1 Physiological Models of Action Potentials Hodgkin and Huxley - PDF document

Scientific Method Observe natural phenomenon. MODEL Summarize observations in the form of a working or tentative hypothesis that is consistent with the observations. Use the hypothesis to generate predictions. Use the hypothesis to generate predictions. Test predictions by performing experiments with proper controls or by making additional observations. Lecture 52 Accept or reject hypothesis. Computational Neuroethology if accepted: develop hypothesis further, or make additional observations. if rejected: modify hypothesis, or consider an alternative hypothesis that is also consistent with original observations and with results of experiments. Models and Fundamental Questions in ANALYSIS LEVEL Neuroscience and in Neuroethology How does the brain… • process sensory information? • recognize stimuli? whole animal • make decisions? • coordinate motor acts? molecular • remember previous stimuli experienced or? motor acts remember previous stimuli experienced or? motor acts performed? cellular subcellular circuits Forms of Models Levels of Modeling • Equations describing dynamic processes. • Space clamped axon model. Data from v-clamp – Solutions to differential equations by analytic methods experiments. Hodgkin & Huxley models simulate (rare) the form of action potentials. – Computer simulation by iteration (more common). • Cable theory plus HH: importance of cell • Neural networks (actually a system of interconnected g geometry, morphology of dendrites. y, p gy elements each governed by equations describing synaptic elements each governed by equations describing synaptic • More than Na + and K + channels: fine tuning the inputs, weights, thresholds and outputs) – solutions by neuromimes (electronic mimics of elements) spike. – or by computer solution to matrix algebra • Analysis of small networks. • Electronic simulators of circuit: chips that mimic circuits in • Modeling the Brain. the brain. • Robots: working models in silicon and metal 1

Physiological Models of Action Potentials Hodgkin and Huxley (1952) Data from intracellular recordings made in 1940’s and 1950s, and from voltage clamp experments in late 1940’s and early 1950’s Squid, Loligo Giant axon Alan Hodgkin (1914- Andrew Huxley (1917-) 1998) Hodgkin and Huxley, 1952 A. L. Hodgkin, A. F. Huxley, and B. Katz Measurement of current- voltage relations in the membrane of the giant axon of Loligo J Physiol April 28, 1952 116 (4) 424-448 Full Text (PDF) Currents carried by sodium and potassium ions through the membrane of the giant axon of Loligo J J. Physiol April 28, 1952 116 (4) 449-472 Full Text (PDF) The components of membrane conductance in the giant axon of Loligo J Physiol April 28, 1952 116 (4) 473-496 Full Text (PDF) The dual effect of membrane potential on sodium conductance in the giant axon of Loligo J Physiol April 28, 1952 116 (4) 497-506 Full Text (PDF) A quantitative description of membrane current and its application to conduction and excitation in nerve J Physiol August 28, 1952 117 (4) 500-544 Full Text (PDF) action potential showing the intracellular overshoot during spike. electrode inside squid giant axon Hodgkin, A., and Huxley, A. (1952): A quantitative Physiological Models of Action Potentials description of membrane current and its application to conduction and excitation in nerve. J. Physiol. 117 :500–544. Original Hodgkin-Huxley Model from 1952. Outside of the cell membrane inside the cell g DR is the symbol for the delayed rectifier conductance (K) m, h, and h are variables that vary between 0 to 1 to describe the variable conductances 2

Membrane Current, I m is equal to sum of currents Outside of the cell membrane inside the cell = + + + I I I I I m Na K L C Hodgkin & Huxley, 1952 In order to separate the ionic current from the capacitative current, Hodgkin and Huxley used the voltage clamp and Huxley used the voltage clamp. Thereby setting dV/dt to zero. Thereby setting dV/dt to zero intracellular electrode inside squid giant axon By replacing sodium chloride in the external solution with choline chloride, Hodgkin and Huxley were able to eliminate the sodium current entirely. The remaining current was potassium current and the leak current. Leak current was simply proportional to the leak conductance which was constant. The remainder was potassium. The potassium current changed with time in proportion to the potassium conductance. 3

Membrane Current, I m Membrane Current, I m Outside of the cell membrane Outside of the cell membrane inside the cell inside the cell ( ) ( ) = − I g V E = − I g V E Na Na Na Na Na Na ( ) = − I g V E K K K ( ) = − I g V E L L L dV = I C C m dt Ionic Currents Membrane Current, I m Outside of the cell membrane inside the cell dV ( ) ( ) ( ) = − + − + − + I g V E g V E g V E C m Na Na K K L L m dt 4

Rate of opening of ion channels is IONIC CONDUCTANCES voltage dependent. Time course of ionic currents under voltage clamp conditions. v V resting Simulator Threshold Effect Stimulus duration: Stimulus current: Anodal Break Repetitive Firing: integrate and fire wisc http://www.ywpw.com/cai/software/hhsimu/ rutgers http://www.math.rutgers.edu/courses/338/hodhuxPrg/html/ http://www.cs.cmu.edu/~dst/HHsim/ Rutgers/Pollinger HHSIM Anatomy of K Channel Reveals 4 H-H model results subunits simulated propagated spike Doyle et al (1998) 5

Voltage Gated K-channel preserves Voltage gated Na channels also has 4 subunits the 4 subunit design Not all cells respond the same. Some differences: after addition of c after addition of I A current current, Calcium transiently inactivating activated Potassium K current normal HH after addition of I AHP current slow after hyperpolarization current, Sensitive to Ca Addition of A current can change spiking threshold, AP duration, Adaptation, Repetitive Firing 6

Cable Theory Contributions from Cable Theory The axon is an elongated cylinder made up of resistive membrane surrounded by saline solution on the Calculation of the membrane voltage outside and on the inside. as a function of distance away from a current source. A current step is Each differential length dx of cable applied at x = 0; has the following components: T=inf. is the final value in response to Internal resistance r i which is determined by the resistivity of the a sustained current pulse. solution, by the cross sectional area, solution by the cross sectional area and by the length of the element, dx. External resistance, r e From cable theory: response as a Membrane capacitance: determined function of time. Membrane voltage by the capacitance of membrane in response to a current pulse step at multiplied by surface area of the segment. x = 0; Different distances from the Membrane resistance r m determined source. by the surface area of the membrane and by the resistivity of the membrane. H-H model results simulated propagated spike 7