Solutions for the suggested exercises to accompany the Neuron Tutorial

QUESTION 1: In 20 words or less, what is the relationship between what you
see in window #4 and window #3?  Why do you see action potentials in window
#3 (Dendrite #1 Vm)?


Ans: #4 Shows the Soma membrane potential and the action potentials arising
in the soma.  In #3 (Dendrite #1 Vm) we are seeing passive properties.  The
dendrite compartment is coupled through an axial resistance to the soma, and
we see a smaller amplitude version of the soma Vm.

QUESTION 2: In 10 words or less, what principle does the overlayed plot in
window #2 demonstrate?  (There is a two-word phrase for this.)

Ans: Temporal summation. (The plots of the conductance of the Dendrite #1
excitatory channel show that for spike intervals of less than 3
milliseconds, the conductance is able to build up to a point where the Vm in
the soma has increased to a value which will trigger action potentials.)

QUESTION 3: Make a plot of the input-output transfer function. That is, plot
output rate vs input spikes rate.

Ans: There is a fairly sharp threshold for the generation of multiple
action potentials at an input rate of about 300 spikes/sec.  The curve tends
to flatten out or saturate at input rates greater than 1000 spike/sec.  This
is somewhat similar to the sigmoid curve used to represent the input/output
relation in "connectionist" artificial neural networks.

QUESTION 4: Using only the "synaptic weight for dendrite #1 inhibitory input"
and the three "Source B" parameters (delay, width and interval, inhibit
(suppress) the middle of the three action potentials produced by "Source A"
input. You may not modify any "Source A" parameters, and both the first and
last action potentials must remain. Answer the question by stating the
parameter values you had to use and by submitting hard copy of window #2 if
your system allows you to make prints of the screen.

Ans: The initial set of parameters, (Source A: delay=10, width=50,
interval=2, Dend #1 Exc. Wt.=12) and (Source B: delay=20, width=50,
interval=10, Dend #1 Inh. Wt.=12), had little effect upon the generation of
action potentials.  One solution of the problem is to reduce the source B
burst width to 20 msec and to reduce the spike interval to 2 msec.

QUESTION 5:  Toggle "Plot Soma" to "Plot Dendrite 2". Move the inhibitory
input ("Source B") to Dendrite #2.

For the above configuration, is the inhibitory synapse more or less
effective at suppressing the middle action potential?  Defend your answer
with numbers by varying the synaptic weights used in this configuration and
the previous one.  Give reasons for the results which you see.

Ans: Many of the solutions for QUESTION 4 will have the same effect for this
new configuration.  However, to properly judge the relative effectiveness of
the two configurations, we need to compare the minimum inhibitory synaptic
weights or spike rates needed to suppress the middle spike.  With a Source B
spike rate of 2 msec, as in the solution above, a minimum weight of 8.5 will
be needed to suppress the middle spike. In this new configuration, a weight
of at least 9 is required, because the stimulus is applied further from the
soma.  Thus, the decrease in soma membrane potential will be less, due to
the increased axial resistance and the shunting conductance in dentrite
section #1.

QUESTION 6:  Reverse the inputs. That is, place the excitatory input on
dendrite #2 and the inhibitory input on dendrite #1.

For the above configuration, is the inhibitory synapse more or less
effective at suppressing the middle action potential?  Defend your answer in
the same manner as in QUESTION 5, and explain the differences between this
situation and the previous one.

Ans: With a Source B spike interval of 2 msec as before, a synaptic weight
of only 8 is sufficient to prevent the middle action potential from
occuring.  For the reasons given in QUESTION 5, the effect of the inhibition
will be greater when it is applied closer to the soma.

QUESTION 7: Using various numbers of inserted segments, with a sub-threshold
epsp at dendrite section #2, estimate the length constant, "lambda", for this
dendrite.  Express your answer in units of "number of segments" and compare
your result with the predictions of theory.

Ans: Present an excitatory input to dendrite #2 from Source A with a weight
of 10, using the default timing parameters (a spike interval of 10 msec).
Compare the heights of the peaks of the membrane potential in the two
dendrite sections by toggling the "Plot Soma/Plot Dend2" button to show the
dendrite #2 membrane potential.  Use the "scale" buttons on the graphs to
pick an appropriate vertical scale (-75 to -65 mV).  If we call the peak
height V1 for dendrite #1 and V2 for dendrite #2, we should expect an
attenuation with distance x given by V1/V2 = exp(-x/lambda).  If we measure
x in terms of the number of cable segments, N, we have x = N+1, since we
have to count dendrite #2 as well.  By progressively adding cable sections
and plotting V1/V2 vs. x, we can find the value x=lambda at which
V1/V2=0.37.  Depending upon the care with which the peak heights are
measured, this produces values of the attenuation constant roughly in the
range of 9 to 11.  Theory predicts that lambda is given by the square root of
Rmem/Raxial.  For the values given for the dendrites in the "Cell
Parameters" menu, this predicts lambda=10.0.