Bursting Pacemaker Neurons

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Bursting Pacemaker Neurons
Based on Models of Respiratory Rhythm Generation
in the Pre-Botzinger Complex. I. Bursting
Pacemaker Neurons Robert.J. Butera, John Rinzel,
Jeffery C. Smith
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IntroductionPre-Bötzinger complex

• Pre-Bötzinger complex is the hypothesized site
  for
• respiratory rhythm generation
• It is housed in the rostral ventrolateral medulla

Part B, Photo labeling the ventrolateral medulla
(pre-Bötzinger complex area approximated by
dashed line).
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Pacemaker Neurons

• Pre-Bötzinger complex houses the pacemaker
  neurons
• It is hypothesized that contribution of both a
  pacemaker-based kernel and a pattern-formatting
  network driven by the kernel is responsible for
  the respiratory rhythm generation (Hybrid model).
• Some pacemaker neurons receive tonic excitatory
  inputs (from the mundane neurons) necessary to
  bring the membrane potential into the voltage
  window where bursting occurs.
• These neurons are classified as conditional
  bursting pacemakers.

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Background of the Research Paper

• In earlier models respiratory rhythm generation
  was postulated to arise from network
  interactions, specifically inhibitory
  connections. But in such models the rythmicity
  ceased when synaptic inhibition was blocked.
• In the hybrid model, for which this paper is a
  segway, inhibitory interactions are not
  essential, mimics the actual in vitro and en bloc
  experiment results.
• The objective of this paper is modeling the
  rhythm and inspiratory burst generation in the
  kernel operating in vitro.

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Model Development

• Two models have been proposed for neurons
  responsible for
• rhythm and inspiratory burst generation in vitro.

• Model 1
• Based on one-compartment Hodgkin-Huxley model.
• Bursting occurs by virtue of fast activation
  and slow activation of a persistent Sodium
  current INa-P

• Model 2
• Based on model 1.
• Bursting occurs by virtue of fast-activating
  persistent Sodium current INa-P (inactivation
  term h removed) and slow activation of
  Potassium current IKs

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Model 1
It is composed of five ionic currents across the
plasma membrane a fast sodium current, INa a
delayed rectifier potassium current, IK a
persistent sodium current, INaP a passive
leakage current, ILand a tonic current, Itonic_e
(although this last current is considered to be
inactive in these models)
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Model 1 - Formulation
Where, x8? mP,m,h,n and x ? h,n
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Model 2
The second model is identical to the model 1
except with the addition of a slow K current,
IKS. (The removal of the inactivation term "h"
from INaP is not visible in the model diagram.)
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Model 2 - Formulation
Where, x8? mP,m,k,n and x ? k,n
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How does model 1 work?
Dynamic response of model 1 as a function of EL
membrane potential
EL-60 mV
A closer look
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Nullclines - m83 , n84, h8
(in) activation
V (mV)
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EL-57.5 mV
EL-54 mV
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Results from research article.
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Bursting to tonic spiking
EL-57.5 mV
EL-54 mV
EL-60 mV
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Model 1- Animation

• The two kinds of currents in this model are
• Spike generating currents - INa IK
• Sub threshold currents (INaP IL called Isub).
• The bursting cycle can be understood like this
• When gNaP increases beyond a critical value, Isub
  is large enough to initiate a burst.
• The firing of action potentials gradually
  inactivates h (slow variable)
• The bursting terminates when INaP is inactivated
  sufficiently and the cell hyperpolarizes.
• Now h gradually de-inactivates increasing Isub,
  to trigger another burst and so on

Isub vs Time
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Bifurcation Mechanism
EL-65 mV Silent
EL-58 mV Bursting
EL-55 mV Beating
SN bif. - saddle-node bifurcation HC bif -
saddle-homoclinic bifurcation subH -
subcritical Andronov-Hopf bifurcation.
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Model 2 -Results
EL-40 mV
EL-50 mV
EL-59.5 mV
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Results from research article
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Model 2 -working

• Model 2 operates in a very similar fashion as
  Model 1, the difference being the slow activation
  persistent sodium current INaP is replaces by a
  slow activation of potassium current IKS

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Difference between Models 1 2
2
1

• Burst initiated by INaP, terminated by
  inactivating INaP
• Membrane conductance gm increases through the
  silent phase
• The membrane potential remains flat during the
  inter burst interval
• Burst duration decreases with depolarization
• Supports bursting over a small range of EL
• (-60 to -54 mV)

• Burst initialed by INaP, terminated by activating
  IKS sufficiently
• Membrane conductance gm decreases through the
  silent phase
• The membrane potential interval not as flat
  during the inter burst interval
• Burst duration does not decrease with
  depolarization
• Supports bursting over double the range of EL as
  model 1
• (-59.5 to -40 mV)

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Both models go through a regime of silence
bursting and beating
In both models a minimum value of gNaP is
required to support bursting. If gNaP is too
low, only quiescence , or for higher values
beating are supported.
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Miscellaneous Comments

• The same effects of chaging EL can be obtained by
  fixing EL and varying the parameter gtonic
  (Itonic) or Iapp ( gL (v-EL) in model 2). Some of
  these results shown below.

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Summary

• Model 1 is found to be more consistent with
  experimental data.
• The relative flat interburst interval is due to
  the fact that the subthreshold currents are all
  balanced and add up to zero.
• These are minimal models that provide a
  believable explanation for generating multistate,
  voltage-dependent behavior observed in the
  Pre-Botzinger pacemaker neurons.
• Although the actual burst generating currents
  still need to be unidentified in the
  Pre-Botzinger neurons

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Questions?
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Happy Holidays
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Neuron Xmas tree!!
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References

• RT-PCR reveals muscarinic acetylcholine receptor
  mRNA in the pre-Bötzinger complex, Jiunu Lai,
  Xuesi M. Shao, Richard W. Pan, Edward Dy, Cindy
  H. Huang, and Jack L. Feldman
• Models of Respiratory Rhythm Generation in the
  Pre-Botzinger Complex. I. Bursting Pacemaker
  Neurons, ROBERT J. BUTERA, JR.,1,2 JOHN
  RINZEL,13 AND JEFFREY C. SMITH1
• The Dynamic Range of Bursting in a Model
  Respiratory Pacemaker Network , Janet Best, Alla
  Borisyuk, Jonathan Rubin, David Terman, Martin
  Wechselberger
• All simulations performed using Matlab 7.0 , with
  a ode15s solver and absolute and relative
  tolerance of 10-6.