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Volume 16, Number 11,
Issue of June 1, 1996
pp. 3760-3774
Copyright ©1996 Society for Neuroscience
Metabotropic Glutamate Receptor Activation in Cerebellar Purkinje
Cells as Substrate for Adaptive Timing of the Classically Conditioned
Eye-Blink Response
John C. Fiala,
Stephen Grossberg, and
Daniel Bullock
Department of Cognitive and Neural Systems, Boston University,
Boston, Massachusetts 02215-2411
ABSTRACT
INTRODUCTION
MATHEMATICAL MODEL
RESULTS
DISCUSSION
FOOTNOTES
REFERENCES
ABSTRACT
To understand how the cerebellum adaptively times the classically
conditioned nictitating membrane response (NMR), a model of the
metabotropic glutamate receptor (mGluR) second messenger system in
cerebellar Purkinje cells is constructed. In the model, slow responses,
generated postsynaptically by mGluR-mediated phosphoinositide
hydrolysis and calcium release from intracellular stores, bridge the
interstimulus interval (ISI) between the onset of parallel fiber
activity associated with the conditioned stimulus (CS) and climbing
fiber activity associated with unconditioned stimulus (US) onset.
Temporal correlation of metabotropic responses and climbing fiber
signals produces persistent phosphorylation of both AMPA receptors and
Ca2+-dependent K+ channels.
This is responsible for long-term depression (LTD) of AMPA receptors.
The phosphorylation of Ca2+-dependent
K+ channels leads to a reduction in baseline
membrane potential and a reduction of Purkinje cell population firing
during the CS-US interval. The Purkinje cell firing decrease
disinhibits cerebellar nuclear cells, which then produce an excitatory
response corresponding to the learned movement. Purkinje cell learning
times the response, whereas nuclear cell learning can calibrate it. The
model reproduces key features of the conditioned rabbit NMR: Purkinje
cell population response is timed properly; delay conditioning occurs
for ISIs of up to 4 sec, whereas trace conditioning occurs only at
shorter ISIs; mixed training at two different ISIs produces a
double-peaked response; and ISIs of 200-400 msec produce maximal
responding. Biochemical similarities between timed cerebellar learning
and photoreceptor transduction, and circuit similarities between the
timed cerebellar circuit and a timed dentate-CA3 hippocampal circuit,
are noted.
Key words:
classical conditioning;
nictitating membrane response;
cerebellum;
long-term depression;
metabotropic glutamate receptors;
AMPA receptors;
neural network
INTRODUCTION
The cerebellum is involved in the learned timing
of classically conditioned eye blinks. Maladaptively timed conditioned
responses (CRs) occur after cerebellar cortical lesions (McCormick and
Thompson, 1984 ; Perrett et al., 1993 ). Neural activity patterns in
cerebellar Purkinje cells and interpositus nuclear cells precede and
model the CR (McCormick et al., 1982 ; Thompson and Krupa, 1994 ). Direct
stimulation of mossy fiber inputs to the cerebellum can substitute for
external conditioned stimulus (CS) presentation, whereas direct
stimulation of the source of climbing fibers can serve as the
unconditioned stimulus (US) (Steinmetz et al., 1989 ). Classical
conditioning with direct brain stimulation results in an adaptively
timed CR and a correspondingly timed increase in interpositus activity
(Steinmetz, 1990b ).
A number of mechanisms have been proposed to explain timing of eye
blinks, including delay lines (Zipser, 1986 ; Moore et al., 1989 ), slow
responses in neurons (Grossberg and Schmajuk, 1989 ; Bartha et al.,
1991 ; Grossberg and Merrill, 1992 , 1996 ; Jaffe, 1992 ; Bullock et al.,
1994 ), and temporal evolution of the network activity pattern
(Chapeau-Blondeau and Chauvet, 1991 ; Buonomano and Mauk, 1994 ). Given
that eye blinks may be delayed for up to 4 sec after onset of the CS
(Gormezano, 1966 ), there do not seem to be delay lines of sufficient
length in cerebellar cortex (Freeman, 1969 ). Noise in network activity
pattern models seem to preclude their operation over these long
intervals as well (Bounomano and Mauk, 1994). The most likely candidate
mechanism is a slow neuron response. Given the above evidence that
timing occurs in cerebellar cortex and the fact that granule cells seem
to have only short latency responses (Thompson and Bower, 1993 ), the
simplest explanation is that slow responses in Purkinje cells are the
operative mechanism in adaptive timing. We hypothesize that Purkinje
cell slow responses are produced by activation of metabotropic
glutamate receptors (mGluRs) and that the latency of the mGluR response
spans the range of conditionable eye-blink interstimulus intervals
(ISIs).
Experimental study of metabotropic responses in Purkinje cells is
difficult. Slow excitatory postsynaptic potentials mediated by mGluRs
have been observed in some preparations (Batchelor and Garthwaite,
1993 ; Batchelor et al., 1994 ) but not in others (Miyakawa et al.,
1992 ; Midtgaard et al., 1993 ; Eilers et al., 1995 ). This difficulty may
be related to the fact that the endoplasmic reticulum (ER) is
reorganized rapidly in Purkinje cells after perfusion with artificial
media such that normal release of calcium from intracellular stores is
blocked (Takei et al., 1994 ). In the present study, the basic
hypothesis was tested by constructing a mathematical model of the mGluR
response in Purkinje cells. Simulations of the model demonstrate how
adaptive mechanisms within Purkinje cells can produce a temporal
regulation of the firing rate of these cells that times the
disinhibition of interpositus nuclear cells and thereby ``opens a
timed gate'' that enables gains learned at the nuclear stage to
modulate ongoing movements (Fig. 1). The model suggests
new experiments that can be used to test which metabotropic pathways
influence the learned timed response.
Fig. 1.
Basic neuronal circuitry of the cerebellum that
forms the basis for the present model of adaptive timing of eye blinks.
Inhibitory neurons, dark; excitatory neurons,
white. PC, Purkinje cell; BA, basket
cell; ST, stellate cell; GR, granule cell;
PF, parallel fiber; MF, mossy fiber;
CF, climbing fiber; N, cerebellar nuclear cell;
PN, precerebellar neuron that issues mossy fibers;
IO, inferior olive; CS, conditioned stimulus;
CR, conditioned response; US, unconditioned
stimulus.
[View Larger Version of this Image (24K GIF file)]
MATHEMATICAL MODEL
The biochemistry of adaptively timed cerebellar learning
The present work develops a model that links behavioral properties
of adaptively timed classical conditioning to the biochemistry and
biophysics of metabotropic glutamate responses in the cerebellum. A key
paradigm for studying cerebellar classical conditioning is the rabbit
nictitating membrane response (NMR). The NMR can be delay- or
trace-conditioned to an auditory, vibrotactual, or light CS (Gormezano,
1966 ). The CS usually is paired with a periorbital shock or air-puff
US. To reach the same level of performance, trace conditioning, in
which the CS terminates before US onset, requires five times as many
learning trials as delay conditioning, in which the CS and US overlap
in time. Asymptotic performance levels of 95-98% CRs can be obtained
within three or four delay-conditioning sessions, each consisting of
50-60 CS-US pairings with an ISI of 250 msec and an intertrial
interval of 1 min. The amplitude of individual CRs is correlated
positively with the frequency of CRs. The more generic term
strength of CR is used to refer to either amplitude of
individual CRs or CR frequency.
An individual CR has a distinctive topography with a number of
timing-related properties. The CR is timed adaptively such that the
peak amplitude occurs near the expected onset of the US. CR onset is
smooth, such that the CR onset typically occurs much before expected
onset of the US. The CS must precede the US by more than 50 msec for
successful conditioning (Smith et al., 1969 ). The onset of the CS can
precede the US by up to 4 sec in delay conditioning (Gormezano, 1966 ),
whereas trace conditioning cannot be obtained when the CS precedes the
US by >2 sec (Solomon et al., 1986 ). The strength of the CR depends on
the ISI, the time between onset of CS and onset of US, in a
characteristic way. CR strength is maximal at ISIs of 200-400 msec and
is reduced at shorter or longer ISIs (Smith et al., 1969 ). This
property traditionally is referred to as the inverted-U
property of the CR. The strength of CRs diminishes more quickly as a
function of long ISIs for trace versus delay conditioning.
When the NMR is conditioned to a particular ISI1,
such that the peak response occurs at that time, continued conditioning
to a different ISI2 will produce a discrete peak
shift in which the response peak at ISI1
diminishes and a new response peak grows at ISI2
(Coleman and Gormezano, 1971 ). Alternating between two different ISIs
during training with a single CS will produce a double-peaked CR (Fig.
2), each peak coincident with one of the ISIs (Hoehler
and Leonard, 1976 ; Millenson et al., 1977 ).
Fig. 2.
NMRs after mixed ISI delay conditioning. Group
200F received all 200 msec ISI trials. Group P n/8 received
mixed trials in a ratio of n 200 msec to 8 n
700 msec ISI trials. Group 700F received all 700 msec ISI trials. As
shown in the right-hand column, 700 msec CS test trials
result in double-responding. (Reprinted with permission from Millenson
et al., 1977 .)
[View Larger Version of this Image (25K GIF file)]
The cerebellum has been posited as a locus of conditioned NMR timing
(Perrett et al., 1993 ). A properly timed neural expression of the CR
occurs in the interpositus nucleus of the cerebellum, as revealed by
electrophysiological recordings (McCormick et al., 1982 ; Steinmetz,
1990b ). Interpositus neurons exhibit a firing pattern that resembles
the conditioned NMR topography; however, interpositus responses precede
the NMR by 50 msec or more (Thompson and Krupa, 1994 ). Such a temporal
precedent is required if the interpositus is the originator of the
response and the slow muscle-plant system is to produce eyelid closure
that peaks at US onset (Bartha and Thompson, 1992a ,b).
Direct stimulation of inputs to cerebellum can substitute for external
CS presentation during conditioning of an adaptively timed response in
the cerebellum. An auditory CS (tone) normally activates the cerebellum
via mossy fibers that originate in the pontine nuclei (Steinmetz et
al., 1987 ). Conditioning with direct stimulation of mossy fibers as the
CS results in properly timed CRs (Steinmetz et al., 1986 ). The ISI may
be as long as 2000 msec or as short as 100 msec, and CRs may peak near
the time of the expected US (Steinmetz, 1990a ). Interpositus expression
of the CR has the same timing properties in conditioning with direct
brain stimulation as when peripheral stimulation is used (Steinmetz,
1990b ). This evidence suggests strongly that a delayed response to the
CS can be generated by the cerebellar network.
Earlier work has developed lumped neural models of how adaptive timing
of neural responses may occur. These models have successfully simulated
key properties of timed behavior and neural spiking and have given
credence to the hypothesis that adaptive timing is produced by
selective enhancement of certain responses from an entire
spectrum of responses distributed through time (Grossberg
and Schmajuk, 1989 ; Grossberg and Merrill, 1992 ). The present work has
used these model properties as a point of departure for interpreting
and modeling biochemical properties of Purkinje cells in the cerebellar
cortex that are consistent with the behavioral and neural data. In the
model, the CS activates mGLUR responses that are used for spectral
timing in eye-blink conditioning. The CS does this by activating mossy
fibers, which in turn activate granule cells whose parallel fibers
synapse on Purkinje cells (Fig. 1). The mGluRs are located just outside
of the synaptic junction with parallel fiber terminals (Nusser et al.,
1994 ).
Metabotropic response model
Purkinje cells of the cerebellar cortex express mGluRs of
the subtype mGluR1 (Fig. 3). Releases of glutamate from
parallel fiber terminals activate mGluR1 receptors by binding to the
receptor (Blackstone et al., 1989 ). The activated receptor binds the
G-protein/GDP complex, which promotes the exchange of GTP for GDP and
cleavage of the G-protein into and  components (Berstein et
al., 1992 ). The G component of the G-protein
diffuses to phospholipase C (PLC) in the cell membrane and enables its
enzymatic activity. Activated PLC
(PLC · G · GTP) catalyzes the
production of the second messengers inositol trisphosphate
(IP3) and diacylglycerol (DAG) from
phosphatidylinositol 4,5-bisphosphate (PIP2)
(Blackstone et al., 1989 ). IP3 diffuses through
the cytoplasm to the membrane of the ER. IP3
binds to receptors in this membrane (IP3R),
opening calcium channels and allowing Ca2+ to
flow into the cytoplasm. The rapid increase of the cytosolic calcium
concentration activates a Ca2+-dependent
K+ conductance, which leads to hyperpolarization
and a decrease in excitability (Khodakhah and Ogden, 1993 ).
Fig. 3.
Components of the metabolic transmission
pathway within a Purkinje cell dendrite. DAG,
Diacylglycerol; G, guanine nucleotide-binding protein;
glu, glutamate; mGluR1, metabotropic
glutamate receptor subtype 1; PKC, protein kinase
C; PLC, phospholipase C;
PIP2, phosphatidylinositol
4,5-bisphosphate; IP3, inositol
1,4,5-trisphosphate.
[View Larger Version of this Image (53K GIF file)]
The binding of glutamate to mGluR exhibits first-order kinetics with a
Hill coefficient of 1 and Kd of 0.296 µM (Thomsen et al., 1993 ). With the inclusion
of an inactivated state, the time course of mGluR activation is modeled
by:
|
(1)
|
and
|
(2)
|
where B is the concentration of bound, activated
receptor, Bmax is the concentration of
available receptors, and A is the concentration of
inactivated receptors; [glu] is the concentration of
glutamate to which the receptors are exposed as a result of CS input.
The calcium- and DAG-dependent protein kinase, protein kinase C (PKC),
regulates the inactivation of receptors and the G-protein-mediated
response (Nakanishi, 1988 ; Catania et al., 1991 ; Herrero et al., 1994 ;
Yarfitz and Hurley, 1994 ). Protein kinase C activity in the model is
given by the variable C (below).
Activated mGluRs stimulate the activation of G-proteins. The
rate of G-protein activation increases linearly with the concentration,
B, of activated receptors (Berstein et al., 1992 ). The
concentration of activated G-proteins is given by the variable
G:
|
(3)
|
The final term represents G-protein inactivation by PKC (Nestler
and Duman, 1994 ; Yarfitz and Hurley, 1994 ).
In addition to PLC activity dependent on the presence of activated
G-protein, cerebellar membranes contain a form of PLC activated by
cytoplasmic calcium (Mignery et al., 1992 ). The production of
IP3 by PLC is thus modeled by:
|
(4)
|
where I is the IP3 concentration.
Calcium-dependent PLC activity exhibits a steep dependence on calcium
with half-maximal activation in the range of 1-20
µM (Homma et al., 1988 ; Mignery et al., 1992 ).
Therefore we chose a Hill coefficient of 2 and
Kd of 20 µM for
this PLC activation:
|
(5)
|
DAG is produced in conjunction with IP3 by
PIP2 hydrolysis. Therefore the amount,
D, of DAG is given by:
|
(6)
|
PKC is activated by binding a calcium ion and DAG (Schwartz and
Kandel, 1991 ), as in:
|
(7)
|
IP3 binding to IP3R in
ER membrane is one-to-one with half-maximal binding at 100-300
nM (Joseph et al., 1989 ; Watras et al., 1991 ;
Missiaen et al., 1994 ). Assuming that this reaction is fast compared
with other reactions in the model yields as a formula for the fraction
of bound receptors:
|
(8)
|
IP3 binding is required to open the
IP3R calcium channels and release calcium into
the cytosol, but channel opening also demonstrates a biphasic
dependence on the cytosolic concentration of calcium (Joseph et al.,
1989 ; Iino, 1990 ; Bezprozvanny et al., 1991 ). A similar biphasic
calcium dependence is seen in the ryanodine-sensitive calcium channels
of endoplasmic and sarcoplasmic reticulum (Meissner et al., 1986 ;
Bezprozvanny et al., 1991 ). A fragmentary sequence homology between the
ryanodine receptor (RyR) and IP3R underlies the
functional similarities of these channels (Furuichi and Mikoshiba,
1995 ). RyR and IP3R contain at least two types of
binding sites for Ca2+ or
Ca2+-activated proteins, one stimulating channel
opening and another inhibiting it (Chen et al., 1992 ; Chen and
MacLennan, 1994 ).
We model IP3R kinetics with six states:
Here,
{S2,S5}
represents the receptor with Ca2+ bound to the
stimulating site and
{S3,S6}
with Ca2+ bound to the inhibitory site. The
cooperativity of the later binding produces a Hill coefficient of
n = 1.65 (Meissner et al., 1986 ). By considering
IP3 binding to be at equilibrium with respect to
the Ca2+ binding reactions, the channel kinetics
are described by two differential equations:
|
(9)
|
|
(10)
|
The channel open state is Ro,
and Ri is the channel inhibited (closed) by
calcium binding. At steady state, the open probability is:
|
(11)
|
With proper choice of parameters, this model is in agreement with
the open probability data of Bezprozvanny et al. (1991) , as shown in
Figure 4.
Fig. 4.
Open probability of IP3R in
model (dashed line) and in experiments with
IP3R reconstituted into planar lipid bilayers
(Bezprozvanny et al., 1991 ) in the presence of 2 µM IP3. Normalized from
maximum open probability of 15%. Model parameter values:
Rmax = 1, k13/k12 = 0.81, k15/k14 = 0.0556, n = 1.65.
[View Larger Version of this Image (13K GIF file)]
As depicted in Figure 3, the cytoplasmic calcium concentration in
Purkinje cells is regulated by two transport systems, a Na/Ca exchanger
in the plasmalemma (Staub et al., 1992 ) and a
Ca2+-ATPase pump in the reticular membrane (Villa
et al., 1991 ; Takei et al., 1992 ). The exchanger has a low affinity for
cytosolic Ca2+ (1-10 µM)
but a high capacity, whereas the ATPase pump has a smaller capacity and
a much higher affinity (0.2 µM) (Yamada et al.,
1989 ). The ATPase pump in reticular membrane exhibits a cooperativity
of two calcium ions per transfer (De Meis and Inesi, 1982 ), and the
calcium flux thus can be characterized by a Hill equation of the
form:
|
(12)
|
The exchanger is at equilibrium when (Carafoli, 1987 ):
|
(13)
|
where ext denotes extracellular ion
concentrations, V is plasma membrane potential, F
is the Faraday constant, R is the gas constant, and
T is thermodynamic temperature. Assuming the other ionic
concentrations are relatively constant, the Ca2+
flux produced by the exchanger is proportional to (Hodgkin and Nunn,
1987 ):
|
(14)
|
where c0 is the equilibrium
concentration, above, and 2 µM is the
half-activation point.
Therefore, by Equations 9, 10 and 12, 13, 14, the cytoplasmic calcium
concentration can be described by:
|
(15)
|
We assume that calcium flux into the cytoplasm from the
ER does not produce a significant change in the concentration of free
Ca2+ in the lumen. Although the concentration of
free Ca2+ in ER is not known, total calcium is in
the range of 4-10 mM (Baumann et al., 1991 ).
The intracellular calcium response affects the Purkinje cell membrane
potential. Two conductances are principally involved: a
depolarizing conductance attributable to the electrogenic nature of the
Na/Ca exchanger (Glaum et al., 1992 ; Staub et al., 1992 ) and a
hyperpolarizing Ca2+-dependent
K+-conductance (Fagni et al., 1991 ; Khodakhah and
Ogden, 1993 ). Because adequate data on the
Ca2+-dependent
K+-conductance in Purkinje cells are not
available (De Schutter and Bower, 1994a ), our model is derived from
data on the mGluR-activated Ca2+-dependent
K+-conductance in cultured cerebellar granule
cells (Fagni et al., 1991 ).
As shown in Figure 5A, the dependency of open
probability on voltage follows the Boltzmann relation with an
e-fold change in Po per 22.5 mV.
The half-activation values (V0) of this
equation vary linearly with the log of the cytoplasmic calcium
concentration. Fitting a straight line to the data of Figure
5A gives:
|
(16)
|
where voltage is given in millivolts and calcium concentration in
micrometers. (A similar relation holds for
Ca2+-dependent K+ channels
in other preparations; Bielefeldt and Jackson, 1994 .) Combining this
result with the Boltzmann relation gives an expression for channel
opening in terms of calcium concentration and membrane potential (Fig.
5B):
|
(17)
|
The reversal potential of Purkinje cell potassium channels is
~ 85 mV (De Schutter and Bower, 1994a ). Thus, incorporating the
calcium-driven plasma membrane currents attributable to Equations 14
and 17, membrane potential is:
|
(18)
|
where is the peak conductance of the
Ca2+-dependent K+ channel.
This conductance is modulated through conditioning, as described in the
next section.
Fig. 5.
A, Voltage and calcium dependencies of
the mGluR-activated Ca2+-dependent
K+ channels of cultured cerebellar granule cells.
(Reprinted with permission from Fagni et al., 1991 .) B,
Equation 17 plotted as a function of voltage for various cytoplasmic
calcium concentrations.
[View Larger Version of this Image (16K GIF file)]
The baseline membrane potential, Vb,
is used to set an approximate level of tonic activity. It has been
observed (De Schutter and Bower, 1994b ) that a resting potential of
~ 68 mV as commonly seen in Purkinje cells in vitro gives
rise to a quiescent state in which there is little or no tonic
simple-spike activity. Purkinje cells in vivo, on the other
hand, have a continual background level of parallel fiber activity,
which gives them a more depolarized resting potential of ~ 50 mV.
This elevated baseline potential gives rise to a state of tonic
simple-spike firing. We assume that Vb = 50mV, such that when the mGluR activation raises intracellular
calcium levels, a net increase or decrease in simple-spike firing rate
is produced on the basis of whether the Na/Ca exchange- and
Ca2+-dependent K+-currents
depolarize or hyperpolarize the cell.
Learning model
The processes hypothesized to mediate learning in the present
model are depicted in Figure 6, which shows how climbing
fiber and parallel fiber signals (top) can affect receptors
(bottom) that control transmembrane current. The hypothesis
is primarily based on evidence for long-term depression (LTD) of AMPA
receptors at the parallel fiber-Purkinje cell synapses (Ito, 1991 ; Ito
and Karachot, 1992 ). LTD is a result of phosphorylation of AMPA
receptors, but there are additional substrates for phosphorylation that
also affect the Purkinje cell response, especially the metabotropic
response component, as described below.
Fig. 6.
Processes mediating learning of a timed
response in cerebellar Purkinje cells. AMPA,
Amino-3-hydroxy-5-methyl-4-isoxazole propionic acid-sensitive glutamate
receptor; cGMP, cyclic guanosine monophosphate;
DAG, diacylglycerol; glu, glutamate;
GC, guanylyl cyclase; gK,
Ca2+-dependent K+ channel
protein; GTP, guanosine triphosphate;
IP3, inositol 1,4,5-trisphosphate;
NO, nitric oxide; NOS, nitric oxide synthase;
P, phosphate; PLC, phospholipase C;
PKC, protein kinase C; PKG, cGMP-dependent
protein kinase; PP-1, protein phosphatase-1. NOS is probably
not localized in Purkinje cell, as discussed in text.
[View Larger Version of this Image (19K GIF file)]
Stimulation of the mGluR1 receptor activates PKC by the
production of DAG and the release of Ca2+
intracellularly (Nishizuka, 1986 ). PKC activation is necessary for
induction of LTD of AMPA receptors (Linden and Conner, 1991). The
mGluR1 receptor must be present (Aiba et al., 1994 ; Shigemoto et al.,
1994 ) and activated (Linden et al., 1991 ; Daniel et al., 1992 ; Hartell,
1994 ) for LTD to occur; however, Kasono and Hirano (1995) reported
recently that an intracellular IP3 increase in
conjunction with AMPA-receptor activation and depolarization is
sufficient for LTD. Blockage of IP3 binding to
IP3R (Kasono and Hirano, 1995 ) or blockage of the
intracellular Ca2+ rise (Sakurai, 1990 ; Konnerth
et al., 1992 ) prevents LTD. Therefore, it seems that the metabotropic
second messenger responses in the parallel fiber-activated pathway are
important for LTD induction.
Climbing fiber stimulation is the second pathway involved in LTD.
Climbing fiber activation strongly depolarizes the Purkinje cell and
produces Ca2+ spiking and plateau potentials in
the dendrites (Llinás and Sugimori, 1992 ). It has been proposed
that the influx of Ca2+ into the Purkinje
cell from the extracellular media after climbing fiber activation was
directly responsible for LTD (Ito, 1984 ; Linden et al., 1995 ), but an
alternative explanation is that the Ca2+ spiking
provides a means to ensure sufficient depolarization to activate nitric
oxide (NO) synthase in the terminals of basket and stellate
interneurons (Ito and Karachot, 1992 ; Linden and Conner, 1993). The
axons of basket and stellate cells climb along the dendrites of
Purkinje cells, often in close proximity with climbing fibers (Palay
and Chan-Palay, 1974 ). Activation of NO synthase produces a rise in NO,
which permeates the membranes of Purkinje cells. NO elevation is
essential for the production of LTD and for concomitant motor learning
(Crepel and Jaillard, 1990 ; Ito, 1991 ; Shibuki and Okada, 1991 ).
Cerebellar Purkinje cells are replete with components of the cGMP
system. Purkinje cells possess abundant guanylyl cyclase (Bredt et al.,
1990 ). Elevated NO levels stimulate guanylyl cyclase to produce cGMP
from GTP (Nestler and Duman, 1994 ). Purkinje dendrites also contain
high levels of a Ca2+/calmodulin-dependent
phosphodiesterase, which hydrolyzes cGMP (Nestler and Duman, 1994 ).
High levels of cGMP-dependent protein kinase (PKG) in the brain are
found only in cerebellar Purkinje cells (Nestler and Greengard, 1984 ).
The principal substrate for PKG is G-substrate, a protein found only in
Purkinje cells of the cerebellum (Nestler and Greengard, 1984 ).
Climbing fiber stimulation may be replaced by cGMP application in the
induction of LTD (Ito and Karachot, 1992 ; Shibuki and Okada, 1992 ).
Elevated cGMP levels activate PKG, which phosphorylates G-substrate.
Phosphorylated G-substrate inhibits protein phosphatase-1 (PP-1) (Ito
and Karachot, 1992 ). Application of an exogenous protein phosphatase
inhibitor, such as calyculin or microcystin-LR, can also substitute for
climbing fiber activation in LTD induction (Ajima and Ito, 1995 ). PP-1
dephosphorylates two target proteins, the AMPA receptor (Ito and
Karachot, 1992 ), and the Ca2+-dependent potassium
conductance, gK (Reinhart and Levitan,
1995 ). Dephosphorylation of G-substrate is produced by calcineurin, a
Ca2+-activated protein phosphatase (King et al.,
1984 ). Phosphorylation of AMPA receptors underlies the LTD of
AMPA-mediated EPSPs (Ito and Karachot, 1992 ). An increase in the open
probability of Ca2+-dependent
K+ channels in plasma membrane is produced by
phosphorylation of these proteins by PKC (Baraban et al., 1985 ;
Reinhart and Levitan, 1995 ). Thus, simultaneous activation of PKG
and PKC will result in a persistent phosphorylation of the target
proteins. Interestingly, behavioral learning in
Drosophila (Griffith et al., 1994 ) and
Hermissenda (Alkon, 1984 ; Nishizuka, 1986 ) is also dependent
on phosphorylation of Ca2+-dependent
K+ channels.
In summary, learning in the present model is based on the
hypothesis that a robust and maintained level of phosphorylation of
specific target proteins is obtained by an increase in the
mGluR1-mediated Ca2+ and DAG signals, coincident
with an increase in cGMP through the climbing fiber pathway. Note that
this assumes that substantial increases in cytoplasmic free
Ca2+ in spines are not induced by climbing fiber
activation under normal conditions. It is likely that spine heads are
insulated from these Ca2+ increases by the
activity of inhibitory interneurons (Callaway et al., 1995 ). Extinction
of the learned response results from dephosphorylation produced by
activation of the mGluR pathway alone, without a coincident climbing
fiber signal. We model this learning process as follows, with a system
that avoids unnecessary details of the processes depicted in Figure
6.
A climbing fiber burst produces a rapid increase in [cGMP] followed
by an exponential decay. We describe this signal by a dual exponential
function:
|
(19)
|
where 1 and 2
are the decay and rise-time constants, respectively. Each conditioning
trial starts with CS onset at t = 0. The onset of the US
occurs at t = s.
The Ca2+-dependent activation of calcineurin
involves multiple calcium/calmodulin binding sites on the regulatory
subunit of the enzyme and exhibits a Hill coefficient of 3 (Burroughs
et al., 1994 ; Stemmer and Klee, 1994 ). Thus, the level of activated
calcineurin, N, is described by:
|
(20)
|
Learning can now be expressed as change in , the
peak conductance for the Ca2+-dependent
K+ channel:
|
(21)
|
Because our model proposes that the learned Purkinje response
topography arises primarily from the interaction between the
metabotropic pathway and the Ca2+-dependent
K+ channel, the phosphorylation of AMPA receptors
and their individual responses were omitted from the present
simulations (see Discussion). We note, however, that if an equation
analogous to Equation 21 governs AMPA
dephosphorylation/phosphorylation, then climbing fiber-parallel fiber
coincidence would produce AMPA receptor LTD and parallel fiber activity
alone would produce AMPA receptor LTP, consistent with data of Sakurai
(1988) and Hirano (1990) .
Modeling and parameter assumptions
To simplify numerical simulation of the model, only three
compartments are considered with respect to chemical concentrations at
a given site: extracellular, cytosol, and lumen of the ER.
Extracellular and reticular Ca2+ concentrations
are assumed constant and uniform, relative to cytoplasmic
concentrations. Within the cytoplasmic compartment, all points are
considered to have the same concentration; that is, the temporal delays
produced by diffusion are ignored. This is reasonable for the present
simulations because diffusional delays in this second messenger pathway
are only 10-20 msec (Lamb and Pugh, 1992 ), a tiny fraction of the
expected overall response time.
The CR expressed at the interpositus is influenced by a number of
Purkinje cells distributed in the cortex. Thus, there are multiple
mGluR response sites that contribute to the behavioral response. For
simulation purposes, we consider 10-60 such sites, as described below.
Each site was simulated by an identical set of equations (1-21) with
identical parameters except for Bmax, which
was varied over a range. This range of values was selected to produce
responses in the observed behavioral response range of ~0.1-4 sec.
Although the variation in the number of mGluR receptors in cerebellar
response pathways is not known, this assumption seems reasonable,
because this kind of variation is seen in other cell preparations. For
example, neuroblastoma cells exhibit different individual
[Ca2+]cyt response
latencies (range, 0.4-20 sec) after carbachol application (Wang et
al., 1995 ). Because the carbachol concentration was always the same in
these experiments, latency variation is produced by variation in the
number of metabotropic receptors.
Simulations were performed on a 486-based computer, using a
fourth-order Runga-Kutta algorithm with a step size in the range of
0.0005-0.002 sec. Simulations used the parameters given in Table
1. Hill coefficient, ion concentration, and dissociation
constant values were taken from the literature, where possible. Other
parameters were fit to published data in cases where such data were
available, such as with IP3R kinetics. The
results are not particularly sensitive to any given parameter value.
Values near the given values produce the same qualitative results.
RESULTS
Response to mGluR activation
As shown in Figure 7A, activation of
mGluR by glutamate results in a rise in intracellular calcium
attributable to release from ER. The calcium response builds slowly as
IP3 accumulates, until the threshold for
activation of positive feedback is reached. The positive feedback of
calcium on IP3 production and on the
IP3R channel opening results in a rapid rise in
[Ca2+]cyt. As the calcium
level increases further, the biphasic nature of the
IP3R calcium dependency (Fig. 4) switches the
feedback from excitatory to inhibitory. Calcium release is thereby
terminated. The intracellular calcium level is returned quickly to the
resting level by the action of the calcium pump in ER membrane and the
Na/Ca exchanger in the plasma membrane. Because mGluR is inactivated
during the calcium transient, the IP3 levels also
return to baseline after the calcium transient. If the receptor
continued to activate G-proteins after the initial response,
intracellular calcium oscillations would develop, as observed in many
preparations (Berridge et al., 1988 ; Devor et al., 1991 ).
Fig. 7.
Model responses to mGluR activation. Parameters as
described in text, with [glu] = 10 µM,
Bmax = 1.5. A, Rise in
cytoplasmic calcium concentration after release from endoplasmic
reticulum. B, The plasma membrane potential driven by the
Na/Ca exchange current in the absence of
Ca2+-dependent K+ current
( = 0). C, The plasma membrane potential
change when both Na/Ca exchange current and
Ca2+-dependent K+ current
are present ( = 100).
[View Larger Version of this Image (9K GIF file)]
Because the Na/Ca exchanger is electrogenic, it will produce a
depolarizing membrane current from resting potential (Fig.
7B). The membrane depolarization produced by this current
may be responsible for the slow EPSPs observed in Purkinje cells after
activation of mGluR at the parallel fiber-Purkinje cell synapse, as
discussed below (Batchelor and Garthwaite, 1993 ; Batchelor et al.,
1994 ). When the Ca2+-dependent
K+ current is also activated by the intracellular
calcium transient, the net effect on the membrane potential can be
hyperpolarization rather than depolarization (Fig. 7C).
Thus, if the input to the Purkinje cell elevates its membrane potential
and establishes a certain rate of simple-spike firing, the firing rate
can be decreased from this level during the calcium transient by the
activation of the Ca2+-dependent
K+ conductance. This ``pause'' in Purkinje cell
firing will allow an increase in activity in the interpositus cells,
which govern the eye-blink response (Bullock et al., 1994 ). If the
Purkinje cell pause is made adaptive, then a mechanism for eye-blink
conditioning is realized.
Population response
Large quantities of glutamate are released presynaptically after
activation. It has been estimated that the postsynaptic concentration
of glutamate in the center of the synapse reaches levels >1
mM (Clements et al., 1992 ). Metabotropic
receptors, however, are located at the periphery of the synapse (Nusser
et al., 1994 ). This means that a much lower level of glutamate will
reach these receptors. This concentration at the periphery will exhibit
a slower decay than that in the synaptic cleft. Therefore, we assume
that in response to maintained parallel fiber firing of sufficient
frequency, the population of mGluR receptors at the synapse will be
exposed to a 10 µM level of glutamate.
Many of the G-protein-coupled receptor types use the second
messenger system involving PLC and IP3-mediated
calcium release (McGonigle and Molinoff, 1994 ). Responses mediated by
these receptors can exhibit a wide range of temporal latencies.
Serotonergic and muscarinic receptor responses can exhibit latencies of
a few seconds to >30 sec (Berridge et al., 1988 ; Devor et al., 1991 ).
The photoresponse attributable to activation of rhodopsin in the
invertebrate photoreceptor has latencies on the order of tens of
milliseconds (Fuortes and Hodgkin, 1964 ). The rapidity of the response
for a given receptor type is dependent on the level of G-protein
activation. This, in turn, is dependent on the level of activation of
receptors. Assuming a relatively constant glutamate level of 10 µM, latency of the response will be dependent
on the number of available receptors in the vicinity of the parallel
fiber synapse.
Thus, variation in the number of mGluR1 receptors,
Bmax, at different synapses produces
intracellular calcium responses with different latencies. Figure
8 demonstrates the effect of variation of
Bmax. A spectrum of calcium
responses spanning the behaviorally relevant interval for eye blinks of
~4 sec is created in Purkinje cells by choosing
Bmax in the range of 0.1-500. The
particular values used in generating a given spectrum are given in the
associated figure caption. No other parameters are varied in producing
these responses. The present model is thus a biochemically derived
variant of a spectral timing model (Grossberg and Schmajuk,
1989 ; Grossberg and Merrill, 1992 ; Bullock et al., 1994 ). The spectrum
of response times can be used to learn an adaptively timed eye blink,
as discussed below.
Fig. 8.
Spectrum produced by variation in
Bmax in response to sustained [glu]
concentration. Bmax = {360, 21, 4.7, 1.73, 0.97, 0.625, 0.458, 0.368, 0.315, 0.283, 0.261, 0.245, 0.236,
0.23, 0.226}; these receptor concentration values were chosen to give
approximately equally spaced responses spanning 4 sec. With a sustained
[glu] input, [Ca2+] spike response can be
observed out to ~5 sec if the Bmax
distribution is allowed to range down to 0.
[View Larger Version of this Image (24K GIF file)]
Although for purposes of simulation we assumed that the latency
variations are attributable wholly to a natural spectrum of
Bmax values, it is possible that variance
in other mGluR pathway components may contribute to generation of
different latencies. For example, variations in
IP3R density or in luminal calcium stores, which
affect the rate of mGluR-mediated Ca2+ release,
will affect response latency.
The model exhibits different calcium response properties to transient
versus maintained agonist concentrations. Although maintained parallel
fiber inputs produce a spectrum that spans 4 sec, a transient parallel
fiber activation of 50 msec duration admits only a spectrum spanning
~2 sec. This is because the dynamics engendered by a 50 msec stimulus
fail to generate a [Ca2+] spike in mGluR
pathways whose Bmax values are associated
with longer latencies. Figure 9 shows the spectral
response properties of the model to 50 msec parallel fiber activations.
This difference in the spectral properties of transient versus
maintained inputs is analogous to the differences in the maximal ISIs
for trace versus delay eye-blink conditioning (Smith et al., 1969 ;
Solomon et al., 1986 ).
Fig. 9.
Spectrum produced by variation in
Bmax in response to a 50 msec [glu]
application. Bmax = {360, 18, 6.5, 3.9, 3.18, 2.93, 2.87, 2.859, 2.858, 2.8579}; values within the indicated
range were chosen to give equally spaced responses. The value 2.585 is
the smallest Bmax for which the 50 msec
[glu] stimulus was sufficient to induce a
[Ca2+] spike in the mGluR pathway.
[View Larger Version of this Image (16K GIF file)]
Measurement of the potential of a population of Purkinje cells in slice
reveals a slow response after brief activation of parallel fibers
(Batchelor and Garthwaite, 1993 ; Batchelor et al., 1994 ). The response
has a slow rise-time, with a peak at 300-700 msec and a slow decay
over several seconds (Fig. 10A). The
response is observable in a bath of ionotropic glutamate and GABA
antagonists, which suggests that the response is mediated by mGluRs at
the parallel fiber-Purkinje cell synapses. This type of response is
the result of the summation of the individual signals in a spectrum,
such as that of Figure 8 or 9. Figure 10B shows the
summation of the potential changes produced by Na/Ca exchange current
in a heterogeneous population of mGluR response pathways. This
population signal, P(t), is computed by:
|
(22)
|
where N is number of response pathways,
Vi = (Vi Vb) is the mGluR-induced potential change
in a given pathway, is a constant scaling factor, and
Vb is the baseline resting potential of the
population.
Fig. 10.
A, Metabotropic glutamate response in
a slice population of Purkinje cells recorded using the three-chamber
grease-gap method. (Reprinted with permission from Batchelor and
Garthwaite, 1993 .) B, Model population response produced by
summation of spectral components in response to a 150 msec agonist
application at the arrow, with = 0.1, N = 60, Bmax = {360, 170, 100, 65, 42, 29, 21, 15.7, 12, 9.2, 7.2, 5.8, 4.7, 3.8, 3.15, 2.65, 2.25, 1.96, 1.73, 1.55, 1.4, 1.27, 1.15, 1.06, 0.97, 0.89, 0.82, 0.763, 0.706, 0.66, 0.625, 0.59, 0.555, 0.525, 0.5, 0.478, 0.458, 0.44, 0.422, 0.407, 0.393, 0.38, 0.368, 0.357, 0.347, 0.338, 0.33, 0.322, 0.315, 0.309, 0.303, 0.298, 0.293, 0.288, 0.283, 0.279, 0.275, 0.271, 0.267, 0.264}; values within the indicated range were chosen to give a
smooth population response. This distribution was used for all
results except those reported in Figures 8 and 9.
[View Larger Version of this Image (17K GIF file)]
As shown in Figure 10, even though the individual responses are
localized in time, the population signal is broad and smooth because of
distribution of the localized signals throughout a long interval. This
population response phenomenon also is seen in other
IP3-mediated response systems, such as histamine
receptors of HeLa cells (Bootman, 1994 ).
Conditioning
Given a CS-activated spectrum of responses distributed among a
population of response pathways, a US input can select spectral
components that will produce the desired behavioral response (Grossberg
and Schmajuk, 1989 ). In the present model, the CS is parallel fiber
activation of mGluRs, whereas the climbing fibers produce the [cGMP]
increase at US onset. Figure 11 shows the population
response during 36 pairings of a 600 msec CS and a 100 msec US. The CS
and US coterminate, such that the ISI is 500 msec. Note that the rate
of learning is accelerated from that observed in experiments to
decrease simulation time. Also, learning is asymptotic because of the
balance between CS-driven dephosphorylation and CS- and US-driven
phosphorylation. CS-driven dephosphorylation alone causes extinction of
the learned response.
Fig. 11.
Progress of model population response during 30 pairings of CS and US at an ISI of 500 msec. Initially, mGluR
activation produces a depolarizing response, but as learning
progresses, a timed hyperpolarization is realized. Spectral components
are the same as for Figure 10B.
[View Larger Version of this Image (16K GIF file)]
Those mGluR response pathways that have PKC activity at the time of
climbing fiber activation correlated with US onset exhibit a persistent
phosphorylation of Ca2+-dependent
K+ channels. This increases the peak conductance
of these channels in response to the intracellular calcium transient,
such that these pathways produce a more hyperpolarizing response after
repeated pairings. Thus, those Purkinje cells whose CS-activated mGluR1
pathway has a latency that approximates the ISI will exhibit a
progressive decrease in simple-spike firing during the CS-US interval.
Other Purkinje cells will exhibit increases in simple-spike firing in
the CS-US interval attributable to the depolarizing Na/CA exchanger as
well as the AMPA receptor input. Those cells exhibiting a decrease in
firing will realize a minimum firing rate near the expected time of US
onset. These characteristics are in agreement with in vivo
recordings of Purkinje cell activity during eye-blink conditioning
(Berthier and Moore, 1986 ; Thompson, 1990 ).
Interpositus nuclear cells receive input from a population of Purkinje
cells. Therefore, the population response shown in Figure 11 is
responsible for the observed CR-related activity in interpositus. In
agreement with recordings from interpositus (Fig. 12),
the population response peak occurs before the time of the expected US.
Both the latency of the response peak and the response onset latency
decrease during learning.
Fig. 12.
Average nictitating membrane movement
(top) and peristimulus histogram of interpositus nucleus
neural activity (bottom) during classical conditioning of a
rabbit with a 25 msec pontine stimulation as the CS and an air-puff
delivered 225 msec later as the US. (Reprinted with permission from
Steinmetz, 1990b .)
[View Larger Version of this Image (7K GIF file)]
The strength of the CR depends on ISI in a characteristic way. CR
strength is maximal at ISIs of 200-400 msec and is reduced at shorter
or longer ISIs (Smith et al., 1969 ; Steinmetz, 1990a ). By taking the
depth of the population response as a measure of CR strength, it is
possible to reconstruct the CR strength-ISI dependency curve produced
by the model. Figure 13 shows the curve for the model
in comparison with the experimental data obtained by Steinmetz (1990a) .
Strength of CR in the experiment is calculated as percentage CRs over
test trials. For the model, CR strength is calculated by the magnitude
of hyperpolarization below the baseline value of 50 mV. As shown in
the figure, the model reproduces the characteristic ISI dependency as
measured behaviorally.
Fig. 13.
Comparison of CR strength-ISI dependency curves
for the model and the behavioral data. Data of Steinmetz (1990a) is
normalized to 86% CRs. Model data are the magnitude of the learned
hyperpolarization below 50 mV, normalized to the amount of
hyperpolarization obtained at asymptote during training with an ISI of
250 msec.
[View Larger Version of this Image (17K GIF file)]
A spectral timing model is able to produce double-responding after
conditioning with two different ISIs in alternation. Figure
14 depicts the effect of conditioning with alternating
ISIs of 350 msec and 1000 msec. A double-peaked CR is produced with
peaks near the expected times of the US, and with the Weber law
property (compare Fig. 2) whereby the earlier peak is narrower and the
later peak broader. The figure also demonstrates extinction of a
learned response with repeated presentation of the CS alone.
Fig. 14.
Progress of population response during
first 10 extinction trials after 30 CS-US pairings with alternating
ISIs of 350 and 1000 msec. After conditioning, the 1100 msec CS2 is
used to elicit a double-peaked CR.
[View Larger Version of this Image (17K GIF file)]
Two sites of learning need to be considered in eye-blink conditioning:
cerebellar cortex and interpositus. Although the present model focuses
on learning in cortex, the result is compatible with an additional
learning site in the interpositus (Fig. 1). Learning at mossy fiber
synapses on nuclear cells can provide a learned gain that can be
expressed through the interpositus when Purkinje cell activity pauses.
In this way, learning at Purkinje cells opens a timed gate that enables
learned gains at the intracerebellar nuclei to control a movement at
the appropriate time. We have demonstrated previously that the
existence of this type of interpositus learning in conjunction with
cortical learning can explain the maladaptively timed CRs, which can
occur after cortical lesions (Bullock et al., 1994 ).
DISCUSSION
As described in the introduction, the most parsimonious
explanation for direct mossy fiber stimulation producing a timed
response in interpositus is that a timing function is present in the
cerebellum. The present model demonstrates that the
mGluR1-phosphoinositide hydrolysis second messenger system in
cerebellar Purkinje cells can perform a timing function, both in
maintaining a CS trace for association with a temporally remote US and
in the delayed onset of the CR.
The basic scheme of Figure 6 for control of phosphorylation has been
recognized for many years (Nestler and Greengard, 1984 , their Fig.
9.3). It is important to realize, however, that the cGMP signal that
increases levels of phosphorylation is antagonized by the parallel
fiber-mediated intracellular calcium signal, which decreases
phosphorylation. The fact that the cGMP signal corresponds to a US
signal, whereas the mGluR activation corresponds to a CS signal, makes
it clear that conditioning is obtainable only when activation of these
pathways occurs in temporal conjunction. Activation of the mGluR
pathway alone gradually reverses the effects of any previous
conjunctive activation.
LTD of AMPA receptors
Although the phosphorylation of AMPA receptors is not crucial to
behavioral learning in the model, it certainly has some bearing
in vivo. The exact role played by the AMPA receptor in
eye-blink conditioning remains an unresolved issue. It is not even
clear whether AMPA receptor activation is necessary for AMPA receptor
LTD (Linden et al., 1993 ). Nonetheless, it seems that the mechanisms
inducing AMPA receptor LTD are also responsible for behavioral
learning, possibly through the phosphorylation of
Ca2+-dependent K+ channels.
The fact that mGluR1 is critical for induction of AMPA receptor LTD
(Aiba et al., 1994 ; Shigemoto et al., 1994 ) motivates our hypothesis
that it is temporal correlation of the mGluR1-mediated second
messengers and the climbing fiber-evoked cGMP signal that produce
behavioral learning.
Aiba et al. (1994) reported loss of AMPA receptor LTD and diminished
but extant eye-blink conditioning in mice lacking mGluR1. Furthermore,
the eye blink seems to be timed correctly, although a detailed study
over various ISIs was not conducted. This would seem to argue that
mGluR1 is not involved in timing; however, another possible explanation
for this finding is that mGluR5, which also couples to phosphoinositide
hydrolysis, is able to partially replace mGluR1 functionally in the
mutant mice. The mGluR5 subtype is present in Purkinje cells of
immature rat brain (Abe et al., 1992 ), but during development is
normally supplanted by a proliferation of mGluR1 (Shigemoto et al.,
1992 ). To completely rule out a role for mGluR-mediated
phosphoinositide hydrolysis in timing, both subtypes would need to be
eliminated.
A recent report by Linden et al. (1995) demonstrates that activation of
the NO/cGMP pathway is not required for LTD in culture. It suffices to
depolarize Purkinje cells (3 sec of +10mV) significantly in conjunction
with application of glutamate. Kasono and Hirano (1994) found that the
depolarization can be replaced by an artificial elevation of
intracellular calcium to 6 µM in LTD induction.
Linden et al. (1995) reported that the LTD they observed is blocked by
PKC inhibitors but not inhibitors of PKG. According to the model of
Figure 6, a large enough
[Ca2+]cyt rise can evoke
LTD in the absence of cGMP. This is attributable to the fact that
calcium activates PLC, which produces DAG. The combination of high
levels of calcium and DAG could drive PKC phosphorylation beyond that
recoverable by baseline protein phosphatase activity. This can be
realized in Equation 21 by assuming nonzero resting levels of cGMP. Our
hypothesis, however, is that this situation is not occurring in
vivo. Both mGluR1-activated PKC and climbing fiber-activated PKG
must be present for LTD.
A possible role for AMPA receptor LTD could be to unblock the
mGluR-mediated response, which is inhibited by AMPA receptor
stimulation (Lonart et al., 1993 ). The mechanism studied by Lonart et
al. (1993) seems to involve AMPA activation of voltage-dependent
calcium channels and subsequent activation of a calcium-dependent
protein kinase. In the present model, significant calcium influx would
result in activation of calcium-dependent PLC and thus would invariably
stimulate, rather than inhibit, formation of IP3.
Therefore, LTD does not seem to unblock mGluR responses in the Purkinje
cell. The manner of interaction between mGluR and AMPA receptors in
cerebellar Purkinje cells awaits further investigation.
Purkinje cell and invertebrate photoreceptor
The biochemistry of the invertebrate photoresponse is similar to
the biochemistry of the Purkinje cell mGluR response. In the
invertebrate photoreceptor light activates rhodopsin. Activated
rhodopsin stimulates PLC through a G-protein (Yarfitz and Hurley,
1994 ), as described above for mGluR. In both invertebrate
photoreceptors and Purkinje cells, activated PLC catalyzes the
production of the second-messengers IP3 and DAG
from PIP2, and IP3
subsequently releases calcium from intracellular stores. The rapid
increase of the cytosolic calcium concentration in the invertebrate
photoreceptor activates a plasma membrane Na+
conductance, which produces a depolarizing photoresponse (Shin et al.,
1993 ). The specific mechanisms that activate this conductance in the
invertebrate photoreceptor are not well understood, but they may
involve Ca2+-stimulated increases in cGMP
(Bacigalupo et al., 1991 ; Richard et al., 1995 ).
The photoreceptor is a site of associative conditioning in marine
mollusks such as Hermissenda (Alkon, 1984 ; Crow, 1988 ).
Repeated pairings of light and rotation with a forward ISI results in a
persistent suppression of photokinesis in these animals (Matzel et al.,
1990 ). This behavioral change is affected by a modification of
voltage-dependent and Ca2+-dependent
K+ conductances within the photoreceptor (Alkon,
1986 ). Similarly, the Purkinje cell seems to play an essential role in
certain forms of classical conditioning. Our theory proposes that, like
the invertebrate photoreceptor, behavioral learning in the cerebellum
can be produced by persistent modification of a
Ca2+-dependent K+
conductance.
The biochemical cascade producing the invertebrate photoresponse is
designed to remain sensitive to light over a wide range of stimulus
intensities and durations. Weak signals are amplified and prolonged by
the positive feedback in the biochemical cascade. This amplification
results in a single absorbed photon opening 1000 plasma membrane
channels and eliciting a current transient of several nanoamps in
Limulus ventral photoreceptors (Nagy, 1991 ). The
photocurrent in response to a maintained stimulus is reduced through
negative feedback in the second messenger pathway, ensuring that a
transient photoresponse can be produced even at high background
intensities (Fuortes and Hodgkin, 1964 ). A similar mechanism seems to
occur in turtle cones (Baylor and Hodgkin, 1974 ) and has been modeled
by a Ca2+-mediated gating function (Carpenter and
Grossberg, 1981 ).
Our theory suggests that the Purkinje cell uses something very similar
to the robust signal transduction mechanism of photoreception for the
specialized purpose of forming associations between temporally
separated stimuli. In both cases, there is a functional need to respond
reliably to signals whose intensity and duration may vary over a wide
range. In the photoreceptor, this variation is attributable to changes
in photon density. In the cerebellar cortex, it is attributable to
variations in the number of convergent CS-activated cells. The
mechanisms in question may have evolved to improve the signal-to-noise
ratio in response to weak signals by amplifying and prolonging them
without losing sensitivity or temporal resolution to more intense
signals. Whether this relationship between Purkinje cell and
invertebrate photoreceptor represents convergent evolution or a true
homology is an open question. Homology is possible because associative
learning arises in the invertebrates and probably postdates the
evolution of photoreceptors, whereas cerebellar and Purkinje cells are
not found until the vertebrates, for which the cerebellum is virtually
a defining feature. Data on protochordates may be able to shed light on
this question.
Another link warranting exploration is with the dentate-CA3 circuit in
hippocampus, which exhibits adaptive timing (Hoehler and Thompson,
1980 ; Berger et al., 1986 ) and seems to use mechanisms on the circuit
level that are similar in many respects to those used here. Grossberg
and Merrill (in press) have discussed how the hippocampal circuit may
fit into a larger model neural architecture for timed reinforcement
learning, attention, and movement control through interactions between
the hippocampal system and cerebellum, among other brain regions. Taken
together, these functional similarities suggest that learned timing in
the cerebellum uses a specialized version of neural mechanisms that are
of much broader occurrence and functional significance.
FOOTNOTES
Received Oct. 18, 1995; revised March 1, 1996; accepted March 4, 1996.
This research was supported in part by the Advanced Research Projects
Agency (ONR N00014-92-J-4015) and the Office of Naval Research (ONR
N00014-92-J-1309 and N00014-95-1-0409) to J.C.F.; the Air Force Office
of Scientific Research (AFOSR F49620-92-J-0225), the National Science
Foundation (NSF IRI-90-24877), and the Office of Naval Research (ONR
N00014-92-J-1309 and N00014-95-1-0409) to S.G.; and the National
Science Foundation (NSF IRI-90-24877) and the Office of Naval Research
(ONR N00014-92-J-1309 and N00014-95-1-0409) to D.B.
Correspondence should be addressed to Professor Stephen Grossberg,
Department of Cognitive and Neural Systems, Boston University, 677 Beacon Street, Boston, MA 02215-2411.
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