Biomedical Engineering Reference
In-Depth Information
3.9
Duncan et al. are interested in measuring the changes in the membrane perme-
ability of eye lenses with age. They incubated in an artificial aqueous humor
solution (35°C) with the following composition: 130-mM NaCl, 5-mM KC1,
0.5-mM MgCl
2
, 1-mM CaCl
2
, 10-mM NaHCO
3
, and 5-mM glucose, buff-
ered with 10 mM HEPES to pH 7.3. They reported the intracellular sodium
content for a lens from 20-year-old person to be 25 mM where as it is 40 mM
for a lens from a 60-year-old person. However, there is no significant differ-
ence in the intracellular content of potassium. The membrane potentials are
−
20 mV for 20-year-old and 60-year-old lenses, respectively. As-
suming that the lens is permeable to Na
+
and K
+
ions, calculate the change in
the permeability of Na
+
ions to K
+
ions with age.
50 mV and
−
Consider a cell membrane with Na
+
(out)
150 mM, Na
+
(in)
15 mM, K
+
(out)
3.10
=
=
5 mM, K
+
(in)
150 mM, Cl
−
(out)
155 mM, and Cl
−
(in)
=
=
=
=
10 mM. The
70 mV. The concentration of
Na
+
and K
+
across the cell membrane are maintained by the Na
+
/K
+
pumps,
each of which pumps 3Na
+
out and 2K
+
in.
resting potential across this cell membrane is
−
(a) Calculate the Nernst potentials for Na
+
, K
+
, and Cl
−
, respectively.
(b) Using the Goldman equation, calculate the membrane potential. The
concentrations of Na
+
, K
+
, and Cl
−
inside and outside of the cell are given
above, and the relative permeabilities of the individual ions are
P
=
1,
P
=
0.04,
P
=
0.45.
+
+
−
K
Na
Cl
(c) What will happen if the flow of K
+
is blocked across the leak channels?
What will be the membrane potential predicted by the Goldman equation
in this case [personal communication with Dr. Nada Bowtany, Rutgers
University, 2004]?
3.11
Cartilage consists of extracellular matrix containing collagen and glycosami-
noglycans, the long sugar chains. Under physiological conditions, collagen is
electroneutral, while the glycosaminoglycans have a fixed negative charge A
−
.
Thus, cartilage can be modeled as a compartment containing fixed negative
charges that cannot move into the surrounding medium. On the other hand,
ions in the surrounding medium freely flow in and out of the cartilage matrix.
Shirin wanted to measure the concentration of the fixed negative charges in-
side cartilage. She dissected a piece of articular cartilage from a bovine (cow)
knee and placed it in a 0.15M NaCl solution at pH
7.4. By placing elec-
trodes inside the cartilage, and in the surrounding bath, she measured a volt-
age difference of
=
−
25 mV.
