Simulation of an action potential using the Hodgkin-Huxley Model in PythonNathan LawMedical Biophysics 3970Western University03/24/13

Supervised by Dr. Andrea SodduMedical PhysicistThe Department of Physics and AstronomyCOMA Science Group

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Source: Neil Fraser: http://vv.carleton.ca/~neil/neural/neuron-a.html

Background

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Source: Breedlove, et al., Biological Psychology, Fourth Edition, Sinauer Associates© 2008 Sinauer Associates and Sumanas, Inc.

The Action Potential (AP)• rapid reversal of the resting membrane potential (RMP) depolarization

• permeability of membrane to ions changes with membrane potential (MP)

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Source [1]: Neil Fraser: http://vv.carleton.ca/~neil/neural/neuron-a.htmlSource [2]: Hodgkin-Huxley (1952): http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1392413/pdf/jphysiol01442-0106.pdf

Source: Candace Thompson: http://www.studyblue.com/notes/note/n/action-potentials/deck/1448117

Motivation• Why model an action potential?

• estimate parameters

• determine/prove correlation between variables

• test new and hypothetical situations

• make quantitative and qualitative predictions

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Objectives1) Develop a simulation for an action potential using Python based on the Hodgkin-Huxley model.

2) Compare and contrast the Hodgkin-Huxley model with empirical data based on the giant squid axon.

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Hodgkin-Huxley (1952): http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1392413/pdf/jphysiol01442-0106.pdf

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Circuit Diagram Interpretation

iRV Ohm’s Law

yyym RiVV )(

y

ymy

R

VVi

)(

R

1 g e,conductanc

)( ymyy VVgi

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Derivation of Equations

The Hodgkin-Huxley Model• A mathematical model that describes action potential initiation and propagation based on the giant squid axon

• model is based on four first-order ordinary differential equations

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)()()( 34llNaNaKKM VVgVVhmgVVng

dt

dVCI

nndt

dnnn )1(

mmdt

dmmm )1(

hhdt

dhhh )1(

(2)

(1)

(4)

(3)

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Methods• differential equations from: A Quantitative Description of Membrane Current And It’s Application To Conduction And Excitation In Nerve: A. Hodgkin & A. Huxley (1952)

• all parameters based on paper

• Python (programming language)

• Spyder (scientific Python development environment)

Define Variables based on empirical data

Define a time scale and an array of membrane

potentials

Input equations based on Hodgkin-Huxley

model

Plot

Methods•Code development:

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Methods• Define variables:

Variable Value

vrest 0 #mV

EK -12 #mV

ENa 115 #mV

El 10.613 #mV

gKbar 36 #mS/cm^2

gNabar 120 #mS/cm^2

glbar 0.3 #mS/cm^2

cm 1 #uF/cm^2

ts 100ms

dt 0.025

v (-100,250) #mV

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Results

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Results

Discussion• Qualitative Analysis

• there is a hump during the depolarization phase in the calculated model

• the peak in the calculated model is sharper

• during repolarization, the calculated model is not smooth

• slope of the repolarization phase may be too steep

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Discussion

Above: Change in Membrane Potential with Respect to Time (Hodgkin Huxley Model)

Above: Original tracing of membrane action potential recorded at 9.1°C (Empirical Model)

Conclusion• equations closely replicate the behaviour of a measured action potential

• good approximation of electrical characteristics of excitable cells

• not perfect

Future Research & Implications• Simplification of the model

• Model groups of neurons, a bundle of axons, such as in a nerve

Acknowledgements• Dr. Andrea Soddu PhD

References• Breedlove, et al., Biological Psychology, Fourth Edition, Sinauer Associates © 2008 Sinauer Associates and Sumanas, Inc.

• Thompson, C. (2013). Action Potentials. Medicine 2015 at Howard University College of Medicine. Retrieved March 8th, 2013. http://classconnection.s3.amazonaws.com/117/flashcards/693117/jpg/picture1321109256503.jpg

• Fraser, N. (1998). The Biological Neuron. Schematic of Biological Neuron. Retrieved March 5th, 2013. http://vv.carleton.ca/~neil/neural/neuron-a.html

• Hodgkin, A. L.; Huxley, A. F. (1952). "A quantitative description of membrane current and its application to conduction and excitation in nerve". The Journal of physiology 117 (4): 500–544.PMC 1392413. PMID 12991237

Questions? Comments?