Assignment #4
Lipids and Membranes
CHEM 237 DE Spring
2009
1.
For this problem, any constants needed are found in the table on p. 13 of your textbook; assume 37
o
C for the
temperature.
Using the equation for the free energy of transport (inside, C
I
, to outside, C
O
),
Δ
G
=
RT ln (C
O
/C
I
)
calculate the
Δ
G of transport for Ca
2+
, from the inside to the outside, with an inside concentration of [Ca
2+
] of 0.1
2+
] of 1 mM, assuming there is no membrane potential.
Now, taking into consideration
the membrane potential,
Δ
&, of 50 mV (inside negative), and the equation
Δ
G
=
RT ln (C
I
/C
O
)
+
Z
F
Δ
&
How does the
Δ
G change when the membrane potential is considered?
Explain the difference.
Could a Ca
2+
ATPase active transporter be used to transport Ca
2+
in this instance?
ANSWER:
(5 marks for each calculation)
The Ca
2+
is going from inside to outside, so we use
the equation as indicated above (corrected from the original version of the assignment).
Using the value of R of
8.3145 J K
-1
mol
-1
and 37
o
C, or 310
o
K:
Δ
G
=
RT ln (C
O
/C
I
)
Δ
G =
(8.3145 J K
-1
mol
-1
) (310
o
K) ln (10
-3
M/10
-7
M)
Δ
G
=
2577 J mol
-1
(9.21)
Δ
G
=
23,734 J/mol = 23.7 kJ/mol
If we take the membrane potential into consideration,
Δ
G
=
RT ln (C
O
/C
I
)
+ Z f
Δ
&
Δ
G =
(8.3145 J K
-1
mol
-1
) (310
o
K) ln (10
-3
M/10
-7
M)
+
(2) 96,485 J V
-1
mol
-1
(0.05 V)
Δ
G
=
23,734 J/mol
+
9,648 J/mol
Δ
G
=
33,382 J/mol =
33.4 kJ/mol
(4 marks)
Now, why should the
Δ
G change?
Think about the environment that the Ca
2+
is in.
Inside the cell, the Ca
2+
is in a more negative environment (more negative charges than
positive charges), and the transport process takes the positive Ca
2+
from the nice, cozy (-)
environment into the less accommodating (+) environment outside the cell.
No wonder the
Δ
G becomes more unfavorable!
(3 marks)
What about ATP?
Clearly, this transport process is unfavorable, and coupling to
ATP hydrolysis is required to transport the Ca
2+
.
But is one ATP enough?
When we consider
the membrane potential, the
Δ
G is 33.4 kJ/mol, and ATP only yields -30.5 kJ/mol, which is
not enough.
Granted, we are only considering
Δ
G
o’
values, and these values can change if we
were to consider
Δ
G
’
values.
2.
Assume that you are investigating this Ca
2+
ATPase that transports Ca
2+
out of the cell as discussed in
problem 1.