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 : Neil Fraser: http://vv.carleton.ca/~neil/neural/neuron-a.html Source : Hodgkin-Huxley (1952): http://www.ncbi.nlm.nih.gov/pmc/ articles/PMC1392413/pdf/jphysiol01442-0106.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/PMC1392413/pdf/jphysiol01442-0106.pdf Department of Medical Biophysics Derivation of Equations V iR Ohm’s Law (V m V y ) i y R y iy (V m V y ) conductanc e, g 1 R Ry i y g y (V m V y ) 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 I CM dV g K n (V V K ) g Na m h (V V Na ) g l (V V l ) 4 3 dt dn (1) n (1 n ) n n (2) m (1 m ) m m (3) h (1 h ) h h (4) dt dm dt dh dt 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 #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 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 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?