Department of Neurobiology, University of Pittsburgh School of Medicine, Pittsburgh, Pennsylvania 15261
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ABSTRACT |
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Schobesberger, Hermann,
Diek W. Wheeler, and
John P. Horn.
A Model for Pleiotropic Muscarinic Potentiation of Fast Synaptic
Transmission.
J. Neurophysiol. 83: 1912-1923, 2000.
The predominant form of muscarinic excitation in
the forebrain and in sympathetic ganglia arises from m1 receptors
coupled to the Gq/11 signal transduction pathway.
Functional components of this system have been most completely mapped
in frog sympathetic B neurons. Presynaptic stimulation of the B neuron
produces a dual-component muscarinic excitatory postsynaptic potential
(EPSP) mediated by suppression of voltage-dependent M-type
K+ channels and activation of a voltage-insensitive cation
current. Evidence from mammalian systems suggests that the cation
current is mediated by cyclic GMP-gated channels. This paper describes the use of a computational model to analyze the consequences of pleiotropic muscarinic signaling for synaptic integration. The results
show that the resting potential of B neurons is a logarithmic function
of the leak conductance over a broad range of experimentally observable
conditions. Small increases (<4 nS) in the muscarinically regulated
cation conductance produce potent excitatory effects. Damage introduced
by intracellular recording can mask the excitatory effect of the
muscarinic leak current. Synaptic activation of the leak conductance
combines synergistically with suppression of the M-conductance (40 20 nS) to strengthen fast nicotinic transmission. Overall, this effect
can more than double synaptic strength, as measured by the ability of a
fast nicotinic EPSP to trigger an action potential. Pleiotropic
muscarinic excitation can also double the temporal window of summation
between subthreshold nicotinic EPSPs and thereby promote firing.
Activation of a chloride leak or suppression of a K+ leak
can substitute for the cation conductance in producing excitatory muscarinic actions. The results are discussed in terms of their implications for synaptic integration in sympathetic ganglia and other circuits.
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INTRODUCTION |
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Muscarinic synapses regulate activity throughout
the nervous system, from the cerebral cortex to peripheral autonomic
ganglia. When muscarinic transmission in the forebrain is impaired by
drugs, or by neurodegenerative disorders such as Alzheimer's disease, the cognitive effects include memory loss and dementia (Lawrence and Sahakian 1998; Levey 1996
; Perry et
al. 1999
; Winkler et al. 1998
). Although these
profound behavioral phenomena remain poorly understood in terms of the
underlying neural circuitry, there is considerable evidence that
cholinergic pathways play a modulatory role in the cortex. The case for
modulation rests largely on the diffuse anatomic organization of
central cholinergic pathways and the modulatory influence of muscarinic
receptors on voltage-dependent ion channels (Brown et al.
1997
; Caulfield 1993
; Descarries et al.
1997
; Hasselmo 1995
). Advancing to the next
level of analysis poses a more difficult challenge. Three experimental
problems generally arise whenever one attempts to relate the molecular details of muscarinic modulation to neural circuit dynamics. First, muscarinic receptors often regulate multiple ionic conductances through
complex transduction pathways, whose frequent branch points and
intersections are difficult to dissect. It therefore remains generally
unclear how the subcomponents of a muscarinic response combine to
influence synaptic integration. Second, muscarinically controlled
conductance changes can be quite small and comparable in magnitude to
perturbations introduced by intracellular recording. This suggests that
recording damage may confound experiments by obscuring the normal
influence of muscarinic modulation. Third, it remains difficult to
activate muscarinic synapses selectively, even in brain slices, and
thereby test how they modulate other synapses (Cole and Nicoll
1983
, 1984
; Madison et al. 1987
).
Here, we solve these three generic problems by considering sympathetic ganglia, a system whose relative simplicity facilitates experimentation and the building of computational models.
In paravertebral sympathetic ganglia one can resolve several distinct
muscarinic mechanisms and observe how they interact with fast
ionotropic synapses. The cell-specific expression of muscarinic
synapses has been defined most clearly in bullfrog sympathetic ganglia,
where preganglionic activity drives two forms of synaptic inhibition
(Dodd and Horn 1983b; Horn and Dodd 1981
; Shen and Horn 1996
) and a slow excitatory postsynaptic
potential (EPSP) (Nishi and Koketsu 1968
; Tosaka
et al. 1968
). This paper focuses on the excitatory mechanism.
The pleiotropic nature of muscarinic excitation has been studied
extensively in sympathetic neurons of the frog and rat, and in
sympathetically derived neuroblastoma cell lines. Muscarinic agonists
depolarize B neurons in frog ganglia by suppressing voltage-dependent M-potassium channels (gM) and by
increasing a background leak conductance
(gleak) (Adams and Brown
1982; Akasu et al. 1984
; Brown and Adams
1980
; Jones 1985
; Kuba and Koketsu
1974
; Kuffler and Sejnowski 1983
; Tsuji
and Kuba 1988
). In rat sympathetic neurons and in the NG108-15
cell line, it has been further determined that m1-type receptors
regulate M-current through the Gq/11 protein (Caulfield 1993
). Although this pathway also activates
phospholipase C and releases Ca2+ from
intracellular stores, the role of these effects in channel regulation
remains controversial (Marrion 1997
). Nonetheless, there
has been considerable recent progress in identifying the protein
subunits that form the M-channel (Selyanko et al. 1999
; Wang et al. 1998
) and in identifying modulatory effects
of Ca2+on M-channel gating (Marrion
1996
, 1997
; Selyanko and Brown
1996
). Comparatively less is known about the increase in
gleak during muscarinic excitation. In
frog B neurons, the muscarinic gleak appears to be cation selective, voltage-insensitive, and relatively small (<7 nS), and it is thought to exert little influence on excitability (Jones 1985
; Kuba and Koketsu
1974
; Tsuji and Kuba 1988
). Other work suggests
that the muscarinic gleak may be
mediated by cyclic nucleotide-gated cation channels
(gCNG). In N1E-115 neuroblastoma,
muscarinic excitation stimulates intracellular Ca2+ release,
Ca2+-sensitive synthesis of nitric oxide,
accumulation of cyclic GMP, and activation of
gCNG (Mathes and Thompson
1996
; Thompson 1997
; Trivedi and Kramer
1998
). This might explain earlier studies of mammalian
sympathetic neurons, which localized nitric oxide synthase in cell
bodies (Sheng et al. 1993
) and showed an indirect
association between the muscarinic elevation of cyclic GMP,
depolarization, and increased background conductance (Ariano et
al. 1982
; Briggs et al. 1982
; Hashiguchi
et al. 1978
; Kebabian et al. 1975a
,b
; McAfee and Greengard 1972
). Contemporaneous experiments
on frog sympathetic ganglia also demonstrated muscarinic stimulation of cyclic GMP accumulation but failed to detect any electrophysiological consequences (Weight et al. 1974
, 1978
).
In hindsight, it is clear that all of these pioneering studies were
hampered by the technical difficulty of measuring small conductance changes.
Our goal in developing a conductance-based model was to circumvent the
problems introduced by recording damage and explore the consequences of
dual-component muscarinic excitation. How do
gM and
gCNG interact with fast nicotinic
transmission to initiate action potentials? The answer to this question
has broad implications for understanding sympathetic circuit function.
It has recently been discovered that >90% of frog B neurons are
multiply innervated by axons forming one strong connection and one to
four weak connections, respectively dubbed as primary and secondary
nicotinic synapses (Karila and Horn 2000). Although
secondary EPSPs are generally subthreshold in strength, they can
trigger action potentials through summation or by interaction with a
slow peptidergic EPSP. The conductance changes that mediate peptidergic
excitation of frog B neurons appear identical to those controlled by
muscarinic receptors (Jones 1985
; Katayama and
Nishi 1982
; Kuffler and Sejnowski 1983
). These
observations have all been incorporated into a stochastic theory, whose
central prediction is that sympathetic ganglia function as variable
synaptic amplifiers of preganglionic activity (Karila and Horn
2000
). The theory further predicts that slow muscarinic and
peptidergic EPSPs increase synaptic gain by enhancing the strength of
secondary nicotinic synapses and by lengthening the temporal window of
summation between secondary EPSPs. The model that we now describe
explains how changes in gM and
gCNG combine synergistically to
promote synaptic amplification in sympathetic ganglia.
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METHODS |
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The simple monopolar shape of frog sympathetic B neurons makes
them electrotonically compact (Yamada et al. 1989). The
model cell we studied had a single isopotential compartment and
followed the Hodgkin-Huxley formalism. In the master equation
(Eq. 1), the sum of all ionic currents
(Iionic), together with the capacitive current (C = membrane capacitance; V = membrane potential; t = time), is equal to the current
injected through an intracellular electrode
(Iinjected). Under normal
physiological conditions, in the absence of an electrode,
Iinjected = 0. We assumed a specific membrane capacitance of 1 µF/cm2 and set
C to 100 pF, which corresponds to a spherical cell with a
radius of 28.2 µm. This falls within the observed size range of
living B cells taken from adult bullfrogs (4-6 in. body length) (Dodd and Horn 1983a
) and agrees with experimental
measurements of their membrane capacitance (Jones 1987
)
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(1) |
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(2) |
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Leak conductances
The three components of leak conductance included a background
leak (gleak) that helps set the
resting membrane potential, a damage leak
(gelec) introduced by an intracellular
recording electrode, and a cyclic nucleotide-gated leak
(gCNG) controlled by muscarinic
receptors. The magnitude of each conductance and the associated
reversal potentials were varied as required for different simulations.
Because all the leak conductances are voltage insensitive and remain
constant over the time scale of fast EPSPs and action potentials (i.e.,
A = 1), they sum linearly (Eq. 3), and their
net reversal potential (Eleaktotal)
is given by a chord conductance equation (Eq. 4)
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(3) |
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(4) |
M-conductance
The M-current was modeled using the same kinetic scheme
(Eqs. 5-8) that was originally developed to describe
voltage-clamp currents recorded from B neurons (Adams et al.
1982; Yamada et al. 1989
). We generally set
M = 40 nS and
EK =
90 mV, based on whole cell recordings from dissociated B neurons (Jones 1989
).
Exceptions are found in Fig. 4, B and D
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(5) |
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(6) |
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(7) |
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(8) |
Fast nicotinic conductance
The fast nicotinic EPSP was modeled by calculating a synaptic
current (Eq. 9) and scaling it with a kinetic template
(Eq. 10). The template (st)
was created (Fig. 2A) by
inverting a synaptic current recorded at 60 mV (taken from Fig.
6A in Shen and Horn 1995
), scaling the peak
to a dimensionless value of 1, and fitting the resultant waveform with
the sum of two exponentials (t = time in ms).
Esyn was set to 0 mV (Shen and
Horn 1995
), and
syn was varied as a free parameter
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(9) |
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(10) |
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Action potential
To assess the strength of nicotinic synapses, we modeled a
simplified action potential mechanism whose threshold (37 mV) was
physiologically realistic (Jones 1987
; Karila and
Horn 2000
). The action potential was constructed from two
conductances that control a fast Na+ current
(Eq. 11, m activation, h inactivation)
and a delayed-rectifier K+ current (Eq. 12, n activation, p inactivation)
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(11) |
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(12) |
The delayed rectifier (K = 2 µS)
in our model was based on the original experimental analysis in B
neurons (Adams et al. 1982
) and had kinetics similar to
those described by Yamada et al. (1989)
. In B neurons,
the activation of gK is best fit by n squared (Adams et al. 1982
; Block
and Jones 1996
; Klemic et al. 1998
). We followed
the convention of shifting the voltage dependence of
n
by 20 mV (Yamada et al.
1989
) to better align it with the experimental data (see Fig.
16 in Adams et al. 1982
). Although
gK does not inactivate in B neurons
(Adams et al. 1982
; Block and Jones 1996
;
Klemic et al. 1998
), we examined the effect of including
an inactivation process (Fig. 2, C and D) that
was patterned after the node of Ranvier (Yamada et al. 1989
). Inactivation (p) systematically lowered the
maximum iK at all voltages (Fig. 2,
E and F), but its inclusion in the model had
negligible effect on the action potential threshold (0.1 mV) and did
not alter the results.
Numerical integration
The system of ordinary differential equations (ODE) that describes the model was numerically integrated on a 300-MHz Pentium II computer (WinNT4.0) using an implicit fourth-order Runge-Kutta algorithm. The procedure was implemented with phase-plane software (WinPP, written by Dr. G. Bard Ermentrout, ftp://ftp.math.pitt.edu/pub/bardware). The model is available in executable ODE files (http://horndell9goldi.neurobio.pitt.edu). WinPP permits integration with a fixed or variable time step. We compared both methods and found that the variable time step was not appreciably faster, presumably due to the model's simplicity. The standard approach for integrating equations was therefore to choose a constant time step that gave correct solutions and convenient resolution. In simulations to construct current-voltage (I-V) relations (i.e., Figs. 3 and 4), a time step of 0.25 ms was adequate. Brief intervals (50 µs) were used in simulations that contained synaptic potentials and action potentials (i.e., Figs. 5-7).
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Voltage-clamp currents were simulated by setting dV/dt to 0 (Eq. 1), making V the independent variable, and solving for Iionic. I-V relations were generated by controlling V with a step function of variable amplitude. In current-clamp simulations, a software flag was used to trigger the kinetic template (st) for the nicotinic synapse, and Eq. 1 was solved for V. Illustrations were prepared using Igor 3.14 (PC edition, Wavemetrics, Lake Oswego, OR).
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RESULTS |
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Importance of the leak conductance
The first task in constructing the model B neuron was to select
parameters that reproduce experimentally observed resting behavior. In
the voltage range between 40 and
80 mV, the steady-state I-V relation of the frog B neuron is dominated by M-current
and a leak current (Adams et al. 1982
; Jones
1989
). Consequently, gM and
gleak are both critical for
controlling the resting potential (Vrest) and input resistance
(Rin). In practice, these resting properties are difficult to measure accurately because intracellular recording perturbs the leak. We therefore began by examining the interplay between gM,
gleak, and recording damage.
Variation in the data describing B neurons serves to define the
parameter space for the model. It was estimated originally that
M = 84 nS,
gleak = 10 nS, and
Eleak =
10 mV (Adams et al.
1982
). This work employed two-electrode recordings to
voltage-clamp large B neurons (C = 150-400 pF) in
isolated ganglia. Subsequent whole cell patch recordings from smaller
dissociated B neurons (C = 75 pF) yielded lower values
for all three parameters (
M = 27-37
nS, gleak = 3-5 nS,
Eleak =
55 to
75 mV) (Jones
1989
). Using these different data sets, Adams et al.
(1982)
calculated that Vrest =
53 mV, and Rin = 42 M-
, whereas
Jones (1989)
estimated that Vrest
65 to
75 mV, and
Rin
300 M-
. The discrepancies presumably arise from differences in cell size, the larger shunt conductance (gelec) introduced by dual
microelectrodes, and the perturbations caused by tissue culture and
whole cell dialysis. However, after normalizing the conductance data
for cell size by dividing it by C, the most striking
difference is in the leak selectivity
(Eleak).
To analyze the influence of Eleak,
voltage-clamp currents and I-V relations were simulated in a
two-conductance model B neuron (Fig. 3A) of intermediate
size (diameter = 56 µm, C = 100 pF). We set
M = 40 nS, which gives a conductance
density of 0.4 nS/pF and falls within the range of the whole cell data
(0.36-0.49 nS/pF). The leak parameters were initially set as
gleak = 3 nS and
Eleak =
60 mV, consistent with
minimal damage in the best patch recordings. Using these parameters, we
simulated a family of voltage-clamp currents (Fig. 3B) by
following a typical experimental protocol for constructing
I-V relations and measuring
gM. The membrane was held at
30 mV,
where 62% of gM is activated
(Eq. 8), and was stepped systematically to hyperpolarized
potentials. Each response begins with an instantaneous current
(Iinst) whose magnitude reflects the
membrane conductance at the holding potential and the amplitude of the
voltage step. Iinst is followed by a
slowly relaxing current caused by deactivation of
gM.
IM relaxes more rapidly at
hyperpolarized potentials and reverses polarity at
90 mV, which is
EK (Fig. 3B). The
steady-state current (Iss) at the end
of the test pulse reflects the new conductance. On repolarization the
instantaneous current is reduced, thereby showing that total membrane
conductance decreases during the hyperpolarizing test pulse. Plotting
Iinst and
Iss as functions of V
completes the task of reproducing the classical experimental findings
(compare Fig. 3C with Fig. 5 in Adams et al.
1982
; and Fig. 1 in Jones 1989
). Graphic
analysis of the simulated I-V data provided a check for
internal consistency of the model by testing its ability to recover
starting parameters (Fig. 3C). At potentials negative to
80 mV, where gM is completely
deactivated, the linear slope (3 nS) of the steady-state I-V
relation reflects gleak, and
extrapolation correctly reveals its ionic selectivity
(xintercept = Eleak). The K+
selectivity of gM is recovered from
the intersection between Iinst and
Iss at
90 mV. Activation of
gM (Eq. 8) introduces
curvature into the steady-state I-V relation at potentials
positive to
80 mV.
We could now dissociate the influence of leak selectivity from that of
leak magnitude. Holding gleak
constant, Eleak was changed from 60
to
10 mV to reproduce the disparity between the microelectrode and
patch recording data. The 50-mV shift in
Eleak had no effect on the form of
clamp currents evoked by voltage jumps (Fig. 3B) but offset
their baselines by 150 pA. The offset was evident as a parallel inward
shift in the steady-state and instantaneous I-V relations
(Fig. 3C). The inward current depolarized
Vrest from
69 to
57 mV and reduced
Rin from 145 to 51 M-
. The
magnitude of the current shift is a simple consequence of Ohm's law
(
ileak = gleak ×
Eleak = 3 nS × {
50
mV} =
150 pA). The drop in
Rin arises from the increased slope of
the I-V relation at its new point of intersection with the
zero current axis (Fig. 3C).
The general nonlinear dependence of
Vrest on leak conductance and
selectivity was mapped by systematically varying each parameter (Figs.
3D and 4). Vrest, defined
as the point where Iionic = 0, usually
lies in the curved region of the steady-state I-V relation, at the balance point between voltage-insensitive inward leak current and voltage-sensitive outward M-current. The only exception occurs when
Eleak is more negative than the
activation range for gM. When
Eleak
80 mV, then
gM
0 and
Vrest converges at
Eleak, regardless of
gleak's magnitude (Fig.
3D). Otherwise, Vrest
diverges as a nonlinear function of
Eleak and
gleak (Fig. 3D). This
raises a basic question. Given that leak current varies linearly with gleak and
Eleak, how can changing the leak
parameters produce nonlinear shifts in
Vrest? Because the model has only two
conductances, the explanation must lie in the voltage dependence of
gM.
Activation of M-current introduces curvature into the steady-state I-V relation, and this curvature accounts for all nonlinearity in the control of Vrest. We have already shown how a selective change in Eleak produces a purely parallel shift of the I-V relation and alters its intersection with the zero-current axis (Fig. 3C). In this manner, the inherent curvature of the I-V relation dictates the nonlinearity between Eleak and Vrest. The effect of selectively changing gleak is more complicated. Altering gleak causes the slope of the leak current to rotate around Eleak, and the entire steady-state I-V relation changes shape as it rotates around Eleak (Fig. 4A). Increases in gleak thus act to linearize the I-V relation.
Plotting Vrest as a logarithmic
function of gleak (Fig. 4B)
revealed a sigmoidal relation with asymptotes at
EK and
Eleak. Varying
M (10, 40, and 80 nS) over its
experimentally observed range (Adams et al. 1982
;
Jones 1989
) produces a parallel shift in
Vrest without altering its logarithmic
dependence on gleak in the
experimentally relevant range. Figure 4A illustrates the point by showing that successive threefold increments in
gleak from 1 to 27 nS each depolarize
Vrest by 6 mV. In other simulations,
M was set to 40 nS, and we
varied the equilibrium potential for each current. This demonstrated
that Eleak controls the right asymptote of the sigmoidal relation (Fig. 4C) and that
EK controls the left asymptote (Fig.
4D). Although the two-conductance model becomes relatively
simple in the steady-state, it does not have an easy analytic solution
that can give the results obtained by numerical integration. We could,
however, describe most of the numerical data by using a relatively
simple empiric expression (Eq. 13). The midpoint along the
y-axis was defined as V50,
the average of EK and
Eleak (Eq. 14). When
Vrest = V50 in the two-conductance model, it
can be shown using Eqs. 1 and 14 that
gleak = gM. This conductance, defined as
gL50, can be calculated from Eq. 15, in which
V50 (Eq. 8) is the steady-state activation of
gM at
V50. In Eq. 13,
b is an arbitrary slope factor whose value was fit as a free
parameter. The value of b changes with
Eleak and
EK (Fig. 4, C and
D)
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(13) |
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(14) |
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(15) |
Form of pleiotropic muscarinic currents
Three forms of muscarinic excitation have been identified in
frog B neurons and most clearly resolved in experiments by Tsuji and Kuba (1988). In one group of neurons, a dual-component
muscarinic response is mediated by pleiotropic suppression of
M (<50%) and activation of a
cation conductance (<7 nS). In the other groups, only one component is
found. It remains unclear whether this diversity reflects functional
specialization in three types of B neurons or variations in recording
damage. Before examining the consequences of pleiotropy, we needed to
first reproduce the three forms of muscarinic currents (Fig. 5) in a
model containing gleak,
gM, and
gCNG.
Muscarinic depolarization of B neurons is slow, with an onset that
takes seconds and a duration that can last minutes. For simplicity, we
ignored the synaptic kinetics of slow muscarinic currents and simulated
M and
gCNG at different constant levels. Figure 5 compares the membrane currents produced by 50% suppression of
M, by activation of 4 nS
gCNG
(ECNG = 0 mV), and by the combination of both. Figure 5A illustrates simulated clamp currents
evoked by voltage jumps from
30 to
60 mV and from
60 to
90 mV.
Responses in the more depolarized voltage range contain large
M-currents, whereas those in the hyperpolarized range are dominated by
leak current. Full steady-state I-V relations (Fig.
5B) were constructed by computing families of voltage jumps
from a holding potential of
30 mV. Muscarinic synaptic currents were
then obtained by subtracting the excited from control I-V
relations (Fig. 5C) (for comparison with experimental data,
see Fig. 1 in Tsuji and Kuba 1988
).
Modulation of the nicotinic synapse and the emergence of synergy
Having captured the steady-state features of muscarinic
pleiotropy, the model was expanded to include a fast nicotinic EPSP with a realistic time course and an action potential with a realistic threshold (Figs. 1B and 2). The nicotinic synaptic
conductance (gsyn) was then scaled
until the resulting fast EPSP just barely crossed threshold and
triggered an action potential. This was defined as the threshold
synaptic conductance (Fig. 6A). Changes in
threshold-gsyn were then measured to
determine how different forms of muscarinic excitation altered the
strength of nicotinic synapses. This revealed the potent excitatory
effect of activating gCNG. To cite a
specific example in terms of the reduction in threshold-gsyn, a 4.65-nS increase in
gCNG was equivalent to suppressing M by 20 nS (Fig. 6A).
More importantly, the combined effect of both conductance changes was
greater than the sum of the individual effects. In other words,
pleiotropic muscarinic excitation yields functional synergy when
evaluated in terms of the consequences for fast synaptic transmission.
Is the synergy between suppression of
gM and activation of
gCNG a general property of
metabotropic excitation? To answer this question we systematically
varied gCNG (0-4 nS) and
M (100 to 50%) over their
physiological ranges (Adams and Brown 1982
; Kuba and Koketsu 1974
; Tsuji and Kuba 1988
). Figure
6B shows how threshold-gsyn decreased as
M was suppressed at
three different levels of gCNG. When
gCNG was increased, so did the
curvature of the relation. The simple graphic representation in Fig.
6B reveals that the combined effect of both conductance
changes is always greater than the sum of the individual conductance
changes, regardless of the initial and final conditions. When plotted
in three dimensions (not shown),
threshold-gsyn formed a smooth surface
whose maximum (10.06 nS) was in the resting cell (0 nS
gCNG, 100%
M) and whose minimum (4.19 nS) was
during full excitation (4 nS gCNG,
50%
M). These data show the
muscarinic decrease in threshold-gsyn
and can effectively double the strength of nicotinic synapses. Using threshold-gsyn to calculate a synergy
surface revealed a relation that resembled an upturned taco chip (Fig.
6C). The chip shows that maximal synergy (i.e., 37%) occurs
when the muscarinic changes in both conductances are maximal.
The enhanced efficacy of the nicotinic synapse during muscarinic
excitation was not simply a consequence of membrane depolarization. The
decreases in threshold-gsyn produced
by injecting current to mimic muscarinic depolarization were always
smaller than those caused by M
suppression and larger than those caused by activation of
gCNG. The effect has complex dynamics,
but it can be explained qualitatively in terms of the steady-state
I-V relation. In essence, all three types of depolarization
produce different effects on Rin,
which in turn influences the ability of a fast nicotinic current to
drive the membrane potential to threshold. Depolarizing current
injection produces a parallel shift in the I-V relation, like that produced by shifting Eleak
(Fig. 3C). The consequence is a decrease in
Rin, but not in the ultimate path to
threshold. Equivalent depolarization can be produced by suppressing
M (Fig. 5B), but in this
case the overall slope conductance goes down. At the depolarized
potential, Rin is less than it had
been originally, but higher than in the cell depolarized by current
injection. More importantly, reducing
M increases membrane resistance
along the entire voltage trajectory to threshold. The consequence is to
enhance the efficacy or strength of fast synaptic currents. By
contrast, increasing gCNG produces a
rotational effect, which increases the slope conductance at every point
along the I-V relation (Fig. 4A) and thus makes
the nicotinic current less effective than in the case of current
injection. However, for small changes in the leak, the change in
Rin is small, and the effect is not much different from that produced by current injection.
The synergy that emerges from muscarinic pleiotropy is a robust
phenomenon that does not depend critically on the absolute magnitude of
Na or
K. The balance between these
conductances and the stimulus strength determines whether the model is
inexcitable, fires once, fires repetitively and then accommodates, or
fires repetitively without accommodation. Under our standard action potential parameters (Fig. 1A), the model was excitable and
fired repetitively in response to strong muscarinic depolarization, but
it always accommodated and became quiescent after a few action potentials. This reproduces the essential behavior of real B neurons. Over a range of conditions that give this pattern of excitability (
Na = 600-4,200 nS and
K = 1,500-3,500 nS), muscarinic
pleiotropy always yielded synergy. One might imagine that muscarinic
depolarization would increase inactivation of the delayed rectifier
(p) or the sodium conductance (h) and thereby
alter synergy. However, such effects turn out to be relatively minor.
When p was removed from the model (Fig. 2, C and
E), maximal synergy was 36%, a decrease of only 1%. The
contribution of h was slightly larger and more complex.
During the depolarization caused by maximal muscarinic excitation
(e.g., Fig. 6), h decreased from 0.99 to 0.88. Simply eliminating h from the model made it unstable. Realistic
excitability could be restored by decreasing
Na or increasing
K. Raising
K to 3,500 nS, while holding
Na = 800 nS and keeping h
and p intact, had little effect on the resting value of
threshold-gsyn, which increased by
<1%. Under these conditions maximal synergy was 33%, and when
h was eliminated from the model, it increased to 39%.
Taking the alternative tack of reducing
Na while holding
K constant confirmed that sodium
channel inactivation has only a small influence on the magnitude of
muscarinic synergy.
We next examined the consequences of regulating other leak
conductances. In particular we evaluated the effects of increasing a
chloride leak (gCl) and decreasing a
potassium leak (gLK). Both types of
conductance changes have been observed during metabotropic stimulation
of mammalian neurons (Bertrand and Galligan 1994; Cassell and McLachlan 1987
; Caulfield
1993
; Marsh et al. 1995
). Activating a 4-nS
gCl (with
ECl =
40 mV) decreased
threshold-gsyn by 20.1% and yielded
37.6% synergy when combined with 50% suppression of
M. Removing 1 nS of
gLK from the standard resting leak (3 nS, Eleak =
90 mV) decreased
threshold-gsyn by 12.2% and yielded 7.9% synergy when combined with 50% suppression of
M.
Muscarinic modulation of temporal interaction between nicotinic EPSPs
In addition to modulating the strength of nicotinic synapses,
muscarinic excitation may influence the temporal summation of subthreshold nicotinic EPSPs. We examined this possibility by simulating the interaction between pairs of nicotinic EPSPs. For the
simulation in Fig. 7, nicotinic gsyn
was set to 55% threshold-gsyn. In the
resting cell, the second nicotinic EPSP in a pair generated an action
potential when the temporal window of summation
(tsum) was 6 ms. Combining 25%
suppression of
M (40
30 nS) with activation of 3 nS gCNG more than
doubled tsum (
13 ms). Selective changes in
M or
gCNG each enhanced
tsum on their own, but once again the
pleiotropic effect was greater than the sum of its parts (Fig. 7).
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DISCUSSION |
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We have studied a minimal model of the frog B neuron after constraining it with experimental data. Only two conductances, gleak and gM, were needed to reproduce the resting behavior of the B neuron and explain its perturbation by recording damage and by pleiotropic muscarinic excitation. The central goal of the work was to determine how dual-component muscarinic excitation interacts with fast synaptic transmission to initiate postsynaptic firing. The results show that a small increase in cation conductance exerts potent excitatory effects, which can be obscured by modest recording damage. More importantly, muscarinic activation of the cation conductance combines synergistically with suppression of the M-conductance to strengthen nicotinic synapses and enhance temporal integration. The nonlinear effects unmasked by metabotropic regulation of leak currents are directly attributable to the voltage dependence of M-current. These results are discussed in terms of their implications for sympathetic function, their limitations, and their applicability to other cells and circuits. We begin by considering the rationale for taking a bottom-up approach.
Why study a minimal model?
Our model (Fig. 1B) is a cyber-knockout. We have
deleted the Na+ pump and seven conductances
mediated by L-type Ca2+ channels, N-type
Ca2+ channels, A-type K+
channels, mini and maxi Ca2+-activated
K+ channels, Q/H-type cation channels, and at
least one type of voltage-dependent Na+ channel.
These mechanisms are all known to be present in frog B neurons, and
indeed many were incorporated in an earlier computational model
described by Yamada et al. (1989). The
strophanthidin-sensitive pump current in B cells is 20 pA (Jones
1989
). It hyperpolarizes Vrest
in our model by 2 mV without producing significant consequences. The
rationale for not including additional conductances was to keep the
model simple and to avoid the unnecessary introduction of ad hoc
assumptions. By doing so, it was possible to constrain all the
parameters for resting and synaptic conductances with experimental data
and to create an action potential that had realistic threshold
behavior. Adding the other conductances would become important if one
needed to consider repetitive firing. However, reproducing this
behavior was not required to answer the first-order questions about
muscarinic pleiotropy.
Two new principles emerged from the analysis. First,
Vrest depends logarithmically on
gleak (Fig. 4). This helps to explain why estimates of Vrest in sympathetic
neurons tend to be clustered in a fairly narrow range (i.e., 50 to
60 mV, Fig. 3D), irrespective of recording damage
(Adams and Harper 1995
; Karila and Horn
2000
). Second, metabotropic changes in
ileak and
iM combine synergistically to modulate
fast excitatory transmission (Figs. 6 and 7). The synergistic effects
are not limited to cation leaks, but can also arise from an increased
chloride leak or a decreased K+ leak.
Can the model apply elsewhere?
We have hypothesized that the regulated leak conductance in frog B
neurons is a cyclic GMP-gated cation channel (Fig. 1A). Adding a molecular dimension to the model was not essential from the
computational point of view. Instead, it serves to create a fingerprint
for identifying homologous mechanisms in other cells. In hippocampal
CA1 pyramidal neurons, for example, m1 muscarinic receptors and
metabotropic gluR5 glutamate receptors are coupled to the
Gq/11 signaling pathway and may each regulate
gM and
gCNG (Conn and Pin
1997; Kingston et al. 1996
; Marino et al.
1998
). Do these conductances also interact synergistically in
the hippocampus to strengthen fast glutamatergic transmission?
Obviously one cannot say. Hippocampal neurons have a complex
electrotonic structure, and their firing properties are more
complicated than in our model. Nonetheless, it would be interesting to
know whether the model contains a kernel that is preserved in other guises.
Implications for sympathetic circuit function
Although the pleiotropic nature of slow muscarinic and peptidergic
EPSPs in sympathetic neurons has been appreciated for some time, the
functional significance of these mechanisms for ganglionic integration
remains largely unknown (Akasu et al. 1984; Jones 1985
; Katayama and Nishi 1982
; Kuba and
Koketsu 1974
; Kuffler and Sejnowski 1983
;
Tsuji and Kuba 1988
). Ever since the discovery of
M-current, most attention in the field has been focused on the ability
of slow EPSPs to enhance repetitive firing by reducing accommodation.
As it turns out, this effect depends on another conductance change that
acts in concert with
M suppression, and it is not limited to sympathetic neurons. Muscarinic agonists stimulate repetitive firing in sympathetic neurons and cortical pyramidal cells by inhibiting M-current and the afterhyperpolarization (AHP) current (Adams et al. 1986
; Caulfield
1993
; Cole and Nicoll 1983
; Goh and
Pennefather 1987
; McCormick and Prince 1986
;
Nicoll et al. 1990
). In frog B neurons, the action
potential has a long hyperpolarizing afterpotential that is controlled
by low-conductance Ca2+-activated
K+ channels
(gAHP). The
gAHP does not contribute to
Vrest or the slow EPSP, but it is
inhibited by muscarinic agonists and luteinizing hormone releasing
hormone (LHRH) (Adams et al. 1986
).
In what appears to be another case of synergy, the metabotropic changes in iM and iAHP
combine to regulate the accommodation of repetitive firing during
sustained depolarization (Goh and Pennefather 1987
).
The potent influence of muscarine and LHRH on accommodation led
to an earlier proposal that slow synaptic regulation of repetitive firing molds ganglionic amplification of activity (Horn
1992). However, experiments to test this hypothesis in the
secretomotor B system and the vasomotor C system have shown that
synaptic regulation of repetitive firing is unlikely to occur under
physiological conditions (Jobling and Horn 1996
;
Thorne and Horn 1997
). This conclusion is buttressed by
in vivo recordings, which show that frog B and C neurons fire in
irregular patterns at low average frequencies (Ivanoff and Smith
1995
).
Recently, a new theory of ganglionic integration has been
developed from the analysis of subthreshold fast nicotinic EPSPs in
frog B neurons and the irregular nature of preganglionic activity patterns in vivo (Karila and Horn 2000). Until these
experiments, it had been widely believed that B neurons receive their
nicotinic innervation through a single primary synapse. This created a
paradox because primary synapses are very strong and generate fast
EPSPs that inevitably drive B cells to fire action potentials. How then could muscarinic modulation influence nicotinic transmission? The
recent experiments make clear that virtually all B neurons receive a
small number of secondary nicotinic synapses that drive subthreshold
fast synaptic activity (Karila and Horn 2000
). Secondary fast EPSPs can reach threshold through temporal summation and interaction with slow EPSPs. However, it remains difficult to assess
experimentally the strength of secondary synapses and to resolve how
they are amplified by individual components of a slow EPSP. The
conductance-based model enabled us to simulate these interactions in
detail while setting aside the presynaptic facilitation and inhibition
that further complicate experimental analysis (Karila and Horn
2000
; Shen and Horn 1995
, 1996
).
The model predicts that postsynaptic muscarinic excitation can more
than double the strength of nicotinic synapses by reducing
threshold-gsyn from 10.06 to 4.19 nS (Fig.
6B). This is encouraging because one would expect secondary nicotinic conductances to fall within this range based on the
independent experimental analysis of synaptic currents and quantal
content (Karila and Horn 2000
; Shen and Horn
1995
). More importantly, the present results suggest that
realistic levels of muscarinic excitation are sufficient to boost
subthreshold secondary nicotinic EPSPs above threshold (Fig. 6) and to
enhance the temporal window for suprathreshold summation
(tsum; Fig. 7). In the context of a
stochastic model of ganglionic integration (Karila and Horn
2000
), these findings indicate that muscarinic excitation will
enhance the activity-dependent synaptic amplification of preganglionic
activity by sympathetic neurons. The synergy arising from muscarinic
pleiotropy may function to make synaptic amplification more efficient.
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ACKNOWLEDGMENTS |
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We are especially grateful to B. Gutkin for helping initiate this work, and we thank G. B. Ermentrout, E. Frank, and E. Aizenman for reading the manuscript.
This work was supported by National Institute of Neurological Disorders and Stroke Grant NS-21065 and by Schrödinger Postdoctoral Fellowship J1519-BIO from the Austrian Science Fund to H. Schobesberger.
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FOOTNOTES |
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Address for reprint requests: J. P. Horn, Dept. of Neurobiology, University of Pittsburgh School of Medicine, E1440 Biomedical Science Tower, Pittsburgh, PA 15261.
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.
Received 4 May 1999; accepted in final form 9 December 1999.
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REFERENCES |
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