CML_Oral_Presentation

The Effect of the Epilepsy-Associated
R1648H Sodium Channel Mutation
on Neuronal Excitability: A Model
Study
Chris Locandro & Robert Clewley
Neuroscience Institute, Department of
Mathematics & Statistics, Georgia State
University

Introduction: The Utility of Modeling
in Neuroscience
• Why Model?
– Explore pathological parameter values (e.g. effect of
mutations)
– Explore the effects of drugs/environmental conditions
– Understand a complex system or a particular mechanism
– Predict short-term future of a system
– Ethical constraints, limits on human experimentation
•Examples
•IBM’s Blue Brain Project

Experimental Question/Goals
• How does the R1648H sodium channel
mutation affect the excitability of a CA3
neuron model and why?
• Understand how the mutant sodium channel
interacts with other currents to give rise to
epileptiform activity (in progress)

CA3 Hippocampal Neuron Model
Xu & Clancy 2008 PLoS ONE
•Hyperexcitability of neurons in the hippocampus has been implicated in
forms of epilepsy

The Hodgkin-Huxley (HH) Model
• Quantitative model of
action potential
generation in single
neurons
• Membrane as an
equivalent circuit
• Ohm’s Law, Kirchhoff’s
Law, Charging of a
Capacitor

Ion Channel Kinetics
m = Activation
h = Inactivation
High Voltages: Large m, Small h
Low Voltages: Small m, Large h

The R1648H Mutation
• Neuronal NaV1.1 channel
• Missense mutation (Domain IV):
R1648H
From Avanzini 2003 Lancet Neurol.
Clancy & Kass 2004 Biophys J

Markov Chains & The Clancy Model
• Channel can reside in 1 of 14 hypothetical states
• Each state has a probability (0-1), which changes as a function of incoming
and outgoing rates
• Na current is a function of the probability of the channel being in the open
state
Wild-Type
States
(Upper)Mutant
States
(Upper &
Lower)

Methods
• Computer simulation using Python/PyDSTool
• Embedding Markov models into full, single-
compartment neuron models
• Reproducing output of Clancy/Xu models for
validation
• f-I curves and spike/burst metrics to
characterize excitability
• Derivative event detection for simple HH
model
Clewley 2004

Methods (cont.)
• Simple Neuron Embedding:
• Inserting an ion channel model into a previously developed
full-neuron model is not trivial, so we manually control
potassium to ensure a proper spike:

Results: Effects of the Mutation on Ion
Channel Function
1) Increase in Peak Current:
2) Impaired/Incomplete
Inactivation:

Results: Simple HH Model Embedding
• f-I Curves: frequency
response of a neuron
to constant stimulus
currents (could be
input from a pre-
synaptic neuron) of
different magnitudes
•Effective measure of
neuronal excitability
Iapp = 5 pA

Results: CA3 Hippocampal Neuron
•Apply transient (5 ms) stimulus current of 0.5 pA:
•Mutant neuron responds with much higher frequency and continues firing, even
though the applied stimulus is gone

Conclusions
• The mutation induces subtle changes in spike metrics
of the simple HH model, but does not significantly alter
excitability
• The mutation causes drastic dynamical changes when
embedded into a complex, physiologically relevant
neuron model
• These findings illustrate that the interplay between the
sodium current and other currents in the complex
neuron model gives rise to unpredictable emergent
properties
• We’ve also shed light on a mechanism of
hyperexcitability that may underlie seizure
generation/propagation in epilepsy

Future Directions
• Use dynamical system reduction techniques to
understand how the Na+ current is interacting
with other currents to cause the macroscopic
burst change
• Incorporate ion channel model into another
previously developed model of CA1/CA3 neurons
and compute “excitability measure”
• Develop protocol for integration of ion channel
models into complex neuron models with
different time scales
Nowacki et al. 2011 Prog Biophys Mol Biol

References
• Clancy CE, Kass RS (2004) Theoretical investigation of the neuronal Na
channel SCN1A: abnormal gating and epilepsy. Biophys J 86:2606 –2614.
• Xu J, Clancy CE (2008) Ionic Mechanisms of Endogenous Bursting in CA3
Hippocampal Pyramidal Neurons: A Model Study. PLoS ONE 3(4): e2056.
doi:10.1371/journal.pone.0002056
• Nowacki J, Osinga HM, Brown JT, Randall AD, Tsaneva-Atanasova K (2011)
A unified model of CA1/3 pyramidal cells: an investigation into
excitability.Prog Biophys Mol Biol, 105(1-2):34-48.
• RH Clewley, WE Sherwood, MD Lamar, JM Guckenheimer (2004).
PyDSTool: a software environment for dynamical systems modeling.
http://pydstool.sourceforge.net
• Avanzini G., Franceschetti S. (2003). Cellular biology of epileptogenesis.
Lancet Neurol. 2, 33–42. doi: 10.1016/S1474-4422(03)00265-5.
• http://bluebrain.epfl.ch/

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