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

€

CdV

dt= I stim − INa − IK − ILeak − IA − IM − IAHP − IKC − ICaL − ICaN − ICaT

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

€

CdV

dt= Iapplied − INa − IK − ILeak

Ion Channel Kinetics

€

INa = m3h V − ENa( )m = Activationh = Inactivation

€

dx

dt=α x (V ) 1− x( ) − β x (V )x

High Voltages: Large m, Small hLow 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

€

INa = g NaPO (V − ENa )

Wild-Type States

(Upper)Mutant States

(Upper & Lower)

Clancy & Kass 2004 Biophys J

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:

€

CdV

dt= Iapplied − g NaPO V − ENa( ) + g K n4 V − EK( ) + g l V − El( )( )

€

dV

dt= 0.5

Clancy & Kass 2004 Biophys J

• 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/