Modelling Single Nerve Dynamics Hodgkin-Huxley Equations Peter - PowerPoint PPT Presentation

Modelling Single Nerve Dynamics Hodgkin-Huxley Equations Peter Schuster Institut für Theoretische Chemie und Molekulare Strukturbiologie der Universität Wien Seminar lecture Wien, 26.04.2004

Neurobiology Neural networks, collective properties, nonlinear dynamics, signalling, ... The human brain 10 11 neurons connected by � 10 13 to 10 14 synapses

Neurobiology Neural networks, collective properties, nonlinear dynamics, signalling, ... A single neuron signaling to a muscle fiber

B A Christof Koch, Biophysics of Computation. Information Processing in single neurons. Oxford University Press, New York 1999.

Christof Koch, Biophysics of Computation. Information Processing in single neurons. Oxford University Press, New York 1999.

Christof Koch, Biophysics of Computation. Information Processing in single neurons. Oxford University Press, New York 1999.

Neurobiology Neural networks, collective properties, nonlinear dynamics, signalling, ... d V 1 = − − − − − − 3 4 I g m h ( V V ) g n ( V V ) g ( V V ) Na Na K K l l d t C M dm = α − − β Hogdkin-Huxley OD equations ( 1 m ) m m m dt dh = α − − β ( 1 h ) h h h dt dn = α − − β ( 1 n ) n n n dt A single neuron signaling to a muscle fiber

d V 1 = − − − − − − 3 4 I g m h ( V V ) g n ( V V ) g ( V V ) Na Na K K l l d t C M dm = α − − β ( 1 m ) m m m dt dh = α − − β ( 1 h ) h h h dt dn = α − − β ( 1 n ) n n n dt Hogdkin-Huxley OD equations Hhsim.lnk Simulation of space independent Hodgkin-Huxley equations: Voltage clamp and constant current

∂ ∂ 2 1 V V = + − + − + − π 3 4 C g m h ( V V ) g n ( V V ) g ( V V ) 2 r L ∂ ∂ Na Na K K l l 2 R x t ∂ m = α − − β ( 1 m ) m Hodgkin-Huxley PDEquations ∂ m m t ∂ h = α − − β ( 1 h ) h Travelling pulse solution: V ( x,t ) = V ( � ) with ∂ h h t � = x + � t ∂ n = α − − β ( 1 n ) n n n ∂ t Hodgkin-Huxley equations describing pulse propagation along nerve fibers

[ ] 2 1 d V d V = θ + − + − + − π 3 4 C g m h ( V V ) g n ( V V ) g ( V V ) 2 r L M Na Na K K l l ξ ξ 2 R d d d m Hodgkin-Huxley PDEquations θ = α − − β ( 1 m ) m m m ξ d Travelling pulse solution: V ( x,t ) = V ( � ) with d h θ = α − − β ( 1 h ) h h h � = x + � ξ t d d n θ = α − − β ( 1 n ) n n n ξ d Hodgkin-Huxley equations describing pulse propagation along nerve fibers

100 50 ] V m [ V 0 -50 1 2 3 4 5 6 � [cm] T = 18.5 C; θ = 1873.33 cm / sec

T = 18.5 C; θ = 1873.3324514717698 cm / sec

T = 18.5 C; θ = 1873.3324514717697 cm / sec

40 30 20 ] V m [ 10 V 0 -10 6 8 10 12 14 16 18 � [cm] T = 18.5 C; θ = 544.070 cm / sec

T = 18.5 C; θ = 554.070286919319 cm/sec

T = 18.5 C; θ = 554.070286919320 cm/sec

Propagating wave solutions of the Hodgkin-Huxley equations

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