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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 I_NCM 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

	ABSTRACT

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS Cell and network models Ionic currents Ca2+ buffering Synaptic currents Network topology RESULTS DISCUSSION REFERENCES

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 I_NCM could provide a cellular mechanism for features of the neuronal activity observed during performance of delayed matching tasks. In particular, I_NCM 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 I_NCM

	INTRODUCTION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS Cell and network models Ionic currents Ca2+ buffering Synaptic currents Network topology RESULTS DISCUSSION REFERENCES

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 I_NCM 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 I_NCM 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 I_NCM 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 I_NCM current. This work has been published previously in abstract form (Fransén et al., 1999b, 2000).

	MATERIALS AND METHODS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS Cell and network models Ionic currents Ca2+ buffering Synaptic currents Network topology RESULTS DISCUSSION REFERENCES

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).

	Cell and network models

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS Cell and network models Ionic currents Ca2+ buffering Synaptic currents Network topology RESULTS DISCUSSION REFERENCES

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 I_NCM. 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.

View larger version (31K): [in this window] [in a new window]   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.

View this table: [in this window] [in a new window]   Table 1.   Compartment profile for the pyramidal cell

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: R_M, 5.0 m²; R_A, 1.0 m; C_M, 0.01 F/m². The value of the membrane reversal potential E_m 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 GABA_B) as part of the leakage current. Note that because the K⁺ current is represented separately, its conductance should be added to the value of R_M 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⁺ (K_dr) currents responsible for fast action potentials, a high-threshold Ca²⁺ current (Ca_L), a calcium-dependent K⁺ current (K_AHP), a fast calcium- and voltage-dependent K⁺ current (K_C), a potassium leak current (K_leak), a persistent-type Na current (NaP), a noninactivating muscarinic K⁺ current (K_M), and the muscarinic activated, nonspecific Ca²⁺-sensitive cationic current I_NCM (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.

View this table: [in this window] [in a new window]   Table 2.   Compartment profile for the stellate cell

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 K_AHP current is stronger in pyramidal cells than in stellate cells, and the K_M 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 I_h 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 K_dr), a high-threshold Ca²⁺ current (Ca_L), a calcium-dependent K⁺ current (K_AHP), a fast calcium- and voltage-dependent K⁺ current (K_C), a potassium leak current (K_leak), a persistent-type Na current (NaP), and a hyperpolarization-activated nonspecific cation current I_h (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.

View this table: [in this window] [in a new window]   Table 3.   Compartment profile for the interneuron

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 K_dr), a high-threshold Ca²⁺ current (Ca_L), a calcium-dependent K⁺ current (K_AHP), and a potassium leak current (K_leak). The K_AHP 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 GABA_A and GABA_B 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.

	Ionic currents

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS Cell and network models Ionic currents Ca2+ buffering Synaptic currents Network topology RESULTS DISCUSSION REFERENCES

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; I_h, 20 mV; and I_NCM, 0 mV.

Na, K_dr. 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 K_dr(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:

View this table: [in this window] [in a new window]   Table 4.   Conductance profile of the pyramidal cell

View this table: [in this window] [in a new window]   Table 5.   Conductance profile of the stellate cell

View this table: [in this window] [in a new window]   Table 6.   Conductance profile of the interneuron

Na.

gate exponent = 2;

gate exponent = 1.

Na(soma).

gate exponent = 3;

gate exponent = 1.

K_dr.

gate exponent = 2.

K_dr(soma).

gate exponent = 4.

Ca_L. 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.

K_AHP. 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.

K_C. 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.

K_M. 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 I_h 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 I_h (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 I_h to allow subthreshold oscillations to develop.


gate exponent = 1;


gate exponent = 1.

K_leak. The K_leak conductance was considered to be linear and uniformly distributed with a reversal potential of: E_rev = 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 I_NCM 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 I_NCM current to replicate experimental traces.

Here we focus on the Ca-sensitive component of I_NCM. Recent evidence suggests that I_NCM 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.

	Ca2+ buffering

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS Cell and network models Ionic currents Ca2+ buffering Synaptic currents Network topology RESULTS DISCUSSION REFERENCES

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 (K_C), 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 K_AHP above were too slow to effectively represent K_C, so different dynamics were necessary. Similarly, the slower changes in I_NCM relative to K_AHP required use of the slower calcium dynamics for I_NCM 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.

	Synaptic currents

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS Cell and network models Ionic currents Ca2+ buffering Synaptic currents Network topology RESULTS DISCUSSION REFERENCES

Synaptic conductances between neurons were modeled with an  function (Bower and Beeman, 1995): g_syn = (A × g_max)/(_d  r) (e^t/_d  e^t/_r), where g_max is the peak synaptic conductance, _r is the rising time constant, _d is the decaying time constant, g_syn is the synaptic conductance at time t, and A is a scaling constant set to yield a maximum conductance of g_max.

For the NMDA current, the conductance was multiplied with the magnesium block conductance described previously (Zador et al., 1990): g_Mg = 1/(1 + 0.018e^60 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). GABA_A is 70% of GABA_B 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 g_max can be found in Tables 8-11.

View this table: [in this window] [in a new window]   Table 7.   Synaptic parameters

View this table: [in this window] [in a new window]   Table 8.   Pure delay activity and match enhancement

View this table: [in this window] [in a new window]   Table 9.   Match suppression and non-match enhancement

View this table: [in this window] [in a new window]   Table 10.   Non-match suppression

View this table: [in this window] [in a new window]   Table 11.   Larger network

	Network topology

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS Cell and network models Ionic currents Ca2+ buffering Synaptic currents Network topology RESULTS DISCUSSION REFERENCES

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.

	RESULTS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS Cell and network models Ionic currents Ca2+ buffering Synaptic currents Network topology RESULTS DISCUSSION REFERENCES

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).

View larger version (15K): [in this window] [in a new window]   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.

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 I_NCM (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 (Ca_L) (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 I_NCM current and block of potassium currents I_KAHP and I_KM brings the cell closer to its firing threshold. If the neuron then discharges, the spike-associated calcium influx potentiates I_NCM, 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 I_NCM current; and (3) the sustained activation of the I_NCM current depolarizes the cell sufficiently to cause generation of another action potential, thereby repeating the cycle.

View larger version (30K): [in this window] [in a new window]   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.)

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 I_NCM 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 I_NCM 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 I_NCM 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 I_NCM 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, I_NCM 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 I_NCM 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 I_NCM to induce additional spiking after the end of the initial afferent input. However, the subthreshold depolarization attributable to I_NCM 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 I_NCM. In this case, the neuron will spike during the initial stimulus period, but the absence of I_NCM 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 I_NCM 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