In particular, I want you to draw the states and weights diagram for the
ligand binding case and then to ﬁnd
Z
. With
Z
in hand, use both of the
formulas above to obtain the average occupancy and show they yield the
same result. Plot your result as a function of concentration. To make the
plots, assume that the binding energy gained upon binding is 10 k
B
T.
3. Opening Probability of LigandGated Channels.
In class I gave a discussion of the behavior of ligandgated ion chan
nels. Give a brief description of the nicotinic acetylcholine receptor. Then,
draw a states and weights diagram (explain all of your assumptions, explain
all of the multiplicity factors, etc.) and use the MonodWymanChangeux
(MWC) model philosophy (i.e. that there are two states each of which can
be occupied or unoccupied by ligands) to compute
p
open
(
c
), where
c
is the
concentration of ligand. Make a plot of this open probability as a function
of concentration with a log scale on the xaxis and for several choices of pa
rameters:
±
open

±
closed
= 2
,
5 k
B
T and
K
closed
d
=
fK
open
d
with
f
= 1
,
10
,
100.
Explain the signiﬁcance of these choices of
f
. What is
p
open
at zero ligand
concentration? What is
p
open
at saturating concentrations of ligand?
3
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 Winter '09
 Nicotinic acetylcholine receptor, PBOC, photobleached region, ﬁnal concentration c∞

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