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?

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 (two should be enough), what does the over-
layed plot in window #2 demonstrate?

Ans: Temporal summation. (The plots of the conductance of the Dendrite #1
excitatory channel show that for spike intervals of less than 6
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
input rate vs output spikes rate.

Ans: In the range of 0.2 to 1 input spike/msec, the output rate is roughly
linear.


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=20, width=50,
interval=3, Dend #1 Exc. Wt.=10) and (Source B: delay=50, width=20,
interval=10, Dend #1 Inh. Wt.=10), had little effect upon the generation of
action potentials.  One solution of the problem is to increase the weight of
the inhibitory connection from source B to 20 and to reduce the spike
interval to 3 msec.  Another solution is to use a weight of 15, width of 15
msec and interval of 2 msec.  A "brute force" solution is to leave the
Source B timing parameters alone and to clobber the inhibitory channel with
a huge weight of 100.

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.  Explain what is happening.

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 3 msec, as in the first solution
above, a weight of 19 will be sufficient to suppress the middle spike. In
this new configuration, a weight of at least 20 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 3 msec as before, a synaptic weight
of only 17 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.
