Lecture8(11) - r i depend on the radius a of axon 2 2 m m i...

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Neurons as Conductors of Electricity (Lecture 8)
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How does current flow in a neuron in response to synaptic input? How does this current flow determine the response of the cell? How fast and how far the current spreads depends on the capacitive and resistive properties of the membrane.
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Current injection into a model spherical cell R m =1/g m , g m =g Na +g K +g Cl E L R m
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Membrane Capacitance Since a charge difference exists across the cell membrane, it acts as a capacitor . The capacitance C is a measure of how much charge Q the capacitor will accumulate when a potential V is applied: / ; ; C C Q V dQ dV I I C dt dt = = =
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Current injection into a model spherical cell E L I i =g m (V m -E L ), g m =1/R m I m = CdV m /dt + g m (V m -E L ) R m
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m
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r m - membrane resistance of 1cm of axon ( cm) r i – longitudinal (axial) resistance of 1cm of axon ( Ω/ cm) / 0 0 x x in V V e V r I λ - = = λ is the distance at which V is 1/e of V 0 (i.e where V is about 37% of V 0 )
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/ 0 / x x m i in m i V V e r r r r r λ - = = =
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Passive propagation is more efficient in thick axons. r m and
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Unformatted text preview: r i depend on the radius a of axon 2 2 m m i i R r a R r a π = = / 2 3 / 2 / 2 x x m i in m i V V e aR R r R R a λ-= = = m m CR τ= Passive Propagation (subthreshold input) Active Spike Propagation Increasing axon diameter decreases axial resistance and increases the length constant / 2 m i aR R λ= 2 / i i r R a π = Myelin reduces the ability of current to leak out of the axon and thus increases the distance along the axon that a current can flow passively (larger λ ). It also decreases membrane capacitance C this allows the membrane to respond faster to current (smaller τ m ) In many neurons, the most efficient spike propagation is achieved by combination of active and passive propagation / / (1 ) m t m L m m V E I g e τ-= +-/ / m t m L m m V E I g e-= + m m CR τ= / L m m V E I g ∞ = +-membrane time constant...
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This note was uploaded on 01/31/2011 for the course CBNS 120 taught by Professor Adams during the Winter '10 term at UC Riverside.

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Lecture8(11) - r i depend on the radius a of axon 2 2 m m i...

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