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Unformatted text preview: x=0 μ m time V o l t a g e c h a n g e 0 250 500 distance ( μ m) Stimulus 250 μ m 250 μ m rec 1 at 0 μ m rec 2 at 250 μ m rec 3 at 500 μ m time time What properties of a neuron are responsible for voltage dropping (attenuating) as a function of space? II.C. How does voltage change in a neuron as we get further away from the injection point? We can record voltage at remote locations We can model the influx of sodium as a current source & the recording electrodes as voltmeters Δ Vf inal at x = 250 μ m II.C.1. What does the voltage change over space look like for a step injection of current II.C.2 What causes the voltage to attenuate as you record further from the injection point? Internal resistance The internal environment of a neuron offers resistance to ion movement Membrane resistance The membrane has protein channels that allow ions to escape When taken together, both the internal and membrane resistance lead to voltage attenuation in space Δ Vf inal at x = 500 μ m V o l t a g e c h a n g e a t t im e = ∞ V o l t a g e c h a n g e a t t im e = ∞ 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 How do we model & calculate ... 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 We will provide examples to demonstrate how the the time constant can effect the ability of...
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This note was uploaded on 11/16/2011 for the course NPB NPB 100 taught by Professor Campbell during the Spring '10 term at UC Davis.
- Spring '10