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<html><pre>
This is the readme for the models for the paper:
Prescott SA, Ratte S, De Koninck Y, Sejnowski TJ. Pyramidal neurons
switch from integrators in vitro to resonators under in vivo-like
conditions. J. Neurophysiol. In press.
Abstract: During wakefulness, pyramidal neurons in the intact brain
are bombarded by synaptic input that causes tonic depolarization,
increased membrane conductance (i.e. shunting), and noisy fluctuations
in membrane potential; by comparison, pyramidal neurons in acute
slices typically experience little background input. Such differences
in operating conditions can compromise extrapolation of in vitro data
to explain neuronal operation in vivo. For instance, pyramidal neurons
have been identified as integrators (i.e. class 1 neurons according to
Hodgkin's classification of intrinsic excitability) based on in vitro
experiments, but that classification is inconsistent with the ability
of hippocampal pyramidal neurons to oscillate/resonate at theta
frequency since intrinsic oscillatory behavior is limited to class 2
neurons. Using long depolarizing stimuli and dynamic clamp to
reproduce in vivo-like conditions in slice experiments, we show that
CA1 hippocampal pyramidal cells switch from integrators to resonators,
i.e. from class 1 to class 2 excitability. The switch is explained by
increased outward current contributed by the M-type potassium current
I(M), which shifts the balance of inward and outward currents active
at perithreshold potentials and thereby converts the spike initiating
mechanism as predicted by dynamical analysis of our computational
model. Perithreshold activation of I(M) is enhanced by the
depolarizing shift in spike threshold caused by shunting and/or sodium
channel inactivation secondary to tonic depolarization. Our
conclusions were validated by multiple comparisons between simulation
and experimental data. Thus, even so-called "intrinsic" properties may
differ qualitatively between in vitro and in vivo conditions.
Model Notes:
The Morris-Lecar-type model included here shows how spike initiating
dynamics can be influenced by external factors like the level of
background synaptic input. High levels of synaptic input cause
shunting (i.e. increased membrane conductance) and tonic
depolarization which can cause activation/inactivation of
voltage-sensitive currents. In this study, we show that shunting
and/or tonic depolarization can convert a neuron exhibiting class 1
excitability (spike initiation through a saddle-node on invariant
circle bifurcation) to class 2 excitability (spike initiation through
a subcritical Hopf bifurcation). One importance consequence is that
class 2 neurons can oscillate/resonate whereas class 1 neurons cannot.
In the first model, ML(noNainactivation).ode, there is no sodium
channel inactivation. Try varying gshunt and/or gM to add/remove
shunting and adaptation from the model. Be sure to include
small-amplitude noise (sigma>0) in order to see noise-induced
oscillations.
In the second model, ML(withNainactivation).ode, sodium channel
inactivation is included. Strength of inactivation is controlled by
alpha_h; set alpha_h to 1 to turn off this mechanism. In this model,
other parameters have been adjusted to correspond to those described
in Figure 9B of the paper.
The main idea is that shunting and/or tonic depolarization (causing
inactivation of sodium channels or activation of M channels) will lead
to depolarizing shift in voltage threshold. Shifting threshold
influences how strongly certain currents will activate at voltages
just below threshold. Increased subthreshold activation of the
delayed-rectifier potassium current can lead to high-frequency
oscillations. Increased subtheshold activation of the M-type
potassium current can lead to theta-frequency oscillations. An
important conclusion of this study is that although M-type potassium
current is present in CA1 pyramidal neurons, that current may not be
strongly activated at subthrehsold potentials under in vitro
conditions whereas it would more strongly activated under in vivo
conditions because of the shift in threshold caused by background
synaptic input. The resulting shift in balance of inward and outward
currents near threshold can qualitatively change the spike initiating
mechanism, with important consequences for the integrative properties
of the neuron.
The code contains numerous comments that help explain the model. For
more information about XPP, visit
<a href="http://www.scholarpedia.org/article/XPPAUT">http://www.scholarpedia.org/article/XPPAUT</a> or
<a href="http://www.math.pitt.edu/~bard/xpp/xpp.html">http://www.math.pitt.edu/~bard/xpp/xpp.html</a>.