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

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Lecture 52 Computational Neuroethology Scientific Method

Observe natural phenomenon. Summarize observations in the form of a working or tentative hypothesis that is consistent with the

• bservations.

Use the hypothesis to generate predictions.

MODEL

Use the hypothesis to generate predictions. Test predictions by performing experiments with proper controls or by making additional observations. Accept or reject hypothesis. if accepted: develop hypothesis further, or make additional observations. if rejected: modify hypothesis, or consider an alternative hypothesis that is also consistent with original

• bservations and with results of experiments.

Models and Fundamental Questions in Neuroscience and in Neuroethology

How does the brain…

• process sensory information?
• recognize stimuli?
• make decisions?
• coordinate motor acts?
• remember previous stimuli experienced or? motor acts

remember previous stimuli experienced or? motor acts performed?

ANALYSIS LEVEL

whole animal molecular subcellular cellular circuits

Forms of Models

• Equations describing dynamic processes.

– Solutions to differential equations by analytic methods

(rare)

– Computer simulation by iteration (more common).

• Neural networks (actually a system of interconnected

elements each governed by equations describing synaptic elements each governed by equations describing synaptic inputs, weights, thresholds and outputs)

– solutions by neuromimes (electronic mimics of elements) – or by computer solution to matrix algebra

• Electronic simulators of circuit: chips that mimic circuits in

the brain.

• Robots: working models in silicon and metal

Levels of Modeling

• Space clamped axon model. Data from v-clamp
• experiments. Hodgkin & Huxley models simulate

the form of action potentials.

• Cable theory plus HH: importance of cell

geometry, morphology of dendrites. g y, p gy

• More than Na+ and K+ channels: fine tuning the

spike.

• Analysis of small networks.
• Modeling the Brain.

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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

Alan Hodgkin (1914- 1998) Andrew Huxley (1917-)

Squid, Loligo Giant axon intracellular electrode inside squid giant axon action potential showing the

• vershoot during spike.

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 LoligoJ J. Physiol April 28, 1952 116 (4) 449-472 Full Text (PDF) The components of membrane conductance in the giant axon ofLoligo 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)

Hodgkin, A., and Huxley, A. (1952): A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol.117:500–544.

Physiological Models of Action Potentials

Original Hodgkin-Huxley Model from 1952.

Outside of the cell membrane inside the cell gDR 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

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Hodgkin & Huxley, 1952

Membrane Current, Im is equal to sum of currents

Outside of the cell membrane inside the cell

C L K Na m

I I I I I + + + =

In order to separate the ionic current from the capacitative current, Hodgkin and Huxley used the voltage clamp Thereby setting dV/dt to zero and Huxley used the voltage clamp. 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.

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Membrane Current, Im

Outside of the cell membrane inside the cell

( )

Na Na Na

E V g I − =

Membrane Current, Im

Outside of the cell membrane inside the cell

( ) ( ) ( )

dt dV C I E V g I E V g I E V g I

m C L L L K K K Na Na Na

= − = − = − =

Membrane Current, Im

Outside of the cell membrane inside the cell

( ) ( ) ( )

dt dV C E V g E V g E V g I

m L L K K Na Na m

+ − + − + − =

Ionic Currents

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IONIC CONDUCTANCES

Time course of ionic currents under voltage clamp conditions. V resting v

Rate of opening of ion channels is voltage dependent. Simulator

wisc

rutgers Rutgers/Pollinger

http://www.math.rutgers.edu/courses/338/hodhuxPrg/html/ http://www.ywpw.com/cai/software/hhsimu/

http://www.cs.cmu.edu/~dst/HHsim/

HHSIM

Threshold Effect

Stimulus duration: Stimulus current: Anodal Break Repetitive Firing: integrate and fire

H-H model results

simulated propagated spike

Anatomy of K Channel Reveals 4 subunits

Doyle et al (1998)

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Voltage Gated K-channel preserves the 4 subunit design

Voltage gated Na channels also has 4 subunits Not all cells respond the same. Some differences:

normal HH

after addition of c current, Calcium activated Potassium after addition of IA current transiently inactivating K current after addition of IAHP current slow after hyperpolarization current, Sensitive to Ca

Addition of A current can change spiking threshold, AP duration, Adaptation, Repetitive Firing

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Cable Theory

The axon is an elongated cylinder made up of resistive membrane surrounded by saline solution on the

• utside and on the inside.

Each differential length dx of cable has the following components: Internal resistance ri which is determined by the resistivity of the solution by the cross sectional area solution, by the cross sectional area, and by the length of the element, dx. External resistance, re Membrane capacitance: determined by the capacitance of membrane multiplied by surface area of the segment. Membrane resistance rm determined by the surface area of the membrane and by the resistivity

• f

the membrane.

Contributions from Cable Theory

Calculation of the membrane voltage as a function of distance away from a current source. A current step is applied at x = 0; T=inf. is the final value in response to a sustained current pulse. From cable theory: response as a function of time. Membrane voltage in response to a current pulse step at x = 0; Different distances from the source.

H-H model results

simulated propagated spike