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The Journal of Neuroscience, February 1, 2002, 22(3):1081-1097
Simulations of the Role of the Muscarinic-Activated
Calcium-Sensitive Nonspecific Cation Current
INCM in Entorhinal Neuronal Activity during
Delayed Matching Tasks
Erik
Fransén1,
Angel A.
Alonso2, and
Michael E.
Hasselmo3
1 Department of Numerical Analysis and Computer
Science, Royal Institute of Technology, S-100 44 Stockholm, Sweden,
2 Department of Neurology and Neurosurgery, Montreal
Neurological Institute and McGill University, Montreal, QC H3A Canada,
and 3 Department of Psychology, Program in Neuroscience,
and Center for Biodynamics, Boston University, Boston, Massachusetts
02215
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ABSTRACT |
Entorhinal lesions impair performance in delayed matching tasks,
and blockade of muscarinic cholinergic receptors also impairs performance in these tasks. Physiological data demonstrate that muscarinic cholinergic receptor stimulation activates intrinsic cellular currents in entorhinal neurons that could underlie the role of
entorhinal cortex in performance of these tasks. Here we use a network
biophysical simulation of the entorhinal cortex to demonstrate the
potential role of this cellular mechanism in the behavioral tasks.
Simulations demonstrate how the muscarinic-activated calcium-sensitive
nonspecific cation current INCM could provide a cellular mechanism for features of the neuronal activity observed during performance of delayed matching tasks. In particular, INCM could underlie (1) the maintenance of
sustained spiking activity during the delay period, (2) the enhancement of spiking activity during the matching period relative to the sample
period, and (3) the resistance of sustained activity to distractors.
Simulation of a larger entorhinal network with connectivity chosen
randomly within constraints on number, distribution, and weight
demonstrates appearance of other phenomena observed in unit recordings
from awake animals, including match suppression, non-match enhancement,
and non-match suppression.
Key words:
delayed match to sample; delayed non-match; stellate
cells; pyramidal cells; medial entorhinal cortex; afterhyperpolarization; working memory; biophysical modeling; computer
simulation; nonspecific cationic current
INCM
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INTRODUCTION |
Lesions of the entorhinal and
perirhinal cortices impair performance in delayed non-match to sample
(DNMS) tasks in both non-human primates (Zola-Morgan et al.,
1993 ; Leonard et al., 1995) and rats
(Otto and Eichenbaum, 1992). In delayed non-match to
sample tasks, stimuli are presented sequentially, and animals must
respond to a particular stimulus if that stimulus does not match the
previously presented stimulus. The role of the entorhinal cortex in
these tasks may involve activation of muscarinic cholinergic receptors, because performance in delayed matching tasks is impaired by systemic injections of muscarinic cholinergic antagonists (Bartus and
Johnson, 1976; Penetar and McDonough, 1983).
Encoding of stimuli in a recognition memory task is impaired by local
infusions of scopolamine into the perirhinal (and entorhinal) regions
but not by infusions into the dentate gyrus or inferotemporal cortex
(Tang et al., 1997), and microdialysis shows a 41%
increase in acetylcholine levels in the perirhinal cortex during
performance of this task (Tang and Aigner, 1996). Data
from slice preparations of entorhinal cortex demonstrate a possible
cellular mechanism for cholinergic modulation of entorhinal memory
function. In physiological recordings from layer II principal cells in
slice preparations (Klink and Alonso,
1997a,b),
application of the cholinergic agonist carbachol causes long-term
depolarizations, which have been termed plateau potentials. If neurons
generate an action potential during cholinergic modulation, because of
cholinergic depolarization or current injection, these neurons show
sustained spiking activity. Modeling presented here demonstrates how
plateau potentials and sustained spiking activity could arise from
muscarinic cholinergic activation of a calcium-sensitive nonspecific
cation current INCM for which in
vitro physiological data have been obtained (Klink and Alonso, 1997a,b; Magistretti et al., 2001) (J. Magistretti, L. Ma, M. H. Shalinsky, and A. A. Alonso, unpublished
observations). A current causing afterdepolarization also
appears in prefrontal cortical neurons, but shows voltage dependence
(Andrade, 1991; Haj-Dahmane and Andrade,
1996, 1998).
Simplified models of short-term memory capacity have been inspired by
these data (Lisman and Idiart, 1995; Jensen and
Lisman, 1996,
1998).
The INCM could provide a potential
mechanism for the selective maintenance of spiking activity in a subset
of entorhinal cortical neurons for working memory function in
behavioral tasks. Unit recording in awake behaving animals demonstrates
specific patterns of spiking activity occurring during performance of
delayed matching tasks (Suzuki et al., 1997;
Young et al., 1997). These include stimulus-selective
spiking activity during the delay period, enhancement of the spiking
response to stimuli that match the previously presented sample
stimulus, and resistance of sustained activity to distractors.
Simulations presented here demonstrate how these phenomena could
directly arise from INCM in individual
entorhinal neurons. In addition, a number of studies have shown match
suppression, in which spiking activity is weaker in response to a
stimulus that matches the previously presented sample (Suzuki et
al., 1997; Young et al., 1997), as well as
non-match enhancement and non-match suppression. Simulations of a large network with connectivity chosen randomly within constraints on number,
distribution, and weight demonstrate how these additional phenomena can
arise from network interactions of neurons with the intrinsic
properties provided by the INCM current. This work has been published previously in abstract form
(Fransén et al.,
1999b,
2000).
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MATERIALS AND METHODS |
The GENESIS simulation package (Bower and Beeman,
1995) was used to model intrinsic properties of neurons in
layer II of the entorhinal cortex. Separate compartmental biophysical
simulations were developed for layer II stellate neurons, layer II
pyramidal neurons, and layer II interneurons. The models used
Hodgkin-Huxley representations of a range of intrinsic currents that
underlie membrane potential changes in these neurons. The simulations
presented here focus on how acetylcholine causes sustained
depolarization and spiking activity in the pyramidal cells, and how
these phenomena might underlie sustained activity and match enhancement
during performance of delayed non-match to sample tasks (Young
et al., 1997). Additional network simulations demonstrate that
inclusion of inhibitory interneurons and inclusion of both
stimulus-specific and nonspecific cells provides potential mechanisms
for match suppression and non-match enhancement and suppression
(Suzuki et al., 1997; Young et al.,
1997).
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Cell and network models |
In these simulations, the entorhinal cortex layer II stellate
and pyramidal cells (Klink and Alonso, 1997c) and
interneurons (Jones and Buhl, 1993) have been reduced to
equivalent cylinder models.
Entorhinal layer II pyramidal cells
The properties of entorhinal pyramidal cells were simulated with
biophysical models containing multiple compartments, with an emphasis
on the calcium-sensitive nonspecific cation current INCM. The compartmental structure of these
simulations is shown in Figure 1. The
pyramidal cell is composed of six compartments, one representing the
soma, three representing the apical dendrite, one representing a basal
dendrite, and one representing all but one basal dendrite lumped
together, to constitute the main "load" to the soma. The proximal
of the apical compartments, the basal dendrite, and the lump
compartment are all connected to the soma. The lengths and cross
sections of the three apical dendrite compartments were adjusted to
give the dendrite a length constant of 2 (sealed-end condition). The
compartment profiles are found in Table
1. Simulations with just a soma
compartment and its conductances showed that dendritic compartments
were not necessary to obtain robust spiking activity during delay
periods in the cell. However, these dendritic compartments were
important for matching a range of features in the data, including spike
shape, afterhyperpolarization shape, and spike-frequency accommodation,
as well as providing a more realistic attenuation of excitatory
synaptic input.
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Figure 1.
Schematic representation of the compartmental
models used in the simulation of the intrinsic properties of entorhinal
neurons, including pyramidal cells (top), stellate cells
(middle), and interneurons (bottom). The
dimensions of each component of the model are summarized in the
figure.
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Passive properties. Simulations of the passive membrane
properties of the cell used the standard equivalent circuit
representation for each compartment (Bower and Beeman,
1995).
The passive parameters are as follows:
RM, 5.0  m2;
RA, 1.0 m;
CM, 0.01 F/m2. The
value of the membrane reversal potential Em
depends on contributions from leakage Na+ and
leakage Cl currents. (The K+
leak current is explicitly represented as a separate current.) One may
also view synaptic background activation with slow kinetics (e.g., NMDA
and GABAB) as part of the leakage current. Note that because the K+ current is represented separately,
its conductance should be added to the value of
RM given above when making comparisons with other data.
Active properties of pyramidal cells. The simulations
included multiple currents underlying the active properties of the
membrane, including both currents sensitive to changes in membrane
potential and currents sensitive to intracellular calcium
concentration. Equations describing the currents can be found in the
section on ionic currents; the respective conductances are found in
Table 4. The pyramidal cell model includes the following membrane
currents listed in the section on ionic currents (with the appropriate subsection listed in parentheses): the Na+ (Na) and
K+ (Kdr) currents
responsible for fast action potentials, a high-threshold Ca2+ current (CaL), a
calcium-dependent K+ current
(KAHP), a fast calcium- and
voltage-dependent K+ current
(KC), a potassium leak current
(Kleak), a persistent-type Na current
(NaP), a noninactivating muscarinic K+ current
(KM), and the muscarinic activated,
nonspecific Ca2+-sensitive cationic current
INCM (NCM). The compartment where spikes
are initiated (the soma in this case) has Na and K currents with faster
kinetics [Na(soma) and K(soma)], based on previous work (Traub
et al., 1994). In the experimental preparation, there are
indications of a T-type Ca current (Bruehl and Wadman, 1999), but because these simulations result in relatively
depolarized membrane potentials, this current was not included. To
evaluate the ionic mechanisms of delay activity, additional simulations were performed with individual currents deleted.
Stellate cells
The properties of stellate cells were simulated with biophysical
simulations containing multiple compartments. These simulations were
developed for previous work on the mechanisms of subthreshold membrane
potential oscillations in stellate cells (Fransén et al.,
1998; Dickson et al., 2000) (E. Fransén, Alonso, and M. E. Hasselmo, unpublished
observations). The compartmental structure of these simulations
is shown in Figure 1. The stellate cell is composed of seven
compartments. One compartment represents the soma; one compartment
represents the initial segment; three compartments connected in
succession represent the primary, secondary, and tertiary segments of a
single principal dendrite; and two connected compartments represent all
remaining dendrites lumped together. The addition of the separate
initial segment compartment differs from the pyramidal cell. The
lengths and cross sections of the three principal dendrite compartments
were adjusted to give the dendrite a length constant of 2 (sealed-end
condition). The compartment profiles are found in Table
2.
Passive properties. Simulations of the passive membrane
properties of the cell used the same properties described above for pyramidal cells.
Active properties of stellate cells. Simulations of stellate
cells included most of the same active currents included in the simulations of pyramidal cells, with adjustments in parameters to
account for some of the differences in the intrinsic properties of
these neurons. The KAHP current is
stronger in pyramidal cells than in stellate cells, and the
KM current is not present in stellate cells. As
a consequence of the difference in conductance amplitudes,
spike-frequency adaptation is stronger in pyramidal cells than in
stellate cells. The stellate cells include a
hyperpolarization-activated nonspecific cation current
Ih that is not included in the pyramidal cell
models. Equations describing the currents can be found in the section
on ionic currents; the respective conductances are found in Table 5.
The stellate cell model includes the following currents described in
the section on ionic currents (with the appropriate subsection in
parentheses): the Na+ and K+
currents responsible for fast action potentials (described in sections
Na and Kdr), a high-threshold
Ca2+ current (CaL), a
calcium-dependent K+ current
(KAHP), a fast calcium- and
voltage-dependent K+ current
(KC), a potassium leak current
(Kleak), a persistent-type Na current
(NaP), and a hyperpolarization-activated nonspecific cation current
Ih (H).
Interneurons
The interneuron is modeled to replicate the basic
properties of a fast-spiking nonadapting type cell. The interneuron is
composed of six compartments, with one representing the soma, three
representing a principal dendrite, and two representing all but one of
the dendrites lumped together. The interneuron model does not have the
separate initial segment compartment. The compartment profiles are
found in Table 3.
Passive properties. Simulations of the passive membrane
properties of the cell used the same properties described above for stellate cells.
Active properties. The interneuron model has the
Na+ and K+ currents responsible
for fast action potentials (Na and Kdr),
a high-threshold Ca2+ current
(CaL), a calcium-dependent
K+ current (KAHP), and
a potassium leak current (Kleak). The
KAHP was set at very weak values, consistent
with the absence of spike-frequency accommodation in these neurons. The
compartment where spikes are initiated (the soma in this case) has Na
and K currents with faster kinetics [Na(soma) and K(soma)], as in previous models (Traub et al., 1994). Ionic conductances
are found in Table 6.
Modeling of synaptic interactions
Synaptic currents in a postsynaptic neuron were activated by the
membrane potential in the associated presynaptic neuron crossing a
threshold value of  0.025 V. After a conductance delay of 2 msec, a
synaptic current was initiated in the postsynaptic cell with a dual
exponential time course (Bower and Beeman, 1995).
Synaptic contacts on the cells were either of a mixed AMPA/kainate and
NMDA type or of a mixed GABAA and GABAB type.
Equations describing the currents can be found in the section on
synaptic currents; the respective parameters are found in Table 7.
The simulations included a conductance-based noise source. This
represents potential effects of channel noise (White et al., 1998) or synaptic noise on actual neural function. The noise
was generated from a Poisson process and was placed on the proximal lumped dendritic compartment.
Network models
The interaction of different cell types was analyzed in network
simulations of different sizes. Many of the interactions of different
cell types could be captured in small circuit simulations including six
simulated neurons (see Fig. 6). These simulations included two neurons
representing input to entorhinal cortex layer II, two simulated layer
II pyramidal cells, one simulated layer II stellate cell, and one
simulated layer II interneuron. One of the simulated pyramidal cells
received input from only one input neuron, representing the
odor-specific responses observed during unit recording (Young et
al., 1997). The other simulated pyramidal cell received input
from both input neurons, representing the odor nonspecific cells
observed during recordings (Young et al., 1997). The
input neurons did not contact the inhibitory interneuron, but the
pyramidal cells, stellate cell, and interneuron were all interconnected
with synaptic properties summarized in Table 7.
Larger-scale network simulations explored the interaction of larger
numbers of neurons during several stages of a delayed matching task.
They show how a single network of cells, with connectivity chosen
randomly within constraints on number, distribution within a local
neighborhood, and weight, can display many of the unit response types
reported in experimental data (Suzuki et al., 1997; Young et al., 1997). See the section on network topology.
Computational methods
Biophysical simulations were developed using the GENESIS
simulation package (Bower and Beeman, 1995). The
Crank-Nicholson (Hines, 1984) method for numerical
solution to differential equations was used (with modifications). A
time step of 150 µsec was used for the simulations.
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Ionic currents |
Voltage-dependent conductances were modeled using a
Hodgkin-Huxley type of kinetic model. The following reversal
potentials were used: Na+, +55 mV;
K+, 75 mV; Ca2+, +80 mV;
Ih, 20 mV; and
INCM, 0 mV.
Na, Kdr. The Na+
current responsible for fast action potentials had kinetics taken from
a model of hippocampal pyramidal cells (Traub et al.,
1991, 1994). The
pyramidal cell and the interneuron have Na and K currents with faster
kinetics [described in a separate section below and labeled
Na(soma) and Kdr(soma)] on the
compartment where spikes are initiated (Traub et al.,
1994). Both the Na as well as the K current were shifted +5 mV
from the model by Traub et al.
(1991, 1994) to
make the spiking threshold more positive (around 50 mV). The
spatial distribution and maximal
conductance of all currents on the different
compartments are found in Tables 4-6. The maximal conductances were
adjusted to match experimental data (Alonso and Klink,
1993) on the action potential rate of depolarization
(Na+) and rate of repolarization
(K+) as well as spike threshold, amplitude, and
duration of action potentials. The currents used the following
equations:
Na.
gate exponent = 2;
gate exponent = 1.
Na(soma).
gate exponent = 3;
gate exponent = 1.
Kdr.
gate exponent = 2.
Kdr(soma).
gate exponent = 4.
CaL. The high-threshold Ca2+ current was
modeled according to previous models (Traub et al.,
1994). The maximal conductance was set to the same value as in
previous work (Traub et al., 1994).
gate exponent = 2.
KAHP. The calcium-dependent K+
(afterhyperpolarization) current was modeled according to previous
models (Traub et al., 1991), with the slope set at 30 and the saturation set at 30 (arbitrary units). The maximal conductance
was adjusted to match the slow afterhyperpolarization (sAHP) depth in
experimental data (Alonso and Klink, 1993).
gate exponent = 1.
KC. The fast calcium- and voltage-dependent
K+ current was modeled according to previous work
(Traub et al., 1991). The maximal conductance was
adjusted to match the fast afterhyperpolarization (fAHP) depth and
Ca-dependent spike repolarization rate (Alonso and Klink,
1993).
gate exponent = 1.
KM. The slowly activated voltage-dependent
K+ current was modeled according to Bhalla
and Bower (1993). The maximal conductance was adjusted to match
the length of the suprathreshold plateau after a spike in the presence
of a Ca block (Alonso and Klink, 1993).
gate exponent = 1.
H. The hyperpolarization-activated nonspecific cation current
Ih was modeled according to previous work
(Dickson et al., 2000) (Fransén Alonso, and
Hasselmo, unpublished observations). The maximal conductance was
adjusted to comply with voltage-clamp data as well as current-clamp
data on the "sag" produced by Ih (Dickson et al., 2000).
gate exponent = 1;
gate exponent = 1.
NaP. The persistent-type slowly inactivating Na+
current was modeled according to experimental data (Magistretti
et al., 1999) for the steady-state activation and inactivation
and kinetics of inactivation and for the reversal potential, and
according to McCormick and Huguenard (1992) for the
kinetics of activation and the exponents of the activation rates
m and h. The maximal conductance was adjusted to
the conductance of Ih to allow subthreshold oscillations to develop.
gate exponent = 1;
gate exponent = 1.
Kleak. The Kleak conductance
was considered to be linear and uniformly distributed with a reversal
potential of: Erev = 0.075 V.
NCM. The nonspecific Ca2+-dependent cationic current
was modeled using a framework similar to the calcium-dependent
K+ current found in previous work (Traub et
al., 1991). Time constants for the
INCM were derived by replicating
experimental data (Klink and Alonso,
1997a,b). Note
that these experimental data were fitted by modifying the total
kinetics of both the calcium diffusion and the
INCM current to replicate experimental traces.
Here we focus on the Ca-sensitive component of
INCM. Recent evidence suggests that
INCM also has a calcium-insensitive component, but this is not explicitly modeled in our simulations. The
resting potential of our simulations, before any input has been
presented, corresponds to a resting state with cholinergic modulation
that would include conductance contributions attributable to the
calcium-insensitive component. The maximal conductance was adjusted to
produce spiking frequencies similar to those observed during delay
activity and during match enhancement in recordings of single units in
awake rats performing a delayed non-match to sample task (Young
et al., 1997).
gate exponent = 1.
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Ca2+ buffering |
The Ca2+ diffusion and buffering was modeled
according to previous techniques (Traub et al., 1991;
McCormick and Huguenard, 1992). To take into account the
differences in distances and diffusion constants for the calcium
influencing each of the different currents, the calcium kinetics was
modeled separately for each case, consistent with separate calcium
compartments and reaction pathways within the cell. In addition, until
calcium-clamp data exist on the individual currents, it is not possible
to separate the kinetics of the calcium concentration from the kinetics
of the channel itself. Therefore, the models of the concentration and
of the individual currents should be seen as a unit.
Following the convention used in Traub et al. (1991),
the calcium concentration has arbitrary units. Because the calcium
concentration is converted to an effect on rate parameters of the
calcium-sensitive channel, the absolute concentration of calcium can be
arbitrary, although we have tried to keep the magnitude in a range
similar to millimolar to enable comparisons. For the calcium related to the calcium-dependent K+ current, the diffusion rate
constant of 0.1 sec was set to give a spike-frequency adaptation rate
according to Alonso and Klink (1993). The minimal
[Ca2+]i was set to 5.0 × 103.
For the fast calcium- and voltage-dependent K+
current (KC), the calcium values were 0.5 msec and 5.0 × 106, respectively, and the
related values for the non-specific Ca2+-dependent
cationic current were 1.333 sec and 1.0 × 105, respectively. This was determined by tuning
the channel to replicate data obtained during blockade of calcium
influx by Klink and Alonso (1993). The changes in
the concentration of calcium used for KAHP above were too slow to effectively represent
KC, so different dynamics were necessary.
Similarly, the slower changes in INCM relative
to KAHP required use of the slower calcium
dynamics for INCM described above. In addition,
the conversion factor,  , from charge density to concentration for
each component and compartment is found in Tables 4-6. Because this
conversion factor converts channel current to calcium concentration,
valence is implicitly addressed by using current.
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Synaptic currents |
Synaptic conductances between neurons were modeled with an  function (Bower and Beeman, 1995):
gsyn = (A × gmax)/( d r) (et/ d et/r), where
gmax is the peak synaptic conductance,
r is the rising time constant,
d is the decaying time constant,
gsyn is the synaptic conductance at time
t, and A is a scaling constant set to yield a
maximum conductance of gmax.
For the NMDA current, the conductance was multiplied with the magnesium
block conductance described previously (Zador et al., 1990): gMg = 1/(1 + 0.018e60 V).
Before determining the synaptic conductance values, the relative
proportions of the various components were fixed according to the
following experimental data: The NMDA component has the same
postsynaptic potential (PSP) height as AMPA at 72 mV (Alonso et al., 1990). GABAA is 70% of GABAB
at 66 mV (Gloveli et al., 1999).
The synaptic conductances were adjusted so that firing rates would
resemble those observed in recordings of entorhinal units from rats
performing a delayed non-match to sample task (Young et al.,
1997) for the various parts of an experiment (i.e., sample, delay, and test). Note that firing rates
were matched to firing rates observed in rats, but for
phenomena of match as well as non-match
enhancement and non-match suppression,
the relative changes in firing rates were adjusted to match
those observed in monkeys
(Suzuki et al., 1997). The values of
r and d can be
found in Table 7. The values of gmax can
be found in Tables 8-11.
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Network topology |
Smaller example networks were used to illustrate the fundamental
features of connectivity that could result in specific phenomena observed in unit recordings of entorhinal neurons during delayed matching tasks. These simple example networks used the basic
connectivity summarized in Figure 6, with synaptic conductances found
in Tables 8-10. Table 8 shows the synaptic conductances for
Figure 7, Table 9 shows conductances for Figures 8 and 9A,
and Table 10 shows conductances for Figure 9B.
To demonstrate that these simple interactions could easily be obtained
with connectivity chosen randomly within constraints on number,
distribution, and weight, a larger network simulation was developed. As
shown in Figure 10, the larger network consists of one population of 12 input cells representing association cortices projecting into the
entorhinal cortex, one population of 30 stellate cells, one population
of 18 pyramidal cells, and one population of 12 interneurons. The
relative proportion of EC cells was determined according to
experimental findings (Alonso and Klink, 1993), although these estimates may be subject to differences in the probability of
sampling different types of neurons.
The input cells were divided into three equal groups representing three
stimuli (A, B, and C). A did not overlap at all
with B or C, but B and C
had moderate overlap. The existence of a connection was determined
randomly within a window of possible connections. The connection
strengths from one of the inputs to either the stellates or the
pyramidal cells had a uniform value for a central set of connections
and decreasing values for neurons at the sides of the central
projection, to provide fully activated cells as well as weakly
activated cells. The input cells contacted both stellates and pyramidal cells.
The stellate cells, pyramidal cells, and interneurons connected to the
other cell types according to a localized scheme. Geometrically, each
population was uniformly spaced on a line of unit length. A pair of
presynaptic and postsynaptic cells from two cell populations corresponded if they occupied the same position within the line. A
presynaptic cell was first randomly selected and a postsynaptic cell
was thereafter randomly selected within a window centered around the
corresponding cell in the postsynaptic type. The resulting percentage
of connectivity between individual populations of cell types is shown
in Figure 10, and the total number of connections between different
populations is shown in Table 12. Additionally, as a control, the
number of connections, window width, and conductance values were varied
to test the sensitivity of the model.
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RESULTS |
Single-cell mechanisms for sustained spiking activity
The compartmental biophysical models of entorhinal layer II
pyramidal cells were used to simulate intracellular recording data from
this type of cell obtained in brain slice preparations of the
entorhinal cortex (Alonso and Klink, 1993; Klink and Alonso, 1993). The parameters of the intrinsic currents listed
in Materials and Methods were adjusted to simulate specific examples of
the intrinsic properties observed during these intracellular
recordings. As shown in Figure 2,
simulations were tuned to replicate the properties of spike shape and
spike-frequency accommodation observed in the experimental data in the
absence of cholinergic modulation. This figure follows the same time
course for stimulation that is shown in Figure 10A of
Alonso and Klink (1993).
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Figure 2.
Spike-frequency accommodation in a simulated layer
II pyramidal cell during membrane depolarization in response to a 265 msec simulated current injection. This cell contains a wide range of
voltage- and calcium-dependent currents. The figure displays the
response properties of the neuron in the absence of cholinergic
modulation.
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In physiological recordings from pyramidal cells in brain slice
preparations (Klink and Alonso,
1997a,b),
application of the cholinergic agonist carbachol causes long-term
depolarizations, which have been termed plateau potentials. These
plateau potentials appear to arise from muscarinic receptor activation
of a nonspecific cation current INCM
(Magistretti, MA, Shalinsky, and Alonso, unpublished
observations). This nonspecific cation current has a sensitivity
to intracellular calcium concentration changes caused by calcium influx
through voltage-gated calcium channels (CaL) (Magistretti et al.,
2001). Experimental data show that the muscarinic-activated,
calcium-sensitive, nonspecific cation currents have the potential to
cause sustained repetitive spiking activity in single neurons
(Klink and Alonso, 1997b). The combined cholinergic
muscarinic receptor activation of the INCM current and block of potassium currents
IKAHP and IKM brings the cell closer to its firing threshold. If the neuron then
discharges, the spike-associated calcium influx potentiates INCM, leading to additional
depolarization. The spiking necessary to induce sustained firing can
also be induced by synaptic input or current injection.
As shown in Figure 3, computational
modeling of this current demonstrates potential mechanisms for the
generation of sustained spiking activity in single neurons. The
self-sustained generation of spiking activity results from the
following cycle: (1) each action potential causes an influx of calcium
through voltage-sensitive calcium channels; (2) the inflow of calcium
replenishes the pool of calcium acting to enhance the activity of the
calcium-sensitive INCM current; and (3)
the sustained activation of the INCM
current depolarizes the cell sufficiently to cause generation of
another action potential, thereby repeating the cycle.
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Figure 3.
Simulation of delay activity and match enhancement
in a pyramidal cell during a delayed matching task attributable to
cholinergic enhancement of the INCM
current. Traces show responses to two 600 msec current injections with
a 2400 msec delay between injection. A, Generation of
sustained spiking activity during the delay period. At the start of the
simulation, muscarinic activation of the
INCM current causes subthreshold
activation. During an initial 600 msec current injection, spike
generation causes an influx of calcium through voltage-sensitive
calcium channels. This calcium influx activates the calcium-sensitive
INCM, causing generation of an additional
spike well after the end of the current injection. This causes
additional calcium influx which causes additional
INCM activation and additional
depolarization, resulting in sustained spiking behavior. The response
to a subsequent 600 msec current injection shows considerably greater
spiking activity than the response to the first current injection.
B, Generation of match enhancement. Even without
spiking during the delay period, the activation of the
INCM by the initial spiking activity
persists long enough that a residual depolarization at the end of the
delay period results in greater spiking activity during the second
current injection. C, Without cholinergic activation of
INCM the response of the cell is similar
during the two current injection periods. D, Timing of
current injection during sample and test periods. E,
Sustained spiking during the delay period with
INCM in the range of saturation, which
causes acceleration to asymptotically approach a lower stable firing
rate. F, Interaction of the simulated pyramidal cell from
A with feedback inhibition also allows a stable firing
frequency during sustained spiking activity. In this simple example, a
single inhibitory interneuron responds to pyramidal cell spiking
activity and causes feedback inhibition that maintains spiking activity
at a moderate frequency during the delay period. (At the end of the
delay, the neuron still shows match enhancement in response to the
second current injection.)
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Delay activity and match enhancement
This intrinsic cellular mechanism could underlie certain aspects
of the neuronal firing activity observed in the entorhinal cortex
during performance of a continuous DNMS (cDNMS) task with odors in rats
(Young et al., 1997). In particular, the cellular mechanism in single neurons could account for the spiking phenomena observed during the performance of these tasks, including (1) delay
activity, and (2) match enhancement (Young et al.,
1997). The term delay activity refers to the stimulus-selective
activity induced by a sample stimulus that can be maintained after the stimulus ends and throughout the delay period until the next stimulus is presented. The term match enhancement refers to trials in which an
individual neuron generates more spikes in response to a test stimulus
that matches the preceding sample stimulus than were generated in
response to the same test stimulus when it did not match the preceding
sample stimulus.
Cholinergic modulation of INCM could
provide a mechanism for stimulus-selective delay activity and match
enhancement. If there is an increase in acetylcholine levels during
performance of the task, then the spiking activity induced in a set of
neurons by a specific sensory stimulus (i.e., a single odor) can be
maintained because of the repetitive activation mechanism described
above, as shown in Figure 3. In these simulations, we replicated the time course of different components of the behavioral cDNMS task used
during in vivo unit recordings from the entorhinal cortex (Young et al., 1997). The task is simulated with a 600 msec current injection representing afferent input to the entorhinal
cortex during sniffing of one odor during the stimulus period of the task, followed by a 2400 msec delay period with no current injection, and followed by a 600 msec current injection representing afferent input to the entorhinal cortex during sniffing of the same odor during
the next stimulus period (corresponding to a match condition). (Fig.
3D illustrates the timing of current injection.)
The trace in Figure 3A shows how a neuron responds after
simulated cholinergic activation of the
INCM current. A suprathreshold input
causes spiking during the stimulus period, which causes calcium influx
through voltage-sensitive calcium channels. This calcium influx causes
additional activation of the calcium-sensitive
INCM current, which depolarizes the
membrane sufficiently to cause another action potential even after the
end of the depolarizing current injection. Each subsequent spike causes
sufficient depolarization to induce another spike, allowing
self-sustained spiking activity throughout the delay period until the
next stimulus is given. When the second presentation of the same
stimulus occurs, the cell is already depolarized by INCM activation, such that it responds to
the "match" stimulus with considerably greater spiking than the
initial response to that same stimulus. A comparison of this match
period with the preceding stimulus period corresponds to the match
enhancement observed previously (Young et al., 1997).
Thus, INCM provides an intrinsic mechanism
appropriate for both the sustained delay activity and the match
enhancement phenomenon. Between the spiking activity produced by the
current injection and the spikes produced by the
INCM depolarization, there may be an interval without spikes. This interval also appears before sustained spiking in experimental data from brain slice preparations, as seen in
Figure 5A.
The top example in Figure 3A shows match enhancement after
delay activity, but neurophysiological studies indicate that many neurons show match enhancement even without delay activity
(Young et al., 1997). The trace in Figure 3B
shows that match enhancement can be observed in the simulation even in
the absence of sustained delay activity. This could provide another
neurobiological mechanism for performing matching that does not depend
on maintaining activity during the delay. In this example, the spiking
activity during the initial depolarization does not cause sufficient
activation of INCM to induce additional
spiking after the end of the initial afferent input. However, the
subthreshold depolarization attributable to
INCM persists during the delay period, causing enough residual depolarization that a new afferent input at the
end of the delay period causes generation of a larger number of spikes.
Thus, match enhancement can occur without delay activity. This
subthreshold depolarization decays with a time constant of 3.6 sec,
which is sufficiently slow enough to mediate match enhancement after a
3 sec interval. This suggests that match enhancement after longer
delays without spiking results from input from neurons showing
persistent activity or from longer-term synaptic changes. Figure
3B may be compared with in vitro experimental
data in Figure 5B showing stronger responses to a second
identical current injection even when there is no delay activity. The
trace in Figure 3C shows what happens without cholinergic
enhancement of INCM. In this case, the
neuron will spike during the initial stimulus period, but the absence
of INCM activation prevents the neuron
from showing sustained depolarization and spike generation during the
delay period. In addition, the absence of a depolarization during the
delay prevents the neuron from generating increased spiking activity
during the match stimulus. Thus, it fires the same number of spikes in
response to the match stimulus that it did in response to the previous
input. In this framework, cholinergic activation of the
calcium-sensitive INCM is important to the
intrinsic mechanisms for sustained activity and match enhancement. This
is consistent with data showing that muscarinic cholinergic antagonists
cause impairments of behavioral performance in delayed match to sample
tasks (Bartus and Johnson, 1976; Penetar and
McDonough, 1983; Tang et al., 1997).
The simulation in Figure 3A shows acceleration of the firing
rate attributable to the internal buildup of calcium, which causes a
persistent increase in firing rate. This acceleration can be avoided by
having the INCM current in the range of
saturation, so that additional depolarization does not cause additional
activation of the current. This causes a stable rate of firing to be
obtained more rapidly during the delay period, as shown in Figure
3E. This acceleration of the firing rate can also be
prevented by network interactions. For example, feedback inhibition in
the network allows initial acceleration during the delay period to
reach an asymptotically stable firing frequency at the end of the
delay, as shown in Figure 3F. In this example, even the
addition of a single interneuron mediating feedback inhibition can
prevent the simulated pyramidal cell in Figure 3F from
showing continuous acceleration of the firing rate. The neuron reaches
a stable firing rate during the delay period but still shows match
enhancement during the second current injection relative to the sample
stimulus. Delay activity of this sort can be obtained in experiments
with concentrations of carbachol as low as 2 µM, which is
comparable with the range of physiologically realistic endogenous
concentrations of acetylcholine. In experiments in layer V, delay
activity of this sort can be induced by stimulation of synaptic input
as well as direct current injection. Figure 3, E and
F, may be compared with in vitro data in Figure
5A showing sustained spiking after current injection.
Additional simulations were performed to further evaluate the role of
INCM in this delay activity. In
particular, we found no change in delay activity after individual
removal of either the NaP current or
KM. (In these simulations, the resting potential
was kept the same with a 0.04 nA current injection after deleting
NaP and with a 0.02 nA current injection after deleting KM.) The delay activity could also be maintained
after combined deletion of NaP,
KM, Ca, and
KAHP from the simulation. (For the calcium
current, the charge flow was removed from the calculation, but the flow
of calcium to the calcium concentration was kept so that all
calcium-dependent currents would remain unaffected.) Note that
evaluation of the sustained spiking activity requires that the cell
still generate normal action potentials, which required retention of
the Na, Kdr, and
KC currents. Kleak
was retained to maintain resting potential. The importance of the NCM current was also demonstrated by showing in an otherwise
intact simulation that a reduction of INCM
by 27% prevented any delay activity. (In this simulation, resting
potential was maintained with a depolarizing current injection of 0.016 nA.)
The intrinsic mechanism of INCM for
generation of sustained spiking activity appears to be resistant to
brief periods of interference, which could cause inhibitory input to
the neurons in the network. This is consistent with the fact that delay
activity can sometimes persist through presentation of intervening
stimuli in a delayed matching to sample (DMS) task (Suzuki et
al., 1997). As shown in Figure 4,
the neurons are resistant to a range of short duration hyperpolarizing
current injections. Only after the current injection exceeds a 3-4 sec
duration does the neuron terminate the sustained spiking activity.
Figure 4 (top, left and right) may be
compared with in vitro experimental data in Figure
5A showing resistance of sustained spiking to
hyperpolarizing current injections. This resistance to
hyperpolarization arises from the lack of voltage dependence of
INCM. The length of the resistance to
hyperpolarization depends upon the conductance of
INCM. At the values shown in Figure 4, the
delay activity survives a 3 sec hyperpolarization but not a 3.5 sec
hyperpolarization. With a 5% decrease in NCM conductance,
the delay activity withstands 2 sec but not 2.5 sec of
hyperpolarization. With a 10% increase, the delay activity withstands
4 sec but not 4.5 sec of hyperpolarization. A dominant effect of
distractor stimuli during delayed matching might be depolarization of
neurons within the network. Therefore, we also tested the effect of a
0.5 nA depolarizing current injection. Spiking rate was increased
during the injection, but delay activity persisted after depolarizing
injections of any duration. Experimental data from slice preparations
also shows that depolarizing current injections do not terminate
sustained spiking activity (Alonso, unpublished
observations).
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Figure 4.
Sustained activity can resist periods of
hyperpolarization, suggesting that this mechanism of working memory can
resist moderate interference. These simulations show the membrane
potential during simulation of muscarinic enhancement of the
INCM. In each trace, synaptic input from
the cell at the bottom causes generation of a series of
spikes (action potentials are truncated to ease viewing of subthreshold
membrane potential changes). After the EPSPs have ended, the membrane
potential continues to rise due to activation of
INCM, resulting in sustained spiking
activity. In each of the top four traces,
hyperpolarizing current injections of different durations are
simulated. In the first three durations, spiking activity is terminated
during hyperpolarization but commences again after hyperpolarization
has ended. This is possible because of the lack of voltage dependence
of INCM. Only when hyperpolarization
persists for 3-4 sec does sustained spiking activity terminate. The
bottom trace shows the activity of the input cell.
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Match enhancement and delay activity in experimental data
The simulations described above were primarily developed to
replicate in vivo data on match enhancement and delay
activity. However, as noted above they can also be compared with
available data on such phenomena observed during whole-cell patch
recording in brain slice preparations of the entorhinal cortex, as
shown in Figure 5. Figure 5A
shows an example of persistent spiking activity appearing after a
current injection. This trace also shows that the sustained spiking
activity is not terminated by hyperpolarizing current injections.
Figure 5B shows that even without delay activity, the
recorded neuron shows a stronger spiking response to the second of two
identical current injections.
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Figure 5.
Experimental data showing examples of sustained
spiking activity and match enhancement during whole-cell patch
recording in slice preparations of entorhinal cortex. Recordings were
performed in standard Ringer's solution with 100 µM
picrotoxin and 1 mM kynurenic acid added to block synaptic
transmission. The cholinergic agonist carbachol was present in a
concentration of 20 µM. A, Sustained spiking
activity after current injection. In the presence of carbachol, spiking
induced by a short current injection is followed by sustained spiking
activity after a brief interval. This spiking activity accelerates and
persists despite two hyperpolarizing pulses presented at the
middle of the trace. The amplitude of the current
pulses was 50 pA. B, Match enhancement without delay
activity. Because of cholinergic activation of the
INCM, the neuron fires more spikes in
response to the second repetition of the same current injection,
despite the absence of spiking during the delay. The amplitude of the
current pulses is 40 pA.
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Examples of network mechanisms for neuronal activity during delayed
matching tasks
The intrinsic activation of INCM
described in the previous section cannot account for all of the
phenomena observed during unit recording in delayed non-match to sample
and delayed match to sample tasks. For example, the spiking activity
observed in these experiments shows phenomena such as match suppression as well as non-match enhancement and non-match suppression. However, simple network interactions could underlie these additional spiking phenomena. We have tested potential mechanisms in small example networks, as shown in this section. Although these effects have been
selectively tuned in these small networks, they can appear in a larger
network with connectivity chosen randomly within constraints on number,
distribution, and weight (see below).
As described in Materials and Methods and illustrated in Figure
6, the small example networks contain two
input neurons (stim A and stim B), a selective pyramidal cell that
receives input only from stim A (pyramidal cell A), a nonselective
pyramidal cell that receives input from both stim A and stim B
(pyramidal cell AB), a stellate cell, and an interneuron. Thus, these
simulations include the experimental finding that some cells show
stimulus specificity, whereas others do not. For simplicity, no cells
showing specificity to stim B are shown.
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Figure 6.
Connectivity of the minimal network simulation.
The network represents layer II of the medial entorhinal cortex. In
this layer, the principal cells are stellate cells and pyramidal cells
together with an interneuron-type cell, as found in the rat
(Alonso and Klink, 1993) and in the primate (P. Buckmaster, D. Amaral, and Alonso, unpublished data). This diagram
shows the principal connectivity, but not all connections are present
in all simulated networks. The network receives synaptic connections
from input cells (stim A and stim B). The network
contains two simulated pyramidal cells, including one representing
cells with stimulus selectivity (pyr A, which
receives afferent input only from stim A) and one
representing cells with nonspecific responses (pyr
AB, which receives afferent input from both stim A and
stim B). The network also contains a stellate cell
(stel), which receives input from stim A
and stim B and from both pyramidal cells. The pyramidal
cells connect with one another and with the inhibitory interneuron
(int), which sends inhibitory connections to all neurons. In
the larger model (Fig. 10), the number of stellate cells is
larger than the number of pyramidal cells, as found in experimental
data; here the network represents a minimal set of cell types to
exemplify various cell types that have been classified in the
literature according to their firing characteristic. Connection
strengths for individual examples are summarized in Tables
8-10.
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Figure 7 demonstrates how delay activity
can appear in a selective subset of neurons for a specific input
pattern. The network receives afferent input from input neuron A, which
more strongly activates pyramidal cell A. The spiking activity in
pyramidal cell A is sufficient to result in regenerative activity
during the delay period in this neuron, but not in a neuron that
received slightly less afferent input (pyramidal cell AB). Note that
excitatory synaptic transmission attributable to regenerative spiking
activity in pyramidal cell A also drives spiking during the delay
period in the stellate cell and in the interneuron. Thus, synaptic
connectivity can cause delay activity in neurons that have no intrinsic
mechanisms for that delay activity. Note also that the activity in the
stellate cell only appears during the delay period, and not during the sample or test periods. The presence of
INCM in a subset of neurons can drive
network activity even if the synaptic connectivity alone would not
allow sustained spiking activity. The synaptic conductances for this
simulation are shown in Table 8.
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Figure 7.
Delay activity in the network simulation. The
simulated membrane potential is plotted for a 3.8 sec period for six
different neurons: Input neurons stim A and stim B, a stellate cell,
pyramidal cells A and AB, and an inhibitory interneuron. For a match
trial, input cell stim A is activated during a 600 msec sample period,
providing excitatory afferent input to both pyramidal cell A and
pyramidal cell AB. This input is sufficient to cause pyramidal cell A
to show sustained spiking during the 2.4 sec delay period, because of
the regenerative activity of INCM. This
spiking activity drives spiking in the stellate cell and interneuron.
Stim A is activated again during the matching period, resulting in
match enhancement. Action potentials are truncated in this figure.
Synaptic conductances are summarized in Table 8.
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Match suppression
In addition to the match enhancement described above, many
researchers have described suppression of the response to the second viewing of a particular stimulus in the entorhinal cortex (Fahy et al., 1993; Suzuki et al., 1997; Young
et al., 1997) and inferotemporal cortex (Miller and
Desimone, 1993,
1994). In most studies, both match enhancement and match
suppression are reported, but studies have often focused on match
suppression (Miller and Desimone, 1993, 1994), and
sometimes only match suppression is reported without any match
enhancement (Fahy et al., 1993). This match suppression
could arise from a number of different physiological mechanisms. Here
we demonstrate how network interactions could result in match
suppression as an indirect effect of INCM. In these network simulations, lateral inhibition from neurons undergoing match enhancement causes match suppression in other neurons.
Figure 8 demonstrates match suppression
in a subset of neurons within the network simulation. In this example,
input from stim A activates both pyramidal cells, similar to the
example in Figure 7. These pyramidal cells maintain subthreshold
depolarization during the delay period, which causes match enhancement.
However, the stellate neuron in this example has stronger inhibitory
connections from the inhibitory interneuron. This results in match
suppression in the stellate cell because of the feedback inhibition
activated by the pyramidal cells showing match enhancement. The
synaptic conductances are summarized in Table 9.
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Figure 8.
Network simulation demonstrating match suppression
attributable to network interactions. The network contains the same set
of neurons described in Figure 7. Input from stim A
activates both pyramidal cell A and pyramidal cell AB for 600 msec and
causes subthreshold depolarization during the delay period. This
results in increased depolarization and in a greater number of spikes
in both pyramidal cells when input from stim A arrives during the match
period. However, in contrast to Figure 7, stronger inhibitory
connectivity to the stellate cell causes this neuron to show match
suppression (i.e., it generates fewer spikes in response to the match
stimulus than to the preceding sample stimulus). Action potentials are
truncated in this figure. Synaptic conductances are summarized in Table
9.
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Non-match enhancement and suppression
Studies on spiking activity in the entorhinal cortex in rats used
a continuous delayed non-match to sample paradigm in which each
stimulus is simultaneously a sample stimulus for the next trial and a
match stimulus for the preceding trial (Young et al., 1997). A continuous recognition task has also been used in
monkeys (Fahy et al., 1993), in which stimuli were both
sample and match stimuli (although that task required a response to a
familiar stimulus even if there were many intervening stimuli since its previous presentation). In those continuous matching tasks, only match
enhancement and match suppression could be quantified. However, other
studies in monkeys have used discrete trial matching tasks in which
each trial involves presentation of a single sample stimulus followed
by a delay period during which several test stimuli can be presented
sequentially for matching (Miller and Desimone, 1994; Suzuki et al., 1997). After the matching stimulus
appears, there is an intertrial interval before the next sample
stimulus is presented (Miller and Desimone, 1994;
Suzuki et al., 1997). In these studies, the response
during the sample period can be used as a baseline and it is possible
to differentiate match suppression from non-match enhancement. In
non-match enhancement, presentation of stimuli during the match
stimulus induces more spikes on average when the stimulus does not
match the stimulus presented during the sample period. In non-match
suppression, presentation of a stimulus during the test period
generates fewer spikes if it does not match the stimulus during the
sample period.
Figure 9 shows examples of non-match
enhancement and non-match suppression. Here the features of the
nonselective cell (pyramidal cell AB) play an important role along with
the INCM current in inducing these
effects. In Figure 9A, non-match enhancement occurs in the
stellate cell from a change in the relative level of excitation and
inhibition in the network. Synaptic parameters are the same as in
Figure 8 (Table 9). During the sample period, input neuron stim A
activates both pyramidal cell A and pyramidal cell AB; this causes
strong activation of the inhibitory interneuron, resulting in a small
number of spikes in the stellate cell. During the match period,
activation of input neuron stim B only activates the nonselective
pyramidal cell AB. This neuron shows a match enhancement attributable
to subthreshold depolarization during the delay period, giving stronger
excitatory input to the stellate cell, but the lack of spiking in
pyramidal cell A results in less spiking of the interneuron, giving
less inhibitory input to the stellate cell. The combination of these
effects results in a stronger response in the stellate cell for the
non-match input (non-match enhancement). In a separate simulation, when
given input from stim B followed by repetition of stim B input, the
network responds both times with five spikes, as opposed to six spikes
for the stim B response after stim A. Thus, the network shows non-match enhancement both in a comparison of the second (test) stimulus with the
first (sample) stimulus and when comparing the test response in match
versus non-match conditions. As shown in Figure 9B, altering the simulation by adding an excitatory connection from pyramidal cell
AB (instead of pyramidal cell A) to the interneuron can cause non-match
suppression instead of non-match enhancement. Here the match
enhancement in pyramidal cell AB causes greater interneuron spiking,
which results in an overall decrease in spiking activity in the
stellate cell during the non-match trial. The synaptic weights for this
simulation are summarized in Table 10.
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Figure 9.
Network simulation demonstrating non-match
enhancement and non-match suppression. The network contains the same
set of neurons described in previous figures. A, Non-match
enhancement (same network as Fig. 8). During the sample period, input
from stim A activates both pyramidal cell A and pyramidal
cell AB for 600 msec and causes sustained subthreshold depolarization
during the delay period. During the match period, input from stim B
activates only pyramidal cell AB. This results in a greater number of
spikes in pyramidal cell AB. The interneuron has strongest input from
the silent stim A, which results in less feedback inhibition during the
test stimulus. Increased input from pyramidal cell AB and decreased
inhibition from the interneuron causes a greater response in the
stellate cell for the non-match condition. Action potentials are
truncated in both parts of this figure. Synaptic conductances are the
same as in Table 9. B, Non-match suppression (same network
as Fig. 9). This example has the same features as Figure 8A,
except that there is a stronger excitatory connection from pyramidal
cell AB to the inhibitory interneuron. The result is that the greater
activity of pyramidal cell AB during the test presentation causes
greater feedback inhibition and a net decrease in the spiking activity
of the stellate cell during the non-match period. Synaptic conductances
are summarized in Table 10.
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Sensitivity to changes in synaptic conductances
The sensitivity of the networks to changes in synaptic parameters
was analyzed extensively in simulations changing the magnitude of
synaptic conductances (listed in Tables 8-10). In 48 simulations, each
of the categories of synaptic conductances listed in Tables 8-10 for
connections between stellate cells, pyramidal cells, and inhibitory
interneurons was changed one at a time. Thus, each of the six values in
the table was tested, as well as the related NMDA value for excitatory
cells and the related GABAB value for inhibitory
connections. For each value, the network was tested with a 20%
increase and a 20% decrease in that value. The category of neuronal
response of the stellate cell was then evaluated to see if it correctly
produced a match enhancement, match suppression, non-match enhancement,
or non-match suppression. An increase of 20% of any synaptic
connection strength produced the correct response in every one of 24 tests. For a decrease of 20%, all except 1 of the 24 tests gave a
correct type of output. In that single case, only a 5% decrease could
be tolerated. Thus, 47 out of 48 tests gave a correct type of output
for a 20% change in synaptic conductance. In separate simulations, the
sensitivity to "background" cellular spiking was addressed
(Alonso and Garcia-Austt, 1987; Stewart et al.,
1992). In in vivo recordings by Mizumori et
al. (1992), it was found that 60% of the cells fired at a rate
of 0-1 Hz. With a cellular background rate of 0.5 Hz in the
simulation, delay activity as well as match- and non-match enhancement
and suppression were produced just as reported above without the background.
Repetition suppression
In addition to the role of INCM in
working memory phenomena, there are a number of additional mechanisms
that can play a role. We have not explored the full range of synaptic
mechanisms for these phenomena but have explored the potential role of
the calcium-activated potassium current
IKAHP in suppression of the response
during stimulus repetition. Suppression of response has been shown in
unit recordings from inferotemporal neurons during repetitive
presentation of visual stimuli (Miller et al., 1991).
This repetition suppression and the match suppression described above
could arise from activation of the IKAHP
current. This has been analyzed previously in more abstract simulations of the inferotemporal cortex (Sohal and Hasselmo, 2000).
However, the long interval between the sample presentation and the
match presentation in most experiments (Suzuki et al.,
1997; Young et al., 1997) requires a rather slow
time constant for the IKAHP in the model.
Most of the simulations presented here have included an
IKAHP with a more standard time constant
of decay of 100 msec. However, a number of studies have shown that a
component of the IKAHP can have a time
constant significantly slower than 100 msec (Alonso and Klink,
1993; Storm, 1993; Saar et al., 2001). If we include a current with a slower time constant, we can account for some match suppression and repetition suppression. In
these simulations (data not shown), repeated activation of a single
cell causes less spiking on subsequent presentations because of the
residual potassium current persisting after the first activation of the
cell. This results from the calcium influx during initial spiking,
which activates potassium currents with a slow time course.
Multiple different matching phenomena arise from connectivity in a
large network
The preceding section showed simple examples of small-scale
network interactions that could underlie phenomena observed in unit
recordings from the entorhinal cortex during DNMS and DMS tasks,
including match suppression and non-match enhancement and suppression.
This section demonstrates that these types of phenomena can arise in a
simple, natural manner because of connectivity chosen randomly within
constraints on number, distribution, and weight in a larger-scale
simulation of interacting populations of neurons in the entorhinal
cortex. The connectivity properties of this larger network are
summarized in Materials and Methods, in
Figure 10, and in Tables 11 and 12.
This larger network simulation was tested for responses to matching
stimuli (in which the first presentation of stimulus pattern A is
followed by another presentation of the same stimulus pattern) and to
non-matching stimuli (in which presentation of stimulus pattern A is
followed by presentation of a different stimulus pattern B). This
simulation uses the relative percentage of cell types found in
experimental studies (Alonso and Klink, 1993).
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Figure 10.
Connectivity in the larger network simulation.
Top, This figure shows a schematic representation of the
population of 12 input cells, 30 stellate cells, 18 pyramidal cells,
and 18 inhibitory interneurons. The percentage of synaptic connectivity
between the different populations is summarized next to the appropriate
arrow. The individual location of and number of connections
for each cell were determined randomly. The strength and number of
connections in the network are summarized in Tables 11 and 12.
Bottom, Illustration of the constraints on connectivity
between regions. Presynaptic neurons could contact postsynaptic neurons
of the same index and within a window of varying width (width 2 shown
here). Dotted lines represent potential connections allowed
by the window. The solid line represents the connection that
was randomly selected.
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Activity during matching
Connectivity chosen randomly within constraints on number,
distribution, and weight in the larger network simulation resulted in a
range of response properties resembling neuronal recordings during
presentation of matching stimuli (repeated activation of input neurons
4-7), as shown in Figure 11. Figure 11
shows the membrane potentials of some individual simulated neurons in
the network, which included 12 input neurons, 30 stellate cells, 18 pyramidal cells, and 12 interneurons. Synaptic connectivity was
assigned randomly within general constraints mapping input to
particular numerical ranges of neurons in the network. Neurons in the
center and left columns of Figure 11
received input from input neurons 4-7, but the input from neurons 4-7
also contacted other neurons receiving primary input from neurons
8-11. The number of connections within the network was assigned
randomly between the pyramidal cells, stellate cells, and interneurons,
with the constraint of being local. As shown in Figure 11, the
connectivity chosen randomly within constraints on number,
distribution, and weight results in a diverse range of firing patterns
during this match trial, including phenomena corresponding to most of
the cell types observed during unit recording in awake behaving animals
(Suzuki et al., 1997; Young et al.,
1997), including match enhancement (pyr 12), match suppression
(stel 13), pure delay activity (stel 17), and pure cue activity (pyr
8). Note that in unit recording experiments done in the entorhinal
cortex of awake animals, it has not been possible to distinguish
stellate cells from pyramidal cells. Thus, unit properties described in
chronic recordings from awake animals could reflect recordings of
either of the different morphological subtypes modeled in these
simulations. There was no uncontrolled spreading of activity between
the neurons primarily representing input A and those primarily
representing input B. However, the inputs from neurons 4-7 (input A)
and 8-11 (input B) had overlapping inputs to some of the cells in the
network. Therefore, the match enhancement shown here can be analyzed to
determine whether it is selective for one input (e.g., input A) without
appearing for the overlapping input (e.g., input B). There were neurons
that showed selective enhancement, and this selective enhancement has been quantified in a larger range of networks discussed below.
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Figure 11.
Overview of activity in the larger, random
connected network during a matching trial (repeated activation of input
neurons 4-7). Neurons on the left side of the arrays received input
from input neurons 4-7, but this input could also influence activity
in neurons receiving primary input from neurons 8-11. Connectivity
within the network was assigned randomly with the general constraint
that it would primarily contact nearby cells and have the connection
strengths listed in Table 11. This results in a diverse range of firing
patterns during this match trial, without selective tuning of specific
connections. The random number and type of interconnections results in
a range of experimentally observed phenomena, including match
enhancement (pyr 12), match suppression (stel 13), pure delay activity
(stel 17), and pure cue activity (pyr 8). Obtaining these phenomena did
not require selective tuning of specific synaptic connections.
|
|
This simulation demonstrates that these neuronal response subtypes can
be obtained because of connectivity chosen randomly within constraints
for defined network interactions between individual subclasses of
neurons. They can result from an interaction of specific intrinsic
cellular properties (including the INCM and IKAHP) with the excitatory and
inhibitory interactions of neurons within different populations. The
specific example networks shown in the preceding section arise in a
simple and natural manner from interactions of neurons within a larger
network, without complicated fine tuning of individual synaptic connections.
Activity during non-matching
Similar to the result for the matching phenomena, the phenomena
observed during non-match trials can also be obtained in a simple
manner in the larger network simulation with connections chosen
randomly within constraints on the number, distribution, and weight of
synapses. The response of the larger network to a non-match is shown in
Figure 12. Here, the network initially receives activation of input neurons 4-7. Then, after a delay period,
the network receives activation of input neurons 8-11. The neurons in
the columns on the left of Figure 12
primarily receive connections from neurons 4-7, but there is some
activation of neurons receiving primary input from neurons 8-11.
Similarly, the input from neurons 8-11 primarily activates a different
set of neurons but causes some activation of neurons getting input from
4-7. The neurons receiving greater input from both sets of input
neurons correspond to the nonselective cells used in the example
simulations above (pyramidal cell AB) and play an important role in
mediating some of the non-match phenomena that can be observed in the
network. As shown in Figure 12, this network shows examples of the
experimental phenomena observed in unit recordings from awake animals
during non-matching, including non-match enhancement (stel 20),
non-match suppression (stel 18), delay activity (stel 17), input
specificity (pyr 13), and input non-specificity (pyr 11). Thus, the
specific examples of circuitry underlying non-match phenomena shown in
the previous section arise in a simple manner within a larger network
because of random selection of internal connectivity within constraints
rather than because of selective tuning of individual synaptic
connections.
View larger version (25K):
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Figure 12.
Activity in the larger, random connected network
during a non-match trial (activation of input neurons 4-7 was followed
after a delay by activation of input neurons 8-11). Membrane
potentials are shown for the component neurons in the network during
the non-matching stimulation. Neurons on the left side of the arrays
primarily received connections from input neurons 4-7, and a separate
set of neurons primarily received connections from input neurons 8-11,
but the random overlap of input and connectivity between these two
populations of neurons allows interactions resulting in non-match
phenomena. The connectivity selected randomly within constraints of
number, distribution, and weight resulted in a range of experimentally
observed phenomena, including non-match enhancement (stel 20),
non-match suppression (stel 18), delay activity (stel 17), input
specificity (pyr 13), and input nonspecificity (pyr 11).
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Sensitivity of large simulation to connectivity changes
In separate simulations, we also tested variations in the number
and distribution of synaptic connections between different populations
of neurons. We varied both number of connections (increasing by 50, 100, and 150%) and window width (unchanged, one cell wider on both
sides, or two cells wider on both sides). For each match or non-match
simulation, we counted how many of the classes of neuronal response
were still present in the simulation. The classes considered were
enhancement, suppression, delay activity, cue (match), or stimulus
specificity (non-match) (i.e., four classes). The average number of
classes appearing in 18 tests was 3.3 (out of 4 classes). In additional
simulations, the sensitivity to background cellular spiking was tested
using the same background rate of 0.5 Hz described above. In these
conditions of background activity, all categories of neural response
types still appeared in both the match and non-match conditions.
To analyze the specificity of the enhancement for the sample stimulus,
we quantified whether cells showing enhancement to one of the
overlapping stimuli (stimulus A or stimulus B) would show selective
enhancement for only the match stimulus. That is, if the cell responds
to stimulus A and shows match enhancement to the second presentation of
stimulus A, to be selective it must not show enhancement to the
non-matching stimulus B that overlaps with stimulus A. This analysis
was only performed for cells that responded to both stimulus A and
stimulus B as sample stimuli. We tested the selectivity of match
enhancement for 10 different networks. There was an average of 8.3 cells per network showing match enhancement, out of which an average of
1.7 cells showed selective match enhancement as defined above. Thus,
~20% of cells showing match enhancement were selective for just one
sample stimulus. The remaining 80% either did not respond to the other
overlapping stimulus or showed nonselective enhancement. For the
selective enhancement cells, the sample stimulus evoked an average of
6.6 spikes and the matching stimulus evoked an average of 9.7 spikes. For these same selective enhancement cells, the overlapping sample stimulus evoked an average of 7.4 sample spikes but the overlapping non-matching stimulus evoked an average of 4.4 spikes.
| |
DISCUSSION |
The simulations presented here demonstrate that the muscarinic
activation of the calcium-sensitive nonspecific cation current INCM could underlie the plateau potentials
and bursting activity observed with intracellular recording from
pyramidal cells in slice preparations of the entorhinal cortex
(Klink and Alonso, 1997a,b; Magistretti et al., 2001)
(Magistretti, Ma, Shalinsky, and Alonso, unpublished
observations). Network simulations support the theory that the
cholinergic activation of this current could underlie properties of the
unit activation observed in the entorhinal cortex during performance of
continuous delayed non-match to sample tasks in rats (Young et
al., 1997) and during performance of delayed match to sample
tasks by monkeys (Miller et al., 1993; Suzuki et
al., 1997). In particular, as shown in Figures 3, 7, 11, and 12, the current directly induces sustained spiking during the delay period of the task, as well as the enhancement of spiking during the
matching period relative to the response to the same stimulus during
the sample period. As shown in Figure 4, this sustained spiking
activity can withstand short periods of hyperpolarization which could
result from distractor stimuli. The muscarinic enhancement of the
INCM current may be further enhanced by
the blockade of potassium currents, which makes the cell more
electrotonically compact (Menschik and Finkel,
1998) (Alonso, unpublished observations). This
would allow somatic generated spikes to more strongly activate dendritic calcium channels, and thereby further enhance the activation of dendritic INCM currents.
Network interactions between cells could underlie additional phenomena
observed in unit recording from awake animals (Suzuki et al.,
1997; Young et al., 1997). These phenomena
include: (1) match suppression (Figs. 8, 11), which could result from
inhibition by interneurons driven by other neurons undergoing match
enhancement; (2) non-match enhancement (Figs. 9A, 12) which
could result from strong excitatory input from nonselective cells; and
(3) non-match suppression (Figs. 9B, 12), which could result
from greater activation of inhibitory interneurons by nonselective
cells. These are examples of potential network mechanisms for the
firing properties of neurons in vivo, but do not exclusively
cover all the possible mechanisms. In the larger network simulation,
these response properties arose naturally from the randomly connected
network, without any procedure focused on tuning of synaptic
connections, suggesting that a network with the intrinsic phenomena
described here easily manifests the various response properties
described in unit recording from behaving animals. When classifying
cells according to their firing properties, cells can be classified as
stimulus selective or nonselective. Our simulations may provide one
explanation for the role of the nonselective cells. In the non-match
simulations, the differential action of the selective and the
nonselective cells and their connectivity to interneurons provide a
mechanism for causing non-match enhancement and suppression activity.
Other potential mechanisms for match suppression
In the simulations presented here, match suppression arises
because of inhibition from neurons showing match enhancement
attributable to INCM or attributable to
activation of slow IKAHP. However, other
potential mechanisms could underlie the phenomena of match suppression.
It is possible that during the initial viewing of a stimulus,
cholinergic modulation is at high levels, whereas subsequent viewing of
a matching stimulus might cause feedback suppression of cholinergic
modulation, which decreases the neuronal activity in response to the
stimulus (Sohal and Hasselmo, 2000). This type of match
suppression should be sensitive to cholinergic blockade. In contrast,
match suppression might also arise from the self-organization of
feedforward connections with a combination of synaptic enhancement and
synaptic depression (Sohal and Hasselmo, 2000;
Bogacz et al., 2001). These mechanisms might be less
sensitive to cholinergic blockade, and this possibility is supported by the absence of a change in match suppression with local infusion of
cholinergic antagonists during recording in the inferotemporal cortex
(Miller and Desimone, 1993). In these cases, match
suppression may be more sensitive to increases in cholinergic
influences because of local infusion of the acetylcholinesterase
blocker physostigmine. Some studies describe an active reset mechanism
such that consecutive presentation of a stimulus as a sample does not
induce match suppression, even if the intervening match presentations
show suppression (Miller et al.,
1991, 1993). This
phenomena could arise if spike frequency accommodation mediates match
suppression and higher levels of acetylcholine during the sample phase
suppress this accommodation. In this case, scopolamine should block the
active reset mechanism. The muscarinic antagonist scopolamine should
block match enhancement mediated by INCM,
but the lack of an effect of scopolamine on match suppression does not
necessarily rule out involvement of INCM
in match suppression during control conditions. Cholinergic blockade by
scopolamine might decrease INCM, but would
simultaneously unmask several potassium currents normally blocked by
muscarinic cholinergic receptor activation, which could thereby
increase AHPs and increase the resulting match suppression in
experimental studies. In addition, cholinergic blockade could also
enhance the magnitude of calcium currents reduced by cholinergic modulation (Magistretti et al., 2001).
Cholinergic modulation of entorhinal cortical function
As yet no data have specifically tested the involvement of
INCM in delay activity in vivo, but
research does support cholinergic modulation of such activity. If
cholinergic activation of INCM is
important to provide intrinsic mechanisms for self-sustained spiking
activity, then blockade of this muscarinic cholinergic activation
should reduce sustained spiking activity during the delay period and
match enhancement. This effect of muscarinic antagonists could underlie
the behavioral impairments in delayed matching tasks seen with systemic
injections of muscarinic antagonists (Bartus and Johnson,
1976; Penetar and McDonough, 1983). In addition to this role in short-term memory function, sustained activity in the
entorhinal cortex could also be very important for effective encoding
of long-term representations through synaptic modification in the
hippocampal formation. If it plays this role in buffering information
for encoding into long-term memory, then blockade of sustained
entorhinal activity by muscarinic antagonists could also underlie the
impairments of encoding for subsequent recognition or recall observed
with local infusion of the antagonist scopolamine into the perirhinal
cortex in monkeys (Tang et al., 1997) or with systemic
injections of scopolamine in monkeys (Aigner and Mishkin, 1986; Aigner et al., 1991) and human subjects
(Ghonheim and Mewaldt, 1975; Peterson,
1977).
Relation to cholinergic modulation in the prefrontal cortex
Intracellular recording has demonstrated that cholinergic
modulation also induces sustained depolarizations after spiking in
slice preparations of the prefrontal cortex (Andrade,
1991; Haj-Dahmane and Andrade,
1996, 1998).
The current in the prefrontal cortex also has calcium-sensitive
properties but differs from the current described here in that it is
voltage dependent. These data were used to support previous models of
working memory function that are dependent on afterdepolarization
(Lisman and Idiart, 1995; Jensen and Lisman,
1996, 1998). These
previous models focused on the simultaneous working memory for multiple
stimuli and did not incorporate the same level of biophysical detail as
the models presented here, but they used essentially the same mechanism
described here. Muscarinic cholinergic modulation of currents in
prefrontal cortical neurons could therefore also contribute to
sustained spiking activity, which has been observed during many
different types of delayed match to sample tasks during recording from
the prefrontal cortex (Fuster, 1973; Wilson et
al., 1993; Miller et al., 1996).
Possible relationship to other models of working memory
A number of other models have been developed for sustained
activity during working memory function. Most of these models focus on
the role of synaptic connectivity in maintaining network activity. One
set of studies has focused on the role of synaptic NMDA receptors in
allowing previously activated neurons to remain active because of the
fact that NMDA receptors will cause stronger currents in neurons that
are already depolarized (Lisman et al., 1998;
Durstewitz et al., 2000). The slower time course of NMDA
receptor currents has also been emphasized in these models, because
these slower dynamics could allow networks to maintain sustained
spiking activity with lower firing rates (Fransén and
Lansner, 1995; Seung, 1996; Lisman et
al., 1998). The neuromodulatory effects of dopamine on
sustained activity were examined in great detail with a simulation containing biophysically detailed representations of prefrontal cortical neurons (Durstewitz et al., 2000). That
simulation focused on the dopaminergic enhancement of persistent sodium
currents (NaP) and NMDA currents, showing that those effects enhanced
the stability of sustained network activity, although they could not allow single neurons to sustain activity. Sustained activity dependent on the pattern of synaptic connectivity may be more appropriate for
encoding of familiar stimuli, whereas intrinsic cellular mechanisms could mediate sustained activity for novel stimuli. Consistent with
this, functional magnetic resonance imaging suggests that the
prefrontal cortex shows greater activation during working memory for
familiar stimuli, whereas medial temporal cortices show stronger
activity during working memory for novel stimuli (Stern et al.,
2001). The intrinsic mechanisms described in here are not
incompatible with the existence of synaptic mechanisms for sustained
activity, although they may result in differences in spike timing and
stability properties. Explicit representation of the cellular
mechanisms that could contribute to spiking activity patterns during
delayed match to sample tasks will allow more detailed experimental
analysis and comparison of the candidate mechanisms for these activity patterns.
| |
FOOTNOTES |
Received April 4, 2001; revised Nov. 8, 2001; accepted Nov. 9, 2001.
This work was supported by National Institutes of Health Grants MH61492
and MH60013, by National Science Foundation Grant IBN9996177, and by a
grant from the Human Frontier Science Program.
Correspondence should be addressed to Dr. Michael E. Hasselmo,
Department of Psychology, Program in Neuroscience, and Center for
Biodynamics, Boston University, 64 Cummington Street, Boston, MA 02215. E-mail: hasselmo{at}bu.edu.
| |
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S. J. Bang and T. H. Brown
Muscarinic Receptors in Perirhinal Cortex Control Trace Conditioning
J. Neurosci.,
April 8, 2009;
29(14):
4346 - 4350.
[Abstract]
[Full Text]
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N. Axmacher, D. P. Schmitz, I. Weinreich, C. E. Elger, and J. Fell
Interaction of Working Memory and Long-Term Memory in the Medial Temporal Lobe
Cereb Cortex,
December 1, 2008;
18(12):
2868 - 2878.
[Abstract]
[Full Text]
[PDF]
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B. Tahvildari, A. A. Alonso, and C. W. Bourque
Ionic Basis of ON and OFF Persistent Activity in Layer III Lateral Entorhinal Cortical Principal Neurons
J Neurophysiol,
April 1, 2008;
99(4):
2006 - 2011.
[Abstract]
[Full Text]
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M. E. Hasselmo
Arc length coding by interference of theta frequency oscillations may underlie context-dependent hippocampal unit data and episodic memory function
Learn. Mem.,
November 15, 2007;
14(11):
782 - 794.
[Abstract]
[Full Text]
[PDF]
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M. Yoshida and A. Alonso
Cell-Type Specific Modulation of Intrinsic Firing Properties and Subthreshold Membrane Oscillations by the M(Kv7)-Current in Neurons of the Entorhinal Cortex
J Neurophysiol,
November 1, 2007;
98(5):
2779 - 2794.
[Abstract]
[Full Text]
[PDF]
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R. A. Koene and M. E. Hasselmo
First-In-First-Out Item Replacement in a Model of Short-Term Memory Based on Persistent Spiking
Cereb Cortex,
August 1, 2007;
17(8):
1766 - 1781.
[Abstract]
[Full Text]
[PDF]
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P. A. Lipton, J. A. White, and H. Eichenbaum
Disambiguation of Overlapping Experiences by Neurons in the Medial Entorhinal Cortex
J. Neurosci.,
May 23, 2007;
27(21):
5787 - 5795.
[Abstract]
[Full Text]
[PDF]
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N. S. Desai and E. C. Walcott
Synaptic bombardment modulates muscarinic effects in forelimb motor cortex.
J. Neurosci.,
February 22, 2006;
26(8):
2215 - 2226.
[Abstract]
[Full Text]
[PDF]
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R. A. Koene and M. E. Hasselmo
An Integrate-and-fire Model of Prefrontal Cortex Neuronal Activity during Performance of Goal-directed Decision Making
Cereb Cortex,
December 1, 2005;
15(12):
1964 - 1981.
[Abstract]
[Full Text]
[PDF]
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J. McGaughy, R. A. Koene, H. Eichenbaum, and M. E. Hasselmo
Cholinergic Deafferentation of the Entorhinal Cortex in Rats Impairs Encoding of Novel But Not Familiar Stimuli in a Delayed Nonmatch-to-Sample Task
J. Neurosci.,
November 2, 2005;
25(44):
10273 - 10281.
[Abstract]
[Full Text]
[PDF]
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K. Schon, A. Atri, M. E. Hasselmo, M. D. Tricarico, M. L. LoPresti, and C. E. Stern
Scopolamine Reduces Persistent Activity Related to Long-Term Encoding in the Parahippocampal Gyrus during Delayed Matching in Humans
J. Neurosci.,
October 5, 2005;
25(40):
9112 - 9123.
[Abstract]
[Full Text]
[PDF]
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S. Kunec, M. E. Hasselmo, and N. Kopell
Encoding and Retrieval in the CA3 Region of the Hippocampus: A Model of Theta-Phase Separation
J Neurophysiol,
July 1, 2005;
94(1):
70 - 82.
[Abstract]
[Full Text]
[PDF]
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C. Wyart, S. Cocco, L. Bourdieu, J.-F. Leger, C. Herr, and D. Chatenay
Dynamics of Excitatory Synaptic Components in Sustained Firing at Low Rates
J Neurophysiol,
June 1, 2005;
93(6):
3370 - 3380.
[Abstract]
[Full Text]
[PDF]
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T. I. Netoff, M. I. Banks, A. D. Dorval, C. D. Acker, J. S. Haas, N. Kopell, and J. A. White
Synchronization in Hybrid Neuronal Networks of the Hippocampal Formation
J Neurophysiol,
March 1, 2005;
93(3):
1197 - 1208.
[Abstract]
[Full Text]
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K. Schon, M. E. Hasselmo, M. L. LoPresti, M. D. Tricarico, and C. E. Stern
Persistence of Parahippocampal Representation in the Absence of Stimulus Input Enhances Long-Term Encoding: A Functional Magnetic Resonance Imaging Study of Subsequent Memory after a Delayed Match-to-Sample Task
J. Neurosci.,
December 8, 2004;
24(49):
11088 - 11097.
[Abstract]
[Full Text]
[PDF]
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J. Magistretti, L. Ma, M. H. Shalinsky, W. Lin, R. Klink, and A. Alonso
Spike Patterning by Ca2+-Dependent Regulation of a Muscarinic Cation Current in Entorhinal Cortex Layer II Neurons
J Neurophysiol,
September 1, 2004;
92(3):
1644 - 1657.
[Abstract]
[Full Text]
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M. R. Tinsley, J. J. Quinn, and M. S. Fanselow
The Role of Muscarinic and Nicotinic Cholinergic Neurotransmission in Aversive Conditioning: Comparing Pavlovian Fear Conditioning and Inhibitory Avoidance
Learn. Mem.,
January 1, 2004;
11(1):
35 - 42.
[Full Text]
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D. A. McCormick, Y. Shu, A. Hasenstaub, M. Sanchez-Vives, M. Badoual, and T. Bal
Persistent Cortical Activity: Mechanisms of Generation and Effects on Neuronal Excitability
Cereb Cortex,
November 1, 2003;
13(11):
1219 - 1231.
[Abstract]
[Full Text]
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P. Zhong, Z. Gu, X. Wang, H. Jiang, J. Feng, and Z. Yan
Impaired Modulation of GABAergic Transmission by Muscarinic Receptors in a Mouse Transgenic Model of Alzheimer's Disease
J. Biol. Chem.,
July 11, 2003;
278(29):
26888 - 26896.
[Abstract]
[Full Text]
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TOP
ABSTRACT
INTRODUCTION
![&agr;<SUB>m</SUB>(V)=<FR><NU>320×10<SUP>3</SUP>(0.0131−V)</NU><DE><IT>exp</IT>[(0.0131−V)/0.004]−1</DE></FR>,](/content/vol22/issue3/fulltext/1081/img001.gif)
![&bgr;<SUB>m</SUB>(V)=<FR><NU>280×10<SUP>3</SUP>(V−0.0401)</NU><DE><IT>exp</IT>[(V−0.0401)/0.005]−1</DE></FR>,](/content/vol22/issue3/fulltext/1081/img002.gif)
![&agr;<SUB>h</SUB>(V)=128<IT>exp</IT>[(0.017−V)/0.018],](/content/vol22/issue3/fulltext/1081/img003.gif)
![&bgr;<SUB>h</SUB>(V)=<FR><NU>4×10<SUP>3</SUP></NU><DE>1+<IT>exp</IT>[(0.040−V)/0.005]</DE></FR>,](/content/vol22/issue3/fulltext/1081/img004.gif)
![&agr;<SUB>m</SUB>(V)=<FR><NU>800×10<SUP>3</SUP>(0.0172−V)</NU><DE><IT>exp</IT>[(0.0172−V)/0.004]−1</DE></FR>,](/content/vol22/issue3/fulltext/1081/img005.gif)
![&bgr;<SUB>m</SUB>(V)=<FR><NU>700×10<SUP>3</SUP>(V−0.0422)</NU><DE><IT>exp</IT>[(V−0.0422)/0.005]−1</DE></FR>,](/content/vol22/issue3/fulltext/1081/img006.gif)
![&agr;<SUB>h</SUB>(V)=320<IT>exp</IT>[(0.042−V)/0.018],](/content/vol22/issue3/fulltext/1081/img007.gif)
![&bgr;<SUB>h</SUB>(V)=<FR><NU>10×10<SUP>3</SUP></NU><DE>1+<IT>exp</IT>[(0.042−V)/0.005]</DE></FR>,](/content/vol22/issue3/fulltext/1081/img008.gif)
![&agr;<SUB>m</SUB>(V)=<FR><NU>16×10<SUP>3</SUP>(0.0351−V)</NU><DE><IT>exp</IT>[(0.0351−V)/0.005]−1</DE></FR>,](/content/vol22/issue3/fulltext/1081/img009.gif)
![&bgr;<SUB>m</SUB>(V)=250<IT>exp</IT>[(0.020−V)/0.040],](/content/vol22/issue3/fulltext/1081/img010.gif)
![&agr;<SUB>m</SUB>(V)=<FR><NU>30×10<SUP>3</SUP>(0.0172−V)</NU><DE><IT>exp</IT>[(0.0172−V)/0.005]−1</DE></FR>,](/content/vol22/issue3/fulltext/1081/img011.gif)
![&bgr;<SUB>m</SUB>(V)=450<IT>exp</IT>[(0.012−V)/0.040],](/content/vol22/issue3/fulltext/1081/img012.gif)
![&agr;<SUB>m</SUB>(V)=<FR><NU>1.6×10<SUP>3</SUP></NU><DE>1+<IT>exp</IT>[<UP>−</UP>72(V−0.065)]</DE></FR>,](/content/vol22/issue3/fulltext/1081/img013.gif)
![&bgr;<SUB>m</SUB>(V)=<FR><NU>20×10<SUP>3</SUP>(V−0.0511)</NU><DE><IT>exp</IT>[(V−0.0511)/0.005]−1</DE></FR>,](/content/vol22/issue3/fulltext/1081/img014.gif)
![&agr;<SUB>m</SUB>([<UP>Ca</UP><SUP><UP>2+</UP></SUP>])=<IT>min</IT>(30×[<UP>Ca</UP><SUP><UP>2+</UP></SUP>], 30),](/content/vol22/issue3/fulltext/1081/img015.gif)
![&bgr;<SUB>m</SUB>(V)=2000[<IT>exp</IT>([0.0065−V]/0.027)]−&agr;<SUB>m</SUB>;](/content/vol22/issue3/fulltext/1081/img019.gif)
![&agr;<SUB>m</SUB>(V)=2000[<IT>exp</IT>([0.0065−V]/0.027)],](/content/vol22/issue3/fulltext/1081/img021.gif)
![&tgr;<SUB>m</SUB>(V)=<FR><NU>1</NU><DE>3.3 <IT>exp</IT>[(V+0.035)/0.040]+<IT>exp</IT>[<UP>−</UP>(V+0.035)/0.020]</DE></FR>,](/content/vol22/issue3/fulltext/1081/img023.gif)
![m<SUB><IT>inf</IT></SUB>(V)=<FR><NU>1</NU><DE>1+<IT>exp</IT>[<UP>−</UP>(V+0.035)/0.005]</DE></FR>,](/content/vol22/issue3/fulltext/1081/img024.gif)
![&tgr;<SUB>m</SUB>(<IT>fast</IT>)(V)=<FR><NU>0.00051</NU><DE><IT>exp</IT>[(V−0.0017)/0.010]+<IT>exp</IT>[<UP>−</UP>(V+0.34)/0.052]</DE></FR>,](/content/vol22/issue3/fulltext/1081/img025.gif)
![m<SUB><IT>inf</IT>(<IT>fast</IT>)</SUB>(V)=<FR><NU>1</NU><DE>[1+<IT>exp</IT>[V+0.0742]/<FENCE>0.00978</FENCE>]<SUP>1.36</SUP></DE></FR>,](/content/vol22/issue3/fulltext/1081/img026.gif)
![&tgr;<SUB>m</SUB>(<IT>slow</IT>)(V)=<FR><NU>0.0056</NU><DE><IT>exp</IT>[(V−0.017)/0.014]+<IT>exp</IT>[<UP>−</UP>(V+0.26)/0.043]</DE></FR>,](/content/vol22/issue3/fulltext/1081/img027.gif)
![m<SUB><IT>inf</IT>(<IT>slow</IT>)</SUB>(V)=<FR><NU>1</NU><DE>[1+<IT>exp</IT>([V+0.00283]/0.0159)]<SUP>58.5</SUP></DE></FR>,](/content/vol22/issue3/fulltext/1081/img028.gif)
![&tgr;<SUB>m</SUB>(V)=<FR><NU>1</NU><DE>&agr;<SUB>m</SUB>+&bgr;<SUB>m</SUB></DE></FR>, <UP>where </UP>&agr;<SUB>m</SUB>(V)=<FR><NU>0.091×10<SUP>6</SUP>(V+0.038)</NU><DE>1−<IT>exp</IT>[<UP>−</UP>(V+0.038)/0.005]</DE></FR>](/content/vol22/issue3/fulltext/1081/img029.gif)
![<UP>and </UP>&bgr;<SUB>m</SUB>(V)=<FR><NU><UP>−</UP>0.062×10<SUP>6</SUP>(V+0.038)</NU><DE>1−<IT>exp</IT>[(V+0.038)/0.005]</DE></FR>,](/content/vol22/issue3/fulltext/1081/img030.gif)
![m<SUB><IT>inf</IT></SUB>(V)=<FR><NU>1</NU><DE>1+<IT>exp</IT>[<UP>−</UP>(V+0.0487)/0.0044]</DE></FR>,](/content/vol22/issue3/fulltext/1081/img031.gif)
![&tgr;<SUB>h</SUB>(V)=<FR><NU>1</NU><DE>&agr;<SUB>h</SUB>+&bgr;<SUB>h</SUB></DE></FR>, <UP>where</UP> &agr;<SUB>h</SUB>(V)=<FR><NU><UP>−</UP>2.88V−0.0491</NU><DE>1−<IT>exp</IT>[(V−0.0491)/0.00463]</DE></FR>](/content/vol22/issue3/fulltext/1081/img032.gif)
![<UP>and </UP>&bgr;<SUB>h</SUB>(V)=<FR><NU>6.94V+0.447</NU><DE>1−<IT>exp</IT>[<UP>−</UP>(V+0.447)/0.00263]</DE></FR>,](/content/vol22/issue3/fulltext/1081/img033.gif)
![h<SUB><IT>inf</IT></SUB>(V)=<FR><NU>1</NU><DE>1+<IT>exp</IT>[(V+0.0488)/0.00998]</DE></FR>,](/content/vol22/issue3/fulltext/1081/img034.gif)
![&agr;<SUB>m</SUB>([<UP>Ca</UP><SUP><UP>2+</UP></SUP>])=<IT>min</IT>(0.02×[<UP>Ca</UP><SUP><UP>2+</UP></SUP>], 10),](/content/vol22/issue3/fulltext/1081/img035.gif)
Compound via MeSH
