Low-Voltage-Activated Calcium Channels in the Lamprey Locomotor Network: Simulation and Experiment
Jesper Tegnér1,
Jeanette Hellgren-Kotaleski1, 2,
Anders Lansner2, and
Sten Grillner1
1 Nobel Institute for Neurophysiology, Department of Neuroscience, Karolinska Institute, S-171 77 Stockholm; and 2 Studies of Artificial Neural Systems, Department of Numerical Analysis and Computing Science, Royal Institute of Technology, S-100 44 Stockholm, Sweden
 |
ABSTRACT |
Tegnér, Jesper, Jeanette Hellgren-Kotaleski, Anders Lansner, and Sten Grillner. Low-voltage-activated calcium channels in the lamprey locomotor network: simulation and experiment. J. Neurophysiol. 77: 1795-1812, 1997. To evaluate the role of low-voltage-activated (LVA) calcium channels in the lamprey spinal locomotor network, a previous computer simulation model has been extended to include LVA calcium channels. It is also of interest to explore the consequences of a LVA conductance for the electrical behavior of the single neuron. The LVA calcium channel was modeled with voltage-dependent activation and inactivation using the m3h form, following a Hodgkin-Huxley paradigm. Experimental data from lamprey neurons was used to provide parameter values of the single cell model. The presence of a LVA calcium conductance in the model could account for the occurrence of a rebound depolarization in the simulation model. The influence of holding potential on the occurrence of a rebound as well the latency at which it is elicited was investigated and compared with previous experiments. The probability of a rebound increased at a more depolarized holding potential and the latency was also reduced under these conditions. Furthermore, the effect of changing the holding potential and the reversal potential of the calcium dependent potassium conductance were tested to determine under which conditions several rebound spikes could be elicited after a single inhibitory pulse in the simulation model. A reduction of the slow afterhyperpolarization (sAHP) after the action potential reduced the tendency for a train of rebound spikes. The experimental effects of
-aminobutyric acid-B(GABAB) receptor activation were simulated by reducing the maximal LVA calcium conductance. A reduced tendency for rebound firing and a slower rising phase with sinusoidal current stimulation was observed, in accordance with earlier experiments. The effect of reducing the slow afterhyperpolarization and reducing the LVA calcium current was tested experimentally in the lamprey spinal cord, during N-methyl-D-aspartate (NMDA)-induced fictive locomotion. The reduction of burst frequency was more pronounced with GABAB agonists than with apamin (inhibitor of K(Ca) current) when using high NMDA concentration (high burst frequency). The burst frequency increased after the addition of a LVA calcium current to the simulated segmental network, due to a faster recovery during the inhibitory phase as the activity switches between the sides. This result is consistent with earlier experimental findings because GABAB receptor agonists reduce the locomotor frequency. These results taken together suggest that the LVA calcium channels contribute to a larger degree with respect to the burst frequency regulation than the sAHP mechanism at higher burst frequencies. The range in which a regular burst pattern can be simulated is extended in the lower range by the addition of LVA calcium channels, which leads to more stable activity at low locomotor frequencies. We conclude that the present model can account for rebound firing and trains of rebound spikes in lamprey neurons. The effects of GABAB receptor activation on the network level is consistent with a reduction of the calcium current through LVA calcium channels even though GABAB receptor activation will affect the sAHP indirectly and also presynaptic inhibition.
 |
INTRODUCTION |
In the lamprey locomotor system, the spinal circuitry underlying locomotion has been characterized in considerable detail (see Grillner et al. 1995
). On the segmental spinal level, it consists of local excitatory interneurons (Buchanan and Grillner 1987
), which ipsilaterally excite motor neurons, and inhibitory premotor interneurons, notably the crossed, caudally projecting interneurons that provide reciprocal inhibition between the left and right sides, thus assuring alternating activity (Buchanan 1982
). In addition, the cellular properties of circuit neurons play an important role in the basic mode of operation. For instance, the slow afterhyperpolarizations (sAHP) after each action potential summate during repetitive firing, and the N-methyl-D-aspartate (NMDA) receptor-induced membrane properties may help in terminating the burst activity on the active side (El-Manira et al. 1994
; Sigvardt et al. 1985
; Wallén and Grillner 1987
). Thus the central pattern generator network operates through an interaction between intrinsic membrane properties and synaptic interactions. The spinal network is normally activated from the brain stem via glutamatergic synaptic transmission (NMDA and non-NMDA receptors) (Grillner et al. 1991
; McClellan and Grillner 1984
; Ohta and Grillner 1989
), whereas experimentally the isolated spinal cord also can be activated by adding excitatory amino acids to the bath (Cohen and Wallén 1980
; Grillner et al. 1981
, 1991
).
Computer simulations on the network level have been essential for gaining insight into the mode of operation of this network. Detailed model neurons of the Hodgkin-Huxley type (Hodgkin and Huxley 1952
) equipped with Na+, K+, Ca2+, and calcium-dependent potassium channels, K(Ca), were used to simulate the segmental network (Grillner et al. 1988
; Hellgren et al. 1992
; Wallén et al. 1992
). The model network exhibited a broad frequency range comparable with that seen experimentally. In addition, simulations of the brain stem-spinal cord network, including movement sensory-related feedback (Ekeberg 1993
; Tråvén et al. 1993), has been performed to analyze to what extent the model system can account for the experimental observations. During forward swimming, there is a rostrocaudal delay between the segments that is ~1% of the cycle duration (i.e., a constant phase lag). The intersegmental coordination also has been modeled in detail using Hodgkin-Huxley neurons (Waddén et al. 1995) and in a more abstract level by representing the segments as a chain of nonlinear oscillators (Cohen et al. 1992
; Kopell 1988
; Williams 1992
).
Different modulatory systems control the activity of the spinal circuitry, for example GABAergic and serotonergic neurons, act on Ca2+ and K(Ca) channels, respectively (Matsushima et al. 1993
; Tegnér et al. 1993
; Wallén et al. 1989
). The ability of some of these cellular mechanisms to account for the effects observed on the network level has been tested in the previous simulations discussed above. In this study, we investigate further the GABAergic modulation of one type of calcium channel that is activated at low membrane potentials to produce action potentials. This low-voltage-activated (LVA) calcium conductance can be activated after a preceding hyperpolarization. Calcium channels have been classified into two main groups (Nowycky et al. 1985
; Tsien et al. 1988
). The high-voltage-activated class (HVA) includes the P (Mintz et al. 1992
; Usowicz et al. 1992
), N, and L type. The T channels are included in the LVA group. When a neuron is kept depolarized, the LVA calcium channels become inactivated. If a neuron is hyperpolarized by an inhibition, the inactivation is removed (i.e., deinactivation), and, consequently, a LVA calcium current is activated that can produce a rebound depolarization and possibly an action potential. LVA calcium channels have been observed in a number of systems, such as sensory dorsal cells in the lamprey (Christenson et al. 1993
) and mammalian dorsal root ganglion cells (Carbone and Lux 1984
), thalamic relay neurons (Bal and McCormick 1993
; Coulter et al. 1989
; Huguenard and Prince 1992
), and cerebellar inferior olivary neurons (Llinás and Yarom 1981
). The LVA calcium conductance has been modeled previously in the thalamocortical relay neurons (Destexhe et al. 1993a
,b
, 1994
; Huguenard and McCormick 1992
; McCormick and Huguenard 1992
; Rush and Rinzel 1994
; Wang et al. 1991
).
In the lamprey, the somatodendritic effects of
-aminobutyric acid-B (GABAB) receptor activation have been studied on premotor interneurons and motorneurons (Matsushima et al. 1993
) where both LVA and HVA calcium currents were found to be reduced by GABAB receptor activation. At the network level, GABAB receptor activation decreases the burst frequency (Tegnér et al. 1993
). The purpose of this study was to model the LVA calcium current using the Hodgkin-Huxley formalism based on available experimental data (Matsushima et al. 1993
), to investigate whether the LVA calcium model can account for the experimental findings at the cellular level, to experimentally compare network effects of the sAHP and the LVA calcium current, respectively, and to examine if the frequency reduction induced by GABAB receptor activation could be due to the reduction of the LVA calcium conductance. In addition to the somatodendritic GABAB effects on LVA and HVA calcium currents, there is also a presynaptic modulation on primary afferents (Christenson and Grillner 1991
) and propriospinal interneurons via GABAA and GABAB receptors (Alford and Grillner 1991
; Alford et al. 1991
).
 |
METHODS |
Single cell, segmental population model and data analysis of the simulations
SINGLE CELL MODEL.
We have used a compartmentalized Hodgkin-Huxley cell model (Brodin et al. 1991
; Ekeberg et al. 1991
; Hellgren et al. 1992
; Hodgkin and Huxley 1952
; Tråvén et al. 1993; Wallén et al. 1992
), containing a soma, a small initial segment compartment, and a three-compartment dendritic tree. Parameters of the cell model have been matched previously to the properties of lamprey spinal neurons (Brodin et al. 1991
; Ekeberg et al. 1991
). The soma is equipped with Na+, K+, high-voltage-activated calcium, low-voltage-activated calcium (see below), and K(Ca) channels. The initial segment has sodium and potassium conductances. The three dendritic compartments have, in addition to their passive properties, ion channels representing input synapses. The inhibitory synapses are located on the dendritic compartment adjacent to the soma whereas the excitation is placed on the second dendritic compartment (Ekeberg et al. 1991
; Russell and Wallé
1983). Excitatory and inhibitory synaptic effects are modeled as conductance increases in the respective dendritic compartment. On the excitatory side, there are voltage-dependent NMDA receptor channels as well as fast
-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA)/kainate synapses, both of which are saturating. This accounts for the fact that the synaptic conductance cannot grow without limit as the firing frequency of the presynaptic cell increases (Tråvén et al. 1993). Even though it is likely that active conductances are present on the dendrites, we have not extended the cell model in this direction, because sufficient data is as yet lacking. In all single cell simulations, only the steady state condition was analyzed. Parameters used in this study for the single cell (without LVA properties) are found in Table 1 in Brodin et al. (1991)
and Tråvén et al. (1993).
POPULATION SEGMENT.
To model a single segment of the spinal cord, a population of model neurons was used. A single segment consisted of five crossed inhibitory interneurons (C) and seven excitatory interneurons (E) on each side (see also Fig. 10) because it represents at least one-third of the estimated number of C and E cells (Buchanan and Grillner 1987
; Buchanan et al. 1989
). A subsampling was done to restrict the computational demands. To behave more realistically, cell sizes, synaptic conductances, and delays were distributed normally with a standard deviation of 15% (Hellgren et al. 1992
). Background noise was added (as a constant) when the segmental population network was simulated, except when stated. The initial transient part lasted for 1-2 s, and the simulation data was analyzed only after 3 s when regular activity appeared. Parameters for synaptic strength are found in Hellgren et al. (1992)
. The lateral interneurons that were included in earlier models (Buchanan 1992
; Grillner et al. 1988
; Wallén et al. 1992
; Williams 1992
) are not required in the cell population model, and because there is no evidence to suggest that they play a significant role, they are not included (Fagerstedt et al. 1995
; Hellgren et al. 1992
).

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| FIG. 10.
Simulation model of segmental network. Model consists of 5 inhibitory (c) interneurons in 1 hemisegment, reciprocally inhibiting other hemisegment. Seven excitatory (E) interneurons are added on each side of segment.
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DATA COLLECTION AND ANALYSIS.
The simulations used the UNIX-based simulation program SWIM (Ekeberg et al. 1994
) running on DEC machines. The single-cell simulations were analyzed by using MATLAB (MathWorks), and the frequency for the network simulations was calculated automatically by detection of the individual spikes. The term burst frequency refers to the number of bursts per second, i.e., the reciprocal of the cycle duration that is the time interval between the midpoints of two successive bursts. The coefficient of variation was calculated as the ratio of the standard deviation and mean.
Model of LVA calcium channel, calcium pool, and implementation into SWIM
The functional significance of the LVA calcium conductance is that an inhibitory input can remove the inactivation and elicit a rebound. The following definitions will be used: when the neuron elicits a depolarization larger than the holding potential, it will be referred to as a rebound depolarization; if an action potential is elicited, it is called a rebound spike. The term rebound refers either to a rebound spike or a rebound depolarization.
Based on previous experimental (Bal and McCormick 1993
; Coulter et al. 1989
; McCormick and Huguenard 1992
) and simulation (Destexhe et al. 1993a
,b
, 1994
; Huguenard and McCormick 1992
; Rush and Rinzel 1994
; Wang et al. 1991
) studies on thalamic relay cells and thalamic nucleus reticularis (nRT) neurons, we have extended our previous Hodgkin-Huxley based cell model (Ekeberg et al. 1991
) to include a LVA calcium conductance that underlies the rebound. Following previous work (Coulter et al. 1989
; Destexhe et al. 1993b
; Rush and Rinzel 1994
; Wang et al. 1991
), we have used the m3h form for the conductance for reasons given below. The important point is that the LVA calcium current has an inactivation (a low value of h) in addition to the activation (a large value of m). This means that the channel is modeled using three states (open, closed, and inactivated) and first-order reactions with different rate constants give the transition rates between the states (Hille 1992
; Hodgkin and Huxley 1952
). It is important that the net conductance is in the correct potential range, to some extent independently of the choice between the m3h or m2h form, to allow the possibility of scaling the net conductance by tuning the maximal conductance parameter GLVA. The parameters in the cell model thereafter are tuned by comparison with experimental data on lamprey neurons (Matsushima et al. 1993
).
Briefly, the potential for each compartment is computed by the following differential equation (Ekeberg et al. 1991
)
|
(1)
|
The passive model thus consists of a system of coupled differential equations, with one equation for each compartment. The conductance Gm represents the passive leakage current through the membrane. The equilibrium potential of the leak is Eleak and Gcore is the conductance through which the compartments are connected.
The Ichannels term represents the summed currents entering into the compartment through all active ion channels. The current through LVA calcium channels, entering the soma compartment, has a sodium-like model, but with different kinetics (different parameter values describing the m and h variables) and is computed as
|
(2)
|
where ELVA is the reversal potential for the LVA calcium channels, which, in our simulations, is set to +150 mV (Llinás and Yarom 1981
; McCormick and Huguenard 1992
), which is also the reversal potential for the high-voltage-activated calcium currents in the earlier modeling studies on lamprey neurons (Ekeberg et al. 1991
). Furthermore, GLVA is the maximum calcium conductance through the membrane (determined to 2.5 mS/cm2 in this study) and m and h are the degrees of activation and deinactivation of the LVA channels, respectively.
The activation of the LVA channels is described by
|
(3)
|
where
is the rate by which the channels switch from a closed to an open state and
is the rate for the reverse. The
and
parameters depend only on the membrane potential in the soma and are given by the following expressions (Ekeberg et al. 1991
; Frankenhaeuser and Huxley 1964
)
|
(4)
|
The inactivation process of the LVA channels is described by a similar set of equations
|
(5)
|
|
(6)
|
Thus because a low value of h represents a large degree of inactivation whereas a large value corresponds to deinactivation, we will refer to h itself as deinactivation.
Like most other neurons, lamprey spinal neurons exhibits spike frequency adaptation, which is due to K(Ca) channels. During continuous firing, the intracellular calcium level is increased and activates a K(Ca) current. It therefore has been important to model the intracellular calcium in addition to the K(Ca) channels. The intracellular calcium has been modeled previously by using two different "intracellular pools": a fast CaAP pool for the calcium inflow during the action potential and a slow CaNMDA pool for calcium entering through the NMDA channels (Brodin et al. 1991
). Both the fast (CaAP pool) and slow (CaNMDA pool) calcium pools have parameters for calcium ion influx and decay. In addition, for the CaNMDA pool, a variable between 0 and one is added, representing the Mg2+ block. There is a possibility that the calcium inflow through LVA channels also could contribute to the activation of IK(Ca) current. In the present simulations, however, we have not assumed this to be the case. However, a third calcium pool was added to the simulation program SWIM for the intracellular LVA calcium. The pool is modeled in a similar manner as the other two pools but separate parameters for the influx and decay of the LVA calcium pool is provided to allow for the possibility that the intracellular LVA calcium could have different kinetics compared with the other two pools. This third calcium pool has not been used in this study because there is no direct experimental evidence suggesting that the calcium entering through the LVA calcium channel activates a K(Ca) channel and because we aimed at using as small a model as possible to account for experimental data on single cells (Matsushima et al. 1993
). This, however, will be investigated further in a later study (Tegnér and Grillner, in preparation).
In summary, in this study, we have implemented into the UNIX-based simulation program SWIM (Ekeberg et al. 1994
), the LVA calcium conductance and the possibility of letting the LVA calcium pool influence the K(Ca) channels. In this study, we tried to account for the experimental data using a simplified model without a separate LVA calcium pool. In a later study, we will test the possible interaction among LVA calcium, LVA calcium pools, and the IK(Ca) current.
Experimental protocol and data analysis
PROTOCOL.
Experiments were done on adult lampreys (Ichthyomyzon unicuspis) anesthetized with tricaine methane sulphonate (MS222, 100 mg/l). The spinal cord and the notochord were dissected in cooled physiological saline and pinned down in a Sylgard-lined chamber (Rovainen 1974
; Wallén et al. 1985
) and perfused with oxygenated saline containing (in mM) 91 NaCl, 2.1 KCl, 2.6 CaCl2, 1.8 MgCl2, 20 NaHCO3, and 4 glucose (pH = 7.4). Fictive locomotion was induced by adding NMDA (Tocris Neuramin) to the saline (Grillner et al. 1981
). The GABAB agonist baclofen (Tocris Neuramin) and the inhibitor of K(Ca) channels, apamin (Sigma), also were used in this study. The efferent motor activity was recorded by using glass suction electrodes attached to two reciprocal ventral roots exiting from the spinal cord. Intracellular recording data and recording methods are described in Matsushima et al (1993)
.

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| FIG. 1.
Activation and inactivation for a rebound near spike threshold. A: a rebound spike ( ) occurred when a 100-ms pulse of 0.18 nA was given. Spike itself is a conventional sodium potassium spike with a slow afterhyperpolarization (sAHP) caused by K(Ca) channels. On the other hand, a current amplitude of 0.125 nA resulted in a rebound depolarization (- - -), which is above holding potential ( 54 mV). B: degree of activation (m). Note that initial m value is ~0.6 (see also Fig. 4A) because simulation trace begins when a steady state value has been reached. C: degree of deinactivation (h). Note smaller amount of removal of inactivation for smaller current pulse (- - -) during the negative current step. D: net effect of activation and deinactivation (m3h), which is proportional to total inward current given by ILVA = (ELVA Esoma)GLVAm3h.
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DATA COLLECTION AND ANALYSIS.
Data was acquired using a personal computer (486 PC-type) with AD/DA interface programs (AXOTAPE; Axon Instruments). Data were analyzed usingDATAPAC from Run Technologies.
 |
RESULTS |
Single cell
The parameters for the LVA calcium channel used in our cell model were arranged in the following manner as a first approximation, steady state activation and deinactivation curves and time constants were taken from the literature (McCormick and Huguenard 1992
; Wang et al. 1991
). Second, a fine tuning was done by using experimental data from lamprey spinal neurons (Matsushima et al. 1993
) in which the amplitude and duration of the hyperpolarizing current pulses were varied (Figs. 2 and 3). The simulations presented in Figs. 5-9 for the single model cell essentially followed (to be detailed below) from this tuning.

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| FIG. 2.
Tuning of pulse current amplitude dependency of the rebound response. A: a lamprey neuron was given a 100-ms negative current pulse of increasing magnitude (A1-A3). A small current pulse (A1) gave a slight rebound depolarization whereas a large pulse amplitude gave a larger rebound depolarization (A2). In A3, an even larger pulse was sufficient to elicit a rebound spike. B: simulation of current pulse amplitude dependence. Same pattern is observed using current amplitudes of 0.10 (top  ), 0.125 (- - -) and 0.16 nA (bottom  ). Scale bar applies to both experimental recordings and simulation, and bar below voltage traces indicates duration of negative current pulse.
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| FIG. 3.
Tuning of current duration dependency of the rebound response. A: a lamprey neuron was given a fixed current amplitude with variable duration, 20 ms (A1), 40 ms (A2), and 60 ms (A3). Note that a 40-ms pulse occasionally failedto elicit a rebound spike. Bar below voltage traces indicates duration of negative current pulse. B: simulation using 20-, 40-,50-, and 60-ms duration of the current pulse ( 0.24 nA). Model cell is tuned to elicit a rebound when a 50-ms pulse is given but not if duration is 40 ms. Net effect of activation (m, B2) and deinactivation (h, B3) is shown in B4. A longer pulse duration removes a larger degree of inactivation (top - - -, B3) leading to a larger m3h factor (B4).
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| FIG. 5.
Role of holding potential for rebound. A: a lamprey neuron is held at 3 different holding potentials by continuous current injection in DCC mode. Same current amplitude and duration was used in A1-A3. No rebound spike occurs if cell is held at 58 mV (A1). If holding is changed to either 55 (A2) or 53 mV (A3), a rebound spike is elicited. Note that latency for spike at 55 mV is longer compared with that when cell is held at 53 mV. There is also a tendency for a rebound depolarization after first spike when cell is held at 53 mV ( , A3). Bar below voltage traces indicates duration of negative current pulse. B: simulated neuron is held at 53 mV (B1, - - -), 55 mV (B1, middle  ), and 58 mV (B1,  ). There is no rebound spike at 58 mV and rebound spikes appear with latency differences similar to experiments when model cell is held at 55 and 53 mV. Net effect of activation (m, B2) and deinactivation (h, B3) is shown in B4 (m3h factor). Note also large m3h factor initially after release of negative current pulse. Duration of current pulse is 100 ms in A and B.
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ACTIVATION AND DEINACTIVATION KINETICS DURING A REBOUND DEPOLARIZATION AND THE EFFECTS ON SINGLE CELL PARAMETERS OF USING VARIABLE STIMULATION AMPLITUDE AND DURATION.
One advantage of using simulations is the possibility of investigating how the activation and inactivation changes during a rebound depolarization. In Fig. 1, a model neuron is given a 100-ms hyperpolarizing pulse of two different amplitudes to illustrate the difference between a sub- and a suprathreshold stimulation for eliciting a rebound depolarization and a spike, respectively. The model neuron is held at
54 mV, and the larger negative current pulse elicits a rebound spike after the hyperpolarization is ended (solid line in Fig. 1A). Because the potential is clamped to
54 mV, the activation (m) and deinactivation (h) will reach a steady state value determined by their steady state kinetics (see Fig. 4). A high m value corresponds to a large degree of activation (Fig. 1B) and thus a low h value, which indicates that the LVA calcium channels are inactivated (Fig. 1C). The factor m3h therefore be will >0 in the steady state condition when the model cell is held at
54 mV. The applied negative pulse will remove the inactivation and consequently h increases (Fig. 1C) on a time scale determined by its time constant (see below) at a given voltage. Similarly, m is reduced (Fig. 1B) during the negative current pulse. When the pulse is released, the channel starts to activate faster than the rate of inactivation. The consequence of this difference in time constants is that a sizeable inward current develops (Fig. 1D) that depolarizes the membrane potential to the extent that a spike is elicited (Fig. 1A, solid line). It should be noted that when the spike is repolarized, the sAHP is sufficient to remove the inactivation of the LVA channels (Fig. 1C, solid line). However, if a smaller current pulse is used, the amount of inactivation removed will be smaller (Fig. 1C, dashed line) and as a result, a smaller net inward LVA calcium current will occur which elicits only a rebound depolarization (Fig. 1A, dashed line).

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| FIG. 4.
Activation and deinactivation curves for the LVA calcium channel. A: command voltage-dependence of steady state deinactivation ( ) and activation (- - -) calculated using values in Table 1 and Eq. 8. B: m3h curve. C: command voltage dependence of time constant for activation (Eq. 7). D: command voltage dependence of time constant for deinactivation. Note slower time scale for deinactivation.
|
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In the example given above, the parameters were given values according to Table 1. The general idea was to use only a small number of experimental features to test to what extent other properties on the single cell level could follow from these. First, we used the size of the hyperpolarization induced by the negative pulse necessary for triggering a rebound spike using similar holding potential as in experiment (Matsushima et al. 1993
). We changed the A-C values (Table 1) and the maximal conductance for the channel, GLVA (we did not modify the reversal potential), and we accepted the values when the required hyperpolarization values were in the order of 2-3 mV from the values found in the experiments (Matsushima et al. 1993
). Experimentally, it is found that the probability of eliciting a rebound spike increases when the hyperpolarization pulse amplitude is increased (Fig. 2A2). The response amplitude is modified from a rebound depolarization (Fig. 2A1) and (Fig. 2A2) to a rebound spike (Fig. 2A3). When the membrane potential of the model cell (Fig. 2B) was held constant, a similar hyperpolarizing pulse amplitude dependency is present. After a subthreshold pulse, a rebound depolarization is observed both experimentally (Fig. 2A, 1 and 2) and in the simulation (Fig. 2B, dashed and solid line below spike threshold). Increasing the pulse amplitude results in a rebound spike (Fig. 2, A3 and B).
The second experimental characteristic used was the increased amplitude of the rebound depolarization with an increase in the duration of the negative current pulse at a given holding potential. A 20-ms pulse (Fig. 3A1) elicited only a rebound depolarization whereas a 40-ms pulse (Fig. 3A2) elicited a larger depolarization and sometimes a rebound spike. Spiking occurred regularly with an even longer (60 ms) pulse (Fig. 3A3). The model cell (Fig. 3B) showed a similar dependence on duration, because, with increasing duration, the rebound depolarization increased to elicit a rebound spike at 50 ms. In Fig. 3B, 2-4, the activation (m), deinactivation (h), and the net result (m3h) are shown (see METHODS). The activation (m variable) increases clearly with a longer pulse, although the kinetics for the activation are relatively fast (in the order of 5 ms, Fig. 4C). The inactivation (Fig. 3B3) is a slower process (see also Fig. 4D). This means that the longer duration of the pulse, the larger the removal of inactivation (h increases). Note also that in the trace in which the action potentials are elicited a substantial removal of inactivation occurs. The net effect is that a larger m3h factor is generated by using a longer pulse (Fig. 3B4, dashed line, the longest pulse) leading to a larger inward current and consequently to a rebound spike.
STEADY STATE KINETICS FOR THE ACTIVATION AND DEINACTIVATION.
Using the 12 different A-C values represented in Table 1 (see also METHODS), the time constants for activation and deinactivation were calculated from the following equations: (Hille 1992
)
|
(7)
|
and the steady state activation and deinactivation by (Hille 1992
)
|
(8)
|
The steady state kinetics for activation and deinactivation and their respective time dependence as shown in Fig. 4. The degree of inactivation is dependent on the holding potential (Fig. 4A, h
, solid line). If a model cell is held at a depolarized potential, the channel is inactivated to a large degree (small h), and consequently a hyperpolarizing step will remove this inactivation. The activation (Fig. 4A, m
, dashed line) on the other hand is lowered when the model cell is hyperpolarized. However, because the deinactivation and activation curves intersect at a non-zero level, an interval exist in which the m3h factor becomes large enough to induce a sizeable inward current (Fig. 4B). Obviously m3h will be 0 whenever either m or h is 0. An important feature of the LVA calcium is the short time scale for activation (
m) shown in Fig. 4C, and the long time scale for deinactivation (
h) shown in Fig. 4D, approximately in the range of 30-350 ms depending on the holding potential. For example, if a model cell is held below spike threshold and a negative current step, sufficient to elicit a rebound spike, is given then the potential during the negative step is usually
70 mV or larger and
h consequently is >100 ms while
m is ~5 ms. The functional consequence of this arrangement is that the rate of inactivation during the release of the negative current step is slow enough to permit a transient inward current to be generated.
ROLE OF HOLDING POTENTIAL FOR THE LATENCY OF REBOUND SPIKES AND THE OCCURRENCE OF SEVERAL REBOUND SPIKES.
The closer the holding potential is to the threshold for eliciting an action potential, the larger the likelihood to elicit a large rebound depolarization or spike (Matsushima et al. 1993
). The holding potential threshold for the occurrence of a rebound spike (for a given pulse amplitude and duration) was around
55 mV in the cell illustrated in Fig. 5A, 1-3. The second observation is that the spike occurs earlier when the cell is more depolarized (Fig. 5A, 3 compared with 2). Note also that at
53 mV, a second rebound depolarization occurs because the AHP following the first spike has removed the inactivation of the LVA calcium channel e.g., deinactivated the LVA calcium channel (arrow in Fig. 5A3). This also was found in the simulations (Fig. 5B) when a hyperpolarizing pulse of similar amplitude as in the experiments was provided. In Fig. 5B1, the model cell is held at
58 mV (the lowermost solid line) and there is no rebound spike, whereas at
55 mV (middle solid line) or
53 mV (dashed line), a rebound spike occurs. The spike also occurs earlier when the model cell is more depolarized (compare the dashed line with the top solid line in Fig. 5B1). This occurs because the difference between the holding potential and spike threshold has been reduced. If the model cell is held in the "rebound range", the rebound depolarization will be larger the more depolarized the model cell and eventually an action potential will be elicited. Furthermore, at a more depolarized level the m3h factor will be larger as shown in Fig. 5B4 (see also Fig. 4B). Note how the activation (m) increases with degree of depolarization (Fig. 5B2) and how the deinactivation, (h in Fig. 5B3) changes with holding potential. A large m3h factor (Fig. 5B4) means a large LVA calcium current resulting in a larger depolarization when the hyperpolarizing pulse is released. The most important factor is the m value, which at more depolarized potentials gives a larger m3h factor initially after the negative pulse is released, even though the h value is smaller when the model cell is held at
53 mV as compared with
55 mV. The slight difference in the time scale of activation may also play a role (Fig. 4C). From the tuning of the model (Figs. 2 and 3), it follows that the holding potential threshold for the spikes is similar and that there is a shorter latency to spike when the model cell is more depolarized and is stimulated in a similar manner to the experiments.
Another important property of lamprey neurons (Matsushima et al. 1993
) is their ability to produce a sustained firing following a single negative current pulse, hereafter referred to as a rebound train (Fig. 6). If a neuron is held at the potential just below the threshold for the action potential, a single hyperpolarizing current pulse can give rise to a long-lasting spike train. It also should be noted that the voltage slope during the negative pulse is positive when the cell is held at
52 mV (indicated in Fig. 6A with a solid line) but not if the holding potential is changed to
55 mV (Fig. 5A2) in this cell. The simulations here are used with the purpose of analyzing 1) the factors determining whether there will be a single rebound spike or a train and 2) the factors that determine the slope during the negative current pulse at depolarized holding potentials. The difference between a given holding potential and the reversal potential for the sAHP is a crucial factor for the first set of factors above in 1.Figure 6D shows a parameter plot of the holding potential and the reversal potential of the sAHP for the simulation model. A rebound train occurs in the upper part of the parameter space in which the model cell is more depolarized and/or the sAHP reversal potential is more negative, whereas in the lower part, there is only a single rebound spike. In conclusion, the sAHP has to be large enough compared with the holding potential to remove the inactivation sufficiently to generate an inward LVA calcium current (m3h factor in Fig. 6E3) and trigger a new rebound spike. Figure 6, B and C, shows two simulations with repetitive and single rebound spikes, respectively, with parameter values as indicated in Fig. 6D. Because the reversal potential for the sAHP was important for the occurrence of rebound firing, the effect of increasing and decreasing the maximal conductance of the sAHP also was tested. A reduction or increase of the conductance of the sAHP by 20% modifies the location of the boundary line (solid line, Fig. 6D) separating the parameter plot into single spikes and rebound trains. Thus a conductance decrease, at a given holding and reversal potential of the sAHP at the boundary in the control, forces either the reversal potential of the sAHP to be lowered or holding the model neuron at a more depolarized membrane potential in order to elicit a train of rebound spikes (dashed-dotted line, Fig. 6).

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| FIG. 6.
Factors responsible for occurrence of a rebound train. A: a 100-ms current pulse elicits a train of rebound spikes (3 last spikes are indicated by arrowheads) in a lamprey neuron when cell is held at 52 mV (this is same cell as in Fig. 5A). Note positive slope on voltage during negative current pulse as indicated ( ). Scale bar also applies to B and C. B: simulated cell is held at 48.5 mV, and reversal potential of slow afterhyperpolarization (sAHP) is changed from 80 to 77 mV. Note similar positive slope during negative current pulse as compared with experiment in A. C: simulated cell is held at 54 mV, and reversal potential of sAHP is changed from 80 to 85 mV. Note that under these conditions, no positive slope during negative current pulse and only a single rebound spike is evoked. Bar below voltage traces in A-C indicates duration of negative current pulse. D: parameter plot of holding potential and reversal potential of sAHP vs. occurrence of a train of rebound spikes or not. A similar current is used in all cases, and simulations in B and C are indicated in D. Line connecting s separates parameter area in which a rebound train occurs or not. - - -, how boundary between single spikes and rebound trains is translated if maximal conductance of sAHP is increased (+20%) or decreased ( 20%). E: this shows activation (m, E1) and deinactivation (h, E2), and net effect (E3) for simulations in B ( ) and C(- - -). Note larger degree of activation when model cell is held at a more positive holding potential, resulting in a larger net current even though degree of removal of inactivation is larger (E2, - - -) when model cell is held at a more hyperpolarized potential.
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When the model cell is held at a more depolarized level (Fig. 6B,
48.5 mV), the slope is positive during the negative current pulse in contrast to when the model cell is held at
54 mV (Fig. 6C). The m3h factor (Fig. 6E3, solid line, compare also with Fig. 4B) is >0 during the negative current step at the more depolarized holding potential, indicating that a positive calcium current will develop during the pulse and depolarize the model cell slightly during the negative current pulse. The underlying cause of this phenomena is the larger degree of activation (Fig. 6E1, solid line) at the more depolarized holding potential combined with a certain amount of deinactivation with a longer time constant (Fig. 6E2, solid line) resulting in a larger m3h value (compare Figure 6E1, dashed line, which corresponds to the
54 mV holding used in Fig. 6C). We therefore conclude that the depolarizing slope occurring during a negative current pulse at a depolarized holding potential can be accounted for by a LVA calcium current.
Other aspects of the rebound are in which holding potential range it occurs and how the amplitude of the negative voltage deflection depends on the holding potential (Fig. 7). When the model cell is held at
61 mV (Fig. 7A, solid line), a rebound spike occurs, whereas at
64 mV (Fig. 7A, dashed line), no rebound occurs even if the current amplitude is increased (not shown); this compares well with the experimental range (Fig. 7B, dashed line). The degree of activation (m) is reduced markedly when the holding potential is lowered (see also Fig. 4A), and the m3h factor thereby will become negligible at potentials below
62 mV (Fig. 4B); this accounts for the lower holding potential limit of the rebound spike.

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| FIG. 7.
Holding potential determines if a rebound spike occurs as well as size of amplitude of hyperpolarization during negative current step. A: holding model cell at 61 mV ( ) elicits a rebound spike whereas at 65 mV (- - -), it does not. Note that even if current pulse amplitude is increased, no spike occurs when model cell is held at 65 mV (not shown). Bar below voltage traces indicates duration of negative current pulse. B: - - -, holding potential range (abscissa) in experiments where a rebound spike occurs (note that this does not indicate amplitude of hyperpolarization). Curves ( ) show relation between size of hyperpolarization induced by a fixed negative current pulse and holding potential. , experimental values; *, simulated values. Same current is used (0.25 nA) in simulations.
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Another observation in the experiments was that the amplitude of the potential change in response to the negative current increases (range from
11 to
14 mV) when the holding potential is depolarized (Fig. 7B, solid line,
). A curve with a similar shape (see also DISCUSSION) was obtained in the simulations (Fig. 7B, solid line, *). A model neuron with a LVA calcium current will have a positive inward current when the holding potential is depolarized (see Fig. 4); this means that less positive current will be needed in the rebound range to depolarize the model cell to a certain level. However, during the negative current pulse, this maintained inward current will be reduced due to a reduction in m leading to a larger hyperpolarization caused by the negative current step in the rebound range, as compared with a more hyperpolarized holding potential at which this LVA calcium conductance is not present (not illustrated). Therefore, the amplitude of the hyperpolarizing step will be larger when the model cell is held in a range where a rebound occurs, that is, in the potential range in which the inactivation of the LVA calcium channel could be removed by a negative current step.
In conclusion, when the model cell is extended with a LVA calcium channel, it accounts for a number of experimentally established properties, including rebound spike trains, the positive slope during the negative current steps at depolarized levels, the holding potential range of the rebound depolarization and the fact that the amplitude of negative voltage deflections during the current step is larger in the rebound range.
SIMULATION OF GABAB RECEPTOR INDUCED EFFECTSON REBOUND PROPERTIES AND SINUSOIDAL STIMULATION.GABAB receptor-activation through the agonist baclofen reduces the LVA calcium current in voltage-clamp experiments (Matsushima et al. 1993), and it also decreases the rebound depolarization and the tendency for rebound firing (Fig. 8A, 1 and 2). Therefore, a reduction of the LVA calcium conductance can be used to simulate this effect of GABAB receptor activation. When the conductance is reduced by 30% (as estimated from voltage-clamp experiments) in the simulations the rebound spiking (Fig. 8B1, solid line) is prevented (Fig. 8B1, dashed line), although a rebound depolarization occurs in response to the same current amplitude. Even if the current strength is increased sufficiently to induce a larger hyperpolarization during the negative current step, no rebound spike occurs. In Fig. 8B2 successive reduction of the conductance is simulated, resulting in progressively smaller rebound depolarizations (dashed lines). The negative voltage deflection (top dashed line) in Fig. 8B1 is somewhat smaller than during application of the same current amplitude used in the control. The underlying mechanism is the same as with the increased amplitude of the hyperpolarization when a model cell is held in the rebound range (Fig. 7). The "tonic" LVA calcium current at a depolarized level is smaller in the steady state when the LVA calcium conductance is reduced, and, consequently, the removal of this smaller inward current will result in a smaller depolarizing effect on the membrane potential during the negative step as compared to the control.
To mimic the oscillatory behavior of neurons during fictive locomotion, current was injected using a sinusoidal waveform (Fig. 9A) (see Matsushima et al. 1993
). Addition of 20 µM baclofen induces a slower rising phase for the potential and consequently a delay of the first spike. This current is due to a LVA calcium current (Matsushima et al. 1993
). This effect can be simulated by reducing the conductance for the LVA calcium channel by 30% (Fig. 9B, dashed line), resulting in a delayed first spike (Fig. 9B, solid line). Figure 9, C and D, illustrates the dynamic changes in activation and de-inactivation during the cycle, and Fig. 9E shows the resulting m3h factor. This delay of the spike is essentially due to the reduced m3hg factor (the g refers to the maximal LVA calcium conductance, GLVA, see also Fig. 9E, dashed line) for the calcium current resulting in a smaller net inward current than in control (Fig. 9E, solid line). A modification of LVA calcium currents is a sensitive mechanism, because the depolarization of the membrane potential (Fig. 9B, dashed line) without eliciting a spike results in an increased degree of inactivation (Fig. 9D, dashed line), which in itself further delays the occurrence of a spike. In conclusion, by a small reduction of the conductance, a large effect on the timing of the first spike could be induced.

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| FIG. 8.
Effect of reduction of conductance of low-voltage-activated (LVA) calcium current. A: an intracellular recording in which a rebound spike is elicited in control but not in 20 µM baclofen because -aminobutyric acid-B (GABAB) receptor agonist that reduces LVA calcium conductance (A2) prevents the rebound spike. Addition of 20 µM baclofen reduces calcium current and only a rebound depolarization is observed. B: in B1, reduction is simulated by reducing conductance for LVA calcium channel by 30%. In control ( ), a current of 0.175 nA was used, and when conductance was reduced by 30% (- - -), following currents were used: 0.175, 0.20, and 0.22 nA. Traces corresponding to largest current pulse are indicated in figure. Hence, even a larger current compared with control failed to elicit a rebound spike. In B2, different amounts of reduction (- - -, 15% bottom; 30% middle; 50% top) were simulated using a 0.175 nA current pulse, and holding potential was changed accordingly to changes induced by different steady state level of LVA calcium due to different amounts of reduction of that conductance.
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| FIG. 9.
Experimental and simulation data on the effect of sinusoidal current stimulation. A: experiment with sinusoidal current injection (1.4 Hz) in control and after addition of 20 µM baclofen (GABAB receptor agonist), which delays first spike. B: control ( ) and LVA calcium channel reduction (30%, - - -) in simulation. Note that reduced conductance (- - -) delays first spike. C: degree of activation (m). D: degree of deinactivation (h). E: net effect of activation, deinactivation, and reduced conductance (- - -) compared with control ( ). Conductance is included in addition to m3h factor because baclofen effects are simulated by reducing maximal conductance for LVA calcium channel. Note increased delay in reduced case (- - -, also indicated, , in A and D) after the spike has occurred in control due to inactivation (D) when model cell is depolarized.
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Network
BURSTING FREQUENCY IN A SINGLE POPULATION SEGMENT WITH LOW VOLTAGE-ACTIVATED CALCIUM CHANNELS.
Activation of GABAB receptors (baclofen) reduces the burst frequency when the network is driven by NMDA (Tegnér et al. 1993
) or AMPA/kainate (Tegné
and Grillner, unpublished results). The single segmental network used in the present simulations (see Hellgren et al. 1992
) consisted of seven excitatory (E) and five crossing inhibitory (C) interneurons (see Fig. 10 and METHODS). Activity was induced either by simulated AMPA/kainate (Fig. 11A) or NMDA excitation (Fig. 11B). If LVA calcium channels were added to all model cells in the network, the burst frequency was increased at given AMPA/kainate level (Fig. 11A1). With an increase in the LVA calcium conductance, the faster the burst frequency increased for a given level of AMPA/kainate. The 1.0 level corresponds to the conductance used in the single cell simulations (Figs. 1-9). Essentially the same effect is observed if the network is driven by NMDA (Fig. 11B1), although the NMDA frequency relation is S-shaped. However, at the higher LVA calcium conductance (1.5 times the single cell simulation level), the burst frequency curve deviates, at an NMDA level of 0.6 corresponding to the steepest rising phase, as compared with burst frequency curves with lower levels of LVA conductance. Thus this corroborates that the LVA conductance level in the single cell simulations are in the correct order of magnitude. The frequency increase due to the LVA calcium channels when the network is driven either by NMDA or AMPA/kainate is due to the faster rising phase, as the network switches from activity in one hemisegment to the other. The effect on the frequency is solely due to the C cells in the simulations because removing the LVA calcium channels on E cells is without effect. This is expected as the C cells are crucial for the switch from activity on one side to the other. Another factor that also may contribute is a general depolarization of the model cells in the network since an inward steady state current occurs at membrane potentials above
60 mV. This contribution is, however, small. This conclusion is based on comparisons of the membrane potential for model cells in the network when either the frequency was increased by elevating the background AMPA/kainate level or by increasing the LVA calcium conductance. The outcome of this analysis was that an increase in AMPA/kainate increases the membrane potential much more than the effect of an increased LVA calcium conductance. However, the depolarization after the release of the hyperpolarization of the inhibited hemisegment was faster with an increased LVA calcium conductance.

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| FIG. 11.
Effect on frequency and regularity analyzed by simulating a single segmental network. A: -amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA)/kainate induced rhythmic activity. Addition of LVA calcium conductance increases frequency (A1). The 1.0 level (multiplicative factor of LVA calcium conductance) corresponds to tuning made for single model cell. In A2, coefficient of variation is shown. B: N-methyl-D-aspartate (NMDA)-induced rhythmic activity in which addition of a LVA calcium conductance increase frequency. Background AMPA/kainate level is 3 (Hellgren et al. 1992 ). No clear effect on coefficient of variation could be observed when LVA calcium channels were added (B2).
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GABAB receptor activation reduces the HVA calcium currents and thereby the sAHP (Matsushima et al. 1993
), the LVA calcium currents (Matsushima et al. 1993
), and the amplitude of the excitatory and inhibitory synaptic transmission through presynaptic inhibition from network interneurons (Alford and Grillner 1991
; Alford et al. 1991
). To address the mechanism(s) responsible for the experimentally observed frequency reduction induced by baclofen (Tegnér et al. 1993
), fictive locomotion was induced by NMDA in the lamprey spinal cord preparation (Fig. 12). Under control conditions, the frequency is ~2.2 Hz whereas addition of apamin, which markedly reduces the sAHP, reduced the frequency to ~2.0 Hz. This slight reduction is in accordance with earlier studies (El-Manira et al. 1994
), in which it was found that at low locomotor frequencies an addition of apamin markedly reduced the frequency or caused a complete breakdown of the rhythmic activity. At higher frequencies (2-2.5 Hz), the effect of apamin on locomotor frequency was small (Fig. 12B). If baclofen was added (n = 3), the frequency was reduced more markedly (1.3 Hz). This means that the experimentally induced GABAB receptor effect on the frequency of the motor activity is not only due to the sAHP mechanism, but, in addition, to a reduction of the current through the LVA calcium channels and/or to presynaptic inhibition (see DISCUSSION).

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| FIG. 12.
Effect of experimentally reducing LVA calcium current during fictive locomotion. A: NMDA (150 µM) is used to induce rhythmic activity in lamprey spinal cord. Extracellular recordings are made from a ventral root. B: addition of 2.5 µM apamin, which markedly reduces sAHP has a small effect on frequency. C: addition of 20 µM baclofen reduces frequency.
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| FIG. 13.
Effect of adding LVA calcium channels on regularity of bursting when segmental network is driven by a low level of AMPA/kainate. A: only AMPA/kainate drive (level 1.0 in arbitrary units is used). Two reciprocal C model neurons are shown. No noise is used. B: LVA calcium level is same as in single cell tuning simulations. C: Increased level of LVA calcium.
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EFFECTS OF LVA CALCIUM CHANNELS ON THE REGULARITY OF FICTIVE LOCOMOTION IN A SIMULATION MODEL.
It has been observed previously that an AMPA/kainate-driven model network exhibits a more regular burst pattern at higher frequencies than an NMDA-driven network (Hellgren et al. 1992
; Wallé
et al. 1992). This is confirmed in these simulations by calculating the coefficient of variation (see METHODS) for both the AMPA/kainate (Fig. 11A2) and the NMDA driven network (Fig. 11B2). The most regular activity is found with the AMPA/kainate-drive ~5 Hz (Fig. 11A2). The addition of LVA calcium channels does not affect the degree of regularity as measured by the coefficient of variation either in the AMPA/kainate (Fig. 11A2) or in the NMDA condition (Fig. 11B2).
Another way to address the issue of regularity is to test if the addition of LVA calcium channels could influence the network when it is driven with a low excitatory drive. It should be noted that in this range the network is not operating in a bursting manner because the excitatory drive is too small. However, in Fig. 13A, a simulated network is activated by a low level of AMPA/kainate (1.0 arbitrary units), and the activity is mainly dominated by single reciprocal spikes from two reciprocal C model neurons. When LVA calcium channels are added, a more burst-like pattern appears (Fig. 13B). This is an effect of the enhanced depolarization in the rising phase, leading to several spikes. In these simulations, there is no noise, but the effects also are observed if noise is used, although they are less pronounced. When using noise, the probability for an occasionally larger depolarization increases, leading to more sustained firing. In conclusion, LVA calcium channels appear to be more important for frequency regulation than for the stability of the rhythm. The LVA calcium channels, however, could be important in the lower frequency range and possibly extend the frequency range in which the network can produce a regular pattern of activity.
 |
DISCUSSION |
We have extended the previously developed cell model (Brodin et al. 1991
; Ekeberg et al. 1991
; Hellgren et al. 1992
; Tråvén et al. 1993) with a LVA calcium channel that can account for the rebound properties of the single cell (Matsushima et al. 1993
); this allows a test of the functional consequences of the LVA calcium channels on the network level. An earlier model of the lamprey spinal neuron (Ekeberg et al. 1991
) was sufficiently realistic to account for the firing behavior, for adaptive mechanisms using K(Ca), and for NMDA-induced oscillations in tetrodotoxin (Brodin et al. 1991
).
Characteristics of the rebound and single cell simulations
The LVA calcium-induced rebound occurs in a certain range of membrane potentials. It is characterized by the following properties: there is a "holding potential window" (around
60 to
50 mV) within which the rebound occurs, the amplitude of the rebound increases with the amplitude of the hyperpolarizing (inhibitory) pulse, the amplitude of the rebound increases with the duration of the hyperpolarizing (inhibitory) pulse, and, finally, if the neurons are held at a depolarized level close to the action potential threshold, a single hyperpolarizing pulse, can generate a sequence of rebound spikes due to the rebound depolarization after each postspike afterhyperpolarization. This appears to be of particular importance in the inhibitory reciprocally connected C interneurons. The LVA calcium property thus makes the neuron more excitable, which could be interpreted as a cellular mechanism playing a similar role as the post inhibitory rebound (PIR) property does in the model introduced by Perkel and Mulloney (1974)
. The PIR variable in their model increases as the model neuron receives inhibitory impulses leading to an increased excitability. The deinactivation of the LVA calcium current during the negative current pulse thus plays a similar role as the PIR variable. After the cell model was tuned to experimental data by essentially using the second and third properties above, the single cell model was tested by performing simulations under conditions for which it was not initially tuned. The sensitivity of the parameter variation for the simulation results is stated whenever relevant.
ROLE OF HOLDING POTENTIAL.
The simulation model captured the holding potential dependence for the existence and variation in the latency of rebound spikes (Fig. 5). The increasing m3h factor at more depolarized levels can account for the difference in latency of the rebound spikes (Fig. 5, A2, A3, and B1), because larger net inward current is created, initially leading to a shorter delay for the first rebound spike. This simulation result is due to the fact that the model cell is held on the side of the m3h curve at which the slope is positive (see also Fig. 4B). Hence, this result is sensitive to the B values (for
and
, see Table 1) because they essentially determine at which holding potential the m and h curves will intersect. The magnitude of the voltage separation between m1/2 and h1/2 determines the magnitude and voltage relationship of the m3h factor. The absolute value of
m as determined by A
m is also important, as it affects the rise time of the voltage when the negative current is released at a given holding potential. A reduced latency could be of importance at the network level because with a larger excitatory drive, cells tend to be more depolarized, and they will be activated with an action potential with a shorter delay when equipped with a LVA calcium current, everything else being equal.
REBOUND TRAIN.
It was also important to determine under what conditions a rebound train could be evoked after a single stimulus in the simulations because, experimentally, it was not clear why a rebound train could be evoked. A key factor determining whether a single or several rebound spikes (rebound train) would occur was the holding potential for a given reversal potential of the sAHP (EKCa). The sAHP had to be large enough as compared with the holding potential to remove the inactivation of the LVA calcium current to a sufficient degree. This constraint suggests that the parameter value used for the reversal potential of the sAHP in earlier simulations (Brodin et al. 1991
; Ekeberg et al. 1991
; Hellgren et al. 1992
; Tråvén et al. 1993) should be lowered from
80 to around
85 mV (Fig. 6D) if a rebound train is to be evoked in the holding range of
52 mV. This conclusion is also supported by experimental data, which suggest a reversal potential for the sAHP around
85 mV (see Fig. 1A in Matsushima et al. 1993
). Additionally, a modification of the conductance for the sAHP in the simulations affects the model neurons' ability to fire a train of rebound spikes. A change in the GsAHP essentially follows changes in EKCa. A decrease of the GsAHP reduces the tendency of rebound trains for a given holding potential. A more depolarized value of the EKCa also reduces the occurrence of rebound trains. This could be important for the regularity of network activity (see below). For a given cell, the reversal potential does not change significantly over time whereas it may be differ among different cells.
SLOW DEPOLARIZATION DURING A HYPERPOLARIZING STEP.
It was found experimentally and subsequently in the simulations, somewhat unexpectedly, that neurons held at a more depolarized membrane potential showed a sag during the negative current step (Fig. 6A). The simulations showed that there was a larger m3h factor during the negative current step (Fig. 6E3) at more depolarized levels, due to a larger degree of activation (m) resulting in an inward LVA current causing a depolarization. Thus the LVA channels could account for this sag in the experiments, however, it cannot be excluded that other conductances could be involved as well.
POTENTIAL RANGE.
The potential range in which a depolarization occurred during the negative current step coincides with that at which the neuron is able to generate a rebound. The holding potential range, in which a rebound could occur was similar in experiments and simulations (Fig. 7). Furthermore, the holding potential influences the amplitude of the hyperpolarization in a similar manner in experiments as well as in simulations (except at the most depolarized level) and the hyperpolarization during the negative current step (Fig. 7B). The U shape of the experimental curve was unexpected. When a cell is held in the rebound range, the LVA calcium current will be non-zero (see also Fig. 4B), and when the cell subsequently is hyperpolarized by a negative current pulse, the size of the inward LVA calcium current will be reduced, leading to a larger hyperpolarization as compared with the condition in which there is no LVA calcium current at the holding potential. Thus the solid line in Fig. 7B would be linear if the cell had been lacking LVA calcium channels. A neuron equipped with a LVA calcium current will be hyperpolarized to a larger degree by an inhibitory input within the LVA voltage range. Consequently, a larger degree of inactivation will be removed and a stronger rebound response will be elicited.
LIMITATIONS.
In conclusion, the cell model can account for a number of experimental details on the single cell level. There are, however, some differences between the simulation model and the experiments, for example, the curve in Fig. 7B. Even though the overall shape is similar, the minimum voltage occurs at different holding potentials. The onset of the increase of the hyperpolarized response (Fig. 7B) is similar, which indicates that the m3h (Fig. 4B) is correct in the lower voltage range. The minimum voltage in the simulations occurs, however, at a more depolarized potential level as compared with the experiments. This is due to the fact that the m3h does not decrease sufficiently in the higher voltage range. This is of minor importance for the behavior around threshold of the rebound. Another difference is that there is an afterpotential in the simulations when the model cell is held at
58 mV (Fig. 5B1) that is not present in the particular recording illustrated (Fig. 5A1). These differences between the simulations and experiments are presumably not crucial, as the real cells are heterogeneous with regard to their LVA calcium properties (the maximal LVA conductance for example). For example, the positive slope during the negative current step occurs experimentally at different holding potentials (compare Fig. 2A and Fig. 6A), and there is no rebound depolarization in Fig. 5A1, whereas the same current stimulation in another cell evokes a rebound spike even at a more negative holding potential (Fig. 7B).
Another source for the differences between the simulations and experiments could be the simplifications made in the construction of the cell model. The original cell model (Ekeberg et al. 1991
) is of intermediate complexity, which means that there is not a full representation of the dendritic tree, due to insufficient data, although the model does have several compartments. The underlying reason for this choice is that the most important property to capture, at least initially (Brodin et al. 1991
; Ekeberg et al. 1991
), was the electrical behavior of the cells together with the interplay between ion channels and the intracellular calcium pools to perform simulations on the network level. Another constraint was the lack of data on distribution of different channels in the dendritic tree in lamprey neurons (Christensen and Teubl 1979
; Wallén et al. 1988
). As the modeling described in this study is built upon these premises, the LVA calcium channels were placed on the soma (together with the other ionic channels), even though it is likely that they also are localized further out in the dendritic tree. Such a modification would probably modify the maximal LVA calcium conductance level (GLVA). In conclusion, the cell model appears to be sufficiently complex to account for the rebound properties but simple enough to allow an analysis on the network level.
How does the LVA calcium model compare with LVA calcium models in other systems?
Extensive experimental and computational studies have been carried out on thalamocortical relay neurons, which also posses a LVA calcium current (Bal and McCormick 1993
; Coulter et al. 1989
; Destexhe et al. 1993a
,b
, 1994
; Huguenard and McCormick 1992
; McCormick and Huguenard 1992
; Rush and Rinzel 1994
; Wang et al. 1991
). The main difference is that the net LVA calcium conductance is activated at a more depolarized level for lamprey neurons compared with thalamocortical relay neurons. In particular, the m1/2 and h1/2 are ~5 mV more depolarized in lamprey neurons. During fictive locomotion, a typical spinal neuron will have a trough potential below the LVA voltage range that is below the peak of the m3h factor, which is approximately at
50 mV (Fig. 4B) and subsequently will depolarize to spike threshold and then repolarize back to the trough potential again. Thalamocortical relay neurons have a resting potential around
60 to
65 mV at which the LVA calcium current is inactivated and an inhibitory input is required to remove the inactivation to produce a rebound (compare with Fig. 4B). In comparison, the membrane potentials of lamprey neurons are below the voltage needed for an activation of the LVA calcium conductance during the "nonspiking" phase, whereas the membrane potential of thalamocortical relay neurons are above the working range of their LVA calcium conductance during their silent phase. The inferior olivary neurons are similar to the thalamocortical relay neurons with a resting potential at
65 mV, and the peak LVA calcium conductance occurs at approximately
85 mV(Llinás and Yarom 1981
) as compared with the lamprey LVA calcium channel, which has the peak approximately at
50 mV (see Fig. 4B).
Recently, a novel type of LVA calcium current has been observed in nRT neurons (Huguenard and Prince 1992
), which underlies the prolonged calcium-dependent burst firing. It is similar to the lamprey LVA calcium current because the activation and inactivation ranges are depolarized compared to the LVA calcium current previously described in the thalamocortical relay neurons [m1/2 is
50 mV compared with
59 mV and h1/2 is
78 mV compared with
81 mV in the study of Huguenard and Prince (1992)
]. The net lamprey LVA calcium conductance is closer to the LVA calcium current for nRT neurons than for thalamocortical relay neurons. In addition, the
m peak is around
60 mV for nRT (the
m peak in our model lamprey neuron is positive to
60 mV, see Fig. 4C) compared with
m peak, which is around
80 mV for the thalamocortical relay neurons. Interestingly, nRT neurons can generate rhythmic sequences of LVA calcium spikes when action potentials are blocked (using tetrodotoxin) and the LVA calcium spikes are separated by a calcium-dependent afterhyperpolarization (Bal and McCormick 1993
). However, the LVA calcium current for nRT has a nearly voltage-independent deinactivation, which does not seem to be the case for spinal lamprey neurons (Matsushima et al. 1993
). This should be investigated further using cultured lamprey neurons (El-Manira and Bussiéres 1995
). This voltage independence of the deinactivation gives a longer burst firing for nRT neurons; this may be a critical factor in initiating intrathalamic and thalamocortical oscillations (Huguenard and Prince 1992
). Because the nRT neurons project to the thalamocortical relay neurons, they may induce reverberatory rhythmic activity. In contrast, the lamprey simulation model does not generate oscillations when a constant continuous current is injected (tested in various voltage ranges, not shown). In the model of thalamocortical relay neurons (Wang et al. 1991
), self-sustained oscillations (nonspiking model) could be evoked if the m
and h
were translated closer together than observed experimentally. This has been further analyzed in a spiking model (Rush and Rinzel 1994
), and either increasing the maximal LVA calcium conductance (GLVA) or prolonging the
h (multiplying by a factor of 3) produced self-sustained oscillations (with spikes). This possibility was tested in the lamprey model by increasing GLVA (by a factor of 4-5) after which self-sustained LVA calcium oscillations could be evoked. However, we have not yet looked for or observed such oscillations experimentally but this is something that should be tested.
Simulation of GABAB-receptor-induced reduction of LVA calcium
The GABAB-receptor-induced reduction of the LVA calcium current during a single negative current step (Fig. 8) and during sinusoidal stimulation, also was simulated (Fig. 9). Of special interest, in the latter case, was the observation that the LVA calcium conductance was reduced and the first spike was delayed due to a slower rising phase. As a consequence, the additional effect of a gradually increasing the degree of inactivation of the LVA calcium channel resulted in a further delay of the first spike. The consequence is that a small reduction induced by GABAB receptor activation could have a pronounced effect on the timing of the first spike.
What role do LVA calcium channels play during fictive locomotion?
Activation of GABAB receptors can reduce the burst frequency (Tegnér et al. 1993
). This can be accomplished by several mechanisms: by inducing an increasing presynaptic inhibition (Alford and Grillner 1991
; Alford et al. 1991
) on premotor interneurons, a reduction of the sAHP (Matsushima et al. 1993
), and a reduction of the LVA calcium current (Matsushima et al. 1993
).
The sAHP mechanism is an important regulating factor for the burst frequency. The main contribution with respect to frequency and regularity of the burst pattern is in the low burst frequency range (induced by 25-75 µM NMDA) whereas in the higher burst frequency range (200 µM NMDA) only the regularity (detected if the coefficient of variation is measured) of the bursting pattern is affected if the sAHP is reduced by apamin (El-Manira et al. 1994
). This is confirmed in the present study (Fig. 12, A and B) by using a high level of NMDA. However, when baclofen is added to the same preparation, a marked reduction of the frequency occurs (Fig. 12C). Taken together, this suggests that the effects of baclofen is not mediated by an sAHP mechanism in this frequency range. In addition, the network simulations showed that an addition of a LVA calcium channel conductance could increase the frequency (Fig. 11, A1 and B1). In conclusion, this makes it likely that the LVA calcium factor plays a complementary and probably a larger role as a frequency regulator as compared with the sAHP mechanism in this higher burst frequency range. We can not, however, exclude that there might be other actions mediated by GABAB receptor activation that have not yet been detected that could influence the burst rate.
The addition of LVA calcium channels to the simulated network when operating in a bursting mode did not make the pattern more regular as estimated by the coefficient of variation (Fig. 11, A2-B2). This is consistent with earlier experiments in which the regularity of the burst pattern did not decrease when the GABAB receptor activity was increased by adding baclofen to the network (Tegnér et al. 1993
). However, the LVA calcium currents could be important for the regularity of the simulated network when the excitatory drive is low (Fig. 13). The LVA calcium induces a more burst-like activity because of the fast rising phase and increased tendency for trains of rebound spikes. This is to be compared with the finding (Perkel and Mulloney 1974
) that an addition of a post inhibitory rebound (PIR) to a pair of reciprocally connected nonpacemaker model neurons induces an alternating burst activity. An inhibitory pulse in their model could trigger a stable burst pattern, and it should be noted that the lamprey model neurons are not pacemakers when they are driven only by low levels of AMPA/kainate. In addition, if the conductance of the K(Ca) channel (GKCa) is reduced, the tendency for rebound trains is reduced (Fig. 6D). Interestingly, the K(Ca) channels are also important for the regularity of the bursting pattern in the low frequency range (El-Manira et al. 1994
). Thus the K(Ca)-induced reduction of the ability of neurons firing rebound trains could contribute to the importance of the K(Ca) channels for the regularity of the burst pattern in the low frequency range. Taken together, this suggests that the LVA calcium currents could be important for the regularity in the low frequency range because the LVA calcium will give the neuron an ability for sustained firing, and, in this sense, it could extend the functional frequency range by allowing regular bursting even though the excitatory drive is low.
 |
ACKNOWLEDGEMENTS |
Thanks to Dr. Örjan Ekeberg for developing the SWIM simulation software as well as providing useful help in the initial phase of this project during which the code was modified. We also are indebted to Drs. Lennart Brodin, Abdel El-Manira, David Parker, and Peter Wallén for valuable comments on the manuscript.
This work was supported by the Medical Research Council (Project No. 3026), the Swedish Natural Science Research Council (Project No. B-AA/BU03531), the Swedish National Board for Industrial and Technical Development (NUTEK, Project No. 8425-5-03075), and the Swedish Society for Medical Research.
 |
FOOTNOTES |
Address for reprint requests: J. Tegnér, Nobel Institute for Neurophysiology, Dept. of Neuroscience, Karolinska Institute, S-171 77 Stockholm, Sweden.
Received 24 June 1996; accepted in final form 13 December 1996.
 |
REFERENCES |
-
ALFORD, S.,
CHRISTENSON, J.,
GRILLNER, S.
Presynaptic GABAA and GABAB receptor-mediated phasic modulation in axons of spinal motor interneurons.
Eur. J. Neurosci.
3: 107-117, 1991.[Medline]
-
ALFORD, S.,
GRILLNER, S.
The involvement of GABAB receptors and coupled G-proteins in spinal gabaergic presynaptic inhibition.
J. Neurosci.
12: 3718-3728, 1991.
-
BAL, T.,
MCCORMICK, D.
Mechanisms of oscillatory activity in guinea-pig nucleus reticularis thalami in vitro: a mammalian pacemaker.
J. Physiol. Lond.
468: 669-691, 1993.[Abstract]
-
BRODIN, L.,
TRÅVÉN, H.,
LANSNER, A.,
WALLÉN, P.,
EKEBERG, Ö.,
GRILLNER, S.
Computer simulations of N-methyl-D-aspartate (NMDA) receptor induced membrane properties in a neuron model.
J. Neurophysiol.
66: 473-484, 1991.[Abstract/Free Full Text]
-
BUCHANAN, J. T.
Identification of interneurons with contralateral, caudal axons in the lamprey spinal cord: synaptic interactions and morphology.
J. Neurophysiol.
47: 961-975, 1982.[Abstract/Free Full Text]
-
BUCHANAN, J. T.
Neural network simulations of coupled locomotor oscillators in the lamprey spinal cord.
Biol. Cybern.
66: 367-374, 1992.[Medline]
-
BUCHANAN, J.,
GRILLNER, S.
Newly identified "glutamate interneurons" and their role in locomotion in the lamprey spinal cord.
Science Wash. DC
236: 312-314, 1987.[Medline]
-
BUCHANAN, J. T.,
GRILLNER, S.,
CULLHEIM, S.,
RISLING, M.
Identification of excitatory interneurons contributing to generation of locomotion in lamprey: structure, pharmacology, and function.
J. Neurophysiol.
62: 59-69, 1989.[Abstract/Free Full Text]
-
CARBONE, E.,
LUX, H. D. A
low voltage-activated, fully inactivating ca channel in vertebrate sensory neurones.
Nature Lond.
310: 501-501, 1984.[Medline]
-
CHRISTENSEN, B. N.,
TEUBL, W. P.
Localization of synaptic input on dendrites of a lamprey spinal cord neurone from physiological measurements of membrane properties.
Exp. Brain Res.
297: 319-333, 1979.
-
CHRISTENSON, J.,
GRILLNER, S.
Primary afferents evoke excitatory amino acid receptor mediated epsps, that are modulated by presynaptic GABAB receptors in lamprey.
J. Neurophysiol.
66: 2141-2149, 1991.[Abstract/Free Full Text]
-
CHRISTENSON, J.,
HILL, R.,
BONGIANNI, F.,
GRILLNER, S.
Presence of low voltage activated calcium channels distinguish touch from pressure sensory neurons in the lamprey spinal cord.
Brain Res.
608: 58-66, 1993.[Medline]
-
COHEN, A. H.,
WALLÉN, P.
The neuronal correlate of locomotion in fish. "Fictive swimming" induced in an in vitro preparation of the lamprey spinal cord.
Exp. Brain Res.
41: 11-18, 1980.[Medline]
-
COHEN, A. H.,
ERMENTROUT, B.,
KIEMEL, T.,
KOPELL, N.,
SIGVARDT, K.,
WILLIAMS, T. L.
Modelling of intersegmental coordination in the lamprey central pattern generator for locomotion.
Trends Neurosci.
15: 434-438, 1992.[Medline]
-
COULTER, D.,
HUGUENARD, J.,
PRINCE, D.
Calcium currents in rat thalamocortical relay neurons: kinetics properties of the transient low-threshold current.
J. Physiol. Lond.
414: 587-604, 1989.[Abstract]
-
DESTEXHE, A.,
BABLOYANTZ, A.,
SEJNOWSKI, T.
Ionic mechanisms for intrinsic slow oscillations in thalamic relay neurons.
Biophys. J.
65: 1538-1552, 1993a.[Abstract]
-
DESTEXHE, A.,
CONTRERAS, D.,
SEJNOWSKI, T.,
STERIADE, M. A
model of spindle rhythmicity in the isolated thalamic reticular nucleus.
J. Neurophysiol.
72: 803-818, 1994.[Abstract/Free Full Text]
-
DESTEXHE, A.,
MCCORMICK, D.,
SEJNOWSKI, T. A
model for 8-10 Hz spindling in interconnected thalamic relay and reticularis neurons.
Biophys. J.
65: 2473-2477, 1993b.[Abstract]
-
EL-MANIRA, A. E.,
BUSSIÉRES, N.
Culture of identified lamprey brainstem-spinal cord neurons and characterization of calcium channels.
Soc. Neurosci. Abstr.
21: 270, 1995.
-
EKEBERG, Ö. A
combined neuronal and mechanical model of fish swimming.
Biol. Cybern.
69: 363-374, 1993.
-
EKEBERG, Ö.,
HAMMARLUND, P.,
LEVIN, B.,
LANSNER, A.
SWIM
a simulation environment for realistic neural network modeling.
In: Neural Network Simulation Environments,
edited by
and J. Skrzypek
. Hingham, MA: Kluwer, 1994 -
EKEBERG, Ö.,
WALLÉN, P.,
LANSNER, A.,
TRÅVÉN, H.,
BRODIN, L.,
GRILLNER, S. A
computer based model for realistic simulations of neural networks. I. The single neuron and synaptic interaction.
Biol. Cybern.
65: 81-90, 1991.[Medline]
-
EL-MANIRA, A.,
TEGNÉR, J.,
GRILLNER, S.
Calcium-dependent potassium channels play a critical role for burst termination in the locomotor network in lamprey.
J. Neurophysiol.
72: 1852-1861, 1994.[Abstract/Free Full Text]
-
FAGERSTEDT, P.,
WALLÉN, P.,
GRILLNER, S.
Activity of interneurons during fictive swimming in the lamprey.
IBRO Congress Neurosci. Abstr.
1: 346, 1995.
-
FRANKENHAEUSER, B.,
HUXLEY, A. F.
The action potential in the myelinated nerve fibre of xenopus laevis as computed on the basis of voltage clamp data.
J. Physiol. Lond.
171: 302-315, 1964.[Medline]
-
GRILLNER, S.,
BUCHANAN, J.,
LANSNER, A.
Simulations of the segmental burst generating network for locomotion in lamprey.
Neurosci. Lett.
89: 31-35, 1988.[Medline]
-
GRILLNER, S.,
DELIAGINA, T.,
EKEBERG, Ö.,
MANIRA, A. E.,
HILL, R. H.,
LANSNER, A.,
ORLOVSKY, G.,
WALLÉN, P.
Neural networks that coordinate locomotion and body orientation in lamprey.
Trends Neurosci.
18: 270-279, 1995.[Medline]
-
GRILLNER, S.,
MCCLELLAN, A. D.,
SIGVARDT, K.,
WALLÉN, P.,
WILÉN, M.
Activation of NMDA receptors elicits "fictive locomotion" in lamprey spinal cord in vitro.
Acta Physiol. Scand.
113: 549-551, 1981.[Medline]
-
GRILLNER, S.,
WALLÉN, P.,
BRODIN, L.,
LANSNER, A.
Neuronal network generating locomotor behavior in lamprey: circuitry, transmitters, membrane properties and simulations.
Annu. Rev. Neurosci.
14: 169-199, 1991.[Medline]
-
HELLGREN, J.,
GRILLNER, S.,
LANSNER, A.
Computer simulation of the segmental neural network generating locomotion in lamprey by using populations of network interneurons.
Biol. Cybern.
68: 1-13, 1992.[Medline]
-
HILLE, B.
In: Ionic Channels of Excitable Membranes,
, 2nd ed.. Sunderland, MA: Sinauer Associates Inc., 1992
-
HODGKIN, A. L.,
HUXLEY, A. F. A
quantitative description of membrane current and its application to conduction and excitation in nerve.
J. Physiol. Lond.
117: 500-544, 1952.[Medline]
-
HUGUENARD, J.,
MCCORMICK, D.
Simulations of the currents involved in rhythmic oscillations in thalamic relay neurons.
J. Neurophysiol.
68: 1373-1383, 1992.[Abstract/Free Full Text]
-
HUGUENARD, J.,
PRINCE, D. A
novel T-type current underlies prolonged Ca2+-dependent burst firing in GABAergic neurons of rat thalamic reticular nucleus.
Neuroscience
10: 3804-3817, 1992.
-
KOPELL, N.
Toward a theory of modelling central pattern generators.
In: Neural Control of Rhythmic Movements in Vertebrates,
edited by
A. H. Cohen,
S. Rossignol,
and S. Grillner
. New York: John Wiley, 1988, p. 369-413
-
LLINÁS, R.,
YAROM, Y.
Properties and distribution of ionic conductances generating electroresponsiveness of mammalian inferior olivary neurones in vitro. J.
Physiol. Lond.
315: 569-584, 1981.[Abstract]
-
MATSUSHIMA, T.,
TEGNÉR, J.,
HILL, R.,
GRILLNER, S.
GABAB receptor activation causes a depression of low- and high-voltage-activated Ca2+ currents, postinhibitory rebound, and postspike afterhyperpolarization in lamprey neurons.
J. Neurophysiol.
70: 2606-2619, 1993.[Abstract/Free Full Text]
-
MCCLELLAN, A. D.,
GRILLNER, S.
Activation of "fictive swimming" by electrical microstimulation of brainstem locomotor regions in an in vitro preparation of the lamprey central nervous system.
Brain Res.
300: 357-361, 1984.[Medline]
-
MCCORMICK, D.,
HUGUENARD, J. A
model of the electrophysiological properties of thalamocortical relay neurons.
J. Neurophysiol.
68: 1384-1400, 1992.[Abstract/Free Full Text]
-
MINTZ, I. M.,
VENEMA, V. J.,
SWIDEREK, K. M.,
LEE, T. D.,
BEAN, B. P.,
ADAMS, M. E.
P-type calcium channels blocked by the spider toxin
-aga-iva.
Nature Lond.
355: 827-829, 1992.[Medline] -
NOWYCKY, M. C.,
FOX, A. P.,
TSIEN, R. W.
Three types of calcium channel with different calcium agonist sensitivity.
Nature Lond.
316: 440-443, 1985.[Medline]
-
OHTA, Y.,
GRILLNER, S.
Monosynaptic excitatory amino acid transmission from the posterior rhombencephalic reticular nucleus to spinal neurons involved in the control of locomotion in lamprey.
J. Neurophysiol.
62: 1079-1089, 1989.[Abstract/Free Full Text]
-
PERKEL, D. H.,
MULLONEY, B.
Motor pattern production in reciprocally inhibitory neurons exhibiting postinhibitory rebound.
Science Wash. DC
18: 181-183, 1974.
-
ROVAINEN, C. M.
Synaptic interactions of identified nerve cells in the spinal cord of the sea lamprey.
J. Neurophysiol.
154: 207-223, 1974.
-
RUSH, M.,
RINZEL, J.
Analysis of bursting in a thalamic neuron model.
Biol. Cybern.
71: 281-291, 1994.[Medline]
-
RUSSELL, D. F.,
WALLÉN, P.
On the control of myotomal motoneurones during "fictive swimming" in the lamprey spinal cord in vitro.
Acta Physiol. Scand.
117: 161-170, 1983.[Medline]
-
SIGVARDT, K. A.,
GRILLNER, S.,
WALLÉN, P.,
DONGEN, P. A. M.
Activation of nmda receptors elicits fictive locomotion and bistable membrane properties in the lamprey spinal cord.
Brain Res.
336: 390-395, 1985.[Medline]
-
TEGNÉR, J.,
MATSUSHIMA, T.,
MANIRA, A. E.,
GRILLNER, S.
The spinal GABA system modulates burst frequency and intersegmental coordination in the lamprey: differential effects of GABAA and GABAB receptors.
J. Neurophysiol.
69: 647-657, 1993.[Abstract/Free Full Text]
-
TRÅVÉN, H.,
BRODIN, L.,
LANSNER, A.,
EKEBERG, Ö.,
WALLÉN, P.,
GRILLNER, S.
Computer simulations of NMDA and non-NMDA receptor-mediated synaptic drive
sensory and supraspinal modulation of neurons and small networks.
J. Neurophysiol.
70: 695-709, 1993.[Abstract/Free Full Text] -
TSIEN, R. W.,
LIPSCOMBE, D.,
MADISON, D. V.,
BLEY, K. R.,
FOX, A. P.
Multiple types of neuronal calcium channels and their selective modulation.
Trends Neurosci.
11: 431-438, 1988.[Medline]
-
USOWICZ, M. M.,
SUGIMORI, M.,
CHERKSEY, B.,
LLINÁS, R.
P-type calcium channels in the somata and dendrites of adult cerebellar purkinje cells.
Neuron
9: 1185-1199, 1992.[Medline]
-
WADDEN, T.,
HELLGREN-KOTALESKI, J.,
LANSNER, A.,
GRILLNER, S.
Simulations of intersegmental coordination using a continuous network model.
In: The Neurobiology of Computation: Proceedings of the Third Annual Computation and Neural Systems Conference,
edited by
and J. M. Bower
. Boston, MA: Kluwer, 1995
-
WALLÉN, P.,
BUCHANAN, J.,
GRILLNER, S.,
HILL, R.,
CHRISTENSON, J.,
HÖKFELT, T.
Effects of 5-hydroxytryptamine on the afterhyperpolarization, spike frequency regulation, and oscillatory membrane properties in lamprey spinal cord neurons.
J. Neurophysiol.
61: 759-768, 1989.[Abstract/Free Full Text]
-
WALLÉN, P.,
CARLSSON, K.,
LILJEBORG, A.,
GRILLNER, S.
Three-dimensional reconstruction of neurons in the lamprey spinal cord in whole-mount, using a confocal laser scanning microscope.
J. Neurosci. Methods
24: 91-100, 1988.[Medline]
-
WALLÉN, P.,
EKEBERG, Ö.,
LANSNER, A.,
BRODIN, L.,
TRÅVÉN, H.,
GRILLNER, S. A
computer-based model for realistic simulations of neural networks. II. The segmental network generating locomotor rhythmicity in the lamprey.
J. Neurophysiol.
68: 1939-1950, 1992.[Abstract/Free Full Text]
-
WALLÉN, P.,
GRILLNER, S.
N-methyl-D-aspartate receptor-induced, inherent oscillatory activity in neurons active during fictive locomotion in the lamprey.
J. Neurosci.
7: 2745-2755, 1987.[Abstract]
-
WALLÉN, P.,
GRILLNER, S.,
FELDMAN, J. L.,
BERGFELT, S.
Dorsal and ventral myotome motorneurons and their input during fictive locomotion in lamprey.
J. Neurosci.
11: 654-661, 1985.
-
WANG, X.,
RINZEL, J.,
ROGAWSKI, A. A
model of the T-type calcium current and the low-threshold spike in thalamic neurons.
J. Neurophysiol.
66: 839-850, 1991.[Abstract/Free Full Text]
-
WILLIAMS, T. L.
Phase coupling in simulated chains of coupled oscillators representing the lamprey spinal cord.
Neural Comp.
4: 546-558, 1992.