Biomedical Engineering Reference
In-Depth Information
concept to cells, but this requires finding the osmotic pressure of a mixture of solute
molecules. We use Dalton's Law to determine the osmotic pressure inside a cell.
A mixture of chemicals, with concentrations
c
1
,
c
2
,
c
3
...
, dissolved in water has
the total osmotic pressure equal to the sum of the partial osmotic pressures,
Π
,of
each chemical. Thus,
Π
=
Π
1
+
Π
2
+
Π
3
+··· =
RT
(
c
1
+
c
2
+
c
3
+···
)
(1.1)
The total osmotic pressure inside a cell,
Π
in
is therefore
10
−
3
mol
RT
(
140
+
12
+
4
+
148
)
×
1L
10
−
3
m
3
10
4
Pa
Π
in
=
×
=
7
.
8
×
(1.2)
1L
where we used the concentrations given above and a physiological temperature of
T
31 J/mol K. Cell walls would be expected to
burst under such large pressures. However, they do not, because the exterior fluid also
exerts an osmotic pressure in the opposite direction. The cell exterior is composed of
4mM K
+
, 150 mM Na
+
, 120 mM Cl
−
=
310 K and the gas constant is
R
=
8
.
and 34 mM A
−
. As a consequence, the total
osmotic pressure of the cell exterior,
Π
out
, is given by
10
−
3
mol
RT
(
4
+
150
+
120
+
34
)
×
1L
10
−
3
m
3
10
4
Pa (1.3)
Π
out
=
×
=
7
.
9
×
1L
Here,
Π
out
are very similar,
the osmotic pressure difference between the exterior and interior part of the cell
is very small, as it is the net pressure exerted on the cell wall that matters most.
For fragile animal cells, it therefore becomes vitally important to keep their interior
and exterior osmotic pressures closely matched. The cell has a sophisticated control
mechanism to do this.
If two solutions have the same osmotic pressure, we call them iso-osmotic. How-
ever, if the pressures are different, the one at higher pressure is called hypertonic and
the one at lower pressure is called hypotonic. When cells are placed in a solution and
neither swell nor shrink we call the solution isotonic. In the tissues of most marine
invertebrates the total osmotic concentration is close to that of the sea water. The
salt concentration of sea water is about 500 mM. As long as the salt concentration
remains near this value the blood of many crabs is isotonic with that of sea water.
When it is outside this range, the system maintains the osmotic pressure difference
across its membrane through the activity of ion pumps and the process is known as
osmoregulation.
The cell composition begins to drift away from its optimal mixture if the ion
pumps (which will be discussed in detail later in the topic) are chemically destroyed.
Across the cell wall the osmotic pressure difference then rises, causing the cell to
swell, become turgid, and eventually explode. The cells of bacteria and plants are
not osmotically regulated since their cell walls are able to withstand pressures in
the range of 1-10 atm. The minimum work performed when
n
moles of solute are
Π
out
is a large osmotic pressure but because
Π
in
and
Search WWH ::
Custom Search