1) Two different-diameter cylindrical dendrites on a cerebellar Purkinje neuron have the following passive membrane properties. Assume the external resistance is zero and that the dendrites are cylindrical structures with homogenous membrane properties along their entire

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1) Two different-diameter cylindrical dendrites on a
cerebellar Purkinje neuron have the following passive
membrane properties. Assume the external resistance is
zero and that the dendrites are cylindrical structures with
homogenous membrane properties along their entire
length.
Im, ohm
ri, ohm/cm
Cm, F/cm
х сm
Dendrite 1
2х 106
1х 1010
2 x 10--9
Dendrite 2
2 X 104
1 X 106
2 X 10-8
An excitatory synaptic input impinges on each of these
dendrites at a distance of o.o2 cm from the cell body.
Activation of these synapses causes a depolarization of the
postsynaptic cell, which is called an excitatory postsynaptic
potential (EPSP). When a subthreshold EPSP occurs at this
synapse, the amplitude of the EPSP decays along an
exponential time course back to the resting potential.
a) Would the decay rate in dendrite 1 be faster, slower, or
the same as in dendrite 2? Justify your answer
quantitatively.
b) The amplitude of the EPSP decreases as a function of
distance away from the synapse. In which dendrite would
the amplitude decrease more with distance. Justify your
answer quantitatively.
II
Transcribed Image Text:12:31 N A all This document contains ink, shapes and . 1) Two different-diameter cylindrical dendrites on a cerebellar Purkinje neuron have the following passive membrane properties. Assume the external resistance is zero and that the dendrites are cylindrical structures with homogenous membrane properties along their entire length. Im, ohm ri, ohm/cm Cm, F/cm х сm Dendrite 1 2х 106 1х 1010 2 x 10--9 Dendrite 2 2 X 104 1 X 106 2 X 10-8 An excitatory synaptic input impinges on each of these dendrites at a distance of o.o2 cm from the cell body. Activation of these synapses causes a depolarization of the postsynaptic cell, which is called an excitatory postsynaptic potential (EPSP). When a subthreshold EPSP occurs at this synapse, the amplitude of the EPSP decays along an exponential time course back to the resting potential. a) Would the decay rate in dendrite 1 be faster, slower, or the same as in dendrite 2? Justify your answer quantitatively. b) The amplitude of the EPSP decreases as a function of distance away from the synapse. In which dendrite would the amplitude decrease more with distance. Justify your answer quantitatively. II
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