Simulation of an action potential using the HodgkinHuxley

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

Background Source: Neil Fraser: http: //vv. carleton. ca/~neil/neural/neuron-a. html Department of Medical Biophysics

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

The Action Potential (AP) • rapid reversal of the resting membrane potential (RMP) depolarization • permeability of membrane to ions changes with membrane potential (MP) Source [1]: Neil Fraser: http: //vv. carleton. ca/~neil/neural/neuron-a. html Source [2]: Hodgkin-Huxley (1952): http: //www. ncbi. nlm. nih. gov/pmc/ articles/PMC 1392413/pdf/jphysiol 01442 -0106. pdf Department of Medical Biophysics

Source: Candace Thompson: http: //www. studyblue. com/notes/note/n/actionpotentials/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 Department of Medical Biophysics

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

Circuit Diagram Interpretation Hodgkin-Huxley (1952): http: //www. ncbi. nlm. nih. gov/pmc/ articles/PMC 1392413/pdf/jphysiol 01442 -0106. pdf Department of Medical Biophysics

Derivation of Equations Ohm’s Law Department of Medical Biophysics

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

Methods • Code development: 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 • Define variables: Variable Value vrest 0 #m. V EK -12 #m. V ENa 115 #m. V El 10. 613 #m. V g. Kbar 36 #m. S/cm^2 g. Nabar 120 #m. S/cm^2 glbar 0. 3 #m. S/cm^2 cm 1 #u. F/cm^2 ts 100 ms dt 0. 025 v (-100, 250) #m. V Department of Medical Biophysics

Results Department of Medical Biophysics

Results Department of Medical Biophysics

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

Discussion Above: Original tracing of membrane action potential recorded at 9. 1°C (Empirical Model) Above: Change in Membrane Potential with Respect to Time (Hodgkin Huxley 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 Ph. D

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 8 th, 2013. http: //classconnection. s 3. amazonaws. com/117/flashcards/693117/jpg /picture 1321109256503. jpg • Fraser, N. (1998). The Biological Neuron. Schematic of Biological Neuron. Retrieved March 5 th, 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?