lecture_10_6a

lecture_10_6a - II.C. How does voltage change in a neuron...

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The internal resistance and membrane resistance both contribute to voltage attenuation in space II.C. How does voltage change in a neuron as we get further away from the injection point? (cont’d) II.C.3 .. neurons II.C.3.a. The model Segment of free nerve ending Δ V(x) = I*R in [e -(x/ λ ) ] = Δ V ss(inject) [e -(x/ λ ) ] Membrane resistance of a unit length of neuron (in Ω -cm) Internal resistance of a unit length of neuron (in Ω /cm) Magnitude of injected current Input resistance of the cell where λ =(r m /r i ) 1/2 is the patch of neuron’s space or length constant and Δ V ss = I*R in is the steady state voltage change at the injection point (note in the graph Δ Vss(x) is not limited to the injection point) is the distance it takes for the voltage change to drop by 63% If we increase the membrane resistance, r m , will the cell's voltage attenuate more or less as we get farther away from the injection point? ________ If we increase r m , we _______ λ . Therefore, by ________ λ , voltage will attenuate less as we get further from the injection point. r i Voltage attenuates less r m λ r m λ Why? _____________________________________________ As an exercise, you might want to fill in the rest of the chart above. In general, increasing λ decreases attenuation as shown on the chart below. The value λ is useful because it gives us a single parameter with which to determine how rapidly the cell's voltage will attenuate as a function of distance. r i Voltage attenuates more II.C.3.c Properties of λ internal axoplasmic resistance II.C.3.b. The space constant equation λ 2 λ 2 We can model the system as a resistor network Cell with larger λ less Fewer ions leak out of the CM per unit distance increase increasing Note looking at Steady state voltage only For simplicity assume R in and r m not related Δ V ss
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V(x,t) = λ 2 ( δ 2 V/ δ x 2 )- τ ( δ v/ δ t) The truth II.D.2 The simplified unified equation II.D.1 The cable equation The time and space equations can be simplified & combined into a unified equation by making certain assumptions that are acceptable for this class. Δ
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lecture_10_6a - II.C. How does voltage change in a neuron...

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