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Simulation of an action potential using the Hodgkin-Huxley Model in Python Nathan Law Medical Biophysics 3970 Western University 03/24/13 Supervised by Dr. Andrea Soddu Medical Physicist The Department of Physics and Astronomy COMA Science Group

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Department of Medical Biophysics Source: Neil Fraser: Background

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

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The Action Potential (AP) rapid reversal of the resting membrane potential (RMP) depolarization permeability of membrane to ions changes with membrane potential (MP) Department of Medical Biophysics Source [1]: Neil Fraser: Source [2]: Hodgkin-Huxley (1952): articles/PMC /pdf/jphysiol pdfhttp://www.ncbi.nlm.nih.gov/pmc/ articles/PMC /pdf/jphysiol pdf

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

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Motivation Why model an action potential? estimate parameters determine/prove correlation between variables test new and hypothetical situations make quantitative and qualitative predictions Department of Medical Biophysics

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Objectives 1) 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. Department of Medical Biophysics

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Hypothesis Hodgkin-Huxley model will closely replicate the empirical data based on a single action potential from the giant squid variation of parameters will result in a better fitting AP spike Department of Medical Biophysics

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Hodgkin-Huxley (1952): articles/PMC /pdf/jphysiol pdfhttp://www.ncbi.nlm.nih.gov/pmc/ articles/PMC /pdf/jphysiol pdf Department of Medical Biophysics Circuit Diagram Interpretation

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Ohm’s Law Department of Medical Biophysics Derivation of Equations

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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 Department of Medical Biophysics (2) (1) (4) (3)

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Department of Medical Biophysics 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)

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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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Department of Medical Biophysics Methods Define variables: VariableValue vrest0 #mV EK-12 #mV ENa115 #mV El #mV gKbar36 #mS/cm^2 gNabar120 #mS/cm^2 glbar0.3 #mS/cm^2 cm1 #uF/cm^2 ts100ms dt0.025 v(-100,250) #mV

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Department of Medical Biophysics Results

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Department of Medical Biophysics Results

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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 Department of Medical Biophysics

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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)

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Conclusion equations closely replicate the behaviour of a measured action potential good approximation of electrical characteristics of excitable cells not perfect

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Future Research & Implications Simplification of the model Model groups of neurons, a bundle of axons, such as in a nerve

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Acknowledgements Dr. Andrea Soddu PhD

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References Breedlove, et al., Biological Psychology, Fourth Edition, Sinauer Associates © 2008 Sinauer Associates and Sumanas, Inc.Sinauer Associates Thompson, C. (2013). Action Potentials. Medicine 2015 at Howard University College of Medicine. Retrieved March 8 th, /picture jpg /picture jpg Fraser, N. (1998). The Biological Neuron. Schematic of Biological Neuron. Retrieved March 5 th, 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 PMID "A quantitative description of membrane current and its application to conduction and excitation in nerve"PMC PMID

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