Models of Autoinhibition of Neurotransmitter Release

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Models of Autoinhibition of Neurotransmitter
Release

• Richard Bertram
• Dept. of Mathematics
• and
• Kasha Institute of Biophysics
• Florida State University

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Collaborators and Funding
Gerald Zamponi
Jessie Swanson
Mohammad Yousef
Michelle Arnot
Zhong-Ping Feng
Dept. of Mathematics
Florida State University
Dept. of Physiology and Biophysics
University of Calgary
R. Bertram is supported by NSF grant DMS 0311856
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Synaptic Transmission
Electron micrograph, X 60,000, K. Harriman
Basic mechanism
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Sources of Presynaptic Plasticity
Following a single impulse or an impulse train,
the postsynaptic response to an impulse can be
depressed or facilitated.

• Depression Due to depletion of readily
  releasable pool of vesicles.
• Enhancement Can be due to the buildup of Ca2 in
  the synaptic terminal, or saturation of buffer,
  or something else.
• G-proteins Activation of these can attenuate or
  enhance the synaptic signal. Target is typically
  Ca2 or K channels.

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Objective
Use experimental data from human embryonic kidney
(HEK) cells transfected with Ca2 channels and
G-protein subunits to calibrate the mathematical
model. Use the mathematical model to predict
the effects of G-protein action on
neurotransmitter release.
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Regulation by G-Proteins

• Many chemical messengers can act as ligands for
• G-protein-coupled receptors. These include
• GABA
• Adenosine
• Glutamate
• Dopamine
• Serotonin

Binding of glutamate to metabotropic receptors in
the synaptic terminal leads to activation of G
proteins and, quite often, the inhibition of Ca2
channels. Observed in the hippocampus,
cerebellum, neocortex, striatum, and the brain
stem.
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G-Protein Inhibition of Ca2 Channels
outside
inside
Binding of G?? puts a Ca2 channel into a
reluctant state, with a reduced open probability.
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G-Protein-Mediated Autoinhibition
Transmitter molecules released by a synapse may
bind to G protein-coupled receptors on the
synapse itself, inhibiting Ca2 channels and
reducing future transmitter release.
EPSCs from dopamine synapses in the striatum. S1
is a train of 3 impulses at 100 Hz. S2 is
a single impulse 200 ms later.
Depression in wild-type (closed) vs. D2-R
knockouts (open).
Benoit-Marand et al. (2001)
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Relief from Inhibition
In many cases, G protein channel inhibition can
be relieved by depolarization.
Data from HEK cells transfected with N-type Ca2
channels and G?? dimers. From Bertram et al.
(2002).
Without prepulse, the total current is smaller
and the channel kinetics are slower. This latter
feature is called kinetic slowing.
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Differential Properties of G?? Isoforms
There are 55 known G?? dimeric isoforms.
Different isoforms produce different degrees
of inhibition and kinetic slowing.
Data from HEK cells transfected with N- or P-type
Ca2 channels and G?? dimers. Arnot et al, J.
Physiol. 527203, 2000.
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Kinetics also Depend on Ca2Channel ? Subunit

• Ca2 channel ? subunit forms the channel pore.
  The
• subunit is a cytosolic domain that has recently
  been
• shown to influence G-protein channel inhibition.

Transfected HEK cells with N-type channel ?
subunit, various ? subunits, and G?3?2 dimers.
From Feng et al, J. Biol. Chem. 27645051, 2001.
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A Model for G-Protein Inhibition
The Bertram and Behan model (1999) focuses on the
binding of activated G-proteins to Ca2 channels,
and is based on a model by Boland and Bean
(1993). When bound, the channel enters a
reluctant state. G-proteins unbind, and
the channel returns to a willing state, when the
membrane is depolarized.
(willing)
(reluctant)
where
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G-Protein Inhibition Model

• 7 ODEs needed for the 8 Ca2 channel states.
• 2 ODEs needed for presynaptic membrane
  potential.
• 1-4 ODEs needed for Ca2 binding to release
  sites.
• 3 ODEs needed for postsynaptic response.

Total 13 or more ODEs
A simpler phenomenological model for Ca2
channel inhibition and postsynaptic
effects captures the dynamics of G-proteins.
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Minimal Channel Model
Ca2 Channel Model
WProbwilling state RProbreluctant state

Fraction of bound G-protein receptors
is an increasing function of Vpre
By law of mass action, noting that WR1
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Minimal Postsynaptic Model
The effects of presynaptic G-proteins are build
into the postsynaptic response
,
s fraction of bound postsynaptic receptors
The postsynaptic response
is an increasing function
of Vpre and is right-shifted by G-protein
inhibition.
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Experiments Used for G-Protein Unbinding Constant
(k-)
G?1?2
G?2?2
In two-state model, ?act reflects time required
for a channel to move from a reluctant to a
willing state. ?act obtained from data (Feng, et
al., 2001). This is used to set the G
protein unbinding rate, k-.
The unbinding rate can be calculated for
different G?? dimers and different Cav? subunits.
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Hormonal Regulation
Concentration of bound G-protein receptors is
independent of presynaptic or postsynaptic
activity.
Hormonal regulation, via adenosine or serotonin,
for example.
Many experiments performed by examining effects
of bath application of G-protein agonist.
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Synaptic Facilitation ThroughRelief of G-Protein
Inhibition
Simulation with G?3-?1 combination.
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Autoinhibition of Transmitter
For example, glutamate feedback onto
presynaptic metabotropic receptors.
?a500 msec
Fraction of bound autoreceptors, a,
determines G-protein binding rate, k.
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Synaptic Depression Through Autoinhibition
Simulation with G?3-?1 combination, 10 Hz
stimulus frequency.
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Filter Thresholds Vary forDifferent Isoform
Combinations
The threshold frequency, the frequency above
which presynaptic impulse trains are transmitted
in their entirety, depends on the G-protein
unbinding rate ?-.
Model results
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Autoinhibition Filters OutLow-Frequency Noise
Consider a 5x5 grid of presynaptic cells subject
to autoinhibition projecting to a 5x5 grid of
postsynaptic cells. High-frequency trains (black)
are signal, low-frequency trains (colored) are
noise.
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Retrograde G-Protein Activation
Release of substances from the postsynaptic cell
can act in a retrograde fashion on presynaptic
G-protein-coupled receptors. Examples
endocannabinoids (Brown et al, 2003) and
oxytocin (Hirasawa et al, 2001).
Fraction of bound autoreceptors, a, now
depends on electrical activity of the
postsynaptic cell rather than the presynaptic
cell.
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Summary

• G-protein inhibition of N- and P-type Ca2
  channels is ubiquitous.
• Kinetic slowing and relief from inhibition vary
  depending on activated G-protein G?? isoform and
  Ca2 channel ? subunit.
• Depending on circumstances, G-proteins can
  mediate synaptic facilitation or depression.
• G-protein mediated autoinhibition can remove
  low-frequency noise, transmitting only the
  high-frequency signal. Acts as a high-pass
  filter.
• Presynaptic G-proteins can be activated by
  hormones, through autoreceptors, or through
• a retrograde action of the postsynaptic cell.

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References

• Arnot, M. I., S. C. Stotz, S. E. Jarvis, G. W.
  Zamponi, Differential modulation
• of N-type ?1B and P/Q-type ?1A calcium
  channels by different G protein
• ? subunit isoforms, J. Physiol.
  527203-212, 2000.
• Benoit-Marand, M., E. Borrelli, G. Gonon,
  Inhibition of dopamine release
• via presynaptic D2 receptors Time course
  and functional characteristics
• in vivo, J. Neurosci. 219134-9141, 2001.
• Bertram, R., M. I. Arnot, G. W. Zamponi, Role for
  G protein G?? isoform
• specificity in synaptic signal processing
  A computational study, J. Neurophysiol.
  872612-2623, 2002.
• Bertram, R., J. Swanson, M. Yousef, Z.-P. Feng,
  G. W. Zamponi, A minimal
• model for G protein-mediated synaptic
  facilitation and depression,
• J. Neurophysiol. 901643-1653, 2003.
• Boland, L. M. and B. P. Bean, Modulation of
  N-type calcium channels in
• bullfrog sympathetic neurons by luteinizing
  hormone-releasing hormone
• kinetics and voltage dependence, J.
  Neurosci. 13516-533, 1993.

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References

• Brown, S. P., S. D. Brenowitz, W. G. Regehr,
  Brief presynaptic bursts evoke synapse-specific
  retrograde inhibition mediated by endogenous
  cannabinoids, Nature Neurosci. 61048-1057, 2003.
• Feng, Z.-P., M. I. Arnot, C. J. Doering, G. W.
  Zamponi, Calcium channel
• ? subunits differentially regulate the
  inhibition of N-type channels by individual G?
  isoforms, J. Biol. Chem. 27645051-45058, 2001.
• Hirasawa, M., S. B. Kombian, Q. J. Pittman,
  Oxytocin retrogradely inhibits evoked, but not
  miniature, EPSCs in the rat supraoptic nucleus
  role of N- and P/Q-type calcium channels, J.
  Physiol. 532595-607, 2001.