for the
short-latency response observed after lesions of the cerebellar
cortex
The hypothesis presented in the last section suggests an
explanation for the effects on response retention observed after removal of the cerebellar cortex. Although the original lesion studies
focused on lobe HVI of the cerebellar cortex (see Fig. 9) and
reported variable effects on conditioned response acquisition and
expression (Yeo et al., 1984; Lavond et al., 1987), we have reported
previously reliable disruption of conditioned response timing after
lesions of the anterior lobe of the cerebellar cortex (see Fig. 9)
(Perrett et al., 1993; Garcia and Mauk, 1998). When made in previously
trained animals, these lesions produced conditioned responses that were
smaller in amplitude, had a fixed, short-latency onset, and could not
be modified with further training (see example in Fig.
6a). Similarly Figure
6b shows that after an extensive lesion (80% of Purkinje
cells were removed) of the simulated cerebellar cortex, the appropriate
timing of conditioned responses was abolished such that the onset and
peak of the response occurred immediately after the presentation of the
CS. In agreement with previously reported data, further training after
the lesion was incapable of restoring the appropriate timing of
conditioned responses (data not shown). Our simulations predict that
these seemingly unmodifiable short-latency responses
unmasked by lesions of the cerebellar cortex are a result of the LTP
that was induced in CS-activated mfnuc synapses during conditioning.
Apparently, these short-latency responses are not observed before the
lesion is made because the nucleus cells are being strongly inhibited
by the Purkinje cells during the early part of the CS (Fig.
4b,c).
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Figure 6.
Real and simulated effects of complete
disconnection of the cerebellar cortex. a,
Pharmacological blockage of cerebellar cortex output reduces the
amplitude and abolishes the timing of the conditioned responses.
Without the cortex, the responses display a short and relatively fixed
latency to onset that is independent of the prelesion timing of the
responses. b, Similar results are produced in the
simulations with removal of 80% of the Purkinje cells. As in Figure 4,
the short and long horizontal lines indicate
presentation of the US and CS, respectively.
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Predicted effects of partial lesions of the cerebellar cortex
In contrast to the relatively permanent effects of complete
lesions, the simulations make the unusual prediction that partial lesions of the cerebellar cortex should produce a characteristic pattern of postlesion responding that is neither permanent nor a simple
dilution of the full effect (Fig. 7).
Because the simulations predict that increased Purkinje cell activity
suppresses the tendency of the nucleus cell to respond early in the CS
(Fig. 4b,c), partial lesions should unmask short-latency
responses as well as spare a timed component (Fig. 7a).
Moreover, if there is sufficient learning capacity remaining in the
spared Purkinje cells, it should be possible with further training to
diminish the lesion-induced short-latency component. Indeed Figure
7c shows that after a partial lesion that removed 40% of
the simulated Purkinje cells, further training produced a large
increase in the activity of the remaining Purkinje cells during the
early parts of the CS. This increase resulted from additional LTP at
grPkj synapses spared by the lesion and active during the early
portions of the CS, when climbing fiber activity is being inhibited
below its normal level by the short-latency component of the
conditioned response. The additional inhibition from the Purkinje cells
was eventually able to counteract the excitation provided by the
simulated mossy fiber input to the nucleus, thus restoring the
prelesion timing of the conditioned response (Fig.
7a).
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Figure 7.
Real and simulated effects of partial lesions of
the cerebellar cortex. a, Effects on response timing
produced by removal of 40% of the simulated Purkinje cells. Each
trace is the average output of the simulated nucleus
cells over 20 trials. Labels on the left
indicate the session from which each response is taken. The bottom 12 sweeps represent the output of a previously trained simulation over the
two sessions before the lesion (Pre 10, Pre 9). The
remaining sweeps show response timing over six sessions of training
after the removal of 40% of the Purkinje cells. Initially, the
simulation produces responses with both well timed and short-latency
components. With additional training, the simulation restored the
ability to delay the responses appropriately. b,
Eyelid responses from a rabbit that received a small lesion in the
anterior lobe of the cerebellar cortex. The responses displayed the
postlesion pattern predicted by the simulations. The initial postlesion
responses show both short-latency and well timed components. With
additional postlesion training, response timing gradually recovered to
normal levels. c, The simulated activity of Purkinje
cells before and after the lesion. The responses of the Purkinje cells
are divided into early and late components as in Figure 4. Over the
initial acquisition period, the Purkinje cells learned to increase
activity early in the CS and decrease activity late in the CS. After
the lesion, the simulated Purkinje cells that were spared by the lesion
underwent additional learning, acquiring even more robust increases in
responding early in the CS. These increases are responsible for the
gradual decline of the short-latency component of the response and the
return to relatively normal response timing. d,
Parasagittal section showing the placement of the electrolytic lesion
for the animal whose data are shown in b. The
black arrow points to the damage in the
anterior lobe.
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Although the effects shown in Figure 7a are specific to a
lesion that removed 40% of the Purkinje cells, we conducted a detailed examination of the effects observed after lesions of different sizes.
In general, lesions that removed <20% of the cerebellar cortex had
little or no effect on the onset latency of the simulated conditioned
response. Lesions that removed 20-40% of the Purkinje cells decreased
the onset of the conditioned response, but the short-latency component
was smaller than that shown in Figure 7a. As the size of the
simulated lesion increased from 40 to 70%, the short-latency component
observed after the lesion increased in size, and more postlesion
training was required before the timing of the conditioned response was
restored. Finally, for lesions that removed >70% of the Purkinje
cells, the short-latency component could not be fully extinguished even
after prolonged postlesion training. Although it is not possible to
infer the precise size of the lesion from our histological analysis,
the range of effects displayed by lesions of 20-70% of our simulated Purkinje cells corresponded well with the range of behavioral effects
observed after the small electrolytic lesions discussed below.
Testing the predicted partial-lesion effect
We have tested these predictions by making small electrolytic
lesions of the anterior lobe of well trained rabbits. We focused on the
anterior lobe because, in contrast to the variable effects observed
after lesions of lobe HVI (Yeo et al., 1984; Lavond et al., 1987),
extensive lesions that included the anterior lobe have resulted
previously in reliable disruption of conditioned response timing
(Perrett et al., 1993; Perrett and Mauk, 1995). In many of these
animals, we observed the predicted pattern of postlesion responding.
Figure 7b shows the prelesion and postlesion responding of a
representative animal. Before the lesion this animal showed the
characteristic adaptively timed conditioned responses. The initial
responses after a small electrolytic lesion of the anterior lobe (Fig.
7d) show both short-latency and adaptively timed components.
Over the course of 6 d of postlesion training, response timing
gradually returned to near normal.
We observed this pattern of responding in a total of nine animals with
small lesions of the anterior lobe (Figs.
8, 9).
Although the lesions were not always successful in producing an effect, histological analysis revealed that for most of these failures, the
lesion did not affect the anterior lobe of the cerebellar cortex. Thus,
in only one case did we observe damage to the anterior lobe that failed
to produce a clear disruption in conditioned response timing (Fig. 9,
top left NO EFFECT example), and in no case did we observe damage that excluded the anterior lobe but resulted
in disrupted timing (Fig. 9). To make quantitative comparisons between
the simulated partial-lesion effects and the responding observed in the
nine rabbits, we made use of two measures of response timing. The first
measure is simply the latency to onset of the conditioned responses.
Figure 8a shows the changes in latency to onset for the
simulations and the nine rabbits. A one-way repeated measures ANOVA
indicated that the lesions produced a significant decrease in latency
to onset in the rabbits [F(12,96) = 6.146; p < 0.001]. Subsequent post
hoc analysis also showed that the rabbits displayed a
significant recovery in latency to onset over the 6 d of
postlesion training (Fig. 8a; days indicated by an * are
different from baseline, p < 0.05). Separate
t test comparisons for each half session reveal only two
points where the rabbit data differed significantly from the simulation
(Fig. 8a; indicated by  , p < 0.05 for a
t test between a mean and a population). The second measure
of response timing used was a ratio of early-response amplitude
(initial 200 msec of the CS) and late-response amplitude (during the
final 200 msec). Using this measure (Fig. 8b), a score of
1.0 indicates that the short-latency component was as large as the
adaptively timed component, whereas a score of 0.0 indicates that there
was no short-latency component. Figure 8b shows the similarity in the changes in this early/late ratio for simulated and
for rabbit responses. Both groups showed an increase in this ratio
after the lesion and then a gradual return to the prelesion value.
One-way ANOVA with repeated measures and subsequent post hoc tests revealed (1) a significant increase after the
lesions in rabbits [F(12,96) = 6.589;
p < 0.001], (2) a significant recovery over the
6 d of training (Fig. 8b; points indicated
by an * are different from baseline, p < 0.05), and
(3) no significant differences between rabbits and the simulations
(p > 0.05 for all time points). Raw traces for
two rabbits ordered according to early/late amplitude ratio during
different days are shown in Figure 8c, and the sample histology from four animals included in this study are shown in Figure
9.
View larger version (43K):
[in this window]
[in a new window]
|
Figure 8.
A comparison of simulated lesion effects with
group data from nine rabbits with small lesions of the anterior lobe of
the cerebellar cortex. a, Change in latency to onset of
the responses for the simulation (black
circles) and nine rabbits (gray
squares) during 6 d of postlesion training.
Top, How this response measure was calculated for two
sample traces. b, Same comparison as in
a for the ratio of the response amplitude early in the
CS versus that late in the CS. c, Sample raw
traces for two rabbits during the last training session
before the lesion (top traces) and during
the first (middle traces) and last
(bottom traces) sessions after the
lesion. For easy examination, the early period is shown in
black, and the traces have been arranged
from top to bottom according to the
decreasing early/late amplitude ratio. E, Early;
L, late.
|
|
View larger version (86K):
[in this window]
[in a new window]
|
Figure 9.
Examples of the electrolytic lesions from four of
the nine animals that showed a lesion effect (left; PARTIAL
EFFECT ) and from four of the animals in which the lesions
produced no effect (right; NO EFFECT). The
effective lesions shown on the left are from four of the
nine animals whose data are shown in Figure 8. For the effective
lesions, each section shows a parasagittal view ~5 mm lateral from
the midline. The gray arrow in the
top left histology shows the approximate
location of lobe HVI (emphasized by many eyelid-conditioning studies).
The black arrows show effective lesion
sites within the anterior lobe (the site associated with disruption in
conditioned response timing). For the ineffective lesions, the plane of
section is more variable, possibly indicating for some that the lesion
was placed too medial or too lateral.
|
|
| |
DISCUSSION |
We have shown that simulations based on the well characterized
synaptic organization of the cerebellum are able to emulate conditioning of properly timed responses. In the simulations, response
timing is produced not only by learning to respond at reinforced times
but also by learning to suppress responding at incorrect times. This
variant of Pavlov's inhibition of delay hypothesis predicts a complex
pattern of responding after a partial lesion of the cerebellar cortex.
An empirical test of this prediction using small, electrolytic lesions
of the cerebellar cortex revealed the pattern of responding predicted
by the simulations. Specifically, the initial postlesion responses
retained the properly timed component at reinforced times but also
showed a new, short-latency component at nonreinforced times. As
predicted by the simulations, further training then produced a decrease
in the short-latency component, nearly restoring the responses to their
original prelesion timing. In contrast to these partial-lesion effects,
complete lesions in the simulations reproduced previously published
data showing that extensive lesions of the anterior lobe of the
cerebellar cortex abolish response timing permanently, even after
extensive postlesion training (Perrett and Mauk, 1995).
The simulations suggest that proper response timing is produced by
three interacting factors. First, connectivity within the cerebellar
cortex produces slight variations in the subsets of granule cells that
are active at different times during the CS. This temporal code creates
the potential for differential responding at different times during CS.
Second, US-activated climbing fiber inputs induce LTD at grPkj
synapses active around the time of US presentation. This eventually
leads to decreased Purkinje cell activity during the CS, contributing
to a conditioned response via disinhibition of the nucleus cells.
Alone, this learning would promote relatively poorly timed responses
that are inappropriately broad. Thus, of equal importance for adaptive
response timing is the induction of LTP at grPkj synapses that are
active during the early parts of the CS. In the simulations this
extinction-promoting plasticity has two related consequences. It
reverses the induction of LTD at grPkj synapses that are equally
active at early and late periods of the CS. This helps sharpen the
timing of the response by delaying and decreasing the duration of the
learned pause in Purkinje cell activity. The induction of LTP at
grPkj synapses also allows the cortex to compensate for the learned
increase in strength of the mossy fiber synapses, whose activity is
quite strong just after CS onset. This latter learning produces
increases in Purkinje cell activity that strongly inhibit the nucleus
cells early during the CS presentation, also helping to delay the
conditioned response until the appropriate time. Thus, the simulations
support the idea originally proposed by Pavlov (1927) that adaptive
timing could be achieved by learning via extinction not to respond
early in the CS as well as by learning via acquisition to respond later in the CS when the US normally occurs.
The potential importance of these two processes is supported by the way
in which the behavior of the Purkinje cells in the simulations closely
resembles recordings of Purkinje cells during expression of conditioned
eyelid responses in ferret (Hesslow and Ivarsson, 1994). The simulated
Purkinje cells, like the Purkinje cells recorded by Hesslow and
Ivarsson, show an initial increase in activity just after CS onset
followed by a decrease that is delayed to produce an adaptively timed
response. Although this pattern of activity has not been seen in all
studies monitoring Purkinje activity during expression of eyelid
responses (Berthier and Moore, 1986; Gould and Steinmetz, 1994), these
authors have taken great care to ensure that the recordings were
obtained from the region of cerebellar cortex responsible for eyelid
movements (Hesslow, 1994).
The simulation results offer potential explanations for the effects
produced by both complete and partial lesions limited to the anterior
lobe of the cerebellar cortex. Although the effects observed after
lesions of lobe HVI of the cerebellar cortex have remained primarily
controversial (Yeo et al., 1984), previous studies showed that
extensive lesions of the anterior lobe of the cerebellar cortex abolish
response timing permanently and yield responses with short latencies
(see Fig. 9 for location of these lobes) (Perrett and Mauk, 1995). The
present simulation results suggest that the short-latency responses
seen after a complete anterior lobe lesion and the short-latency
component seen after a partial lesion are caused by the removal of
Purkinje cells that have learned, via the induction of LTP, to suppress short-latency responding encouraged by plasticity at the mfnuc synapses. In the case of a complete lesion, the short-latency responses
are relatively unchanged by subsequent training (Perrett and Mauk,
1995). In contrast, we have shown here that with small lesions limited
to the anterior lobe of the cerebellar cortex, the short-latency
component can be reversed. The simulation results suggest that this
compensation is possible as long as there is a sufficient number of
Purkinje cells remaining to permit learning of additional suppression
of the short-latency component.
The usefulness of a computer simulation is not necessarily related to
its ability to produce the proper output, because this can be
accomplished in a number of artificial ways. Instead, the goal of the
present simulations was to examine how adaptive timing of conditioned
responses arises naturally from realistic inputs via interactions
between the connectivity of the cerebellar network and bidirectional
plasticity at grPkj synapses. This seems in contrast to many
previous models that used hypothetical properties specifically designed
to accomplish timing. For example, models have used such artificial
properties as tapped delay lines (Moore et al., 1989), arrays of
CS-activated elements with different time constants (Bullock et al.,
1994), or arrays of CS-activated elements that oscillate at different
frequencies and phases (Gluck et al., 1990). Instead, our approach has
been to build simulations comprised of layers of integrate-and-fire
cells whose physiological properties are based on their cerebellar
counterparts. These neurons are interconnected according to the known
geometry of their projections and their divergence/convergence and
numeric ratios. In addition, all simulated cells displayed spontaneous
activity consistent with their known physiological firing frequencies,
and the activity of cerebellar inputs was based on existing recording
data. It is also important that the present results were not peculiar
to a particular set of parameters. Although the strength and time course of synaptic connections were carefully matched to
electrophysiological data whenever possible, it was still necessary to
stipulate values for a few relatively unconstrained parameters. We
found that the behavior of the simulations did not change qualitatively
across a wide range in these free parameters.
The current simulations represent a significant advance over a
less-sophisticated predecessor (Buonomano and Mauk, 1994). The previous
version was endowed only with LTD at the grPkj synapses and thus was
unable to learn to extinguish or suppress responses during
nonreinforced times. For the previous model there were also many more
free parameters related to synaptic conductances. To obtain response
timing these parameters were set in a way that made granule cell
activity vary considerably from one time step to the next. Although
this variation allowed responses with appropriately adaptive timing, it
also conferred the simulation with a fatal flaw. This tendency to
produce extreme variations in granule cell activity also made the
network very sensitive to the slightest variation or noise in the
CS-activated mossy fiber inputs. Indeed, this network could learn only
under the artificial circumstance of perfect trial-to-trial consistency
in the activity of the mossy fiber inputs.
In contrast, the present simulation, with its better-constrained
synaptic parameters and ability both to learn and to suppress responses, acquires properly timed responses with noisy mossy fiber and
climbing fiber inputs based on published recordings (Aitkin and Boyd,
1978; Sears and Steinmetz, 1991). By generating only slight variations
in granule activity during the CS, the network is much less affected by
noisy inputs. The capacity for learning to suppress responses at
nonreinforced times during the CS then sharpens response timing via a
process akin to Pavlov's inhibition of delay (Pavlov, 1927). Thus, our
approach has been to improve the simulation via the elimination of
errors of omission rather than by adding artificial features to make it
workerrors of commission. In doing so, the simulation has achieved a
level of realism sufficient not only to account for previous findings but also (1) to reproduce naturally the firing characteristics of key
cells and (2) to generate complex predictions that are then borne out
by experimental test.
| |
APPENDIX: BUILDING A COMPUTER SIMULATION OF THE CEREBELLUM |
Network connectivity
The connectivity of the cerebellar cortex was based on the neural
network implemented by Buonomano and Mauk (1994). Briefly, there were
104 granule cells, 900 Golgi cells, 600 mossy fiber inputs, 60 basket cells, and 20 Purkinje cells. In scaling
the network to computationally feasible dimensions, it was assumed that
the convergence/divergence ratios were more important than the cell
ratios. Thus, each granule cell received excitatory synaptic inputs
from two to six mossy fibers and inhibitory inputs from three Golgi
cells. Each Golgi cell received excitatory inputs from 100 granule
cells and 20 mossy fibers. Each basket cell received excitatory inputs
from 250 granule cells, and each Purkinje cell was contacted by 8000 granule cells and a single climbing fiber. All these connections were
randomly chosen from a pool of possible synapses given the known
geometry of dendritic spans and maintaining converge/divergence ratios
within an order of magnitude. In addition to the cerebellar cortex
circuitry described above, this simulation implemented the connectivity
of the cerebellar deep nuclei. Thus, the activity of six nucleus cells
represented the sole output of the simulation. Each of these output
cells received inhibition from 15 Purkinje cells and excitatory inputs
from 100 mossy fibers. Finally, the climbing fiber was inhibited by all
six nucleus cells. Consistent with anatomical and physiological
observations, the circuit was modeled as a closed loop in which the
Purkinje cells inhibit nucleus cells that inhibit the climbing fiber
providing input to the Purkinje cells (Miall et al., 1998; Voogd and
Glickstein, 1998).
Simulation of synaptic potentials
Synaptic current was given by:
|
(1)
|
where  syn scales synaptic strength,
Esyn is the synaptic reversal
potential, and gsyn(t)
gives the time course of the underlying conductance as expressed
by:
|
(2)
|
where the summation steps through all presynaptic inputs,
Si represents a spike in the
ith presynaptic input, wi is
the synaptic weight of the ith presynaptic input, and
 syn is the decay time constant for the
synaptic potential. Thus, synaptic currents were simulated with an
instantaneous rise and an exponential decay by summing all inputs of a
particular type into a single current that saturates at 1.0 and decays
at the rate of . The specific values for and
PSPmax (which gives a more intuitive measure of
maximum synaptic strength than does syn
used in the simulation have been summarized in Table 1.
These values were chosen on the basis of the wealth of
electrophysiological data that exists for cerebellar synapses (see
Table 1, References). In fact there were only two connections (the
mossy fiberGolgi cell and the nucleusclimbing fiber) for which
electrophysiological data are currently unavailable. For
the results presented here, we used prototype AMPA
conductance parameters for the mossy fiberGolgi cell synapse.
However, the conclusions that were drawn from the results did not vary
over a wide range of parameters for this connection as long as Golgi
cells fired at their known physiological rate of 10-50 Hz. The
parameters for the nucleusclimbing fiber synapse could also be
varied over a wide range without affecting the results. This is
because, as reported previously (Kenyon et al., 1998), this connection
is self-regulated via changes in the strength of modifiable
synapses to produce the slow background activity of climbing fibers
(~1 Hz).
Simulation of single neurons
All cells were simulated using a standard leaky integrate-and-fire
representation based on the idea expressed in Equation 3 that a
neuron's membrane potential is determined by summing synaptic and leak
conductances:
|
(3)
|
where the first term represents the contribution from the leak
conductance to the change in membrane potential and the second term
summates over all different types of synapses contacting the
postsynaptic cell. The only cells that were not represented in this way
were the mossy fibers. In the simulation, these input cells do not
receive any presynaptic inputs, and thus according to Equation 3 their
membrane potential would be stuck at Vrest = El. To simulate the observed range of
mossy fiber activity and the inherent variability in firing rate, we
depolarized each mossy fiber by an amount taken randomly in each time
step from a Gaussian distribution as indicated in Equation 4:
|
(4)
|
Each of the 600 mossy fibers could be assigned a preferred rate of
activity (range from 10 to 50 Hz) by assigning it a specific distribution mean.
The leaky integrate-and-fire implementation ignores the active membrane
properties of neurons, which are dependent on the presence of multiple
voltage- and time-dependent ionic currents. Because the detailed
voltage-clamp data that would be needed to specify these currents is
available only for a few cases, the specification of an appropriate set
of parameters would become primarily a matter of conjecture and subject
to error. Instead of requiring the specification of all these
parameters, the leaky integrate-and-fire neuron fires a spike whenever
the membrane potential exceeds a threshold level ( ). The relative
refractory period and spike accommodation were simulated by increasing
the threshold to a maximum value (max) after
each spike and allowing it to decay to its initial value with a time
constant given by  .
Simulation of plasticity
Two sets of connections were modifiable in our simulations. The
synapses between granule and Purkinje cells changed according to the
following equation:
|
(5)
|
where   gr =  0.00036 and
+gr = 0.00001 are constants that represent the
magnitude of the step decreases and increases in synaptic weight,
respectively, GRi is 1 whenever the ith granule cell fires and 0 otherwise, and CF(50) is 1 for
the 50 msec after a climbing fiber spike and 0 otherwise. Thus, the first term implements the well known rule for LTD by decreasing the
weight of the granule synapse by a constant amount when the granule
cell is active within 50 msec after a climbing fiber spike. The second
term implements LTP at this connection by increasing the weight of the
synapse when it is active in the absence of a climbing fiber input in
the previous 50 msec (Sakurai, 1987; Hirano, 1990; Salin et al., 1996).
The simulation also implements bidirectional plasticity controlled by
Purkinje cell activity at the mossy fiber to cerebellar nucleus
synapse (Miles and Lisberger, 1981; Medina and Mauk, 1999). This
plasticity rule is given by the following equation:
|
(6)
|
where mf = 0.000001 and
+mf = 0.0002 are constants that represent the
magnitude of the step decreases and increases in synaptic weight,
respectively, and MFi is 1 whenever the
ith mossy fiber fires and 0 otherwise.
 LTDPKJ(50) is a binary parameter that equals 1 whenever the average Purkinje cell activity seen in the preceding 50 msec by the postsynaptic nucleus cell increases over a threshold value
(~80 Hz). Similarly, LTPPKJ(50) equals 0 except
when average Purkinje cell activity falls below a threshold value
(~40 Hz). The results did not depend on the precise threshold values
as long as LTD was induced during higher than normal inhibition of the
nucleus by the Purkinje cells and LTP was induced during lower than
normal inhibition. Synaptic weights were restricted to the interval
[0,1] by preventing further changes in the same direction when the
synaptic weights reached 0 or 1.
Simulation of eyelid conditioning
Because CS and US map onto the mossy fiber and climbing fiber
pathways, respectively (McCormick et al., 1985; Steinmetz et al., 1985,
1988; Mauk et al., 1986; Lewis et al., 1987), these stimuli were
simulated by altering the activity of these cells according to
empirical data. Mossy fibers are known to be strongly activated either
phasically or tonically (in a 3:1 ratio approximately) by tone stimuli
(Aitkin and Boyd, 1978) (Fig. 1). Thus, phasic mossy fibers were
simulated by randomly choosing 3% of the mossy fibers and increasing
the means of their Gaussian distributions (Eq. 4) for the first 20 msec
of the CS. In addition, the means for an additional 1% of the mossy
fibers (tonic mossy fibers) were increased for the whole duration of
the CS. Histograms for these inputs are shown in Figure 1. The activity
of the rest of the mossy fibers did not change during the CS. Although
the choice of 4% as the number of mossy fibers conveying information
about the CS is subject to judgment, we feel that it captures the idea that stimuli will not engage all the mossy fibers to the cerebellum but
rather must exist against a background of activity. In general, the
more mossy fibers that were engaged by the CS, the quicker learning
proceeded. Figure 1 also shows how the US activates the climbing fiber
pathway (Sears and Steinmetz, 1991). Thus, to simulate presentation of
the US, the climbing fiber was given a step-depolarizing pulse of
constant magnitude that lasted 20 msec. This pulse was enough to
produce a climbing fiber spike during the initial training trials.
However, as training proceeded and climbing fibers began to be
inhibited by the increased nucleus activity associated with the
conditioned response, the depolarizing pulse was not always successful
in producing a climbing fiber spike (Sears and Steinmetz, 1991).
| |
FOOTNOTES |
Received Feb. 15, 2000; revised April 27, 2000; accepted May 1, 2000.
This research was supported by National Institutes of Health Grants MH
57051 and MH 46904.
Correspondence should be addressed to Dr. Michael D. Mauk, Department
of Neurobiology and Anatomy, University of Texas Medical School, 6431 Fannin, Houston, TX 77030. E-mail: mmauk{at}nbal9.med.uth.tmc.edu.
| |
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ABSTRACT
INTRODUCTION
