1Laboratories of Origin, Department of Neurobiology and Anatomy, W. M. Keck Center for the Neurobiology of Learning and Memory, The University of Texas-Houston Medical School, Houston, 77225; and 2Department of Electrical and Computer Engineering, Rice University, Houston, Texas 77251
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ABSTRACT |
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Baxter, Douglas A., Carmen C. Canavier, John W. Clark Jr., and John H. Byrne. Computational Model of the Serotonergic Modulation of Sensory Neurons in Aplysia. J. Neurophysiol. 82: 2914-2935, 1999. Serotonergic modulation of the sensory neurons that mediate the gill- and tail-withdrawal reflexes of Aplysia is a useful model system for studies of neuronal plasticity that contributes to learning and memory. The effects of serotonin (5-HT) are mediated, in part, via two protein kinases (protein kinase A, PKA, and protein kinase C, PKC), which in turn, modulate at least four membrane currents, including a S ("serotonin-sensitive") K+ current (IK,S), a steeply voltage-dependent K+ current (IK-V), a slow component of the Ca2+-activated K+ current (IK,Ca-S), and a L-type Ca2+ current (ICa-L). The present study investigated how the modulation of these currents altered the spike duration and excitability of sensory neurons and examined the relative contributions of PKA- and PKC-mediated effects to the actions of 5-HT. A Hodgkin-Huxley type model was developed that described the ionic conductances in the somata of sensory neurons. The descriptions of these currents and their modulation were based largely on voltage-clamp data from sensory neurons. Simulations were preformed with the program SNNAP (Simulator for Neural Networks and Action Potentials). The model was sufficient to replicate empirical data that describes the membrane currents, action potential waveform and excitability as well as their modulation by application of 5-HT, increased levels of adenosine cyclic monophosphate or application of active phorbol esters. In the model, modulation of IK-V by PKC played a dominate role in 5-HT-induced spike broadening, whereas the concurrent modulation of IK,S and IK,Ca-S by PKA primarily accounted for 5-HT-induced increases in excitability. Finally, simulations indicated that a PKC-induced increase in excitability resulted from decreases of IK,S and IK,Ca-S, which was likely the indirect result of cross-talk between the PKC and PKA systems. The results provide several predictions that warrant additional experimental investigation and illustrate the importance of considering indirect as well as direct effects of modulatory agents on the modulation of membrane currents.
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INTRODUCTION |
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By changing the waveform of action potentials and
excitability, serotonin (5-HT)-induced modulation of membrane currents
in the sensory neurons that mediate the gill- and tail-withdrawal reflexes of Aplysia is believed to be a key mechanism
underlying short-term heterosynaptic facilitation (for recent review,
see Byrne and Kandel 1996). The first-discovered
"serotonin-sensitive" current was a novel K+
current that was termed the S current
(IK,S) (Klein et al.
1982
). Acting via elevated levels of intracellular adenosine
cyclic monophosphate (cAMP) and the subsequent activation of protein
kinase A (PKA), application of 5-HT decreased the magnitude of
IK,S (Fig.
1A) (Baxter and Byrne
1990a
; Bernier et al. 1982
; Jarrard et
al. 1993
; Ocorr and Byrne 1985
; Pollock
and Camardo 1987
; Pollock et al. 1985
;
Shuster and Siegelbaum 1987
; Shuster et al.
1985
; Siegelbaum et al. 1982
; Sugita et
al. 1997a
; Walsh and Byrne 1989
). Because 5-HT
produced a broadening of the action potential and enhanced the
excitability of sensory neurons, both of these changes originally were
attributed to the reduction of IK,S
(e.g., Klein et al. 1986
). It has become clear, however,
that the mechanisms underlying the 5-HT-induced changes in the
biophysical properties of sensory neurons are more complicated than the
activation of a single second-messenger/protein kinase system and the
modulation of a single K+ current.
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Several additional components contribute to 5-HT-induced modulation of
action potentials and excitability of sensory neurons (Fig.
1B). First, elevated levels of cAMP modulate at least three currents in addition to IK,S.
Walsh and Byrne (1989) described a slow component of the
Ca2+-activated K+ current
(IK,Ca-S) that was active near the
resting potential of the cell and that was decreased by intracellular
injection of cAMP (or application of 5-HT). Braha et al.
(1993
; see also Edmonds et al. 1990
;
Eliot et al. 1993
) reported that intracellular injection
of cAMP (or application of 5-HT) enhanced a dihydropyridine-sensitive and slowly inactivating component of the Ca2+
current similar to the L-type Ca2+ current
(ICa-L). Baxter and Byrne
(1989
; see also White et al. 1994
) reported that
application of 5-HT decreased the conductance and slowed the kinetics
of a large, steeply voltage-dependent K+ current
(IK-V). Goldsmith and
Abrams (1992)
reported that application of analogues of cAMP
partially mimicked the 5-HT-induced slowing of the activation kinetics
of IK-V. Similarly, Hochner and
Kandel (1992)
reported that specific blockers of PKA partially
blocked the 5-HT-induced slowing of the activation kinetics of
IK-V. These results indicate that the
5-HT-induced modulation of IK-V is
mediated, at least in part, by the cAMP/PKA system. Moreover, studies
of Goldsmith and Abrams (1992
; see also Shuster
et al. 1991
) suggested that the originally described
IK,S consisted of two components, a
moderately voltage-dependent and slowly-activating component (IK,S-V), and an instantaneous (i.e.,
time-independent) "steady-state" component that was activated at
the resting potential (IK,S-I). Thus
5-HT-induced increases in the levels of cAMP can lead to the modulation
of a complex array of membrane currents with diverse biophysical properties.
Second, in addition to the cAMP/PKA system, application of 5-HT
activates protein kinase C (PKC) (Sossin 1997;
Sossin and Schwartz 1992
; Sossin et al.
1994
; see also Sacktor and Schwartz 1990
).1
Moreover, pharmacological activation of PKC [i.e., application of
active phorbol esters such as 4
12-deoxyphorbol 13-isobutyrate (DPB), 4
-phorbol 12,13-diacetate (PDAc), phorbol dibutyrate (PDBu), phorbol myristate (PMA)] mimics some aspects of 5-HT-induced
modulation of membrane currents. Braha et al. (1993)
reported that activation of PKC mimicked the 5-HT-induced increase of
ICa-L and that blockers of PKC blocked
5-HT-induced modulation of ICa-L.
Sugita et al. (1994a)
found that activation of PKC
mimicked and partially occluded the 5-HT-induced modulation of
IK-V.2
Thus 5-HT-induced modulation of membrane current appears to involve at
least two kinase systems (i.e., PKA and PKC) that act on an array of
membrane conductances.
Third, recent studies indicate that there is cross-talk between the PKC
and PKA cascades. Sugita et al. (1997a) reported that activation of PKC induced an increase in the level of cAMP in sensory
neurons. It is likely that the PKC-induced increase in cAMP leads to
activation of PKA and subsequent PKA-mediated modulation of membrane
currents. For example, activators of PKC induced a modest increase in
the excitability of sensory neurons, thereby partially mimicking a well
know cAMP effect (Sugita et al. 1997a
; see also
Baxter and Byrne 1990a
; Manseau et al.
1998
). In contrast, biochemical evidence indicates that
translocation of PKC was not induced by analogues of cAMP
(Sacktor and Schwartz 1990
). These results suggest that
some of the biophysical effects that have been attributed directly to
the PKC cascade may be indirect effects that result from cross-talk
between the PKC and PKA cascades.
Because of overlapping responses to electrical and pharmacological stimulation and because of cross-talk between second messenger/protein kinase cascades, it is difficult to accurately assess the how the modulation of specific membrane currents (i.e., IK,S, IK-V, IK,Ca-S, ICa-L) or how the PKA- versus PKC-mediated modulation of membrane currents contribute to 5-HT-induced spike broadening and excitability enhancement. The present study addresses these issues by developing and analyzing a Hodgkin-Huxley-type mathematical model of the sensory neuron. First, previously published voltage-clamp data were used to develop mathematical descriptions of the ionic conductances in the somata of sensory neurons. Second, simulations investigated whether the known modulatory actions of 5-HT on membrane currents are sufficient to account for the empirically observed increases in spike duration and excitability. Third, simulations investigated the relative contributions of individual currents to the overall effects of 5-HT. Fourth, simulations investigated the consequences of cross-talk between the PKC and PKA cascades. Finally, an empirical study was conducted to test the predicted contribution of IK,Ca-S to accommodation. The results indicated that the model was sufficient to simulate the basic features of action potential and excitability data from sensory neurons; concurrent modulation of IK,S and IK,Ca-S contributed significantly to 5-HT-induced increases in excitability; and modulation of IK-V contributed significantly to 5-HT-induced spike broadening. The simulations also provided several predictions that can help guide future experimental analysis, and the results illustrate that the actions of modulatory agents and second messengers cannot be understood on the basis of their direct effects alone. It is also necessary to consider indirect effects that occur through cross-talk between second-messenger systems and Ca2+-dependent processes.
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METHODS |
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Model development
GENERAL FEATURES.
The simulations were performed with SNNAP (Simulator for Neural
Networks and Action Potentials) (Ziv et al. 1994).
Version 5 of SNNAP was used and the software was run under the Windows 95/NT operating systems on PC-type microcomputers (Baxter and Byrne 1999
). The Euler method with a fixed time step of 30-µs was used for numerical integration. When simulations were begun, there
typically was a small (<500 µV), brief (~1 s) transient before the
resting membrane potential settled to its steady-state value (
50 mV).
To avoid analysis during this or any other transient,
10 s of
simulated time was allowed to elapse before data were taken.
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SIMULATING 5-HT-INDUCED MODULATION OF MEMBRANE CURRENTS.
To simulate 5-HT-induced modulation of membrane currents, selected
parameters of the model were set to the values indicated in the column
labeled "5-HT-induced modulation" in Table
2. The actions of 5-HT were simulated by
decreasing the conductances of IK,S
(both IK,S-V and
IK,S-I) to ~50% of their control
values and decreasing the conductance of
IK,Ca-S to ~20% of its control value. The magnitudes of these changes were estimated from published data. Cell-attached patch-clamp studies of the channels mediating IK,S indicated that application of
5-HT or injection of cAMP closed between 46 and 53% of the channels in
any given patch (Shuster et al. 1985; Siegelbaum
et al. 1986
). Thus PKA-mediated and 5-HT-induced modulation of
IK,S were simulated by decreasing the
conductances of IK,S-I and
IK,S-V by ~50%. Similarly, the
voltage-clamp studies of Walsh and Byrne (1989)
indicated that application of 5-HT or injection of cAMP blocked between
30 and 100% of the total IK,Ca-S (the
average was ~77 ± 8%). Thus PKA-mediated and 5-HT-induced modulation of IK,Ca-S were simulated
by decreasing the conductances of
gK,Ca-S to 23% of its control value.
In addition, the actions of 5-HT were simulated by increasing the
conductance of ICa-L to 250% of its
control value, which was based on published data indicating that
application of 5-HT induced an average increase in
ICa of 220 ± 36% (Eliot
et al. 1993
). Finally, the actions of 5-HT were simulated by
modifying the properties of IK-V. This modification was more complex than simply decreasing
gK-V, however. White et al.
(1994)
reported that in addition to decreasing
gK-V, 5-HT slowed the kinetics for its
activation and inactivation. Thus the mathematical description of
5-HT-induced modulation of IK-V
included increases in the time constants of activation and inactivation
(
A and
B,
respectively). The magnitude of these changes in the present study were
adjusted so as to reproduce the data of White et al.
(1994)
. This ensemble of modifications to the model was assumed
to represent the maximal effects of 5-HT. This assumption was based on
previously published dose-response curves for 5-HT-induced modulation
of sensory neurons (Jarrard et al. 1993
; Ocorr
and Byrne 1985
; Stark et al. 1996
; see also Bacskai et al. 1993
). The reported
EC50 values for the actions of 5-HT ranged from
0.8 to 14 µM and average EC50 was 8 ± 3 µM. The previously published empirical studies, which provided the data for the present model, used an average concentration of 30 ± 5 µM 5-HT. Thus we assumed that a maximal effect was achieved in the
majority of previous experimental studies, and the results of these
studies were combined. Finally, this ensemble of modifications to the
model that reflect 5-HT-induced modulation represented the steady-state
actions of 5-HT. Thus the present study did not simulate the time
dependency of 5-HT modulation (for review, see Byrne and Kandel
1996
).
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SIMULATING THE ACTIVATION OF PKA.
Although it is not clear from the available empirical results that all
of the modulatory changes that are induced by elevated levels of cAMP
are mediated via activation of PKA (e.g., Braha et al.
1993), in the present study, these modulatory changes were referred to collectively as "PKA-mediated modulation." To simulate the modulatory actions of PKA, selected parameters of the model were
set to the values indicted in the column labeled "PKA-mediated modulation" in Table 2. Because PKA is believed to mediate many of
the actions of 5-HT, many of the PKA-mediated parameter changes were
identical to those described above for 5-HT-induced modulation. For
example, the conductances for IK,S
(both IK,S-I and
IK,S-V) and
IK,Ca-S were reduced to ~50 and
~20% of their control values, respectively, and the conductance for
ICa-L was increased to 250% of its
control value. The modulation of IK-V
was different, however. In the presence of 5-HT, the conductance as
well as the activation and inactivation time constants
(
A and
B)
were modulated. The available empiric data suggest that PKA only
modulates
A, and this modulation is
equivalent to ~64% of that produced by 5-HT (Goldsmith and
Abrams 1992
; Hochner and Kandel 1992
). Thus the actions of PKA on IK-V were simulated
by slowing its activation kinetics to a level 64% of that used to
simulate the actions of 5-HT.
SIMULATING ACTIVATION OF PKC.
To simulate the modulatory actions of PKC, selected parameters of the
model were set to the values indicted in the column labeled
"PKC-mediated modulation" in Table 2. Activation of PKC has been
found to partially mimic and occlude the modulatory actions of 5-HT on
some membrane current [e.g., ICa-L
(Braha et al. 1993) and
IK-V (Sugita et al.
1994a
)]. Thus some of the PKC-mediated parameter changes were
similar or identical to those described earlier here for 5-HT-induced
modulation. Specifically, gCa-L was
increased to 250% of its control value,
gK-V was reduced, and the kinetics of
its inactivation were slowed to match the data of White et al.
(1994)
. As suggest by the data of Sugita et al.
(1994a)
, the actions of PKC on
IK-V were simulated by slowing its
activation kinetics to a level 75% of that used to simulate the
actions of 5-HT and by modifying the conductance and inactivation kinetics of IK-V to levels identical
to those used to simulated the actions of 5-HT. In addition, to its
direct effects on membrane conductances, activation of PKC stimulated
an increase in the intracellular levels of cAMP equivalent to ~60%
of the increase in cAMP that was induced by 5-HT (Sugita et al.
1997a
). Thus the modulatory effects of PKC also included
changes to conductances that were modulated by elevated levels of cAMP,
such as gK,S-I, gK,S-V, and
gK,Ca-S. The simulated actions of PKC
decreased these conductances to a level equivalent to ~60% the
PKA-mediated modulation (see Table 2).
In vitro preparation
Experimental procedures to measure the excitability of
sensory neurons have been described in detail previously (Baxter
and Byrne 1990a). Briefly, all experiments were performed on
clusters of somata of sensory neurons that were surgically isolated
from the ventrocaudal cluster of pleural ganglia in A. californica. Dissections were performed after anesthetizing the
animals by injecting a volume of isotonic MgCl2
equal to about one-half of the volume of the animal. An isolated
cluster was pinned to the floor of a recording chamber, which was
coated with a silicon elastomer and had a volume of ~300 µl. The
static bathing solution of artificial sea water (ASW; Instant Ocean,
Aquarium Systems, Mentor, OH) was buffered to pH 7.6 with 10 mM Trizma
(Sigma Chemical, St. Louis, MO) and was maintained at 15°C.
Conventional two-electrode current-clamp techniques were used. Sensory
neurons were impaled with two glass capillary microelectrodes that were
filled with 3 M potassium acetate and that had resistances of 2-6
M
. The membrane potential of the sensory neuron was monitored and
was maintained at
45 mV by manually adjusting the constant DC current output of the current passing electrode. Excitability was measured by
counting the number of action potentials elicited during a 1-s, 2-nA
constant-current pulse. These stimulating current pulses were separated
by 60 s. To ensure that the responses to the stimulating current
were stable, at least three examples of excitability were recorded
before and after bath application of TEA (Eastman Kodak, Rochester,
NY). Small, concentrated aliquots TEA were added to the bath such that
the final bath concentration of TEA was 2 mM. Data were collected from
the last stimulus in ASW and from the first stable response after
bath application of TEA.
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RESULTS |
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Simulating membrane currents, action potentials, and excitability in control conditions
The first test of the model was to examine how well it simulated
the biophysical properties of sensory neurons under control conditions.
To simulate control conditions, the parameters of the model were set
the values indicated in Table 1. These values produced a model sensory
neuron with a resting membrane potential of 50 mV and an input
resistance of 27 M
. (The input resistance was measured by injecting
a hyperpolarizing current pulse from a resting potential of
50 mV.)
These values are within the range of previously reported empirically
measured values. A survey of the published literature indicated that in
vitro preparations of sensory neurons have resting membrane potentials
ranging from
38 to
55 mV and input resistances ranging from 10 to
50 M
. The available published data suggested that sensory neurons
have an average resting potential of about
48 mV and an average input resistance of ~27 M
(Baxter and Byrne 1989
,
1990a
,b
; Cleary et al. 1998
; Pollock et
al. 1985
; Walsh and Byrne 1989
; White et al. 1994
; Wright and Kirschman
1995
).4
Figure 3 illustrates simulated membrane
currents that were elicited by voltage-clamp protocols similar to those
used in previous empiric studies. The current responses of the model
were in general agreement, both in time course and magnitude, with
published examples of isolated ionic currents in sensory neurons (cf.
Baxter and Byrne 1989
, 1990a
,b
; Braha et al.
1993
; Edmonds et al. 1990
; Eliot et al.
1993
; Goldsmith and Abrams 1992
; Hochner
and Kandel 1992
; Klein et al. 1980
, 1982
;
Pollock et al. 1985
; Scholz and Byrne 1987
; Sugita et al. 1994a
,b
; Walsh and
Byrne 1989
; White et al. 1994
; see also
Adams and Gage 1979a
; Byrne 1980a
;
Farquharson and Jahan-Parwar 1984
, Fieber
1995
; Gilly et al. 1997
).
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The simulated voltage-clamp experiments illustrated that the model
accurately reproduced the data from which it was derived. The more
complex biophysical properties of sensory neurons (e.g., the waveform
of the action potential and its excitability), however, emerge from
interactions among this ensemble of membrane currents and from
interactions between the membrane conductances and the intracellular
concentration of Ca2+. To examine how well the
present model simulated these emergent properties, single actions
potentials were elicited with a brief (3 ms) depolarizing current pulse
(15 nA) (Fig. 4A) and the
excitability of the cell was measured as the number of spikes elicited
by a series of 1-s depolarizing current pulses of increasing amplitude (Fig. 4B). These techniques closely mimicked protocols used
in previous experimental studies (e.g., Baxter and Byrne
1990a; Braha et al. 1993
; Hochner and
Kandel 1992
; Stark et al. 1996
; Sugita et
al. 1992
; Wright and Kirschman 1995
) and allowed
for analysis of the waveform of the action potential without
contamination from the stimulating current.
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From the resting potential of 50 mV, the model produced an action
potential that reached a voltage of ~41 mV at its peak (i.e., the
spike had a total amplitude of 91 mV; Fig. 4A). The duration
of the simulated spike, which was measured as the time between the peak
voltage and the point on the falling phase at which the membrane
potential was 10% of the peak, was 4.9 ms. There are many examples of
sensory neuron action potentials in the published literature with which
to compare the results of the present simulation (e.g., Baxter
and Byrne 1990a
; Braha et al. 1993
; Critz
et al. 1991
; Eliot et al. 1994
; Ghirardi
et al. 1992
; Goldsmith and Abrams 1992
;
Hochner and Kandel 1992
; Jarrard et al.
1993
; Klein 1993
; Mercer et al.
1991
; Stark et al. 1996
; Sugita et al.
1992
, 1994b
, 1997b
; Wright and Kirschman 1995
). Results from these empirical studies indicated that in vitro
preparations of sensory neurons generally have an action potential with
a total amplitude of ~90 ± 14 mV and a duration of ~5.1 ± 2.7 ms (means ± SE). In response to 1-s depolarizing current
pulses, the model sensory neuron exhibited accommodation similar to
that observed empirically (Fig. 4B). The simulated responses
to 1-, 2-, and 3-nA depolarizing current pulses were 1, 3, and 6 spikes, respectively. A survey of the published literature indicated
that in vitro preparations of sensory neurons generally produced an
average of ~1.8 ± 1.4 spikes in response to a 1-nA pulse;
~3.6 ± 0.9 spikes in response to a 2-nA pulse and ~5.4 ± 1.3 spikes in response to a 3-nA pulse (cf. Baxter and Byrne
1990a
; Braha et al. 1993
; Cleary et al. 1998
; Critz et al. 1991
; Dale et al.
1987
; Eliot et al. 1994
; Ghirardi et al.
1992
; Goldsmith and Abrams 1992
; Hochner
and Kandel 1992
; Jarrard et al. 1993
;
Klein et al. 1986
; Manseau et al. 1998
; Mercer et al. 1991
; Stark and Carew 1999
;
Stark et al. 1996
; Sugita et al. 1992
;
Wright and Kirschman 1995
; Wright et al. 1996
). The close agreement between the simulated responses of the model (i.e., membrane currents, spike waveform, and excitability) and empiric results indicated the mathematical descriptions of the available empirical data were sufficient to reproduce several key biophysical properties of sensory neurons in control conditions and that additional simulations of the model may provide insights into the mechanisms underlying serotonergic modulation of spike duration and excitability of sensory neurons.
Simulating serotonergic modulation of membrane currents, action potentials, and excitability
A second test of the model was to examine how well it simulated
the 5-HT-induced modulation of the biophysical properties of sensory
neurons. The simulated actions of 5-HT induced a steady-state depolarization of the resting membrane potential of ~4.1 mV and an
increase in the input resistance of the model sensory neuron to ~34
M (i.e., an increase to ~126% of the control value). A survey of
previously published empirical results indicated that in sensory
neurons, 5-HT induces depolarizations ranging from 2.9 to 5.7 mV (the
average depolarization was ~4.5 mV) and increases in input resistance
ranging from 110 to 140% of control values (the average increase was
~130% of control) (cf. Braha et al. 1993
;
Stark et al. 1996
; Walsh and Byrne 1989
;
Wright and Kirschman 1995
). The simulated responses were
in general agreement with empirical observations in that 5-HT induced a
decrease in resting membrane conductance and a depolarizing of the
resting membrane potential.
SEROTONERGIC MODULATION OF SPIKE DURATION.
To allow for direct comparisons between action potentials (and
measurements of excitability) simulated in control conditions and in
the simulated presence of 5-HT, a constant bias current (0.11 nA) was
applied to the model to maintain the resting membrane potential at
50
mV during 5-HT-induced modulation. In the simulated presence of 5-HT
and from a resting potential of
50 mV, the model produced an action
potential with a total amplitude of ~96 mV and a duration of 6.8 ms
(i.e., the duration was increased to ~139% of control; Fig.
5A). Although 5-HT-induced
increases in spike amplitude are not a parameter generally investigated
in empirical studies, a review of the published literature indicated that on average 5-HT induces an increase of ~3 mV in the amplitude of
spikes. Thus the simulated increase in spike amplitude was consistent
with empirical studies. Similarly, the simulated increase in spike
duration was in general agreement with empirical studies. A survey of
the published literature indicated that on average 5-HT induced an
increase in spike duration to ~140% of control (cf. Baxter
and Byrne 1990a
; Braha et al. 1993
; Critz
et al. 1991
; Eliot et al. 1994
; Ghirardi
et al. 1992
; Goldsmith and Abrams 1992
;
Hochner and Kandel 1992
; Hochner et al.
1986a
,b
; Jarrard et al. 1993
; Mercer et
al. 1991
; Pollock et al. 1985
; Stark and Carew 1999
; Stark et al. 1996
; Sugita et
al. 1992
, 1994a
; Wright and Kirschman 1995
;
Wright et al. 1996
). The close agreement between the
empirical and simulated results suggest that our current understanding of the 5-HT-induced modulation of membrane currents is sufficient to
account for 5-HT-induced spike broadening. The relative contribution of
the various modulatory actions of 5-HT to spike broadening will be
considered in the following text.
|
SEROTONERGIC MODULATION OF EXCITABILITY.
As described previously (see Fig. 4B), the excitability of
the model cell was measured as the number of spikes elicited by a
series of 1-s depolarizing current pulses of increasing amplitude. In
the simulated presence of 5-HT, the model no longer exhibited accommodation (Fig. 5B). Rather, the model fired spikes
throughout the 1-s depolarizing current pulses. The simulated responses
to 1-, 2-, and 3-nA depolarizing current pulses were 4, 8, and 11 spikes, respectively. A survey of the published literature indicated that in the presence of 5-HT, sensory neurons fired an average of ~7,
~9, and ~10 spikes during 1-, 2-, and 3-nA depolarizing current
pulses, respectively (cf. Baxter and Byrne 1990a;
Braha et al. 1993
; Critz et al. 1991
;
Eliot et al. 1994
; Ghirardi et al. 1992
;
Goldsmith and Abrams 1992
; Hochner and Kandel
1992
; Jarrard et al. 1993
; Klein et al.
1986
; Mercer et al. 1991
; Stark and Carew
1999
; Stark et al. 1996
; Sugita et al.
1997b
; Wright and Kirschman 1995
; Wright
et al. 1996
). Although there was a small difference between the
simulated response to a 1-nA current pulse and the average empirical
response (see DISCUSSION), there was a general agreement
between the model and the empirical data in that sensory neurons did
not exhibit accommodation in the presence of 5-HT. The specific
membrane currents that mediated the 5-HT-induced anti-accommodation
will be considered in the following text.
SEROTONERGIC MODULATION OF MEMBRANE CURRENTS.
As a first step toward gaining an understanding of which 5-HT-modulated
currents mediated changes in excitability and spike duration,
simulations investigated the relative contributions of
IK,S,
IK-V,
IK,Ca-S, and
ICa-L to 5-HT difference currents. In
previous voltage-clamp studies (cf. Baxter and Byrne 1989, 1990b
; Braha et al. 1993
; Critz et al.
1992
; Hochner and Kandel 1992
; Klein et
al. 1982
; Sugita et al. 1994a
,b
; White et
al. 1994
), 5-HT difference currents were generated by
subtracting currents in the presence of 5-HT from control currents.
This subtraction yields the net total current modulated by 5-HT. Figure
6 illustrates a simulated voltage-clamp
experiment from which 5-HT difference currents were generated. Membrane
currents in the model were elicited by voltage-clamp pulses from a
holding potential of
70 to
20 mV (Fig. 6A) and to 20 mV
(Fig. 6B). Currents were elicited first while the parameters
of the model were set to their control values (see Table 1) and again
after the parameters had been adjusted to reflect the simulated
presence of 5-HT (see Table 2). The 5-HT difference currents were
generated by subtracting the 5-HT responses from the control responses.
Thus 5-HT-induced decreases in net outward membrane currents were
represented as upward deflections in the difference currents, and
conversely, downward deflections represented 5-HT-induced increases in
net outward current.
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Simulating the effects of elevated levels of cAMP
To gain additional insights into how the modulation of specific
currents and the activation of different second-messenger/protein kinase cascades contribute to 5-HT-induced changes in spike duration and excitability, simulations examined how the currents modulated as a
consequence of elevated levels of cAMP effected the biophysical properties of the model sensory neuron. A survey of the published literature indicated that in the presence of elevated levels of cAMP,
sensory neurons fired an average of ~7, ~11, and ~12 spikes during prolonged depolarizing current pulses of 1, 2, and 3 nA, respectively (cf. Baxter and Byrne 1990a; Braha
et al. 1993
; Goldsmith and Abrams 1992
;
Hochner and Kandel 1992
; Jarrard et al.
1993
; Klein et al. 1986
; see also Sugita
et al. 1997a
). Thus elevated levels of cAMP fully mimicked, and
to some degree exceeded, the actions of 5-HT on accommodation in
sensory neurons. In contrast, elevated levels of cAMP did not appear to
fully mimic the actions of 5-HT on spike broadening. A survey of the
published literature indicated that on average elevated levels of cAMP
induced an increase in spike duration to ~119% of control (cf.
Baxter and Byrne 1990
; Goldsmith and Abrams
1992
; Hochner and Kandel 1992
; Klein
1993
; Sugita et al. 1992
, 1994b
; see also
Abrams et al. 1984
; Jarrard et al. 1993
).
These empirical observations suggested that currents modulated by
elevated levels of cAMP preferentially modulate accommodation and to a
lesser degree spike duration.
PKA-MEDIATED MODULATION OF SPIKE DURATION AND EXCITABILITY.
As described previously, a constant bias current (see Table 2) was
applied to the model to maintain the resting membrane potential at 50
mV during PKA-mediated modulation. In the simulated presence of
elevated levels of cAMP and from a resting potential of
50 mV, the
model produced an action potential with a total amplitude of ~93 mV
and a duration of 5.7 ms (i.e., the duration was increased to 116% of
control; Fig. 8A). Although
very little empirical data is available regarding PKA-mediated
increases in spike amplitude, that which are available suggest that
PKA-mediated modulation induces a slight increase in spike amplitude
(Baxter and Byrne 1990a
; Goldsmith and Abrams
1992
; Sugita et al. 1994b
). The magnitude of the
simulated PKA-mediated spike broadening was ~40% of the simulated
effect of 5-HT on spike duration (see preceding text). This
intermediate response to PKA by the model was similar to the available
empirical data, which suggested that magnitude of the spike broadening
induced by elevated cAMP was ~47% of the average response to 5-HT
(see preceding text).
|
RELATIVE CONTRIBUTION OF INDIVIDUAL CURRENTS TO PKA-MEDIATED SPIKE
BROADENING.
To evaluate which currents mediated PKA-induced changes in spike
duration (and excitability, see following text) the modulation of
individual currents was removed selectively from the ensemble of
PKA-mediated actions, and simulation tested the effects of these
manipulations on PKA-mediated spike broadening (and excitability enhancement). For example, previous qualitative models attributed 5-HT-induced spike broadening to PKA-mediated decreases in
IK,S (e.g., Kandel and Schwartz
1982; for review, see Byrne and Kandel 1986
). A
prediction of such a model would be that spike broadening would be
blocked if the modulation of IK,S was
removed from the ensemble of PKA-mediate actions (see Table 2). A
simulation to test this predication found that removing only the
modulation of IK,S (both
IK,S-I and
IK,S-V) had no effect on PKA-mediated spike broadening (not shown). Alternatively, enhancement of an inward
current (e.g., ICa) has been suggested
to mediate spike broadening (e.g., Klein and Kandel
1978
). A simulation to test this predication found that
removing only the modulation of ICa-L had no effect on PKA-mediated spike broadening (not shown). The only
manipulation that was found to block PKA-mediated spike broadening was
the removal of modulation of IK-V
(i.e., slowing of its activation kinetics; Fig.
9A). When only modulation of
IK-V was removed (i.e., PKA-mediated
modulation of IK,S,
IK,Ca-S, and
ICa-L remained as indicated in Table 2
but the parameters for IK-V were set
to the control values indicated in Table 1), the control spike and the
"modulated" spike were virtually indistinguishable. Thus the simulations indicated that modulation of
IK-V played the key role in
PKA-mediated increases of spike duration.
|
RELATIVE CONTRIBUTION OF INDIVIDUAL CURRENTS TO PKA-MEDIATED INCREASES OF EXCITABILITY. A similar set of simulations was used to examine which currents and their modulation contributed to PKA-mediated increases in excitability of the model cell, and the results suggested that increases in excitability emerged from a complex interactions among several contributing factors.
First, simulations considered the contribution of PKA-mediated increase of ICa-L. One might predict that enhancing an inward current would help to increase excitability and that removing the modulation of ICa-L would reduce PKA-mediated increases in excitability. Simulations found, however, that removing only modulation of ICa-L increased the magnitude of PKA-mediated changes in excitability. In previous simulations in which all PKA-mediated actions were included, a 1-s, 1-nA depolarizing current pulse elicited four spikes (Fig. 9B1), whereas an identical pulse elicited five spikes after the modulation of ICa-L was removed (Fig. 9B2). This result can be explained, in part, when one considers the indirect effects of increased Ca2+ influx via the enhanced component of ICa. Removing the PKA-mediated enhancement of ICa-L decreased the total intracellular levels of Ca2+ during the stimulating current pulse to 77% of the levels that were obtained when ICa-L was modulated. Note, that this decrease occurred despite the fact that five spikes were elicited by the test pulse (Fig. 9B2) rather than the four spikes that occurred were when all of the PKA-mediated actions were simulated (Fig. 9B1). The decreased levels of intracellular Ca2+, in turn, produced less activation of IK,Ca-S. In the simulation without modulation of ICa-L, the amplitude of IK,Ca-S at end of the 1-s stimulating current pulse was reduced to 75% of the amplitude of IK,Ca-S at the same point in time in the simulation with all of the PKA-mediated actions in place. And, as illustrated in the following text, IK,Ca-S is a current that tended to reduce excitability. These results suggested that modulation ICa played an important, albeit indirect, role in regulating excitability. Thus additional simulations were preformed to test some of the assumptions that were incorporated into the model descriptions of ICa (see METHODS). Simulations examined the role of Ca2+-dependent inactivation of Ca2+ currents (both ICa-L and ICa-N). If Ca2+-dependent inactivation of ICa was removed from the model and all other parameters were set to the values for PKA-mediated modulation (Table 2), then a 1-s, 1-nA depolarizing current pulse elicited only three spikes (not shown). In addition, simulations examined the consequences of increasing the magnitude of PKA-mediated modulation of ICa-L. If the magnitude of PKA-mediated modulation of ICa-L was increased from 250 to 500% and all other parameters were set to the values for PKA-mediated modulation (Table 2), then a 1-s, 1-nA depolarizing current pulse elicited only three spikes (not shown).5 Both of these manipulations (i.e., removing Ca2+-dependent inactivation and increasing the magnitude of PKA-mediated modulation) increased Ca2+ influx and thereby increased the activation of IK,Ca-S and decreased excitability. Second, simulations considered the contribution of IK,S (both IK,S-I and IK,S-V) to PKA-induced increases of excitability. These currents were active near the resting potential of the model cell and did not inactivate. Thus one might predict that reducing an outward current would help to increase excitability and that removing the modulation of IK,S would reduced PKA-mediated increases in excitability. Simulations confirmed this prediction. In the simulation without modulation of IK,S (Fig. 9B3), a 1-s, 1-nA depolarizing current pulse elicited only two spikes, whereas four spikes were elicited when all of the PKA-mediated actions were included (Fig. 9B1). Third, simulations considered the contribution of IK,Ca-S to PKA-induced increases of excitability. As with IK,S, IK,Ca-S was active near the resting potential of the model cell and did not inactive. Moreover, the activation of IK,Ca-S was indirectly regulated by the level of spiking activity in the model cell. As more spikes were generated, the intracellular levels of Ca2+ increased and the activation of IK,Ca-S increased, and this increase in outward current opposed further spiking. Thus one might predict that down regulating this negative feedback loop (i.e., IK,Ca-S) would help to increase PKA-induced enhancement of excitability. Simulations confirmed this prediction. In the simulation without decrease of IK,Ca-S (Fig. 9B4), a 1-s, 1-nA depolarizing current pulse elicited only one spike, whereas four spikes were elicited when all of the PKA-mediated actions were included (Fig. 9B1). These results and those described above indicated that concurrent decreases of IK,S and IK,Ca-S were necessary for PKA-induced increases of excitability to occur.ROLES OF IK,S AND
ICA-L IN PKA-INDUCED BROADENING OF TEA
SPIKES.
The simulations described in the preceding text indicated the
modulation of IK,S and
ICa-L did not play important roles in PKA-induced spike broadening (see Fig. 9A). Previous
empirical studies, however, have suggested that modulation of these two currents should contribute significantly to spike broadening (e.g., Abrams et al. 1984; Belardetti et al.
1986
; Castellucci et al. 1982
; Klein and
Kandel 1978
; Klein et al. 1982
; Pieroni
and Byrne 1992
; Pollock et al. 1985
;
Siegelbaum et al. 1986
). The discrepancy between the
results of the present simulation study and previous empirical studies
may be explained, in part, by differences in the conditions under which
the modulation of spike broadening were studied. Often empirical
studies examined spike broadening in the presence of high
concentrations of TEA and thereby blocking IK-V and
IK,Ca and maximizing the relative
contributions of IK,S and
ICa-L to PKA-mediated spike
broadening. Simulations examined whether the presence of high (100 mM)
concentrations of TEA created conditions in which the roles of
modulation of IK,S and
ICa-L in spike broadening were
enhanced (Fig. 10).
|
Simulating PKC-mediated modulation of action potentials and excitability
The results described above indicated that modulation of IK,Ca-S and IK,S via PKA could completely account for 5-HT-induced increases in excitability, but that PKA-mediated modulation of IK-V could accounted for only ~50% of 5-HT-induced spike broadening. To determine whether PKC-mediated modulation of IK-V could more completely account for 5-HT-induced spike broadening, simulations examined how the currents modulated by activation of PKC effected the biophysical properties of the model sensory neuron.
In the simulated presence of activated PKC and from a resting potential
of 50 mV, the model produced an action potential with a total
amplitude of ~96 mV and a duration of ~6.4 ms (i.e., the duration
was increased to ~134% of control; Fig.
11A). The data of
Sugita et al. (1992
; see also Bhara et al.
1993
; Sugita et al. 1994a
, 1997b
) indicated that
activation of PKC induced an average increase in spike duration to
~126% of control and a slight increase in the spike amplitude. In
addition to increasing the duration of the action potential, the
simulated actions of PKC also induced a slight increase in the
excitability of the model. In response to 1-s current pulses of 1, 2, and 3 nA, the model produced two, four, and seven spikes, respectively
(compare with Fig. 4B). A survey of the published literature
indicated that in response to a 1-s, 2-nA current pulse, sensory
neurons produced between three and nine spikes while in the presence of active phorbol esters (the average response was ~5 spikes) (cf. Braha et al. 1993
; Manseau et al. 1998
;
Sugita et al. 1992
, 1997a
). Thus the results of the
model were in general agreement with the available empirical data.
Moreover, results indicated that activation of PKC closely mimicked the
actions of 5-HT on spike broadening and, to a lesser degree, the
actions of 5-HT on accommodation in sensory neurons. These observations
suggested that currents modulated by activation of PKC preferentially
modulate spike duration.
|
RELATIVE CONTRIBUTION OF INDIVIDUAL CURRENTS TO PKC-MEDIATED SPIKE BROADENING. To evaluate which currents mediated PKC-induced changes in spike duration, the modulation of individual currents was selectively removed from the ensemble of PKC-mediated actions and simulation tested the effects of these manipulations on PKC-mediated spike broadening. As with similar investigations of which current mediated PKA-induced spike broadening (see preceding text), removing only the modulation of ICa-L, or only IK,S (both IK,S-I and IK,S-V), or only IKCa-S had no effect on PKC-mediated spike broadening (not shown). The only manipulation that blocked PKC-mediated spike broadening was the removal of modulation of IK-V (Fig. 12A). When only modulation of IK-V was removed, the control spike and the modulated spike were virtually indistinguishable. Thus the simulations indicated that modulation of IK-V played the key role in modulation of spike duration by both PKA and PKC.
|
RELATIVE CONTRIBUTION OF INDIVIDUAL CURRENTS TO PKC-MEDIATED INCREASES OF EXCITABILITY. Because activation of PKC can induce an increase in levels of cAMP, PKC can have both direct effects on some conductances (i.e., gK-V and gCa-L) and indirect effects that results from activation of PKA (see Fig. 1B). Individual components of the ensemble of PKC-mediated actions were removed selectively, and simulations examined how these manipulations altered PKC-induced increases of excitability. First, simulations considered the contribution of PKC-induced increase of ICa-L (i.e., a direct effect of PKC). If only the increase of ICa-L was removed from the ensemble of PKC-mediated actions, then the number of spikes elicited by the test pulse was increased from seven (Fig. 12B1) to nine (Fig. 12B2). Similar results were obtained if only the modulation of IK-V was removed; i.e., the test pulse elicited nine spikes (not shown). Second, simulations considered the contribution of IK,S (both IK,S-I and IK,S-V) to PKC-induced increases of excitability. If only the PKC-induced decrease of IK,S was removed (i.e., an indirect effected mediated via cross-talk with the cAMP/PKA system), the number of spikes elicited by the test pulse was decreased from seven (Fig. 12B1) to five (Fig. 12B3). Finally, simulations considered the contribution of IK,Ca-S. If only the decrease of IK,Ca-S was removed (i.e., an indirect effect mediated via cross-talk), the number of spikes elicited by the test pulse was reduced to only four (Fig. 12B4). These results indicated that the direct actions of PKC on membrane conductances do not contribute to increased excitability of the model cell. Indeed, PKC-mediated modulation of IK-V and ICa-L contributed to a reduction of excitability. Rather, PKC-induced increases in excitability resulted from its indirect actions on membrane conductances that were modulated via PKA (i.e., IK,S and IK,Ca-S).
Simulating biophysical correlates of long-term sensitization
Modulation of the intrinsic cellular properties of sensory neurons
in Aplysia is believed to be an important mechanism
contributing to several examples of learning, and previous studies have
demonstrated that long-term sensitization training affected at least
two biophysical properties of tail sensory neurons (Cleary et
al. 1998; Scholz and Byrne 1987
). Specifically,
training reduced the net outward current elicited by brief depolarizing
voltage-clamp steps and the kinetics and voltage-sensitivity of the
modulated outward current were similar to
IK,S (Scholz and Byrne
1987
). In addition, training increased the excitability of
sensory neurons (Cleary et al. 1998
). Although an
increase in excitability is consistent with modulation of
IK,S, it is not known whether
modulation of IK,S alone is sufficient
to account for the twofold increase in excitability that is observed
after training. To address this issue, simulations examined the
increase in excitability that was induced by decreasing only
IK,S (Fig.
13). In simulated control conditions, a
1-s, 2-nA current pulse elicited three spikes (Fig. 13A).
After the values for gK,S-I and
gK,S-V were reduced to reflect their
modulation by 5-HT (see Table 2), an identical test elicited four
spikes (Fig. 13B), which is less than the twofold increase previously reported (Cleary et al. 1998
). This result
suggests that modulation of an additional current(s) may be necessary
to fully account for the effects of training. One possibility is IK,Ca-S, which like
IK,S makes an important contribution
to excitability. After both IK,S and
IK,Ca-S were reduced, the 1-s, 2-nA
test pulse elicited the expected twofold increase in excitability
(i.e., 6 spikes; Fig. 13C). These results suggest that
decreases of IK,S alone cannot fully
account for the observed increase in sensory neuron excitability after
behavioral training and that an addition current, possibly
IK,Ca-S, is modulated.
|
An empirical test of a key prediction from the model
The simulations presented above made several predictions that can be used to guide experimental investigations (see DISCUSSION). One of these predictions was related to the role of IK,Ca-S in regulating the excitability of sensory neurons. A decrease in IK,Ca-S played a key role in both PKA- and PKC-mediated increases of excitability (Figs. 9B3 and 12B3). In addition, IK,Ca-S was active at the resting potential and became the predominant component of 5-HT difference current at membrane potentials <0 mV (Fig. 7). These results suggested that IK,Ca-S contributed to accommodation and that the excitability of sensory neurons could be increased by selectively reducing IK,Ca-S. Figure 14 illustrates the results of simulation and experimental studies that examined this prediction.
|
Experimentally, one method of selectively decreasing
IK,Ca is to apply low concentrations
(2-5 mM) of TEA (e.g., Walsh and Byrne 1989).
Empirically derived dose-response relationships between the
concentration of external TEA and the magnitude of
IK,Ca indicated that 2 mM should
reduce IK,Ca (presumably both
IK,Ca-F and
IK,Ca-S) to ~25% of its control
value (Baxter and Byrne 1989
; Herman and Gorman
1981
). In addition, 2 mM TEA should reduce the magnitude of
IK-V to ~80% of its control value.
Thus to simulate the presence of a low concentration of TEA,
gK,Ca-F and
gK,Ca-S were both reduced to 25% and
gK-V was reduced to 80% of their
control values. The excitability of the model cell in the simulated
presence of 2 mM TEA was tested by injecting a 1-s, 2-nA depolarizing
current pulse. The test pulse elicited nine action potentials in the
simulated presence of a low concentration of TEA (Fig. 14A2)
as compared with three action potentials that were elicited by an
identical current pulse in simulated control conditions (Fig.
14A1). Thus the simulations predicted that a low
concentration of TEA should block accommodation.
The effects of a low concentration of TEA on accommodation also were examined experimentally (Fig. 14B). In control saline, a 1-s, 2-nA depolarizing current pulse elicited six action potentials, whereas an identical current pulse elicited 11 spikes in the same cells after bath application of 2 mM TEA. Summary data from four similar experiments were illustrated in Fig. 14B3. The number of spikes elicited by 1-s, 2-nA current was significantly increased in the presence of 2 mM TEA. The close agreement between the simulated results and the empirical observations supports the prediction of the model that IK,Ca plays key role in regulating accommodation of sensory neurons and that its down regulation by 5-HT contributes to increases in excitability.
![]() |
DISCUSSION |
---|
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---|
The present study incorporated the available voltage-clamp data on the currents in sensory neurons and their modulation by 5-HT into a Hodgkin-Huxley-type mathematical model of the soma of a sensory neuron. The model successfully mimicked key biophysical properties of the sensory neuron, such as the waveform of its action potential and accommodation of spiking during prolonged (i.e., 1 s) stimulation. Moreover, the model reproduced several types of plasticity in the sensory neuron soma, such as increases in the duration of the action potential and excitability in response to the application of 5-HT as well as the responses of sensory neurons to activation of PKA and PKC. Analyses of the model were able to differentiate the effects of the various known modulatory actions of 5-HT on membrane conductances and to evaluate their relative contribution of 5-HT-induced plasticity. In addition, the results from these simulations made several testable predictions that can help to guide future experimental studies.
Roles of IK-V, IK,S, IK,Ca-S, and ICa-L in 5-HT induced plasticity
Results from the current model indicated that IK-V was the major current responsible for repolarization of the action potential, hence, the modulation of IK,V was the key determinant of action potential broadening induced by either 5-HT, PKC, or PKA. The varying degrees to which experimental manipulations modified the properties of IK-V were reflected directly in the magnitude of spike broadening that they induced. The simulated actions of PKA modulated only the activation time constant of IK-V, and although this was sufficient to reduce the outward current early in voltage-clamp steps, it was not as effective as the actions of PKC or 5-HT, which both slowed the activation and decreased the conductance. Thus the simulated actions of PKA produced less broadening of the action potential than either PKC or 5-HT.
The modulation of excitability emerged from the complex interactions among multiple factors and required the concurrent modulation of several conductances. The roles of IK-V and ICa-L in regulating excitability were paradoxical, as modulation of these currents increased Ca2+ influx, which in turn increased the activation of IK,Ca, thus constituting a negative feedback loop in the control of excitability. This negative feedback loop was overcome to a limited degree by down regulation of other outward currents, namely IK,S. Before dramatic increases in excitability could be achieved, however, it was necessary to reduced the gain of the negative feedback loop by down regulating IK,Ca-S. Thus the results of the present study suggested a prominent role for the modulation of IK,Ca-S in mediating 5-HT-induced increases of excitability.
Relative contributions of PKA- and PKC-mediated actions to serotonergic modulation of sensory neurons
Although PKA and PKC modulated an identical set of membrane
conductances, there were relatively subtle variations in the degrees to
which the two protein kinases modulated the currents, and these differences could explain the different physiological response that
have been attributed to PKA and PKC. Empirical studies have indicated
that activation of PKA can mimic fully the actions of 5-HT on
excitability but can mimic only partially 5-HT-induced spike broadening
(e.g., Baxter and Byrne 1990a; Sugita et al. 1994b
). Conversely, empiric studies have indicated that
activation of PKC can induce spike broadening comparable with that of
5-HT but that activation of PKC induced only moderated increases in excitability (Sugita et al. 1992
, 1997a
). The present
simulations illustrated that although PKA modulated
IK-V, the degree of this modulation
was inadequate to broaden the spike to the same extent as 5-HT. The
PKA-mediated modulation of the currents that regulate excitability,
however, was equal to that produced by 5-HT. Indeed, PKA-induced
increases in excitability exceeded that induced by 5-HT in some cases.
Similar results have been observed in empirical studies (e.g.,
Baxter and Byrne 1990a
). Conversely, PKC modulated the
membrane currents that regulate excitability to a lesser degree than
PKA, and PKC induced greater broadening, which acted indirectly to
decrease excitability. Thus the simulated actions of PKC did not
produce increases in excitability comparable to 5-HT. These results
indicate that no one second-messenger/protein kinase system can account
fully for the actions of 5-HT. The combined actions of PKC and PKA were
necessary to account for the previously described actions of 5-HT on
the biophysical properties of sensory neurons.
The present study did not investigate two important features of the
relative contributions of PKA and PKC to serotongeric modulation,
however. These are the temporal development the PKA- and PKC-mediated
modulation after application of 5-HT and the mechanisms of interactions
between the PKA and PKC cascades. Implicit in the formulation of the
present model was the concept that the modulation of
IK,S and
IK,Ca-L by PKC was indirect and
ultimately was mediated via PKA, which was activated after PKC-induced
increases in levels of cAMP. In such a serial interaction, some of the
modulatory effects of PKC would be blocked by experimental
manipulations that specifically block PKA. Specifically, PKC-induced
increases in excitability would be prevented by blocking PKA if the
interaction was serial in nature. These issues have not been
investigated experimentally. In addition, the present model assumed
that the PKC-mediated modulation of
IK,V was direct and was not mediated in anyway via its interactions with the cAMP/PKA cascade. This assumption appears to be valid because many of the modulatory actions
of PKC (and 5-HT) on IK-V are not
mimicked by PKA (Goldsmith and Abrams 1992;
Hochner and Kandel 1992
; Sugita et al.
1994a
) Thus the two protein kinase cascades appear to converge
on IK-V and modulated this conductance
via parallel pathways.
In addition to varying in the degree to which they modulate a common
set of membrane conductances, the PKA and PKC cascades may differ in
the rates at which they become active after application of 5-HT. The
actions of PKC appear to develop relatively slowly, whereas as the
actions of PKA appear to develop more rapidly (Hochner and
Kandel 1992; Sugita et al. 1992
; for review, see
Byrne and Kandel 1996
). Thus the spike broadening that
is observed soon after application of 5-HT is believed to be mediated
via the PKA cascade, whereas spike broadening at later times is
believed to be mediated to a greater extent via the PKC cascade.
Current limitations of the SNNAP software precluded developing models
that could investigate the temporal development of serotonergic
modulation of sensory neurons. In addition, the present model was
developed from data describing the steady-state modulation of membrane
currents by 5-HT, PKA, and PKC, and thus the results of the present
study represent the steady-state modulation of the biophysical
properties of sensory neurons.
Discrepancies between the properties of the model and empirical observations
Although the model was able to accurately simulate many key
features of the biophysical properties of sensory neurons and their
modulation, there were some discrepancies between the simulated properties of the cell and the available empirical data. The predicated 5-HT-induced increases in excitability during a 1-s, 1-nA current pulse
were less than the average empiric observation. The model predicted a
response of four spikes, whereas the empirical data suggested an
average response of about seven spikes. This discrepancy may indicate
that the model would benefit from additional refinements. For example,
nothing is know about the Na+ current in these
sensory neurons. A more accurate description of important component of
the model may resolve this discrepancy. Moreover, the results of the
present study indicated that IK,Ca-S played a key role in regulating excitability. The present description of this current was based on a minimum of assumptions, and it did not
incorporate voltage- and/or time-dependent activation or inactivation.
It may be possible to correct this discrepancy by incorporating some
degree of voltage-dependent activation of IK,Ca-S that further enhances the
excitability of the cell at the resting membrane potentials in the
presence of 5-HT. Indeed, the data of Walsh and Byrne
(1989) suggested that some nonlinear characteristics for this
conductance at membrane potentials <0 mV. Given the important role of
IK,Ca-S that is predicted by the present study, additional investigation of this current appears to be
warranted (see following text).
Predictions from the model
The results of the present study make several predictions that can
help to guide future experimental studies. First, the present study
suggests that IK,Ca-S plays an
important role in regulating excitability. The original work of
Walsh and Byrne (1989) investigated the contribution
that modulation of this current makes to the modulatory effects of 5-HT
(and cAMP) on membrane currents, but they did not investigate how
modulating this current might effect the spike or excitability of
sensory neurons. The present study was the first to consider this
issue, and as an initial step toward testing this prediction, the
actions of a low concentration of TEA on excitability were investigated
experimentally. The results of the experiment agreed with the
prediction of the model that blocking
IK,Ca would enhance excitability. The
important role that IK,Ca-S played in
the current model indicates that this current warrants additional
empirical characterization. Second, the present study suggests that
Ca2+-dependent inactivation of
ICa also contributes to the regulation of excitability. This aspect of Ca2+ currents in
sensory neurons has not been investigated. More generally, the
simulations suggested a more comprehensive investigation is warranted
of how multiple factors interact to regulate excitability. Finally, the
development of this model highlights a significant deficit in the
current characterization the biophysical properties of sensory neurons.
Nothing is known about the Na+ current(s) in
these cells or the extent to which Na+ current
may be modulated. Although the current model appears to accurately
simulate many properties of sensory, incorporating a more accurate
description of the Na+ current may reveal new
insights into the biophysical properties and modulation of sensory
neurons. In summary, the present model quantifies the current state of
knowledge regarding serotonergic modulation of membrane currents in
sensory neurons of Aplysia and can provide a theoretical
framework to use in the design and interpretation of experiments to
further our understanding of these phenomenon.
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APPENDIX |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
The membrane potential (Vm) of
the sensory neuron was given by the differential
equation
![]() |
(A1) |
![]() |
(A2) |
![]() |
(A3a) |
![]() |
(A3b) |
![]() |
(A4a) |
![]() |
(A4b) |
![]() |
(A4c) |
![]() |
(A4d) |
The model of the sensory neuron also incorporated a relatively simple
description of an intracellular pool of Ca2+ (see
Fig. 2B). The dynamics of this pool were described by a first order process and the concentration of Ca2+
in the pool was obtained by solving the differential equation
![]() |
(A5) |
![]() |
(A6) |
![]() |
(A7) |
![]() |
(A8) |
![]() |
ACKNOWLEDGMENTS |
---|
The SNNAP modeling software and the input files for the simulations in the present study can be obtained at http://nba19.med.uth.tmc.edu/public/publish/dbaxter.
This work was supported by grants from the National Institutes of Health (R01-RR-11626 and P01-NS-38310).
Present address of C. C. Canavier: Dept. of Psychology, University of New Orleans, New Orleans, LA 70148.
![]() |
FOOTNOTES |
---|
Address for reprint requests: D. A. Baxter, Dept. of Neurobiology and Anatomy, W. M. Keck Center for the Neurobiology of Learning and Memory, The University of Texas-Houston Medical School, P.O. Box 20708, Houston, TX 77225.
The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
1
Recent evidence suggests that 5-HT also activates
mitogen-activated kinase (MAPK) (Michael et al. 1998)
and possibly Ca2+/calmodulin-dependent kinase II (CamKII)
(Nakanishi et al. 1997
). There is no evidence at this
time, however, that these kinases modulate membrane conductances.
2
Activation of PKC by phorbol esters also has been
reported to increase the magnitude of Ca2+-activated
K+ currents (IK,Ca)
(Critz and Byrne 1992). This effect of phorbol esters,
however, does not appear to be mimicked by 5-HT (Walsh and Byrne
1989
).
3
At the resting membrane potential, there was a small,
but finite, conductance to Ca2+, which in turn, lead to a
small level of activation of IK,Ca-S. Using
Faraday's constant and the volume of a sensory neuron with a radius of
10 µm, the Ca2+ current at the resting potential was
calculated to yield a basal concentration of intracellular
Ca2+ equivalent to ~21 nM (higher if one assumes smaller
intracellular volumes) (see Yamada et al. 1998).
4
Note, data indicate that sensory neurons in isolated
culture have input resistances >100 M (e.g., Dale et al.
1987
; Manseau et al. 1998
). These data were not
included in the present analysis.
5 Increasing the PKA-mediated modulation of ICa-L to 500% did, however, increase the duration of the PKA-modulated spike to 124% of control (not shown). Similarly, if the magnitude of 5-HT-induced modulation of ICa-L was increased to 500%, the duration of the 5-HT-modulated spike was increased to 147% of control (not shown).
Received 21 August 1998; accepted in final form 12 July 1999.
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