2_5_09_CableTheory_1

# 2_5_09_CableTheory_1 - Outline of the Lecture Cable Theory...

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Outline of the Lecture Outline of the Lecture Cable Theory for Axons and Dendrites Cable Theory for Axons and Dendrites Cable Equation         Multi-compartment Model            Cable Equation         Multi-compartment Model            Shunting Shunting

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Cable Theory Describes  Cable Theory Describes  Potential Propagation in  Potential Propagation in  Dendrites and Axons Dendrites and Axons
Propagation in dendrites takes time and spreads potentials generated remotely.

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Equivalent-circuit models for action potentials are RC circuits with many conductances.
r m c m r L Δx 2a Cable models use radii ( e.g. , a = 2 μ m), specific membrane resistances ( e.g. , r m = 1 MΩ mm 2 ) and capacitances ( e.g. , c m = 10 nF mm -2 ), and intracellular resistivities ( e.g. , r L = 1 kΩ mm).

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Cable Equation: τ m v t = l 2 2 v x 2 - v + r m i e With typical values (see Slide 5): τ m = r m c m = 10 ms λ = ar m 2 r L =1 mm
Three Examples of Solutions of the Cable Equation: 1.Infinite, Steady-State Cable with Current Injection at the Middle…

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The potential falls with distance from the injection point, since current escapes at various points of the neural cable.
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