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Modelling Single Nerve Dynamics Hodgkin-Huxley Equations Peter - - PowerPoint PPT Presentation
Modelling Single Nerve Dynamics Hodgkin-Huxley Equations Peter - - PowerPoint PPT Presentation
Modelling Single Nerve Dynamics Hodgkin-Huxley Equations Peter Schuster Institut fr Theoretische Chemie und Molekulare Strukturbiologie der Universitt Wien Seminar lecture Wien, 26.04.2004 Neurobiology Neural networks, collective
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Neurobiology
Neural networks, collective properties, nonlinear dynamics, signalling, ...
The human brain 1011 neurons connected by 1013 to 1014 synapses
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Neurobiology
Neural networks, collective properties, nonlinear dynamics, signalling, ...
A single neuron signaling to a muscle fiber
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B A
Christof Koch, Biophysics of Computation. Information Processing in single neurons. Oxford University Press, New York 1999.
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Christof Koch, Biophysics of Computation. Information Processing in single neurons. Oxford University Press, New York 1999.
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Christof Koch, Biophysics of Computation. Information Processing in single neurons. Oxford University Press, New York 1999.
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Neurobiology
Neural networks, collective properties, nonlinear dynamics, signalling, ...
) ( ) ( ) ( 1
4 3 l l K K Na Na M
V V g V V n g V V h m g I C t d V d − − − − − − =
m m dt dm
m m
β α − − = ) 1 ( h h dt dh
h h
β α − − = ) 1 ( n n dt dn
n n
β α − − = ) 1 (
Hogdkin-Huxley OD equations
A single neuron signaling to a muscle fiber
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) ( ) ( ) ( 1
4 3 l l K K Na Na M
V V g V V n g V V h m g I C t d V d − − − − − − =
m m dt dm
m m
β α − − = ) 1 ( h h dt dh
h h
β α − − = ) 1 ( n n dt dn
n n
β α − − = ) 1 (
Hogdkin-Huxley OD equations
Hhsim.lnk
Simulation of space independent Hodgkin-Huxley equations: Voltage clamp and constant current
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L r V V g V V n g V V h m g t V C x V R
l l K K Na Na
π 2 ) ( ) ( ) ( 1
4 3 2 2
− + − + − + ∂ ∂ = ∂ ∂ m m t m
m m
β α − − = ∂ ∂ ) 1 ( h h t h
h h
β α − − = ∂ ∂ ) 1 ( n n t n
n n
β α − − = ∂ ∂ ) 1 (
Hodgkin-Huxley PDEquations Travelling pulse solution: V(x,t) = V( ) with
- = x +
t
Hodgkin-Huxley equations describing pulse propagation along nerve fibers
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Hodgkin-Huxley PDEquations Travelling pulse solution: V(x,t) = V( ) with
- = x +
t
[ ]
L r V V g V V n g V V h m g d V d C d V d R
l l K K Na Na M
π ξ θ ξ 2 ) ( ) ( ) ( 1
4 3 2 2
− + − + − + =
m m d m d
m m
β α ξ θ − − = ) 1 ( h h d h d
h h
β α ξ θ − − = ) 1 ( n n d n d
n n
β α ξ θ − − = ) 1 (
Hodgkin-Huxley equations describing pulse propagation along nerve fibers
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50
- 50
100 1 2 3 4 5 6
- [cm]
V [ m V ]
T = 18.5 C; θ = 1873.33 cm / sec
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T = 18.5 C; θ = 1873.3324514717698 cm / sec
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T = 18.5 C; θ = 1873.3324514717697 cm / sec
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- 10
10 20 30 40 V [ m V ] 6 8 10 12 14 16 18
- [cm]
T = 18.5 C; θ = 544.070 cm / sec
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T = 18.5 C; θ = 554.070286919319 cm/sec
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T = 18.5 C; θ = 554.070286919320 cm/sec
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Propagating wave solutions of the Hodgkin-Huxley equations
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Web-Page for further information: http://www.tbi.univie.ac.at/~pks
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