Biophysics Fall 2011 
Homework 3
You are encouraged to work together, but each of you needs to hand in your own
solution. The solution needs to be typed, not handwritten.
1.
Dimoglobin revisited
Imagine a box with N O
2
molecule which can
be distributed amongst
Ω
sites. This simple
lattice model of the solution is intended to
account for the entropy available to the O
2
molecules when they are in solution. A
representation of this system is shown in the
Figure. Use the dimoglobin energy we used in
the lecture E =
ε
(
σ
1
+
σ
2
) + J
σ
1
σ
2
,
and
Boltzmann weights to construct the partition
function.
Find the expressions of the probabilities of 0, 1, or 2 oxygen bound to dimoglobin and
plot the results as a function of oxygen partial pressure. Use c
0
= 760 mmHg and plot the
oxygen partial pressure on a logarithmic scale from c = 10
2
to c = 10
2
mmHg, as in Fig.
7.13. Use the following parameters for
ε
and J: (a)
ε
= 3 k
B
t, J = 1 k
B
t, (b)
ε
= 3 k
B
t, J =
4 k
B
t.
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 Fall '11
 staff
 Physics, Partial Pressure, Work, Carbon monoxide, Oxygen partial pressure

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